fluid os 2012

Fluidos de Reservorio

G. Fondevila

Actividades en la

Ingeniería de Reservorios

• Observaciones

• Asunciones (Hipótesis)

• Cálculos

• Decisiones

(L.P. Dake – The Practice of Reservoir Engineering)

Responsabilidades Técnicas en la

Ingeniería de Reservorios• Determinar, en conjunto con los geólogos, geofísicos y

petrofísicos, los recursos (hidrocarburos originales “in situ”).

• Determinar la fracción de estos hidrocarburos que puede ser (razonablemente) recuperada.

• Llevar la recuperación a una escala temporal (pronósticos).

• Efectuar el control de reservorios operativo, durante toda la vida del proyecto.


Rol del Ingeniero/a de Reservorios


Definiciones

• Reservorio: Acumulación de hidrocarburos con vinculación hidráulica entre todos sus puntos.

• Yacimiento: Uno o más reservorios de hidrocarburos agrupados y/o relacionados entre sí, dentro de una misma trampa geológica. En un mismo yacimiento pueden coexistir múltiples reservorios separados vertical o lateralmente por rocas impermeables y/o barreras geológicas locales.

• Trampa: Configuración que impide la normal movilidad de los hidrocarburos provocando su acumulación. Puede ser de origen estructural, estratigráfica o combinada.

The Need to Understand

Phase Behavior

• As oil and gas are produced from the reservoir, they are subjected to a series of pressure, temperature, and compositional changes.

• Such changes affect the volumetric and transport behavior of these reservoir fluids and, consequently, the produced oil and gas volumes.

(M.A. Barrufet)

The Need to Understand

Phase Behavior

• Type of reservoir fluid determines depletion and production strategies and the design of surface facilities

• Except polymer flooding, all of EOR methodsrely on the phase behavior of reservoir fluids andfluids injected into the reservoir.

• This behavior is used to classify the recovery method (i.e., thermal, miscible, chemical, etc.), and to design the recovery process.

(M.A. Barrufet)

Major Definitions

• System: A body of matter with finite boundaries (physical or virtual)

• Closed System: Does not exchange matter with surroundings but may exchange energy (heat).

• Open System: Does exchange matter and energy with surroundings.

(M.A. Barrufet)

Major Definitions

• Homogeneous System: Intensive properties change continuously and uniformly (smoothly)

• Heterogeneous System: System made up of two or more phases in which the intensive properties change abruptly at phase-contact surfaces

(M.A. Barrufet)

Major Definitions

• Phase: A portion of the system which

has homogeneous intensive properties

and it is bounded by a physical surface.

• Interface: Separates two or more

phases. These phases are solid,

liquid(s), and gas.

(M.A. Barrufet)

Major Definitions

• Intensive Properties: Independent

of system mass (i.e density)

• Extensive Properties: Dependent

of system mass (i.e volume)

(M.A. Barrufet)

Major Definitions

• Properties: Characteristics of a system (phase) that may be evaluated quantitatively, i.e.

− Phase density (liquid, gas, solid)

− Phase compositions

− Isothermal compressibility

− Surface tension

− Viscosity

− Heat capacity

− Thermal conductivity

(M.A. Barrufet)

Major Definitions

• Component: A molecular species,

defined or hypothetical.

– Defined: Cl, C2, H2O, etc.

– Hypothetical: lumped defined (i.e. C2-C6), or undefined C7

+ , C20+

(M.A. Barrufet)

Major Definitions

• State: Condition of a system at a

particular time determined when all

intensive properties are fixed

(M.A. Barrufet)

Diagrama PT: Sustancia Pura

Diagrama PT: 2 Componentes

Diagrama PT: Múltiples Componentes

Diagrama PT: Definiciones

Tipos de Fluido de Reservorio

• ¿De qué depende el tipo de fluido de reservorio?:– Composición de la mezcla de HC en el reservorio.

– Temperatura Inicial de reservorio (Tres)

– Presión Inicial de reservorio (Pi).

– Ubicación de la Temperatura de Reservorio respecto a la Temperatura Crítica y al punto Cricondentérmico.

• Pueden ser clasificados en dos tipos:– Reservorios de Petróleo: Temperatura del Reservorio (Tres), es menor

a la Temperatura Crítica (Tc). Están clasificados en:

– Subsaturados: Presión Inicial (Pi) es mayor a la Presión de burbuja (Pb).

– Saturados: Presión Inicial (Pi) es igual a la Presión de burbuja (Pb).

– Con Casquete/Calota de Gas: Presión Inicial (Pi) es menor a la Presión de burbuja (Pb).

– Reservorios de Gas: Temperatura del Reservorio (Tres), es mayor a la Temperatura Crítica (Tc).

Existen 5 Tipos de Fluidos de Reservorio:

• Reservorios de Petróleo:

– Petróleo Negro

– Petróleo Volátil

• Reservorios de Gas:

– Gas Retrógrado

– Gas Húmedo

– Gas Seco

Petróleo Negro

Petróleo Volátil

Gas Retrógrado (Gas y Condensado)

Gas Húmedo

Gas Seco

Comparación Composición

ComponentePetróleo

Negro

Petróleo

Volátil

Gas

Retrógrado

Gas

HúmedoGas Seco

C1 48.8 64.4 87.1 91.4 95.8

C2 2.8 7.5 4.4 3.5 2.7

C3 1.9 4.7 2.3 1.2 0.3

C4 1.6 4.1 1.7 1.1 0.5

C5 1.2 3.0 0.8 0.4 0.1

C6 1.6 1.4 0.6 0.3 0.1

C7+ 42.1 14.9 3.8 2.1 0.4

100.0 100.0 100.0 100.0 100.0

PM C7+ 230 180 160 140 -

GOR [scf/stb] 1,200 2,500 9,000 >15,000 >100,000

°API 35 50 60 >60 -

Whitson

SPE 28214

Heavy Components ControlReservoir Fluid Behavior

William D. McCain Jr.

Se definen 5 tipos de fluido de reservorio (petróleo negro, volátil, gas + condensado, gas húmedo y gas seco) debido a que cada uno necesita diferentes técnicas de ingeniería para producirlo.

El mismo debe ser definido bien temprano en la explotación de un reservorio, ya que es un factor crítico para la toma de decisiones sobre cómo producir el fluido.

Introducción (1)

El tipo de fluido de reservorio se debe definir con una muestra representativa del mismo en laboratorio.

Igualmente existen “reglas de dedo” basadas en RGP inicial, densidad y color de líquido de tanque, que pueden indicar el tipo de fluido.

Estos fluidos son mezclas de hidrocarburos que van desde componentes livianos (ej: metano) hasta moléculas no volátiles ultra-pesadas.

Introducción (2)

Los petróleos negros se caracterizan por tener una gran cantidad de moléculas pesadas. Los petróleos volátiles poseen menos de estas moléculas, y así hasta llegar a gas seco que es puramente metano.

Generalmente en laboratorio a las moléculas pesadas se las concentra en un pseudo-componente llamado “C7+”.

En cuanto a RGP, los petróleos negros es la más baja y en gas húmedo es mucho mayor.

GO

R in

icia

l

C7+ %molar

GO

R in

icia

l

C7+ %molar

GASES

PETRÓLEOS

Petróleos Negros y Volátiles (1)

Los petróleos negros y volátiles ambos están en fase líquida en el reservorio.

Exhiben punto de burbuja cuando se depleta el reservorio (baja la presión).

Ambos liberan gas en reservorio cuando la presión está por debajo de la presión de burbuja.

El gas que liberan los petróleos negros es usualmente gas seco. A medida que la presión decrece el gas puede llegar a ser húmedo. Pero esto ocurre en el final de la vida de explotación.


El gas que proviene de petróleos volátiles es usualmente gas retrógrado.

Este gas va a condensar una gran cantidad de líquido en condiciones de superficie.

Por eso en las ecuaciones de balance de masa (lo van a ver en ingeniería de reservorios...) la hipótesis es que el gas que sale del reservorio permanece como gas en superficie.

Por ende los petróleos volátiles no pueden tratarse con balance de masa sino con simuladores composicionales.


En la ecuación de balance de masa para petróleos negros es que es una mezcla de dos componentes: petróleo y gas.

Sobre el punto de burbuja (sólo tenemos líquido) el balance de masa se puede realizar tanto para petróleo negros como volátiles.

Indicadores (límite inferior petróleos volátiles):− GOR > 300 m3/m3

− Densidad > 40 °API

− Bo > 2

− %molar C7+ < 20%

Petróleos Volátiles y Gas Retrógrado (1)

En condiciones de reservorio los petróleos volátiles demuestran punto de burbuja y los gases retrógrados punto de rocío, al bajar la presión.

GOR = 600 m3/m3 y %molar C7+ = 12.5 % puede tomarse como un límite razonable entre petróleos volátiles y gases retrógrados.

Estos límites deben ser tomados como guías, ya que se pueden encontrar petróleos volátiles con GOR > 600 m3/m3 y %molar C7+ < 12.5%, y viceversa con los gases retrógrados.

GO

R in

icia

l

C7+ %molar

Petróleos Volátiles y Gas Retrógrado (2)

El condensado que se forma debajo de la presión de rocío es prácticamente inmóvil, por lo que se pierde para la producción.

Esto causa una disminución en la permeabilidad efectiva al gas debido a que la saturación de líquido va aumentando.

En general se ve una disminución marcada en la producción de gas cuando la presión se encuentra por debajo del punto de rocío.

Gases Retrógrados y Húmedos (1)

Se han visto gases con comportamiento retrógrado con GOR = 27000 m3/m3.

Aparentemente, todos los gases que demuestran condensación en superficie, liberan un poco de condensado en fondo.

La ecuación de balance de masa de gases se puede aplicar a gases húmedos:

− Combinando el gas de superficie y el condensado para determinar el gas en reservorio.

− Obtener el equivalente gaseoso del condensado de superficie a la producción de gas en superficie.

Gases Retrógrados y Húmedos (2)

%molar C7+ por debajo de 4% se puede considerar un gás húmedo, aunque poco líquido condense en reservorio.

Para ese %molar, se aplica un GOR de 2700 m3/m3 (según la figura 1) por lo que también se puede tomar como límite entre gases retrógrados y húmedos.

El GOR de un reservorio de gas húmedo se mantiene constante a lo largo de la vida del reservorio.

Gases Húmedos y Secos

Ambos permanecen en fase gaseosa al bajar la presión en reservorio. Ninguno muestra punto de rocío y liberación de condensado en reservorio.

La diferencia es que los gases húmedos liberan condensado en condiciones de superficie, mientras que un gas seco siempre permanece como gas.

El efecto de la liberación de condensado en superficie es despreciable si es menor que 55 m3 condensado / 1 MM m3 de gas.

GOR = 18000 m3/m3 puede ser usado como límite.

Fluidos de Reservorios

Gases

G. Fondevila

Fuentes

• “Equations of State and PVT Analysis” T. Ahmed

• “Fundamentals of Reservoir Engineering”, L.P. Dake

• SPE 75721: “Simplified Correlations for Hydrocarbon

Gas Viscosity and Gas Density – Validation and

Correlation of Behavior Using a Large-Scale Database”,

F.E. Londono, R.A. Archer and T.A. Blasingame, Texas

A&M U.

Ecuación de los Gases Ideales• El gas es una de las pocas substancias donde su estado

queda definido por la presión, el volumen que ocupa y la temperatura mediante una simple relación entre estos 3 parámetros.

• Ecuación de gases ideales:

pV = nRT• Esta ecuación es el resultado de la combinación de los

esfuerzos de Boyle, Charles, Avogadro y Gay Lussac, pero es solo aplicable a presiones cercanas a la atmosférica.

• Hipótesis de los Gases Ideales:– No existen fuerzas de interacción (atracción o repulsión) entre

las moléculas de gas.

– Choques que se producen entre las mismas son perfectamente elásticos.

– El volumen de las moléculas de gas es totalmente despreciable en comparación con el volumen total que ocupa el mismo.

Ecuación de los Gases Reales

• Ecuación de van der Waals (para 1 mol de gas):

(p + a/V2)*(V – b) = RT• Esta ecuación trata de representar los efectos

de interacción de las moléculas de los gases (atracción y repulsión, parámetro a) y además tiene el cuenta el volumen que ocupan estas moléculas (parámetro b), ambos efectos comienzan a ser visibles al aumentar la presión.

• Esta ecuación puede ser reducida a:

pV = ZnRT

Z = Vol gas real / Vol gas ideal

Ecuación de los Gases Reales

• Determinación del factor de compresibilidad Z:– Manera experimental: es el método más preciso,

pero consume mucho tiempo de laboratorio y dinero, y la precisión obtenida no es determinante como para no utilizar las correlaciones o cálculos existentes.

– Correlaciones:• Standing & Katz: para determinar el factor Z

• Sutton & Brown: para determinar las propiedades pseudo-críticas del gas a partir de la gravedad específica (en el caso que no tengamos una cromatografía del mismo).

– Cálculo directo del Z: Existen diferentes metodologías de cálculo hoy en día que representan a la correlación de Standing & Katz, podemos mencionar:

• Hall-Yarborough• Dranchuk-Abou-Kassem

Correlación Standing & Katz

• Se utiliza para determinar el factor de compresibilidad Z.

• Requiere saber la composición del gas.• Para utilizar la correlación, necesitamos conocer

las propiedades pseudo-críticas del gas (las propiedades de cada componente se encuentran tabuladas):– Ppc = Σ (yi . Pci)

– Tpc = Σ (yi . Tci)

• Luego calculamos la presión y temperatura pseudo-reducidas:– Ppr = P/Ppc

– Tpr = T/Tpc

Correlación Standing & Katz

Correlación Sutton & Brown

Esta correlación sirve para

determinar las propiedades

pseudocríticas del gas (Ppc y

Tpc) cuando no tenemos la

composición del mismo, pero sí

la gravedad específica γg.

Propiedades Elementos Puros

Cálculo Propiedades del Gas Natural (1)

Cálculo de Propiedades del Gas (2)

Factor Volumétrico de Formación del Gas: Bg

Compresibilidad del Gas

Resumen Cálculo de Propiedades

• Peso Molecular:– PM_gas = Σ (yi * PMi)

• Gravedad Específica:– SG_gas (γg) = Dens_gas / Dens_aire = PM_gas / PM_aire

– Dens_aire = 1.223 kg/m3

– PM_aire = 28,93 gr/mol

• Bg:– Bg = Vol fondo / Vol sup

– Vol fondo = ZnR Tfondo/Pfondo

– Vol sup = nR Tsup/Psup

– Bg = Z (Tfondo/Tsup) (Psup/Pfondo)

• Compresibilidad del gas real:– Cg = - 1/V dV/dP = 1/P – 1/Z dZ/dP ≈ 1/P

Efecto de Impurezas en el Gas

• Generalmente los gases naturales vienen acompañados

de elementos no hidrocarburos, a ser:

– Nitrógeno (N2)

– Dióxido de Carbono (CO2)

– Sulfuro de Hidrógeno (H2S)

• A un gas se lo clasifica como “dulce” o “amargo”

dependiendo del contenido de H2S en el mismo.

• La presencia de impurezas (generalmente por encima

de un 5% total en composición) puede generar errores a

la hora de calcular correctamente el Z.

Corrección por Impurezas

Cálculo Directo de Z (1): Dranchuk & Abu-Kassem

Cálculo Directo de Z (2): Hall-Yarborough

Compresibilidad del Gas: Correlación de Trube

cpr = cg * Ppc cg = cpr / Ppc

donde cpr la obtenemos de la correlación de Trube

Viscosidad del Gas

Cálculo de Viscosidad del Gas:Correlación de Carr-Kobayashi-Burrows

Paso 1

Paso 1: Obtenemos viscosidad del gas a presión armosférica y temperatura de interés = µgatm


Paso 2

Paso 2: Obtenemos los coeficientes multiplicadores para cada presión pseudo-reducida

Cromatografía Gas

Componente Fracción

C1 91.6%

C2 3.8%

C3 1.2%

iC4 0.3%

nC4 0.4%

iC5 0.1%

nC5 0.2%

C6 0.6%

C7+ 0.2%

N2 1.2%

CO2 0.4%

PVT GasPressure Z Bg cg ρρρρg µµµµg

(kg/cm²) ( ) (m3/stm3) (psi-1) (g/cc) (cp)

1.0 0.999 1.2384 6.81E-02 0.001 0.0127

19.5 0.977 0.0642 3.69E-03 0.012 0.0129

37.9 0.957 0.0323 1.93E-03 0.024 0.0132

56.4 0.939 0.0213 1.32E-03 0.036 0.0135

74.9 0.923 0.0158 1.00E-03 0.049 0.0139

93.3 0.910 0.0125 8.03E-04 0.062 0.0144

111.8 0.899 0.0103 6.66E-04 0.075 0.0150

130.2 0.892 0.0088 5.64E-04 0.088 0.0157

148.7 0.888 0.0077 4.83E-04 0.101 0.0164

167.1 0.888 0.0068 4.17E-04 0.113 0.0173

185.6 0.890 0.0061 3.62E-04 0.125 0.0182

204.0 0.895 0.0056 3.17E-04 0.137 0.0191

222.5 0.903 0.0052 2.78E-04 0.148 0.0201

241.0 0.913 0.0049 2.46E-04 0.159 0.0211

259.4 0.925 0.0046 2.18E-04 0.169 0.0220

277.9 0.939 0.0043 1.95E-04 0.178 0.0230

296.3 0.954 0.0041 1.74E-04 0.187 0.0240

314.8 0.970 0.0039 1.57E-04 0.195 0.0249

333.2 0.987 0.0038 1.42E-04 0.203 0.0258

351.7 1.006 0.0037 1.29E-04 0.210 0.0266

370.1 1.025 0.0035 1.18E-04 0.217 0.0275

PVT Gas - Z

0.88

0.90

0.92

0.94

0.96

0.98

1.00

1.02

1.04

0 50 100 150 200 250 300 350 400

Presión [kg/cm2]

Z

PVT Gas - Bg

0.001

0.01

0.1

1

10

0 50 100 150 200 250 300 350 400

Presión [kg/cm2]

Bg

[m

3/m

3]

PVT Gas - cg

0.0001

0.001

0.01

0.1

1

0 50 100 150 200 250 300 350 400

Presión [kg/cm2]

cg

[p

si-1

]

PVT Gas - ρg

0.00

0.05

0.10

0.15

0.20

0.25

0 50 100 150 200 250 300 350 400

Presión [kg/cm2]

ρρ ρρg

[g

r/cc]

PVT Gas - µg

0.000

0.005

0.010

0.015

0.020

0.025

0.030

0 50 100 150 200 250 300 350 400

Presión [kg/cm2]

µµ µµg

[cp

]

Correlación Standing & KatzUso de Correlación:

1. Obtengo Ppc y Tpc (presión y

temperatura pseudo-críticas):

• Ppc = Σ (yi * Pci)

• Tpc = Σ (yi * Tci)2. Calculo Tpr:

• Tpr = Tres/Tpc

3. Calculo Ppr:

• Ppr = P/Ppc

4. Entro con Ppr y llego a la curva

de Tpr, luego leo z.

5. Ejemplo:

• Tpr = 1.8

• Ppr = 2

• Z = 0.92

Correlación Sutton & BrownUso de Correlación:

1. Calculo GEg del gas:

• GEg = PM_gas / PM_aire

• PM_gas = Σ (yi * PMi)• PM_aire 28.93 gr/mol

2. Obtengo Tpc y Ppc del gráfico.

3. Ejemplo:

• GEg = 0.7

• Tpc = 390 °R

• Ppc = 670 psia

• También puedo usar las

ecuaciones que aparecen en el

gráfico para obtener Tpc y Ppc a

partir de la GEgas.

Compresibilidad del Gas: Correlación de Trube

cpr = cg * Ppc cg = cpr / Ppc

donde cpr la obtenemos de la correlación de Trube

Uso de Correlación:

1. Elijo curva de Tpr.

2. Entro con Ppr.

3. Leo el valor de cpr.

4. Ejemplo:

1. Curva Tpr = 1.8

2. Ppr = 2

3. cpr = 0.54

4. cg = cpr / Ppc

Cálculo de Viscosidad del Gas:Carr-Kobayashi-Burrows

Paso 1

Paso 1: Obtenemos viscosidad del gas a presión armosférica y temperatura de interés = µgatm

Uso de Correlación:

1. Elijo curva de Tres.

2. Entro con PM del gas.

3. Leo el valor de µgas1atm.4. Ejemplo:

1. Tres = 200 °F2. PMgas = 20

3. µgas1atm = 0.0123


Paso 2

Paso 2: Obtenemos los coeficientes multiplicadores para cada presión pseudo-reducida

Uso de Correlación Paso 2:

1. Marco línea de Tpr.

2. Leo el multiplicador de viscosidad para

cada curva de Ppr.

3. Calculo viscosidad para cada Ppr.

4. Ejemplo (flecha celeste):1. Tpr = 1.8

2. Curva Ppr = 2

3. Multiplicador = 1,15

4. Viscosidad @ Ppr 2 = visc_1atm *

multiplicador = 0.0123 * 1.15 = 0.0141

Copyright 2002, Society of Petroleum Engineers Inc.

This paper was prepared for presentation at the SPE Gas Technology Symposium held in Calgary, Alberta, Canada, 30 April–2 May 2002.

This paper was selected for presentation by an SPE Program Committee following review of information contained in an abstract submitted by the author(s). Contents of the paper, as presented, have not been reviewed by the Society of Petroleum Engineers and are subject to correction by the author(s). The material, as presented, does not necessarily reflect any position of the Society of Petroleum Engineers, its officers, or members. Papers presented at SPE meetings are subject to publication review by Editorial Committees of the Society of Petroleum Engineers. Electronic reproduction, distribution, or storage of any part of this paper for commercial purposes without the written consent of the Society of Petroleum Engineers is prohibited. Permission to reproduce in print is restricted to an abstract of not more than 300 words; illustrations may not be copied. The abstract must contain conspicuous acknowledgment of where and by whom the paper was presented. Write Librarian, SPE, P.O. Box 833836, Richardson, TX 75083-3836, U.S.A., fax 01-972-952-9435.

Abstract

The focus of this work is the behavior of gas viscosity and gas density for hydrocarbon gas mixtures. The viscosity of hydro-carbon gases is a function of pressure, temperature, density, and molecular weight, while the gas density is a function of pressure, temperature, and molecular weight. This work pre-sents new approaches for the prediction of gas viscosity and gas density for hydrocarbon gases over practical ranges of pressure, temperature and composition. These correlations can be used for any hydrocarbon gas production or transport-ation operations.

In this work we created an extensive database of measured gas viscosity and gas density (>5000 points for gas viscosity and >8000 points for gas density). This database was used to evaluate existing models for gas viscosity and gas density. In this work we provide new models for gas density and gas viscosity, as well as optimization of existing models using this database.

The objectives of this research are:

l To create a large-scale database of measured gas vis-cosity and gas density data which contains all of the in-formation required to establish the applicability of var-ious models for gas density and gas viscosity over a wide range of pressures and temperatures.

l To evaluate a number of existing models for gas vis-cosity and gas density.

l To develop new models for gas viscosity and gas den-sity using our research database — these models are proposed, validated, and presented graphically.

For this study, we created a large-scale database of gas pro-perties using existing sources available in the literature. Our data-base includes: composition, viscosity, density, tempera-ture, pressure, pseudoreduced properties and the gas com-pressibility factor. We use this database to evaluate the appli-cability of the existing models used to estimate hydrocarbon gas viscosity and gas density (or more specifically, the z-factor). Finally, we provide new models and calculation pro-cedures for estimating hydrocarbon gas viscosity and we also provide new optimizations of the existing equations-of-state (EOS) typically used for the calculation of the gas z-factor.

Introduction

Hydrocarbon Gas Viscosity

NIST — SUPERTRAP Algorithm: The state-of-the-art mechan-ism for the estimation of gas viscosity is most likely the com-puter program SUPERTRAP developed at the U.S. National Institute of Standards and Technology1 (NIST). SUPERTRAP was developed from pure component and mixture data, and is stated to provide estimates within engineering accuracy from the triple point of a given substance to temperatures up to 1,340.33 deg F and pressures up to 44,100 psia. As the SUPERTRAP algorithm requires the composition for a parti-cular sample, this method would not be generally suitable for applications where only the mixture gas gravity and composi-tions of any contaminants are known.

Carr, et al. Correlation: Carr, et al.2 developed a two-step procedure to estimate hydrocarbon gas viscosity. The first step is to determine the gas viscosity at atmospheric condi-tions (i.e., a reference condition). Once estimated, the vis-cosity at atmospheric pressure is then adjusted to conditions at the desired temperature and pressure using a second correla-tion. The gas viscosity can be estimated using graphical cor-relations or using equations derived from these figures.

Jossi, Stiel, and Thodos Correlation: Jossi, et al.3 developed a relationship for the viscosity of pure gases and gas mixtures which includes pure components such as argon, nitrogen, oxygen, carbon dioxide, sulfur dioxide, methane, ethane, pro-pane, butane, and pentane. This "residual viscosity" relation-ship can be used to predict gas viscosity using the "reduced" density at a specific temperature and pressure, as well as the molecular weight. The critical properties of the gas (specifi-

SPE 75721

Simplified Correlations for Hydrocarbon Gas Viscosity and Gas Density — Validation and Correlation of Behavior Using a Large-Scale Database F.E. Londono, R.A. Archer, and T. A. Blasingame, Texas A&M U.

2 F.E. Londono, R.A. Archer, and T. A. Blasingame SPE 75721

cally the critical temperature, critical pressure, and critical density) are also required.

Our presumption is that the Jossi, et al. correlation (or at least a similar type of formulation) can be used for the prediction of viscosity for pure hydrocarbon gases and hydrocarbon gas mixtures. We will note that this correlation is rarely used for hydrocarbon gases (because an estimate of the critical density is required) — however; we will consider the formulation given by Jossi, et al. as a possible model for the correlation of hydrocarbon gas viscosity behavior.

The "original" Jossi, et al. correlation proposed for gas vis-cosity is given by:

)(10)( 41

4JST,rg f ρξµµ =

+− −∗ .........................(1)

where:

ρρ

ρρρ

43

2

0.0093324 0.040758

0.058533 0.023364 0.1023 )(

JST,rJST,r

JST,rJST,rJST,rf

+−

++=

......................................................................................(2)

32

21

61

cw

c

pM

T=ξ .............................................................(3)

and,

ρr,JST = ρ/ρc, JST Reduced density, dimensionless ρ = Density at temperature and pressure, g/cc ρc = Density at the critical point, g/cc Tc = Critical temperature, deg K pc = Critical pressure, atm Mw = Molecular weight, lb/lb-mole µg = Gas viscosity, cp µ* = Gas viscosity at "low" pressure, cp

The Jossi, et al. correlation is shown in Figs. 1 and 2. Jossi, et al.3 reported approximately 4 percent average absolute error and also stated that this correlation should only be applied for values of reduced density (ρr) below 2.0. The behavior of the "residual" gas viscosity function is shown in Figs. 1 and 2.

Lee, Gonzalez, and Eakin, Correlation: The Lee, et al.5 cor-relation evolved from existing work in the estimation of hydrocarbon gas viscosity using temperature, gas density at a specific temperature and pressure, and the molecular weight of the gas. This correlation is given by:

)exp(10 4 YXKg ρµ −= ................................................(4)

where:

TMTM

Kw

w++

+=

19.26 209.2 ) 0.01607 (9.379

1.5

.................................(5)

wMT

..X 0.01009

49864483 +

+= ...........................(6)

XY 2224.0447.2 −= ................................................................................................

and,

ρ = Density at temperature and pressure, g/cc Mw = Molecular weight of gas mixture, lb/lb-mole T = Temperature, deg R µg = Gas viscosity at temperature and pressure, cp

Lee, et al.4 reported 2 percent average absolute error (low pressures) and 4 percent average absolute error (high pres-sures) for hydrocarbon gases where the specific gravity is be-low 1.0. For gases of specific gravity above 1.0 this relation is purported to be "less accurate."

The range of pressures used by Lee, et al.5 in the development of this correlation is between 100 and 8,000 psia and the tem-perature range is between 100 and 340 deg F. This correlation can also be used for samples which contain carbon dioxide — (in particular for carbon dioxide concentrations up to 3.2 mole percent). Fig. 3 shows the behavior of the Gonzalez, et al.5

data (natural gas sample 3) compared to the Lee, et al.4 hydro-carbon gas viscosity correlation.

Hydrocarbon Gas Density

A practical issue pertinent to all density-based gas viscosity models is that an estimate of gas density must be known. Al-though there are many equation of state (EOS) correlations for gas density (or more specifically, the gas z-factor) we found that these EOS models do not reproduce the measured gas densities in our database to a satisfactory accuracy. This ob-servation led us towards an effort to "tune" the existing models (refs. 6-8) for the z-factor using the data in our database.

For reference, the definition of gas density for real gases is given by:

RTwM

zp

.37621

=ρ (ρ in g/cc) ...................................... (8)

where:

ρ = Density at temperature and pressure, g/cc p = Pressure, psia Mw = Molecular weight, lb/lb-mole z = z-factor, dimensionless T = Temperature, deg R R = Universal gas constant, 10.732 (psia cu ft)/(lb-mole

deg R) 62.37 = Conversion constant: 1 g/cc = 62.37 lbm/ft3

The real gas z-factor is presented as an explicit function of the pseudoreduced pressure and temperature as predicted by the "Law of Corresponding States"9 (see Figs. 4-6, where we use the data of Poettmann and Carpenter10). It is important to note that EOS models are implicit in terms of the z-factor, which means that the z-factor is solved as a root of the EOS. This must be considered in the regression process — the regression formulation must include the solution of the "model" z-factor as a root of the EOS.

Dranchuk-Abou-Kassem,6 Nishiumi-Saito,7 and Nishiumi8 provide EOS representations of the real gas z-factor. In parti-

SPE 75721 Simplified Correlations for Hydrocarbon Gas Viscosity and Gas Density — 3 Validation and Correlation of Behavior Using a Large-Scale Database

cular, the Dranchuk-Abou-Kassem result is based on a Han-Starling form of the Benedict-Webb-Rubin equation of state (EOS) and is considered to be the current standard for the prediction of gas density.

z-Factor Model: Dranchuk-Abou-Kassem (ref. 6)

The DAK-EOS6 is given by:

2113

22

1110

5287

9287

6

55

44

332

1

)exp()A(1

2

1

rr

rr

rrr

rrr

rrrrr

AT

A

T

A

T

AA

T

A

T

AA

T

A

T

A

T

A

T

AAz

ρρ

ρ

ρρ

ρ

−++

+−

+++

+++++=

.....(9)

where:

z = z-factor, dimensionless Tr = Reduced temperature, dimensionless ρr = ρ/ρc, Reduced density, dimensionless ρ = Density at temperature and pressure, g/cc ρc = Critical density, g/cc (zc=0.27)

We must note that the definition of critical density is a matter of some debate — in particular, how is critical density esti-mated when this is also a property of the fluid? As such, we use the "definition" of ρc as given by Dranchuk and Abou-Kassem6:

0.27) (where == ccc zrzTrp

zρ

and the "original" parameters given by Dranchuk and Abou-Kassem (ref. 6) for hydrocarbon gases are:

A1 = 0.3265 A7 =-0.7361 A2 =-1.0700 A8 = 0.1844 A3 =-0.5339 A9 = 0.1056 A4 = 0.01569 A10 = 0.6134 A5 =-0.05165 A11 = 0.7210 A6 = 0.5475.............................................................(10)

The Dranchuk-Abou-Kassem (DAK-EOS) is compared to the data of Poettmann and Carpenter10 in Figs. 7-9. We note that the "original" DAK-EOS agrees quite well with the data trends, and would, in the absence of data to the contrary, seem to be adequate for most engineering applications. However, we would like to extend the range of this relation as well as provide a more statistically sound correlation of the EOS (i.e., add more data to the regression process).

z-Factor Model: Nishiumi-Saito (ref. 7)

The Nishiumi-Saito model (NS-EOS)7 adds a few more terms to the original Dranchuk-Abou-Kassem expression, and is given by:

255

44

332

11 rrrrr T

A

T

A

T

ATA

Az ρ

−−−−+=

22410

59

287

6 rrrrr T

A

T

A

T

ATA

A ρ

−−−−+

52410

59

287

11 rrrrr T

A

T

A

T

ATA

A ρ

++++

)exp()1( 215

215

21814

913

312

rrrrrr

AAT

A

T

A

T

Aρρρ −+

+++

.................................................................................... (11)

where:

z = z-factor, dimensionless Tr = Reduced temperature, dimensionless ρr = ρ/ρc, Reduced density, dimensionless ρ = Density at temperature and pressure, g/cc ρc = Critical density, g/cc (zc=0.27)

Our perspective in utilizing the NS-EOS is that this relation is purported to provide better performance in the vicinity of the critical isotherm — which is traditionally a region where the DAK-EOS has been shown to give a weak performance. We will compare the performance of the DAK and NS-EOS relations in detail once these relations are regressed using our gas density (z-factor) database.

Correlation of Hydrocarbon Gas Viscosity

In this section we provide comparisons and optimizations of existing correlations for hydrocarbon gas viscosity (refs. 3 and 4), as well as a new correlation for hydrocarbon gas viscosity that is implicitly defined in terms of gas density and tempera-ture. Our approach is to use an extensive database of gas vis-cosity and gas density data, derived from a variety of literature sources (refs. 11-15). This database contains 2494 points ta-ken from pure component data and 3155 points taken from mixture data. More data were available in the literature — however, the data points chosen for this study satisfy the fol-lowing criteria:

l Temperature is greater than 32 deg F.

l Density measurement is available for each measure-ment of gas viscosity. (This criterion was not ap-plied for selection of points for the correlation of gas viscosity at one atmosphere.)

l Gas composition must be representative of a natural gas (e.g., data for binary mixtures containing decane were excluded (ref. 4)).

l Liquid or liquid-like (i.e., unusually high) viscosi-ties were excluded from consideration.

Gas Viscosity: Jossi, et al. (ref. 3)

In this section we test the performance of the Jossi, et al. model for gas viscosity against viscosity values from our database. We then propose a "refitted" form of the Jossi, et al. model where the coefficients of the original model were ad-


justed using regression to better match the viscosity values provided in our database. Fig. 10 shows the results of the original Jossi, et al. model when applied to our database — we note that there are significant departures from the 45 degree straight line (conformance to this straight line would indicate perfect agreement between the measured and calculated gas viscosity values). There are 2494 pure component data points given on this plot, where this data match has an average absolute error of 5.26 percent in the prediction of gas viscos-ity. We wish to note that our database does include gas vis-cosity values measured at reduced density values greater than 2.0. We note that such points were not included in the original study by Jossi, et al.

In an attempt to minimize the error between our data and the Jossi, et al. model, we refitted the coefficients of the Jossi, et al. model using non-linear regression techniques. The generic form of the Jossi, et al. model is written in the form:

)(10)( 41

4JST,rg f ρξµµ =

+− −∗ .......................(12)

where:

ρ

ρρρρ

4

32

5

4 3 2 1 )(

JST,r

JST,rJST,rJST,rJST,r

f

fffff

+

+++=

....................................................................................(13)

32

1

ec

ew

ec

pM

T=ξ .........................................................(14)

The "optimized" coefficients obtained from the "refitting" the Jossi, et al. model are:

f1 = 1.03671E-01 f2 = 1.31243E-01 f3 = 1.71893E-02 f4 = -3.12987E-02 f5 = 8.84909E-03

e1 = -1.21699E-01 e2 = 3.91956E-01 e3= -1.50857E-01 ................................................................................... (15)

and the variables are defined in the same fashion as the ori-ginal correlation proposed by Jossi, et al. — where the most important issue is that this correlation is limited to pure com-ponent data. This means that the critical density is directly tied to the component — no alternate definition is permitted.

The performance of our "optimized" version of the Jossi, et al. model for gas viscosity is shown in Fig. 11. This plot shows better conformance to the 45 degree line than the original Jossi, et al. model shown in Fig. 10. The average absolute error for the optimized Jossi, et al. model is 4.43 percent (as compared to 5.26 percent for the original Jossi, et al. model). For reference, Jossi, et al. reported an average absolute error of 4 percent when they presented their model (fitted to a variety of fluids — including non-hydrocarbon samples). It is relevant to note that Jossi, et al. used a relatively small database of pure component data.

We must also note that our optimization of this model re-quires the gas viscosity at one atmosphere (µ∗) — in this case we used an independent correlation for µ∗ based on the rele-vant data from our database. This correlation for µ∗ is an inde-pendent development and is discussed in a later section.

Gas Viscosity: Lee, et al. (ref. 4)

The Lee, et al. model for gas viscosity was utilized in a similar manner to the Jossi, et al. model — i.e. the performance of the original model was first assessed using our database, and then the coefficients of this relation were optimized using the data-base of gas viscosity. We note that in this work we have utilized data for both pure components and gas mixtures.

Fig. 12 shows the performance of the Lee, et al. model on 4909 points from our database. This figure shows that gas vis-cosity is under predicted by the Lee, et al. model at the higher end of the gas viscosity scale. The average absolute error associated with the comparison of this model with our viscosity database is 3.34 percent.

The coefficients of the Lee, et al. model were then optimized using the gas viscosity database in order to improve the per-formance of the model. These results are shown in Fig. 13. For the optimization the Lee, et al. relation, the correlation model was cast in the following form:

)exp(10 4 YXKg ρµ −= ..................................................(16)

where:

TMkkTMkk

Kw

kw

+++

=

54

21

) (

3..................................................(17)

wMxTx

xX 32

1 +

+= ...............................................(18)

XyyY 21 −= .................................................................(19)

The optimized coefficients for this model are:

k1 = 1.67175E+01 k 2 = 4.19188E-02 k3 = 1.40256E+00 k 4 = 2.12209E+02 k 5 = 1.81349E+01

x1 = 2.12574E+00 x2 = 2.06371E+03 x3 = 1.19260E-02

y1 = 1.09809E+00 y2 = -3.92851E-02

....................................................................................(20)

The average absolute error for this "optimized" model is 2.29 percent. Lee, et al. reported average absolute errors of 2 to 4 percent for their original model — where we recall that the original Lee, et al. correlations were generated using a less comprehensive database.


Gas Viscosity: Proposed "Implicit" Model

Our correlation work based on a "non-parametric" regression algorithm16 shows that gas viscosity is primarily a function of the following variables:

l Gas viscosity at 1 atm, l Gas density, and l Temperature.

We found that pressure and molecular weight could be dis-carded as explicit variables for this model (these are included implicitly in the gas density function). We then developed a new gas viscosity model, which is simply a generic expansion of the Jossi, et al. model using additional temperature and den-sity dependent terms.

The relationship between the residual viscosity function (i.e., µg-µ1atm) and the gas density appears to be univariate, as shown in Fig. 14. A log-log plot of the residual viscosity data from our database shows significant scatter at low densities — where this behavior reveals a strong dependence of gas viscos-ity on temperature at low densities (see Fig. 15).

By observation we found that the "uncorrelated" distribution of data formed in the low-density range is directly related to temperature. We propose a rational polynomial model in terms of gas density with temperature-dependent coefficients and used nonlinear regression to fit our proposed model to temperature and gas density data. This model is given as:

)(1 ρµµ fatmg += ..................................................... (21)

32

32)(

ρρρ

ρρρρ

hgfe

dcbaf

+++

+++= ......................................... (22)

2210 TaTaaa ++= ................................................... (23)

2210 TbTbbb ++= .................................................... (24)

2210 TcTccc ++= ..................................................... (25)

2210 TdTddd ++= ................................................... (26)

2210 TeTeee ++= ..................................................... (27)

2210 TfTfff ++= ................................................... (28)

2210 TgTggg ++= .................................................. (29)

2210 ThThhh ++= .................................................... (30)

The numerical values for the parameters of our proposed "im-plicit" model for gas viscosity (Eqs. 21 to 30) are given as fol-lows:

a0 = 9.53363E-01 a1 = -1.07384E+00

a2 = 1.31729E-03

b0 = -9.71028E-01 b1 = 1.12077E+01 b2 = 9.01300E-02

c0 = 1.01803E+00 c1 = 4.98986E+00 c2 = 3.02737E-01

d0 = -9.90531E-01 d1 = 4.17585E+00 d2 = -6.36620E-01

e0 = 1.00000E+00 e1 = -3.19646E+00 e2 = 3.90961E+00

f0 = -1.00364E+00 f1 = -1.81633E-01

f2 = -7.79089E+00

g0 = 9.98080E-01 g1 = -1.62108E+00 g2 = 6.34836E-04

h0 = -1.00103E+00 h1 = 6.76875E-01 h2 = 4.62481E+00

................................................................................ (31)

A total of 4909 points were used in the regression calculation of these parameters (2494 pure component data and 2415 gas mixture data). The performance of the model is shown in Fig. 16. We note excellent agreement with the 45 degree straight-line trend. The average absolute error for this model as com-pared to our database is 3.05 percent. We also note there are non-hydrocarbon components such as carbon dioxide (0.19 to 3.20 percent), nitrogen (0.04 to 15.80 percent) and helium (0.03 to 0.80 percent) present in some of the gas mixtures used to develop these correlations.

Gas Viscosity: Hydrocarbon Gas Viscosity at 1 Atmosphere

In order to utilize both new and existing correlations for gas viscosity, it is imperative that we estimate the viscosity of a hydrocarbon gas mixture at 1 atm. We propose a new correla-tion for this purpose — where this correlation is given only as a function of the temperature (in deg R) and the gas specific gravity (as a surrogate for molecular weight of the mixture). The generic form of this relation is given by:

+++

+++=

)ln()ln()ln()ln(1

)ln()ln()ln()ln()ln(

321

32101 TbTbb

TaTaaa

gg

ggatm γγ

γγµ .......(32)

In this correlation we used 261 data points for the gas viscos-ity at 1 atm where 135 of these are pure component data and 126 are gas mixture data. This new correlation gives an aver-age absolute error of 1.36 percent. Fig. 17 illustrates the com-parison of the calculated gas viscosity at 1 atm and the mea-sured gas viscosity at 1 atm.

The numerical values of the parameters obtained for the new gas viscosity model for viscosity at 1 atm model (Eq. 32) are given by:

a0 = -6.39821E+00 a1 = -6.045922E-01 a2 = 7.49768E-01 a3 = 1.261051E-01

b1 = 6.97180E-02 b2 = -1.013889E-01 b3 = -2.15294E-02 ....................................................................................(33)

Correlation of Hydrocarbon Gas Density (z-factor)

Gas Density: Dranchuk-Abou-Kassem (DAK-EOS)

In this section we present the results of our regression work where we fitted the DAK-EOS to our gas density database. This was a multi-step process where we first perform regress-ion of the DAK-EOS onto the "standard" and pure component


databases. The "standard" database is a tabular rendering of the Standing and Katz z-factor chart. These data are presumed to accurately represent an "average" trend according to the "Law of Corresponding States".

After the "calibration" of the EOS, we can then use the mix-ture (and pure component) data to establish correlations for pseudocritical properties (we must correlate pseudocritical temperature and pressure because we will not be able to esti-mate these parameters independently — recall that we pre-sume we have only the mixture gravity of the gas, not a full compositional analysis).

The "first step" regression (EOS to database) is shown on Fig. 18, where we note a very strong correlation. The associated plots for comparing the models and data for this case are shown in Figs. 19-21 — we also observe a strong correlation (with only minor errors) near the critical isotherm. Coeffi-cients for the DAK-EOS obtained from regression (using the Poettmann-Carpenter10 "standard" database) are:

A1 = 3.024696E-01 A7 =-1.118884E+00 A2 = -1.046964E+00 A8 = 3.951957E-01 A3 = -1.078916E-01 A9 = 9.313593E-02 A4 = -7.694186E-01 A10 = 8.483081E-01 A5 = 1.965439E-01 A11 = 7.880011E-01 A6 = 6.527819E-01

................................................................................. (34a)

The average absolute error associated with this case is 0.412 percent (5960 data points). For reference, the original work by Dranchuk and Abou-Kassem (ref. 6) was based on a data-base of 1500 points and yielded an average absolute error of 0.486 percent.

Coefficients for the DAK-EOS regression using the "combin-ed" database (Poettmann-Carpenter10 data and pure component data) are:

A1 = 2.965749E-01 A7 =-1.006653E+00 A2 = -1.032952E+00 A8 = 3.116857E-01 A3 = -5.394955E-02 A9 = 9.506539E-02 A4 = -7.694000E-01 A10 = 7.544825E-01 A5 = 2.183666E-01 A11 = 7.880000E-01 A6 = 6.226256E-01

................................................................................. (34b)

For this case we obtained an average absolute error of 0.821 percent (8256 points). We note that this error is higher than error we obtained using the Poettmann-Carpenter10 "stan-dard" database — however, this error is (certainly) still accep-table.

We now pursue the "second step" of this development by applying the optimized DAK-EOS on our mixture and pure component database (for the z-factor) as a mechanism to de-velop relations for estimating the pseudocritical temperature and pressure.

In Fig. 22 we present the calculated versus measured values of z-factor for the "mixtures/pure component" calibration. We

note that 6032 data points were used (gas mixtures and pure component samples), and that we achieved an average abso-lute error of 3.06 percent for this case. In performing this regression, we simultaneously defined the new mixture rules for the DAK-EOS (i.e., correlations of pseudocritical tempera-ture and pressure as quadratic polynomials as a function of the gas gravity).

Figs. 23 and 24 present the results of the optimized DAK-EOS for the z-factor coupled with the optimized quadratic relations used to model the pseudocritical temperature and pseudocriti-cal pressure (as a function of gas specific gravity). The opti-mized quadratic equations for the pseudocritical temperature and pressure of a given sample are given in terms of the gas specific gravity as follows: (DAK-EOS case only)

2059277089725 ggpc ...p γγ −−= ..............................(35)

20194475493940 ggpc ...T γγ −+= ...............................(36)

where,

ppc = Pseudocritical pressure, psia Tpc = Pseudocritical temperature, deg R γg = Gas specific gravity (air = 1.0)

Eqs. 35 and 36 were calibrated using the DAK-EOS (and the coefficients for the DAK-EOS were taken from Eq. 34b). For the optimized DAK-EOS based on our research database, we note that only the combination of Eqs. 9, 34b, 35, and 36 can be used be used to estimate the z-factor for gas mixtures.

In summary, we have recalibrated the DAK-EOS against three databases – the Poettmann-Carpenter10 data (5960 points), an extended database which includes the Poettmann-Carpenter10

data and additional pure component data (8256 points), and a database of pure component and mixture data (6032 points).

In the first two cases we provide new coefficients to replace the original DAK-EOS (which was similarly defined by the original authors using pure component data). The average ab-solute errors for these cases were 0.486 percent and 0.821 per-cent, respectively.

Lastly, we applied the optimized DAK-EOS based on the "combined" database (Poettmann-Carpenter10 data and pure component data) (i.e., the combination of Eqs. 9 and 34b) for the case of gas mixtures and developed new models for the pseudocritical pressure and pseudocritical temperature as functions of gas gravity. This model resulted in an overall average absolute error of 3.06 percent for z-factors estimated using the DAK-EOS (and the quadratic polynomials for Tpc and ppc.

Gas Density: Nishiumi-Saito (NS-EOS)

This section follows a procedure similar to the previous work which provided new forms of the DAK-EOS. The first step was to "refit" the coefficients of the NS-EOS model using the Poettmann-Carpenter10 database.


The results from this regression are:

A1 = 2.669857E-01 A9 =-2.892824E-02 A2 = 1.048341E+00 A10 =-1.684037E-02 A3 = -1.516869E+00 A11 = 2.120655E+00 A4 = 4.435926E+00 A12 =-5.046405E-01 A5 = -2.407212E+00 A13 = 1.802678E-01 A6 = 6.089671E-01 A14 = 8.563869E-02 A7 = 5.174665E-01 A15 = 4.956134E -01 A8 = 1.296739E+00

................................................................................. (37a)

The average absolute error achieved in this regression was 0.426 percent (5960 points), which is slightly higher than the DAK-EOS result for the same case (0.412 percent).

The refitting procedure was also performed on the extended database of the Poettmann-Carpenter10 data and pure com-ponent data (8132 points). We note that we used fewer data for the regression as compared to the same case for the DAK-EOS (8256 points) — we found it necessary to delete certain extreme points in this regression, particularly values near the critical isotherm. The regression coefficients for this case are:

A1 = 4.645095E-01 A9 =-1.941089E-02 A2 = 1.627089E+00 A10 =-4.314707E-03 A3 = -9.830729E-01 A11 = 2.789035E-01 A4 = 5.954591E-01 A12 = 7.277907E-01 A5 = 6.183499E-01 A13 =-3.207280E-01 A6 = 4.109793E-01 A14 = 1.756311E -01 A7 = 8.148481E-02 A15 = 7.905733E -01 A8 = 3.541591E-01

................................................................................. (37b)

The average absolute error for this model was 0.733 percent, which is somewhat better than the DAK-EOS result for the same case (0.821 percent).

In a similar manner to the DAK-EOS case, we also considered gas mixtures by developing new relations for the pseudo-critical pressure and temperature for use with the NS-EOS. The results for this case are:

25156098181621 ggpc ...p γγ −+= ......................(38)

21493865429146 ggpc ...T γγ −+= ........................(39)

The performance for the NS-EOS (using the coefficients from Eqs. 37a and 37b) is shown in Figs. 25 to 27 (NS-EOS case only). The results for the "mixture" case are shown Fig. 28, and we note that this version of the NS-EOS has an average absolute error of 2.55 percent (with a database of 5118 points) and is uniquely defined by Eqs. 11, 37b, 38, and 39.

We note that we again used fewer data in this regression than the corresponding case for the DAK-EOS (5118 points for the NS-EOS and 6032 points for the DAK-EOS). This was necessary due to poor regression performance of the Tpc and ppc parameters — and, as before, we removed extreme values — those near the critical isotherm, high pressure/high tem-perature data, and cases of very high molecular weight. We appreciate that this issue may cause concerns — however,

based on our procedures and vigilance in the regression pro-cess, we remain confident that the Tpc and ppc correlations for this case (i.e., NS-EOS) are both accurate and robust.

Conclusions

The following conclusions are derived from this work:

l The new correlations presented in this work for gas viscosity, z-factor, and gas viscosity at 1 atm are ap-propriate for applications in petroleum engineering.

l The original Jossi, et al.3 and Lee, et al.4 correlations for gas viscosity appear to yield acceptable behavior compared to our database, the average absolute errors (AAE) for these correlations are as follows:

— Jossi, et al. original:3 AAE = 5.26 percent — Lee, et al. original:4 AAE = 3.34 percent

However, the "refits" of these correlations (using our research database) exhibit significantly better repre-sentations of the data:

— Jossi, et al. "refit:" AAE = 4.43 percent — Lee, et al. "refit:" AAE = 2.29 percent

For reference, the Jossi, et al. correlation was fit us-ing pure component data only (2494 points) — and can only be applied to pure component data (this is a requirement of the Jossi, et al. formulation). The Lee, et al. correlation was fit using both pure compo-nent and gas mixture data (4909 points), and should be considered appropriate for general applications.

l Our new "implicit" viscosity correlation (given as a function of density) works well for pure gases and for gas mixtures over a wide range of temperatures, pres-sures, and molecular weights. The average absolute error for the new "implicit" viscosity correlation is 3.05 percent for our combined database of pure com-ponent and natural gas mixture data (4909 total points).

l Our new correlation for gas viscosity at 1 atm gave an average absolute error of 1.36 percent based on 261 data points (135 pure component data and 126 gas mixture data).

l Although carbon dioxide, nitrogen, and helium were present in some of the gas mixtures, the new gas viscosity correlations match our research database very well — and, by extension, these correlations should work well (without correction) for practical applications where relatively small amounts of non-hydrocarbon impurities are present.

l The original work by Dranchuk and Abou-Kassem (DAK-EOS) for the implicit correlation of the real gas z-factor used 1500 data points and gave an aver-age absolute error of 0.486 percent.6 Refitting the DAK-EOS to our research database we considered two cases — the "standard" database given by Poett-mann and Carpenter10 (5960 points) and the "standard and pure component" database (the Poettmann and


Carpenter data combined with the pure component data) (8256 points).

The average absolute errors (AAE) for the DAK-EOS correlations are:

—DAK-EOS "standard" AAE = 0.412 percent —DAK-EOS "standard/pure" AAE = 0.821 percent

We performed a similar effort with the Nishiumi and Saito EOS7 (NS-EOS) using the same databases as for the DAK-EOS and obtained the following results:

—NS-EOS "standard" AAE = 0.426 percent —NS-EOS "standard/pure" AAE = 0.733 percent

l For the case of gas mixture densities, we developed quadratic formulations to represent the pseudocritical temperature and pressure as functions of the gas specific gravity. A combined database of pure com-ponent and gas mixture data was used in this optimi-zation.

Using the "optimized" DAK-EOS as a basis, we ob-tained an average absolute error of 3.06 percent (6032 data points) for the gas mixture correlation. Proceeding in a similar fashion using the "optimized" NS-EOS, we obtained an average absolute error of 2.55 percent (5118 data points).

Recommendations and Future Work

1. Further work should include investigations of the ex-plicit effects of non-hydrocarbon components such as water, nitrogen, carbon dioxide, and hydrogen sulfide on both gas viscosity and gas density (i.e., the gas z-factor).

2. This work could be extended to consider density and viscosity behavior of rich gas condensate and volatile oil fluids — however, we are skeptical that any sort of "universal" viscosity relation can be developed.

Nomenclature

AAE = Absolute error, percent p = Pressure, psia pc = Critical pressure, atm ppc = Pseudocritical pressure, psia ppr = Pseudoreduced pressure, dimensionless pr = Reduced pressure, dimensionless Mw = Molecular weight, lbm/lb-mole T = Temperature, deg F Tc = Critical temperature, deg K Tpc = Pseudocritical temperature, deg R Tpr = Pseudoreduced temperature, dimensionless Tr = Reduced temperature, dimensionless R = Universal gas constant, 10.732 (psia cu ft)/(lb-

mole deg R) z = z-factor, dimensionless ρ = Density, g/cc ρr = Reduced density, dimensionless µ1atm = Gas viscosity at 1 atm, cp

µ* = Gas viscosity at low pressures used by Jossi, et al.4, cp

µg = Gas viscosity, cp γg = Gas specific gravity (air=1.0), dimensionless yN2, CO2, H2S = Mole fraction of the non-hydrocarbon

component (fraction)

Subscripts

c = critical value pc = pseudocritical value r = reduced variable pr = pseudoreduced variable

Acknowledgements

The authors wish to acknowledge the Department of Petro-leum Engineering at Texas A&M University for the use of computer and reference services.

References

1. Huber, M. L: Physical and Chemical Properties Division, National Institute of Standards and Technology, Gaithers-burg, MD.

2. Carr, N.L. Kobayashi, R., and Burrows, D.B.: "Viscosity of Hydrocarbon Gases Under Pressure," Trans., AIME (1954) 201, 264-272.

3. Jossi, J.A., Stiel, L.I., and Thodos G.: "The Viscosity of Pure Substances in the Dense Gaseous and Liquid Phases," AIChE Journal (Mar. 1962) Vol. 8, No.1; 59-62.

4. Lee, A.L., Gonzalez, M.H., and Eakin, B.E.: "The Vis-cosity of Natural Gases," JPT (Aug. 1966) 997-1000; Trans., AIME (1966) 234.

5. Gonzalez, M.H., Eakin, B.E., and Lee, A.L.: "Viscosity of Natural Gases," American Petroleum Institute, Mono-graph on API Research Project 65 (1970).

6. Dranchuk, P.M., and Abou-Kassem, J.H.: "Calculation of z-Factors for Natural Gases Using Equations of State," Journal of Canadian Petroleum (Jul.-Sep. 1975) 14, 34-36.

7. Nishiumi, H. and Saito, S.: "An Improved Generalized BWR Equation of State Applicable to Low Reduced Tem-peratures," Journal of Chemical Engineering of Japan, Vol. 8, No. 5 (1975) 356-360.

8. Nishiumi, H.: "An Improved Generalized BWR Equation of State with Three Polar Parameters Applicable to Polar Substances," Journal of Chemical Engineering of Japan, Vol. 13, No. 3 (1980) 178-183.

9. Standing, M.B., Katz, D.L.: "Density of Natural Gases," Trans., AIME (1942) 146, 140.

10. Poettmann, H.F., and Carpenter, P.G.: "The Multiphase Flow of Gas, Oil, and Water Through Vertical Flow String with Application to the Design of Gas-lift Instal-lations," Drilling and Production Practice, (1952) 257-317.

11. Lee, A.L.: "Viscosity of Light Hydrocarbons," American Petroleum Institute, Monograph on API Research Project 65 (1965).


12. Diehl, J., Gondouin, M., Houpeurt, A., Neoschil, J., Thelliez, M., Verrien, J.P., and Zurawsky, R.: "Viscosity and Density of Light Paraffins, Nitrogen and Carbon Di-oxide," CREPS/Geopetrole (1970).

13. Golubev I.F., "Viscosity of Gases and Gas Mixtures, a Handbook," This paper is a translation from Russian by the NTIS (National Technical Information Service) (1959).

14. Stephan, K., and Lucas, K.: "Viscosity of Dense Fluids," The Purdue Research Foundation (1979).

15. Setzmann U., and Wagner, W.: "A New Equation of State and Tables of Thermodynamic Properties for Methane Covering the Range from the Melting Line to 625 K at Pressures up to 1000 MPa," J. Phys. Chem. Ref. Data (1991) Vol. 20, No 6; 1061-1155.

16. Xue, G., Datta-Gupta, A., Valko, P., and Blasingame, T.A.: "Optimal Transformations for Multiple Regression: Application to Permeability Estimation from Well Logs," SPEFE (June 1997), 85-93.

17. McCain, W. D., Jr.: "The Properties of Petroleum Fluids," Second Edition, Penn Well Publishing Co., Tulsa, OK (1990) 90-146.

18. Brill, J. P. and Beggs, H. D.: "Two-Phase Flow in Pipes," University of Tulsa. INTERCOMP Course, The Hague, (1974).

Figure 1 – The "residual" gas viscosity function versus reduc-ed density for different pure substances of similar molecular weights (Jossi, et al.3).

Figure 2 – The "residual viscosity" function versus reduced density for different pure components — note the effect of temperature at low reduced densities (Jossi, et al.3).

Figure 3 – Gas viscosity versus temperature for the Gonzalez, et al.5 data (natural gas sample 3) compared to the Lee, et al.4 hydrocarbon viscosity correlation.


Figure 4 – Real gas z-factor, as attributed to Standing and Katz,9 plotted as a function of the pseudoreduced pressure (data of Poettmann and Carpenter10).

Figure 5 – Real gas z-factor, as attributed to Standing and Katz,9 plotted as a function of the pseudoreduced pressure divided by the pseudoreduced tempera-ture (data of Poettmann and Carpenter10).

Figure 6 – Real gas z-factor, as attributed to Standing and Katz,9 plotted as a function of the pseudoreduced density function (data of Poettmann and Carpen-ter10).

Figure 7 – Real gas z-factor, as attributed to Standing and Katz,9 plotted as a function of the pseudoreduced pressure (data of Poettmann and Carpenter10) compared to the original DAK-EOS (coefficients from Eq. 10).


Figure 8 – Real gas z-factor, as attributed to Standing and Katz,9 plotted as a function of the pseudoreduced pressure divided by the pseudoreduced tempera-ture (data of Poettmann and Carpenter10) compared to the original DAK-EOS (coefficients from Eq. 10).

Figure 9 – Real gas z-factor, as attributed to Standing and Katz,9 plotted as a function of pseudoreduced den-sity (data of Poettmann and Carpenter10) compared to the original DAK-EOS (coefficients from Eq. 10).

Figure 10 – Jossi, Stiel, and Thodos4 correlation for hydrocar-bon gas viscosity tested with our database (Car-tesian format).

Figure 11 – Optimized Jossi, Stiel, and Thodos4 correlation for hydrocarbon gas viscosity optimized using our database (Cartesian format).


Figure 12 – Lee, Gonzalez, and Eakin5 correlation for hydrocar-bon gas viscosity tested with our database (Car-tesian format).

Figure 13 – Optimized Lee, Gonzalez, and Eakin5 correlation for hydrocarbon gas viscosity optimized using our database (Cartesian format).

Figure 14 – Cartesian plot of the residual viscosity versus den-sity for hydrocarbon gases.

Figure 15 – Log-log plot of residual viscosity versus density for hydrocarbon gases.


Figure 16 – Cartesian plot of the calculated versus the mea-sured viscosity for hydrocarbon gases, the vis-cosity is calculated using the proposed implicit model for gas viscosity (in terms of gas density and temperature).

Figure 17 – Cartesian plot of the calculated versus the mea-sured gas viscosity at 1 atm, the gas viscosity at 1 atm is calculated using the new rational polynomial model (Eq. 32).

Figure 18 – Log-log plot of the calculated versus the measured z-factor — the z-factor is calculated using the op-timized Dranchuk and Abou-Kassem6 EOS (coeffi-cients from Eqs. 34a and 34b).

Figure 19 – Real gas z-factor, as attributed to Standing and Katz,9 plotted as a function of the pseudoreduced pressure (data of Poettmann and Carpenter10) com-pared to the optimized DAK-EOS (coefficients from Eqs. 34a and 34b).


Figure 20 – Real gas z-factor, as attributed to Standing and Katz,9 plotted as a function of the pseudoreduced pressure divided by the pseudoreduced tempera-ture (data of Poettmann and Carpenter10) compared to the optimized DAK-EOS (coefficients from Eqs. 34a and 34b).

Figure 21 – Real gas z-factor, as attributed to Standing and Katz,9 plotted as a function of pseudoreduced den-sity (data of Poettmann and Carpenter10) compared to the optimized DAK-EOS (coefficients from Eqs. 34a and 34b).

Figure 22 – Log-log plot of the calculated versus the measured z-factor, the z-factor is calculated using the opti-mized DAK-EOS and the new quadratic equations for the pseudocritical properties (coefficients from Eqs. 34b, 35, and 36).

Figure 23 – Pseudocritical pressure behavior predicted from correlations (including pure component data) — the new correlations for ppc are derived from the opti-mized DAK-EOS and the optimized NS-EOS.


Figure 24 – Pseudocritical temperature behavior predicted from correlations (including pure component data) — the new correlations for Tpc are derived from the opti-mized DAK-EOS and the optimized NS-EOS.

Figure 25 – Real gas z-factor, as attributed to Standing and Katz,9 plotted as a function of the pseudoreduced pressure (data of Poettmann and Carpenter10) com-pared to the optimized NS-EOS (coefficients from Eqs. 37a and 37b).

Figure 26 – Real gas z-factor, as attributed to Standing and Katz,9 plotted as a function of the pseudoreduced pressure divided by the pseudoreduced tempera-ture (data of Poettmann and Carpenter10) compared to the optimized NS-EOS (coefficients from Eqs. 37a and 37b).

Figure 27 – Real gas z-factor, as attributed to Standing and Katz,9 plotted as a function of pseudoreduced den-sity (data of Poettmann and Carpenter10) compared to the optimized DAK-EOS (coefficients from Eqs. 37a and 37b).


Figure 28 – Log-log plot of the calculated versus the measured z-factor, the z-factor is calculated using the opti-mized NS-EOS and the new quadratic equations for the pseudocritical properties (coefficients from Eqs. 37b-39).

Fluidos de Reservorio

Parámetros PVT

Parámetros PVT

• En los reservorios de gas tenemos una ecuación de

estado que describe el comportamiento del fluido en

función de cambios en la Presión y Temperatura:

– PV = ZnRT

• En los reservorios de petróleo, lamentablemente no

tenemos una ecuación de estado que lo represente,

por lo que tenemos que medir estos parámetros en

laboratorio, realizando un análisis exhaustivo del

comportamiento de los mismos.

Petróleo Subsaturado y Saturado

Muestreo

• Es muy importante tener en cuenta que el muestreo de un reservorio de debe ser

realizado al comienzo de la explotación del mismo (una de las primeras tareas a

realizar) para que la muestra sea representativa.

• El tipo de muestreo va a depender del tipo de fluido de reservorio. Tenemos dos

tipos de muestreo:

– Muestra de fondo: este tipo de muestreo puede ser realizado cuando la presión de

fluencia (presión de fondo del pozo cuando se encuentra en producción) está por

encima de la presión de saturación del fluido. Este tipo de muestreo es utilizado para

petróleos negros o volátiles.

– Muestra de superficie y recombinación: este tipo de muestreo se utiliza para petróleos

negros y volátiles, como así para gas retrógrado y gas húmedo. Se toma una muestra de

gas y una muestra de líquido en las salidas del separador. La recombinación se realiza

según la RGP (GOR) correspondiente en ese momento.

• Durante el muestreo es muy importante que las condiciones de producción del

pozo se mantengan constantes a lo largo del mismo (GOR cte, Qprod cte, etc.). Se

debe producir el pozo por un periodo de tiempo para asegurar la limpieza en las

inmediaciones del pozo y luego al menor caudal posible para asegurar una presión

alta de fluencia, que esté por encima de la presión de saturación.

Muestra de Fondo

Muestra de Superficie

*Se debe corregir el GOR de campo informado, debido a que el mismo es informado sobre el líquido de tanque.

Definición de Parámetros PVT

• Rs = Relación de gas disuelto, es el volumen de gas que va a disolver 1 m3 de petróleo en superficie a una determinada presión y la temperatura de reservorio.

– Unidades: scf/stb, Nm3/m3

– Factor de conversión: 5,615 scf/stb = 1 Nm3/m3

• Bo = Factor volumétrico de formación del petróleo, es el volumen de petróleo ocupado en fondo por 1 m3 de petróleo en superficie, junto con su gas disuelto, a una determinada presión y temperatura de reservorio.

– Unidades: rb/stb, m3/m3

– Factor de conversión: 1 rb/stb = 1 m3/m3

• Bg = Factor volumétrico de formación del gas, es el volumen de gas que ocupa 1 m3 de gas en superficie, a una determinada presión y temperatura del reservorio.

– Unidades: rb/scf, m3/Nm3

– Factor de conversión: 0,1781 rb/scf = 1 m3/Nm3


Petróleo Subsaturado


Petróleo Saturado

Bt = Bo + (R – Rs)*Bg

Liberación Flash (Expansión a masa constante)

Liberación Diferencial

Pasos de un PVT

1. Determinación composición de (muestreo en superficie):

– Gas de separador

– Gas de tnk

– Líquido de tnk

2. Expansión Flash para:

– Determinación del Punto de Burbuja (Pb) o Punto de Rocío (Pd).

– En Petróleos se obtiene la compresibilidad del petróleo en la zona monofásica (P > Pb): co = -1/Bo*∆Bo/∆P

3. Expansión Diferencial para determinar Bo, Rs, Bg, z.

Pasos de un PVT

4. Ensayos de separador:

– Expansión Flash a través de diferentes presiones de Separador para determinar presión óptima de separación y corregir los datos de la expansión diferencial.

– 1er Flash: Pb, Tres -> Psep_i, Tsep

– 2do Flash: Psep_i, Tsep -> Pcs, Tcs

– Correcciones:

• Bo_corregido = Bod * Bofb_sepopt / Bodb

• Rs_corregido = Rsd * Rsfb_sepopt / Rsdb

5. Composición del efluente de las diferentes etapas de la liberación diferencial.

6. Medición de viscosidad y densidad en función de la presión.

Corrección de GOR

Si el muestreo fue en superficie, se debe corregir el GOR medidopara realizar una correcta recombinación:

A. Corrección por líquido de separador:

– GOR medido = Gas de sep (no corregido) / Pet de tnk (STD)

– GOR sep_nc = Gas de sep (no corregido) / Pet de sep (STD) =

= GOR medido * Pet de tnk (STD) / Pet de sep (STD)

B. Corrección por GE del gas:

– GOR sep_nc = Gas de sep (no corregido) / Pet de sep (STD)

– GE medido -> Z medido

– GE lab -> Z lab

– GOR sep = GOR sep_nc * Z lab / Z medido

2. Expansión Flash para la determinación del

Punto de Burbuja (Pb) o Punto de Rocío (Pd).

3. Expansión Diferencial para determinar parámetros PVT: Bo, Rs y Bg.

4. Expansión Flash a través de diferentes presiones de Separador.

5. Composición del efluente de las diferentes etapas la liberación diferencial.

6. Determinación de curvas de viscosidad y densidad en función de la presión.

PVT Black Oil

Compañía : XXXXXXXXXXXXXX Yacimiento : XXXXXXXXXXXXXX Pozo : XXXXXX

página-6-

DATOS OBTENIDOS DE LAS PLANILLAS DE TOMA DE MUESTRAY CONFIRMADOS POR PERSONAL DE XXXXXXXXXXXXX

Formación Quintuco2471.5 - 2475.5 mbbp

Presión Estática del Reservorio 2334 psi @ 2474 mbbpTemperatura de la capa productiva 91.5 °C @ 2474 mbbp

2.7/8" a 2449 mbbp

Estado del Pozo CerradoProfundidad del Packer 2449 mbbpProfundidad del Tapón 2539 mbbpFecha de toma de muestra 04/04/01Profundidad del muestreo 2430 mbbpPresión a prof de muestreo 2273 psiTemperatura a prof del muestreo 90.4 ºCPresión estática de boca 20 psiProducción de petroleo diaria 122.4 m3/dNivel de petroleo 710 mbbpPorcentaje de agua 0%Contacto gas-petróleo 710 mbbpMuestra 1 2Nº de Botellón 14308 28312Fecha de toma de muestra 04/04/01 04/04/01Tiempo de cierre del Pozo 12 hs. 14 hs.Tiempo de bajada del tomamuestras 60 min. 60 min.Presión de apertura del tomamuestras 960 psi 940 psiTemp de transferencia de la muestra 13 ºC 11 ºCTemperatura ambiente 14 ºC 11 ºCcm3 para elevar la presión a 2400 psi 35.7 36Presión de transferencia de la muestra 2800 psi 2800 psiPresión de embarque de la muestra 2500 psi 2500 psicm3 retirados del botellón de líquido 30 30Presión de burbuja de campo 1140 psi @ 13 ºC 1135 psi @ 10 ºC

Presión de apertura del botellón 2735 psia @19.2°CPresión de burbuja del botellón 1180.1psia @ 19.5 °C

Mediciones efectuadas en el laboratorio

Características del pozo

Intervalo productor

Diámetro de Tubing

Condiciones de la toma de muestra (muestra de fondo)

Compañía : XXXXXXXXXXXXX Yacimiento : XXXXXXXXXXXXX Pozo : XXXXXX

página-7-

[Kg/cm2]abs [psia] Experim. Ajustada [Kg/cm2]abs [psia] Experim. Ajustada

212.75 3026.0 821.75 821.74 80.57 1146.0 810.00 810.00179.00 2546.0 819.16 819.18 78.81 1121.0 807.00 807.00144.90 2061.0 816.68 816.66 77.76 1106.0 804.00 804.00107.29 1526.0 813.94 813.95

Pb 82.97 1180.1 812.23 812.23

Presión Lectura de bomba Presión Lectura de bomba

EXPANSIÓN A MASA CONSTANTE Y 19.5°CRELACIÓN PRESIÓN-VOLUMEN DEL FLUIDO DE RESERVORIO

Botellón: XXXXX

Estado bifásicoEstado monofásico

802

804

806

808

810

812

814

816

818

820

822

82450 70 90 110 130 150 170 190 210 230

PRESIÓN [Kg/cm2]

Lect

ura

de B

omba

[cm

3 ]

P. de Burbuja


página-8-

Composición de la muestra


página-9-

COMPONENTE Densidad Peso[g/cm3 ] Molecular

Metano 0.009 0.114 0.344 16.04Etano 0.029 0.205 0.484 30.07Propano 0.214 1.025 0.508 44.09i-Butano 0.166 0.604 0.563 58.12n-Butano 0.672 2.440 0.584 58.12i-Pentano 0.703 2.058 0.625 72.15n-Pentano 1.252 3.662 0.631 72.15Hexanos 2.285 5.742 0.691 84.00Heptanos 4.000 8.797 0.729 96.00Octanos 4.799 9.469 0.752 107.00Nonanos 4.188 7.307 0.771 121.00Decanos 4.174 6.577 0.785 134.00Undecanos 3.809 5.471 0.796 147.00Dodecanos 3.204 4.202 0.807 161.00Tridecanos 3.205 3.867 0.819 175.00Tetradecanos 3.102 3.447 0.830 190.00Pentadecanos 3.640 3.730 0.840 206.00Hexadecanos 2.586 2.459 0.847 222.00Heptadecanos 2.401 2.139 0.855 237.00Octadecanos 2.785 2.343 0.860 251.00Nonadecanos 2.497 2.005 0.865 263.00Eicosanos y Sup 50.279 22.338 0.930 475.20

100.000 100.000PROPIEDADES MEDIDAS EXPERIMENTALMENTEDensidad media @ 15.5°C [g/cm3 ] 0.8491Gravedad (°API) 35.1Peso Molecular Medio 215.6PROPIEDADES CALCULADASDensidad media @ 15.5°C [g/cm3 ] 0.8491Gravedad (°API) 35.1Peso Molecular Medio 211.1PROPIEDADES CALCULADAS DE LA FRACCION C7+Porcentaje Molar 84.149Densidad @ 15.5°C [g/cm3 ] 0.865Peso Molecular Medio 237.5

COMPOSICION MOLECULAR DEL PETROLEO DE TANQUE OBTENIDO A PARTIR DE UNA SEPARACION FLASH @ P. ATM. Y 20.6 °C

[% en peso] [% Molar]

Valores AsignadosBotellón: 14308

CROM ATOGRAM A


página-10-

Gas de Petróleo Valores AsignadosFlash de Flash

[% Molar] [% Molar]Nitrogeno 1.411 0.622 0.804 28.013Dióxido de Carbono 0.093 0.041 0.809 44.010Metano 59.548 0.114 26.330 0.344 16.04Etano 13.136 0.205 5.909 0.484 30.07Propano 13.244 1.025 6.415 0.508 44.09i-Butano 2.428 0.604 1.409 0.563 58.12n-Butano 5.467 2.440 3.775 0.584 58.12i-Pentano 1.505 2.058 1.814 0.625 72.15n-Pentano 1.601 3.662 2.753 0.631 72.15Hexanos 0.961 5.742 3.633 0.691 84.00Heptanos 0.455 8.797 5.118 0.729 96.00Octanos 0.109 9.469 5.341 0.752 107.00Nonanos 0.032 7.307 4.098 0.771 121.00Decanos 0.010 6.577 3.680 0.785 134.00Undecanos 5.471 3.058 0.796 147.00Dodecanos 4.202 2.348 0.807 161.00Tridecanos 3.867 2.161 0.819 175.00Tetradecanos 3.447 1.926 0.830 190.00Pentadecanos 3.730 2.085 0.840 206.00Hexadecanos 2.459 1.374 0.847 222.00Heptadecanos 2.139 1.195 0.855 237.00Octadecanos 2.343 1.309 0.860 251.00Nonadecanos 2.005 1.120 0.865 263.00Eicosanos y Sup 22.338 12.485 0.930 475.20

100.000 100.000 100.000PROPIEDADES MEDIASG. Esp. (aire=1) 0.966Densidad @ 15.5°C [g/cm3 ] 0.8491 0.7850Peso Molecular Medio 28.0 215.6 130.4PROP. CALCULADAS DE LA FRACCIÓN C7+Porcentaje Molar 0.606 84.149 47.299Densidad @ 15.5°C [g/cm3 ] 0.865 0.865Peso Molecular Medio 99.9 237.5 236.7PARÁMETROS GLOBALES DE ESTE ENSAYORelación GAS-PETRÓLEO: 73.4 m3/m3 en condiciones STDFracción molar de gas 0.4411Fracción molar de líquido 0.5589 Condiciones del FLASH (no equil.)Factor de Volumen del Flash 1.169 De 212.9 Kg/cm²abs

F. de Volumen Calculado y 20.6 °C @Pb & T Reserv 1.275 hasta 1.03 Kg/cm²abs

y 20.6 °C

COMPOSICION MOLECULAR DEL FLUIDO DE RESERVORIO, A PARTIR DE UNA SEPARACION FLASH @ P. ATM. Y 20.6 °C

COMPONENTEBotellón: 14308

Fluido de reservorio

recombinado [% Molar]

Densidad [g/cm³]

Peso Molecular


página-11-

Expansión a masa constante


página-12-

Estado monofásico Estado bifásicoVolumen relativo Volumen relativo

Experim. Ajustado Experim. Ajustado

212.89 0.9853 0.9853 1.323E-04 110.57 1.0099 1.0099176.97 0.9902 0.9902 1.448E-04 98.87 1.0561 1.0561

Pr 164.10 0.9920 0.9921 1.492E-04 82.67 1.1491 1.1493159.97 0.9927 0.9927 1.506E-04 71.77 1.2424 1.2422141.97 0.9954 0.9954 1.567E-04128.97 0.9975 0.9975 1.611E-04

Pb 113.60 1.0000 1.0000 1.663E-04

Vr = 1.02122 + -2.0727E-04 x P + 1.8055E-07 x P² para P>PbVr = 1 + ( 113.60 - P ) / ( 9.1311E-03 x P² + 1.7508E+00 x P ) para P<Pb Donde P = Presión y Vr = Volumen Relativo

EXPANSIÓN A MASA CONSTANTE Y 91.5 °CRELACIÓN PRESIÓN-VOLUMEN DEL FLUIDO DE RESERVORIO

Presión [Kg/cm2]abs


Coef. de Compresib 1/[Kg/cm²]

0.950

1.000

1.050

1.100

1.150

1.200

1.250

1.300

50 100 150 200 250

PRESIÓN [Kg/cm2]abs

Vol.

Rel

ativ

o

P. de Burbuja


página-13-

Liberación Diferencial


página-14-


Rd [m3/m3]

Rl [m3/m3]

Pb 113.60 75.22 0.00

97.37 66.62 8.60

81.47 58.32 16.91

65.57 49.97 25.26

49.67 41.48 33.74

33.77 32.64 42.59

17.87 22.48 52.74

1.03 0.00 75.22

LIBERACION DIFERENCIAL A 91.5 °CRELACIÓN GAS-PETRÓLEO

(Disuelto [Rd] y Liberado [Rl])

0

20

40

60

80

0 20 40 60 80 100 120


RG

P [m

3 /m3 ]

Gas Disuelto

Gas Liberado


página-15-

Estado monofásico Estado bifásico


Factor de Volumen (Bo)


Factor de Volumen (Bo)

212.89 1.2664 97.37 1.2637

176.97 1.2727 81.47 1.2434

Pr 164.10 1.2751 65.57 1.2226

159.97 1.2759 49.67 1.2010

141.97 1.2794 33.77 1.1776

128.97 1.2821 17.87 1.1488

Pb 113.60 1.2853 1.03 1.0629

LIBERACION DIFERENCIAL A 91.5 °CFACTOR DE VOLUMEN DE PETRÓLEO (Bo)

1.00

1.05

1.10

1.15

1.20

1.25

1.30

0 50 100 150 200 250


Bo

P. de Burbuja


página-16-

Estado monofásico Estado bifásicoPresión

[Kg/cm2]abs

Densidad [g/cm3 ]


Densidad [g/cm3 ]

212.89 0.7435 97.37 0.7390

176.97 0.7398 81.47 0.7451

Pr 164.10 0.7384 65.57 0.7516

159.97 0.7379 49.67 0.7586

141.97 0.7359 33.77 0.7662

128.97 0.7344 17.87 0.7754

Pb 113.60 0.7325 1.03 0.7996

LIBERACION DIFERENCIAL A 91.5 °CDENSIDAD DEL PETRÓLEO

0.720

0.730

0.740

0.750

0.760

0.770

0.780

0.790

0.800

0.810

0 50 100 150 200 250


Den

sida

d [g

/cm

3 ]

P. de Burbuja


página-17-

Estado monofásico Estado bifásicoPresión

[Kg/cm2]abs

Viscosidad [cP]


Viscosidad [cP]

212.89 1.005 97.37 0.874176.97 0.939 81.47 0.933

Pr 164.10 0.919 65.57 1.013159.97 0.910 49.67 1.123141.97 0.878 33.77 1.252128.97 0.850 17.87 1.440

Pb 113.60 0.823 1.03 2.088

LIBERACION DIFERENCIAL A 91.5 °CVISCOSIDAD DEL PETRÓLEO

0.60

0.80

1.00

1.20

1.40

1.60

1.80

2.00

2.20

0 50 100 150 200 250


Visc

osid

ad [c

p]

P. de Burbuja


página-18-

Presión [Kg/cm²]absCOMPONENTE 97.37 81.47 65.57 49.67 33.77 17.87 1.03Nitrogeno 3.633 3.031 2.373 1.678 1.063 0.465 0.159

Dióxido de Carbono 0.057 0.071 0.079 0.087 0.112 0.138 0.097

Metano 79.841 79.476 78.489 76.451 71.771 60.127 20.580

Etano 7.828 8.384 9.212 10.461 12.686 16.970 18.579

Propano 4.815 5.130 5.669 6.574 8.400 12.847 27.756

i-Butano 0.704 0.739 0.808 0.932 1.200 1.915 5.994

n-Butano 1.476 1.539 1.675 1.929 2.475 3.984 13.951

i-Pentano 0.417 0.424 0.452 0.513 0.645 1.037 4.232

n-Pentano 0.473 0.477 0.505 0.571 0.713 1.141 4.505

Hexanos 0.379 0.367 0.383 0.422 0.509 0.785 2.624

Heptanos 0.232 0.220 0.215 0.246 0.285 0.406 0.949

Octanos 0.088 0.088 0.088 0.087 0.092 0.121 0.378

Nonanos 0.038 0.037 0.036 0.034 0.036 0.045 0.139

Decanos 0.018 0.017 0.016 0.015 0.015 0.019 0.056

100.000 100.000 100.000 100.000 100.000 100.000 100.000

PROPIEDADES MEDIASG. Esp. (aire=1) 0.722 0.727 0.737 0.759 0.805 0.926 1.479

Factor de Desviación ('Z') 0.884 0.895 0.907 0.921 0.936 0.952 0.993

Peso Molecular Medio 20.9 21.1 21.4 22.0 23.4 26.9 42.9

P. Molec de la Fracción C7+ 102.9 103.0 103.0 102.3 101.8 101.4 102.4

Viscosidad [cp] 0.0150 0.0143 0.0137 0.0129 0.0120 0.0114 0.0099

Factor de Volumen (Bg) 0.01189 0.01438 0.01810 0.02426 0.03627 0.06974 1.25859

P. Caloríf. Inf. [Kcal/m3] 9,790 9,924 10,150 10,522 11,203 12,845 20,045

P. Caloríf. Sup. [Kcal/m3] 10,796 10,941 11,186 11,587 12,318 14,080 21,801

LIBERACION DIFERENCIAL A 91.5 °CCOMPOSICIÓN MOLECULAR DEL EFLUENTE

0.01

0.1

1

10

100

0 20 40 60 80 100

PRESIÓN [Kg/cm²]abs

Com

posi

ción

N2

CO2

C1

C2

C3

i-C4

n-C4

i-C5

n-C5

C6

C7

C8

C9

C10


página-19-

Valores AsignadosCOMPONENTE [% en peso] [% Molar] Densidad Peso

[g/cm3] MolecularMetano 0.001 0.010 0.344 16.04Etano 0.010 0.070 0.484 30.07Propano 0.112 0.522 0.507 44.09i-Butano 0.108 0.380 0.563 58.12n-Butano 0.488 1.719 0.584 58.12i-Pentano 0.595 1.687 0.624 72.15n-Pentano 1.146 3.251 0.631 72.15Hexanos 2.308 5.622 0.691 84.00Heptanos 4.342 9.255 0.729 96.00Octanos 5.362 10.253 0.752 107.00Nonanos 4.710 7.964 0.771 121.00Decanos 4.713 7.198 0.785 134.00Undecanos 4.338 6.038 0.796 147.00Dodecanos 3.658 4.649 0.807 161.00Tridecanos 4.194 4.904 0.818 175.00Tetradecanos 2.777 2.991 0.830 190.00Pentadecanos 3.607 3.583 0.840 206.00Hexadecanos 3.533 3.257 0.847 222.00Heptadecanos 2.927 2.527 0.855 237.00Octadecanos 2.892 2.358 0.860 251.00Nonadecanos 2.927 2.277 0.865 263.00Eicosanos y Sup 45.251 19.485 0.930 475.20

100.000 100.000PROPIEDADES MEDIDAS EXPERIMENTALMENTEDensidad media @ 15.5°C [g/cm3] 0.8499Gravedad (°API) 35.0Peso Molecular Medio 219.3PROP. CALCULADAS A PARTIR DE LOS VALORES ASIGNADOSDensidad media @ 15.5°C [g/cm3] 0.8451Gravedad (°API) 35.9Peso Molecular Medio 204.6PROPIEDADES CALCULADAS DE LA FRACCION C7+Porcentaje Molar 86.739Densidad @ 15.5°C [g/cm3] 0.858Peso Molecular Medio 224.7

COMPOSICIÓN MOLECULAR DEL PETRÓLEO DE TANQUE OBTENIDO AL FINAL DE LA LIBERACIÓN DIFERENCIAL

CROM ATOG RAM A


página-20-


Factor de desviación del gas

1 97.37 0.8842 81.47 0.8953 65.57 0.9074 49.67 0.9215 33.77 0.9366 17.87 0.9527 1.03 0.993

LIBERACION DIFERENCIAL A 91.5 °CFACTOR DE DESVIACIÓN DEL GAS ('Z')

0.86

0.88

0.90

0.92

0.94

0.96

0.98

1.00

0 20 40 60 80 100 120

PRESIÓN [Kg/cm2 ]abs

Fact

or d

e D

esvi

ació

n [Z

]


página-21-


Factor de volumen del gas (Bg)

1 97.37 0.01192 81.47 0.01443 65.57 0.01814 49.67 0.02435 33.77 0.03636 17.87 0.06977 1.033 1.2586

LIBERACION DIFERENCIAL A 91.5 °CFACTOR DE VOLUMEN DEL GAS

0.000

0.010

0.020

0.030

0.040

0.050

0.060

0.070

0.080

0 20 40 60 80 100 120


Bg


página-22-


Viscosidad del gas (Bg)

1 97.37 0.01502 81.47 0.01433 65.57 0.01374 49.67 0.01295 33.77 0.01206 17.87 0.01147 1.03 0.0099

LIBERACION DIFERENCIAL A 91.5 °CVISCOSIDAD DEL GAS

0.009

0.010

0.011

0.012

0.013

0.014

0.015

0.016

0 20 40 60 80 100 120


Visc

osid

ad [c

p]


página-23-

Valores Asignados

PRODUCTOS CONDENSABLES (L/1000m3 ) Densidad Peso

Presión [Kg/cm2 ] [g/cm3 ] MolecularCOMPONENTE 97.37 81.47 65.57 49.67 33.77 17.87 1.03Nitrogeno - - - - - - - 0.803 28.02D. de Carbono - - - - - - - 0.809 44.01Metano - - - - - - - 0.300 16.04Etano - - - - - - - 0.356 30.07Propano 177.3 188.9 208.8 242.1 309.3 473.1 1022.1 0.507 44.09i-Butano 30.8 32.3 35.3 40.8 52.4 83.7 262.0 0.563 58.12n-Butano 62.2 64.8 70.6 81.3 104.3 167.9 587.9 0.584 58.12i-Pentano 20.4 20.8 22.1 25.1 31.6 50.8 207.2 0.624 72.15n-Pentano 22.9 23.1 24.5 27.7 34.5 55.2 218.1 0.631 72.15Hexanos 20.3 19.7 20.5 22.6 27.3 42.1 140.6 0.664 84.00Heptanos 13.0 12.3 12.0 13.7 15.9 22.7 53.1 0.727 96.00Octanos 5.3 5.3 5.3 5.3 5.6 7.3 22.9 0.749 107.00Nonanos 2.5 2.5 2.4 2.3 2.4 3.0 9.3 0.768 121.00Decanos 1.3 1.2 1.2 1.1 1.1 1.4 4.0 0.782 134.00

356.1 370.9 402.7 461.9 584.4 907.1 2527.3

PRODUCTOS CONDENSABLES ACUMULATIVOS (L/1000m3 )Presión [Kg/cm2 ]

COMPONENTE 97.37 81.47 65.57 49.67 33.77 17.87 1.03Nitrogeno+ - - - - - - -D. de Carbono+ - - - - - - -Metano+ - - - - - - -Etano+ - - - - - - -Propano+ 356.1 370.9 402.7 461.9 584.4 907.1 2527.3

i-Butano+ 178.7 182.0 193.9 219.8 275.1 434.1 1505.2

n-Butano+ 148.0 149.7 158.6 179.1 222.7 350.3 1243.1

i-Pentano+ 85.7 84.9 88.0 97.8 118.4 182.5 655.2

n-Pentano+ 65.3 64.1 65.8 72.7 86.8 131.7 448.0

Hexanos+ 42.4 41.0 41.4 45.0 52.3 76.5 229.8

Heptanos+ 22.1 21.3 20.9 22.4 25.0 34.4 89.2

Octanos+ 9.1 9.0 8.9 8.7 9.1 11.7 36.2

Nonanos+ 3.8 3.7 3.5 3.4 3.5 4.4 13.3

Decanos+ 1.3 1.2 1.2 1.1 1.1 1.4 4.0

LIBERACION DIFERENCIAL A 91.5 °CCONTENIDO DE PRODUCTOS CONDENSABLES DEL EFLUENTE


página-24-


Coef. de Compresib. 1/[Kg/cm2]

Gas Disuelto [m3/m3]

Factor de Volumen del

Petróleo (Bo)

Factor de Volumen del

Gas (Bg)

Densidad [g/cm3 ]

Viscosidad del Petróleo

[cP]

Viscosidad del Gas

[cP]

Factor de Desviación

del Gas 'Z'

212.89 1.323E-04 1.2664 0.7435 1.005

176.97 1.448E-04 1.2727 0.7398 0.939

Pr 164.10 1.492E-04 1.2751 0.7384 0.919

159.97 1.506E-04 1.2759 0.7379 0.910

141.97 1.567E-04 1.2794 0.7359 0.878

128.97 1.611E-04 1.2821 0.7344 0.850

Pb 113.60 1.663E-04 75.22 1.2853 0.7325 0.823

97.37 66.62 1.2637 0.01189 0.7390 0.874 0.0150 0.884

81.47 58.32 1.2434 0.01438 0.7451 0.933 0.0143 0.895

65.57 49.97 1.2226 0.01810 0.7516 1.013 0.0137 0.907

49.67 41.48 1.2010 0.02426 0.7586 1.123 0.0129 0.921

33.77 32.64 1.1776 0.03627 0.7662 1.252 0.0120 0.936

17.87 22.48 1.1488 0.06974 0.7754 1.440 0.0114 0.952

1.03 0.00 1.0629 1.25859 0.7996 2.088 0.0099 0.993

LIBERACION DIFERENCIAL A 91.5 °CRESUMEN DE LOS VALORES OBTENIDOS

Compañía : XXXXXXXXXXXXX Yacimiento : XXXXXXXXXXXXX Pozo : XXXXXXX

página-25-


Gas liberado (cond reservorio)

[m3/m3 ]Pr 164.10 0.00

Pb 113.60 0.0097.37 0.0881.47 0.1965.57 0.3649.67 0.6433.77 1.2017.87 2.86

LIBERACION DIFERENCIAL A 91.5 °CVOLUMEN DE GAS LIBERADO EN CONDICIONES DE RESERVORIO

(Relativo al volumen a presión de burbuja)

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

0 50 100 150 200 250Presión [Kg/cm2]abs

Gas

libe

rado

(con

d. re

s.) [

m3 /m3 ]

P. de Reservorio


página-26-

Estado Monofásico Estado Bifásico


Factor de Reducción del

Volumen


Factor de Reducción del

Volumen212.89 0.9853 97.37 0.9832176.97 0.9902 81.47 0.9674

Pr 164.10 0.9921 65.57 0.9512159.97 0.9927 49.67 0.9344141.97 0.9954 33.77 0.9162128.97 0.9975 17.87 0.8938

Pb 113.60 1.0000 1.03 0.8270

* Volumen relativo al Volumen a la Presión de Burbuja

LIBERACION DIFERENCIAL A 91.5 °CFACTOR DE REDUCCIÓN DEL VOLUMEN DE PETRÓLEO (Shrinkage factor)*

0.800

0.820

0.840

0.860

0.880

0.900

0.920

0.940

0.960

0.980

1.000

0 50 100 150 200 250


Red

ucci

ón d

el p

etró

leo

P. de Burbuja


página-27-

Rsfb: Gas disuelto del ensayo flashRl: Gas liberado en el ensayo diferencial

Presión Rs=Rsfb - Rl * Bofb / Bodb[Kg/cm2]abs 16 [Kg/cm²]abs 12 [Kg/cm²]abs 8 [Kg/cm²]abs 4 [Kg/cm²]abs

113.60 67.92 67.02 66.25 66.8297.37 59.55 58.65 57.88 58.4581.47 51.47 50.58 49.81 50.3765.57 43.35 42.45 41.68 42.2549.67 35.09 34.20 33.43 34.0033.77 26.49 25.59 24.82 25.3917.87 16.61 15.72 14.95 15.521.03 0.00 0.00 0.00 0.00

AJUSTE DE LA RELACIÓN GAS PETRÓLEO A LAS CONDICIONES DE SEPARADOR

0.0

10.0

20.0

30.0

40.0

50.0

60.0

70.0

80.0

0 50 100 150


RG

P

16 [Kg/cm²]abs 12 [Kg/cm²]abs 8 [Kg/cm²]abs 4 [Kg/cm²]abs


página-28-

Bod: Factor de volumen del ensayo diferencialBofb: Factor de volumen del ensayo flashBodb: Factor de volumen del punto de burbuja del ensayo diferencial

Presión Bo=Bod * Bofb/Bodb[Kg/cm2]abs 16 [Kg/cm²]abs 12 [Kg/cm²]abs 8 [Kg/cm²]abs 4 [Kg/cm²]abs

113.60 1.2505 1.2468 1.2435 1.245997.37 1.2293 1.2256 1.2224 1.224881.47 1.2096 1.2060 1.2028 1.205165.57 1.1894 1.1858 1.1827 1.185049.67 1.1683 1.1648 1.1618 1.164033.77 1.1456 1.1421 1.1392 1.141417.87 1.1175 1.1142 1.1113 1.11341.03 1.0629 1.0629 1.0629 1.0629

AJUSTE DEL FACTOR DE VOLUMEN A LAS CONDICIONES DE SEPARADOR

1.05

1.10

1.15

1.20

1.25

1.30

0 50 100 150


Bo

16 [Kg/cm²]abs 12 [Kg/cm²]abs 8 [Kg/cm²]abs 4 [Kg/cm²]abs


página-29-

Ensayos de separación


página-30-

Presión [Kg/cm2 ]abs

COMPONENTE 16.00 12.00 8.00 4.00Nitrogeno 2.186 2.023 1.850 1.646Dióxido de Carbono 0.097 0.101 0.103 0.101Metano 78.926 76.565 73.178 67.699Etano 10.443 11.351 12.344 13.195Propano 5.877 6.917 8.435 10.747i-Butano 0.605 0.741 0.976 1.469n-Butano 1.173 1.447 1.941 3.073i-Pentano 0.243 0.301 0.414 0.710n-Pentano 0.281 0.347 0.476 0.831Hexanos 0.100 0.122 0.168 0.308Heptanos 0.049 0.060 0.082 0.154Octanos 0.015 0.018 0.025 0.048Nonanos 0.004 0.005 0.007 0.013Decanos 0.001 0.002 0.002 0.004

100.000 100.000 100.000 100.000PROPIEDADES MEDIASG. Esp. (aire=1) 0.711 0.734 0.770 0.838Factor de Desviación ('Z') Calc. 0.952 0.962 0.972 0.984Peso Molecular Medio 20.6 21.3 22.3 24.3P. Molecular de la Fracción C7+ 100.8 100.7 100.7 100.7P. Caloríf. Inf. [Kcal/m3] 9,823 10,144 10,633 11,543 P. Caloríf. Sup. [Kcal/m3] 10,835 11,180 11,705 12,680

ENSAYOS DE SEPARACIÓN FLASH A 25.0 °CANÁLISIS DE LOS GASES DE SEPARADOR

0.01

0.1

1

10

100

3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

Presión [Kg/cm²]abs

Com

posi

ción

N2CO2C1C2C3i-C4n-C4i-C5n-C5C6C7C8C9C10


página-31-

ENSAYOS DE SEPARACIÓN FLASH A 25.0 °CRELACIÓN GAS-PETRÓLEO(De Separador, Tanque y Total)

PRESION DE RELACION GAS-PETRÓLEO [m3/m3]SEPARADOR [Kg/cm2 ] abs

SEPARADOR TANQUE TOTAL

16.00 45.05 22.87 67.9212.00 49.31 17.71 67.028.00 54.53 11.72 66.254.00 62.18 4.64 66.82

0

10

20

30

40

50

60

70

80

3 4 5 6 7 8 9 10 11 12 13 14 15 16 17


RG

P [m

3 /m3 ]

TOTAL

SEPARADOR

TANQUE


página-32-

ENSAYOS DE SEPARACIÓN FLASH A 25.0 °CFACTOR DE VOLUMEN DE PETRÓLEO

PRESION [Kg/cm2 ]abs

FACTOR DE VOLUMEN Bo [m3/m3 ]

1 16.00 1.25052 12.00 1.24683 8.00 1.24354 4.00 1.24595

Bo = (Vol de Petróleo a Pb y T de Reservorio) / (Vol Petróleo de TK STD)

1.20

1.22

1.24

1.26

1.28

1.30

3 4 5 6 7 8 9 10 11 12 13 14 15 16 17


Bo

[ m

3 /m3 ]


página-33-

PRESION [Kg/cm2 ]abs

DENSIDAD [g/cm3]

GRAVEDAD API

1 16.00 0.8426 36.432 12.00 0.8419 36.583 8.00 0.8412 36.714 4.00 0.8417 36.615

ENSAYOS DE SEPARACIÓN FLASH A 25.0 °CDENSIDAD DEL PETRÓLEO DE TANQUE

33.0

34.0

35.0

36.0

37.0

38.0

39.0

40.0

3 4 5 6 7 8 9 10 11 12 13 14 15 16 17


°API


página-34-

Presión de Separador [Kg/cm2 ] abs

16.0 12.0 8.0 4.0

Presión de Separador [psig] 213 156 99 42

Volumen líquido @ Pb & T Reserv 100.00 100.00 100.00 100.00

Volumen de Líquido de Separador (Cond Sep) 85.88 85.02 83.86 81.98

Volumen de Gas de Separador STD 3602 3955 4385 4991

Volumen de Líquido de Tanque STD 79.97 80.21 80.42 80.26

Volumen de Gas de Tanque STD 1829 1421 943 372

G. Esp. del Gas de Separador (Aire=1) 0.711 0.734 0.770 0.838

G. Esp. del Gas de Tanque (Aire=1) 1.221 1.249 1.273 1.258

Densidad del Líquido de Tanque STD 0.8426 0.8419 0.8412 0.8417

NOTAS

Todos los valores se normalizan con respecto a 100 cc de fluido de reservorio en condiciones de Presión de Burbuja y Temperatura de Reservorio.

A partir de la presente tabla, es posible derivar todos los Factores de Volumen y Relaciones Gas-Petróleo de interés.

ENSAYOS DE SEPARACIÓN FLASH A 25.0 °CRESUMEN DE DATOS VOLUMÉTRICOS


página-35-

Caracterización del petróleo


página-36-

VISCOSIDAD DEL PETRÓLEO DE TANQUEEN FUNCIÓN DE LA TEMPERATURA

Temperatura [°C]

Viscosidad [cp]

1 69.8 3.062 89.5 2.21Tr 91.5 2.143 110.5 1.66

120110100-10 0 10 20 30 40 50 60 70 80 901

2

3

4

5

6

7

8

9

10

Temperatura [°C]

Visc

osid

ad [c

p]

CHAPTER 2

PVT ANALYSIS FOR OIL

2.1 INTRODUCTION

In Chapter 1, the importance of PVT analysis was stressed for relating observedvolumes of gas production at the surface to the corresponding underground withdrawal.For gas this relationship could be obtained merely by determining the single or twophase Z−factor, and using it in the equation of state. The basic PVT analysis requiredto relate surface production to underground withdrawal for an oil reservoir isnecessarily more complex due to the presence, below the bubble point pressure, ofboth a liquid oil and free gas phase in the reservoir.

This chapter concentrates on defining the three main parameters required to relatesurface to reservoir volumes, for an oil reservoir, and then proceeds to describe howthese parameters can be determined in the laboratory by controlled experimentsperformed on samples of the crude oil.

The subject is approached from a mechanistic point of view in merely recognising thatPVT parameters can be determined as functions of pressure by routine laboratoryanalysis. No attempt is made to describe the complex thermodynamic processesimplicit in the determination of these parameters. For a more exhaustive treatment ofthe entire subject the reader is referred to the text of Amyx, Bass and Whiting1 .

Finally, a great deal of attention is paid to the conversion of PVT data, as presented bythe laboratory, to the form required in the field. The former being an absolute set ofmeasurements while the latter depend upon the manner of surface separation of thegas and oil.

2.2 DEFINITION OF THE BASIC PVT PARAMETERS

The Pressure−Volume−Temperature relation for a real gas can be uniquely defined bythe simple equation of state

pV = ZnRT (1.15)

in which the Z−factor, which accounts for the departure from ideal gas behaviour, canbe determined as described in Chapter 1, sec. 5. Using this equation, it is a relativelysimple matter to determine the relationship between surface volumes of gas andvolumes in the reservoir as

sc

sc

Tp 1 pE 35.37 (scf / rcf )p T Z ZT

= × × = (1.25)

Unfortunately, no such simple equation of state exists which will describe the PVTproperties of oil. Instead, several, so-called, PVT parameters must be measured bylaboratory analysis of crude oil samples. The parameters can then be used to express

PVT ANALYSIS FOR OIL 44

the relationship between surface and reservoir hydrocarbon volumes, equivalent toequ. (1.25).

The complexity in relating surface volumes of hydrocarbon production to theirequivalent volumes in the reservoir can be appreciated by considering fig. 2.1.

oil

stock tankoil

(a)

solution gas

gas

oil

stock tankoil

(b)

free gas+

solution gas

SURFACE

RESERVOIR

Fig. 2.1 Production of reservoir hydrocarbons (a) above bubble point pressure,(b) below bubble point pressure

Above the bubble point only one phase exists in the reservoir − the liquid oil. If aquantity of this undersaturated oil is produced to the surface, gas will separate from theoil as shown in fig. 2.1(a), the volume of the gas being dependent on the conditions atwhich the surface separation is effected. In this case, it is relatively easy to relate thesurface volumes of oil and gas to volumes at reservoir conditions since it is known thatall the produced gas must have been dissolved in the oil in the reservoir.

If the reservoir is below bubble point pressure, as depicted in fig. 2.1(b), the situation ismore complicated. Now there are two hydrocarbon phases in the reservoir, gassaturated oil and liberated solution gas. During production to the surface, solution gaswill be evolved from the oil phase and the total surface gas production will have twocomponents; the gas which was free in the reservoir and the gas liberated from the oilduring production. These separate components are indistinguishable at the surface andthe problem is, therefore, how to divide the observed surface gas production intoliberated and dissolved gas volumes in the reservoir.

Below bubble point pressure there is an additional complication in that the liberatedsolution gas in the reservoir travels at a different velocity than the liquid oil, when bothare subjected to the same pressure differential. As will be shown in Chapter 4, sec. 2,the flow velocity of a fluid in a porous medium is inversely proportional to the fluidviscosity. Typically, gas viscosity in the reservoir is about fifty times smaller than forliquid oil and consequently, the gas flow velocity is much greater. As a result, it isnormal, when producing from a reservoir in which there is a free gas saturation, thatgas will be produced in disproportionate amounts in comparison to the oil. That is, one


barrel of oil can be produced together with a volume of gas that greatly exceeds thevolume originally dissolved per barrel of oil above bubble point pressure.

Control in relating surface volumes of production to underground withdrawal is gainedby defining the following three PVT parameters which can all be measured bylaboratory experiments performed on samples of the reservoir oil, plus its originallydissolved gas.

Rs − The solution (or dissolved) gas oil ratio, which is the number of standardcubic feet of gas which will dissolve in one stock tank barrel of oil whenboth are taken down to the reservoir at the prevailing reservoir pressureand temperature (units − scf. gas/stb oil).

Bo − The oil formation volume factor, is the volume in barrels occupied in thereservoir, at the prevailing pressure and temperature, by one stock tankbarrel of oil plus its dissolved gas (units – rb (oil + dissolved gas)/stb oil).

Bg − The gas formation volume factor, which is the volume in barrels that onestandard cubic foot of gas will occupy as free gas in the reservoir at theprevailing reservoir pressure and temperature (units − rb free gas/ssf gas).

Both the standard cubic foot (scf) and the stock tank barrel (stb) referred to in theabove definitions are defined at standard conditions, which in this text are taken as60°F and one atmosphere (14.7 psia). It should also be noted that Rs and Bo are bothmeasured relative to one stock tank barrel of oil, which is the basic unit of volume usedin the field. All three parameters are strictly functions of pressure, as shown in fig. 2.5,assuming that the reservoir temperature remains constant during depletion.

Precisely how these parameters can be used in relating measured surface volumes toreservoir volumes is illustrated in figs. 2.2 and 2.3.

pi

p

T

Phase diagram

P

Bo rb ( oil + dissolved gas) / stb

1 stb oil

+

R scf / stbsisolution gas

Fig. 2.2 Application of PVT parameters to relate surface to reservoir hydrocarbonvolumes; above bubble point pressure.


Fig. 2.2 depicts the situation when the reservoir pressure has fallen from its initial valuepi to some lower value p, which is still above the bubble point. As shown in the P−Tdiagram (inset) the only fluid in the reservoir is undersaturated liquid oil. When this oil isproduced to the surface each stock tank barrel will yield, upon gas oil separation, Rsi

standard cubic feet of gas. Since the oil is undersaturated with gas, which implies that itcould dissolve more if the latter were available, then the initial value of the solution gasoil ratio must remain constant at Rsi (scf/stb) until the pressure drops to the bubblepoint, when the oil becomes saturated, as shown in fig. 2.5(b).

Figure 2.2 also shows, in accordance with the definitions of Bo and Rs, that if Rsi scf ofgas are taken down to the reservoir with one stb of oil, then the gas will totally dissolvein the oil at the reservoir pressure and temperature to give a volume of Bo rb of oil plusdissolved gas. Figure 2.5(a) shows that Bo increases slightly as the pressure is reducedfrom initial to the bubble point pressure. This effect is simply due to liquid expansionand, since the compressibility of the undersaturated oil in the reservoir is low, theexpansion is relatively small.

Typical values of Bo and Rs above the bubble point are indicated in fig. 2.5, these arethe plotted results of the laboratory analysis presented in table 2.4. The initial value ofthe oil formation volume factor Boi is 1.2417 which increases to 1.2511 at the bubblepoint. Thus initially, 1.2417 reservoir barrels of oil plus its dissolved gas will produceone stb of oil. This is a rather favourable ratio indicating an oil of moderate volatilityand, as would be expected in this case, the initial solution gas oil ratio is also relativelylow at 510 scf/stb. Under less favourable circumstances, for more volatile oils, Boi canhave much higher values. For instance, in the Statfjord field in the North Sea, Boi is2.7 rb/stb while the value of Rsi is approximately 3000 scf/stb. Obviously the mostfavourable value of Boi is as close to unity as possible indicating that the oil containshardly any dissolved gas and reservoir volumes are approximately equal to surfacevolumes. The small oil fields of Beykan and Kayaköy in the east of Turkey provide goodexamples of this latter condition having values of Boi and Rsi of 1.05 and 20 scf/stbrespectively.

Below the bubble point the situation is more complicated as shown in fig. 2.3.


pi

p

T

p

rb ( oil + dissolved gas) / stb

1 stb oil

Bo

(R - R ) Bs g rb (free gas) / stb

R = R +s (R - R ) scf / stbs

Fig. 2.3 Application of PVT parameters to relate surface to reservoir hydrocarbonvolumes; below bubble point pressure

In this case each stock tank barrel of oil is produced in conjunction with R scf of gas,where R (scf/stb) is called the instantaneous or producing gas oil ratio and is measureddaily. As already noted, some of this gas is dissolved in the oil in the reservoir and isreleased during production through the separator, while the remainder consists of gaswhich is already free in the reservoir. Furthermore, the value of R can greatly exceedRsi, the original solution gas oil ratio, since, due to the high velocity of gas flow incomparison to oil, it is quite normal to produce a disproportionate amount of gas. Thisresults from an effective stealing of liberated gas from all over the reservoir and itsproduction through the relatively isolated offtake points, the wells. A typical plot of R asa function of reservoir pressure is shown as fig. 2.4.

Rscf / stb

R = Rsi

510 scf / stb

pb Reservoir pressure

4000 scf / sfb

Fig. 2.4 Producing gas oil ratio as a function of the average reservoir pressurefor a typical solution gas drive reservoir


The producing gas oil ratio can be split into two components as shown in fig. 2.3, i.e.

R = Rs +(R−Rs)

The first of these, Rs scf/stb, when taken down to the reservoir with the one stb of oil,will dissolve in the oil at the prevailing reservoir pressure to give Bo rb of oil plusdissolved gas. The remainder, (R − Rs) scf/stb, when taken down to the reservoir willoccupy a volume

s g s gscf rb(R R ) B (R R ) B (rb. free gas / stb)stb scf

− × = − −

(2.1)

and therefore, the total underground withdrawal of hydrocarbons associated with theproduction of one stb of oil is

(Underground withdrawal)/stb = Bo + (R − Rs) Bg (rb/stb) (2.2)

The above relationship shows why the gas formation volume factor has the ratherunfortunate units of rb/scf. It is simply to convert gas oil ratios, measured in scf/stb,directly to rb/stb to be compatible with the units of Bo. While Bg is used almostexclusively in oil reservoir engineering its equivalent in gas reservoir engineering is E,the gas expansion factor, which was introduced in the previous chapter and has theunits scf/rcf. The relation between Bg and E is therefore,

grb 1Bscf 5.615E

=

(2.3)

thus Bg has always very small values; for a typical value of E of, say, 150 scf/rcf thevalue of Bg would be .00119 rb/scf.


B(rb / stb)

o

1.3

1.2

1.1

1.01000 2000 3000 4000

PRESSURE (psia)

p = 3330 psiab

a

b

c

600

400

200

R(scf / stb)

s

1000 2000 3000 4000

1000 2000 3000 4000

B(rb / scf)

g

.010

.008

.006

.004

.002

E(scf / rcf)

- 200

- 100

- 0

PRESSURE (psia)

PRESSURE (psia)

Fig. 2.5 PVT parameters (Bo, Rs and Bg), as functions of pressure, for the analysispresented in table 2.4; (pb = 3330 psia).


The shapes of the Bo and Rs curves below the bubble point, shown in fig. 2.5(a) and(b), are easily explained. As the pressure declines below pb, more and more gas isliberated from the saturated oil and thus Rs, which represents the amount of gasdissolved in a stb at the current reservoir pressure, continually decreases. Similarly,since each reservoir volume of oil contains a smaller amount of dissolved gas as thepressure declines, one stb of oil will be obtained from progressively smaller volumes ofreservoir oil and Bo steadily declines with the pressure.

EXERCISE 2.1 UNDERGROUND WITHDRAWAL

The oil and gas rates, measured at a particular time during the producing life of areservoir are, x stb oil/day and y scf gas/day.

1) What is the corresponding underground withdrawal rate in reservoir barrels/day.

2) If the average reservoir pressure at the time the above measurements are madeis 2400 psia, calculate the daily underground withdrawal corresponding to an oilproduction of 2500 stb/day and a gas rate of 2.125 MMscf/day. Use the PVTrelationships shown in figs. 2.5(a) − (c), which are also listed in table 2.4.

3) If the density of the oil at standard conditions is 52.8 lb/cu.ft and the gas gravity is0.67 (air = 1) calculate the oil pressure gradient in the reservoir at 2400 psia.

EXERCISE 2.1 SOLUTION

1) The instantaneous or producing gas oil ratio is R = y/x scf/stb. If, at the time thesurface rates are measured, the average reservoir pressure is known, then Bo, Rs

and Bg can be determined from the PVT relationships at that particular pressure.

The daily volume of oil plus dissolved gas produced from the reservoir is then

xBo rb, and the liberated gas volume removed daily is syx( R )x

− Bg rb. Thus the

total underground withdrawal is

o s gyx (B ( R )B ) rb / dayx

+ − (2.4)

2) At a reservoir pressure of 2400 psia, the PVT parameters obtained from table 2.4are:

Bo = 1.1822 rb/stb; Rs = 352 scf/stb and Bg = .0012 rb/ scf

Therefore, evaluating equ. (2.4) for x = 2500 stb/d and y = 2.125 MMscf/d gives atotal underground withdrawal rate of

2500 (1.1822 + (850 − 352) × .0012) = 4450 rb/d

3) The liquid oil gradient in the reservoir can be calculated by applying massconservation, as demonstrated in exercise 1.1 for the calculation of the gasgradient. In the present case the mass balance is


Mass of 1 stb of oil Mass of Bo rb of oil+ = +

Rs scf dissolved gasat standard conditions

dissolved gas in thereservoir

or

sc sc

r

o s g

o o

lb lb1(stb) 5.615 R (scf)cu.ft cu.ft

lbB (rb) 5.615cu.ft

ρ ρ

ρ

× × + ×

= × ×

in which the subscripts sc and r refer to standard conditions and reservoirconditions, respectively.

The gas density at standard conditions is

ρsc = γg × 0.0763 (refer equ. (1.30))

= 0.0511 lb/cu ft

Therefore,

sc sc

r

o s go

o

( 5.615) (R )B 5.615

(52.8 5.615) (352 0.0511) 47.37 lb / cu ft1.1822 5.615

ρ ρρ

× + ×=

×× + ×= =

×

and the liquid oil gradient is 47.37/144 = 0.329 psi/ft.

2.3 COLLECTION OF FLUID SAMPLES

Samples of the reservoir fluid are usually collected at an early stage in the reservoir'sproducing life and dispatched to a laboratory for the full PVT analysis. There arebasically two ways of collecting such samples, either by direct subsurface sampling orby surface recombination of the oil and gas phases. Whichever technique is used thesame basic problem exists, and that is, to ensure that the proportion of gas to oil in thecomposite sample is the same as that existing in the reservoir. Thus, sampling areservoir under initial conditions, each stock tank barrel of oil in the sample should becombined with Rsi standard cubic feet of gas.

a) Subsurface sampling

This is the more direct method of sampling and is illustrated schematically in fig. 2.6.


sample chamber

pwf

pipb

pressure

r

Fig. 2.6 Subsurface collection of PVT sample

A special sampling bomb is run in the hole, on wireline, to the reservoir depth and thesample collected from the subsurface well stream at the prevailing bottom holepressure. Either electrically or mechanically operated valves can be closed to trap avolume of the borehole fluids in the sampling chamber. This method will obviously yielda representative combined fluid sample providing that the oil is undersaturated with gasto such a degree that the bottom hole flowing pressure pwf at which the sample iscollected, is above the bubble point pressure. In this case a single phase fluid, oil plusits dissolved gas, is flowing in the wellbore and therefore, a sample of the fluid is boundto have the oil and gas combined in the correct proportion. Many reservoirs, however,are initially at bubble point pressure and under these circumstances, irrespective ofhow low the producing rate is maintained during sampling, the bottom hole flowingpressure pwf will be less than the bubble point pressure pb as depicted in fig. 2.6. In thiscase, there will be saturated oil and a free gas phase flowing in the immediate vicinityof the wellbore, and in the wellbore itself, and consequently, there is no guarantee thatthe oil and gas will be collected in the correct volume proportion in the chamber.

In sampling a gas saturated reservoir, two situations can arise depending on the time atwhich the sample is collected. If the sample is taken very early in the producing life it ispossible that the fluid flowing into the wellbore is deficient in gas. This is because theinitially liberated gas must build up a certain minimum gas saturation in the reservoirpores before it will start flowing under an imposed pressure differential. This, so−called,critical saturation is a phenomenon common to any fluid deposited in the reservoir, notjust gas. The effect on the producing gas oil ratio, immediately below bubble pointpressure, is shown in fig. 2.4 as the small dip in the value of R for a short period afterthe pressure has dropped below bubble point. As a result of this mechanism there willbe a period during which the liberated gas remains in the reservoir and the gas oil ratiomeasured from a subsurface sample will be too low. Conversely, once the liberated gassaturation exceeds the critical value, then as shown in fig. 2.4 and discussedpreviously, the producing well will effectively steal gas from more remote parts of thereservoir and the sample is likely to have a disproportionately high gas oil ratio.


The problems associated with sampling an initially saturated oil reservoir, or anundersaturated reservoir in which the bottom hole flowing pressure has been allowed tofall below bubble point pressure, can be largely overcome by correct well conditioningprior to sampling. If the well has already been flowing, it should be produced at a lowstabilized rate for several hours to increase the bottom hole flowing pressure andthereby re-dissolve some, if not all, of the free gas saturation in the vicinity of the well.Following this the well is closed in for a reasonable period of time during which the oilflowing into the wellbore, under an ever increasing average pressure, will hopefully re-dissolve any of the remaining free gas. If the reservoir was initially at bubble pointpressure, or suspected of being so, the subsurface sample should then be collectedwith the well still closed in. If the reservoir is known to be initially undersaturated thesample can be collected with the well flowing at a very low rate so that the bottom holeflowing pressure is still above the bubble point. With proper well conditioning arepresentative combined sample can usually be obtained.

One of the main drawbacks in the method is that only a small sample of the wellborefluids is obtained, the typical sampler having a volume of only a few litres. Therefore,one of the only ways of checking whether the gas oil ratio is correct is to take severaldownhole samples and compare their saturation pressures at ambient temperature onthe well site. This can be done using a mercury injection pump and accurate pressuregauge connected to the sampler. The chamber normally contains both oil and a freegas phase, due to the reduction in temperature between wellbore and surface. Injectingmercury increases the pressure within the chamber until at a saturation pressurecorresponding to the ambient surface temperature all the gas will dissolve. Thissaturation pressure can be quite easily detected since there is a distinct change incompressibility between the two phase and single phase fluids. If it is experimentallydetermined, on the well site, that successive samples have markedly differentsaturation pressures, then either the tool has been malfunctioning or the well has notbeen conditioned properly.

In addition, it is necessary to determine the static reservoir pressure and temperatureby well testing, prior to collecting the samples. Further details on bottom hole samplingtechniques are given in references 2 and 3 listed at the end of this chapter.

b) Surface recombination sampling

In collecting fluid samples at the surface, separate volumes of oil and gas are taken atseparator conditions and recombined to give a composite fluid sample. The surfaceequipment is shown schematically in fig. 2.7.


gas meter

gassample

oilsample

p

T

st

st

stock tank oil

p

T

sep

sep

well

separator

Fig. 2.7 Collection of a PVT sample by surface recombination

The well is produced at a steady rate for a period of several hours and the gas oil ratiois measured in scf of separator gas per stock tank barrel of oil. If this ratio is steadyduring the period of measurement then one can feel confident that recombining the oiland gas in the same ratio will yield a representative composite sample of the reservoirfluid. In fact, a slight adjustment must be made to determine the actual ratio in whichthe samples should be recombined. This is because, as shown in fig. 2.7, the oilsample is collected at separator pressure and temperature whereas the gas oil ratio ismeasured relative to the stock tank barrel, thus the required recombination ratio is

REQUIRED MEASURED SHRINKAGE

sepscf scf stbR R S

sep.bbl stb sep.bbl = ×

Dimensionally, the measured gas oil ratio must be multiplied by the shrinkage factorfrom separator to stock tank conditions. This factor is usually determined in thelaboratory as the first stage of a PVT analysis of a surface recombination sample byplacing a small volume of the oil sample in a cell at the appropriate separatorconditions and discharging it (flash expansion) to a second cell maintained at the fieldstock tank conditions. During this process some gas will be liberated from the separatorsample, due to the reduction in pressure and temperature, and the diminished stocktank oil volume is measured, thus allowing the direct calculation of S. In order to beable to perform such an experiment it is important that the engineer should accuratelymeasure the pressure and temperature prevailing at both separator and stock tankduring sampling and provide the laboratory with these data.

One of the attractive features of surface recombination sampling is that statistically itgives a reliable value of the producing gas oil ratio measured over a period of hours;furthermore, it enables the collection of large fluid samples. Of course, just as forsubsurface sampling, the surface recombination method will only provide the correct


gas oil ratio if the pressure in the vicinity of the well is at or above bubble pointpressure. If not, the surface gas oil ratio will be too low or too high, depending uponwhether the free gas saturation in the reservoir is below or above the critical saturationat which gas will start to flow. In this respect it should be emphasized that PVT samplesshould be taken as early as possible in the producing life of the field to facilitate thecollection of samples in which the oil and gas are combined in the correct ratio.

2.4 DETERMINATION OF THE BASIC PVT PARAMETERS IN THE LABORATORY ANDCONVERSION FOR FIELD OPERATING CONDITIONS

Quite apart from the determination of the three primary PVT parameters Bo, Rs and Bg,the full laboratory analysis usually consists of the measurement or calculation of fluiddensities, viscosities, composition, etc. These additional measurements will be brieflydiscussed in section 2.6. For the moment, the essential experiments required todetermine the three basic parameters will be detailed, together with the way in whichthe results of a PVT analysis must be modified to match the field operating conditions.

The analysis consists of three parts:

− flash expansion of the fluid sample to determine the bubble point pressure;

− differential expansion of the fluid sample to determine the basic parameters Bo,Rs and Bg;

− flash expansion of fluid samples through various separator combinations toenable the modification of laboratory derived PVT data to match field separatorconditions.

The apparatus used to perform the above experiments is the PV cell, as shown infig. 2.8. After recombining the oil and gas in the correct proportions, the fluid is chargedto the PV cell which is maintained at constant temperature, the measured reservoirtemperature, throughout the experiments. The cell pressure is controlled by a positivedisplacement mercury pump and recorded on an accurate pressure gauge. Theplunger movement is calibrated in terms of volume of mercury injected or withdrawnfrom the PV cell so that volume changes in the cell can be measured directly.

The flash and differential expansion experiments are presented schematically infigs. 2.9(a) and 2.9(b). In the flash experiment the pressure in the PV cell is initiallyraised to a value far in excess of the bubble point. The pressure is subsequentlyreduced in stages, and on each occasion the total volume vt of the cell contents isrecorded. As soon as the bubble point pressure is reached, gas is liberated from the oiland the overall compressibility of the system increases significantly. Thereafter, smallchanges in pressure will result in large changes in the total fluid volume contained inthe PV cell. In this manner, the flash expansion experiment can be used to "feel" thebubble point. Since the cell used is usually opaque the separate volumes of oil andgas, below bubble point pressure, cannot be measured in the experiment andtherefore, only total fluid volumes are recorded. In the laboratory analysis the basic unitof volume, against which all others are compared, is the volume of saturated oil at the


bubble point, irrespective of its magnitude. In this chapter it will be assumed, forconsistency, that this unit volume is one reservoir barrel of bubble point oil (1−rbb).

PVcell

thermaljacket

Heise pressuregauge

mercuryreservoir

mercury pump

Fig. 2.8 Schematic of PV cell and associated equipment

pi

oilvt = vo

Hg

pb

oilvt = 1

Hg

p < pb

oilvt

Hg

gas

(a)

pb

oil

Hg

oil

Hg

gas

vo

vg

p < pb

vo

Hg

oil

(b)

gas

vo = 1

Fig. 2.9 Illustrating the difference between (a) flash expansion, and (b) differentialliberation


Table 2.1 lists the results of a flash expansion for an oil sample obtained by thesubsurface sampling of a reservoir with an initial pressure of 4000 psia andtemperature of 200°F; the experiment was conducted at this same fixed temperature.

Pressure

psia

Relative TotalVolume

vt = v/vb = (rb/rbb)

5000 0.98104500 0.98504000 (pi) 0.99253500 0.99753330 (pb ) 1.00003290 1.00253000 1.02702700 1.06032400 1.10602100 1.1680

TABLE 2.1Results of isothermal flash expansion at 200°F

The bubble point pressure for this sample is determined from the flash expansion as3330 psia, for which the saturated oil is assigned the unit volume. The relative total fluidvolumes listed are volumes measured in relation to this bubble point volume. The flashexpansion can be continued to much lower pressures although this is not usually donesince the basic PVT parameters are normally obtained from the differential liberationexperiment. Furthermore, the maximum volume to which the cell can expand is often alimiting factor in continuing the experiment to low pressures.

The essential data obtained from the differential liberation experiment, performed onthe same oil sample, are listed in table 2.2. The experiment starts at bubble pointpressure since above this pressure the flash and differential experiments are identical.


Pressure

psia

Relative GasVol. (at p and T)

vg

RelativeGas Vol. (sc)

Vg

CumulativeRelative

Gas Vol. (sc)F

Gas expansionFactor

E

Z−factor

Z

Relative OilVol. (at p and T)

vo

3330 (pb ) 1.0000

3000 .0460 8.5211 8.5211 185.24 .868 .9769

2700 .0417 6.9731 15.4942 167.22 .865 .9609

2400 .0466 6.9457 22.4399 149.05 .863 .9449

2100 .0535 6.9457 29.3856 129.83 .867 .9298

1800 .0597 6.5859 35.9715 110.32 .874 .9152

1500 .0687 6.2333 42.2048 90.73 .886 .9022

1200 .0923 6.5895 48.7943 71.39 .901 .8884

900 .1220 6.4114 55.2057 52.55 .918 .8744

600 .1818 6.2369 61.4426 34.31 .937 .8603

300 .3728 6.2297 67.6723 16.71 .962 .8459

14.7 (200°F) 74.9557 .8296

14.7 ( 60°F) 74.9557 .7794

All volumes are measured relative to the unit volume of oil at the bubble point pressure of 3330 psi

TABLE 2.2Results of isothermal differential liberation at 200º F


In contrast to the flash expansion, after each stage of the differential liberation, the totalamount of gas liberated during the latest pressure drop is removed from the PV cell byinjecting mercury at constant pressure, fig. 2.3. Thus, after the pressure drop from2700 to 2400 psia, table 2.2, column 2, indicates that 0.0466 volumes of gas arewithdrawn from the cell at the lower pressure and at 200°F. These gas volumes vg aremeasured relative to the unit volume of bubble point oil, as are all the relative volumeslisted in table 2.2. After each stage the incremental volume of liberated gas isexpanded to standard conditions and re−measured as Vg relative volumes. Column 4 issimply the cumulative amount of gas liberated below the bubble point expressed atstandard conditions, in relative volumes, and is denoted by F = Σ Vg. Dividing values incolumn 3 by those in column 2 (Vg/vg) gives the gas expansion factor E defined inChapter 1, sec. 6. Thus the .0466 relative volumes liberated at 2400 psia will expand togive 6.9457 relative volumes at standard conditions and the gas expansion factor istherefore 6.9457/.0466 = 149.05. Knowing E, the Z−factor of the liberated gas can bedetermined by explicitly solving equ . (1.25) for Z as

sc

sc

Tp 1 pZ 35.37p T E ET

= × × =

and for the gas sample withdrawn at 2400 psia

2400Z 35.37 0.863149.05 660

= × =×

These values are listed in column 6 of table 2.2.

Finally, the relative oil volumes, vo, are measured at each stage of depletion afterremoval of the liberated gas, as listed in column 7.

Before considering how the laboratory derived data presented in table 2.2 areconverted to the required field parameters, Bo, Rs and Bg, it is first necessary tocompare the physical difference between the flash and differential liberationexperiments and decide which, if either, is suitable for describing the separation of oiland gas in the reservoir and the production of these volumes through the surfaceseparators to the stock tank.

The main difference between the two types of experiment shown in fig. 2.9(a) and (b) isthat in the flash expansion no gas is removed from the PV cell but instead remains inequilibrium with the oil. As a result, the overall hydrocarbon composition in the cellremains unchanged. In the differential liberation experiment, however, at each stage ofdepletion the liberated gas is physically removed from contact with the oil andtherefore, there is a continual compositional change in the PV cell, the remaininghydrocarbons becoming progressively richer in the heavier components, and theaverage molecular weight thus increasing.

If both experiments are performed isothermally, in stages, through the same totalpressure drop, then the resulting volumes of liquid oil remaining at the lowest pressurewill, in general, be slightly different. For low volatility oils, in which the dissolved gas


consists mainly of methane and ethane, the resulting oil volumes from eitherexperiment are practically the same. For higher volatility oils, containing a relativelyhigh proportion of the intermediate hydrocarbons such as butane and pentane, thevolumes can be significantly different. Generally, in this latter case, more gas escapesfrom solution in the flash expansion than in the differential liberation, resulting in asmaller final oil volume after the flash process. This may be explained by the fact thatin the flash expansion the intermediate hydrocarbon molecules find it somewhat easierto escape into the large gas volume in contact with the oil than in the case of thedifferential liberation, in which the volume of liberated gas in equilibrium with the oil, atany stage in the depletion, is significantly smaller.

The above description is a considerable simplification of the complex processesinvolved in the separation of oil and gas; also, it is not always true that the flashseparation yields smaller oil volumes. What must be appreciated, however, is that theflash and differential processes will yield different oil volumes and this difference canbe physically measured by experiment. The problem is, of course, which type ofexperiment will provide the most realistic values of Bo, Rs and Bg, required for relatingmeasured surface volumes to volumes withdrawn from the reservoir at the currentreservoir pressure and fixed temperature.

The answer is that a combination of both flash and differential liberation is required foran adequate description of the overall volume changes. It is considered that thedifferential liberation experiment provides the better description of how the oil and gasseparate in the reservoir since, because of their different flow velocities, they will notremain together in equilibrium once gas is liberated from the oil, thus corresponding tothe process shown in fig. 2.9(b). The one exception to this is during the brief periodafter the bubble point has been reached, when the liberated gas is fairly uniformlydistributed throughout the reservoir and remains immobile until the critical gassaturation is exceeded.

The nature of the volume change occurring between the reservoir and stock tank ismore difficult to categorise but generally, the overall effect is usually likened to a non-isothermal flash expansion. One aspect in this expansion during production is worthconsidering in more detail and that is, what occurs during the passage of the reservoirfluids through the surface separator or separators.

Within any single separator the liberation of gas from the oil may be considered as aflash expansion in which, for a time, the gas stays in equilibrium with the oil. If two ormore separators are used then the gas is physically removed from the oil leaving thefirst separator and the oil is again flashed in the second separator. This physicalisolation of the fluids after each stage of separation corresponds to differentialliberation. In fact, the overall effect of multi-stage separation corresponds to theprocess shown in fig. 2.9(b), which is differential liberation, only in this case it is notconducted at constant temperature. It is for this reason that multi-stage separation iscommonly used in the field because, as already mentioned, differential liberation willnormally yield a larger final volume of equilibrium oil than the corresponding flashexpansion.


The conclusion reached, from the foregoing description of the effects of surfaceseparation, is somewhat disturbing since it implies that the volume of equilibrium oilcollected in the stock tank is dependent on the manner in which the oil and gas areseparated. This in turn means that the basic PVT parameters Bo and Rs which aremeasured in terms of volume "per stock tank barrel" must also be dependent on themanner of surface separation and cannot be assigned absolute values.

The only way to account for the effects of surface separation is to perform a series ofseparator tests on oil samples as part of the basic PVT analysis, and combine theresults of these tests with differential liberation data. Samples of oil are put in the PVcell, fig. 2.8, and raised to reservoir temperature and bubble point pressure. The cell isconnected to a single or multi-stage model separator system, with each separator at afixed pressure and temperature. The bubble point oil is then flashed through theseparator system to stock tank conditions and the resulting volumes of oil and gas aremeasured. The results of such a series of tests, using a single separator at a series ofdifferent pressures and at a fixed temperature, are listed in table 2.3 for the same oil asdescribed previously (tables 2.1 and 2.2).

Separator Stock tank Shrinkage factor GORp T p T fsiR

(psia) (° F) (psia) (° F) fbc (stb/rbb) (scf/stb)

200 80 14.7 60 .7983 512150 80 14.7 60 .7993 510100 80 14.7 60 .7932 51550 80 14.7 60 .7834 526

TABLE 2.3Separator flash expansion experiments performed on the oil sample

whose properties are listed in tables 2.1 and 2.2

The shrinkage factor fbc , listed in table 2.3, is the volume of oil collected in the stock

tank, relative to unit volume of oil at the bubble point (stb/rbb), which is the reason forthe subscript b (bubble point). The subscript f refers to the fact that these experimentsare conducted under flash conditions. All such separator tests, irrespective of thenumber of separator stages, are described as flash although, as already mentioned,multi-stage separation is closer to a differential liberation. In any case, precisely whatthe overall separation process is called does not really matter since the resultingvolumes of oil and gas are experimentally determined, irrespective of the title.

fsiR is

the initial solution gas oil ratio corresponding to the separators used and is measuredin the experiments in scf/stb.

Using the experimental separator flash data, for a given set of separator conditions, inconjunction with the differential liberation data in table 2.2, will provide a means ofobtaining the PVT parameters required for field use. It is considered that the differentialliberation data can be used to describe the separation in the reservoir while theseparator flash data account for the volume changes between reservoir and stock tank.


What is required for field use is Bo expressed in rb/stb. In the differential liberation datathe corresponding parameter is vo (rb/rbb), that is, reservoir barrels of oil per unit barrelat the bubble point. But from the flash data it is known that one reservoir barrel of oil, atthe bubble point, when flashed through the separators yields

fbc stb. Therefore, the

conversion from the differential data to give the required field parameter Bo is

f

o bo

b b

v rb rbrbBstb c stb rb

=

Similarly, the solution gas oil ratio required in the field is Rs (scf/stb). The parameter inthe differential liberation data from which this can be obtained is F (cumulative gas volat sc/oil vol at pb = stb/rbb). In fact, F, the cumulative gas liberated from the oil, must beproportional to

fsi sR R− (scf/stb), which is the initial solution gas oil ratio, as determined

in the flash experiment, minus the current solution gas oil ratio at some lower pressure.The exact relationship is

ff

bsi s

b b

rbscf stb scf 1(R R ) F 5.615stb rb stb c stb

− = × ×

Finally, the determination of the third parameter Bg can be obtained directly from thedifferential parameter E as

grb 1 rcf 1 rbBscf E scf 5.615 rcf = ×

Thus the laboratory differential data can be transformed to give the required field PVTparameters using the following conversions

LaboratoryDifferentialParameter

RequiredField

ParameterConversion

vo (rb/ rbb) Bof

oo

b

v rbBc stb

=

(2.5)

F (stb/rbb) Rs fs sib f

5.615 F rbR Rc stb

= −

(2.6)

E (scf/rcf) Bg g1 rbB

5.612 E scf =

(2.7)

EXERCISE 2.2 CONVERSION OF DIFFERENTIAL LIBERATION DATA TO GIVETHE FIELD PVT PARAMETERS Bo, Rs AND Bg

Convert the laboratory differential liberation data presented in table 2.2 to the requiredPVT parameters, for field use, for the optimum separator conditions listed in table 2.3.


EXERCISE 2.2 SOLUTION

The optimum separator pressure in table 2.3 is 150 psia since this gives the largestvalue of the flash shrinkage factor

fbc as 0.7993 (stb/rbb) and correspondingly, the

lowest flash solution gas oil ratio fsiR of 510 scf/stb. Using these two figures the

laboratory differential data in table 2.2 can be converted to give the field parameters Bo,Rs and Bg using equs. (2.5) − (2.7), as follows

Pressure

(psia)f

oo

b

vBc

=

(rb/stb)

ff

s sib

5.615 FR Rc= −

(scf/stb)

g1B

5.615 E=

(rb/scf)

4000 (pi) 1.2417 foi(B ) 510

fsi(R )

3500 1.2480 510

3330 (pb) 1.2511 f

f

obb

1(B )c

= 510 .00087

3000 1.2222 450 .00096

2700 1.2022 401 .00107

2400 1.1822 352 .00119

2100 1.1633 304 .00137

1800 1.1450 257 .00161

1500 1.1287 214 .00196

1200 1.1115 167 .00249

900 1.0940 122 .00339

600 1.0763 78 .00519

300 1.0583 35 .01066TABLE 2.4

Field PVT parameters adjusted for single stage, surface separationat 150 psia and 80°F;

fbc = .7993 (Data for pressures above 3330 psi

are taken from the flash experiment, table 2.1)

The data in table 2.4 are plotted in fig. 2.5(a) − (c).

In summary of this section, it can be stated that the laboratory differential liberationexperiment, which is regarded as best simulating phase separation in the reservoir,provides an absolute set of PVT data in which all volumes are expressed relative to theunit oil volume at the bubble point, the latter being a unique volume. The PVTparameters conventionally used in the field, however, are dependent on the nature ofthe surface separation. The basic differential data can be modified in accordance withthe surface separators employed using equs. (2.5) − (2.7) in which

fbc and fbR are

determined by flashing unit volume of reservoir oil through the separator system. Themodified PVT parameters thus obtained approximate the process of differential


liberation in the reservoir and flash expansion to stock tank conditions. Therefore if,during the producing life of the reservoir, the separator conditions are changed, thenthe fixed differential liberation data will have to be converted to give new tables of Boand Rs using values of

fbc and fsiR appropriate for the altered separator conditions.

This combination of differential liberation in the reservoir and flash expansion to thesurface is generally regarded as a reasonable approximation to Dodson's PVT analysistechnique4. In this form of experiment a differential liberation is performed but aftereach pressure stage the volume of the oil remaining in the PV cell is flashed to stocktank conditions through a chosen separator combination. The ratio of stock tank oilvolume to original oil volume in the PV cell prior to flashing gives a direct measure ofBo, while the gas evolved in the flash can be used directly to obtain Rs. The process isrepeated taking a new oil sample for each pressure step, since the remaining oil in thePV cell is always flashed to surface conditions. This type of analysis, while moreaccurately representing the complex reservoir-production phase separation, is moretime consuming and therefore more costly, furthermore, it requires the availability oflarge samples of the reservoir fluid. For low and moderately volatile crudes, the mannerof deriving the PVT parameters described in this section usually provides a very goodapproximation to the results obtained from the Dodson analysis. For more volatilecrudes, however, the more elaborate experimental technique may be justified.

2.5 ALTERNATIVE MANNER OF EXPRESSING PVT LABORATORY ANALYSISRESULTS

The results of the differential liberation experiment, as listed in table 2.2, provide anabsolute set of data which can be modified, according to the surface separators used,to give the values of the PVT parameters required for field use. In table 2.2 all volumesare measured relative to the unit oil volume at the bubble point. There is, however, amore common way of representing the results of the differential liberation in whichvolumes are measured relative to the volume of residual oil at stock tank conditions.This volume is obtained as the final step in the differential liberation experiment byflashing the volume of oil measured at atmospheric pressure and reservoirtemperature, to atmospheric pressure and 60°F. This final step is shown in table 2.2 inwhich 0.8296 relative oil volumes at 14.7 psia and 200°F yield 0.7794 relative oilvolumes at 14.7 psia and 60°F. This value of 0.7794 is the shrinkage factor for a unitvolume of bubble point oil during differential liberation to stock tank conditions and isdenoted by

dbc . The value of dbc ,is not dependent on any separator conditions and

therefore, relating all volumes in the differential liberation to this value of dbc , which is

normally referred to as the "residual oil volume", will provide an alternative means ofexpressing the differential liberation results.

It should be noted, however, that the magnitude of dbc is dependent on the number of

pressure steps taken in the differential experiment. Therefore, the differential liberationresults, in which all volumes are measured relative to

dbc do not provide an absolute

set of data such as that obtained by relating all volumes to the unit volume of oil at thebubble point.


In the presentation of differential data, in which volumes are measured relative to dbc ,

the values of vo and F in table 2.2 are replace by doB and

dsR where

doB = Differential oil formation volume factor

(rb/stb-residual oil)

anddsR = Differential solution gas oil ratio

(scf/stb-residual oil)

Alternatively, by replacing fbc in equs. (2.5) and (2.6) by

dbc , these parameters can be

expressed as

dd

o bo

b b

v rb rbBc stb residual rb

= −

(2.8)

andd d

d

s sib

5.615 F scfR Rc stb residual

= − − (2.9)

where dsiR is the initial dissolved gas relative to the residual barrel of oil at 60°F, and is

proportional to the total gas liberated in the differential experiment, thus

dd

sib

(Maximum valueof F) scfR 5.615c stb residual

= × − (2.10)

and for the differential data presented in table 2.2

dsi74.9557 5.615R 540 scf stb residual oil

.7794×= = −

The majority of commercial laboratories serving the industry would normally presentthe essential data in the differential liberation experiment (table 2.2) as shown intable 2.5.

There is a danger in presenting the results of the differential liberation experiment inthis way since a great many engineers are tempted to use the

doB and dsR values

directly in reservoir calculations, without making the necessary corrections to allow forthe surface separator conditions. In many cases, the error in directly using the data intable 2.5 is negligible, however, for moderate and high volatility oils the error can bequite significant and therefore, the reader should always make the necessarycorrection to the data in table 2.5 to allow for the field separator conditions, as a matterof course.


Pressure(psia)

Formation Vol. Factord do o bB v / c=

Solution GORd d ds si bR R 5.615 F / c= −

4000 1.2734 5403500 1.2798 540

3300 1.2830 dob(B ) 540

dsi(R )

3000 1.2534 4792700 1.2329 4282400 1.2123 3782100 1.1930 3281800 1.1742 2811500 1.1576 2361200 1.1399 118900 1.1219 142600 1.1038 97300 1.0853 5214.7 (200°F) 1.0644 014.7 ( 60°F) 1.0000 0

TABLE 2.5Differential PVT parameters as conventionally presented by laboratories, in which

Bo and Rs are measured relative to the residual oil volume at 60°F

The conversion can be made by expressing and Rsd, in table 2.5, in their equivalent,absolute forms of vo and F, in table 2.2, using equs. (2.8) and (2.9) and thereafter,using equs. (2.5) and (2.6) to allow for the surface separators. This will result in therequired expressions for Bo and Rs. Alternatively, the required field parameters can becalculated directly as

d f

df d f f

b obo oo o

b b b ob

c Bv vB Bc c c B

= = =

(2.11)

where

do bv / c =doB the differential oil formation volume factor measured relative to the

residual oil volume as listed in table 2.5 (rb/stb-residual);

fobB =fb1/ c is the oil formation volume factor of the bubble point oil (rbb/stb)

determined by flashing the oil through the appropriate surface separatorsand is measured relative to the stock tank oil volume (refer tables 2.3 and2.4); and

dobB =db1/ c is the oil formation volume factor of the bubble point oil determined

during the differential liberation experiment and is measured relative tothe residual oil volume (refer table 2.5) (rbb/stb-residual).

Similarly, the required solution gas oil ratio for use under field operating conditions is,equ. (2.6)


d

f ff d f

bs si si

b b b

c5.615 F 5.615 FR R Rc c c=

− = −

which, using equ. (2.9), can be expressed as

f

f d df

obs si si s

ob

BR R (R R )

B

= − −

(2.12)

where

fsiR = solution gas oil ratio of the bubble point oil, determined by flashing the oil

through the appropriate surface separators, and is measured relative to the oil volumeat 60°F and 14.7 psia (refer tables 2.3 and 2.4) (scf/stb).

dsiR = solution gas oil ratio of the bubble point oil determined during the

differential experiment and measured relative to the residual oil volume at60°F and 14.7 psia (refer table 2.5 and equ. (2.10)) (scf/stb-residual).

The differential data, as presented in table 2.5, can be directly converted to therequired form, table 2.4, using the above relations. For instance, using the followingdata from table 2.5, at a pressure of 2400 psi

doB = 1.2123 (rb /barrel of residual oil at 60°F and 14.7 psia)

dsR = 378 (scf/ —" — )

dobB = 1.2830 (rb / — " — )

dsiR = 540 (scf/ —" — )

while from the separator flash tests (table 2.3), for the optimum separator conditions of150 psia and 80°F

f fob bB (1/ c ) 1.2511(rb / stb)= =

fsiR 510 (scf / stb)=

Therefore, using equ. (2.11)

o1.2511B 1.2123 1.1822 rb stb1.2830

= × =

and equ. (2.12)

s1.2511R 510 (540 378) 352 scf / stb1.2830

= − − × =


2.6 COMPLETE PVT ANALYSIS

The complete PVT analysis for oil, provided by most laboratories, usually consists ofthe following experiments and calculations.

a) Compositional analysis of the separator oil and gas, for samples collected at thesurface, together with physical recombination, refer sec. 2.3(b), or; compositionalanalysis of the reservoir fluid collected in a subsurface sample.

Such analyses usually give the mole fractions of each component up to thehexanes. The hexanes and heavier components are grouped together, and theaverage molecular weight and density of the latter are determined.

b) Flash expansion, as described in sec. 2.4 (table 2.1), conducted at reservoirtemperature. This experiment determines

− the bubble point pressure

− the compressibility of the undersaturated oil as

o oo

o o

dv dB1 1cv dp B dp

= − = − (2.13)

− the total volume vt of the oil and gas at each stage of depletion.

c) Differential liberation experiment as described in sec. 2.4 to determine

− E, Z, F and vo (as listed in table 2.2), with F and vo measured relative to theunit volume of bubble point oil.

Alternatively, by measuring dbc during the last stage of the differential liberation,

the above data can be presented as

− E, Z, dsiR −

dsR (or just dsR ) and

doB (as listed in table 2.5), with dsR and

doB measured relative to residual oil volume. In addition, the gas gravity is

measured at each stage of depletion.

d) Measurement of the oil viscosity at reservoir temperature (generally using therolling ball viscometer1,3), over the entire range of pressure steps from abovebubble point to atmospheric pressure. Gas viscosities are normally calculated atreservoir temperature, from a knowledge of the gas gravity, using standardcorrelations5.

e) Separator tests to determine the shrinkage, fbc , and solution gas oil ratio,

fsiR , of

unit volume of bubble point oil (1 barrel) when flashed through various separatorcombinations (refer table 2.3). Instead of actually performing these tests, in manycases the results are obtained using the phase equilibrium calculationtechnique1.

f) Composition and gravity of the separator gas in the above separator tests.

Copyright 2002, Society of Petroleum Engineers Inc. This paper was prepared for presentation at the SPE Annual Technical Conference and Exhibition held in San Antonio, Texas, 29 September–2 October 2002. This paper was selected for presentation by an SPE Program Committee following review of information contained in an abstract submitted by the author(s). Contents of the paper, as presented, have not been reviewed by the Society of Petroleum Engineers and are subject to correction by the author(s). The material, as presented, does not necessarily reflect any position of the Society of Petroleum Engineers, its officers, or members. Papers presented at SPE meetings are subject to publication review by Editorial Committees of the Society of Petroleum Engineers. Electronic reproduction, distribution, or storage of any part of this paper for commercial purposes without the written consent of the Society of Petrol eum Engineers is prohibited. Permission to reproduce in print is restricted to an abstract of not more than 300 words; illustrations may not be copied. The abstract must contain conspicuous acknowledgment of where and by whom the paper was presented. Write Librarian, SPE, P.O. Box 833836, Richardson, TX 75083-3836, U.S.A., fax 01-972-952-9435.

Abstract

Combinations of data from two laboratory procedures, differential liberation and separator test, are used to determine values of oil formation volume factors and solution gas-oil ratios for pressures below the bubblepoint pressure of the reservoir oil. The equation commonly used to calculate the solution gas -oil ratio is incorrect: the correct equation is derived. The equation used to calculate the oil formation volume factors is correct; however, a derivation illustrating the underlying assumptions has not been published. This derivation is also examined.

Introduction

The bad news is that the equation usually used in the petroleum industry to calculate solution gas -oil ratios from black oil PVT reports,

( ) oSbs sSb sDb sD

oDb

BR R R R ,

B= − − . . . . . . . . . . . . . . . . . . (1)

is incorrectly formulated.

The good news is that the errors at high pressures, where solution gas -oil ratios are more often used, are not severe. A correct formulation of the equation will improve estimates of solution gas -oil ratio throughout the full range of depletion pressures.

Further good news is that the equations used to calculate oil formation volume factors from black oil PVT reports,

( ) ( )o oE oSb bB B B at p>p= . . . . . . . . . . . . . . . . . . . . . (2a)

and

( ) oSbo oD b

oDb

BB B at p<p ,

B= . . . . . . . . . . . . . . . . . . . . . (2b)

are correct. This paper presents a brief discussion of the laboratory procedures, which will lead to the derivations of Eq. 2b and a correct replacement for Eq. 1. Laboratory Procedures The two laboratory procedures that provide the necessary data are the differential liberation (sometimes called differential vaporization or differential distillation) and the separator test (sometimes, incorrectly, called flash test). Each of these laboratory procedures will be described briefly. What will be seen is that each procedure starts with a quantity of reservoir oil in the laboratory cell at its bubblepoint pressure at the reservoir temperature. In each procedure, gas is removed in a sequence of flash vaporizations, with the resulting liquid ending up at atmospheric pressure and 60°F (standard conditions). Differential Liberation. Theoretically, the differential liberation starts with a liquid at some pressure and temperature, then the liquid is partially vaporized, and each small increment of vapor is at once removed from the contact with the liquid.1 Thus, the liquid is in equilibrium at any instant with a small amount of vapor. This procedure is somewhat tedious, so the petroleum industry emulates the differential liberation with a series of flash vaporizations in which a definite fraction of a batch of liquid is vaporized and kept in intimate contact with the liquid until the gas is withdrawn at the end of each step in the series. In practice, the process starts with a sample of reservoir oil at its bubblepoint pressure in the laboratory cell with the temperature controlled at reservoir temperature. A dozen or so steps (the exact number depends on the starting bubblepoint pressure) consisting of flash vaporizations are carried out. Each step starts with a pressure reduction at constant reservoir temperature. This causes gas to be vaporized. The gas is

SPE 77386

Analysis of Black Oil PVT Reports Revisited William D. McCain, Jr., Texas A&M University

2 WILLIAM D. MCCAIN, JR. SPE 77386

allowed to come to equilibrium with the liquid at the lower pressure and reservoir temperature, and then the gas is removed, and its quantity and specific gravity are measured. The volumes of the liquid remaining at the end of each step are determined. The last flash vaporization step ends at atmospheric pressure. Then the temperature of the remaining liquid is reduced to 60°F and the liquid volume is adjusted to maintain the pressure at 0 psig. This final liquid is called the residual liquid from the differential liberation or, simply, residual oil. The volumes of gas removed in all steps are added; this is the amount of gas in solution at bubblepoint pressure. The gas volumes are decremented to determine the gas remaining in solution at the pressure at the end of each step. Finally, the volumes of gas in solution (in standard cubic feet, scf) and the volumes of the oil in the cell (in reservoir barrels, res. bbl) at the end of each step are divided by the volume of the residual oil (at atmospheric pressure and 60°F). These are presented in the laboratory report as gas in solution, scf/residual barrel, and relative oil volume, reservoir barrel/residual barrel. Other properties, such as reservoir oil density, incremental gas specific gravity, and gas compressibility factor, are also measured and reported. Separator Test. The separator test starts with a sample of the reservoir oil at its bubblepoint pressure in the laboratory cell at reservoir temperature (same as the start of the differential liberation). A measured volume of the reservoir oil is expelled through a sequence of two (usually, though sometimes three) flash vaporizations. In the first, at separator temperature and pressure, the gas that was vaporized is removed, and the liquid goes to the second flash at stock-tank temperature and atmospheric pressure. The volume of resulting liquid is determined at atmospheric pressure and 60°F; this liquid is usually called stock-tank oil and the volume is reported in stock-tank barrels, STB, which also could be interpreted as standard barrels. The volumes and specific gravities of the gases from the two flash vaporizations are measured. The two gas volumes are added, and the sum is reported as solution gas-oil ratio at the bubblepoint, scf/STB. The volume of reservoir oil that was expelled at the start of the test is divided by the volume of stock-tank oil (at standard conditions) and reported as oil formation volume factor at the bubblepoint, res. bbl/STB. The density of the stock-tank oil is measured and usually reported in °API. Example Laboratory Data

Table 1 shows selected data from a differential liberation and a separator test for a black oil. The bubblepoint pressure is 3043 psig at a reservoir temperature of 262°F. The quantity and properties of oil and gas produced by the two procedures are different. However, this is difficult to see in the formats in which the data are presented. A comparison of the results of the two procedures may be made by placing the data on a basis of one barrel of reservoir oil at bubblepoint pressure and reservoir temperature. The oil in place at the

bubblepoint is the starting point of both processes and is independent of the process. Table 2 shows this comparison for the data of Table 1. The quantity of oil resulting from the separator test is eighteen percent higher than the oil resulting from the differential liberation. The quantity of gas resulting from the separator test is fifteen percent lower than the gas from the differential liberation. And compositions and properties of the resulting oils and gases differ significantly, as represented by the different API gravities of the oils and specific gravities of the gases. Calculation of Oil Formation Volume Factors

The ratio

oDb b oSb

oDb

oSb b

1 residual bbl

B res. bbl @ p B residual bbl1 STB B STB

B res. bbl @ p

= . . . . . . . . . . . (3)

provides a convenient relationship between residual barrels from the differential liberation and stock-tank barrels from the separator test. The term reservoir barrel at bubblepoint pressure (at reservoir temperature), which appears twice on the left-hand side of Eq. 3, can be eliminated since both laboratory procedures start with the reservoir oil in the laboratory cell at its bubblepoint pressure at reservoir temperature. The change in volume of oil in the reservoir during pressure depletion can be written as

( ) oSboSb o oDb oD

oDb

BB B B B

B− = − . . . . . . . . . . . . . . . . . . . (4)

The units of this equation are

change in res bbl of oil change in res bbl of oil residual bbl

STB residual bbl STB =

Under the assumption that the change in volume (res. bbl) of oil in the reservoir is the result of a differential liberation process, the “change” units in the numerator of each side of the equation are identical. Thus, the equation is correct. Eq. 4 can be rearranged as

oSbo oD

oDb

BB B ,

B= . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (2b)

which is the equation generally used in the petroleum industry to calculate oil formation volume factors from differential liberation and separator test data. Note that the use of Eq. 2b requires that the ratio of the volumes of residual oil to stock-tank oil remains constant (for a particular oil sample), regardless of the starting pressure. The limited experimental data that are available show that this is true.2

SPE 77386 ANALYSIS OF BLACK OIL PVT REPORTS REVISITED 3

There are very limited data to test the results of Eqs. 2a and 2b against measured oil formation volume factors. However, Dodson, et al.,2 provided one set of data. Dodson, et al., proposed a laboratory procedure for determining oil formation volume factors (and solution gas -oil ratios) that is generally considered more accurate than the differential liberation/separator test procedure usually used and discussed in this paper. Unfortunately their “composite liberation,” although considered a superior method,3 requires a large sample of reservoir fluid and is very time consuming in the laboratory. Thus, it is not used in routine laboratory analysis. But Dodson, et al., did provide one example of a routine laboratory report and the results of a composite liberation for the same black oil. Fig. 1 shows values of oil formation volume factor calculated with Eqs. 2a and 2b compared with the more accurate results of the composite liberation. The small differences between the results of Eq. 2b and the data from the composite liberation are approximately one percent, well within experimental accuracy. The composite liberation is an entirely different laboratory procedure; the differential liberation/separator test discussed here is the industry’s (less expensive) method of approximating the composite liberation. Calculation of Solution Gas-oil Ratios Eq. 1 is used commonly in the petroleum industry to combine data from differential liberation and separator tests to calculate solution gas -oil ratios. The validity of this equation can be examined easily by rearrangement:

( ) oSbsSb s sDb sD

oDb

BR R R R

B− = − . . . . . . . . . . . . . . . . . . . (5)

The units are gas liberated in sep test, scf gas libera ted in diff lib, scf residual bbl

STB residual bbl STB =

Eq. 5 shows that the gas volume liberated during the separator test has been set equal to the gas volume liberated during the differential liberation. If the sources of the data are not taken into account, the units, scf/STB, appear to be correct. However, Table 2 shows that the gas liberated during a separator test is significantly different in quantity and quality from the gas liberated during a differential liberation. The ratio BoSb/BoDb in Eq. 5 takes into account the differences in the oils from the separator test and differential liberation, but the differences in the gases are ignored. Thus, the material balance expressed in Eq. 5 must be incorrect. It follows that values of solution gas-oil ratio calculated with Eq. 1 must be in error! In fact, this is illustrated every time the equation is used because calculated values of solution gas -oil ratio are generally negative at low pressures.

The correct formulation is as follows. The equation must calculate the gas remaining in solution in the reservoir oil at a pressure after pressure depletion from pb to some p, Rs, scf/STB. Further, Rs should be the amount of gas to be liberated through a separator/stock-tank sequence. RsSb is the gas originally in solution in the reservoir oil at its bubblepoint pressure as measured in a separator test, scf of gas from sep. test/STB. RsDb–RsD is the volume of gas liberated in the reservoir during a differential liberation from pb to p, scf of diff. lib. gas/residual bbl. The ratio

sSb

sDb

scf of gas from sep. testR STB

scf of gas from diff. lib.Rresidual bbl

takes into account both the difference in the two oils, residual bbl/STB, and the difference in the two gases, scf of gas from sep. test/scf of gas from diff. lib. Thus,

( ) sSbsDb sD

sDb

RR R

R

scf of gas lib. by diff. lib. scf of gas from sep. test, residual bbl

residual bbl scf of gas from diff. lib., STB

−

is the gas differentially liberated converted to scf of sep. gas/STB. The difference between the gas originally in solution and the gas liberated during depletion from pb to p is the gas remaining is solution at p.

( ) sSbs sSb sDb sD

sDb

RR R R R

R= − − . . . . . . . . . . . . . . . . . . (6)

Again, there is the assumption that the differential liberation mimics the depletion in an oil reservoir, i.e., the gas remaining in solution is that left after gas has been removed by differential liberation. Eq. 6 can be rearranged into a simpler form

sSbs sD

sDb

RR R

R= . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (7)

The use of Eq. 7 implies that the ratio of the gas liberated by separator test to the gas liberated by differential liberation be constant (for a particular oil sample), regardless of the starting pressure. The limited available data from Dodson, et al.2 show this to be true. Again, the Dodson, et al.2 data are the only data available to use in comparing the results of Eq. 1 and Eq. 7 with experimental solution gas -oil ratios measured at pressures below bubblepoint pressure of the oil.

4 WILLIAM D. MCCAIN, JR. SPE 77386

Fig. 2 shows the results of Eqs. 1 and 7 using the data from the routine laboratory report compared with the more accurate results of the composite liberation. Eq. 7 gives values of Rs, which fit the composite liberation more closely than the results of Eq. 1. Further, the values of Rs from Eq. 7 converge to zero at 0 psig (as required by the definition of Rs), while the values from Eq. 1 are negative at low pressures. The small differences between the results of Eq. 7 and the composite liberation data in Fig. 2, as well as the good comparison of the results of Eqs. 2a and 2b in Fig. 1, show that the simpler, less costly, routinely used PVT procedures give results adequate for reservoir engineering work. The difference between the results of Eq. 7 and Eq. 1 in Fig. 2 are not very dramatic. However, notice that the Dodson, et al.2 oil does not have much dissolved gas, with Rsb of about 600 scf/STB. Fig. 3 shows that the oil of Table 1, which has about 1000 scf/STB originally in solution, shows a much larger difference between the results of the two equations, about thirty percent at a reservoir pressure of 1100 psig. Conclusions Eqs. 2a, 2b, and 7 are the correct equations for calculating oil formation volume factors and solution gas-oil ratios at reservoir pressures below the bubblepoint pressure when combining the data from differential liberation with separator test data. The use of differential liberation data for these calculations is nearly as accurate as the more costly composite liberation data and is certainly adequate for reservoir engineering calculations. Nomenclature Bo = Oil formation volume factors at pressure,

res. bbl/STB BoSb = Oil formation volume factor at bubblepoint

pressure measured in a separator test, res. bbl @ pb/STB

BoD = Oil relative volumes at pressures less than bubblepoint pressure measured in a differential liberation, res. bbl/residual bbl

BoDb = Oil relative volume at bubblepoint pressure measured in a differential liberation, res. bbl @ pb/residual bbl

BoE = Oil relative volume at pressures above bubblepoint pressure measured in a constant mass expansion, res. bbl/res. bbl @ pb

Rs = Solution gas-oil ratios at pressures less than bubblepoint pressure, scf/STB

RsSb = Solution gas-oil ratio at bubblepoint pressure measured in a separator test, scf from separator test /STB

RsD = Solution gas-oil ratios at pressures less than bubblepoint pressure measured in a differential liberation, scf from differential liberation/residual bbl

RsDb = Solution gas-oil ratio at bubblepoint pressure measured in a differential liberation, scf from differential liberation/residual bbl

References 1. Dodge, B.F.: Chemical Engineering Thermodynamics,

McGraw-Hill, New York (1944), 592. 2. Dodson, C.R., Goodwill, D., and Mayer, E.H.:

“Application of Laboratory PVT Data to Reservoir Engineering Problems,” Trans., AIME (1953) 198, 287–298.

3. Moses, P.L.: “Engineering Applications of Phase Behavior of Crude Oil and Condensate Systems,” J. Pet. Tech. (July 1986) 38, 715–723.

TABLE 1. SELECTED DATA FROM DIFFERENTIAL LIBERATION AND SEPARATOR TEST OF A BLACK OIL

Differential Liberation at 262°F

Pressure, psig

Gas in Solution,

scf/residual bbl

Relative Oil Volume,

res. bbl/residual bbl

Incre-mental

Gas Specific Gravity

3043 1401 2.022 2900 1307 1.965 0.822 2600 1140 1.866 0.867 2300 998 1.783 0.858 2000 868 1.709 0.853 1700 751 1.644 0.856 1400 642 1.584 0.861 1100 537 1.526 0.881 800 436 1.468 0.922 500 331 1.407 1.008 263 235 1.339 1.197 143 176 1.290 1.432 0 0 1.111 2.194 0 at 60°F = 1.000

Gravity of Residual Oil = 43.2°API @ 60°F

SEPARATOR TEST

Flash Vapori -zation

Pres-sure, psig

Temper-ature,

°F

Gas-oil Ratio,

scf/STB

Oil Forma-

tion Volume Factor,

res. bbl/ STB

Stock- tank Oil Gravity, °API @

60°F

Gas Specific Gravity

Separator 100 70 935 0.775 Stock Tank 0 72 102 1.714** 48.0 1.309

1037*

*Solution gas-oil ratio at bubblepoint pressure

**Oil formation volume factor at bubblepoint pressure

SPE 77386 ANALYSIS OF BLACK OIL PVT REPORTS REVISITED 5

Fig. 1 Comparison showing excellent fit of oil formation volume factors calculated from routine laboratory PVT data using Eqs. 2a and 2b with data from composite liberation.

1

1.05

1.1

1.15

1.2

1.25

1.3

0 500 1000 1500 2000 2500 3000 3500 4000

Reservoir pressure, psig

Oil

form

atio

n vo

lum

e fa

ctor

, res

. bbl

/STB

data from composite liberation calculated with Eqs. 2a and 2b

Fig. 2 Comparison of solution gas-oil ratios calculated from routine laboratory PVT data using Eqs. 1 and 7 with data from composite liberation showing that Eq. 7 has a better fit.

-100

0

100

200

300

400

500

600

700

0 500 1000 1500 2000 2500 3000 3500 4000

Reservoir pressure, psigS

olut

ion

gas-

oil r

atio

, scf

/STB

data from composite liberation calculated with Eq. 7 calculated with Eq. 1

Fig. 3 Comparison of solution gas-oil ratios calculated from routine laboratory PVT data using Eqs. 1 and 7, showing that the deviation between the results is greater when initial solution gas-oil ratio is large.

-200

0

200

400

600

800

1000

1200

0 500 1000 1500 2000 2500 3000 3500

Reservoir pressure, psig

So

luti

on

gas

-oil

rati

o, s

cf/S

TB

Eq. 7 Eq. 1

TABLE 2. THE VOLUMES AND PROPERTIES OF THE OIL AND GAS RESULTING FROM THE TWO LABORATO RY PROCEDURES

ARE QUITE DIFFERENT (DATA FROM TABLE 1)

Differential Liberation Separator Test

Volume of oil at standard conditions at end of process

0.495b

residual bbl

res. bbl @ P 0.583

b

STB

res. bbl @ P

Gravity of oil at standard conditions at end of process

43.2°API 48.0°API

Volume of total gas at standard conditions liberated during process

692.9b

scf

res. bbl @ P 605.0

b

scf

res. bbl @ P

Weighted average specific gravity at standard conditions of total gas liberated during process

1.0931 0.8252

88 PHASE BEHAVIOR

This chapter reviews the standard experiments performed by pres-sure/volume/temperature (PVT) laboratories on reservoir fluidsamples: compositional analysis, multistage surface separation,constant composition expansion (CCE), differential liberation ex-pansion (DLE), and constant volume depletion (CVD). We presentdata from actual laboratory reports and give methods for checkingthe consistency of reported data for each experiment. Chaps. 5 and8 discuss special laboratory studies, including true-boiling-point(TBP) distillation and multicontact gas-injection tests, respectively.

Table 6.1 summarizes experiments typically performed on oilsand gas condensates. From this table, we see that the DLE experi-ment is the only test never performed on gas-condensate systems.We begin by discussing standard analyses performed on oil and gas-condensate samples.

6.1.1 General Information Sheet. Most commercial laboratoriesreport general information on a cover sheet of the laboratory report,including formation and well characteristics and sampling condi-tions. Tables 6.2 and 6.31,2 show this information, which may beimportant for correct application and interpretation of the fluid anal-yses. This is particularly true for wells where separator samplesmust be recombined to give a representative wellstream composi-tion. Most of these data are supplied by the contractor of the fluidstudy and are recorded during sampling. Therefore, the representa-tive for the company contracting the fluid study is responsible forthe correctness and completeness of reported data.

We strongly recommend that the following data always be reportedin a general information sheet: (1) separator gas/oil ratio (GOR) instandard cubic feet/separator barrel, (2) separator conditions at sam-pling, (3) field shrinkage factor used ( Bosp), (4) flowing bottom-hole pressure (FBHP) at sampling, (5) static reservoir pressure, (6)minimum FBHP before and during sampling, (7) time and date ofsampling, (8) production rates during sampling, (9) dimensions ofsample container, (10) total number and types of samples collectedduring the drillstem test, and (11) perforation intervals.

6.1.2 Oil PVT Analyses. Standard PVT analyses performed on res-ervoir oils usually include (1) bottomhole wellstream compositionalanalysis through C7, (2) CCE, (3) DLE, and (4) multistage-separa-tor tests. The CCE experiment determines the bubblepoint pressureand volumetric properties of the undersaturated oil. It also givestwo-phase volumetric behavior below the bubblepoint; however,these data are rarely used. The DLE experiment and separator testare used together to calculate traditional black-oil properties, Bo

and Rs, for reservoir-engineering calculations. Occasionally,

instead of a DLE study, a CVD experiment is run on a volatile oil.

Also, the C7 fraction may be separated into single-carbon-number

cuts from C7 through approximately C20 by TBP analysis or simu-

lated distillation (see Chap. 5).

6.1.3 Gas-Condensate PVT Analyses. The standard experimental

program for a gas-condensate fluid includes (1) recombined well-

stream compositional analysis through C7, (2) CCE, and (3) CVD.

The CCE and CVD data are measured in a high-pressure visual cell

where the dewpoint pressure is determined visually. Total volume/

pressure and liquid-dropout behavior is measured in the CCE ex-

periment. Phase volumes defining retrograde behavior are mea-

sured in the CVD experiment together with Z factors and

produced-gas compositions through C7. Optionally, a multistage-

separator test can be performed as well as TBP analysis or simulated

distillation of the C7 into single-carbon-number cuts from C7 to

about C20 (see Chap. 5).

PVT studies usually are based on one or more samples taken during

a production test. Bottomhole samples can be obtained by wireline

with a high-pressure container during either production testing or a

shut-in period. Alternatively, separator samples can be taken during

a production test. Bottomhole sampling is the preferred method for

most oil reservoirs, while recombined samples are traditionally used

for gas-condensate reservoirs.3-8 Taking both bottomhole and sepa-

rator samples in oil wells is not uncommon. The advantage of sepa-

rator samples is that they can be recombined in varying proportions

to achieve a desired bubblepoint pressure (e.g., initial reservoir

pressure); these larger samples are needed for special PVT tests

(e.g., TBP and slim tube among others).

6.2.1 Bottomhole Sample. Table 6.4 shows the reported wellstream

composition of a reservoir oil where C7 specific gravity and molec-

ular weight are also reported. In the example report, composition is

given both as mole and weight percent although many laboratories re-

port only molar composition. Experimentally, the composition of a

bottomhole sample is determined by the following (Fig. 6.1).

1. Flashing the sample to atmospheric conditions.

2. Measuring the volumes of surface gas, Vg , and surface oil, Vo .

3. Determining the normalized weight fractions, wgi and woi, of

surface samples by gas chromatography.

4. Measuring surface-oil molecular weight, Mo , and specific

gravity, o .

CONVENTIONAL PVT MEASUREMENTS 89

TABLE 6.1—LABORATORY ANALYSES PERFORMED ONRESERVOIR-OIL AND GAS-CONDENSATE SYSTEMS

Laboratory Analysis Oils Gas Condensates

Bottomhole sample

Recombined composition

C7+ TBP distillation

C7+ simulated distillation

Constant-composition expansion

Multistage surface separation

Differential liberation N

CVD

Multicontact gas injection

standard, can be performed, and Nnot performed.

5. Converting wgi weight fractions to normalized mole fractionsyi and xi.

6. Recombining mathematically to the wellstream composition, zi.Eqs. 6.1 through 6.5 give Steps 1 through 6 mathematically.

zi Fg yi (1 Fg)xi ; (6.1). . . . . . . . . . . . . . . . . . . . . . . .

Fg 1

1 !133, 300"#M$o#Rs% , (6.2). . . . . . . . . . . . . . . . . .

where RsGOR Vg#Vo in scf/STB from the single-stage flash;

yiw

g i#Mi

&j'C7

"wg j#Mj$ "w

g C 7#M

g C 7$

; (6.3). . . . . . . . .

xiw

o i#Mi

&j'C7

"wo j#Mj$ "w

o C7#M

o C7$

; (6.4). . . . . . . . . .

and Mo C7

w

o C7

"1#Mo$ &

j'C7

"woj#M

j$ . (6.5). . . . . . . . . . . . .

Surface gas usually contains less than 1 mol% C7 material con-sisting mainly of heptanes and octanes; M

g C 7 105 is usually a

good assumption. Surface oil contains less than 1 mol% of the lightconstituents C1, C2, and nonhydrocarbons. Low-temperature dis-tillation can be used to improve the accuracy of reported weightfractions for intermediate components in the surface oil ( C3 throughC6); however, gas chromatography is more widely used.

The most probable source of error in wellstream composition of abottomhole sample is the surface-oil molecular weight, Mo , whichappears in Eq. 6.2 for Fg and Eq. 6.4 for xi. Mo is usually accuratewithin (4 to 10%. In Chap. 5, we showed that the Watson character-ization factor, Kw, of surface oil (Eq. 5.35) should be constant (towithin (0.03 of the determined value) for a given reservoir. Once anaverage has been established for a reservoir (usually requiring threeseparate measurements), potential errors in Mo can be checked. Acalculated Kw that deviates from the field-average Kw by more than(0.03 may indicate an erroneous molecular-weight measurement.

Eqs. 6.1 through 6.4 show that all component compositions areaffected by M

o C 7, which is backcalculated from Mo with Eq.

6.5. Fortunately, the amount of lighter components (particularly C1)in the surface oil are small, so the real effect on conversion fromweight to mole fractions of the surface oil usually is not significant.

6.2.2 Recombined Samples. Tables 6.5 and 6.6 present the separa-tor-oil and -gas compositional analyses of a gas-condensate fluidand recombined wellstream composition. The separator-oil com-position is obtained by use of the same procedure as that used forbottomhole oil samples (Eqs. 6.1 through 6.5). This involves bring-ing the separator oil to standard conditions, measuring properties

TABLE 6.2—EXAMPLE GENERAL INFORMATION SHEETFOR GOOD OIL CO. WELL 4 OIL SAMPLE

Formation Characteristics

Name Cretaceous

First well completed / /19 (m/d/y)

Original reservoir pressure at 8,692 ft, psig 4,100

Original produced GOR, scf/bbl 600

Production rate, B/D 300

Separator temperature, °F 75

Separator pressure, psig 200

Oil gravity at 60°F, °API

Datum 8,000

Original gas cap No

Well Characteristics

Elevation, ft 610

Total depth, ft 8,943

Producing interval, ft 8,684 to 8,700

Tubing size, in. 27/8

Tubing depth, ft 8,600

PI at 300 B/D, B-D/psi 1.1

Last reservoir pressure at 8,500 ft, psig 3,954*

Date / /19 (m/d/y)

Reservoir temperature at 8,500 ft, °F 217*

Well status Shut in 72 hours

Pressure gauge Amerada

Normal production rate, B/D 300

GOR, scf/bbl 600

Separator pressure, psig 200

Separator temperature, °F 75

Base pressure, psia 14.65

Well making water, % water cut 0

Sampling Conditions

Sample depth, ft 8,500

Well status Shut in 72 hours

GOR

Separator pressure, psig

Separator temperature, °F

Tubing pressure, psig 1,400

Casing pressure, psig

Sampled by

Sampler type Wofford

*Pressure and temperature extrapolated to the midpoint of the producing

interval4,010 psig and 220°F.

and compositions of the resulting surface oil and gas, and recombin-

ing these compositions to give the separator-oil composition; Tables

6.5 and 6.6 report the results.

Separator gas is introduced directly into a gas chromatograph,

which yields weight fractions, wg . These weight fractions are con-

verted to mole fractions, yi, by use of appropriate molecular

weights; Tables 6.5 and 6.6 show the results. C7 molecular weight

is backcalculated with measured separator-gas specific gravity, g .

Mg C 7

wg C 7" 1

28.97g

&i'C7

wg i

Mi$ 1

. (6.6). . . . . . .

90 PHASE BEHAVIOR

TABLE 6.3—EXAMPLE GENERAL INFORMATION SHEETFOR GOOD OIL CO. WELL 7 GAS CONDENSATE

Formation Characteristics

Formation name Pay sand

Date first well completed / /19 (m/d/y)

Original reservoir pressure at 10,148 ft, psig 5,713

Original produced-gas/liquid ratio, scf/bbl

Production rate, B/D

Separator pressure, psig

Separator temperature, °F

Liquid gravity at 60°F, °API

Datum, ft subsea 8,000

Well Characteristics

Elevation, ft KB 2,214

Total depth, ft 10,348

Producing interval, ft 10,124 to 10,176

Tubing size, in. 2

Tubing depth, ft 10,100

Open-flow potential, MMscf/D

Last reservoir pressure at 10,148 ft, psig 5,713

Date / /19 (m/d/y)

Reservoir temperature at 10,148 ft, °F 186

Status of well status Shut in

Pressure gauge Amerada

Sampling Conditions

Flowing tubing pressure, psig 3,375

FBHP, psig 5,500

Primary-separator pressure, psig 300

Primary-separator temperature, °F 62

Secondary-separator pressure, psig 20

Secondary-separator temperature, °F 60

Field stock-tank-liquid gravity at 60°F, °API 58.5

Primary-separator-gas production rate, Mscf/D 762.14

Pressure base, psia 14.696

Temperature base, °F 60

Compressibility factor, Fpv 1.043

Gas gravity (laboratory) 0.737

Gas-gravity factor, Fg 0.902

Stock-tank-liquid production rate at 60°F, B/D 127.3

Primary-separator-gas/stock-tank-liquid ratioIn scf/bblIn bbl/MMscf

5,987167.0

Sampled by

For the example PVT report (Tables 6.5 and 6.6), the separator

gas/oil ratio, Rsp, during sampling is reported as standard gas vol-

ume per separator-oil volume (4,428 scf/bbl). In this report, the units

are incorrectly labeled scf/bbl at 60°F, where in fact the separator-oil

volume is measured at separator pressure (300 psig) and tempera-

ture (62°F). The separator-oil formation volume factor (FVF), Bosp,

is 1.352 bbl/STB and represents the volume of separator oil required

to yield 1 STB of oil (i.e., condensate).

The equation used to calculate wellstream composition, zi, is

zi Fgsp yi (1 Fgsp)xi , (6.7). . . . . . . . . . . . . . . . . . . . .

where Fgspmole fraction of wellstream mixture that becomes

separator gas. In the laboratory report, Fgsp is reported as “primary-

separator gas/wellstream ratio” (801.66 Mscf/MMscf), which is

equivalent to mole per mole ( Fgsp0.80166 mol/mol). The re-

ported value of Fgsp can be checked with

Fgsp "1 2, 130 osp

Mosp Rsp

$ 1

, (6.8). . . . . . . . . . . . . . . . . . . . .

where Mosp&N

i1

xi Mi . (6.9). . . . . . . . . . . . . . . . . . . . . . . . . . .

osp in lbm/ft3 is calculated with a correlation (e.g., Standing-Katz9)

or with the relation (62.4o 0.0136g Rs)#Bo, where Rs and

Boseparator-oil values in scf/STB and bbl/STB, respectively;


TABLE 6.4—WELLSTREAM (RESERVOIR-FLUID)COMPOSITION FOR GOOD OIL CO. WELL 4

BOTTOMHOLE OIL SAMPLE

Component mol% wt%Density*(g/cm3) °API*

MolecularWeight

H2S Nil Nil

CO2 0.91 0.43

N2 0.16 0.05

Methane 36.47 6.24

Ethane 9.67 3.10

Propane 6.95 3.27

i-butane 1.44 0.89

n-butane 3.93 2.44

i-pentane 1.44 1.11

n-pentane 1.41 1.09

Hexanes 4.33 3.97

Heptanes plus 33.29 77.41 0.8515 34.5 218

Total 100.00 100.00

*At 60°F.

ostock-tank-oil density; and ggravity of gas released from

the separator oil.Finally, the value of stock-tank-liquid/wellstream ratio in bbl/MMscf

represents the separator barrels produced per 1 MMscf of wellstream.In terms of Fgsp and separator properties, this value equals

bblMMscf

470(1 Fgsp)"Mosp# osp

$Bosp

, (6.10). . . . . . . . . . . . . .

where 470(1 million scf/MMscf)/[(379 scf/lbm mol)(5.615 ft3/bbl)].The separator-oil and -gas compositions can be checked for con-

sistency with the Hoffman et al.10 K-value method and Standing’s11

low-pressure K-value equations.

!"#

The multistage-separator test is performed on an oil sample primari-ly to provide a basis for converting differential-liberation data froma residual-oil to a stock-tank-oil basis. Occasionally, several separa-tor tests are run to help choose separator conditions that maximizestock-tank-oil production. Usually, two or three stages of separationare used, with the last stage at atmospheric pressure and near-ambi-ent temperature (60 to 80°F). The multistage-separator test can alsobe conducted for high-liquid-yield gas-condensate fluids.

Fig. 6.2 illustrates schematically how the separator test is per-formed. Initially, the reservoir sample is at saturation conditions andthe volume is measured ( Vob or Vgd). The sample is then brought tothe pressure and temperature of the first-stage separator. All the gasis removed, and the oil volume at the separator stage, Vosp, is notedtogether with the volume of removed gas, V

g; number of moles of

removed gas, ng; and specific gravity of removed gas,

g. If re-

quested, the gas samples can be analyzed chromatographically togive molar composition, y.

The oil remaining after gas removal is brought to the conditionsof the next separator stage. The gas is removed again and quantifiedby moles and specific gravity. Oil volume is noted, and the processis repeated until stock-tank conditions are reached. Final oil volume,Vo , and specific gravity, o , are measured at 60°F.

Table 6.7 gives results from four separator tests, each consistingof two stages of separation. The first-stage-separator pressure is var-ied from 50 to 300 psig, and stock-tank conditions are held constantat 0 psig and 75°F. GOR’s are reported as standard gas volume perseparator-oil volume, Rsp, and as standard gas volume per stock-tank-oil volume, Rs, respectively.

RspVg

Vosp

(6.11). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

and RsVg

Vo

. (6.12). . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Total GOR is calculated by adding the stock-tank-oil-based GOR’sfrom each separator stage.

Rs&Nsp

k1

"Rs$k . (6.13). . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Separator-oil FVF’s, Bosp, are reported as the ratio of separator-oilvolume to stock-tank-oil volume.

BospVosp

V o

. (6.14). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Accordingly, the relation between separator gas/oil ratio and stock-tank gas/oil ratio at a given stage is

RspRs

Bosp. (6.15). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Because Bosp) 1, it follows that Rsp* Rs.Bubblepoint-oil FVF, Bob, is the ratio of bubblepoint-oil volume

to stock-tank-oil volume.

Bob

Vob

Vo

. (6.16). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

The average gas gravity, g , is used in oil PVT correlations and

to calculate reservoir densities on the basis of black-oil properties.The average gas gravity is calculated from

g

&Nsp

k1

"g$k"Rs$k

&Nsp

k1

"Rs$k

, (6.17). . . . . . . . . . . . . . . . . . . . . . . . . .

Fig. 6.1—Procedure for recombining single-stage separator samples to obtain wellstreamcomposition of a bottomhole sample; BHSbottomhole sampler, GCgas chromatograph,FDP freezing-point depression, and DMdensitometer.

92 PHASE BEHAVIOR

TABLE 6.5—SEPARATOR AND RECOMBINED WELLSTREAM COMPOSITIONSFOR GOOD OIL CO. WELL 7 GAS CONDENSATE

Separator Products Hydrocarbon Analysis

Separator Liquid Separator Gas Wellstream

Component (mol%) (mol%) (gal/Mscf) (mol%) (gal/Mscf)

CO2 Trace 0.22 0.18

N2 Trace 0.16 0.13

Methane 7.78 75.31 61.92

Ethane 10.02 15.08 14.08

Propane 15.08 6.68 1.832 8.35 2.290

iso-butane 2.77 0.52 0.170 0.97 0.317

n-butane 11.39 1.44 0.453 3.41 1.073

iso-pentane 3.52 0.18 0.066 0.84 0.306

n-pentane 6.50 0.24 0.087 1.48 0.535

Hexanes 8.61 0.11 0.045 1.79 0.734

Heptanes plus 34.33 0.06 0.028 6.85 3.904

Total 100.00 100.00 2.681 100.00 9.159

Heptanes-Plus Properties

Oil gravity, °API 46.6

Specific gravityat 60/60°F

0.7946 0.795

Molecular weight 143 103 143

Parameters

Calculated separator gas gravity (air1.000) 0.735

Calculated gross heating value for separator gas at 14.696 psia and60°F, BTU/ft3 dry gas

1,295

Primary-separator-gas*/-separator-liquid* ratio, scf/bbl at 60°F 4,428

Primary-separator-gas/stock-tank-liquid ratio at 60°F, bbl at 60°F/bbl 1.352

Primary-separator-gas/wellstream ratio, Mscf/MMscf 801.66

Stock-tank-liquid/wellstream ratio, bbl/MMscf 133.9

*Primary separator gas and liquid collected at 300 psig and 62°F.

TABLE 6.6—MATERIAL-BALANCE CALCULATIONS FORGOOD OIL CO. WELL 7 GAS-CONDENSATE SAMPLE

Liquid Composition at Specified Pressures(mol%)

Component At 3,500 psig At 2,900 psig At 2,100 psig At 1,300 psig At 605 psig

CO2 0.18 0.18 0.18 0.15 0.08

N2 0.13 0.08 0.06 0.03 0.01

C1 13.18 45.04 32.22 19.69 11.77

C2 8.12 14.05 13.99 12.32 7.44

C3 12.59 9.67 11.25 11.66 9.31

i-C4 3.44 1.14 1.59 1.85 1.64

n-C4 5.21 4.82 6.12 7.35 7.17

i-C5 2.67 1.25 1.77 2.43 2.79

n-C5 5.74 2.16 3.48 4.62 5.50

C6 8.47 3.11 4.55 6.40 8.37

C7+ 40.27 18.51 24.79 33.50 45.91

Total 100.00 100.00 100.00 100.00 100.00

Mo, g#mol 96.6 54.1 64.3 78.2 95.6

MoC7, g#mol 168.8 160.1 152.1 149.9 150.3

o, g#cm3 0.3235 0.2642 0.1625 0.0892 0.0398


Fig. 6.2—Schematic of a multistage-separator test.

pst14.7 psiaTst60°F

where "g$

kseparator-gas gravity at Stage k. This relation is based

on the ideal gas law at standard conditions, where moles of gas are di-

rectly proportional with standard gas volume (vg379 scf/lbm mol).

Table 6.8 gives the composition of the first-stage-separator gas

at 50 psig and 75°F. The gross heating value, Hg , of this gas is calcu-

lated by Kay’s12 mixing rule and component heating values, Hi,

given in Table A-1.

Hg&N

i1

yi Hi . (6.18). . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Component liquid yields, Li, represent the liquid volumes of a

component or group of components that can theoretically be pro-

cessed from 1 Mscf of separator gas (gallons per million standard

cubic feet). Li can be calculated from

Li 19.73yi"Mi

i$ , (6.19). . . . . . . . . . . . . . . . . . . . . . . . . . .

where Mimolecular weight and i component liquid density

in lbm/ft3 at standard conditions (Table A-1). The C7 material in

separator gases is usually treated as normal heptane.

$ %&

6.4.1 Oil Samples. For an oil sample, the CCE experiment is used

to determine bubblepoint pressure, undersaturated-oil density, iso-

thermal oil compressibility, and two-phase volumetric behavior at

pressures below the bubblepoint. Table 6.9 presents data from an

example CCE experiment for a reservoir oil.

Fig. 6.3 illustrates the procedure for the CCE experiment. A blind

cell (i.e., a cell without a window) is filled with a known mass of reser-

voir fluid. Reservoir temperature is held constant during the experi-

ment. The sample initially is brought to a condition somewhat above

initial reservoir pressure, ensuring that the fluid is single phase. As the

pressure is lowered, oil volume expands and is recorded.

The fluid is agitated at each pressure by rotating the cell. This

avoids the phenomenon of supersaturation, or metastable equilibri-

um, where a mixture remains as a single phase even though it should

exist as two phases.13-15 Sometimes supersaturation occurs 50 to

100 psi below actual bubblepoint pressure. By agitating the mixture

at each new pressure, the condition of supersaturation is avoided, al-

lowing more accurate determination of the bubblepoint.

Just below the bubblepoint, the measured volume will increase

more rapidly because gas evolves from the oil, yielding a higher sys-

tem compressibility. The total volume, Vt, is recorded after the two-

phase mixture is brought to equilibrium. Pressure is lowered in steps

of 5 to 200 psi, where equilibrium is obtained at each pressure.

When the lowest pressure is reached, total volume is three to five

times larger than the original bubblepoint volume.

The recorded cell volumes are plotted vs. pressure, and the result-

ing curve should be similar to one of the curves in Fig. 6.4.16 For a

black oil (far from its critical temperature), the discontinuity in vol-

ume at the bubblepoint is sharp and the bubblepoint pressure and

volume are easily read from the intersection of the p-V trends in the

single- and two-phase regions.

Volatile oils do not exhibit the same clear discontinuity in volu-

metric behavior at the bubblepoint pressure. Instead, the p-V curve

is practically continuous in the region of the bubblepoint because

the undersaturated-oil compressibility is similar to the effective

two-phase compressibility. This makes determining the bubble-

point of volatile oils in a blind cell difficult. Instead, a windowed cell

TABLE 6.7—SEPARATOR TESTS (RESERVOIR-FLUID) OFGOOD OIL CO. WELL 4 OIL SAMPLE

SeparatorPressure

(psia)

SeparatorTemperature

(°F)GORb

(ft3/bbl)GORc

(ft3/bbl)

Stock-TankGravity(°API)

FVFd

(bbl/bbl)

SeparatorVolumeFactore

(bbl/bbl)

Flashed-GasSpecificGravity

50to0

75

75

715

41

737

41 40.5 1.481

1.031

1.007

0.840

1.338

100to0

75

75

637

91

676

92 40.7 1.474

1.062

1.007

0.786

1.363

200to0

75

75

542

177

602

178 40.4 1.483

1.112

1.007

0.732

1.329

300to0

75

75

478

245

549

246 40.1 1.495

1.148

1.007

0.704

1.286

aGauge.bIn cubic feet of gas at 60°F and 14.65 psi absolute per barrel of oil at indicated pressure and temperature.cIn cubic feet of gas at 60°F and 14.65 psi absolute per barrel of stock-tank oil at 60°F.dIn barrels of saturated oil at 2,620 psi gauge and 220°F per barrel of stock-tank oil at 60°F.eIn barrels of oil at indicated pressure and temperature per barrel of stock-tank oil at 60°F.

94 PHASE BEHAVIOR

TABLE 6.8—FIRST-STAGE SEPARATOR-GASCOMPOSITION AND GROSS HEATING VALUE FOR

GOOD OIL CO. WELL 4 OIL SAMPLE*

Component mol% gal/Mscf

H2S Nil

CO2 1.62

N2 0.30

C1 67.00

C2 16.04 4.265

C3 8.95 2.449

i-C4 1.29 0.420

n-C4 2.91 0.912

i-C5 0.53 0.193

n-C5 0.41 0.155

C6 0.44 0.178

C7+ 0.49 0.221

Total 100.00 8.793

Heating Value

Calculated gas gravity (air1.000) 0.840

Calculated gross heating value, BTU/ft3

dry gas at 14.65 psia and 60°F

1,405

*Collected at 50 psig and 75°F in the laboratory.

is used to observe visually the first bubble of gas and the liquid vol-umes below the bubblepoint.

Reported data from commercial laboratories usually include bub-blepoint pressure, pb; bubblepoint density, ob, or specific volume,vob(v 1# ); and isothermal compressibility of the undersaturatedoil, co , at pressures above the bubblepoint (Table 6.9). The table alsoshows the oil’s thermal expansion, indicated by a ratio of undersatu-rated-oil volume at a specific pressure and reservoir temperature tothe oil volume at the same pressure and a lower temperature.

Total volumes are reported relative to the bubblepoint volume.

VrtVt

Vob

. (6.20). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Traditionally, isothermal compressibility data are reported for pres-sure intervals above the bubblepoint. In fact, the undersaturated-oilcompressibility varies continuously with pressure, and, becauseVt Vo (Vrt Vro) for p) pb, oil compressibility can be ex-pressed as

c 1Vrt

"+Vrt

+p $T

1Vro

"+Vro

+p $T

; p) pb . (6.21). . . . . . . . .

Fig. 6.3—Schematic of a CCE experiment for an oil and a gascondensate.

TABLE 6.9—CCE DATA (RESERVOIR-FLUID)FOR GOOD OIL CO. WELL 4 OIL SAMPLE

Saturation (bubblepoint) pressure*, psig 2,620

Specific volume at saturationpressure*, ft3/lbm

0.02441

Thermal expansion of undersaturatedoil at 5,000 psiV at 220°F/V at 76°F

1.08790

Compressibility of saturated oil atreservoir temperatureFrom 5,000 to 4,000 psi, vol/vol-psiFrom 4,000 to 3,000 psi, vol/vol-psiFrom 3,000 to 2,620 psi, vol/vol-psi

13.48x10–6

15.88x10–6

18.75x10–6

Pressure/Volume Relations*

Pressure(psig)

Relative volume(L)† Y function‡

5,000 0.9639

4,500 0.9703

4,000 0.9771

3,500 0.9846

3,000 0.9929

2,900 0.9946

2,800 0.9964

2,700 0.9983

2,620** 1.0000

2,605 1.0022 2.574

2,591 1.0041 2.688

2,516 1.0154 2.673

2,401 1.0350 2.593

2,253 1.0645 2.510

2,090 1.1040 2.422

1,897 1.1633 2.316

1,698 1.2426 2.219

1,477 1.3618 2.118

1,292 1.5012 2.028

1,040 1.7802 1.920

830 2.1623 1.823

640 2.7513 1.727

472 3.7226 1.621

* At 220°F.** Saturation pressure.1 Relative volumeV/Vsat in barrels at indicated pressure per barrel at saturation

pressure.‡ Y function( psat p)/(pabs)(V/Vsat 1).

The Vrt function at undersaturated conditions may be fit with a se-

cond!degree polynomial, resulting in an explicit relation for under-

saturated-oil compressibility (see Chap. 3).

Total volumes below the bubblepoint can be correlated by the Y

function,16,17 defined as

Ypb p

p(Vrt 1)

pb p

p!"Vt#Vb$ 1%

, (6.22). . . . . . . . . . . . . .

where p and pb are given in absolute pressure units. As Fig. 6.5

shows, Y vs. pressure should plot as a straight line and the linear

trend can be used to smooth Vrt data at pressures below the bubble-

point. Standing16 and Clark17 discuss other smoothing techniques

and corrections that may be necessary when reservoir conditions

and laboratory PVT conditions are not the same.

6.4.2 Gas-Condensate Samples. The CCE data for a gas condensate

usually include total relative volume, Vrt, defined as the volume of

gas or of gas-plus-oil mixture divided by the dewpoint volume. Z fac-


Fig. 6.4—Volume vs. pressure for an oil during a DLE test (after Standing16).

at

29

0 p

sia

tors are reported at pressures greater than and equal to the dewpoint

pressure. Table 6.10 gives these data for a gas-condensate example.

Reciprocal wet-gas FVF, bgw, is reported at dewpoint and initial

reservoir pressures, where these values represent the gas equivalent

or wet-gas volume at standard conditions produced from 1 bbl of

reservoir gas volume.

bgw "5.615, 10 3$ Tsc

psc

p

ZT 0.198

p

ZT, (6.23). . . . . . . .

with bgw in Mscf/bbl, p in psia, and T in °R.

Most CCE experiments are conducted in a visual cell for gas con-

densates, and relative oil (condensate) volumes, Vro, are reported at

pressures below the dewpoint. Vro normally is defined as the oil vol-

ume divided by the total volume of gas and oil, although some re-

ports define it as the oil volume divided by the dewpoint volume.

' ()) *+ %&

The DLE experiment is designed to approximate the depletion pro-

cess of an oil reservoir18 and thereby provide suitable PVT data to

calculate reservoir performance.16,19-21 Fig. 6.6 illustrates the labo-

ratory procedure of a DLE experiment. Figs. 6.7A through 6.7C

and Table 6.11 give DLE data for an oil sample.

A blind cell is filled with an oil sample, which is brought to a

single phase at reservoir temperature. Pressure is decreased until the

fluid reaches its bubblepoint, where the oil volume, Vob, is recorded.

Because the initial mass of the sample is known, bubblepoint densi-

ty, ob, can be calculated.

The pressure is decreased below the bubblepoint, and the cell is

agitated until equilibrium is reached. All gas is removed at constant

pressure. Then, the volume, Vg; moles, ng; and specific gravity,

g, of the removed gas are measured. The remaining oil volume, Vo,

is also recorded. This procedure is repeated 10 to 15 times at de-

creasing pressures and finally at atmospheric pressure. Residual-oil

volume, Vor, and specific gravity, or , are measured at 60°F.

Other properties are calculated on the basis of measured data

(Vg , Vo , ng , g , Vor, and or), including differential solution

gas/oil ratio, Rsd ; differential oil FVF, Bod ; oil density, o; and gas

Z factor, Z. For Stage k, these properties can be determined from

96 PHASE BEHAVIOR

Fig. 6.5—PVT relation and plot of Y function for an oil sample at pressures below the bubblepoint.

BubblepointTemperature

°5F80

163185205

Pressurepsia

1,9702,4372,5202,615

Volumecm3

82.3086.8887.9289.05

"Rsd$k

&kj1

379"ng$

j

Vor

, (6.24). . . . . . . . . . . . . . . . . . . . . . . .

"Bod$k"Vo$k

Vor

, (6.25). . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

" o$k

Vor(62.4or)&k

j1

"28.97#5.615$"ng$

j"g$

j

"Vo$k

350or&k

j1

0.0764"Rsd$j"g$

j

5.615"Bod$k

,

(6.26). . . . . . . . . . . . . . . . . .

and (Z)k "1#RT$"pVg#ng$

k, (6.27). . . . . . . . . . . . . . . . . .

with Vor and Vo in bbl, Rsd in scf/bbl, Bod in bbl/bbl, Vg in ft3, pin psia, ng in lbm mol, o in lbm/ft3, and T in °R. Note that the sub-script j1 indicates the final DLE stage at atmospheric pressure andreservoir temperature. Reported oil densities are actually calculatedby material balance, not measured directly.

6.5.1 Converting From Differential to Stock-Tank Basis. Perhapsthe most important step in the application of oil PVT data for reservoircalculations is conversion of the differential solution gas/oil ratio,Rsd, and oil FVF, Bod, to a stock-tank-oil basis.16,20 For engineering

calculations, volume factors, Rs and Bo, are used to relate reservoir-

oil volumes, Vo, to produced surface volumes, Vg and Vo; i.e.,

RsVg

Vo

(6.28). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

and BoVo

Vo

. (6.29). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Differential properties Rsd and Bod reported in the DLE report are

relative to residual-oil volume (i.e., the oil volume at the end of the

DLE experiment, corrected from reservoir to standard temperature).

Rsd

Vg

Vor

(6.30). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

and Bod Vo

Vor

. (6.31). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

The equations commonly used to convert differential volume fac-

tors to a stock-tank basis are

Rs Rsb "Rsdb Rsd$"Bob

Bodb

$ (6.32). . . . . . . . . . . . . . . . . .

and Bo Bod"Bob

Bodb

$ , (6.33). . . . . . . . . . . . . . . . . . . . . . . . . . .

where Bobbubblepoint-oil FVF, Rsbsolution gas/oil ratio

from a multistage-separator flash, and Rsdb and Bodbdifferential

volume factors at the bubblepoint pressure. The term ( Bob#Bodb),


TABLE 6.10—CCE DATA FOR GOOD OIL CO.WELL 7 GAS-CONDENSATE SAMPLE

Pressure(psig) Relative volume

Deviation FactorZ

6,000 0.8808 1.144

5,713* 0.8948 1.107**

5,300 0.9158 1.051

5,000 0.9317 1.009

4,800 0.9434 0.981

4,600 0.9559 0.953

4,400 0.9690 0.924

4,300 0.9758 0.909

4,200 0.9832 0.895

4,100 0.9914 0.881

4,000† 1.0000 0.867‡

3,905 1.0089

3,800 1.0194

3,710 1.0299

3,500 1.0559

3,300 1.0878

3,000 1.1496

2,705 1.2430

2,205 1.5246

1,605 2.1035

1,010 3.5665

Pressure/volume relations of reservoir fluid at 186°F.* Reservoir pressure.

** Gas FVF1.591 Mscf/bbl.†Dewpoint pressure.‡Gas FVF1.424 Mscf/bbl.

representing the volume ratio,Vor#Vo , is used to eliminate the resid-

ual-oil volume, Vor, from the Rsd and Bod data. Note that the conver-

sion from differential to “flash” data depends on the separator

conditions because Bob and Rsb depend on separator conditions.

Although, the conversions given by Eqs. 6.32 and 6.33 typically

are used, they are only approximate. The preferred method, as origi-

nally suggested by Dodson et al.,22 requires that some equilibrium

oil be taken at each stage of the DLE experiment and flashed through

a multistage separator to give the volume ratios, Rs and Bo. This lab-

oratory procedure is costly and time-consuming and is seldom used.

However, the method is readily incorporated into an equation-of-

state (EOS) -based PVT program.

(

The CVD experiment is designed to provide volumetric and com-

positional data for gas-condensate and volatile-oil reservoirs pro-

ducing by pressure depletion. Fig. 6.8 shows the stepwise procedure

of a CVD experiment schematically, and Figs. 6.9A through 6.9D

and Table 6.12 give CVD data for an example gas-condensate fluid.

The CVD experiment provides data that can be used directly by

the reservoir engineer, including (1) a reservoir material balance

that gives average reservoir pressure vs. recovery of total well-

stream (wet-gas recovery), sales gas, condensate, and natural gas

liquids; (2) produced-wellstream composition and surface products

vs. reservoir pressure; and (3) average oil saturation in the reservoir

(liquid dropout and revaporization) that occurs during pressure

depletion. For many gas-condensate reservoirs, the recoveries and

oil saturation vs. pressure data from the CVD analysis closely

approximate actual field performance for reservoirs producing by

pressure depletion. When other recovery mechanisms, such as wa-

terdrive and gas cycling, are considered, the basic data required for

reservoir engineering are still taken mainly from a CVD report. This

section provides a description of the data provided in a standard

Fig. 6.6—Schematic of DLE experiment.

CVD analysis, ways to check the data for consistency,23-25 and howto extract reservoir-engineering quantities from the data.23,26

Initially, the dewpoint, pd, or bubblepoint pressure, pb, of the res-ervoir sample is established visually and the cell volume, Vcell, atsaturated conditions is recorded. The pressure is then reduced by300 to 800 psi and usually by smaller amounts (50 to 250 psi) justbelow the saturation pressure of more-volatile systems. The cell isagitated until equilibrium is achieved, and volumes Vo and Vg aremeasured. At constant pressure, sufficient gas, Vg, is removed toreturn the cell volume to the original saturated volume.

In the laboratory, the removed gas (wellstream) is brought to at-mospheric conditions, where the amount of surface gas and conden-sate are measured. Surface compositions yg and xo of the producedsurface volumes from the reservoir gas are measured, as are the vol-umes Vo and Vg , densities o and g and oil molecular weightMo . From these quantities, we can calculate the moles of gas re-moved, ng.

ngVo o

Mo

Vg

379. (6.34). . . . . . . . . . . . . . . . . . . . . . . .

These data are reported as cumulative wellstream produced, np, rel-ative to the initial moles n.

"np

n$

k1n&kj1

(ng)j , (6.35). . . . . . . . . . . . . . . . . . . . . . . . .

where j1 corresponds to saturation pressure and (ng)1 0. Theinitial amount (in moles) of the saturated fluid is known when the cellis charged. The quantity np#n is usually reported as cumulative wetgas produced in MMscf/MMscf, which is equivalent to mol/mol.

Surface compositions yg and xo of the removed reservoir gas andproperties of the removed gas are not reported directly in the labora-tory report but are recombined to yield the equilibrium gas (well-stream) composition, yi, which also represents the equilibrium gasremaining in the cell. The C7 molecular weight of the wellstream,MgC7, is backcalculated from measured specific gravity( w g) and reservoir-gas composition, y. C7 specific gravity ofthe produced gas, gC7 is also reported, but this value is calculatedfrom a correlation.

Knowing the cumulative moles removed and its volume occupiedas a single-phase gas at the removal pressure, we can calculate theequilibrium gas Z factor from

ZpVg

ng RT. (6.36). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

A “two-phase” Z factor is also reported that is calculated assum-ing that the gas-condensate reservoir depletes according to the ma-terial balance for a dry gas and that the initial condition of the reser-voir is at dewpoint pressure.

98 PHASE BEHAVIOR

Fig. 6.7A—DLE data for an oil sample from Good Oil Co. Well 4; differential solution gas/oilratio, Rsd .

p

Z2

"pd

Zd

$"1 Gpw

Gw

$, (6.37). . . . . . . . . . . . . . . . . . . . . . . .

where Gpwcumulative wellstream (wet gas) produced and

Gwinitial wet gas in place. As defined in Eq. 6.37, the term Gpw#Gw

equals np#n reported in the CVD report. From Eq. 6.37, the only un-

known at a given pressure is Z2, and the two-phase Z factor is then giv-

en by

Z2p

"pd#Zd$!1 "np#n$%

. (6.38). . . . . . . . . . . . . . . . . . . . .

Theoretical liquid yields, Li, are also reported for C3 through

C5 groups in the produced wellstreams at each pressure-depletion

stage. These values are calculated with

Li 19.73yi"Mi

i$ (6.39). . . . . . . . . . . . . . . . . . . . . . . . . . . . .

and by summing the yields of components in the particular “plus”

group. For example, the liquid yield of C5 material at CVD Stage

k is given by

"LC5$

k

&C7

ji C5

"Lj$

k 19.73 &C7

ji C5

"yj$

k"Mj

j$ . (6.40). . . . .

Table 6.13 gives various calculated cumulative recoveries basedon the reservoir initially being at its dewpoint. The basis for the cal-culations is 1 MMscf of dewpoint wet gas in place, Gw; the corre-sponding initial moles in place at dewpoint pressure is given by

n Gwvg

1, 106 scf

379 scf#lbm mol 2, 638 lbm mol. (6.41). . . . . . . . .

The first row of recoveries (wellstream) simply represents thecumulative moles produced, np#n, expressed as wet-gas volumes,Gpw, in Mscf.

Gpw nvg"np

n$

(2, 638 lbm mol)"379 scf#lbm mol$

, "1, 103 Mscf#scf$"np

n$

1, 103 "np

n$. (6.42). . . . . . . . . . . . . . . . . . . . . . . . .

Recoveries in Rows 2 through 4 (Normal Temperature Separa-tion, Total Plant Products in Primary-Separator Gas, and Total PlantProducts in Second-Stage-Separator Gas) refer to production whenthe reservoir is produced through a three-stage separator. Fig. 6.10


Fig. 6.7B—DLE data for an oil sample from Good Oil Co. Well 4; differential oil FVF (relativevolume), Bod .

illustrates the process schematically. The calculated recoveries are

based on multistage-separator calculations that use low-pressure K

values and a set of separator conditions chosen arbitrarily or speci-

fied when the PVT study is requested.

6.6.1 Recoveries: “Normal Temperature Separation.” Column

1: Initial in Place. In Column 1, Row 2a the stock-tank oil in solu-

tion in the initial dewpoint fluid (N135.7 STB) is calculated by

flashing 1 MMscf of the original dewpoint fluid, Gw, through a

multistage separator.

Rows 2b through 2d give the volumes of separator gas at each

stage of a three-stage flash of the initial dewpoint fluid: 757.87,

96.68, and 24.23 Mscf, respectively. The mole fraction of well-

stream resulting as a surface gas Fgg is given by

FggGd

Gw

"757.87 96.68 24.23 Mscf#lbm mol$

, "1, 103 scf#Mscf$#"379 scf#lbm mol$

0.8788 lbm mol#lbm mol, (6.43). . . . . . . . . . . . . . .

where Gdtotal separator “dry” gas and the corresponding mole

fraction of stock-tank oil is 0.1212 mol/mol. Fgg is used to calculate

dry-gas FVF (see Eq. 3.41). For the dewpoint pressure, this gives

Bgd

Bgw

Fgg

"psc#Tsc

$"ZT#p$Fgg

"14.7#520$-[0.867(186 460)]#4015.

0.8788

4.487, 10 3 ft3#scf . (6.44). . . . . . . . . . . . . . . . . . .

The producing GOR of the dewpoint mixture for the specified

separator conditions can be calculated as

RpGN !"757.87 96.68 24.23 Mscf#lbm mol$

, "1, 103 scf#Mscf$%#135.7 STB#lbm mol

6, 476 scf#STB. (6.45). . . . . . . . . . . . . . . . . . . . . . . .

The dewpoint solution oil/gas ratio, rsd, is simply the inverse of Rp.

rsd rp 1Rp

1.544, 10 4 STB#scf 154.4 STB#MMscf.

(6.46). . . . . . . . . . . . . . .

Note that specific gravities of stock-tank oil and separator gases arenot reported for the separator calculations.

100 PHASE BEHAVIOR

Fig. 6.7C—DLE data for an oil sample from Good Oil Co. Well 4; oil viscosity, "o .

Column 2 and Higher. On the basis of 1 MMscf of initial dew-

point fluid, Rows 2a through 2d give cumulative volumes of separa-

tor products at each depletion pressure ( Np, Gp1, Gp2, and Gp3).

The producing GOR of the wellstream produced during a depletion

stage is given by

"Rp$

k"Gp1 Gp2 Gp3

$k "Gp1 Gp2 Gp3

$k 1

"Np$

k "Np

$k 1

.

(6.47). . . . . . . . . . . . . . . . . .

For 2,100 psig, this gives

Rp -[(301.57 20.75 5.61) (124.78 12.09 3.16)]

, "1, 103$.#(24.0 15.4)

21, 850 scf#STB. (6.48). . . . . . . . . . . . . . . . . . . . . . . .

In terms of the solution oil/gas ratio,

rs rp 1Rp

121, 580 scf#STB

4.58, 10 5 STB#scf

45.8 STB#scf . (6.49). . . . . . . . . . . . . . . . . . . . . . . . . .

At a given pressure, the mole fraction of the removed CVD gaswellstream that becomes dry separator gas is given by

"Fgg$

k"Gp1 Gp2 Gp3

$k "Gp1 Gp2 Gp3

$k 1

Gw!"np#n$k "np#n$k 1

% .

(6.50). . . . . . . . . . . . . . . . . .

For p2,100 psig, this gives

Fgg [(301.57 20.75 5.61) (124.78 12.09

3.16)]"1, 103$#"1, 106$(0.35096 0.15438)

0.9558 . (6.51). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

The dry-gas FVF at 2,100 psig is

Bgd"14.7#520$!0.762(186 460)#2, 115%

0.9558

6.884, 10 3 ft3#scf . (6.52). . . . . . . . . . . . . . . . . . .

In summary, the information provided in the rows labeled NormalTemperature Separation gives estimates of the condensate andsales-gas recoveries assuming a multistage surface separation. Forexample, at an abandonment pressure of 605 psig, the condensaterecovery is 35.1 STB of the 135.7 STB initially in place (in solutionin the dewpoint mixture), or 26% condensate recovery. Dry-gas re-covery is (685.0237.7910.40)733.21 Mscf of the 878.78


TABLE 6.11—DLE DATA FOR GOOD OIL CO. WELL 4 OIL SAMPLE

Differential Vaporization

Pressure(psig)

SolutionGOR

(scf/bbl*)

RelativeOil Volume(RB/bbl*)

RelativeTotal Volume

(RB/bbl*)

OilDensity(g/cm3)

DeviationFactor

ZGas FVF(RB/bbl*)

IncrementalGas Gravity

2,620 854 1.600 1.600 0.6562

2,350 763 1.554 1.665 0.6655 0.846 0.00685 0.825

2,100 684 1.515 1.748 0.6731 0.851 0.00771 0.818

1.850 612 1.479 1.859 0.6808 0.859 0.00882 0.797

1,600 544 1.445 2.016 0.6889 0.872 0.01034 0.791

1,350 479 1.412 2.244 0.6969 0.887 0.01245 0.794

1,110 416 1.382 2.593 0.7044 0.903 0.01552 0.809

850 354 1.351 3.169 0.7121 0.922 0.02042 0.831

600 292 1.320 4.254 0.7198 0.941 0.02931 0.881

350 223 1.283 6.975 0.7291 0.965 0.05065 0.988

159 157 1.244 14.693 0.7382 0.984 0.10834 1.213

0 0 1.075 0.7892 2.039

1.000**

DLE Viscosity Data at 220°F

Pressure(psig)

Oil Viscosity(cp)

Calculated GasViscosity

(cp)

5,000 0.450

4,500 0.434

4,000 0.418

3,500 0.401

3,000 0.385

2,800 0.379

2,620 0.373

2,350 0.396 0.0191

2,100 0.417 0.0180

1,850 0.442 0.0169

1,600 0.469 0.0160

1,350 0.502 0.0151

1,100 0.542 0.0143

850 0.592 0.0135

600 0.654 0.0126

350 0.783 0.0121

159 0.855 0.0114

0 1.286 0.0093

Gravity of residual oil35.1°API at 60°F.

*Barrels of residual oil.

**At 60°F.

Mscf dry gas originally in place, or 83.4%. These recoveries can be

compared with the reported wet-gas (or molar) recovery of 76.787%

at 605 psig. In addition to recoveries, the calculated results in this

section can be used to calculate solution oil/gas ratio, rs, and dry-gas

FVF, Bgd, for modified black-oil applications.

6.6.2 Recovery: Plant Products. Rows 3 through 5 consider

theoretical liquid recoveries for propane, butanes, and pentanes-

plus assuming 100% plant efficiency. Recoveries in Rows 3 and 4

are for the calculated separator gases from Stages 1 and 2 of the

three-stage surface separation. Recoveries in Row 5 are for the pro-

duced wellstreams from the CVD experiment and represent the ab-

solute maximum liquid recoveries that can be expected if the reser-

voir is produced by pressure depletion. Fig. 6.10 illustrates the

recovery calculations schematically. Liquid volumes (in gal/MMscf

of initial dewpoint fluid) at CVD Stage k are calculated from

(Li)k 19, 730"Mi

i$!&k

j1

"ng

n $j

"yi$j%, (6.53). . . . . . . . .

Fig. 6.8—Schematic of CVD experiment.

102 PHASE BEHAVIOR

Fig. 6.9A—CVD data for gas-condensate sample from Good Oil Co. Well 7; liquid-dropout curve, Vro .

where j 1 represents the dewpoint, yicompositions of well-stream entering the gas plant at various stages of depletion,Micomponent molecular weights, and i liquid component

densities in lbm/ft3 at standard conditions (Table A-1).Calculated liquid recoveries below the dewpoint use the moles of

wellstream produced ( ng#n) and the compositions yi from the sep-arator gas (Rows 3 and 4) or wellstream (Row 5) entering the plant.Column 1 (Initial in Place) gives the total recoveries assuming thatthe entire initial dewpoint fluid is taken to the surface and processed[i.e., k 1 and (ng#n)1 1 in Eq. 6.53].

Note that cumulative recovery of propanes from the first-stageseparator during depletion (1,276 gal) is larger than the liquid pro-pane produced in the first-stage-separator gas of the original dew-point mixture (1,198 gal). This means that the stock-tank oil fromthe separation of original dewpoint mixture contains more propanethan the cumulative stock-tank-oil volumes produced by depletionand three-stage separation.

The results given in Rows 3 and 4 cannot be calculated from re-ported data because surface separator compositions from the three-stage separation are not provided in the report. The results in Row5 can be checked. As an example, consider the C3 recoveries for theinitial-in-place fluid at 2,100 psig.

"LC3$

pd

19, 730 "44.09#31.66$! (1)(0.0837)%

2, 299 gal#MMscf (6.54a). . . . . . . . . . . . . . . . . . . .

and "LC3$

2100

19, 730 "44.09#31.66$ [0.0825(0.05374)

0.0810(0.15438 0.05374)

0.0757(0.35096 0.15438)]

754 gal#MMscf. (6.54b). . . . . . . . . . . . . . . .

For the C5 recoveries at the dewpoint,

"LC5$

pd

19, 730[(72.15#38.96) (0.0091)

(72.15#39.36) (0.0152)

(86.17#41.43) (0.0179) (143#49.6) (0.0685)]

5, 513 gal#MMscf . (6.55). . . . . . . . . . . . . . . . .

6.6.3 Correcting Recoveries for Initial Pressure Greater Than

Dewpoint Pressure. All recoveries given in Table 6.13 assume that

the reservoir pressure is initially at dewpoint. This assumption is

made because initial reservoir pressure is not always known with

certainty when PVT calculations are made. However, adjusting re-

ported recoveries is straightforward when initial pressure is greater

than dewpoint pressure. With QTable as recoveries given in Columns

2 and higher in Table 6.13, Qd as hydrocarbons in place in Column


Fig. 6.9B—CVD data for gas-condensate sample from Good Oil Co. Well 7; equilibrium gascompositions, yi .

Dew

po

int

Pre

ssu

re

1 at dewpoint pressure, and Q as actual cumulative recoveries based

on hydrocarbons in place at the initial pressure,

Q Qd!"p#Z$i"p#Z$d

"p#Z$"p#Z$

d

%; p/ pd , (6.56). . . . . . . . . . . .

Q QTable Qd ; p* pd , (6.57). . . . . . . . . . . . . . . . . . .

and Qd Qd!(p#Z)i

(p#Z)d

1%, (6.58). . . . . . . . . . . . . . . . . . . .

where Qdadditional recovery from initial to dewpoint pres-

sure.

For the example report,

Qd !"5, 728#1.107$"4, 015#0.867$

1%Qd

0.1173Qd , (6.59). . . . . . . . . . . . . . . . . . . . . . . . . . .

recalling that moles of material at dewpoint is 2,638 lbm mol, moles

of material at initial pressure of 5,728 psig is n2, 638(1 0.1173)

2, 947 lbm mol, and the basis of calculations is Gw 1.173

MMscf of wet gas in place at initial pressure of 5,728 psia.

The cumulative wellstream produced at the dewpoint pressure of

4,000 psig is 0.1173(1, 000) 117.3 Mscf. Recovery at 3,500 psig

is 117.3 53.74 171.0 Mscf. Likewise, wet-gas recovery

should be increased by 117.3 Mscf for all depletion pressures in the

CVD table.

For stock-tank-oil recovery, Qd 135.7 STB, so Qd 15.9

STB. Stock-tank-oil recovery at 4,000 psig is 15.9 0 15.9

STB; at 3,500 psig the recovery should be 15.9 6.4 22.3 STB,

and so on.

On the basis of 1 MMscf wet gas at the dewpoint or 1.1173 MMscf

at initial reservoir pressure, the laboratory hydrocarbon pore vol-

ume (HCPV), VpHClab, is the same.

VpHClab "GwBgw$

d

"1, 106$-"14.7520$!0.867(186 460)

4, 015%.

3, 943 ft3

"Gw Bgw$

i

1.1173, 106-"14.7520$!1.107(186 460)

5728%.

3, 943 ft3 . (6.60). . . . . . . . . . . . . . . . . . . . . . . . . .

The actual HCPV of a reservoir is much larger than VpHClab, and the

conversion to obtain recoveries for the actual HCPV is simply

104 PHASE BEHAVIOR

Fig. 6.9C—CVD data for gas-condensate sample from Good Oil Co. Well 7; equilibrium gas Zfactor, Zg .

Qactual Qlab

VpHCactual

VpHClab

, (6.61). . . . . . . . . . . . . . . . . . . . . . .

where Qlablaboratory value given by Eqs. 6.55 and 6.57. As an ex-

ample, suppose geological data indicate a HCPV of 625,000 bbl

(82.45 acre-ft), or 3.509,106 ft3. Then, original wet gas in place is

Gw 1.1173, 106 3.509, 106

3, 943

994.3 MMscf (6.62). . . . . . . . . . . . . . . . . . . . . . . . . . .

and condensate in solution at initial pressure is given by

N 135.7(1.1173) 3.509, 106

3, 943

134, 900 STB . (6.63). . . . . . . . . . . . . . . . . . . . . . . . . .

6.6.4 Liquid-Dropout Curve. Table 6.11 and Figs. 6.9A through

6.9D show relative oil volumes, Vro, measured in the example CVD

experiment. Vro is defined as the volume of oil, Vo, at a given pres-

sure divided by the original saturation volume, Vs. This relative vol-

ume is an excellent measure of the average reservoir-oil saturation

(normalized) that will develop during depletion of a gas-condensate

reservoir. Correcting for water saturation, Sw, the reservoir-oil satu-

ration can be calculated from Vro with

So (1 Sw)Vro . (6.64). . . . . . . . . . . . . . . . . . . . . . . . . . .

For most gas condensates, Vro shows a maximum near 2,000 to2,500 psia. Cho et al.27 give a correlation for maximum liquid drop-

out as a function of temperature and C7 mole percent in the dew-point mixture.

"Vro$max 93.404 4.799 zC7

19.73 ln T , (6.65). . . . . .

with zC7 in mole percent and T in °F. The correlation predicts

(Vro)max23.2% for the example condensate fluid compared with24% measured experimentally (at 2,100 psig). Fig. 6.11 shows val-

ues of (Vro)max vs. T and zC7from Eq. 6.65.Considerable attention usually is given to matching the liquid-

dropout curve when an EOS is used. Some gas condensates have-what is referred to as a “tail,” where liquid drops out very slowly

(sometimes for several thousand psi below the dewpoint) before fi-nally increasing toward a maximum. Matching this behavior with

an EOS can prove difficult, and the question is whether matching thetail is really necessary (see Appendix C).

What really matters for reservoir calculations of a gas-condensatefluid is how much original stock-tank condensate is “lost” because

of retrograde condensation in the reservoir. The shape and magni-


Fig. 6.9D—CVD data for gas-condensate sample from Good Oil Co. Well 7; wet-gas materialbalance.

tude of liquid dropout reflects the change in producing oil/gas ratio,

rp0 rs. A tail on a liquid-dropout curve implies that the producing

wellstream is becoming only slightly leaner (i.e., rs is decreasing

only slightly). The cumulative condensate recovery is given by

Np 1Gp

0

rs dGp , (6.66). . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

where Gpcumulative dry gas produced. Cumulative condensate

production is readily evaluated from a plot of rs vs. Gp.

One of the most important checks of an EOS characterization for

any gas condensate, particularly one with a tail, is Np calculated

from CVD data vs. Np calculated from the EOS characterization. It

is alarming how much the surface condensate recovery can be un-

derestimated if the tail is not matched properly. We do not recom-

mend matching the dewpoint exactly with a liquid-dropout curve

that is severely overpredicted in the region where measured results

indicate little dropout. If the EOS characterization cannot be modi-

fied to honor the tail of liquid-dropout curve, it is preferable to

underpredict the measured dewpoint pressure and match only the

higher liquid-dropout volumes.

In summary, oil relative volume, Vro, is not important per se; how-

ever, the effect of liquid dropout on surface condensate production

should be emphasized. In fact, the effect of shape and magnitude of

liquid dropout on fluid flow in the reservoir is negligible, and any

EOS match will probably have the same effect on fluid flow from the

reservoir into the wellbore (i.e., inflow performance).

6.6.5 Consistency Check of CVD Data. Reudelhuber and Hinds24

give a detailed procedure for checking CVD data consistency that

involves a material-balance check on components and phases and

yields oil compositions, density, molecular weight, and MC7. To-

gether with reported data, these calculated properties allow K values

to be calculated and checked for consistency with the Hoffman et

al.10 method.11,28 Whitson and Torp’s23 material-balance equations

are summarized later. Similar equations can also be derived for a

DLE experiment when equilibrium gas compositions and oil rela-

tive volumes are reported. Reported CVD data include temperature,

T ; dewpoint pressure, pd, or bubblepoint pressure, pb; dewpoint Z

factor, Zd, or bubblepoint-oil density, ob . Additional data at each

Depletion Stage k include oil relative volume, Vro; initial fraction

of cumulative moles produced, np#n; gas Z factor (not the two-

phase Z factor), Z; equilibrium gas composition, yi; and equilibrium

gas (wellstream) C7 molecular weight, Mg C7.

The equilibrium gas density, g; molecular weight, Mg; and well-

stream gravity, w Mg#Mair , are readily calculated at each

106 PHASE BEHAVIOR

TABLE 6.12—CVD DATA FOR GOOD OIL CO. WELL 7 GAS-CONDENSATE SAMPLE 2*

Reservoir Pressure, psig

Component, mol% 5,713** 4,000† 3,500 2,900 2,100 1,300 605 0‡

CO2 0.18 0.18 0.18 0.18 0.18 0.19 0.21

N2 0.13 0.13 0.13 0.14 0.15 0.15 0.14

C1 61.72 61.72 63.10 65.21 69.79 70.77 66.59

C2 14.10 14.10 14.27 14.10 14.12 14.63 16.06

C3 8.37 8.37 8.26 8.10 7.57 7.73 9.11

i-C4 0.98 0.98 0.91 0.95 0.81 0.79 1.01

n-C4 3.45 3.45 3.40 3.16 2.71 2.59 3.31

i-C5 0.91 0.91 0.86 0.84 0.67 0.55 0.68

n-C5 1.52 1.52 1.40 1.39 0.97 0.81 1.02

C7 1.79 1.79 1.60 1.52 1.03 0.73 0.80

C7+ 6.85 6.85 5.90 4.41 2.00 1.06 1.07

Total 100.00 100.00 100.00 100.00 100.00 100.00 100.00

Properties

C7+ molecular weight 143 143 138 128 116 111 110

C7+ specific gravity 0.795 0.795 0.790 0.780 0.767 0.762 0.761

Equilibrium gas deviation factor, Z 1.107 0.867 0.799 0.748 0.762 0.819 0.902

Two-phase deviation factor, Z 1.107 0.867 0.802 0.744 0.704 0.671 0.576

Wellstream produced, cumulative% of initial

0.000 5.374 15.438 35.096 57.695 76.787 93.515

From smooth compositions

C3+, gal/Mscf 9.218 9.218 8.476 7.174 5.171 4.490 5.307

C4+, gal/Mscf 6.922 6.922 6.224 4.980 3.095 2.370 2.808

C5+, gal/Mscf 5.519 5.519 4.876 3.692 1.978 1.294 1.437

Retrograde Condensation During Gas Depletion

Retrograde liquid volume,

% hydrocarbon pore space

0.0 3.3 19.4 23.9 22.5 18.1 12.6

*Study conducted at 186°F.

** Original reservoir pressure.

† Dewpoint pressure.

‡0-psig residual-liquid properties: 47.5°API oil gravity at 60°; 0.7897 specific gravity at 60/60°F; and molecular weight of 140.

Depletion Stage k [and at the dewpoint ( k 1) for a gas-conden-sate sample] from

"Mg$

k&

N

i1

(yi)k Mi , (6.67). . . . . . . . . . . . . . . . . . . . . . . . . .

" g$

k

p "Mg$

k

(Z)k RT

, (6.68). . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

and "g$

k "w

$k"Mg$

k

28.97. (6.69). . . . . . . . . . . . . . . . . . . .

On a basis of 1 mol initial dewpoint fluid ( n 1), the cell vol-ume is

VcellZd RT

pd(6.70). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

for a gas condensate and

VcellMob

ob(6.71). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

for a volatile oil. Oil and gas volumes, respectively, at Stage k are

(Vo)k Vcell (Vro)k

and "Vg$

k Vcell!1 (Vro)k

% . (6.72). . . . . . . . . . . . . . . . . . . .

Moles and mass of the total material remaining in the cell at Stage kare given by

(nt)k 1 "np

n$

k

,

"ng$

k"p$

k"Vg$

k

(Z)k RT,

and (no)k (nt)k "ng$

k, (6.73). . . . . . . . . . . . . . . . . . . . . . . .

and moles and mass of the individual phases remaining in the cell at

Stage k are given by

(mt)k Ms &k

j2

"ng

n $j

"Mg$

j,

"mg$

k "ng

$k"Mg$

k,

and (mo)k (mt)k "mg$

k. (6.74). . . . . . . . . . . . . . . . . . . . . .

In Eqs. 6.73 and 6.74,

"ng

n $j

"np

n$

j

"np

n$

j 1

, (6.75). . . . . . . . . . . . . . . . . . . .

Mssaturated-fluid molecular weight, and (np#n)1 0.

Densities and molecular weights of the oil phase are calculated from


TABLE 6.13—CALCULATED RECOVERIES* FROM CVD REPORTFOR GOOD OIL CO. WELL 7 GAS-CONDENSATE SAMPLE

Reservoir Pressure (psig)

Initial in Place 4,000** 3,500 2,900 2,100 1,300 605 0

Wellstream, Mscf 1,000 0 53.74 154.38 350.96 576.95 767.87 935.15

Normal temperature separation†

Stock-tank liquid, bbl 135.7 0 6.4 15.4 24.0 29.7 35.1

Primary-separator gas, Mscf 757.87 0 41.95 124.78 301.57 512.32 658.02

Second-stage gas, Mscf 96.68 0 4.74 12.09 20.75 27.95 37.79

Stock-tank gas, Mscf 24.23 0 1.21 3.16 5.61 7.71 10.4

Total plant products in primary separator‡

Propane, gal 1,198 0 67 204 513 910 1,276

Butanes, gal 410 0 23 72 190 346 491

Pentanes, gal 180 0 10 31 81 144 192

Total plant products in second-stage

separator‡

Propane, gal 669 0 33 86 149 205 286

Butanes, gal 308 0 15 41 76 108 159

Pentanes, gal 138 0 7 19 35 49 69

Total plant products in wellstream‡

Propane, gal 2,296 0 121 342 750 1,229 1,706

Butanes, gal 1,403 0 73 202 422 665 927

Pentanes, gal 5,519 0 262 634 1,022 1,315 1,589

* Cumulative recovery per MMscf of original fluid calculated during depletion.**Dewpoint pressure.†Recovery basis: primary separation at 500 psia and 70°F, second-stage separation at 50 psia and 70°F, and stock tank at 14.7 psia and 70°F.‡Recovery assumes 100% plant efficiency.

" o$k

(mo)k

(Vo)k

(6.76). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

and (Mo)k(mo)k

(no)k

, (6.77). . . . . . . . . . . . . . . . . . . . . . . . . . . . .

and the oil composition is given by

(xi)k(nt)k(zi)k "ng

$k"yi$k

(nt)k "ng$

k

. (6.78). . . . . . . . . . . . . . . . . . .

K values can be calculated from Ki yi#xi, and zioverall com-position of the mixture remaining in the cell at Stage k .

(zi)k1

(nt)k

!(zi)1 &k

j2

"ng

n $j

"yi$j% . (6.79). . . . . . . . . . .

C7 molecular weight of the oil phase can be calculated from

"Mo C7$

k

(Mo)k &i'C7

(xi)k Mi

"xC7$

k

. (6.80). . . . . . . . . . . . . .

Table 6.6 summarizes these calculations for the sample gas-conden-sate mixture.

Fig. 6.10—Schematic of method of calculating plant recoveries in a CVD report for a gascondensate.

(Separator Gas 1)

(Separator Gas 2)

108 PHASE BEHAVIOR

Fig. 6.11—Calculated maximum retrograde oil relative volumes from the Cho et al.27 correlation.

Heptanes Plus, mol%

Nonphysical

The oil composition at the last depletion state (605 psig for the ex-

ample condensate) can be measured, but it must be requested specif-

ically. Also, the residual-oil molecular weight, Mor, and specific

gravity, or, remaining after depletion at atmospheric pressure are

typically measured and reported as shown in Table 6.12. These val-

ues can be compared with calculated values by use of the material-

balance equations shown earlier.

The material-balance calculations are more accurate for rich gas

condensates and volatile oils. In fact, obtaining reasonable material-

balance oil properties for lean gas condensates is difficult. Some-

times it is useful to modify the reported oil relative volumes (partic-

ularly those close to the dewpoint) to monitor the effect on

calculated oil properties.

An alternative material-balance check that may be even more

useful for determining data consistency (particularly for leaner gas

condensates) involves starting with reported final-stage condensate

composition, (xi)kN, and adding back the removed gases, (yi)k, for

each stage from k N to k 1. This results in the original gas

composition, (zi)k1, which can be compared quantitatively with

the laboratory-reported composition.

,)

1. “Core Laboratories Good Oil Company Oil Well No. 4 PVT Study,” CoreLaboratories, Houston.

2. “Core Laboratories Good Oil Company Condensate Well No. 7 PVTStudy,” Core Laboratories, Houston.

3. Flaitz, J.M. and Parks, A.S.: “Sampling Gas-Condensate Wells,” Trans.,AIME (1942) 146, 13.

4. Katz, D.L., Brown, G.G., and Parks, A.S.: “NGAA Report on SamplingTwo-Phase Gas Streams from High Pressure Condensate Wells,” (Sep-tember 1945).

5. Reudelhuber, F.O.: “Sampling Procedures for Oil Reservoir Fluids,” JPT(December 1957) 15.

6. Clark, N.J.: “Sampling and Testing Oil Reservoir Samples,” JPT (Jan.1962) 12.

7. Clark, N.J.: “Sampling and Testing Gas Reservoir Samples,” JPT(March 1962) 266.

8. Recommended Practice for Sampling Petroleum Reservoir Fluids, API,Dallas (1966) 44.

9. Standing, M.B. and Katz, D.L.: “Density of Natural Gases,” Trans.,AIME, (1942) 146, 140.

10. Hoffmann, A.E., Crump, J.S., and Hocott, C.R.: “Equilibrium Constantsfor a Gas-Condensate System,” Trans., AIME (1953) 198, 1.

11. Standing, M.B.: “A Set of Equations for Computing Equilibrium Ratiosof a Crude Oil/Natural Gas System at Pressures Below 1,000 psia,” JPT(September 1979) 1193.

12. Kay, W.B.: “The Ethane-Heptane System,” Ind. & Eng. Chem. (1938)30, 459.

13. Kennedy, H.T. and Olson, C.R.: “Bubble Formation in SupersaturatedHydrocarbon Mixtures,” Oil & Gas J. (October 1952) 271.

14. Silvey, F.C., Reamer, H.H., and Sage, B.H.: “Supersaturation in Hydrocar-bon Systems: Methane-n-Decane,” Ind. Eng. Chem. (1958) 3, No. 2, 181.

15. Tindy, R. and Raynal, M.: “Are Test-Cell Saturation Pressures AccurateEnough?,” Oil & Gas J. (December 1966) 126.

16. Standing, M.B.: Volumetric and Phase Behavior of Oil Field Hydrocar-bon Systems, eighth edition, SPE, Richardson, Texas (1977).

17. Clark, N.J.: “Adjusting Oil Sample Data for Reservoir Studies,” JPT(February 1962) 143.

18. Moses, P.L.: “Engineering Applications of Phase Behavior of Crude-Oiland Condensate Systems,” JPT (July 1986) 715.

19. Amyx, J.W., Bass, D.M. Jr., and Whiting, R.L.: Petroleum Reservoir En-gineering, McGraw-Hill Book Co. Inc., New York City (1960).

20. Craft, B.C. and Hawkins, M.: Applied Petroleum Reservoir Engineering,first edition, Prentice-Hall Inc., Englewood Cliffs, New Jersey (1959).

21. Dake, L.P.: Fundamentals of Reservoir Engineering, Elsevier ScientificPublishing Co., Amsterdam (1978).

22. Dodson, C.R., Goodwill, D., and Mayer, E.H.: “Application of Labora-tory PVT Data to Reservoir Engineering Problems,” Trans., AIME(1953) 198, 287.

23. Whitson, C.H. and Torp, S.B.: “Evaluating Constant-Volume-DepletionData,” JPT (March 1983) 610; Trans., AIME, 275.

24. Drohm, J.K., Goldthorpe, W.H., and Trengove, R.: “Enhancing the Eval-uation of PVT Data,” paper OSEA 88174 presented at the 1988 OffshoreSoutheast Asia Conference, Singapore, 2–5 February.

25. Drohm, J.K., Trengove, R., and Goldthorpe, W.H.: “On the Quality ofData From Standard Gas-Condensate PVT Experiments,” paper SPE17768 presented at the 1988 Gas Technology Symposium, Dallas,13–15 June.

26. Reudelhuber, F.O. and Hinds, R.F.: “Compositional Material BalanceMethod for Prediction of Recovery From Volatile-Oil Depletion-DriveReservoirs,” JPT (January 1957) 19; Trans., AIME, 210.

27. Cho, S.J., Civan, F., and Starling, K.E.: “A Correlation To Predict Maxi-mum Condensation for Retrograde Condensation Fluids and Its Use inPressure-Depletion Calculations,” paper SPE 14268 presented at the1985 SPE Annual Technical Conference and Exhibition, Las Vegas, Ne-vada, 22–25 September.

28. Clark, N.J.: “Theoretical Aspects of Oil and Gas Equilibrium Calcula-tions,” JPT (April 1962) 373.

# -

g/cm3

bbl,1.589 873 E 01m3

Btu,1.055 056 E00kJcp,1.0* E 03Pa2sft,3.048* E 01m

ft3,2.831 685 E 02m3

F (F 32)/1.8 Cgal,3.785 412 E 03m3

in.,2.54* E00cmlbm mol,4.535 924 E 01kmol

psi,6.894 757 E00kPa

*Conversion factor is exact.

Petróleos Volátiles

Fluidos de Reservorios

G. Fondevila

Diagrama de Fases

Características

• Temperatura Reservorio < TC

• GOR: 350 – 600 m3/m3 (2000 – 3200 scf/stb)

• Densidad > 40 ºAPI (generalmente 45 – 55°API)

• mol% C7+: 12.5 – 20 %

• Bob > 2

• Gran cantidad de volumen de gas liberado una vez alcanzada la presión de saturación.

• Gas liberado por Petróleos Volátiles es de naturaleza

Retrógrada: no puedo hacer un balance de masa convencional (ya que debo tener en cuenta el

condensado aportado por el gas)

PVT Petróleo VolátilMismos Pasos que un PVT Normal, pero además:

•Liberación a Volumen Constante (CVD - Constant Volume Depletion):

• Similar a la liberación diferencial, pero solo libero gas hasta llegar al volumen inicial.

• Mejor manera de representar a lo que ocurre en el reservorio (variación composicional del fluido).

• El camino termodinámico afecta a las propiedades del fluido.

•Se recomienda para este tipo de Petróleos realizar la técnica de Dodson para

PVT: Para cada etapa diferencial, realizar el ensayo flash a condiciones de

separador. Esta técnica requiere de mucho volumen de muestra inicial, es

costosa y lleva mucho tiempo. Esto es debido a que la presión óptima de

separador varía durante el tiempo de explotación.

•En los Ensayos de Separador, se prueban además múltiples etapas de

separación (2 o más).

•En petróleos volátiles, para maximizar la producción de líquido se emplea el

uso de múltiples etapas de separación (2+).

Curvas PVT Típicas

Bo Rs [m3/m3]

P [kg/cm2] P [kg/cm2]

Liberación Volumen Constante

LiqLiq

Gas

Liq

Gas

∆P

Pi P1>

Bajo la presión hasta P1.

Hay liberación de gas, por lo que P1 < Pb.

Saco gas hasta llegar al Volumen Inicial

P1

Vol Cte

Diagrama de Fases

Bajo ∆P, Alta liberación de gas

Pi

Temp Res

Temperatura Reservorio

muy cercana a Tc

¡¡ 50% Vol liq !!

Variación Bo/Bob según el tipo de Petróleo

Tipo A o B Tipo C Tipo D

Gas y Condensado

Diagrama de Fases

Zona de condensación retrógrada

Características

• TCRIT < TRES < TCT

• GOR: 600 – 2700 m3/m3

• Densidad líquido > 40 ºAPI (generalmente > 50°API)

• mol% C7+: 4 – 12.5 %

• Cuando la presión del reservorio se encuentra por debajo del punto de rocío, se produce una condensación de líquido en fondo.

• El condensado liberado en fondo debe alcanzar una saturación crítica mínima para poder fluir, por lo que queda inmóvil en fondo.

• Esta condensación produce una disminución de la permeabilidad relativa al gas por lo que la productividad del reservorio disminuye.

• Se necesitan altas saturaciones de líquido en fondo para que el mismo se vuelva móvil, por lo que la mayoría del condensado queda en fondo.

PVT• Recombinación: Recordemos que por la naturaleza de los Gases

Retrógrados, los mismos deben ser muestreados en superficie y luego las muestras son recombinadas. El pozo debe ser producido a un mínimo caudal para mantener la presión de fluencia (si es posible) por encima del Pd, pero este caudal debe ser mayor al crítico, que nos permita desplazar el condensado generado dentro del pozo (resultado: “ahogamos” el pozo, muestra no representativa de gas “menos rico”).

• Relación PV: Para obtener el Punto de Rocío. Celda visual PVT.

• Líquido Retrógrado: Se obtiene la curva de producción de líquido en función de la depleción. Esta curva se obtiene en liberación a masa constante (flash) y liberación a volumen constante.

• CVD (Depleción a Volumen Constante): Tipo de expansión que representa el tipo de depleción sufrida en el reservorio. Esto es para tener en cuenta el condensado “inmóvil” que queda en el reservorio en contacto con el gas.

Liberación a Volumen Constante (CVD - Constant Volume Depletion):

Expansión Flash Curva PV: Determinación de Pr (visual)

PVT: Gas y Condensado

Composición del efluente a distintas P Curva de producción de líquido en una LVC

Comparación de Recupero de Líquido: CCE vs CVD

Reciclaje de Gas en Gas y Condensado (1)

Reciclaje de Gas en Gas y Condensado (2)

Z bifásico

- Se calcula a partir de una liberación CVD:

Z2f(P) = P / [Pd/Zd * (1 – Gp/GOIS)]

- Donde:

-Z2f: Z bifásico

-P: Presión

-Pd: Punto de Rocío

-Zd: Factor de desviación en Pd

-Gp: Gas producido acumulado a CS

-GOIS: Gas Original In Situ a CS

Bloqueo por líquido en Gas y Condensado

Client: Lucky Offshore Field: Mississippi Canyon 999 Well: OCS-G-999 No. BBB

Table 3: Summary of Results of the Selected Sample

(Sample 1.01)

Reservoir Conditions Pressure (pi) 10,000 Psia Temperature (Ti) 204 °F

Properties

OBM Contamination Wt% Dew Point Pressure (pd)

At Ti 5,975 psia 150°F 5,917 psia 100°F 5,699 psia

Gas-Oil Ratio

Single-stage Flash: 18,640 scf/stb Properties at 60°F STO °API Gas Gravity (Average)

Single-stage Flash: 43.2 0.784 Properties at Reservoir Conditions

Viscosity: cP Compressibillity (Co): 28.8 10-6/psi Density: 0.417 g/cm3 Z Factor: 1.484

Properties at Saturation Conditions

Viscosity: cP Compressibillity (Co): 69.6 10-6/psi Density: 0.345 g/cm3 Z Factor: 1.072

Total Depletion Recovery

Abandonment Pressure: 1000 psia Wellstream Recovery 77.62%

Oilphase - DBR Report # NAM 1112 8


Table 4: C30+ Composition, GOR, °API of Selected Sample (Sample 1.01)

Component Flashed Gas Flashed Liquid Monophasic Fluid MW WT % MOLE % WT % MOLE % WT % MOLE %

N2 28.01 0.62 0.50 0.00 0.00 0.50 0.49 CO2 44.01 12.75 6.57 0.02 0.09 10.17 6.36 H2S 34.08 0.00 0.00 0.00 0.00 0.00 0.00 C1 16.04 53.22 75.30 0.04 0.40 42.46 72.79 C2 30.07 12.70 9.59 0.06 0.32 10.14 9.28 C3 44.10 7.63 3.93 0.13 0.49 6.12 3.81 I – C4 58.12 2.05 0.80 0.09 0.26 1.65 0.78 N – C4 58.12 3.03 1.18 0.20 0.56 2.45 1.16 I – C5 72.15 1.40 0.44 0.23 0.53 1.16 0.44 N – C5 72.15 1.14 0.36 0.26 0.60 0.96 0.37 C6 84.00 3.28 0.86 2.51 4.84 3.13 1.00 C7 96.00 1.37 0.31 6.33 10.50 2.37 0.65 C8 107.00 0.54 0.11 7.48 10.88 1.94 0.47 C9 121.00 0.12 0.02 4.90 6.35 1.09 0.23 C10 134.00 0.09 0.02 5.87 7.28 1.26 0.26 C11 147.00 0.04 0.01 6.19 7.00 1.28 0.24 C12 161.00 0.02 0.00 7.06 7.29 1.44 0.25 C13 175.00 0.01 0.00 8.12 7.71 1.65 0.26 C14 190.00 0.00 0.00 8.40 7.35 1.70 0.25 C15 206.00 0.00 0.00 10.05 8.11 2.03 0.27 C16 222.00 0.00 0.00 5.29 3.96 1.07 0.13 C17 237.00 0.00 0.00 4.84 3.39 0.98 0.11 C18 251.00 0.00 0.00 6.83 4.53 1.38 0.15 C19 263.00 0.00 0.00 3.88 2.45 0.79 0.08 C20 275.00 0.00 0.00 1.87 1.13 0.38 0.04 C21 291.00 0.00 0.00 1.32 0.75 0.27 0.03 C22 300.00 0.00 0.00 0.69 0.38 0.14 0.01 C23 312.00 0.00 0.00 0.72 0.38 0.15 0.01 C24 324.00 0.00 0.00 0.75 0.38 0.15 0.01 C25 337.00 0.00 0.00 0.39 0.19 0.08 0.01 C26 349.00 0.00 0.00 0.41 0.19 0.08 0.01 C27 360.00 0.00 0.00 0.42 0.19 0.09 0.01 C28 372.00 0.00 0.00 0.44 0.19 0.09 0.01 C29 382.00 0.00 0.00 0.91 0.38 0.18 0.01 C30+ 580.00 0.00 0.00 3.29 0.94 0.67 0.03

Calculated MW 22.7 166 27.5 Mole % 3.35 96.65 OBM Contamination Level (wt%) STO Basis Live Oil Basis Stock Tank Oil Properties at Standard Conditions: C30+ Properties Measured Calculated MW 166 166 580 Density (g/cm3) 0.810 0.810 0.950 Single Stage Flash Data Original STO Corrected GOR (scf/stb) 18640 STO Density (g/cm3) 0.810 STO API Gravity 43.2 OBM Density (g/cm3) @60°F



Table 5: Calculated Group Properties for Selected Sample (Sample 1.01)

Properties Flashed Gas Flashed Liquid Monophasic Fluid

Mole % C7+ 0.46 91.91 3.52 C12+ 0.00 49.89 1.673 C20+ 0.00 5.09 0.170 C30+ 0.00 0.94 0.032 Mass % C7+ 2.18 96.46 21.258 C12+ 0.03 65.70 13.314 C20+ 0.00 11.23 2.271 C30+ 0.00 3.29 0.666 Molar Mass C7+ 102.23 172.39 163.48 C12+ 168.60 218.44 218.34 C20+ - 361.78 361.78 C30+ - 580.00 580.00 Density C7+ 0.739 0.816 0.809 C12+ 0.810 0.844 0.844 C20+ - 0.900 0.900 C30+ - 0.950 0.950 STO at 60oF 0.810 Gas Gravity (Air = 1) 0.784 Dry Gross Heat Content (BTU/scf) 3659 Wet Gross Heat Content (BTU/scf) 3595



Table 6: Constant Composition Expansion at Ti

(Sample 1.01)

Pressure Relative Vol % Liquid % Liquid Bulk Compressibilty Z (psia) (Vr=Vt/Vs) (VL/Vt) (VL/Vb) Density (g/cm3) (10-6/psia) Factor

pi 10000 0.828 0 0.417 28.78 1.484 9500 0.841 0 0.410 32.35 1.433 9000 0.856 0 0.403 36.32 1.382 8000 0.891 0 0.387 45.53 1.279 7000 0.937 0 0.368 56.54 1.176

pd 5975 1.000 0 0 0.345 69.58 1.072 5500 1.039 0.22 0.23 0.332 5450 1.044 0.24 0.25 0.330 5000 1.090 0.53 0.58 0.316 4500 1.156 1.83 2.12 0.298 4000 1.251 4.68 5.85 0.276 3500 1.384 6.53 9.04 0.249 3000 1.576 6.92 10.91 0.219 2500 1.866 6.33 11.81 0.185 2000 2.329 5.18 12.06 0.148 1800 2.597 4.62 12.00 0.133



Figure 1: Constant Composition Expansion at Ti – Relative Volume

(Sample 1.01)

0.6

0.8

1

1.2

1.4

1.6

1.8

2

2.2

2.4

2.6

2.8

0 2000 4000 6000 8000 10000 12000

Pressure (psia)

Rela

tive

Volu

me

(Vt/V

t @ P

b)

Figure 2: Constant Composition Expansion at Ti – Liquid Volume %

(SAMPLE 1.01)

0

2

4

6

8

10

12

14

0 1000 2000 3000 4000 5000 6000 7000 8000

Pressure (psia)

Liqui

d Vo

lum

e %

Vl/Vt

Vl/Vd



Table 7: Constant Composition Expansion at 150°F

(Sample 1.01)


pi 10000 0.852 0 0.441 24.14 1.526 9500 0.864 0 0.435 27.03 1.469 9000 0.877 0 0.429 30.24 1.413 8000 0.907 0 0.415 37.67 1.299 7000 0.945 0 0.398 46.58 1.184

pd 5917 1.000 0 0 0.376 57.88 1.060 5500 1.028 0.21 0.22 0.366 5450 1.032 0.23 0.24 0.364 5000 1.069 0.56 0.60 0.352 4500 1.123 2.59 2.91 0.335 4000 1.202 7.22 8.68 0.313 3500 1.317 9.76 12.85 0.286 3000 1.486 10.08 14.97 0.253 2500 1.747 9.06 15.83 0.215 2000 2.181 7.29 15.90 0.172 1800 2.437 6.46 15.74 0.154



Figure 3: Constant Composition Expansion at 150°F – Relative Volume

(Sample 1.01)

0.6

0.8

1

1.2

1.4

1.6

1.8

2

2.2

2.4

2.6

0 2000 4000 6000 8000 10000 12000

Pressure (psia)

Rela

tive

Volu

me

(Vt/

Vt @

Pb)

Figure 4: Constant Composition Expansion at 150°F – Liquid Volume %

(SAMPLE 1.01)

0

2

4

6

8

10

12

14

16

18

20

0 1000 2000 3000 4000 5000 6000 7000 8000

Pressure (psia)

Liqui

d Vo

lum

e %

Vl/Vt

Vl/Vd



Table 8: Constant Composition Expansion at 100°F

(Sample 1.01)


pi 10000 0.869 0 0.465 19.99 1.578 9500 0.879 0 0.460 22.26 1.516 9000 0.890 0 0.454 24.77 1.454 8000 0.915 0 0.442 30.57 1.328 7000 0.946 0 0.427 37.51 1.201

pd 5699 1.000 0 0 0.404 48.33 1.034 5500 1.011 0.10 0.10 0.400 5450 1.014 0.13 0.13 0.399 5000 1.041 0.38 0.40 0.388 4500 1.080 1.59 1.72 0.374 4000 1.139 8.30 9.46 0.355 3500 1.229 13.02 16.00 0.329 3000 1.364 13.96 19.04 0.296 2500 1.583 12.77 20.21 0.255 2000 1.964 10.32 20.27 0.206 1800 2.197 9.12 20.04 0.184



Figure 5: Constant Composition Expansion at 100°F – Relative Volume

(Sample 1.01)

0.6

0.8

1

1.2

1.4

1.6

1.8

2

2.2

2.4

0 2000 4000 6000 8000 10000 12000

Pressure (psia)

Rela

tive

Volu

me

(Vt/

Vt @

Pb)

Figure 6: Constant Composition Expansion at 100°F – Liquid Volume %

(SAMPLE 1.01)

0

2

4

6

8

10

12

14

16

18

20

22

24

0 1000 2000 3000 4000 5000 6000 7000 8000

Pressure (psia)

Liqui

d Vo

lum

e %

Vl/Vt

Vl/Vd



Table 9: Constant Volume Depletion at Ti

(Sample 1.01)

Pressure Total Produced Vapor Properties Calculated Liquid Properties Two Phase Recovery Z Factor MW Density Volume % Density Z Factor*

psia (%) (g/gmol) (g/cm3) (g/cm3)

5975 0.00 1.067 27.39 0.345 0.00 1.067 5200 6.34 0.991 27.21 0.321 0.40 0.784 0.992 4500 13.66 0.926 26.72 0.292 2.03 0.615 0.931 3800 23.11 0.878 25.29 0.246 6.48 0.590 0.882 3200 32.96 0.854 24.17 0.204 8.69 0.603 0.853 2700 42.28 0.845 23.47 0.169 9.38 0.619 0.837 2100 54.25 0.848 22.89 0.127 9.37 0.651 0.826 1500 66.94 0.869 22.57 0.088 8.90 0.681 0.827 1000 77.63 0.899 22.55 0.056 8.29 0.704 0.831

*Z = (Zg*V + ZL*L), where V and L are mole fractions of vapor and liquid at each stage (i,e., after displacing the excess gas to achieve constant volume)



Figure 7: Constant Volume Depletion – Total Recovery %

(Sample 1.01)

0

10

20

30

40

50

60

70

80

90

0 1000 2000 3000 4000 5000 6000 7000

Pressure (psia)

Tota

l Rec

over

y (%

)

Figure 8: Constant Volume Depletion – Retrograde Liquid Deposit

(Sample 1.01)

0

1

2

3

4

5

6

7

8

9

10

0 1000 2000 3000 4000 5000 6000 7000

Pressure (psia)

Retro

grad

e Liq

uid

Depo

sit (%

)



Figure 9: Constant Volume Depletion – Vapor Deviation Factor Z

(Sample 1.01)

0.8

0.85

0.9

0.95

1

1.05

1.1

0 1000 2000 3000 4000 5000 6000 7000

Pressure (psia)

Gas

Z Fa

ctor

Figure 10: Constant Volume Depletion – Vapor Molecular Mass

(Sample 1.01)

20

21

22

23

24

25

26

27

28

0 1000 2000 3000 4000 5000 6000 7000

Pressure (psia)

Gas

MW

(g/g

mol

)



Table 10: Constant Volume Depletion – Vapor Composition

(Sample 1.01)

Component p-psia 5200 4500 3800 3200 2700 2100 MW Mol%

N2 28.01 0.49 0.49 0.50 0.51 0.51 0.51 CO2 44.01 6.36 6.37 6.42 6.47 6.50 6.55 H2S 34.08 0.00 0.00 0.00 0.00 0.00 0.00 C1 16.04 72.85 73.12 74.05 74.86 75.39 75.82 C2 30.07 9.28 9.28 9.27 9.27 9.29 9.34 C3 44.10 3.81 3.80 3.75 3.70 3.68 3.68 I – C4 58.12 0.78 0.78 0.76 0.74 0.73 0.72 N – C4 58.12 1.16 1.15 1.12 1.09 1.06 1.04 I – C5 72.15 0.44 0.44 0.42 0.40 0.39 0.37 N – C5 72.15 0.37 0.36 0.34 0.33 0.31 0.30 C6 84.00 0.99 0.98 0.91 0.84 0.78 0.71 C7 96.00 0.65 0.63 0.57 0.49 0.43 0.36 C8 107.00 0.47 0.45 0.39 0.33 0.27 0.21 C9 121.00 0.23 0.22 0.19 0.15 0.12 0.08 C10 134.00 0.26 0.25 0.21 0.16 0.12 0.08 C11 147.00 0.24 0.23 0.18 0.14 0.10 0.06 C12 161.00 0.24 0.23 0.18 0.12 0.08 0.05 C13 175.00 0.26 0.24 0.18 0.12 0.07 0.04 C14 190.00 0.24 0.23 0.16 0.10 0.06 0.03 C15 206.00 0.27 0.25 0.16 0.09 0.05 0.02 C16 222.00 0.13 0.12 0.07 0.04 0.02 0.01 C17 237.00 0.11 0.10 0.05 0.03 0.01 0.00 C18 251.00 0.15 0.13 0.07 0.03 0.01 0.00 C19 263.00 0.08 0.07 0.03 0.01 0.01 0.00 C20 275.00 0.04 0.03 0.01 0.00 0.00 0.00 C21 291.00 0.02 0.02 0.01 0.00 0.00 0.00 C22 300.00 0.01 0.01 0.00 0.00 0.00 0.00 C23 312.00 0.01 0.01 0.00 0.00 0.00 0.00 C24 324.00 0.01 0.01 0.00 0.00 0.00 0.00 C25 337.00 0.01 0.00 0.00 0.00 0.00 0.00 C26 349.00 0.01 0.00 0.00 0.00 0.00 0.00 C27 360.00 0.01 0.00 0.00 0.00 0.00 0.00 C28 372.00 0.01 0.00 0.00 0.00 0.00 0.00 C29 382.00 0.01 0.01 0.00 0.00 0.00 0.00 C30+ 580.00 0.01 0.00 0.00 0.00 0.00 0.00 Total 100.00 100.00 100.00 100.00 100.00 100.00 Calculated MW 27.21 26.72 25.29 24.17 23.47 22.89 Viscosity (cP) 0.030 0.027 0.024 0.022 0.020 0.017 Heat Content (BTU/scf) - Dry 1450 1423 1344 1282 1243 1210




Table 11: Constant Volume Depletion – Vapor Composition Table 11: Constant Volume Depletion – Vapor Composition

(Sample 1.01) (Sample 1.01)

Component Component p-psia p-psia 1500 1500 1000 1000 MW MW Mol% Mol%

N2 N2 28.01 28.01 0.51 0.51 0.50 0.50 CO2 CO2 44.01 44.01 6.59 6.59 6.61 6.61 H2S H2S 34.08 34.08 0.00 0.00 0.00 0.00 C1 C1 16.04 16.04 75.95 75.95 75.66 75.66 C2 C2 30.07 30.07 9.45 9.45 9.60 9.60 C3 C3 44.10 44.10 3.73 3.73 3.85 3.85 I – C4 I – C4 58.12 58.12 0.73 0.73 0.76 0.76 N – C4 N – C4 58.12 58.12 1.05 1.05 1.09 1.09 I – C5 I – C5 72.15 72.15 0.37 0.37 0.38 0.38 N – C5 N – C5 72.15 72.15 0.29 0.29 0.30 0.30 C6 C6 84.00 84.00 0.66 0.66 0.66 0.66 C7 C7 96.00 96.00 0.30 0.30 0.28 0.28 C8 C8 107.00 107.00 0.16 0.16 0.14 0.14 C9 C9 121.00 121.00 0.06 0.06 0.05 0.05 C10 C10 134.00 134.00 0.06 0.06 0.04 0.04 C11 C11 147.00 147.00 0.04 0.04 0.03 0.03 C12 C12 161.00 161.00 0.03 0.03 0.02 0.02 C13 C13 175.00 175.00 0.02 0.02 0.01 0.01 C14 C14 190.00 190.00 0.01 0.01 0.01 0.01 C15 C15 206.00 206.00 0.01 0.01 0.00 0.00 C16 C16 222.00 222.00 0.00 0.00 0.00 0.00 C17 C17 237.00 237.00 0.00 0.00 0.00 0.00 C18 C18 251.00 251.00 0.00 0.00 0.00 0.00 C19 C19 263.00 263.00 0.00 0.00 0.00 0.00 C20 C20 275.00 275.00 0.00 0.00 0.00 0.00 C21 C21 291.00 291.00 0.00 0.00 0.00 0.00 C22 C22 300.00 300.00 0.00 0.00 0.00 0.00 C23 C23 312.00 312.00 0.00 0.00 0.00 0.00 C24 C24 324.00 324.00 0.00 0.00 0.00 0.00 C25 C25 337.00 337.00 0.00 0.00 0.00 0.00 C26 C26 349.00 349.00 0.00 0.00 0.00 0.00 C27 C27 360.00 360.00 0.00 0.00 0.00 0.00 C28 C28 372.00 372.00 0.00 0.00 0.00 0.00 C29 C29 382.00 382.00 0.00 0.00 0.00 0.00 C30+ C30+ 580.00 580.00 0.00 0.00 0.00 0.00 Total Total 100.00 100.00 100.00 100.00 Calculated MW Calculated MW 22.57 22.57 22.55 22.55 Viscosity (cP) Viscosity (cP) 0.016 0.016 0.014 0.014 Heat Content (BTU/scf) - Dry Heat Content (BTU/scf) - Dry 1191 1191 1189 1189




Table 12: Constant Volume Depletion – Liquid Composition at Abandonment Pressure

(Sample 1.01)

Component MW Wt% Mol% N2 28.01 0.00 0.05 CO2 44.01 0.09 2.38 H2S 34.08 0.00 0.00 C1 16.04 0.24 17.50 C2 30.07 0.16 6.11 C3 44.10 0.19 5.02 I – C4 58.12 0.08 1.64 N – C4 58.12 0.15 2.91 I – C5 72.15 0.10 1.67 N – C5 72.15 0.10 1.58 C6 84.00 0.48 6.60 C7 96.00 0.54 6.50 C8 107.00 0.52 5.64 C9 121.00 0.34 3.22 C10 134.00 0.43 3.75 C11 147.00 0.48 3.75 C12 161.00 0.57 4.11 C13 175.00 0.68 4.53 C14 190.00 0.74 4.50 C15 206.00 0.91 5.14 C16 222.00 0.49 2.58 C17 237.00 0.46 2.27 C18 251.00 0.67 3.08 C19 263.00 0.38 1.69 C20 275.00 0.19 0.79 C21 291.00 0.13 0.54 C22 300.00 0.07 0.27 C23 312.00 0.07 0.27 C24 324.00 0.08 0.28 C25 337.00 0.04 0.14 C26 349.00 0.04 0.14 C27 360.00 0.04 0.14 C28 372.00 0.05 0.14 C29 382.00 0.09 0.29 C30+ 580.00 0.39 0.77 Total 100.00 MW 116.03



Table 13: Calculated Cumulative Recovery at Surface Separators

(Sample 1.01)

Cumulative Recovery per Initial Reservoir Pressure (psia) MMSCF of Original Fluid in Place 5975 5200 4500 3800 3200 2700 2100 1500 1000 Wellstream Produced*, MSCF 1000.00 0.00 63.45 136.63 231.13 329.66 422.85 542.53 669.45 776.29 Stock Tank Liquid - bbls 69.81 0.00 4.33 8.94 13.44 16.86 19.32 21.56 23.31 24.60 Primary Sep. Gas - MSCF 913.04 0.00 57.99 125.20 213.50 307.01 396.43 512.47 636.40 740.95 Stage 2 Gas - MSCF 12.78 0.00 0.81 1.70 2.63 3.40 3.98 4.55 5.02 5.39 Stock Tank Gas - MSCF 20.14 0.00 1.27 2.67 4.16 5.39 6.35 7.29 8.10 8.74 Total Plant Products in Primary Separator Gas - Gallons Ethane Plus 3655.00 0.00 232.27 502.18 860.12 1243.50 1614.21 2102.98 2636.18 3184.38 Propane Plus 1376.63 0.00 87.58 189.92 328.34 479.50 627.87 826.69 1046.99 1277.29 Butanes Plus 544.37 0.00 34.69 75.53 132.31 196.07 259.98 347.45 445.91 549.92 Pentanes Plus 175.26 0.00 11.19 24.49 43.62 65.90 88.90 121.31 158.48 197.86 Total Plant Products in Stage 2 Separator Gas - Gallons Ethane Plus 85.13 0.00 5.38 11.31 17.62 22.85 26.87 30.86 34.25 37.74 Propane Plus 33.34 0.00 2.11 4.45 6.98 9.12 10.79 12.47 13.93 15.45 Butanes Plus 12.54 0.00 0.79 1.68 2.67 3.53 4.21 4.92 5.54 6.19 Pentanes Plus 3.65 0.00 0.23 0.49 0.79 1.07 1.29 1.53 1.74 1.96 Total Plant Products in Stock Tank Gas - Gallons Ethane Plus 425.10 0.00 26.81 56.43 88.36 115.28 136.24 157.38 157.42 176.03 Propane Plus 294.55 0.00 18.59 39.23 61.81 81.14 96.37 111.93 111.94 126.03 Butanes Plus 156.14 0.00 9.88 20.92 33.36 44.31 53.13 62.36 62.37 71.06 Pentanes Plus 52.60 0.00 3.34 7.11 11.52 15.57 18.95 22.62 22.62 26.23 *Wellstream production is from total recovery data in the CVD test.

Table 14: Calculated Instantaneous Yields at Surface Separators

(Sample 1.01)

Pressure psia 5975 5200 4500 3800 3200 2700 2100 1500 1000 SCF 1st Stage Gas/bbl STO Liquid 13079 13403 14570 19630 27298 36463 51715 70709 81424 bbl STO Liquid/MMSCF 1st Stage Gas 76.46 74.61 68.64 50.94 36.63 27.43 19.34 14.14 12.28 bbl STO Liquid/MMSCF Wellstream 69.81 68.18 63.04 47.60 34.77 26.32 18.75 13.81 12.02 Surface Separator Conditions Used: Primary Separator at 575 psia and 74°F Stage 2 Separator at 250 psia and 74°F Stock Tank at 15.025 psia and 60°F



APPENDIX A: DETAILED SINGLE STAGE FLASH DATA



Table 15: C30+ Composition, GOR, °API of Sample 1.02

Component Flashed Gas Flashed Liquid Monophasic Fluid MW WT % MOLE % WT % MOLE % WT % MOLE %

N2 28.01 0.62 0.50 0.00 0.00 0.50 0.49 CO2 44.01 12.75 6.57 0.02 0.09 10.17 6.36 H2S 34.08 0.00 0.00 0.00 0.00 0.00 0.00 C1 16.04 53.22 75.30 0.04 0.40 42.46 72.79 C2 30.07 12.70 9.59 0.06 0.32 10.14 9.28 C3 44.10 7.63 3.93 0.13 0.49 6.12 3.81 I – C4 58.12 2.05 0.80 0.09 0.26 1.65 0.78 N – C4 58.12 3.03 1.18 0.20 0.56 2.45 1.16 I – C5 72.15 1.40 0.44 0.23 0.53 1.16 0.44 N – C5 72.15 1.14 0.36 0.26 0.60 0.96 0.37 C6 84.00 3.28 0.86 2.51 4.84 3.13 1.00 C7 96.00 1.37 0.31 6.33 10.50 2.37 0.65 C8 107.00 0.54 0.11 7.48 10.88 1.94 0.47 C9 121.00 0.12 0.02 4.90 6.35 1.09 0.23 C10 134.00 0.09 0.02 5.87 7.28 1.26 0.26 C11 147.00 0.04 0.01 6.19 7.00 1.28 0.24 C12 161.00 0.02 0.00 7.06 7.29 1.44 0.25 C13 175.00 0.01 0.00 8.12 7.71 1.65 0.26 C14 190.00 0.00 0.00 8.40 7.35 1.70 0.25 C15 206.00 0.00 0.00 10.05 8.11 2.03 0.27 C16 222.00 0.00 0.00 5.29 3.96 1.07 0.13 C17 237.00 0.00 0.00 4.84 3.39 0.98 0.11 C18 251.00 0.00 0.00 6.83 4.53 1.38 0.15 C19 263.00 0.00 0.00 3.88 2.45 0.79 0.08 C20 275.00 0.00 0.00 1.87 1.13 0.38 0.04 C21 291.00 0.00 0.00 1.32 0.75 0.27 0.03 C22 300.00 0.00 0.00 0.69 0.38 0.14 0.01 C23 312.00 0.00 0.00 0.72 0.38 0.15 0.01 C24 324.00 0.00 0.00 0.75 0.38 0.15 0.01 C25 337.00 0.00 0.00 0.39 0.19 0.08 0.01 C26 349.00 0.00 0.00 0.41 0.19 0.08 0.01 C27 360.00 0.00 0.00 0.42 0.19 0.09 0.01 C28 372.00 0.00 0.00 0.44 0.19 0.09 0.01 C29 382.00 0.00 0.00 0.91 0.38 0.18 0.01 C30+ 580.00 0.00 0.00 3.29 0.94 0.67 0.03

Calculated MW 22.7 166 27.5 Mole % 3.35 96.65 OBM Contamination Level (wt%) STO Basis Live Oil Basis Stock Tank Oil Properties at Standard Conditions: C30+ Properties Measured Calculated MW 166 166 580 Density (g/cm3) 0.810 0.810 0.950 Single Stage Flash Data Original STO Corrected GOR (scf/stb) 18640 STO Density (g/cm3) 0.810 STO API Gravity 43.2 OBM Density (g/cm3) @60°F


Inyección de Gas

Procesos de Inyección de Gas

Objetivos:

- Se aplican tanto en reservorio de petróleo como gas y condensado.

- Estás diseñados para mejorar la recuperación de petróleo (líquidos).

- La aplicación principal es el mantenimiento de presión para mantener los caudales de producción.

- en Gas y condensado se utiliza para prevenir la baja recuperación de líquidos por el fenómeno de condensación retrógrada.

- La inyección de gas “pobre” (mayormente CH4 o N2) logra recuperar una cantidad significativa de HC intermedios (C5 a C12)

Inyección de Gas “Pobre” en

Yac. de Gas y Condensado

- La inyección de gas pobre en Gas y Condensado puede ser:

- Miscible: Si la presión de reservorio se encuentra por

encima del Punto de Rocío.

- Si la presión de reservorio está por debajo del Punto

de Rocío, este gas pobre puede “re-vaporizar”

líquidos que fueron liberados en el reservorio.

- Miscibilidad: se define como la condición donde dos

fluidos se encuentran mezclados en alguna

proporción en la cual la mezcla resultante se

encuentra en estado monofásico.

Reciclado de Gas en

Yac. de Gas y Condensado (1)

- El reciclado de gas en reservorios de Gas y Condensado es utilizada para minimizar las pérdidas en la recuperación de líquidos.

- Cuando la presión cae por debajo del Pd (punto de rocío), líquidos condensan en fondo y permanecen como fase inmóvil.

- El gas producido se vuelve menos “rico” y la recuperación final de líquidos puede llegar a bajar hasta 15/20%.

- Para maximizar la recuperación de líquidos la presión de reservorio se debe mantener más alta que el Pd para no permitir la condensación retrógrada.

- Esto se logra re-inyectando el gas producido luego de ser separado y procesado para extraerle todo el condensado.

Reciclado de Gas en

Yac. de Gas y Condensado (2)

- El gas producido no es suficiente para reemplazar el vaciado del reservorio causado por la producción, por lo que se debe “agregar” gas para lograr un mantenimiento de presión completo.

- Si la presión del reservorio está muy por encima del Pd se puede utilizar solamente el gas producido para re-inyección y luego al ir acercándose la presión al Pd se agrega más gas.

- El resultado económico de retrasar las ventas de gas (por su re-inyección) para incrementar el recupero del condensado puede ser prohibitivo.

- Alternativas para hacerlo económico puede ser la re-inyección de parte del gas, comprar gas “pobre” para inyección o utilizar N2.

Inyección de N2 en

Yac. de Gas y Condensado

- La utilización de N2 generado en locación para re-inyección ha sido uno de los métodos más usados para proyectos de reciclado de gas.

- En los 80’s algunos estudios demostraron que el N2 causaba una sustancial condensación de líquido cuando era mezclado junto con gas y condensado. Este comportamiento causó la preocupación de que el N2 podría hasta empeorar el problema de la condensación retrógrada.

- Estudios posteriores de desplazamiento demostraron que prácticamente todo el líquido condensado por el contacto inicial con el N2 fue re-vaporizado con el contacto continuo con N2.

- Ensayos de “slim-tube” demuestran resultados similares en inyección de N2 con respecto a inyección de gas pobre.

Efectos de la Inyección de N2

Inyección de N2 y su influencia en la condensación retrógrada

14 Oilfield Review

Understanding Gas-Condensate Reservoirs

Li FanCollege Station, Texas, USA

Billy W. HarrisWagner & Brown, Ltd.Midland, Texas

A. (Jamal) JamaluddinRosharon, Texas

Jairam KamathChevron Energy Technology CompanySan Ramon, California, USA

Robert MottIndependent Consultant Dorchester, UK

Gary A. PopeUniversity of TexasAustin, Texas

Alexander ShandryginMoscow, Russia

Curtis Hays WhitsonNorwegian University of Science andTechnology and PERA, A/STrondheim, Norway

For help in preparation of this article, thanks to Syed Ali,Chevron, Houston; and Jerome Maniere, Moscow.ECLIPSE 300, LFA (Live Fluid Analyzer for MDT tool), MDT(Modular Formation Dynamics Tester) and PVT Express aremarks of Schlumberger. CHEARS is a mark of Chevron.Teflon is a mark of E.I. du Pont de Nemours and Company.

How does a company optimize development of a gas-condensate field, when

depletion leaves valuable condensate fluids in a reservoir and condensate blockage

can cause a loss of well productivity? Gas-condensate fields present this puzzle.

The first step must be to understand the fluids and how they flow in the reservoir.

A gas-condensate reservoir can choke on itsmost valuable components. Condensate liquidsaturation can build up near a well because ofdrawdown below the dewpoint pressure,ultimately restricting the flow of gas. The near-well choking can reduce the productivity of awell by a factor of two or more.

This phenomenon, called condensateblockage or condensate banking, results from acombination of factors, including fluid phaseproperties, formation flow characteristics andpressures in the formation and in the wellbore.If these factors are not understood at thebeginning of field development, sooner or laterproduction performance can suffer.

For example, well productivity in the Arunfield, in North Sumatra, Indonesia, declinedsignificantly about 10 years after productionbegan. This was a serious problem, since welldeliverability was critical to meet contractualobligations for gas delivery. Well studies,including pressure transient testing, indicatedthe loss was caused by accumulation ofcondensate near the wellbore.1

Arun is one of several huge gas-condensatereservoirs that together contain a significantglobal resource. Other large gas-condensateresources include Shtokmanovskoye field in theRussian Barents Sea, Karachaganak field inKazakhstan, the North field in Qatar thatbecomes the South Pars field in Iran, and theCupiagua field in Colombia.2

This article reviews the combination of fluidthermodynamics and rock physics that results incondensate dropout and condensate blockage.We examine implications for production andmethods for managing the effects of condensatedropout, including reservoir modeling to predictfield performance. Case studies from Russia, theUSA and the North Sea describe field practicesand results.

Forming DewdropsA gas condensate is a single-phase fluid atoriginal reservoir conditions. It consistspredominantly of methane [C1] and other short-chain hydrocarbons, but it also contains long-chain hydrocarbons, termed heavy ends. Under

1. Afidick D, Kaczorowski NJ and Bette S: “ProductionPerformance of a Retrograde Gas Reservoir: A CaseStudy of the Arun Field,” paper SPE 28749, presented atthe SPE Asia Pacific Oil & Gas Conference, Melbourne,Australia, November 7–10, 1984.

2. For a case study of the Karachaganak field: Elliott S,Hsu HH, O’Hearn T, Sylvester IF and Vercesi R: “TheGiant Karachaganak Field, Unlocking Its Potential,”Oilfield Review 10, no. 3 (Autumn 1998): 16–25.

3. Gas-condensate fluids are termed retrograde becausetheir behavior can be the reverse of fluids comprisingpure components. As reservoir pressure declines andpasses through the dewpoint, liquid forms and theamount of the liquid phase increases with pressuredrop. The system reaches a point in a retrogradecondensate where, as pressure continues to decline,the liquid revaporizes.

4. Injection of cold or hot fluids can change reservoirtemperature, but this rarely occurs near productionwells. The dominant factor for fluid behavior in thereservoir is the pressure change. As will be discussedlater, this is no longer the case once the fluid is producedinto the wellbore.

Winter 2005/2006 15

certain conditions of temperature and pressure,this fluid will separate into two phases, a gas anda liquid that is called a retrograde condensate.3

As a reservoir produces, formation temper-ature usually doesn’t change, but pressuredecreases.4 The largest pressure drops occurnear producing wells. When the pressure in agas-condensate reservoir decreases to a certainpoint, called the saturation pressure ordewpoint, a liquid phase rich in heavy endsdrops out of solution; the gas phase is slightlydepleted of heavy ends (right). A continueddecrease in pressure increases the volume of theliquid phase up to a maximum amount; liquidvolume then decreases. This behavior can bedisplayed in a pressure-volume-temperature(PVT) diagram.

The amount of liquid phase present dependsnot only on the pressure and temperature, butalso on the composition of the fluid. A dry gas, bydefinition, has insufficient heavy components togenerate liquids in the reservoir, even with near-well drawdown. A lean gas condensate generates

> Phase diagram of a gas-condensate system. This pressure-volume-ttemperature (PVT) plot indicates single-phase behavior outside the two-phase region, which is bounded by bubblepoint and dewpoint lines. Linesof constant phase saturation (dashed) all meet at the critical point. Thenumbers indicate the vapor phase saturation. In a gas-condensatereservoir, the initial reservoir condition is in the single-phase area to theright of the critical point. As reservoir pressure declines, the fluid passestthrough the dewpoint and a liquid phase drops out of the gas. Thepercentage of vapor decreases, but can increase again with continuedpressure decline. The cricondentherm is the highest temperature at whichttwo phases can coexist. Surface separators typically operate atconditions of low pressure and low temperature.

Temperature

Pres

sure

Initial reservoirInitial reservoirconditionconditionCritical pointCritical point

SeparatorSeparatorconditioncondition

C i d thCricondentherm

Two phase regionTwo-phase region

60%60%

70%70%

80%

90%

100% vapor00% apo

BBBuu

bbbblleepp

ooinntt liinneeDDewwppooiinntt liinnee

a small volume of the liquid phase, less than100 bbl per million ft3 [561 m3 per million m3],and a rich gas condensate generates a largervolume of liquid, generally more than 150 bblper million ft3 [842 m3 per million m3] (above).5

There are no established boundaries in thedefinitions of lean and rich, and furtherdescriptors—such as very lean—are alsoapplied, so these figures should be taken merelyas indicators of a range.

Determining the fluid properties can beimportant in any reservoir, but it plays aparticularly vital role in gas-condensatereservoirs. For example, condensate/gas ratioplays a major role in estimates for the salespotential of both gas and liquid, which areneeded to size surface processing facilities. Theamount of liquid that may be stranded in a fieldis also an essential economic consideration.These considerations and others, such as theneed for artificial lift and stimulationtechnologies, rely on accurate fluid sampling.Small errors in capturing samples, such as anincorrect amount of captured liquid, can havesignificant errors in measured behavior, so greatcare must be taken in the sampling process (see“Sampling for Fluid Properties,” next page).

Once reservoir fluids enter a wellbore, bothtemperature and pressure conditions maychange. Condensate liquid can be produced intothe wellbore, but liquid also can drop out withinthe wellbore because of changes in conditions. Ifthe gas does not have sufficient energy to carrythe liquid to surface, liquid loading or fallback inthe wellbore occurs because the liquid is denserthan the gas phase traveling along with it. If theliquid falls back down the wellbore, the liquidpercentage will increase and may eventuallyrestrict production. Gas lift and pumpingtechnologies that are used to counter thisbehavior will not be discussed in this article.6

16 Oilfield Review

> Examples of rich and lean gas-condensate behavior. When pressure decreases at reservoir temperature, a rich gas (top left) forms a higherttpercentage of liquid than a lean gas (top right). The rich gas drops out more condensate than the lean gas (tt bottom left). The liquid dropout curvettassumes the two phases remain in contact with one another. However, in a reservoir, the mobile gas phase is produced; the liquid saturation in thenear-well region builds until it is also mobile. As a result, eventually condensate blockage can affect formations with both lean and rich gases, andtthe normalized well productivity index (J/J J0) of both can be severely impacted (0 bottom right).tt

Liqu

id d

ropo

ut, %

Pressure, psi

0 2,000 3,000 4,000 5,000 6,0001,0000

5

10

15

20

25

Lean gas condensateLean gas condensateLean gas condensate

Rich gas condensateRich gas condensateRich gas condensate

0

0.2

0.4

0.6

0.8

1.0

0 0.2 0.4 0.6 0.8 1.0

Lean gas condensateL dLean gas condensateg

Rich gas condensateRich gas condensateRich gas condensate

Paverage/Pdewpoint

Prod

uctiv

ity ra

tio, J

/Jo

CriticalCriticalpointpoint

0

1,000

2,000

3,000

4,000

5,000

6,000

150 200 250 300 350 400 450 500 550 600

Temperature, K

Reservoir temperatureReservoir temperature

98 5%98.5%99%99%

99.5%

Pres

sure

, psi

Lean GasCondensate

0

1,000

2,000

3,000

4,000

5,000

6,000

7,000

0 200 300 400 500 600 700 800 900100

Temperature, K

Pres

sure

, psi

CriticalCriticalpointpoint

Reservoir temperatureReservoir temperature

75%75%80%0

85%85%590%90%

95%95%

Rich GasCondensate

5. Gas volumes in this article are given at the conditions thatare considered standard at the measurement location,which is not the same around the world. Conversionsbetween metric and oilfield units are volumetric.

6. For more on artificial lift: Fleshman R, Harryson andLekic O: “Artificial Lift for High-Volume Production,”Oilfield Review 11, no. 1 (Spring 1999): 48–63.

Winter 2005/2006 17

Fluid composition is determined by capturinga representative sample of reservoir fluid.Surface samples can be obtained relativelyeasily by collecting liquid and gas samplesfrom test or production separators. Thesamples are then recombined in a laboratory.However, the result can be unrepresentativeof reservoir conditions, particularly whensampling from a gas-condensate reservoir. Afew examples of potential problems includerecombining the gas and liquid samples atan incorrect ratio, changing productionconditions prior to or during sampling andcommingling zones with different properties.If the liquid content is low when capturingsurface samples, a small loss of the liquid inproduction tubulars or separators couldrender the condensate sample unrepresen-tative of the formation fluid.

Samples can also be collected downholefrom wellbore fluids in gas-condensatereservoirs. This is practical and desirable ifthe wellbore flowing pressure is above thedewpoint pressure, but it is generally notrecommended if the pressure anywhere in thetubing is lower than the dewpoint pressure. Inthat condition, there is two-phase flow in thewellbore. Any liquid forming in the tubingduring or prior to the sampling may segregateto the bottom of the tubing string—where abottomhole sampler collects fluids—potentiallyresulting in an unrepresentative sample withtoo much of the heavier components.

Formation testers have improved signifi-cantly over the past decade. The MDT ModularFormation Dynamics Tester collects fluids bypressing a probe against an uncased boreholewall and withdrawing fluids from a formation.1

The LFA Live Fluid Analyzer module on thetool measures the cleanup of contaminationfrom oil-base drilling or completion fluids,minimizing the wait time and assuring qualitysamples.2 The LFA detector also provides anindication of the amount of methane, otherlight components and liquids. From thesedata, the ratio of methane to liquid providesa measure of the condensate/gas ratio, animportant consideration for early economicevaluation of a prospect. The analysis canalso show zones with different compositionsor compositional gradients.

Measured data from the MDT tool are trans-mitted to surface immediately, so samplingdecisions can be made based on knowledgeof approximate composition and reservoirpressure, another measured parameter. Ifdesired, fluid samples can be collected beforemoving to another downhole location.

For gas condensates that are at pressuresabove the dewpoint in the reservoir, it isimportant to capture and maintain single-phase fluid. If the fluid pressure drops belowdewpoint, it may take a long time torecombine the sample. Even worse, somechanges that occur in a sample on its trip tosurface may be irreversible. By providing

evidence when a fluid goes through itsdewpoint, the LFA measurement can indicatewhen the pressure drawdown is too large andshould be decreased before sampling to keeppressure above the dewpoint.

A sample that is single-phase when collectedshould be kept in a single phase when broughtto surface. Special MDT sample bottles areavailable for this purpose. A single-phasebottle uses a nitrogen cushion to increase thepressure in the sampled fluid.3 The samplecools as it is brought to surface, but thenitrogen cushion on the sample keeps itspressure above the dewpoint.

In most cases, the PVT Express onsite wellfluid analysis service can provide fluidproperty measurements at the wellsite inabout 24 hours, saving the weeks or monthsthat may be needed to get results from alaboratory.4 The PVT Express systems canmeasure gas/liquid ratio, saturationpressure—bubblepoint or dewpoint—composition to C30+, reservoir fluid density,viscosity and oil-base mud contamination.5

These measurements are critical because anoperating company can use them immediatelyto make a decision to complete or to test awell. Rapid turnaround may be crucial whendrilling exploration or development wells froman expensive offshore rig. More completeanalyses can be obtained later from samplessent to a laboratory.

With the basic understanding of whereand how condensate drops out of the gasphase, engineers can devise ways to optimizeproduction of gas and condensate.

Sampling for Fluid Properties

1. Andrews RJ, Beck G, Castelijns K, Chen A, Cribbs ME,Fadnes FH, Irvine-Fortescue J, Williams S, Hashem M,Jamaluddin A, Kurkjian A, Sass B, Mullins OC,Rylander E and Van Dusen A: “QuantifyingContamination Using Color of Crude and Condensate,”Oilfield Review 13, no. 3 (Autumn 2001): 24–43.

2. Betancourt S, Fujisawa G, Mullins OC, Carnegie A,Dong C, Kurkjian A, Eriksen KO, Haggag M, JaramilloAR and Terabayashi H: “Analyzing Hydrocarbons in theBorehole,” Oilfield Review 15, no. 3 (Autumn 2003):54–61.

3. Jamaluddin AKM, Ross B, Calder D, Brown J andHashem M: “Single-Phase Bottomhole SamplingTechnology,” Journal of Canadian PetroleumTechnology 41, no. 7 (July 2002): 25–30.

4. Jamaluddin AKM, Dong C, Hermans P, Khan IA,Carnegie A, Mullins OC, Kurkjian A, Fujisawa G,Nighswander J and Babajan S: “Real-Time and On-Site Reservoir Fluid Characterisation Using SpectralAnalysis and PVT Express,” Australian PetroleumProduction & Exploration Association Journal (2004):605–616.

5. The nomenclature “composition to C30+” indicatescompounds up to 29 carbon atoms are separatelydiscriminated, with the remainder combined into afraction indicated as C30+.

Dewdrops in a ReservoirWhen condensate liquid first forms in a gasreservoir, it is immobile because of capillaryforces acting on the fluids. That is, a microscopicliquid droplet, once formed, will tend to betrapped in small pores or pore throats. Even for rich gas condensates with substantial liquid dropout, condensate mobility, which is theratio of relative permeability to viscosity,remains insignificant away from wellbores. As aconsequence, the condensate that forms in mostof the reservoir is lost to production unlessthe depletion plan includes gas cycling. Theeffect of this dropout on gas mobility is typically negligible.

Near a producing well, the situation isdifferent. Once bottomhole pressure dropsbelow the dewpoint, a near-well pressure sinkforms around the well. As gas is drawn into thepressure sink, liquid drops out. After a brieftransient period, enough liquid accumulatesthat its mobility becomes significant. The gasand liquid compete for flow paths, as describedby the formation’s relative-permeabilityrelationship. Condensate blockage is a result ofthe decreased gas mobility around a producingwell below the dewpoint (right).

Reservoir pressure dropping below thedewpoint has two main results, both negative:gas and condensate production decreasebecause of near-well blockage, and the producedgas contains fewer valuable heavy ends becauseof dropout throughout the reservoir, where thecondensate has insufficient mobility to flowtoward the well.

Large productivity losses have been reportedfor wells in gas-condensate fields. In the Arunfield, which was operated by Mobil, nowExxonMobil, the loss in some wells was greaterthan 50%.7 In another case, Exxon, nowExxonMobil, reported two wells that died due tocondensate blockage.8 Shell and PetroleumDevelopment Oman reported a 67% productivityloss for wells in two fields.9

In another field, the initial productivitydecline has reportedly reversed. The productivityof wells in the moderately rich gas-condensatereservoir declined rapidly when bottomholepressures dropped below dewpoint. This declinecontinued until pressure throughout thereservoir dropped below dewpoint, then gasproductivity began to increase. Compositionalmodeling showed that condensate saturationincreased near the wells to approximately 68%,decreasing gas permeability and therefore gasproductivity. However, when pressure throughoutthe reservoir dropped below dewpoint, some

liquid dropped out everywhere. The gas movingtoward the wellbore was leaner and had lesscondensate to drop out in the near-well region,resulting in decreased condensate saturation toabout 55% and increased gas productivity.10 Thecondensate blockage decreased as the near-wellgas mobility increased.

Condensate BlockageNot all gas-condensate reservoirs are pressure-limited because of near-well condensateblockage, even though all of these fields willexperience condensate blockage. The degree towhich condensate dropout is a productionproblem depends on the ratio of the pressuredrop that is experienced within the reservoir tothe total pressure drop from distant areas of thereservoir to a control point at surface.

If reservoir pressure drop is significant, thenadditional pressure drop due to condensateblockage can be very important for welldeliverability. This condition typically applies ina formation with a low kh, the product ofpermeability and net formation thickness.Conversely, if little of the total pressure dropoccurs in the reservoir, typical of high kh

formations, then adding more pressure drop inthe reservoir due to condensate blockage willprobably have little impact on well deliverability.As a general guideline, condensate blockage canbe assumed to double the pressure drop in thereservoir for the same flow rate.

Conceptually, flow in gas-condensate fieldscan be divided into three reservoir regions,although in some situations not all three arepresent (next page).11 The two regions closest toa well can exist when bottomhole pressure isbelow the dewpoint of the fluid. The third region,away from producing wells, exists only when thereservoir pressure is above the dewpoint.

This third region includes most of thereservoir away from producing wells. Since it isabove the dewpoint pressure, there is only onehydrocarbon phase, gas, present and flowing.The interior boundary of this region occurswhere the pressure equals the dewpointpressure of the original reservoir gas. Thisboundary is not stationary, but moves outward ashydrocarbons are produced from the well andthe formation pressure drops, eventuallydisappearing as the outer-boundary pressuredrops below the dewpoint.

18 Oilfield Review

> Condensate blockage. Once bottomhole pressure in a well fallsbelow the dewpoint, condensate will drop out from the gas phase.Capillary forces favor having condensate in contact with the grains(inset, right). After a brief transient period, the region achieves attsteady-state flow condition with both gas and condensate flowing(inset, top). The condensate saturation, So, is highest near theowellbore because the pressure is lower, which means more liquiddropout. The oil relative permeability, kro, increases with saturation.oThe decrease in gas relative permeability, krg, near the wellboreillustrates the blockage effect. The vertical axis, represented by awellbore, is schematic only.

Distance from borehole

kro

So

ativ

e pe

rmea

bilit

yRe

l

0

0.5

1.0

0 0.5 1.0Condensate saturation

kkkkkrororokkkkkrgrgrgg

krg

Condensateflow channel

Sand grain

Gas flowchannel

Winter 2005/2006 19

In the second region, the condensate-buildupregion, liquid drops out of the gas phase, but itssaturation remains low enough that it isimmobile; there is still single-phase gas flow.The amount of liquid that drops out isdetermined by the fluid’s phase characteristics,as indicated by its PVT diagram. The liquidsaturation increases and the gas phase becomesleaner as gas flows toward the wellbore. Thisregion’s inner-boundary saturation usually isnear the critical liquid saturation for flow, whichis the residual oil saturation.

In the first region, closest to a producingwell, both gas and condensate phases flow. Thecondensate saturation here is greater than thecritical condensate saturation. This regionranges in size from tens of feet for leancondensates to hundreds of feet for rich

condensates. Its size is proportional to thevolume of gas drained and the percentage ofliquid dropout. It extends farther from the wellfor layers with higher permeability than averagesince a larger volume of gas has flowed throughthese layers. Even in a reservoir containing leangas with low liquid dropout, condensateblockage can be significant, because capillaryforces can retain a condensate that builds to ahigh saturation over time.

This near-well condensate blockage regioncontrols well deliverability. The flowingcondensate/gas ratio is essentially constant andthe PVT condition is considered a constant-composition expansion region.12 This conditionsimplifies the relationship between gas and oilrelative permeabilities, making the ratiobetween the two a function of PVT properties.

However, additional relative-permeabilityeffects occur in the near-well region because thegas velocity, and therefore the viscous force, isextreme. The ratio of viscous to capillary forcesis called the capillary number.13 Conditions ofpressure gradient caused by high velocity or lowinterfacial tension have high capillary numbers,indicating that viscous forces dominate, and therelative permeability to gas is higher than thevalue at lower flow rates.

At even higher flow velocities nearer thewellbore, the inertial or Forchheimer effectdecreases the gas relative permeabilitysomewhat.14 The basis of this effect is theinertial drag as fluid speeds up to go throughpore throats and slows down after entering apore body.15 The result is a lower apparentpermeability than would be expected fromDarcy’s law. The effect is usually referred to asnon-Darcy flow.

The overall impact of the two high-velocityeffects is usually positive, reducing the impact ofcondensate blockage. Laboratory corefloodexperiments are needed to measure the inertial and capillary number effects onrelative permeability.

Although the first indication of condensateblockage is typically a productivity decline, itspresence is often determined by pressuretransient testing. A pressure-buildup test can beinterpreted to show the distribution of liquidbefore the well is shut in. The short-timebehavior in the transient test reflects near-wellconditions. Condensate blockage is indicated bya steeper pressure gradient near the wellbore.With longer test times, the gas permeability farfrom the wellbore dominates the response;permeability can be determined from thederivative curve on a log-log plot of pseudo-pressure and shut-in time. If the test continueslong enough—and that shut-in test timedepends on the formation permeability—flowproperties far from the well will be evident.

Gas-Condensate Reservoir ManagementHistorically, condensate liquids have beensignificantly more valuable than the gas, andthis is still true in a few places far from a gasmarket or transport system. The pricedifferential made gas cycling a commonpractice. Injecting dry gas into a formation tokeep reservoir pressure above the dewpointslowly displaces valuable heavy ends that arestill in solution in the reservoir gas. Eventually,the reservoir is blown down; that is, the dry orlean gas is produced at a low bottomhole pressure.

7. Afidick et al, reference 1.8. Barnum RS, Brinkman FP, Richardson TW and

Spillette AG: “Gas Condensate Reservoir Behaviour:Productivity and Recovery Reduction Due toCondensation,” paper SPE 30767, presented at the SPEAnnual Technical Conference and Exhibition, Dallas,October 22–25, 1995.

9. Smits RMM, van der Post N and al Shaidi SM: “AccuratePrediction of Well Requirements in Gas CondensateFields,” paper SPE 68173, presented at the SPE MiddleEast Oil Show, Bahrain, March 17–20, 2001.

10. El-Banbi AH, McCain WD Jr and Semmelbeck ME:“Investigation of Well Productivity in Gas-CondensateReservoirs,” paper SPE 59773, presented at the SPE/CERIGas Technology Symposium, Calgary, April 3–5, 2000.

11. Fevang Ø and Whitson CH: “Modeling Gas-CondensateWell Deliverability,” SPE Reservoir Engineering 11, no. 4(November 1996): 221–230.

12. In a constant-composition expansion condition, the fluidexpands with pressure decline and two phases may form,but no components are removed. This contrasts with thesecond region, which is considered a constant-volumedepletion region, because the liquid phase that formsdrops out from the gas phase and becomes trapped.

13. Henderson GD, Danesh A, Tehrani DH and Al-Kharusi B:“The Relative Significance of Positive Coupling andInertial Effects on Gas Condensate RelativePermeabilities at High Velocity,” paper SPE 62933,presented at the SPE Annual Technical Conference andExhibition, Dallas, October 1–4, 2000.Whitson CH, Fevang Ø and Sævareid A: “GasCondensate Relative Permeability for Well Calculations,”paper SPE 56476, presented at the SPE Annual TechnicalConference and Exhibition, Houston, October 3–6, 1999.

14. Forchheimer PH: “Wasserbewegung durch Boden,”Zeitschrift ver Deutsch Ingenieur 45 (1901): 1782–1788.

15. Barree RD and Conway MW: “Beyond Beta Factors: AComplete Model for Darcy, Forchheimer, and Trans-Forchheimer Flow in Porous Media,” paper SPE 89325,presented at the SPE Annual Technical Conference andExhibition, Houston, September 26–29, 2004.

> Three reservoir regions. Gas-condensate field behavior can be dividedinto three regions once bottomhole pressure, PBH, drops below theHdewpoint pressure, PD. Far from a producing well (3), where the reservoirpressure is greater than PD, there is only one hydrocarbon phase present,Dgas. Closer to the well (2), there is a region between the dewpoint pressureand the point, r1, at which the condensate reaches the critical saturationfor flow. In this condensate-buildup region, both phases are present, butonly gas flows. Once condensate saturation exceeds the critical saturation,both phases flow toward the well (1).

Pres

sure

PD

PBH

r1

Dewpoint pressureDewpoint pressure

Reservoir pressureReservoir pressure

Distance

2 32 32 3reorbo

ell

We

W1

The price of gas has risen to a value thatmakes reinjection a less attractive strategy,unless the fluid is very rich in heavy ends. Gasinjection is now more commonly used as atemporary activity, until a pipeline or othertransport facility is built, or as a seasonalactivity during periods of low gas demand.

Operators also work to overcome condensateblockage. Some techniques are the same in agas-condensate field as they are in a dry-gasfield. Hydraulic fracturing is the most commonmitigating technology in siliciclastic reservoirs,and acidizing is used in carbonate reservoirs.Both techniques increase the effective contactarea with a formation. Production can beimproved with less drawdown in the formation.For some gas-condensate fields, a lowerdrawdown means single-phase production abovethe dewpoint pressure can be extended for alonger time.

However, hydraulic fracturing does notgenerate a conduit past a condensate saturationbuildup area, at least not for long. Once thepressure at the sandface drops below thedewpoint, saturation will increase around thefracture, just as it did around the wellbore.

Horizontal or inclined wells are also beingused to increase contact area within formations.The condensate still builds up around theselonger wells, but it takes a longer time. Theproductivity of the wells remains high longer,but the benefit must be weighed against theincreased well cost.

Some operators have tried shutting in wellsto allow time for the gas and condensate torecombine, but fluid phase behavior generallydoes not favor this approach. Separation of afluid into a gas and liquid phase in the two-phase region of the phase diagram happens

quickly, and after this the phases tend tosegregate, either within a pore or on a largerscale. This phase separation dramatically slowsthe reverse process of recombining gas andliquid. This reversal requires immediate contactbetween the gas and liquid phases.

Another method, cyclic injection andproduction from one well, sometimes called huffand puff injection, uses dry gas to vaporizecondensate around a well and then produce it.This can have short-term benefit for increasedproductivity, but the blockage returns whenproduction begins again and the formation dropsbelow the dewpoint pressure of the currentgas mixture.

In a field test, methanol solvent was injectedinto Hatter’s Pond field, Alabama, USA. In thisfield, production of a gas condensate comesmainly from the lower Norphlet sandstone, butthe field also produces from the Smackoverdolomite. Wells in Hatter’s Pond field are about18,000 ft [5,490 m] deep with 200 to 300 ft [60 to90 m] of net pay. Gas productivity had declinedby a factor of three to five because of condensateand water blockage. The operator, Texaco (nowChevron), pumped 1,000 bbl [160 m3] ofmethanol down tubing at a rate of 5 to 8 bbl/min[0.8 to 1.3 m3/min] into low-permeabilityformations.16 The methanol treatment removesboth oil and water through a multiple-contactmiscible displacement.17 As a result of thetreatment, gas production increased by a factorof three initially, then stabilized at 500,000 ft3/d3

[14,160 m3/d], a factor of two over thepretreatment rate. Condensate productiondoubled to 157 bbl/d [25 m3/d]. Both gas andcondensate rates persisted for more than10 months after treatment.18

Treatment methods have been suggested forremoving condensate blockage through injectionof surfactants mixed with solvents to alterwetting preference in the reservoir. This topicwill be discussed later in this article.

Remobilizing Stranded CondensateThe Vuktyl gas-condensate field in the KomiRepublic, Russia, has been in production since1968. Although productivity was not severelyimpacted by condensate blockage in the field, asignificant amount of condensate dropped out inthe carbonate reservoir. Several condensaterecovery pilots were run in this field.

The field is a long anticline with productionfrom the Middle Carboniferous Moscow andBashkir sequences (above left). The 1,440 m[4,724 ft] thick structure comprises alternating

20 Oilfield Review

> Vuktyl field, Russia. The Vuktyl field in the Komi Republic in western Russia (top) is an anticline,80 km [50 mi] long and up to 6 km [3.7 mi] wide (bottom). The Roman numerals denote gas-processingfacility collection areas. The fluid is predominantly methane [C1], but with a significant amount ofintermediate hydrocarbon components and nitrogen (table, right). The field has three lithotypestt(table, left).tt

0 mi 4

Komi

RRRRRR U S S II I I S S S S S S S S S U U U U U

AAAAAA

ComponentComposition,

% by molevolume

C2

C1

C3

C4

C5+

N2

74.68.93.81.86.44.5

Porosity, %Permeability, mDTypeFine porosity, microvugs, microfracturedPorous, microvugs, microfracturedFractured, microvugs, porous 0.1 to 4513

0.01 to 0.1<0.1 0.1 to 3

3 to 6>6

Winter 2005/2006 21

limestone and dolomite layers, with an averageinterbed thickness of 1.5 m [5 ft]. The reservoirproperties vary widely throughout the field, butthe field has been divided into seven paysequences of three basic types. All three typeshave microfractures and microvugular porosity.Fine pores, low permeability and low porositydistinguish the first type. The third type hasfractures large enough to contribute topermeability. The other type is intermediate.

At discovery, reservoir conditions were36 MPa [5,200 psi] and 61°C [142°F], with 77.5%initial gas saturation. There is a small rimcontaining light oil. Initial gas in place wasabout 430 x 109 m3 [15 x 1012 ft3] and initialcondensate was about 142 million metric tons[1,214 million bbl].19 The initial, stable,producing condensate/gas ratio was 360 g/m3

[87.1 bbl per million ft3].20 The field has anunderlying aquifer, but the water drive wasinsignificant and laterally uneven.

The complex geology of the field, includinghigh-permeability zones that could have acted asthief zones, led the operator, Gazprom, to developthe field with no gas cycling, using depletion gasdrive as the primary production mechanism.

Approximately 170 vertical wells at a typicalspacing of 1,000 to 1,500 m [3,280 to 4,920 ft]were placed in an irregular triangular grid. Mostof the production wells had 10-in. intermediatecasing and 65⁄5

8⁄⁄ -in. production casing. Severalprolific wells had larger, 7 ⁄5⁄⁄ -in. production casing,

allowing 4 ⁄5⁄⁄ -in. tubing. Typical completions in the500- to 800-m [1,640- to 2,625-ft] producing zonewere perforated casing, but some wells usedscreen or openhole completions. The deepestproducers were drilled about 100 to 150 m [328to 492 ft] above the gas/water contact. Atwo-stage hydrochloric acid treatment was themain method of well stimulation.

After nine years, the production plateau was19 x 109 m3/yr [671 x 109 ft3/yr]. A peak stablecondensate production of 4.2 million tons/yr [36 million bbl/yr] occurred during thesixth year of development.

Currently, the Vuktyl field is in its finaldevelopment phase. Reservoir pressure is 3.5 to5 MPa [508 to 725 psi]. Approximate fieldrecoveries are 83% of the gas and 32% of thecondensate, so about 100 million tons[855 million bbl] of condensate remain inthe field.

Experts from Severgazprom, a part of theGazprom Russian Joint Stock Company, and theVNIIGAZ and SeverNIPIgaz institutes conducteda variety of pilot projects in Vuktyl field torecover additional condensate. In 1988, thecompany began the first pilot experiment, usinga solvent to recover stranded condensate.21 Thepilot included six producers, one injection welland three monitor wells (above). The solvent,25,800 tons [293,000 bbl at formation

conditions] of a mixture of propane [C3] andbutane [C4], was injected into the formationfollowed by 35 million m3 [1.24 x 109 ft3] ofseparator gas.22 The intent was to recovercondensate through miscible displacement ofthe solvent bank.

Geophysical observations conducted duringthe experiment indicated that solvent andinjected gas entered the producing intervals ofthe injection well unevenly. Component analysesof samples from the production and monitorwells indicated solvent and injected gas brokethrough only in the two closest monitor wellsand in none of the production wells. Two eventswere seen in these two monitor wells, a changein condensate/gas ratio from 43 to 65 g/m3 [10.4to 15.7 bbl per million ft3] with a decline to theinitial ratio, followed by a second increase from43 to 54 g/m3 [to 13 bbl per million ft3].

Production logging in the monitor wellsrevealed two-phase flow—gas and solvent—onlyin the bottom part of the productive section.Overall, 95% of the solvent was produced from thetwo monitor wells, but condensate recovery wasonly about 0.4%. The pilot study concluded thatthe propane and butane solvent bank was notsufficiently effective in recovering condensate.

A different recovery method, injecting drygas, began in the Vuktyl field in 1993. The gas,from a trunk pipeline that originated in theTyumen district, is injected under pipelinepressure at 5.4 to 7.4 MPa [780 to 1,070 psi]

16. Al-Anazi HA, Walker JG, Pope GA, Sharma MM andHackney DF: “A Successful Methanol Treatment in aGas-Condensate Reservoir: Field Application,” paper SPE 80901, presented at the SPE Production andOperations Symposium, Oklahoma City, Oklahoma, USA,March 22–25, 2003.

17. In a miscible displacement, a solvent allows fluids to mixfreely in a homogeneous mixture. Multiple-contactmiscibility requires sufficient mass transfer between thesolvent and hydrocarbons to achieve miscibility.

18. Al-Anazi et al, reference 16.19. Zhabrev IP (ed): Gas and Gas-Condensate Fields—

Reference Book. Moscow: Nedra, 1983 (in Russian).kTer-Sarkisov RM: The Development of Natural Gas Fields.Moscow: Nedra, 1999 (in Russian).Conversion from mass to volume is based on condensatedensity of 8.55 bbl/ton.

20. Vyakhirev RI, Gritsenko AI and Ter-Sarkisov RM: TheDevelopment and Operation of Gas Fields. Moscow:sNedra, 2002 (in Russian).

21. Ter-Sarkisov RM, Gritsenko AI and Shandrygin AN:Development of Gas Condensate Fields UsingStimulation of Formation. Moscow: Nedra, 1996(in Russian).Vyakhirev et al, reference 20.

22. For more on the role of propane in lowering the dewpointof a gas-condensate field: Jamaluddin AKM, Ye S,Thomas J, D’Cruz D and Nighswander J: “Experimentaland Theoretical Assessment of Using Propane toRemediate Liquid Buildup in Condensate Reservoirs,”paper SPE 71526, presented at the SPE Annual TechnicalConference and Exhibition, New Orleans, September 30–October 3, 2001.

> Plan view with depth to the formation top at a solvent-injection pilotproject near gas-processing facility number 1 (GPF-1). Propane and butanewere injected into Well 103, followed by separator gas. Six productionwells—designated 91, 92, 93, 104, 105 and 106—and three monitor wells—designated 38, 256 and 257—made up the pilot study area. Solvent wasobserved and produced only from the two closest monitor wells: Wells 38and 256.

2 32,30000

2 4002,4002 5002,500

2 6002,600

2 7002,7002 8002,800

2 9002,9003 000 m3,000 m

64

90

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1011011 1021515

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66 93

2573838

103

104

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105

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9186

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Pilot areaProduction well

Injector wellMonitor well

without local compression.23 Formation gas,which is in equilibrium with the retrogradecondensate, is replaced by injected dry gas. Thelight C2 to C4 components and intermediate C5+

fractions evaporate into the dry gas.24 Thus,recovery is improved both by producing moreformation gas, which still contains componentsother than methane, and by vaporizing strandedliquids and producing them along with theinjected gas. In addition, the injected gas causesno problems for the production facilities when itbreaks through. However, a significant volume ofdry gas has to be injected to produce tangibleamounts of condensate.

Engineers monitored the process in bothinjection and production wells using gas-liquidand gas-adsorption chromatography (below).25

Since the injection gas did not contain nitrogen,the nitrogen content was used as the indicatorof formation gas.26

The 1993 pilot test program was expanded toadditional pilot locations in 1997, 2003 and 2004.By the middle of 2005, the operator had injected10 x 109 m3 [354 x 109 ft3] of dry gas into thepilot wells, and recovered a significant amountof liquid. Comparing the recovery with estimatesof production through depletion alone showedthat the pilot area produced an additional

785 thousand tons [9.45 million bbl] of C2 to C4

and 138 thousand tons [1.22 million bbl] of C5+.27

The operators also ran single-well pilotprojects in Vuktyl field. Although blockage wasnot severe enough to cause a dramatic drop inproductivity in this field, the operator soughtways to counteract the increased saturation thathad formed around wells. The treatmentincluded injecting solvent—a mix of ethane andpropane—into a well, followed by dry gas. Aftera sufficient volume of injection, the well wasreturned to production.

When the solvent contacts the trappedcondensate, the solvent, formation gas andcondensate mix freely into a single phase. Thedry gas that follows is able to mix freely with thesolvent mixture. Thus, when the well producesagain, the injected gas, solvent and condensateare produced as a single fluid. As a result,the condensate saturation is at or near zero inthe treated zone. As formation gas follows themixture back through the treated zone, a zone ofincreased condensate saturation will reform,but well productivity can be improved byperiodic treatments.

Treatment volumes ranged from 900 to2,900 tons [10,240 to 33,000 bbl] of solvent and1.2 to 4.2 million m3 [42 to 148 million ft3] of drygas.28 Although the effectiveness varied from wellto well, the treatments generally had goodresults. The productivity of four of the wellsincreased by 20% to 40% over a period rangingfrom 6 months to 1.5 years, followed by a declineto the original production levels (next page).

Modeling Condensate BlockageReservoir-simulation models are commonly usedto predict the performance of gas-condensatefields. The models incorporate rock and fluidproperties to predict the dynamic influence ofcondensate blockage on gas and condensateproduction. However, a typical gridblock of afull-field model (FFM) can be much larger thanthe blockage zone, so a coarse grid model maysignificantly overestimate well deliverability.

The most accurate way to determine near-well behavior of a gas-condensate field is byusing a simulator with a fine grid. There are twoways to do this: use a FFM with local gridrefinement (LGR), or use a single-well modelwith a fine grid near the well.

Modern simulators, such as the ECLIPSE 300reservoir simulation software, include capabilityfor LGR. Small gridblocks can be used nearwellbores or other features—such as faults—that can significantly impact local flow. Farther

22 Oilfield Review

> Dry-gas injection pilot. Separator gas injected into three wells— designated 269, 270 and 273—vaporized stranded condensate for production from surrounding wells (top). Dry gas (blue) broketthrough a few months after the pilot began (middle). Nitrogen in the produced gas (green) graduallydecreased, indicating that less formation gas was being produced. The liquid C5+ fraction (red)indicates a slow decline after gas breakthrough. The results show significant production of formationgas, light (C2 to C4) and intermediate components (C5+) from both produced formation gas andremobilized stranded condensate (table, bottom).

Oct93

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pone

nt c

onte

nt, m

ole

%

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1

2

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4 40

30

20

10

0

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fract

ion,

%

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Component from:

Formation gas,million m3

Formation gas,thousand tons

Strandedcondensate,

thousand tonsDry gas,

million m3

5,9731,996

380238208

Produced gasInjected gas

Produced C2 to C4Produced C5+

10,0357,366

130

270129

2697

195

158

273

133

254151

128

127

100

2,700 m2,700 m2 6002,6002,5002,5002,4002,4002 3002,300

2,2002,2002,1002,100

2,1002,1002,2002,2002,3002 300

131/150132

Injector wellProduction wellPilot area

Winter 2005/2006 23

away from such features, the gridblocks grow toa size typical of a FFM. The cost of using LGRmay be a significant increase in computationtime in some cases.

Another way to examine gas-condensateblockage effects is by using a single-well model.In many cases, radial symmetry allows a well tobe treated in a two-dimensional model, using thedimensions of height and radial distance. Thegridblocks nearest the well are small, nominallyhalf a foot [about 15 cm] in the radial direction.The radial dimension increases with eachgridblock away from the wellbore, until itreaches a maximum size used for the rest of themodel. The fine grid provides good resolutionwhere the flow is highest and the formationsaturation behavior is at its most complex.Capillary, viscous and inertial forces can beappropriately modeled. Far from the wellbore,conditions of pressure and flow can be takenfrom a FFM and applied as boundary conditions.

Sometimes, gas-condensate reservoirsimulations can be performed using a black-oilmodel. This type of model assumes that thereare only two hydrocarbon components in thefluid, oil and gas, and it allows for somepressure-dependent mixing of gas in oil. Thismodel is inappropriate when the compositionschange significantly with time, such as throughgas injection, or when there is a significantcompositional gradient. In those cases, acompositional model with many hydrocarboncomponents is necessary. In addition, some

black-oil models do not include capillarynumber effects, which are important fordetermining well deliverability.

Another way to account for condensateblockage in a full-field model is through the useof pseudopressures. The equation for flow of gasfrom a reservoir to a wellbore can be expressedin terms of a pseudopressure, which is anintegral over pressure. By separately treatingthe three regions described before—two-phaseflow near the well, gas flow with condensatebuildup next, and single-phase gas flow far fromthe well—it is possible to calculate thepseudopressure from the producing gas/oil ratio,PVT properties of the fluid, and gas and oilrelative permeabilities.29 As discussed previously,the constant-composition expansion condition inthe first region simplifies the relative-permeability ratios. This pseudopressuremethod adds little time to running a FFM.

Pseudopressure methods have also beenimplemented in spreadsheet format.30 Thesespreadsheets assume a homogeneous reservoirand a simple black-oil model. They provide fastpredictions that can be used when manysensitivity runs are necessary. A similarsemianalytical method was combined with theeffects of non-Darcy flow and permeabilitylayering. Comparisons using a compositionalsimulator with a fine grid showed that the semianalytical method captured all thenear-well effects accurately and was easy toembed in a FFM at essentially no increase incomputational time.31

Modeling Behavior Around a FractureReservoir simulation modeling was used todetermine the effectiveness of fracturing in theSW Rugeley field in south Texas, USA. Thisfield produces gas condensate from low-permeability—about 1-mD—Frio sand. A well inthis field, which was drilled and completed byWagner & Brown, was hydraulically fracturedinitially, but a rapid decline in productivity ledthe company to refracture the formation aboutthree months later, in June 2002. Productivityimproved, but then continued to decline overthe next few months. The drawdown in thevicinity of the well was below the dewpointpressure, so the company investigated the accumulation of condensate saturationaround a fracture.

Engineers at Schlumberger developed ahomogeneous, radially symmetric, single-wellmodel. This simple model demonstrated thatcondensate blockage could result in a rapidfalloff in productivity. It also provided a meansto quickly check the impact of permeabilityreduction due to compaction caused by pressure decline.

23. Ter-Sarkisov RM, Zakharov FF, Gurlenov YM, Levitskii KOand Shirokov AN: Monitoring the Development of Gas-Condensate Fields Subjected to Dry Gas Injection.Geophysical and Flow-Test Methods. Moscow: Nedra,s2001 (in Russian).Dolgushin NV (ed): Scientific Problems and Prospects ofthe Petroleum Industry in Northwest Russia, Part 2: TheDevelopment and Operation of Fields, ComprehensiveFormation and Well Tests and Logs, A Scientific andTechnical Collection. Ukhta: SeverNIPIgaz, 2005 (in Russian).Vyakhirev et al, reference 20.Ter-Sarkisov et al, reference 21.Ter-Sarkisov, reference 19.

24. For a laboratory study of methane injection into coreswith condensate saturation: Al-Anazi HA, Sharma MMand Pope G: “Revaporization of Condensate withMethane Flood,” paper SPE 90860, presented at theSPE International Petroleum Conference, Puebla,Mexico, November 8–9, 2004.

25. Dolgushin, reference 23.26. Vyakhirev et al, reference 20.27. Dolgushin, reference 23.28. Gritsenko AI, Ter-Sarkisov RM, Shandrygin AN and

Poduyk VG: Methods of Increase of Gas CondensateWell Productivity. Moscow: Nedra, 1997 (in Russian).yVyakhirev et al, reference 20.The density of the solvent mixture is 553 kg/m3.

29. Fevang and Whitson, reference 11.30. Mott R: “Engineering Calculations of Gas-Condensate-

Well Productivity,” SPE Reservoir Evaluation &Engineering 6, no. 5 (October 2003): 298–306.

31. Chowdhury N, Sharma R, Pope GA and Sepehrnoori K:“A Semi-Analytical Method to Predict Well Deliverabilityin Gas-Condensate Reservoirs,” paper SPE 90320,presented at the SPE Annual Technical Conference andExhibition, Houston, September 26–29, 2004.

> Changes in well productivity as a result of injection of ethane andpropane followed by dry gas. The difference of the squares of the reservoirpressure, PR, and the bottomhole pressure,R PBH, as the flow rate increasesHprovides a measure of productivity. Before treatment (blue), the wellrequired a larger pressure difference to produce than it needed afterttreatment (red). Four months after treatment, productivity had degradedslightly (green), but it was still significantly better than productivity beforetthe treatment.

P2 Rese

rvoi

r - P

r2 Bo

ttom

hole

, MPa

2

0

4

8

12

16

0 50 100 150 200 250

Gas-condensate mixture production, thousand m3/d

With these results in hand, Wagner & Brownhad Schlumberger develop a more detailedreservoir model, using ECLIPSE 300 reservoirsimulation software (above). The model wasrefined by history-matching to the gasproduction rate, which also provided a goodcorrelation to the condensate production.Drawdown in the fracture induced the buildupof condensate saturation along the fracture(next page). The average reservoir pressuredropped below the 6,269-psi [43.22-MPa]dewpoint pressure during the modeled period.

With a good history-match, Wagner & Browncould determine whether the fracture providedsignificant gains in productivity. The model wasrerun without the fracture, which resulted in aproduction curve that continued the previousdecline rate (left). The difference between thenonfractured case and the measured productionindicates the success of the fracture job. Over aseven-month period, the cumulative productionattributed to the fracture job was 256 million ft3

[7.25 million m3] of gas and 15,300 bbl [2,430 m3]of condensate. This modeling study verified thesuccess of a field application.

24 Oilfield Review

> History-match of model of SW Rugeley field with a hydraulic fracture. The ECLIPSE 300 model of one well in the Frio sand has small grids around thewell and along the fracture (top left). Smaller grids were also placed at the fracture tips. The field gas-rate history was matched by the simulation (tt topright), yielding good results for condensate rate (tt bottom right). The changes in production after the fracture job were due to fracture cleanup andttchanges in pressure in flowlines. The model indicated the average reservoir pressure dropped below the 6,269-psi dewpoint pressure during thisproduction period (bottom left).tt

Fracture Well

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> The hydraulic fracture effect. Rerunning the Frio well model with no fracture generated a simpledecline curve indicating a significant productivity increase could be attributed to an induced fracture.

Mar2002

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Production historyModel with no fracture

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Winter 2005/2006 25

2,500

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7,500

0

0.1

0.2

0.3

0.2

0.4

0.6

0.8

1.0

Rese

rvoi

r pre

ssur

e, p

siCo

nden

sate

sat

urat

ion,

frac

tion

Gas

rela

tive

perm

eabi

lity,

fract

ion

July 15, 2002 July 25, 2002

2,500

3,750

5,000

6,250

7,500

0

0.1

0.2

0.3

0.2

0.4

0.6

0.8

1.0

Rese

rvoi

r pre

ssur

e, p

siCo

nden

sate

sat

urat

ion,

frac

tion

Gas

rela

tive

perm

eabi

lity,

fract

ion

August 20, 2002 September 20, 2002 December 20, 2002

< C d bl k dCondensate blockage around afracture, Frio model. For each timestep, model results indicatepressure decline (top), condensatesaturation (middle) and gas relativepermeability (bottom). The first twottime steps in July 2002 (left) focustton the immediate vicinity of thefracture and the later three timesteps (below) show a wider viewwof the whole model area. Pressuredeclines rapidly along the fracture(left, top). The approximate dewpointpprofile (oval curves) expands outwardfrom the fracture. The low gaspermeability around the fracture at later time steps indicates thecondensate blockage.

Application of Best PracticesChevron recently completed a study of five gas-condensate reservoirs that are at differentstages of development. The objective was totransfer best practices among variousdevelopment teams.

One of the fields in the study, a North Seareservoir, is a marine turbidite with gross-payinterval of more than 120-m [400-ft] thickness.The average reservoir permeability is 10 to15 mD, with average porosity of 15%. Theoriginal reservoir pressure of 6,000 psi[41.4 MPa] is a few hundred psi [a few Mpa]above the dewpoint pressure, although thedewpoint varies from east to west.32

The bottomhole pressure was below thedewpoint from first production. Thecondensate/gas ratio ranged from 70 bbl permillion ft3 [393 m3 per million m3] in the east to110 bbl per million ft3 [618 m3 per million m3] inthe west. Some wells experienced a productivityreduction of about 80%, most of which occurredin early production.

Chevron followed a step-by-step procedure tounderstand and history-match the field’s gas-condensate behavior. The operator selected coresamples that spanned the range of permeabilityand porosity of the field and fluids that mimicreservoir-fluid behavior—liquid dropout as afunction of pressure, viscosity and interfacialtension—at lower temperature. The companymeasured relative permeability over a rangeof flow conditions and fitted those datato several relative-permeability models for usein simulators.

A spreadsheet using an analyticalpseudopressure method was used to calculatedeliverability. The calculation showed thatproductivity index (PI) decreased from about 80 to about 15 thousand ft3/d/psi [33 to 6 thousand m3/d/kPa], with little differencebased on bottomhole pressure until late in fieldlife (above).

A detailed single-well, compositional flowsimulation using the Chevron CHEARS reservoirsimulator was performed with realistic geology.Far-field boundary conditions came from a full-field model. The simulation honored wellproduction practices and differential depletionin the field. The predictions provided a goodmatch to results from three vertical wells andone inclined well (next page).

This study led to several initiatives in thefield. Hydraulic fracturing to improveproductivity is an active effort in this field, sothese models are being used to betterunderstand fracture effectiveness. In addition,lessons learned from this field regarding theimpact of condensate blocking have been usedextensively in planning for wells in new projectsin other gas-condensate fields.

A Fundamental AlterationThe high price of natural gas on world marketsin recent years has stimulated interest indeveloping gas reservoirs. Companies seek newways to optimize their gas-condensate resources.

Hydraulic fracturing can mitigate the effectof condensate blockage, but it does noteliminate the accumulation of condensate in

26 Oilfield Review

> Spreadsheet model results for a North Sea well. A homogeneous single-well model in a spreadsheetprovided a way to quickly examine different effects. For example, the bottomhole pressure had littleeffect on gas productivity index, PI.

0

10

20

30

40

Gas

PI, t

hous

and

ft3 /d/p

si

7,000 6,000 5,000

Reservoir pressure, psi

Bottomholepressure, psi

2,0001,2501,000500

4,000 3,000 2,000

50

60

70

80

90

32. Ayyalasomayajula P, Silpngarmlers N and Kamath J:“Well Deliverability Predictions for a Low PermeabilityGas Condensate Reservoir,” paper SPE 95529, presentedat the SPE Annual Technical Conference and Exhibition,Dallas, October 9–12, 2005.

33. Fahes M and Firoozabadi A: “Wettability Alteration toIntermediate Gas-Wetting in Gas/Condensate Reservoirsat High Temperatures,” paper SPE 96184, presented atthe SPE Annual Technical Conference and Exhibition,Dallas, October 9–12, 2005.

34. Kumar V, Pope G and Sharma M: “Improving Gas andCondensate Relative Permeability Using ChemicalTreatments,” paper SPE 100529, to be presented at the SPE Gas Technology Symposium, Calgary, May 15–18, 2006.

Winter 2005/2006 27

areas where the pressure in the formation isbelow dewpoint. Dry gas and solvent injectionsare able to mobilize some condensate, but theliquid saturation profile near a producing wellreforms and the blockage effect returns.

New alternatives are being examined inlaboratories. For example, some studies havefocused on ways to prevent fluid buildup byaltering reservoir-rock wettability.

Although mineral surfaces such as quartz,calcite and dolomite prefer to be wetted byliquids rather than gas, there are solids thathave a gas-wetting preference. In particular,fluorinated compounds such as Teflon surfacesare gas-wetting. So, fluorinated solvents havebeen used to alter the wettability of cores.Recently reported results at high temperature—140°C [284°F]—typical of gas-condensatereservoirs showed a strong reversal of wetting ina gas-water-reservoir rock system, but was lesssuccessful in a gas-oil-reservoir rock system.33

Researchers at the University of Texas atAustin conducted laboratory tests using 3Mfluorocarbon surfactants.34 The results onreservoir core samples blocked by condensateindicate about a doubling of the gas andcondensate relative-permeability values aftertreatment. Based upon these promisinglaboratory data, Chevron may test this treatmentin a blocked gas-condensate well sometime in2006. Treatments such as these must be fieldtested under a variety of conditions to fullydevelop and prove the technology. If thetechnique is ultimately successful, then the costof the surfactants used in the treatment will bevery small compared to the benefits of increasedgas and condensate production rates.

The alteration these solvents make in therock addresses a fundamental cause ofcondensate blockage: capillary accumulation ofliquid because of the wetting preference of therock. Avoiding liquid buildup alleviates theproblem of choking production, so that a highproduction rate can be achieved. —MAA

> Single-well simulation results. The simulator gave a good match to bothgas PI (top) and bottomhole pressure (middle) for behavior in a North Seawell. Different layer properties resulted in different extents of condensatesaturation buildup (bottom).

Gas

PI, t

hous

and

ft3/d

/psi

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90

80

70

60

50

40

30

20

10

0

Time, yr

SimulationSimulationSimulation

Field dataField dataField data

Botto

mho

le p

ress

ure,

psi 2,500

3,000

3,500

2,000

1,500

1,000

500

0

Time, yr

Field dataField data

Si l iSimulation

Oil saturation, fraction0 0.40.2

Bore

hole

3.5 4.0 4.5 5.0 5.5

3.5 4.0 4.5 5.0 5.5

Gas Condensate PVT – What’s Really Important and Why?

Curtis H. Whitsona,b,c

Øivind Fevangb Tao Yanga,b

(a) Norwegian U. of Science and Technology (NTNU), (b) PERA a/s

(c) Corresponding author, [email protected] / [email protected]

Paper (© Curtis H. Whitson) presented at the IBC Conference “Optimisation of Gas Condensate Fields”, London, Jan. 28-29, 1999, Cumberland Hotel.

IBC UK Conferences Ltd., Gilmoora House, 57-61 Mortimer Street, London W1N 81X, UK http://www.ibc-uk.com

ABSTRACT

This paper gives a review of the key PVT data dictating recovery and well performance of gas condensate reservoirs. The importance of specific PVT data are put in the context of their importance to specific mechanisms of recovery and flow behavior. Phase behavior important to gas cycling projects is also covered. Modeling gas condensate reservoir fluid systems with an equation of state is discussed, as is EOS modeling of complex fluid systems with strongly varying compositions and PVT properties.

INTRODUCTION It could be argued that the engineering of a gas condensate field is 80% traditional “gas” engineering, and 20% “extra” engineering. The numbers could be 90/10 or 70/30 – but the majority of engineering of any gas condensate field is always the same as the engineering of a gas reservoir without condensate. The main difference between a gas condensate field and a “dry” gas field is the additional income derived from surface condensate production. Condensate production evolves from produced reservoir gas (= produced “wet gas” = produced wellstream) as the wellstream is processed at the surface. The production of reservoir gas can, for the most part, be handled with traditional gas engineering tools.

Gas Condensate PVT – What’s Really Important and Why? C.H. Whitson, Ø. Fevang, and T. Yang

2

From an engineering point of view, the two “extra” issues which must be addressed in a gas condensate reservoir are:

• How the condensate “yield” will vary during the life of a reservoir, and • How two-phase gas/oil flow “near” the wellbore affects gas productivity.

Both of these issues are strongly related to the PVT properties of the fluid system (though productivity is more affected by relative permeability effects). PVT properties important to the engineering of all gas condensate reservoirs includes:

• Z-factor • Gas viscosity

and a few “extra” properties needed to handle the “condensate” part of a gas-condensate reservoir:

• Compositional (C7+) variation with pressure • Oil viscosity and liquid dropout

Dewpoint pressure is implicitly defined by the pressure dependence of compositional variation. As discussed below, the dewpoint is less importance than is commonly thought. The PVT properties listed above are particularly important to reservoirs produced by pressure depletion. For gas condensate reservoirs undergoing gas cycling it may also be important to quantify phase behavior (vaporization, condensation, and near-critical miscibility) which develops in gas cycling below the dewpoint. Compositional grading in gas condensate reservoirs may be important to the design of well placement, estimation of in-place surface volumes, reserves, and prediction of fluid communication vertically (between geologic layers) and areally (between fault blocks). Prediction of a potential underlying oil is often required in discovery wells which are drilled upstructure and encounter only gas which is near-saturated. Here, accurate sampling and PVT modeling are paramount. A PVT modela should describe accurately the key phase, volumetric, and viscosity behavior dictating the key processes affecting rate-time performance and ultimate recoveries of surface gas and oil. Unfortunately, a PVT model may not be capable of accurately describing all PVT properties with equal accuracy. EOS models often have difficulty matching retrograde phenomena (compositional variation of gas, and liquid dropout), particularly when the system is near-critical, or only small amounts of condensation occur just below the dewpoint (“tail-like” retrograde behavior). Oil

a We define a PVT (pressure-volume-temperature) model to include the EOS (equation of state) model describing phase and volumetric behavior, together with the viscosity model (e.g. the Lorentz-Bray-Clark1 or Pedersen et al.2); the viscosity model is not formally linked with the EOS model but makes use of EOS-calculated density.


3

viscosities are also difficult to predict for reservoir condensates, and measured oil viscosities are not usually available for tuning the viscosity model. Consequently, it is important to determine which PVT properties are most important to the accurate engineering of reservoir and well performance for a given field development. Different fields require different degrees of accuracy for different PVT properties, dependent on field development strategy (depletion vs. gas cycling), low or high permeability, saturated or highly undersaturated, geography (offshore vs. onshore), and the number of wells available for delineation and development. Consider the following examples. Example 1. A small offshore “satellite” reservoir with high permeability (kh=4,000 md-m), initially undersaturated by 400 bar, and with a test yield of 300 STB/MMscf. Example 2. A large offshore deep-water reservoir with moderate permeability (kh=1000 md-m), initially saturated or near-saturated (?), large structural relief, and a test yield of 80 STB/MMscf. A single (and very expensive) discovery well has been drilled. Example 3. An onshore “old” undeveloped gas cap with well-defined initial volume (by production oil wells and pressure history), uncertain initial composition (estimated initial yield of 120 STB/MMscf), partially depleted due to long-term production of underlying oil, and low permeability (kh=300 md-m). These three examples require significantly different emphasis in the treatment of PVT data. Why? The reason lies in a coupling of the reservoir and well performance with PVT properties. Every gas condensate reservoir provides a new example with a different set of conditions requiring different emphasis on which PVT data are important. This paper will attempt to explain when and why various PVT properties are important to the development of a particular gas condensate field.

PVT EXPERIMENTS Constant Composition (Mass) Expansion Test The constant composition expansion (CCE) test, sometimes referred to as a constant-mass expansion test, is used to measure dewpoint pressure, single-phase gas Z-factors, and oil relative volume below the dewpoint (“liquid dropout curve”). A sample of reservoir fluid is charged in a visual PVT cell and brought to reservoir temperature and a pressure sufficiently high to ensure single-phase conditions. Pressure is lowered by increasing cell volume until a liquid phase is visually detected (through a glass window). Total cell volume and liquid volume are monitored from the initial reservoir pressure down to a low pressure (dictated by cell and sample size).


4

Constant Volume Depletion Test The constant volume depletion (CVD) test is an extremely important laboratory test which monitors the phase and volumetric changes of a reservoir gas sample (at reservoir temperature) as the pressure drops below the dewpoint and equilibrium gas phase is removed. The CVD test simulates closely the actual behavior of a gas condensate reservoir undergoing pressure depletion, and results from the lab measurements can be used directly to quantify recoveries of surface gas and condensate as a function of pressure below the dewpoint. Combined with single-phase Z-factors from the CCE test, a complete prediction of depletion behavior (recoveries and liquid-yield variation) can be accurately predicted from initial pressure to abandonment. The CVD test involves stepwise lowering the pressure below the dewpoint, with an associated increase in cell volume. After equilibration at each pressure, enough equilibrium gas is removed from the top of the cell to bring the cell back to the original volume occupied at the dewpoint. The amount of gas removed, its composition and Z-factor, and the remaining oil volume in the cell are measured and reported. A “two-phase” Z-factor is also reported for use with the “gas” material balance (see discussion below). Accurate measurement of the removed gas composition is very important to the prediction of condensate recovery and liquid-yield variation – much more important than accurate measurement of retrograde oil volumes. Special laboratory procedures should be followed to ensure accurate CVD compositional measurements (e.g. appropriate heating of tubing used to remove equilibrium gas from the cell). Measurement of the final low-pressure condensate composition allows an important “backward” material balance check.b

INITIAL FLUIDS IN PLACE AND DEPLETION RECOVERIES Gas Z-factor Muz Standing would be happy to hear that the Z-factor is (still) the only PVT property which always needs accurate determination in a gas condensate reservoir (as in a “dry” gas reservoir). The reason is (1) to get an accurate and consistent estimate of the initial gas (and condensate) in place, and (2) to accurately predict the gas (and condensate) recovery as a function of pressure during depletion drive.c Single-phase gas Z-factors are measured experimentally at reservoir temperature and pressures from the initial reservoir pressure to the dewpoint. These data are b The backward material-balance check is made by starting with the final condensate composition and amount (using the reported final oil relative volume and properties), adding incrementally the removed gas from each CVD step, and ending up with a check of the original fluid composition. This check is insensitive to oil relative volume (except the final value), a big advantage over the traditional “forward” material balance which is extremely sensitive to all relative oil volumes and, consequently, can not be used for leaner gas condensates. c It also is important to quantify recovery by depletion for a reservoir which is to be gas cycled, because the evaluation of economics will always involve comparison of the gas cycling project with depletion drive.


5

reported as part of the constant composition expansion test. Z-factors used in the material balance equation below the dewpoint are “back-calculated” from data in the constant volume depletion test. These so-called two-phase Z-factors are “pseudo” (not-physical) properties which should only be used in the traditional gas material balance equation. It is not commonly recognized that condensate recovery is strongly related to the recovery of gas. Gas Z-factors dictate gas and oil recoveries during depletion (together with the amount of water expansion and influx), because recoveries are proportional to (Zi/Z) – i.e. the term [1 - (Zi/Z)(p/pi)]. In fact, at average reservoir pressures above the dewpoint, condensate recovery “exactly” equals the gas recovery. Consequently, condensate recoveries are strongly dependent on accurate description of gas-phase Z-factors (both above and below the dewpoint). As an example for a high-pressure reservoir, a +5% error in Zi and a –5% error in Z at the dewpoint will result in (a) a +5% error in initial gas and initial condensate in place, and (b) a +5 to +10 recovery-% error in recovery of gas and condensate at the dewpoint. Compositional (C7+) Variation During Depletion As mentioned earlier, the distinguishing characteristic of a gas condensate field is the added value from condensate production, in addition to gas. Surface condensate is, for practical purposes, the C7+ contentd of the produced wellstream. This simplification makes the treatment of many engineering calculations easier to understand without loosing engineering accuracy. The condensate rate profile is easy to convert into an economic profile, and engineers can readily relate the two. But how can we readily forecast the condensate rate profile for a gas condensate reservoir? For a surface gas-rate production profile qg(t), the profile of oil rate versus time is given (approximately) by

CVDogCVD7

CVD7go )C(

1)y(1

)y()t(q)t(q ⋅

−⋅≅

+

+ ........................................................................ (1)

o

o

sc

scog MP

TRC

ρ⋅= ....................................................................................................... (2)

where (ρo /Mo) = (ρ7+/M7+)CVD. Time dependence of CVD properties must be correlated with cumulative wet-gas volumes produced,

∫= dtqG wpw ............................................................................................................ (3)

where

qw = qg + qo Cog........................................................................................................ (4)

d The simplification of surface condensate being “essentially” C7+ is a subjective choice. One could easily have chosen C6+ or C5+ without any change in our comments.


6

Given the qw(t) profile and Gpw(t), this can be translated into cumulative wellstream produced from the CVD test, (np/nd)CVD,

(np/nd) = Gpw/Gw – [1 – (p/z)d/(p/z)i] ; p Sd............................................................. (5)

where all CVD properties = initial gas properties for p > pd. Cog represents the surface gas equivalent of one surface oil volume. Equations for converting CVD results to approximate surface product recoveries, including the depletion recovery from initial to dewpoint pressure are:

( )( )

( )( )

( )( )ogsk

ogsi

k

N

1k d

p

i

d

i

dgD Cr1

Cr1

n

n

Z/p

Z/p

Z/p

Z/p1RF

⋅+⋅+

⋅

∆⋅+

−= ∑

=

........................................... (6)

( )( )

( )( )

( )( )ogsk

ogsi

k

N

1k d

p

i

d

i

doD Cr/1

Cr/1

n

n

Z/p

Z/p

Z/p

Z/p1RF

++

⋅

∆⋅+

−= ∑

=

........................................... (7)

og7

7s C

1z1

zr ⋅

−≅

+

+ ...................................................................................................... (8)

A simple spreadsheet calculation using these equations allows quick translation of laboratory CVD data to important engineering and commercial quantification of in-place surface volumes, reserves, and production forecasts. Fig. 1 and Table 1 shows an example calculation using Eqs. 6-8 for a rich-gas condensate. Compositional Variation with Depth Numerous field case histories have shown that composition varies with depth in petroleum reservoirs. Component “segregation” due to gravitational forces is usually given as the physical explanation for the variation in composition. A theoretical model for such variation was already defined by Gibbs in the late 1800’s for an isothermal system under the influence of a constant force field such as gravity. The result of gravitational segregation is that a gas condensate gets richer at greater depths, with increasing C7+ mole fraction (and dewpoint pressure)3. Not all fields show compositional gradients with depth as predicted by the isothermal model. Some fields show practically no gradient over large depths, such as the Cupiagua field in Columbia4 where a near-critical gas condensate with more-or-less constant composition is found over an interval of some 2000 m. Some oil fields have gradients larger than predicted by the isothermal model. Høier5,6 made comprehensive calculations using a number of thermal diffusion models which indicate that thermal gradients typically reduce compositional gradients in gas condensate fluids, while for oils a thermal gradient may cause either a reduction or an increase in compositional gradients. Our concern with compositional gradients in gas condensates will be limited to three topics: (1) assessing the effect of a gradient on in-place surface volumes, (2) assessing the prediction of a gas-oil contact using a theoretical gradient model, and (3) the impact of compositional gradients on depletion (and cycling) recoveries.


7

Variation in C7+ composition with depth will obviously affect the calculation of initial surface condensate in place, compared with a calculation based on a constant composition. Depending on the “location” of the sample used in the constant-composition model, either smaller or larger initial condensate volumes in place can result when compared with a gradient modele. The gradient model will typically give an “optimistic” in-place sensitivity when the gas condensate reference sample is upstructure. If the reference gas sample is downstructure then the gradient model will provide a “pessimistic” in-place sensitivity. For reservoirs with limited control of fluid variation with depth, we recommend using the “in-situ representative” samples available, linear interpolation between these samples, and for sensitivities use both (a) the gradient model for extrapolation beyond the samples and (b) a constant-composition extrapolation. Another interesting feature of near-saturated reservoirs with compositional gradients is that the recoverable condensate volumes by depletion are insensitive to whether the model is initialized with or without a compositional gradient. This lack of sensitivityf will not be apparent if comparisons are made using recovery factors (because initial volumes in place can be quite different for the two models of compositional initialization). A gradient model may also predict a transition from gas to oil which can dramatically affect the initial oil in place volumes (see discussion below). However, a predicted GOC from an upstructure gas sample is, at best, a “possibility”. Results of predicted “oil zones” from gas samples should only be used for sensitivity analysis of a new discovery, or in a reservoir where additional delineation wells are not planned. Dewpoint Pressure Strictly speaking the dewpoint pressure is the pressure where an incipient liquid phase condenses from a gas phase. Practically, the dewpoint marks the pressure where (1) reservoir gas phase composition changes and becomes leaner, and (2) condensate accumulation starts in the reservoir. These two changes can have a profound effect on reservoir and well performance – or, they may have little impact. The importance of the actual dewpoint pressure will vary from reservoir to reservoir, but in most situations accurate dewpoint determination is not important. Why? First, in the context of compositional variation with pressure (and associated variation of condensate yield with pressure) accurate determination of the thermodynamic dewpoint pressure is not of particular importance. In fact, we don’t need to know the “specific” dewpoint at all as long as the variation of composition (C7+ content) with pressure is well defined “near” the thermodynamic dewpoint. e The gradient model requires that a composition be specified at a reference depth with a reference pressure and temperature. f This behavior is readily understood in a black-oil model using a solution oil-gas ratio rs(p) function. The initial variation of rs (and dewpoint) with depth is short-lived when reservoir pressure drops below the dewpoint, as rs of the equilibrium gas through the reservoir becomes (more-or-less) constant at the average reservoir pressure. Because only reservoir gas flows into wells, the producing OGR will reflect the equilibrium rs at average reservoir pressure, which becomes independent of depth when pR<pd.


8

Second, when the bottomhole flowing pressure (BHFP) drops below the dewpoint and two phases start flowing near the wellbore, gas relative permeability drops and well productivity drops. However, as long as BHFP is “anywhere near” the dewpoint the well will have excess deliverability – i.e. we simply reduce the BHFP to produce more gas (even though the well productivity is lower). Only when the BHFP reaches a minimum value (dictated by some delivery-pressure constraint) will the well no longer be able to deliver the desired rate. At this point, well productivity is important. However, this occurs at a BH flowing pressure much lower than the dewpoint. A typical minimum BHFP might be 50-150 bara, while dewpoint pressures are typically 250-400 bara. Whether the BHFP drops below the dewpoint at 400 or 350 bara has little impact on what the well will (or won’t) produce when BHFP reaches a minimum constraint of 100 bara. Another (less common) need for dewpoint pressure is when an underlying saturated oil zone may exist and a PVT model is used to predict the existence and location of the gas-oil contact (GOC). In this case, the PVT model dewpoint should be tuned precisely to an accurately measured dewpoint pressure. It is not uncommon that a predicted GOC may vary 10’s of meters per bar of uncertainty in the (PVT-model) dewpoint pressure. Thus an accurate description of the dewpoint pressure will have an impact on the prediction of initial oil and gas in place, placement of delineation wells, and potential field development strategy. In this situation, accurate dewpoint measurement and equally-accurate modeling of the measured dewpoint should be given due attention. On the other hand, if accurate treatment of the dewpoint pressure is not required (for estimating a GOC), then we recommend using little if any weighting of the measured dewpoint pressure when tuning the PVT model. Instead, priority should be given to matching the variation of C7+ with pressure in the removed gas from a constant volume depletion test.

CONDENSATE BLOCKAGE When BHFP drops below the dewpoint and two-phase gas/oil flow stabilizes in the near-wellbore region, relative permeability to gas (the primary flowing phase) may drop dramatically and the well deliverability is lowered accordingly. Saturations in the near-wellbore region can reach 40-60%, with gas permeability reductions of 0.05-0.2. Flow in the near-wellbore region reaches a steady-state condition in a relatively short time after the BHFP drops below the dewpoint. Flow theory shows that the produced wellstream mixture is constant throughout the “steady-state” region, meaning that if we “captured” the flowing mixture at any point within this region, its composition would be the same as the producing wellstream mixture.g g The flowing mixture composition at some point within the steady-state region will not equal to the overall composition occupying the pore volume (“in-situ” composition) at that point, as the in-situ composition will vary throughout the steady-state region.


9

Permeability reduction in the near-wellbore (steady-state) region is particularly important because most of the pressure drop will be greatest in this region. A relative permeability reduction of 0.1 in the first 10 meters from the wellbore will have significantly greater impact than a krg reduction of 0.1 at a 10-m radial interval some 100 m away from the wellbore. The relative permeability ratio krg/kro in the steady-state (SS) region is given by

krg/kro=(1/Vro – 1)(µg/µo)............................................................................................ (9)

where Vro = Vo/Vt is the CCE oil relative volume of the produced wellstream at any pressure within the SS region. The pressure in the SS region ranges from the BHFP to the dewpoint pressure of the produced wellstream, and most deliverability loss occurs nearest the wellbore where pressures are closer to the BHFP. Given the krg/kro ratio throughout the SS region from Eq. 9, the relative permeability to gas krg can be found directly from the relative permeability relationship. That is, krg(S) = krg(krg/kro(S)). Fevang and Whitson7 have shown that the krg/kro ratio in the SS region does not vary more than about one order of magnitude throughout the life of a reservoir. With regard to uncertainties in PVT properties, and the need to measure (or predict) their values for accurate description of condensate blockage, we can conclude that oil viscosity should be given highest priority because it has the largest uncertainty both experimentally and in predictions. Fig. 2 shows the effect on krg caused by a ±20% error in Vro for values of Vro ranging from 0.5 for a near-critical condensate to 0.005 for a very lean condensate (using µg/µo=0.02/0.2=0.1 and a typical Corey relative permeability relation). Oil Viscosity As discussed above, oil viscosity is important in the proper modeling of “condensate blockage” – i.e. the two-phase gas/oil flow effect on gas relative permeability in the region around the wellbore. Oil viscosity is usually low for reservoir condensates, ranging from 0.1 to 1 cp in the near-wellbore region.h Measurement of condensate viscosities is not made in routine laboratory tests, and it may be difficult to obtain measurements for lean condensates (where volumes of condensate are small). Viscosity correlations are typically unreliable for predicting low oil viscosities, and some approach is needed to ensure accurate and consistent modeling of this important property. We recommend that the oil viscosity model be tuned to measured viscosities of a separator condensate samplei at reservoir temperature and pressures in the range of 100-400 bara. More “appropriate” condensate viscosity measurements can be designed (at greater expense), but having oil viscosity data from a separator oil

h The viscosity of condensate flowing in the near-wellbore region throughout depletion, and particularly when a well goes on decline, will remain fairly constant at a value close to the condensate viscosity of the original reservoir fluid in the pressure range 100-200 bara. This viscosity is typically lower than the viscosity of condensate from a CVD test in the same pressure range, where the difference may be as much as a factor of 2-3. i This idea was suggested by Dr. Jeff Creek, Chevron Oil Company, ca. 1997.


10

sample to tune the viscosity correlation should ensure reasonably accurate oil viscosity predictions of the condensate actually flowing in the near-wellbore region when bottomhole flowing pressures drop below the dewpoint. Gas Viscosity Gas viscosity for most systems will vary from 0.02 to 0.03 cp for all pressure conditions. For near-critical gas condensates and high-pressure gases the viscosity may initially be 0.05 cp, but in most of the near-wellbore region experiencing significant pressure losses the viscosity will be in the lower range of 0.02-0.03 cp. Consequently, the absolute value of viscosity does not vary greatly for a given gas, or from gas to gas system. Viscosity correlations are fairly reliable at predicting accurate gas viscosities, within 5-10% in most cases. What is important with respect to gas viscosities is that consistent viscosities be used in all engineering applications – e.g. well test interpretation, well performance design, reservoir simulation, tubing calculations, pipeline calculations, etc. It is not uncommon that a 15-25% difference in gas viscosities may result using different correlations (by different engineering disciplines). This may result in similar inaccuracies in well performance calculations, even where all flow is single-phase gas! Oil Relative Volume (Liquid Dropout Curve) The oil relative volume or “liquid dropout curve” is perhaps the most familiar property to engineers working with gas condensate fields. The maximum liquid dropoutj is often used as a subjective measure to characterize the richness or leanness of a gas condensate fluid system (perhaps even more common than the liquid yield itself!). Two definitions of oil relative volume Vro are used,

Vro = Vo / Vd ........................................................................................................... (10)

Vro = Vo / Vt = Vo / (Vo+Vg) ..................................................................................... (11)

It is important to differentiate between the two definitions. The first and most common definition is oil volume relative to the dewpoint volume, where this gives a direct measure of the actual volume of oil condensed. The second and more important definition (for engineering purposes) is oil volume relative to total gas+oil volume, where the change in this Vro depends on two effects – the change in oil volume itself and the change in total volume, Vro(p) = Vo(p)/Vt(p). This latter definition is more important because it enters directly in the condensate blockage problem, and at lower pressures (<250 bara) where condensate blockage is particularly important, the change in total volume Vt(p) due to gas expansion becomes even more important than the change in oil volume. Ironically, the liquid dropout curve has little direct impact on reservoir and well performance. Only the CCE liquid dropout Vro=Vo/Vt of a reservoir gas at “lower” pressures has a (second-order) effect on the modeling of condensate blockage. The

j The maximum liquid dropout often occurs at a pressure near 150-250 bara (though higher for near-critical systems), and is approximately correlated to the minimum in equilibrium K-values (Ki=yi/xi) of heavier components (C5+).


11

“average” oil saturation in a gas condensate reservoir during depletion, given approximately by the CVD experiment, is seldom important. Interestingly, the magnitude of maximum liquid dropout does not determine whether condensate blockage will or will not be a problem for a given reservoir. It only has a second-order effect on the relative degree of severity. For example, one reservoir with 35% maximum liquid dropout may have a condensate blockage effect which has no importance to well deliverability, while another reservoir with 2% maximum liquid dropout may have condensate blockage causing a dramatic well deliverability loss. The importance of condensate blockage on well performance is dictated by the relative importance of “reservoir” pressure losses compared to “pipe” (tubing+flowline) pressure losses. For a high-kh (kh=10 000 md-m) rich condensate well the blockage skin may be +30 with a resulting additional pressure loss of only 3 bar, where tubing pressure losses are 300 bar due to high deliverable rates. A lower-kh (kh=500 md-m) lean condensate well may have a blockage skin of +15 with a resulting additional pressure loss of 150 bar, where tubing+flowline pressure losses are 150 bar. Clearly the lean condensate well has a more severe condensate blockage problem than the rich high-kh well.

GAS CYCLING Traditional gas cycling with full pressure maintenance is almost completely unaffected by PVT properties. The gas-gas displacement process is fully miscible, independent of the injection gas, so only the viscosity ratio of the two gases enters into the displacement performance. For practical purposes, reservoir heterogeneities (and mainly layering) dominate recovery performance of a gas cycling project – almost totally for full-pressure maintenance cycling, but also if the reservoir is cycled below the dewpoint. As indicated by Coats8 and others, gas cycling projects below the dewpoint are also affected by the vaporization characteristics of displacement gas on the retrograde condensate. For most gas cycling projects the injection gas is fairly lean and recovery efficiency of the reservoir retrograde condensate depends mostly on vaporization. If injection gas is rich in intermediate components C2-C5 and gas cycling occurs below the (original) dewpoint, an efficient condensing/vaporizing mechanism can develop and, in some cases, develop full miscibility with the gas+condensate reservoir system. This mechanism is described by Høier and Whitson6. Gas Cycling Recovery Efficiency in Swept Zone Let us look at the recovery mechanisms in a gas cycling project in the volume of the reservoir swept by injection gas – the “microscopic” or “pore-level” recovery. At a given time and position in the swept zone, the pressure is either above or below its original dewpoint when the injection gas front arrives. If above the dewpoint, a gas-gas miscible displacement will yield 100% recovery of the current condensate in place. A miscible displacement is guaranteed,


12

independent of the injection gas used, even though the injected gas may be first-contact “immiscible” with the original reservoir gas. Miscibility develops by a simple vaporizing mechanism. If reservoir pressure is below the dewpoint when the displacement front arrives, ultimate recovery of condensate is dictated by two processes: (1) gas-gas miscible displacement of the reservoir gas, and (2) partial vaporization of the retrograde condensate. The condensate recovery by gas-gas miscible displacement is 100% of the condensate in solution in the reservoir gas at the time the front arrives. The recovery efficiency of retrograde condensate by vaporization (Ev) increases gradually as increasing volumes of injection gas sweep this point in the reservoir. We will try to discuss the two mechanisms of condensate recovery for a reservoir undergoing cycling below the dewpoint. Before the gas front arrives, (1) the amount of “condensate in place” in the gas-filled pores continuously decreases below the dewpoint; and (2) the “cumulative retrograde condensate” in the oil-filled pores continuously increases at decreasing pressures. After the gas front arrives, (1) the gas-gas miscible displacement has a 100% efficiency of the condensate remaining in solution in the reservoir gas; and (2) the recovery efficiency of retrograde condensate by vaporization (Ev) rises quickly but then flattens quickly after the front passes. This behavior of Ev is due to the preferential vaporization of “light” C7+ first, leaving behind a heavier condensate which is less efficiently (more slowly) vaporized. The more volumes of injection gas passing over the condensate, the less efficient vaporization becomes. Even if pressure continues to decline, new condensation will not occur because the gas behind the front is lean and has little dissolved condensate. Accurate prediction of the changing vaporization efficiency requires (1) an accurate description of the C7+ molar distribution of the condensate, and (2) the K-values of C7+ components as a function of pressure and overall composition. Because total condensate recovery efficiency in the swept region may be dependent on an accurate description of the component-by-component vaporization process, effort should be made to obtain compositional data which describes the vaporization process. Extra effort should also be given towards fitting these compositional data with the EOS model. However, it is worthwhile to first evaluate the potential for recovery by vaporization of retrograde condensate below the dewpoint prior to obtaining extensive (and expensive) laboratory data of the type described above. Evaluating Gas Cycling Potential Defining the “target” of condensate recovery by gas cycling is important to economic evaluation and field development strategy. The following definitions are useful for defining the target of gas cycling: 1. RFoD is, as previously discussed (Eq. 7), the condensate recovery by pressure

depletion to some reservoir pressure – e.g. the end of production pend, or at the pressure of gas cycling pcycle.

2. RFoM is the recovery of condensate which would be expected at the end of

cycling due to gas-gas miscible displacement with 100% sweep efficiency


13

(Es=100%); it is assumed the gas cycling occurs at a constant pressure pcycling above or below the original dewpoint.

3. RFoV (=100 – RFoM) is the recovery of condensate which would be expected at

the end of cycling due to vaporization of retrograde condensate with 100% sweep efficiency (Es=100%); it is assumed the gas cycling occurs at a constant pressure pcycling below the initial dewpoint. Note, RFoV = 100% for gas cycling above the initial dewpoint.

4. RFoDx is the extra condensate recovery from pressure depletion of the reservoir

volume not swept by injection gas during cycling, (depletion from pcycling to pend). Note, RFoDx = RFoD(pcycling) – RFoD(pend).

5. RFoult is the ultimate condensate recovery due to (a) depletion prior to cycling, (b)

cycling, and (c) depletion after cycling. For pcycling > pd, oDxSoMSoDoult RF)E1(RFERFRF ⋅−+⋅+= ............................................................ (12)

while for pcycling < pd, ( ) oDxSoVVoMSoDoult RF)E1(RFERFERFRF ⋅−+⋅+⋅+= ......................................... (13)

where ES defines the final areal-times-vertical sweep efficiency at the end of cycling, and EV defines the final efficiency of vaporized retrograde condensate (for pcycling below the dewpoint). What components of the ultimate recovery are strongly dependent on PVT properties? We already have defined the dependence of RFoD on PVT properties (Eq. 7), where Z-factors and variation of C7+ in the CVD produced gas phase determine RFoD. It is also easy to show that RFoM is given exclusively by data in the CCE and CVD tests, as is RFoV (= 100 – RFoM). The only other PVT-dependent parameter is EV, which (as mentioned earlier) is determined by (1) the C7+ molar distribution of retrograde condensate, and (2) the K-values of C7+ components as a function of pressure and overall composition. However, EV is only important for cycling below the dewpoint, and often the contribution of vaporization to overall condensate recovery is relatively small. Fig. 3 shows recovery of condensate versus pressure for a high-pressure offshore gas condensate field. Initial pressure is 900 bara, and dewpoint is 400 bara. The calculations are based only on CCE and CVD data, as shown in Table 2. The lower curve gives RFoD(p), the recovery due to pressure depletion. The upper curve gives RFoM(p), the recovery due to gas-gas miscible displacement with 100% sweep efficiency but with no vaporization of retrograde condensate. In this high-pressure reservoir, the additional recovery due to gas cycling will not be realized until late into the life of the field, as pressure approaches the dewpoint and


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recovery is about 30%. In terms of net present value, and depending on when the investment for compressors etc. are required, cycling does not appear attractive. For the same reservoir but initially saturated at the dewpoint of 400 bara, additional condensate recovery by gas cycling is more attractive, as shown in Fig. 4. Here the rapid decline in producing liquid yields will have a pronounced affect on project economy, while successful cycling (high sweep efficiency ES) can provide prolonged initial liquid yields and higher ultimate recovery. For this case, net present value is more positive to a cycling project. In summary, most of the primary evaluation for potential of gas cycling can be quantified by CVD and CCE data. Vaporization effects are often less significant than commonly thought, an observation which follows from the calculation of recovery factors RFoD and RFoM based on CVD and CCE data. When vaporization recovery (RFoV) is important, special multi-contact vaporization tests should be conducted and fit with the PVT model, where variation of C7+ in the equilibrium gas is the most important data. Combined Condensing/Vaporizing Mechanism Historically it has been assumed that any gas cycling project in a gas condensate reservoir was miscible only by the vaporizing gas drive mechanism. Consequently, the MMP has always been assumed equal to the dewpoint pressure. Cycling projects where reservoir pressure drops below the dewpoint were considered "inferior" because only partial vaporization of the retrograde condensate could be expected. For most separator injection gases these traditional assumptions are valid. However, Høier and Whitson6 show that miscible displacement of gas condensates (by the condensing/vaporizing mechanism) can be obtained at pressures far below the dewpoint for continuous or slug injection of gas enriched with components C2-C5. Whether a below-dewpoint miscible displacement can develop in a gas condensate depends on (1) pressure, (2) composition of the injection gas, (3) composition of the retrograde condensate ahead of the front, and (4) physical dispersion or fingering (for slug injection). Although the same conditions also apply for enriched-gas miscible displacement of an oil reservoir, conditions (3) and (4) are particularly important for gas condensates. The most likely candidate for enriched-gas miscible gas cycling below the dewpoint would be rich or near-critical condensates where injection gas is not available in sufficient quantities to maintain reservoir pressure.

“REPRESENTATIVE” SAMPLES Before a field development starts, the primary goal of sampling is to obtain "representative" samples of the fluids found in the reservoir at initial conditions. It may be difficult to obtain a representative sample because of two-phase flow effects near the wellbore. This occurs when a well is produced with a flowing bottomhole pressures below the saturation pressure of the reservoir fluids. It is also commonly thought that “bad” fluid samples result if gas coning or oil coning occurs during sampling.


15

The most representative insitu samples are usually obtained when the reservoir fluid is single phase at the point of sampling, be it bottomhole or at the surface. Even this condition, however, may not ensure representative sampling. And, as shown by Fevang and Whitson9, samples obtained during gas coning in an oil well can provide accurate insitu representative samples if a proper laboratory procedure is followed. Because reservoir fluid composition can vary areally, between fault blocks, and as a function of depth, we are actually interested in obtaining a sample of reservoir fluid that is representative of the volume being drained by the well during the test. Unfortunately, the concept of a "representative" sample is usually a sample that correctly reflects the composition of reservoir fluid at the depth or depths being tested. If we suspect or know that a sample is not "representative" (according to this definition), then we tend to do nothing with the sample. Or we question the validity of the PVT analysis done on the "unrepresentative" sample, and consequently don’t include the measured data when developing the PVT model. We strongly recommend against using this definition of "representivity." First of all, it is a definition that costs our industry in terms of wasted money and time, and lost opportunity. An important point to keep in mind is that:

Any fluid sample that produces from a reservoir is automatically representative of that reservoir. After all, the sample is produced from the reservoir!

The final EOS fluid characterization of a field should match all (accurate) PVT measurements of all (uncontaminated) samples produced from the reservoir, independent of whether the samples are representative of insitu compositions.

Accuracy of PVT Data ,QVLWX5HSUHVHQWLYLW\RI6DPSOH Accurate PVT measurements can be made on both representative and unrepresentative samples. Inaccurate PVT measurements can also be made on both types of samples; bad PVT data should be ignored. Furthermore, an EOS fluid characterization is used to predict compositional changes during depletion which represent a much greater variation than the compositional differences shown by "representative" and "unrepresentative" samples. Another misconception in "representative" fluid sampling of gas condensates is that it is difficult to obtain insitu-representative samples in saturated gas condensate reservoirs (with underlying oil). The exact opposite is true! Fevang and Whitson9 have shown that if a gas condensate is initially saturated and in contact with an underlying oil zone, then a near-perfect insitu-representative sample can be obtained (at the gas-oil contact) – independent of whether the reservoir gas and reservoir oil samples collected are insitu-representative.


16

In summary, all “uncontaminated” samples collected from a reservoir are reservoir representative and, accordingly, should be described accurately by the PVT model. Insitu-representative samples may be difficult to obtain. But even when collected, they may not represent more than a “local” volume of the reservoir, where significant variations in fluid composition exist vertically and areally away from the point of sampling.

EOS MODELING To make EOS calculations, the minimum required input are (1) molar composition, and (2) molecular weight and specific gravity of the heaviest fraction (usually C7+ or C10+). With this minimum information, an EOS can calculate practically any phase and volumetric property of the mixture - e.g., · Bubblepoint or dewpoint pressure at a specified temperature · Pressure-temperature phase envelope · Densities and compressibilities of oil and gas phases · Separator gas-oil ratio and surface gravities · Depletion PVT experiments · Multicontact gas injection experiments Splitting the Plus Fraction Usually, three to five C7+ fractions (or 2 to 3 C10+ fractions) should be used. The Whitson et al.10 splitting/characterization procedure is recommended for the Peng-Robinson EOS. The Pedersen et al.11 method is recommended for the Soave-Redlich-Kwong EOS, where each plus fraction has equal mass fraction. When true boiling point distillation data are available, these data should be used directly, or to define parameters in the splitting model. TBP data can be used, for example, to define the molar distribution parameters DQG LQWKHJDPPDGLVWULEXWLRQmodel, and constants in the specific gravity correlation. Tuning the EOS Model If measured PVT data are available, and they have been checked for accuracyk, the EOS characterization can be modified to improve the predictions of measured data. Manual adjustments of EOS parameters such as binary interaction parameters (BIPs) and heavy component critical properties can be used, though this approach is time consuming (and often frustrating). Nonlinear regression can be used to mathematically minimize the difference between EOS predictions and measured PVT data. A critical aspect of the “tuning” procedure is to properly weigh individual data (and data types) based on the importance of individual data to reservoir and well performance.

k Material balance methods are often useful for checking consistency of depletion experiments (CVD and DLE). The material balance starts at the final stage of the experiment, with known amounts and compositions. Removed gas is then added back from each depletion stage, arriving at the initial fluid. Comparison with the initial composition gives a direct measure of consistency. Another approach is to start the material balance with the initial fluid, back-calculating the oil phase properties and compositions as depletion progresses; this approach is only useful for medium-rich to rich condensates because small errors in Vro have a dramatic effect on the back-calculated oil properties.


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Developing a “Common” EOS Model for Multiple Reservoir Fluids An important requirement in the development of an EOS model is the need to have one set of components to describe all reservoir samples in a given field. This is particularly important if the reservoir fluids from different parts of the reservoir (layers or fault blocks) mix in the reservoir. It also may be important if mixing only occurs at the surface. Our experience has shown that a single set of components and a single set of EOS component properties can be used to describe a wide range of reservoir fluids, ranging from leaner gas condensates to low-GOR oils – fluids which may or may not be in fluid communication initially. Whitson et al.10 propose one method for developing a “common” EOS model for multiple reservoir fluids. Another approach is to develop the EOS model based on a single sample, and then “generate” the other reservoir fluids by flash calculations (saturation pressure, two-phase split, or isothermal gradient). Generating Black-Oil PVT Tables Once the EOS characterization has been developed, a primary application of the EOS is to generate black-oil PVT tables for reservoir simulation, material balance and flow calculations (also pipeflow calculations). The most common application of black-oil PVT is black-oil simulation. The procedure proposed by Whitson and Torp12 is recommended for generating black-oil PVT tables. They suggest using a reference fluid to conduct a depletion test (e.g. CVD), sending the equilibrium reservoir phases separately through a surface separation to obtain (Rs, Bo o) for the oil phase and (rs, BgdDQG g) for the gas phase. Surface densities are taken from the surface separation of the reference fluid. The definition of black-oil PVT properties are:

ratio gasoil- solution = V

V = r

factor volume formation gasdry = V

V = B

ratio oilgas- solution = V

V = R

factor volume formation oil = VV = B

gg

ogs

gg

ggd

oo

gos

oo

OO

where subscripts are defined as: o : reservoir oil phase at p and T g : reservoir gas phase at p and T oo : surface oil from reservior oil (“solution” oil) go : surface gas from reservoir oil ("solution" gas) og : stock-tank oil (condensate) from reservoir gas gg : surface gas from reservoir gas


18

The important black-oil PVT properties for IFIP calculations in gas condensate reservoirs are rs/Bgd = the surface oil in place per reservoir gas volumel, and 1/Bgd = the surface gas in place per reservoir gas volume. The term rs/Bgd is the quantity required by “geologists” to convert reservoir gas pore volumes to surface oil – a kind of “oil FVF (Bo)” for the reservoir gas phase. In fact, for compositionally-grading reservoirs with a transition from gas to oil through an undersaturated (critical) state, the term rs/Bgd should equal Bo – exactly – at the undersaturated gas-oil contact, thereby ensuring continuity and consistency. Some special problems related to generating black-oil PVT tables with an EOS include: 1. How to extrapolate saturated PVT properties to pressures higher than the original

saturation pressure of the reference fluid. 2. Non-monotonic saturated oil properties Bo and Rs for gas condensate systems. 3. Consistency requirements for comparison of black-oil and EOS simulations. 4. Handling saturated reservoirs with a gas overlying an oil, where black-oil PVT

properties from the two fluid systems can be significantly different. 5. Modeling reservoirs with compositional gradients, and how to initialize these

reservoirs in black-oil simulators. Extrapolating Saturated Tables Extrapolating saturated black-oil PVT tables can be done in a number of ways, depending on the reservoir process and why the extrapolation is needed. Extrapolation is usually required for (a) gas injection studies, (b) reservoirs with compositional gradients where the reference sample is undersaturated, or (c) ensuring numerical stability for near-critical fluid systems where pressures may exceed the original saturation pressure during iteration. Methods for extrapolating black-oil PVT tables include: (a) mixing the incipient phase from a saturation pressure of the reference fluid to increase the saturation pressure, usually in a number of steps (“reverse DLE”), (b) using a compositional gradient algorithm, or (c) adding an injection gas in increments and determining the PVT properties of each incremental mixture, or (d) adding injection gas to a “maximum” saturation pressure and then conducting a depletion test – either stopping at the original saturation pressure or continuing all the way to a low (minimum) pressure. The most appropriate method for extrapolating saturated properties may not be obvious. It will often depend on the reservoir process. Several extrapolation methods may be tested in a realistic reservoir simulation model, where results are compared with a fully-compositional EOS model. The extrapolation method which consistently gives results most similar to the EOS model can be said to “best represent” the reservoir process. Comparisons should include initial fluids in place, recoveries, and GOR profiles of individual wells. Non-monotonic Saturated Oil Properties For medium to lean gas condensates we have often found that the saturated oil black-oil PVT properties Bo and Rs are not monotonic – first increasing just below the

l rs/Bgd is equivalent to the compositional “equivalent” C7+ content in the reservoir gas, y7+.


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dewpoint pressure, reaching a maximum, and then decreasing with pressure in a “normal” fashion. The physical explanation for this behavior is that the first condensate which appears is (for lean and medium-lean condensates) quite heavy, with a high surface-oil density (e.g. low API gravity < 40). The “low-gravity” or heavy condensate has, as expectedm, a relatively low Bo and Rs. As more condensate evolves from the reservoir gas, the total reservoir condensate becomes lighter with higher (API) gravity. The change in the gravity has a stronger influence than the decreasing pressure, so the net change in Bo and Rs is to increase with decreasing pressure. As pressure continues to decrease, the condensate gravity stabilizes and “normal” pressure dependence of saturated oil properties results, with Bo and Rs both decreasing at decreasing pressures. One solution we have found useful in this situation is to generate a separate set of black-oil PVT tables, starting with the incipient oil phase of the original reservoir gas at dewpoint, and using a depletion (DLE or CVD) test with this oil. The “oil phase” PVT table (Bo, Rs, and o) from depletion of the incipient oil can then be used together with the “gas phase” PVT table (Bgd, rs g) from depletion of the original reservoir gas. Consistency Between Black-Oil and EOS Models Coats8 addresses the need for compositional EOS models for gas condensate reservoirs. He shows that gas cycling below the dewpoint is the only situation when black-oil modeling may be inadequate. He suggests that an EOS model with at least 3 C7+ fractions should be used to properly model vaporization recovery of retrograde condensate. His results indicate that depletion, single-well modeling, and gas cycling above the dewpoint are properly modeled with a black-oil model. Fevang and Whitson7 show that some modification of black-oil saturated oil viscosities may be needed to ensure accurate single-well modeling of condensate blockage. They show that the oil viscosity in the near-wellbore blockage region is the liquid which condenses from the flowing wellstream, and not a cumulative CVD-type liquid. The flowing blockage-area liquid can be significantly lighter than the CVD-type condensate, and with correspondingly lower viscosity (1.5 to 5 times lower). Handling Saturated Gas/Oil Systems Black-oil PVT properties for a saturated reservoir gas/oil system (gas cap overlying oil) may be difficult to generate using a consistent approach. Traditionally we generate a complete set of PVT tables separately for the reservoir oil and reservoir gas, using a depletion test for the reservoir oil (e.g. DLE) and a depletion test for the reservoir gas (e.g. CVD). From the depletion test of each reservoir phase, the complete set of black-oil PVT tables are consistent only at the initial saturation pressure. That is, the incipient oil from the dewpoint of the reservoir gas is identical to the reservoir oil; and the incipient gas from the bubblepoint of the reservoir oil is identical to the reservoir gas. The saturated oil and gas phases which form from the two depletion tests are different below the original saturation pressure. This leads to differences in PVT properties

m Expected, for example, based on a Standing-type saturated correlations for Bo and Rs.


20

which are not handled consistently in a black-oil simulator. One solution is to use two PVT regions, one for the cells originally in the gas cap, and another region for cells originally in the oil. This solution is incorrect for cells which originally are defined as one “phase” but become the other “phase” due to movement of the gas-oil contact. Still, this may be the best solution in some reservoirs. Initializing Reservoirs with Compositional Gradients Two problems arise when trying to use black-oil simulators for reservoirs with compositional gradients. The one problem is obtaining correct initial surface fluids in place (compared with initialization using an EOS model). The second problem is analogous to that discussed above for saturated gas/oil systems, where PVT properties of the different reservoir fluids are not the same. The best way to ensure accurate initialization of surface gas and surface oil in place is to initialize using Rs and rs versus depth, instead of using saturation pressure versus depth. The more-common practice of initializing with saturation pressure versus depth leads to problems of initial fluid in place because of the second problem mentioned above – i.e. though only one PVT table is used, the black-oil PVT properties of the different reservoir fluids are not the same. Our recommended method of using Rs an rs versus depth for initialization may lead to a small error in recoveries near the initial saturation pressures. However, this error is usually insignificant and always less than errors introduced by wrong initial fluids in place caused by initialization with saturation pressure versus depth. Pseudoization (Grouping Components) Some reservoir processes can not be adequately modeled with a black-oil PVT formulation. Gas injection, near critical oil and gas condensate systems, and laboratory simulations may require fully compositional EOS simulation. The mathematical complexity of integrating an EOS in a reservoir simulator is many times that of using a simple black-oil PVT formulation. The result is a simulator that runs much slower than a black-oil simulator. It may be necessary to economize the number of components used in compositional simulation by "pseudoization" (i.e. reducing the number of components in an EOS characterization). The number of components used in an EOS characterization depends both on computational restraints, and on the desired level of accuracy from the EOS. Some balance between these two requirements is needed to determine the final number of components for solving a given problem. An initial fluid characterization will typically contain from 13 to 20 components, and sometimes more. For best results, a stepwise pseudoization procedure is recommended, whereby several pseudoized characterizations are developed sequentially (e.g. 15, 12, 10, 7, and 5 pseudocomponents). The goal with each pseudoization is to maintain PVT predictions as close to the original full characterization as possible. With this stepwise approach, it is readily determined how few pseudocomponents are necessary to maintain a required similarity to the original


21

full characterization.a Reducing the number of components in a stepwise fashion has three main advantages: 1. It is possible to establish when a further reduction in number of components results

in predicted properties that deviate unacceptably from the original N-component characterization.

2. The procedure usually results in several alternative characterizations with a

common basis. One simulation might require more components than another (e.g. radial single-well study versus full-field simulation). Because several characterizations are available, and they are "related" through the original N-component characterization, more consistency can be expected.

3. Experience has shown that better results are obtained in going from the N-

component characterization to (for example) a 7-component characterization in several steps, than going from an N-component to a 7-component characterization in a single pseudoization.

The recommended stepwise pseudoization procedure is given below: 1. Use regression to develop an EOS characterization so that all relevant and

accurate PVT data are adequately matched. (This is probably the most difficult part of any fluid characterization).

2. Using this tuned EOS, simulate several PVT experiments. Save the results of these

calculations as “data”. The experiments should cover as large as possible the pressure-, temperature-, and composition-space expected in the reservoir during its development. If gas injection is being considered, multicontact gas injection experiments should be included, perhaps several with different injection gas compositions.

3. Reduce the number of components by 2 or 3 by grouping components, e.g., group

iso- and normal-alkanes of butanes and pentanes. 4. Fine tune (by regression) the newly-created pseudo-component EOS parameters.

Recommended parameters include multipliers to EOS constants A and B and volume shift parameter s for each newly-created pseudocomponent separately; and BIPs between methane and the C7+ fractions (collectively).

5. In a subsequent step, regress viscosities for the EOS model with the newly-created

pseudocomponents. 6. Return to step 3, selecting 2 or 3 new components to group. Fig. 5 summarizes an example pseudoization procedure.

a The number of pseudocomponents will vary according to the application. Simulation of depletion processes and water flooding will generally require only 4 or 5 pseudocomponents; immiscible gas injection may require additional pseudocomponents, and developed miscible gas injection will probably require at least 6 to 8 pseudocomponents.


22

CONCLUDING REMARKS We have tried to summarize and detail the importance of various PVT properties on the reservoir and well performance of gas condensate fields. 1. For calculation of initial gas and condensate in place the key PVT data are (a)

initial Z-factor and (b) initial C7+ molar content. In terms of black-oil PVT properties, the two “equivalent” PVT quantities are (a) Bgd and (b) rs/Bgd.

2. The constant composition and constant volume depletion tests provide the key

data for quantifying recovery of produced gas and condensate during depletion. Above the dewpoint depletion recoveries of gas and condensate are equal and are given by the variation of Z-factor with pressure.

3. For calculation of condensate recovery and varying yield (producing oil-gas ratio)

during depletion it is critical to obtain accurate measurement of C7+ (rs) variation in the produced gas from a constant volume depletion test.

4. For near-saturated gas condensate reservoirs producing by pressure depletion,

cumulative condensate produced is insensitive to whether the reservoir is initialized with or without a compositional gradient (even though initial condensate in place can be significantly different for the two initializations).

5. Oil viscosity should be measured and modeled accurately to properly model

condensate blockage and the resulting reduction in gas deliverability. 6. For richer gas condensates, the oil relative volume (from a constant composition

expansion test) has only a “secondary” effect on the modeling of condensate blockage; for lean condensates, Vro has a small effect on blockage.

7. For gas cycling projects above the dewpoint, PVT properties have essentially no

effect on condensate recovery because the displacement will always be miscible. Only the definition of initial condensate in place is important. Gas viscosity has only a minor effect on gas cycling.

8. For gas cycling below the dewpoint, the key PVT properties are Z-factor variation

during depletion, C7+ content in the reservoir gas during depletion, and C7+ vaporized from the reservoir condensate into the injection (displacement) gas.

Nomenclature

Bo = formation volume factor (FVF) of reservoir oil phase Bgd = dry gas FVF of reservoir gas phase Cog = conversion factor for gas-equivalent of surface oil C5+ = Pentanes-plus C6+ = Hexanes-plus


23

C7+ = Heptanes-plus C10+ = Decanes-plus ES = sweep (vertical and areal) efficiency EV = vaporization efficiency of condensate recovery below the dewpoint krg = gas relative permeability kro = oil relative permeability Ki = equilibrium ratio (K-value) of component i Mo = surface oil molecular weight M7+ = C7+ molecular weight N = total number nd = moles of gas at initial (dewpoint) pressure ∆npk = incremental CVD moles of gas produced in stage k p = pressure pb = bubblepoint pressure pd = dewpoint pressure pi = initial pressure ps = saturation pressure psc = standard pressure qo = surface oil production rate q7+ = Heptanes-plus production rate R = universal gas constant rs = solution oil-gas ratio of reservoir gas phase rsi = solution oil-gas ratio at initial pressure Rs = solution gas-oil ratio of reservoir oil phase RFgD = depletion recovery factor of gas RFoD = depletion recovery factor of condensate RFoDx = extra depletion recovery factor of condensate (after gas cycling) RFoM = gas-gas miscible recovery factor of condensate RFoult = ultimate recovery factor of condensate Tsc = standard temperature Vd = oil volume at dewpoint pressure Vg = gas volume Vo = oil volume Vro = oil volume divided by oil volume at saturation pressure Vt = total (gas+oil) volume xi = oil composition yi = gas composition y7+ = C7+ composition in the produced gas z7+ = mole fraction of C7+ of produced wellstream zi = produced wellstream or total mole fraction Z = Z-factor Zi = Initial Z factor

o = surface oil density at standard conditions ρ7+ = surface density of C7+ at standard conditions µg = gas viscosity µo = oil viscosity

REFERENCES

1. Lohrenz, J., Bray, B. G., and Clark, C. R. : “Calculating Viscosities of Reservoir Fluids

From Their Compositions,” J. Pet. Tech. (Oct. 1964) 1171-1176; Trans., AIME, 231.


24

2. Pedersen, K. S., and Fredenslund, Aa., : "An Improved Corresponding States Model for the Prediction of Oil and Gas Viscosities and Thermal Conductivities," Chem. Eng. Sci., 42, (1987), 182.

3. Whitson, C. H. and Belery, P. : "Compositional Gradients in Petroleum Reservoirs," paper SPE 28000 presented at the University of Tulsa/SPE Centennial Petroleum Engineering Symposium held in Tulsa, OK August 29-31, 1994.

4. Lee, S. T., and Chaverra, M. : " Modeling and Interpretation of Condensate Banking for the Near Critical Cupiagua Field," paper SPE 49265 presented for SPE Annual Technical Conference and Exhibition held in New Orleans, Louisiana, 27-30 September, 1998.

5. Høier, Lars: " Miscibility Variation in Compositional Grading Petroleum Reservoirs," Thesis for dr.ing., Norwegian University of Science and Technology, NTNU, Nov.,1997.

6. Høier, Lars and Whitson, C. H. : “Miscibility Variation in Compositional Grading Reservoirs,” paper SPE 49269 presented at the SPE Annual Technical Conference and Exhibition held in New Orleans, Sep 27-30, 1998.

7. Fevang, Øivind and Whitson, C. H. : “Modeling Gas Condensate Well Deliverability,” SPE Reservoir Engineering, (Nov. 1996) 221.

8. Coats, K. H. : "Simulation of Gas Condensate Reservoir Performance," JPT (Oct. 1985) 1870.

9. Fevang, Øivind and Whitson, C. H. : "Accurate Insitu Compositions in Petroleum Reservoirs," paper SPE 28829 presented at the EUROPEC Petroleum Conference held in London, Oct. 25-27, 1994.

10. Whitson, C. H., Anderson, T. F., and Soreide, I. : "C7+ Chracterization of Related Equilibrium Fluids Using the Gamma Distribution," C7+ Fraction Characterization, L. G. Chorn and G. A. Mansoori (ed.), Advances in Thermodynamics, Taylor & Francis, New York (1989) 1.

11. Pedersen, K. S., Thomassen, P. , and Fredenslund, A. : "Characterization of Gas Condensate Mixtures," C7+ Fraction Characterization, L. G. Chorn and G. A. Mansoori (ed.), Advances in Thermodynamics, Taylor & Francis, New York (1989) 1.

12. Whitson, C. H. and Torp, S. B. : "Evaluating Constant Volume Depletion Data," JPT (March, 1983) 610; Trans AIME, 275.

Gas Condensate PVT – What’s Really Important and Why? C.H. Whitson, Ø . Fevang, and T. Yang

25

Table 1 – Approximate Depletion Material Balance Calculations Based on CVD and CCE Test Results.

Table 2 – Approximate Depletion and Gas Cycling Calculations Based on CVD and CCE Tests.

Pressure rs Bgd Visg npw/nd Z-factor Vro RFoD RFgD RFoM RFoV

bara Sm3/Sm3 m3/Sm3 cp % % % % % %

900 8.07E-04 3.69E-03 0.062265 0.0 1.928 0.000 0.0 0.00 100.0 0.0800 8.07E-04 3.83E-03 0.057694 0.0 1.778 0.000 3.6 3.64 100.0 0.0700 8.07E-04 4.01E-03 0.053105 0.0 1.628 0.000 7.9 7.89 100.0 0.0600 8.07E-04 4.24E-03 0.04843 0.0 1.477 0.000 13.0 12.97 100.0 0.0500 8.07E-04 4.56E-03 0.043548 0.0 1.325 0.000 19.2 19.17 100.0 0.0450 8.07E-04 4.78E-03 0.040966 0.0 1.249 0.000 22.8 22.84 100.0 0.0398 8.07E-04 5.07E-03 0.038125 0.0 1.171 0.000 27.2 27.21 100.0 0.0375 7.62E-04 5.21E-03 0.035959 3.3 1.138 2.581 29.5 29.43 96.0 4.0350 7.09E-04 5.39E-03 0.033592 7.1 1.105 5.222 32.1 32.14 91.5 8.5325 6.45E-04 5.61E-03 0.031119 11.4 1.075 7.973 34.7 35.22 86.3 13.7300 5.75E-04 5.89E-03 0.028633 16.1 1.049 10.401 37.3 38.73 80.8 19.2275 5.06E-04 6.24E-03 0.026314 21.2 1.027 12.042 39.8 42.64 75.8 24.2250 4.46E-04 6.70E-03 0.024242 26.6 1.008 12.933 42.1 46.89 71.7 28.3225 3.95E-04 7.28E-03 0.022415 32.5 0.993 13.297 44.3 51.45 68.4 31.6200 3.52E-04 8.04E-03 0.020816 38.6 0.980 13.317 46.4 56.27 65.9 34.1175 3.16E-04 9.06E-03 0.019427 45.1 0.970 13.108 48.4 61.35 64.0 36.0150 2.86E-04 1.04E-02 0.018235 51.9 0.963 12.738 50.2 66.62 62.6 37.4125 2.64E-04 1.24E-02 0.017226 59.0 0.958 12.246 52.0 72.06 61.7 38.3100 2.52E-04 1.55E-02 0.016382 66.2 0.957 11.674 53.6 77.62 61.3 38.7

Data from CVD and CCE Calculated

CVD Data Conversion to Surface Oil and Gas RecoveriesBased on Simplified Surface Flash (Surface Gas = C6- and Surface Oil = C7+)© PERA a/s, programmed by Curtis H. Whitson (19981126)

C7+ Mole Weight 161 kg/kmolC7+ Density 830 kg/m3Cog 122 Sm3/Sm3 (assumed constant)(p/z)i/(p/z)d 0.9120 Approx.

SolutionInput (red) OGR

P Z np/n dnp/nd y7+ rs RFg RFobara % % mol-% Sm3/Sm3 % %

Pi 532 1.2172 0.000 3.996 3.407E-04 0.00 0.00Pd 430 1.0788 0.000 0.000 3.996 3.407E-04 8.80 8.80

408 2.710 2.710 3.339 2.827E-04 11.29 10.87372 7.070 4.360 3.366 2.851E-04 15.29 14.22320 14.720 7.650 2.875 2.423E-04 22.35 19.24272 24.420 9.700 2.245 1.880E-04 31.36 24.21221 36.060 11.640 1.742 1.451E-04 42.22 28.83170 49.130 13.070 1.302 1.080E-04 54.48 32.72121 62.630 13.500 1.055 8.727E-05 67.17 35.9762 79.160 16.530 0.675 5.562E-05 82.76 38.52


26

Fig. 1— Approximate Material Balance Calculations

Based on CVD Test Results.

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.1 1 10 100Vro = Vo / Vt of Flowing Mixture (=Produced Wellstream), %

(Vro not equal to Normalized Oil Saturation !)

k rg

Normal Range for Near-Wellbore Blockage Region

Lean GC Rich GC

EOS Vro is 20% too low

EOS Vro is 20% too high

Fig. 2 – Effect of error in Vro on gas relative permeability in near-wellbore condensate blockage zone.

0

100

200

300

400

500

600

0 10 20 30 40 50 60 70 80 90 100

Surface Gas and Surface Oil Recovery Factors

CV

D (

Res

ervo

ir)

Pre

ssu

re, b

ara

Surface Gas

Surface Oil


27

0

10

20

30

40

50

60

70

80

90

100

0 100 200 300 400 500 600 700 800 900 1000

Pressure, bara

Rec

over

y of

Con

dens

ate,

% IO

IP

InitialPressure

RFoM

RFoD

RFoDx

RFoV

Fig. 3 – Condensate recoveries for pressure depletion and

gas cycling below the dewpoint in a high-pressure undersaturated reservoir.

0

20

40

60

80

100

0 50 100 150 200 250 300 350 400 450

Pressure, bara

Rec

over

y of

Con

dens

ate,

% IO

IP

InitialPressure

=Dewpoint

RFoM

RFoV

RFoD

RFoDx

Fig. 4 – Condensate recoveries for pressure depletion and gas cycling below the dewpoint in a saturated reservoir.


28

Fig. 5 – Example pseudoization procedure reducing an original EOS

characterization with 22 components to multiple pseudoized characterizations.

Component EOS22 EOS19 EOS12 EOS10 EOS9 EOS6 EOS4 EOS3

N2 N2 C1N2 C1N2 C1N2 C1N2 C1N2

CO2 CO2 CO2 CO2 CO2

C1 C1 CO2C2 C02C2

C2 C2 C2 C2 C2 C1N2CO2C2-C6 C1N2CO2C2-C6

C3 C3 C3 C3 C3 C3

IC4 IC4

IC4NC4 IC4NC4 IC4NC4 IC4NC4

NC4 NC4

C3-C6

IC5 IC5

IC5NC5 IC5NC5 IC5NC5 IC5NC5

NC5 NC5

C6 C6 C6 C6 C6 C6

C7 C7 C7

C7C8

C8 C8 C8

C9 C9 C9 C7C8C9F1F2 C7C8C9F1F2 C7C8C9F1F2 C7C8C9F1F2

C10+ F1 F1 C9F1F2

F2 F2

C7C8C9F1-F8

F3 F3

F4 F4 F3-F5

F5 F5

F3-F8 F3-F8 F3-F8 F3-F8

F6 F6

F7 F7 F6-F8

F8 F8

F9 F9 F9 F9 F9 F9 F9 F9

Ecuaciones de Estado (EOS)

¿De qué se trata?

Representar el comportamiento volumétrico de un fluido en función de la presión y la temperatura (PVT) a partir de la composición del mismo a través del modelado mediante ecuaciones de estado.

Historia de las EOS (1)1662: Boyle’s Law - PV = constant at a fixed T

1787: Charles Law - ∆V is proportional to ∆T at constant P

1801: Dalton’s Law - P = sum of the partial pressure

1802: Cagniard de la Tour - Discovery of critical state

1834: Clapeyron - Combined Boyles Law and Charles Law into PV=RT

1873: van der Waals - First EOS and idea of corresponding states

1880: Amagat’s Law - Volume of mixtures

of gases = sum of pure components Volumes

1901: Lewis – Fugacity

1940: Benedict-Webb-Rubin - Eight constant EOS

Historia de las EOS (2)1949: Redlich-Kwong - Two parameter

cubic EOS

1972: Soave - modification of Redlich-

Kwong Temperature dependent

attraction parameter

1976: Peng-Robinson - Two-parameter EOS

1978: Peng-Robinson - improved the α term

in the model for heavier components

1980: Schmidt-Wenzel - Two-parameter

EOS does a better job in predicting liquid

densities

1982: Peneloux et al. - A consistent volume

correction for cubic EOS

Ejemplo: Gases (1)Gases Ideales:

PV = nRT- Desprecio de las fuerzas intermoleculares

(atracción/repulsión)

- Volumen de las moleculas de gas despreciale relativo al volumen ocupado por el gas.

- Todas las colisiones son perfectamente elásticas.

Gases Reales:

PV = ZnRT- Todas las “no idealidades” se corrigen mediante un solo

parámetro: Z

- Z = f(P,V,T,composición), función de las propiedades de los componentes

Ejemplo: Gases (2)

Ley de los Estados Correspondientes:Dos sustancias deben tener propiedades intensivas similares a

condiciones correspondientes respecto de su Temperatura Crítica (Tc) y Presión Crítica (Pc).

Z = f[(T/Tc), (P/Pc), (V/Vc)] = f(Tr, Pr, Vr)

Mezclas:Definir la regla de mezclado:

Propiedad Pseudo Crítica = Promedio Molar de las Propiedades Críticas de los Componentes

Determinar las Propiedades Pseudo Reducidas con las Propiedades Pseudo Críticas.

Utilización• Interpolar Datos• Extrapolar Datos por fuera del modelo/laboratorio.• Consistencia/Chequeo de Calidad de información obtenida

de Laboratorio o Procesos.• Hacer un “PVT virtual” de laboratorio - En fluidos tales como Gas y Condensando / Petróleos

Volátiles, la composición del fluido varía según el camino termodinámico recorrido: Modelado Composicional.

- Esto es difícil de llevar a la práctica en laboratorio (se necesitan celdas de volumen considerable y variación de temperatura durante el ensayo, la cual tarda en estabilizar para todo el sistema).

¿Qué datos necesito?• Temperatura de Reservorio.• Composición del Fluido (o de las Fases)• Propiedades críticas de los componentes (Pci, Tci,

ωi):– Para componentes puros y conocidos, las mismas se

encuentran tabuladas. Pero…– En todos los petróleos existen HC de alto PM, que no

poseen las propiedades críticas definidas.– Estos se agrupan en un (o varios) pseudo-componente,

generalmente C7+, el cual hay que definir Pc, Tc y ω, matcheando el PVT con la salida del simulador. Más adelante ampliamos sobre este tema.

• Coeficientes de Interacción Binarios kij.

EOS Cúbicas

• Van der Waals (1873)• Redlich-Kwong (1948)• Peng-Robinson (1976/1978)

Se denominan cúbicas en término del Volumen o el factor Z:

A.V3+B.V2+C.V+D=0

EOS: Van der Waals (1873)

P=RT/(V-b) - a/V2

- b is the correction for finite volume of gas molecules (sometimes referred to as the excluded volume or repulsion parameter)

- a is the correction for molecular attraction

- a and b are functions of the subject component’s properties (Pc, Tc, Vc)

EOS: Peng-Robinson (1976)

• Peng-Robinson:

a=0 . 457235( RTc )2

Pc

P=RT

V −b−

aαV (V+b ) +b (V −b )

a: parámetro que tiene en cuenta las fuerzas de atracción entre las moléculas.

b: conocido como ”co-volumen”, parámetro que tiene en cuenta el volumen de las moléculas.

b=0 .077796RTcPc

α 0 .5=1+m (1−Tr 0 . 5 )

m=0 .37464+1.54226ω−0 .26992ω2

ω: factor “accéntrico”, tiene en cuenta la desviación de la forma de la molécula con respecto a una esfera. Según Edmister:

ω=37

log ( Pc /14 .7 )

Tc /Tb−1−1

EOS en Mezclas

• Las EOS fueron desarrolladas para componentes puros, y luego extendidas a mezclas. Para ello, se deben definir ciertas “reglas de mezcla”. Las más comunes son:

a ij=√ai a j (1−k ij )

bij=bi +b j

2

kij: parámetro de interacción binaria entre el componente i y el componente j.

Se obtiene de mediciones de laboratorio en equilibrio gas-líquido de mezclas binarias.

Usualmente se los iguala todos a 0, aunque existen varias correlaciones en la literatura para calcularlos: Firoozabadi, Nishiumi, etc.

Sistema de Ecuaciones

• Falta determinar la variación de los xi e yi con respecto a P y T…

• Esto se resuelve gracias al concepto de fugacidad (potencial químico, energía libre de Gibbs): en un estado de equilibrio líquido-valor (VLE), las fugacidades son iguales en ambas fases de un componente i:fi

x = fiy , i = 1, 2, …, n

ln (f

i k

P⋅k i)=∫∞

V k

1− V k

RT ( ∂ P∂ N

ik )T,P,N jdV k

V k− ln ( PV k

RT )

Caracterización C7+

• Se deben definir las propiedades críticas del pseudo-componente que representa a la fracción pesada.

• Esto puede ser realizado mediante:– Matchear las curvas PVT obtenidas en laboratorio

variando Pc y Tc de C7+.– Correlaciones:

• Riazi-Daubert• Katz-Firoozabadi• Etc…

• Conviene estimar las propiedades críticas con una correlación y luego matchear las curvas. Se recomienda matchear la curva PV primero (para ajustar el Pb) y luego comparar con las de Bo y Rs.

Copyright 2007, Society of Petroleum Engineers This paper was prepared for presentation at the 2007 SPE Latin American and Caribbean Petroleum Engineering Conference held in Buenos Aires, Argentina, 15–18 April 2007. This paper was selected for presentation by an SPE Program Committee following review of information contained in an abstract submitted by the author(s). Contents of the paper, as presented, have not been reviewed by the Society of Petroleum Engineers and are subject to correction by the author(s). The material, as presented, does not necessarily reflect any position of the Society of Petroleum Engineers, its officers, or members. Papers presented at SPE meetings are subject to publication review by Editorial Committees of the Society of Petroleum Engineers. Electronic reproduction, distribution, or storage of any part of this paper for commercial purposes without the written consent of the Society of Petroleum Engineers is prohibited. Permission to reproduce in print is restricted to an abstract of not more than 300 words; illustrations may not be copied. The abstract must contain conspicuous acknowledgment of where and by whom the paper was presented. Write Librarian, SPE, P.O. Box 833836, Richardson, Texas 75083-3836 U.S.A., fax 01-972-952-9435.

Summary To predict the phase and volumetric behavior of hydrocarbon mixtures by using an Equation of State; e.g. the Peng and Robinson Equation of State “PREOS”, the critical properties in terms of the critical pressure “pc” and critical temperature “Tc” as well as the acentric factor “ω” must be given for each component present in the mixture including the plus-fraction. For pure compounds, the required properties are well-defined, but nearly all naturally occurring gas and crude oil fluids contain some heavy fractions that are not well defined and are not mixtures of discretely identified components. These heavy fractions often are lumped and called the “plus-fraction” (e.g. C7+ fraction). Adequately characterizing these undefined plus fractions in terms of their critical properties and acentric factors has long been a problem. Changing the characterization of the plus fraction can have a significant effect on the volumetric and phase behavior of a mixture predicted by the PREOS. The inaccuracy of any the cubic equation of state results from the following two apparent limitations:

1. improper procedure of determining coefficients a, b, and α for the plus fraction 2. Equations of state treatment of hydrocarbon components with critical temperatures less than the system temperature

(i.e. methane and nitrogen). Numerous authors have suggested that the EOS is generally not predictive and extensive splitting of the C7+ fraction is often required when matching laboratory data. This paper presents a practical approach for calculating the coefficients a, b, and α of the plus-fraction from its readily available measured physical properties in terms of molecular weight “M” and specific gravity “γ” with the objective of improving the predictive capability of equation of state. The predictive capability of the relationship is displayed by matching a set of laboratory data on several crude oil and gas-condensate systems. In addition; the performance of the proposed method was also compared with predictive PVT results as generated by using PVTSimTM software of Calsep. Additional comparisons are made by comparing the proposed modified PR EOS results with those of Coats and Smart4 regression methodology with PR EOS. This study concludes that when the coefficients of the plus-fraction, i.e. a, b, and α, are determined based on the proposed methodology; splitting of the C7+ into a number of pseudo-components is essentially unnecessary. Introduction An equation of state (EOS) is an analytical expression relating the pressure to the volume and temperature. The expression is used to describe the volumetric behavior, the vapor/liquid equilibria (VLE), and the thermal properties of pure substances and mixtures. Numerous EOS’s have been proposed since van der Waals1 introduced his expression in 1873. These equations were generally developed for pure fluids and then extended to mixtures through the use of mixing rules. The mixing rules are simply a means of calculating mixture parameters equivalent to those of a pure substance. The PREOS2 is perhaps the most popular and widely used EOS. In terms of the molar volume Vm, Peng and Robinson proposed the following two-constant cubic EOS:

( )( )

( ) ( )[ ]bVbbVVTa

bVRTp

mmmm −++−⎥

⎦

⎤⎢⎣

⎡−

= 1

SPE 107331

On Equation of StateTarek Ahmed, Anadarko Petroleum Corp.

2 SPE 107331

van der Waals observed that for a pure component, the first and second isothermal derivatives of pressure with respect to volume are equal to zero at the critical point of the substance. This observation can be expressed mathematically as

0=⎟⎟⎠

⎞⎜⎜⎝

⎛∂∂

CTmVp

2

and

02

2

=⎟⎟⎠

⎞⎜⎜⎝

⎛∂∂

CTmVp

3

Peng and Robinson imposed the above derivative constraints on Equation 1 and solved the resulting two expressions for the parameters a(Tc) and b to give

( ) ( )c

cac p

RTTa2

Ω= 4

and

( )

c

cb p

RTb Ω= 5

where the dimensionless parameters Ωa and Ωb are 0.45724 and 0.07780, respectively. At temperatures other than the Tc, Peng and Robinson adopted Soave’s3 approach for evaluating a(T). The generalized expression for the temperature-dependent parameter is given by a(T) = a(Tc)α(T) 6 where

( )2

11⎪⎭

⎪⎬⎫

⎪⎩

⎪⎨⎧

⎥⎦

⎤⎢⎣

⎡−+=

cTTmTα 7

with m = 0.3746 + 1.5423ω – 0.2699ω2 8 Introducing the compressibility factor 'Z' into Equation 1 gives Z3 + (B – 1)Z2 + (A – 3B2 – 2B)Z – (AB – B2 – B3) = 0 9 where

( )( )2RT

pTaA= 10

and

( )RTbpB= 11

To use Equation 9 for mixtures with its coefficients as expressed by Equations 10 and 11, Peng and Robinson recommend the following classic mixing rules: ( )[ ] ( ) ( ) ( ) ( )[ ] ( )∑∑ −=

iij

jjicjcijimix kTTTaTaxxTa ]1[ αα 12

and ( ) ( )ii

imix bxb ∑= 13

In the application of Equations 12 and 13 to a hydrocarbon mixture, a(T) and b are calculated for each component in the mixture with Equations 4 through 8. Questionable assumptions are made in the application of these equations to the plus fraction and to

SPE 107331 3

hydrocarbon components with critical temperatures less than the system temperature. These assumptions (outlined below) provide the reasoning for the proposed modification of the popular EOS. Assumption 1 – In the derivation of expressions for a(T) and b, as represented by Equations 4 and 5, the critical isotherm of a component is assumed to have a slope of zero and an inflection point at the critical point. The assumption, described mathematically by Equations 2 and 3, is valid only for a pure component. Because the plus fraction lumps millions of compounds that are making up the fraction, it is unlikely that Equations 4 and 5 would provide an accurate representation of the attraction parameter a(T) and the co-volume b. Assumption 2 – The coefficients of Equation 7 were developed by regressing vapor-pressure data from the normal boiling point to the critical point for several pure components. Again, it is unlikely that this equation will suffice for the higher-molecular-weight plus fractions. Assumption 3 – As pointed out previously, the theoretical Ωa and Ωb values in the PREOS arise from imposing the van der Waals critical-point conditions, as expressed by Equations 2 and 3, on Equation 1. These values essentially reflect satisfaction of pure-component density and vapor-pressure data below critical temperature. At reservoir conditions, methane and nitrogen in particular are well above their critical points. Coats and Smart4 pointed out that no theory or clear-cut guide exists to selection or alternation of the Ω for components well above their critical temperatures. Wilson et al.5 showed the distinct effect of the plus fraction’s characterization procedure on all the PVT relationships predicted by an EOS. A number of studies4, 6-10 reported comparisons of EOS and laboratory PVT results for a wide variety of reservoir fluids and conditions; most of these studies emphasize the plus-fraction characterization as the key element in attaining agreement between EOS and laboratory results. Coats and Smart4 presented numerous examples of matching the measured and calculated data for nine reservoir fluids of various degrees of complexity. They observed that without regression or significant adjustment of EOS parameters, the PREOS will not adequately predict observed fluid PVT behavior. Coats and Smart indicated that the adjustment of five parameters in the PREOS is frequently necessary and sufficient for good data match. These parameters are:

• Ωa and Ωb of methane, • Ωa and Ωb of the plus fraction, and • binary interaction coefficient between methane and the C7+ plus fraction kC1-C7+

Whitson9 observed that the method of adjusting the EOS constants Ωa and Ωb for the plus fraction is essentially the same as altering the critical properties of the heavy fraction. Several authors9, 11-15 showed that the ability of the EOS to predict the phase behavior of complex hydrocarbon mixtures can be substantially improved by splitting or breaking down the plus fraction into a manageable number of pseudo-components for EOS calculations. Description of the Proposed Modification of the PREOS Because the inadequacy of the predictive capability of the PREOS lies with the three assumptions outlined above, an approach was devised in this study to remove these assumptions. The approach is based on the fact that the acentric factor and critical properties of the C7+ are not well defined and never measure in the laboratory; however; there are measurements that routinely performed and readily available on the plus fraction that include: the molecular-weight "M", the boiling point "Tb", and specific gravity "γ" . Over the years; many reliable correlations that have developed to cross correlate these parameters from numerous measurements. Therefore; in the eliminating the first two assumptions, 49 hypothetical heavy petroleum fractions (i.e. plus fractions) with physical properties (density, molecular weight, and boiling point) governed by the applicability range of Riazi and Daubert16 equation were generated. Riazi and Daubert developed a simple two-parameter equation for predicting the physical properties of pure compounds and undefined petroleum fractions. The proposed correlation; as shown by Equation 14, is applicable in the molecular-weight rage of 70 to 300 and normal boiling point range of 80 to 650°F. The expression correlates the molecular-weight "M" with the boiling point "Tb" and specific gravity "γ" of the substance; it takes the form: M = a(Tb)b γc exp(dTb + eγ + ƒTbγ) 14 where a = 581.960 b = 0.97476 c = 5.43076 x 10-4 e = 9.53384 ƒ = 1.11056 x 10-3

4 SPE 107331

The specific steps of the proposed modification are outlined below. Step 1 – Each hypothetical heavy fraction with a specified molecular weight, boiling point, and density (specific gravity) is

subjected to 10 temperature and 10 pressure values in the range of 60 to 300°F and 14.7 to 7,000 psia. The specified density is then adjusted to account for the temperature and pressure increases. A total of 100 density values are generated for each hypothetical heavy fraction.

Step 2 – Equation 9 is rearranged and expressed in terms of the density to give

[a(Tc)α(T)b–RTb2-pb3]ρ3–M[a(Tc)α(T)–3pb2–2RTb]ρ2 –M2(pb-RT)ρ–pM3 = 0 15

Step 3 – Equation 15 is incorporated into a nonlinear regression model that uses a(Tc), b, and α(T) as regression variables.

For each hypothetical heavy fraction under consideration, Equation 15 is solved for the density by optimizing the regression variables to match the fraction generated density data.

Step 4 – The optimized regression variables [i.e. a(Tc), b, and α(T)] are correlated with M, γ or T by the following

relationships. For a(Tc) or b of the plus fraction,

( ) ( ) ( )γ

γ 76

5

443

0

or CCDCDCbTa

i

ii

i

iic +⎥

⎦

⎤⎢⎣

⎡++⎥

⎦

⎤⎢⎣

⎡= ∑∑

=

−

=

16

with

+⎟⎟⎠

⎞⎜⎜⎝

⎛=

c

MDγ

Table 1 gives values of C0 through C7 (for a(Tc) and b) of the above expression. For α(T), Peng and Robinson α(T) function as expressed by Equation 7 is modified according to

( )25.052011

⎪⎭

⎪⎬⎫

⎪⎩

⎪⎨⎧

⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎠⎞

⎜⎝⎛−+=

TmTα 17

with

( ) γγγ 72

6542

3210

CCC

MC

MCMCDCC

Dm +++++⎥⎦

⎤⎢⎣

⎡+

= 18

Table 1 includes the values C0 through C7 for Equation 18.

Table 1 – Coefficients of Eqs. 16 and 18

Coefficient a(To) b m C0 -2.433525 x 107 -6.8453198 -36.91776 C1 8.3201587 x 103 1.730243 x 10-2 -5.2393763 x 10-2

C2 -0.18444102 x 102 -6.2055064 x 10-5 1.7316235 x 10-2 C3 3.6003101 x 10-2 9.0910383 x 10-9 -1.3743308 x 10-5

C4 3.4992796 x 107 13.378898 12.718844 C5 2.838756 x 107 7.9492922 10.246122 C6 -1.1325365 x 107 -3.1779077 -7.6697942 C7 6.418828 x 108 1.7190311 -2.6078099

SPE 107331 5

In the elimination of the third assumption, the Peng and Robinson parameters (i.e. a(Tc), b, and m) for methane and nitrogen are altered. For this approach, 100 z-factor values for each component were obtained from appropriate gas-compressibility-factor charts. a(Tc), b and m (to be used in Equation 17) for methane and nitrogen were optimized by incorporating a regression model in solving Equation 9 and matching the z-factor data for each fraction. The optimized values are:

• For Nitrogen: a(Tc) = 4,569.3589, b = 0.46825820, and m = -0.97962859 • For Methane: a(Tc) = 7,709.7080, b = 0.46749727, and m = -0.54976500

Several computational schemes7, 10, 17 for generating binary interaction coefficients were tested for the purpose of providing the modified PREOS with a systematic and consistent procedure for determining the kij. Petersen’s17 computational technique was adopted and appropriately modified to provide the proper EOS coefficients. The technique is described in the following steps. Step 1 – Set: kCO2-N2 = 0.12,

kCO2-hydrocarbons = 0.10, and kN2-hydrocarbons = 0.10

Step 2 – Estimate the binary interaction coefficient between methane and the heptanes-plus fraction, kC1-C7+. To provide this

estimate, the coefficient under consideration was adjusted to minimize the error in calculating the saturation pressures of 12 hydrocarbon mixtures. Results of the study indicate the strong dependency of the calculated optimum values of kC1-C+ on system temperatures. The following linear relationship provides an appropriate estimate of the parameter:

kC1-C7+ = 0.00189(T-460) – 0.297659 19

where: T = system temperature, oR Step 3 – Calculate the binary interaction coefficients between components heavier than methane (i.e. C2, C3….etc.) and the

plus fraction according to the following expression17: kCn-C+ = 0.8 kC(n-1) -C7+ 20

where: n = number of carbon atoms Step 4 – Determine the remaining kij from 17

( ) ( )[ ]( ) ( )[ ]55

7

55

7iC

ijCiij MM

MMkk

−

−=

++− 21

where:

Mi = molecular weight of component i MC7+ = molecular weight of the heptanes-plus fraction Application of the Modified EOS and Discussion of Results To validate the proposed methodology of treating the plus fraction, the modified EOS and PVTSim software were used to simulate a variety of published laboratory PVT tests and compare their predicted results with actual data. The verification procedure is outlined below:

1. In applying the proposed modification, the measured physical properties of the C7+ in terms of molecular weight and specific gravity were maintained as reported and used to calculate the parameters a(Tc), b, and α(T) of the plus-fraction. No splitting of the plus fraction is required in performing the PVT analysis when applying the proposed modification.

2. For all various hydrocarbon mixtures used in the study; PVTSim was allowed to split the C7+ fraction into the following 11 pseudo-components: C7, C8, C9, C10-C12, C13-C14, C15-C16, C17-C19, C20-C22, C23-C25, C26-C30

3. The modified PR EOS model and PVTSim were both tuned to only match the saturation pressure. The PVTSim regressed on the saturation pressure by adjusting the molecular weight of the plus fraction; while the modified PR model used the binary interaction coefficient between C1 and C7+ as the regression variable to match saturation pressure

6 SPE 107331

For convenience and brevity of presenting and discussing results of the study, the following terms are used in the paper: CCE = Constant composition expansion DE = Differential expansion CVE = Constant composition expansion C-S = Coats-Smart tuned model Mod. EOS = Modified Peng-Robinson equation of state PVTSim = Results as predicted by PVTSim software Exp. = Experimental data V/Vs = relative volume from CCE test; i.e. total volume of hydrocarbon system at any given pressure and

temperature divided by the volume at saturation pressure Density Predictions – To test the modified PREOS for its ability to predict the density of complex hydrocarbon mixtures under a wide range of pressures and temperatures, the equation was applied to predict densities of the 15 hydrocarbon mixtures used by Standing and Katz18 to develop their popular correlation and the densities of 11 crude oil systems reported by Coats and Smart4 Table 2 and Figure 1 summarize results of the model and compare the predicted densities with those calculated from the Standing-Katz18 (S-K) and Alani-Kennedy19 (A-K) density correlations. In terms of the overall average absolute deviation, the modified EOS predicted the density of the 26 mixtures with the lowest deviation of 5.58%, which compares favorably with the two density correlations.

Table 2 – Comparison of Predicted Oil Densities with Experimental Data Density (g/cm3)

p (psia)

T (°F)

Exp.

S-K

A-K

Mod. EOS

S-K Data A-1 3,185 120 0.696 0.729 0.720 0.718 A-2 5,270 120 0.745 0.759 0.736 0.745 A-3 8,220 120 0.814 0.817 0.773 0.802 A-4 1,600 120 0.702 0.712 0.701 0.718 B-1 2,915 250 0.697 0.702 0.688 0.663 C-1 2,880 120 0.652 0.655 0.642 0.663 C-2 1,010 120 0.716 0.724 0.712 0.732 C-3 5,330 120 0.712 0.685 0.672 0.712

A-K Data D-1 4,330 120 0.731 0.729 0.714 0.726 E-1 4,195 120 0.753 0.744 0.728 0.748 F-1 3,185 250 0.654 0.670 0.658 0.638 F-2 4,315 250 0.657 0.664 0.656 0.628 F-3 5,330 250 0.677 0.684 0.672 0.648 G-2 3,485 35 0.679 0.675 0.667 0.701 G-3 4,970 35 0.766 0.764 0.748 0.764

C-S Data

.Oil 1 2,520 180 0.768 0.784 0.762 0.764 Oil 2 4,460 176 0.530 0.509 0.537 0.544 Oil 3 2,2115 140 0.736 0.807 0.809 0.752 Oil 3 2,362 160 0.722 0.804 0.796 0.726 Oil 3 2,597 180 0.708 0.795 0.785 0.701 Oil 3 2,792 200 0.695 0.788 0.772 0.683 Oil 4 2,547 250 0.646 0.647 0.651 0.615 Oil 4 2,283 180 0.679 0.679 0.682 0.672 Oil 4 1,958 110 0.711 0.709 0.712 0.719 Oil 6 2,746 234 0.609 0.620 0.623 0.599 Oil7 1,694 131 0.713 0.717 0.735 0.722

Average absolute

error, %

6.58

6.69

5.58

SPE 107331 7

Figure 1. Comparison Of Predicted Densities

0.5

0.55

0.6

0.65

0.7

0.75

0.8

0.85

0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85Exp. oil density

Oil

dens

ity, g

m/c

u cm

Exp. oil densityS-KA-KMod. EOSLinear (Exp. oil density)

Coats-Smart Hydrocarbon Systems – Coats and Smart4 reported a detailed experimental description of several hydrocarbon systems. Nine of the hydrocarbon systems, with the compositions given in Table 3, were used in the study. Coats and Smarts “C-S” used a regression-based PVT program to match the laboratory by tuning parameters of equation of state. Most of their calculations were performed by splitting the heptanes-plus into four fractions.

Table 3 – Coats and Smart Compositional Data Gas 2* Gas 2** Gas 5 Oil 1 Oil 2 Oil 3 Oil 4 Oil 6 Oil 7

CO2 0.00690 0.00610 0.02170 0.00440 0.00900 0.60310 0.02350 0.01030 0.0008N2 0.00420 0.00340 0.00450 0.00300 0.00930 0.00110 0.00550 0.0164

H2S 0.00040 0.00040 C1 0.58320 0.57490 0.70640 0.35050 0.53470 0.07050 0.35210 0.36470 0.2840C2 0.13550 0.13450 0.10760 0.04640 0.11460 0.01570 0.06720 0.09330 0.0716C3 0.07610 0.07520 0.04940 0.02480 0.08790 0.03060 0.06240 0.08850 0.1048C4 0.04030 0.04150 0.03020 0.01660 0.04560 0.03310 0.05070 0.06000 0.0840C5 0.02410 0.02330 0.01350 0.01600 0.02090 0.02680 0.05230 0.03780 0.0382C6 0.01900 0.01790 0.00900 0.05460 0.01510 0.02580 0.04100 0.03560 0.0405C7+ 0.11450 0.12200 0.05880 0.48240 0.16920 0.18510 0.34970 0.30430 0.3597

M+

193

193

153

225

173

189

213

200

252

γ+ 0.8135 0.8115 0.8100 0.9000 0.8364 0.8275 0.8406 0.8366 0.8429T, °F 190 190 267 180 176 179 250 234 131

P, psig 4,450 4,415 4,842 2,520 4,460 2,597 2,547 2,746 1,694

8 SPE 107331

The proposed modification of the Peng-Robinson EOS was tested extensively using the above hydrocarbon system as well as a larger number of unreported fluid studies. Results of the some of applications of the modified PREOS to a selected number of hydrocarbon systems are presented below. Near-Critical Gas Systems – Gas 2 is a near-critical gas-condensate fluid at a reservoir temperature of 190°F. Coats and Smart stated that because of the possibility of a small error in gas measurement during well testing, two slightly different separator gas/liquid ratios are used to obtain the two reservoir fluid compositions given in Table 3. The first sample (Gas 2*) exhibited a saturation pressure and density of 4,465 psia and 28.85 lbm/ft3 and was labeled a dewpoint gas. The second sample (Gas 2**) displayed a bubblepoint of 4,430 psia and a density of 29.54 lbm/ft3 and consequently was labeled a bubblepoint gas. In applying the modified expression to simulate the volumetric behavior of the two systems, Equations 19 through 21 initially were used to determine the binary interaction coefficients for each system. Table 4 lists these values for Gas 2*. The modified equation predicts a dewpoint pressure of 3,890 psia (compared with 3,680 psia for the original PREOS) and a saturation density of 28.45 lbm/ft3. For the bubblepoint gas, the equation predicts a saturation pressure of 3,824 psia (the original PREOS predicts 3,664 psia) and a saturation density of 28.86 lbm/ft3.

Table 4 – Binary Interaction Coefficients for Gas 2* Component Component j

i CO2 N2 C1 C2 C3 i-C4 n-C4 i-C5 n-C5 C6 C7+ CO2 0.000 0.012 0.100 0.100 0.100 0.100 0.100 0.100 0.100 0.100 0.100 N2 0.000 0.100 0.100 0.100 0.100 0.100 0.100 0.100 0.100 0.100 C1 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.001 0.061 C2 0.000 0.000 0.000 0.000 0.000 0.000 0.001 0.049 C3 0.000 0.000 0.000 0.000 0.000 0.001 0.039

i-C4 0.000 0.000 0.000 0.000 0.000 0.031 n-C4 0.000 0.000 0.000 0.000 0.25 i-C5 0.000 0.000 0.000 0.020 n-C5 0.000 0.000 0.016 C6 0.000 0.013 C7+ 0.000

Figure 2 compares experimental CCE data of the dew-point gas in terms of liquid relative volume with those as predicted by PVTSim and the modified PR model. Both models overestimated the liquid volume just below the dew point pressure. However; PVTSim predicted a bubblepoint system when the fluid was flashed below the saturation pressure. A constant volume depletion "CVE " test was also performed on the dew-point gas as shown in Table 5. Results from simulating the test by applying the modified PR EOS are compared with predicted values from experimental and PVTSim as documented graphically in terms of liquid dropout in Figure 3. Table 5 and Figure 3 show that PVTSim failed to recognize the system as a dewpoint gas and predicted a 100% liquid at saturation pressure. The match between the observed data and the modified PR model prediction in terms of liquid dropout is excellent with an average absolute error of 1.05%. A more detailed documentation of results of the proposed EOS for simulating CCE tests is given in Reference 20.

SPE 107331 9

Figure 2. CCE for dewpoint Gas 2*

0

10

20

30

40

50

60

70

80

90

100

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000

Pressure

Rel

t. Vo

l, % Mod. EOS

ExpPVTsim

Table 5 – CVE at 190°F for Dewpoint Gas Pressure (psig)

Component 4,450.0 3,500.0 2,700.0 1,900.0 1,100.0 500.0 500*

CO2 0.00730 0.00767 0.00790 0.00824 0.00874 0.00922 0.00228 N2 0.00000 0.00000 0.00000 0.00000 0.00000 0.0000 0.00000 C1 0.58320 0.71198 0.72463 0.72791 0.71235 0.65973 0.07116 C2 0.13550 0.13745 0.13945 0.14384 0.15417 0.17230 0.06429 C3 0.07610 0.06804 0.06713 0.06782 0.07388 0.09265 0.07722

i-C4 0.02015 0.01640 0.01568 0.01528 0.01625 0.02135 0.03199 n-C4 0.02015 0.01538 0.01447 0.01387 0.01463 0.01961 0.03818 i-C5 0.01205 0.00822 0.00738 0.00666 0.00658 0.00874 0.03124 n-C5 0.01205 0.00783 0.00691 0.00611 0.00592 0.00781 0.03397 C6 0.01900 0.01069 0.00885 0.00719 0.00631 0.00786 0.06607 C7+ 0.11450 0.01634 0.00762 0.00308 0.00117 0.00073 0.58360

Z-Factor Mod. EOS 0.9605 0.8359 0.8016 0.8031 0.8461 0.9061

Experimental 0.9969 0.8402 0.7966 0.8140 0.8603 0.9108 PVTSim 0.976 0.812 0.784 0.798 0.949 0.980

Gp Mod. EOS 0.00000 12.89 25.411 41.007 58.989 73.304


Liquid Dropout (%) Mod. EOS 0.0 56.53 51.0 46.20 41.35 37.25

Experimental 0.0 52.31 49.40 45.33 40.51 36.82 PVTSim 100 61.37 54.91 48.4 41.87 36.69

*Residual liquid composition

10 SPE 107331

Figure 3. LDO for Dewpoint Gas-2*

0

10

20

30

40

50

60

70

80

90

100

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000

Pressure, psi

% L

DO Exp

Mod. EOSPVTsim

Figure 4. CCE for Bubblepoint Gas2**

0

10

20

30

40

50

60

70

80

90

100

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000

Pressure

Rel

. Vol

, % ExpMod. EOSPVTsim

Gas-Condensate System 5 – Gas 5 is a retrograde gas with a reported upper dewpoint pressure of 4,857 psia at 276°F. The model predicts an excellent value of 4,805 psia for the dewpoint pressure. In simulating the CVE and CCE tests for the system, the modified equation and PVTSim show excellent predictive capabilities in reproducing the experimental data, as Table 6 illustrates. The tabulated results compare the observed data with both models in terms of Z factor, liquid dropout, Gp, and V/Vs. The modified expression gives average deviations of 1.6% for the Z-factor, 1.3% for Gp, and 1.9% for liquid dropout. The near-exact match of the modified PR EOS with reported liquid dropout data is documented graphically in Figure 5.

SPE 107331 11

Table 6 – Expansion Data for Gas 5 Pressure (psig)

Component 4,642.0 3,900.0 3,000.0 2,100.0 1,200.0 700.0 700.0*

CO2 0.02170 0.02185 0.02207 0.02237 0.02276 0.02302 0.00611 N2 0.00340 0.00348 0.00355 0.00359 0.00360 0.00356 0.00032 C1 0.70640 0.72207 0.73481 0.74357 0.74575 0.73990 0.08684 C2 0.10760 0.10893 0.11010 0.11124 0.11256 0.11352 0.02989 C3 0.04940 0.04957 0.04970 0.04997 0.05083 0.05216 0.02532

I-C4 0.01510 0.01502 0.01493 0.01491 0.01518 0.01583 0.01246 n-C4 0.01510 0.01490 0.01471 0.01460 0.01490 0.01574 0.01636 I-C5 0.00675 0.00658 0.00639 0.00625 0.00633 0.00681 0.01184 n-C5 0.00675 0.00653 0.00629 0.00610 0.00615 0.00668 0.01428 C6 0.00900 0.00853 0.00802 0.00753 0.00741 0.00814 0.03040 C7+ 0.05880 0.04254 0.02942 0.01986 0.01452 0.01467 0.76619

Z-Factor

Mod. EOS 1.0085 0.9324 0.8870 0.8742 0.8990 0.9290 Experimental 0.985 0.911 0.881 0.882 0.916 0.943

PVTSim 0.990 0.912 0.873 0.870 0.900 0.929

Gp Mod. EOS 0.00000 13.373 29.34 48.29 69.02 80.561


Liquid Dropout (%)


PVTSim 0.0 6.28 10.39 11.16 10.06 9.03 *Residual liquid composition

Figure 5- CVE for Gas 5

0

2

4

6

8

10

12

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000

Pressure, psi

LDO

, %

Mod EOSExpPVTsim

12 SPE 107331

Crude Oil 1 – This oil, with the composition given in Table 3, exhibits a saturation pressure and density of 2,535 psia and 47.96 lbm/ft3 at 180°F. The modified model predicted excellent values for the bubblepoint pressure and saturation density of 2,501 psia and 47.68 lbm/ft3. The modified EOS is tested for its predictive ability by a simulating CCE test. Table 7 compares the predicted and adjusted liquid ratio V/Vs with the observed data. The observed average absolute deviation is 0.156%. Both models are in excellent agreement with the reported values

Table 7 – CCE for Oil 1 at 180°F p V/Vs

(psig) PVTSim Mod. EOS Experimental 5,000 0.9740 0.9739 0.9782 4,000 0.9832 0.9831 0.9662 3,000 0.9940 0.9940 0.9951 2,900 0.9952 0.9952 0.9961 2,800 0.9964 0.9964 0.9971 2,700 0.9977 0.9977 0.9982 2,600 0.9990 0.9990 0.9992 2,520 1.0000 1.0000 1.0000

Crude Oil 2 – This oil is characterized as volatile hydrocarbon system with a reported bubblepoint pressure, ρb, is 4,475 psia at 176°F. Table 8 compares the experimental differential values of Rsbd, Bobd, and oil density at the saturation pressure with those of the PVTSim and modified PR predicted values. PVTSim produced excellent match values at the saturation pressure as compared with the modified PR EOS. However; as shown in Table 9 and expressed graphically in Figures 6 and 7, the modified PR results compare extremely well with the DE test data. A further evaluation of the proposed modified EOS is presented in Table 10 for predicting CVE data on this volatile oil. Both models perform equally well in matching cumulative gas production GP, however; both models failed reproduce acceptable match with the experimental gas deviation factor.

Table 8 – Observed and Predicted Data, Crude Oil 2

Approach pb

(psia) Rsbd

(scf/STB) Bobd

(RB/STB) ρ

(lbm/ft3) Experimental 4,475 3,377 2.921 33.10

PVTSim 3,344 (-25.3) 3345 (-0.95) 2.967 (-1.5) 31.10 (-6.0) Modified EOS 4,502 (0.60) 3,019 (-7.9) 2.675 (-8.4) 33.99 (2.6)

*Numbers in parentheses represent percent error of predictions

Table 9- DE at 176°F for Oil 2 Ρ Rsd (scf/STB Βod (RB/STB)

(psig) PVTSim Mod. EOS

Experimental PVTSim Mod. EOS Experimental

4,460.0 3345.1 3109 3,377 2.967 2.6736 2.921 4,000.0 2723.9 2401 2,351 2.605 2.3039 2.343 3,492.0 2085.4 1909 1,814 2.249 2.0563 2.059 3,003.0 1632.2 1540 1,471 2.004 1.8737 1.886 2,514.0 1265.2 1254 1,205 1.809 1.7351 1.756 2,004.0 985.7 1004 970 1.662 1.6145 1.645 1,534.0 711.4 805 775 1.516 1.5191 1.555 1,001.0 473.1 600 573 1.386 1.4201 1.464

505.0 313.5 409 383 1.291 1.3243 1.372 209.0 285 271 245 1.039 1.2490 1.298

0.0 0 0 000 1.000 1.0601 1.057

SPE 107331 13

Figure 6- DE Rsd for Oil 2 at 176 F

0

500

1000

1500

2000

2500

3000

3500

4000

0.00 500.00 1,000.00 1,500.00 2,000.00 2,500.00 3,000.00 3,500.00 4,000.00 4,500.00 5,000.00

Pressure, psi

Rsd

, scf

/STB PVTsim

Mod. EOSExp Rsd

Figure 7. DE Bod for Oil 2 at 176 F

0

0.5

1

1.5

2

2.5

3

3.5

0.00 500.00 1,000.00 1,500.00 2,000.00 2,500.00 3,000.00 3,500.00 4,000.00 4,500.00 5,000.00

Pressure, psi

Bod

, bbl

/STB PVTsim

Mod. EOSExp

14 SPE 107331

Table 10- CVE at 176°F for Oil 2 Pressure (psig)

Component 4,460.0 3,600.0 2,800.0 2,000.0 1,200.0 600.0 600.0*

CO2 0.00900 0.00984 0.01020 0.01074 0.01158 0.01256 0.00352 N2 0.00300 0.00491 0.00479 0.00454 0.00405 0.00333 0.00020 C1 0.53470 0.73509 0.74529 0.74678 0.73019 0.67668 0.08654 C2 0.11460 0.11526 0.11767 0.12251 0.13386 0.15557 0.06976 C3 0.08790 0.07183 0.07101 0.07187 0.07858 0.10006 0.10309

I-C4 0.02280 0.01624 0.01548 0.01498 0.01568 0.02010 0.03705 n-C4 0.02280 0.01474 0.01381 0.01311 0.01351 0.01739 0.04213 I-C5 0.01045 0.00578 0.00514 0.00457 0.00434 0.00533 0.02363 n-C5 0.01045 0.00541 0.00473 0.00411 0.00381 0.00461 0.02492 C6 0.01510 0.00643 0.00526 0.00419 0.00348 0.00388 0.04092 C7+ 0.16920 0.01447 0.00662 0.00260 0.00092 0.00050 0.56822

Gas Deviation Factors

PVTSim 0.8900 0.8130 0.7820 0.7910 0.8370 Mod. EOS 0.8388 0.8051 0.8011 0.8361 0.8899

Experimental 0.798 0.783 0.788 0.843 0.913

Gρ , % PVTSim 0.00 2.12 13.42 28.84 47.57 63.09


*Residual liquid composition Crude Oil 3 – This CO2 rich system contains 60 mol% CO2. The hydrocarbon system exhibits a saturation pressure and density of 2,612 psia and 44.17 lbm/ft3 at 180°F. Coats and Smart "C-S" presented the results of CCE tests on the system at four different temperatures. Coats and Smart used 12 components system to match the saturation pressure over the reported range of temperatures used in the laboratory. The authors predicted saturation pressure values that are approximately 500 psi lower the experimental values. The tabulated values shown below compare the observed saturation pressures and densities at these four temperatures with those of the modified EOS and Coats and Smart 12 components system. The modified EOS shows excellent match with the oil saturation at the bubble point pressure

Observed and Predicted Data for Crude Oil 3 Temperature (°F) 140 160 180 200 Exp. pb 2,144 2,392 2,627 2,821 ρob, lbm/ft3 45.9 45.1 44.2 43.3 C-S pb 1,776 (-17) -2,000 (-16.5) 2,210 (-16) 2,403 (-14.9) ρob, lbm/ft3 43.1 (-6) 42.3 (-6.2) 41.5 (-6.1) 40.6 (-6.2) Mod. EOS pb 2,082 (-2) 2,210 (-7.0) 2,304 (-12) 2,375 (-15.3) ρob, lbm/ft3 46.9 (2.2) 45.3 (0.5) 43.7 (-1.1) 41.8 (-3.4)

Numbers in Parentheses represent percent error of predictions Crude Oil 4 – The reported experimental data available on the system includes differential expansion results at 110 and 250°F and CCE data at 110, 180 and 250°F. The system is slightly volatile with Bobd = 1.671 and Rsbd = 932 scf/STB at 250°F. Table 11 lists the predicted values for selected PVT properties as compared with the reported values at saturation pressures. Table 12 gives detailed documentation of results of predicting the DE data at the specified temperatures. With adjustment and in terms of the average absolute error, the model predicts Rsd and Bod data at 110°F within 3.5 and 0.77%, respectively. At 250°F, the equation gives results within 6% for Rsd and 3% for Bod.

SPE 107331 15

Table 11 – Observed and Predicted Data, Crude Oil 4 Temperature (°F) 110 180 250

Exp. pb 1,988 2,313 2,577 Rs 701 932 Bobd 1,341 1,671 ρob, lbm/ft3 44.4 42.4 40.3 C-S pb 1,694 (-14.8) 2,033 (-12.1) 2,274 (-11.76) Rsbd 611 (-12.8) 756 (-18.9) Bobd 1.294 (-3.5) 1.517 (-9.2) ρob, lbm/ft3 40.0 (-9.9) 38.4 (9.4) 36.8 (-8.7) Mod. EOS pb 1,695 (-14.7) 2,330 (0.7) 2,655 (3.0) Rsbd 694 (-0.9) 949 (1.8) Bobd 1,323 (-1.3) 1.769 (5.9) ρob, lbm/ft3 44.8 (1.1) 41.96 (-1.0) 38.35 (-4.8)

Numbers in Parentheses represent percent error of the predictions

Table 12 – Expansion Data for Oil 4 DE at 110°F

p Rsd (scf/STB) Bod (RB/STB) (psig) PVTSim Mod. EOS Experimental PVTSim Mod. EOS Experimental

1,958.0 720.0 694 701 1.368 1.3243 1.341 1,753.0 714.7 629 633 1.366 1.2990 1.313 1,557.0 639.8 570 577 1.333 1.2762 1.291 1,354.0 565.1 509 510 1.301 1.2524 1.264 1,153.0 493.8 450 450 1.270 1.2293 1.240 949.0 423.8 391 389 1.239 1.2063 1.217 748.0 356.9 334 330 1.210 1.1839 1.193 548.0 291.5 278 270 1.181 1.1616 1.168 347.0 225.4 220 209 1.151 1.1382 1.144 157.0 155.4 158 143 1.117 1.1120 1.116 75.0 117.2 123 106 1.097 1.0963 1.097 0.0 0.0 000 000 1.015 1.0234 1.024

DE at 250°F

2,547.0 1010.2 948 943 1.724 1.7678 1.671 2,360.0 931.8 863 865 1.680 1.7168 1.636 2,143.0 846.6 784 788 1.633 1.6712 1.595 1,893.0 755.1 690 704 1.583 1.6157 1.553 1,645.0 670.3 604 625 1.536 1.5644 1.512 1,393.0 589.4 522 548 1.491 1.5160 1.473 1,150.0 515.5 450 477 1.450 1.4720 1.436 895.0 441.0 376 407 1.408 1.4275 1.401 647.0 370.2 307 338 1.367 1.3846 1.365 400.0 297.5 237 265 1.323 1.3387 1.326 182.0 219.5 163 190 1.270 1.2858 1.275 87.0 170.0 120 146 1.232 1.2504 1.243 0.0 0.0 000 000 1.054 1.124 1.094

16 SPE 107331

Figure 8- DE Rsd for Oil 4 at 110 F

0

100

200

300

400

500

600

700

800

0.00 500.00 1,000.00 1,500.00 2,000.00 2,500.00

Pressure, psi

Rsd

, scf

/STB PVTsim

Mod. EOSExp.

Crude Oil 6 – This oil exhibits a saturation pressure of 2,746 psia at 234°F. Table 13 gives the reported Rs and Bo and ρo at the bubblepoint pressure compared with the predicted results. Table 14 shows DE data calculated by the EOS before and after adjustment. (For detailed results of CCE data, see Table 6 of Reference 20). In a prediction mode, the modified expression reproduced the entire solution GOR and relative oil volume data with average absolute errors of 6.3 and 1.7%, respectively. (See Table 7 of Reference 20 for CCE predicted data).


Approach pb

(psia) Rsbd

(scf/STB) Bobd

(RB/STB) ρ

(lbm/ft3) Experimental 2,746 1.230 1,866 38.0 Coats-Smart 2,398 (-12.7) 1,002 (-19) 1,659 (-11.1) 35.6 (-6.3)

Modified EOS 2,916 (6.2) 1,233 (0) 1,909 (2.3) 37.40 (-1.6)

Table 14 – Expansion Data for Oil 6 DE at 234°F

p Rsbd (scf/STB) Bobd (RB/STB) (psig) PVTSim Mod. EOS Experimental PVTSim Mod. EOS Experimental

2,746.0 1,321.0 1,232 1,230 1.917 1.9053 1.866 2,598.0 1,288.0 1,142 1,151 1.898 1.8514 1.821 2,400.0 1,178.5 1,048 1,059 1.836 1.7981 1.771 2,200.0 1,076.1 947 972 1.778 1.7385 1.725 1,897.0 934.1 806 849 1.698 1.6562 1.658 1,600.0 807.3 686 737 1.627 1.5864 1.599 1,300.0 688.9 576 631 1.560 1.5222 1.543 1,000.0 577.7 474 529 1.497 1.4624 1.488 700.0 470.1 377 428 1.434 1.4032 1.433 394.0 355.4 273 321 1.363 1.3374 1.371 195.0 265.7 194 231 1.302 1.2826 1.313 112.0 215.9 152 178 1.265 1.2510 1.274 0.0 0.0 000 000 1.052 1.1079 1.086

SPE 107331 17

Fi gure 9. DE Rsd for Oil-6

0.00

200.00

400.00

600.00

800.00

1,000.00

1,200.00

1,400.00

0.00 500.00 1,000.00 1,500.00 2,000.00 2,500.00 3,000.00

Pressure, psi

Rsd

, scf

/STB PVTSim

Mod. EOSExp

Figure 10. DE Bod for Oil-6

1

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

1.9

2

0.00 500.00 1,000.00 1,500.00 2,000.00 2,500.00 3,000.00

Pressure, psi

Bod

, bbl

/STB PVTSim

Mod. EOSExp

Crude Oil 7 – This hydrocarbon system is the least volatile of the oil samples in the Coats and Smart study. The oil shows a bubblepoint of 1,709 psia and a saturation density of 44.5 lbm/ft3 at 131°F. Table 15 shows the predicted PVT properties at saturation pressure compared with the experimental and Coats-Smart model data. Table 16 compares measures DE data with those simulated with both; the modified PREOS PVTSim model. The modified EOS reproduced the observed PVT with average deviations of 7.5% and 1.7% for Rsd and Bod, respectively.

18 SPE 107331


Approach pb

(psia) Rsbd

(scf/STB) Bobd

(RB/STB) ρ

(lbm/ft3) Experimental 1,709 557 1,324 44.5 Coats-Smart 1,531 (-10.4) 542 (-2.7) 1,296 (-2.10 40.7 (-8.5)

Modified EOS 1,572 (-8.0) 624 (12.0) 1,346 (1.7) 45.0 (1.1) Numbers in parentheses represent percent error of predictions

Table 16 – Expansion data for Oil 7

DE at 131°F p Rsd (scf/STB) Bod (RB/STB)

(psig) PVTSim Mod. EOS Experimental PVTSim Mod. EOS Experimental 1,694.0 641.2 624 557 1.369 1.3472 1.324 1,550.0 602.8 587 526 1.352 1.3321 1.311 1,400.0 562.9 550 493 1.334 1.3168 1.298 1,252.0 523.7 513 460 1.317 1.3013 1.285 1,100.0 483.3 475 423 1.299 1.2853 1.270

950.0 443.3 437 389 1.280 1.2694 1.256 798.0 402.3 398 349 1.262 1.2529 1.240 643.0 359.9 358 310 1.242 1.2357 1.224 500.0 319.8 320 273 1.223 1.2192 1.209 350.0 275.4 278 229 1.202 1.2005 1.188 200.0 224.2 230 179 1.175 1.1779 1.160 102.0 178.5 188 137 1.149 1.1562 1.136

0.0 000 000 000 1.017 1.0328 1.034

Red River Crude Oil System – The crude oil system of the Red River Field (Montana) is slightly volatile with Bobd = 1.706 and Rsbd = 921 at 250°F. The modified equation reproduced the observed Bod and Rsd with average deviations of 5.1 and 4.3%, respectively. The PVT properties of the crude oil system at saturation pressure were pb = 2,392 psia, Rsbd = 921 scf/STB, Bobd = 1.706 RB/STB, and ρ = 38.13 lbm/ft3. Those predicted by the modified EOS were pb = 2,497 psia, Rsbd = 1,061 scf/STB, Bobd = 1.8973 RB/STB, and ρ = 36.2 lbm/ft3 for errors of 4.4, 15.2, 11.2 and -5.0% for pb, Rsd, Bod and ρ, respectively. Table 17 gives detailed documentation of stimulated DE test for the system. PVTSim and modified give values for Bod that are considerably higher than the observed data, however; both models match with the CCE data equally well. In terms of Rsd, the modified EOS performed much better than PVTSim in the rang of all the pressures used in conducting the test.

Table 17 – Expansion Data for Red River Crude Oil DE at 250°F

p Rsd (scf/STB) Bod (RB/STB) (psig) PVTSim Mod. EOS Experimental PVTSim Mod. EOS Experimental

2,377.0 1,146.3 1,060 921 1.849 1.8947 1.706 2,250.0 1,081.5 982 872 1.811 1.8428 1.678 1,950.0 939.0 836 761 1.728 1.7509 1.614 1,650.0 809.5 698 657 1.653 1.6622 1.555 1,350.0 690.3 577 561 1.584 1.5843 1.501 1,050.0 578.5 469 467 1.518 1.5144 1.448

750.0 470.9 366 375 1.453 1.4470 1.395 450.0 360.9 266 274 1.384 1.3780 1.334 225.0 265.7 183 191 1.319 1.3170 1.279 125.0 212.0 139 140 1.279 1.2822 1.241

0.0 0.0 000 000 1.059 1.1341 1.102 Wyoming’s Heavy Crude Oil, Teapot Dome Field – This heavy oil contains 9.61 mol% C1 and 75.01 mol% C7+. The plus fraction is characterized by a molecular weight of 223.5 and a specific gravity of 0.8429. The oil exhibits a bubblepoint of 505 psia at 162°F. The PVT properties were pb = 505 psia, Rsbd = 110 scf/STB, Bobd = 1.1098 RB/STB, and ρ = 48.77 lbm/ft3. The model predicted pb = 520 psia, Rsbd = 113 scf/STB, Bobd = 1.1060 RB/STB, and ρ = 48.77 lbm/ft3 with errors of 2.97, 2.7, 0.34, and 0% for pb, Rsbd, Bobd and ρ, respectively. Table 18 shows the close match with the reported data.

SPE 107331 19

Table 18 – Expansion Data for Teapot Dome Crude Oil P,

(psig) Mod. EOS

Rsd, scf/STB Experimental Rsd, scf/STB

Mod. EOS Bod, RB/STB

Experimental Bod, RB/STB

490.3 113 110 1.1060 1.1098 385.3 97 94 1.0991 1.1025 285.3 80 77 1.0920 1.0962 185.3 63 58 1.0840 1.0886 85.3 42 36 1.0740 1.0782 35.3 28 23 1.0665 1.0701

0.0 00 00 1.0481 1.0491 North Sea Gas-Condensate System – The system is characterized by a dewpoint of 6.750 psia at 280°F. The gas contains 73.19 mol% C1 and 8.21 mol% C7+. The plus fraction is characterized by a molecular weight of 148 and a specific gravity of 0.16. The maximum liquid dropout with a value of 21.6% occurs at 3,100 psia. Whitson and Torp10 gave a detailed compositional and experimental analysis of the system. The modified equation predicts a dewpoint pressure of 6,189 psia. Table 19 gives complete results of the CVE simulation. The tabulated values show that the EOS predicts the entire liquid dropout and Z-factor data with average absolute deviations of 4.7 and 1.8%, respectively. Results of the model are generally in excellent agreement with reported data.

Table 19 – CVE at 280°F for the North Sea Reservoir Pressure (psig)

Component 6,750.0 5,500.0 4,300.0 3,100.0 2,100.0 1,200.0 700.0 700.0*

CO2 0.02370 0.02379 0.02399 0.02438 0.02493 0.02568 0.02630 0.00748 N2 0.00310 0.00320 0.00327 0.00334 0.00338 0.00337 0.00332 0.0037 C1 0.73190 0.75710 0.77263 0.78619 0.79345 0.79296 0.78412 0.10353 C2 0.07800 0.07950 0.08034 0.08126 0.08227 0.08376 0.08523 0.02357 C3 0.03550 0.03574 0.03577 0.03585 0.03619 0.03730 0.03903 0.01904

I-C4 0.00710 0.00706 0.00700 0.00694 0.00696 0.00721 0.00774 0.00600 n-C4 0.01450 0.01426 0.01403 0.01381 0.01379 0.01438 0.01570 0.01572 I-C5 0.00640 0.00620 0.00601 0.00580 0.00569 0.00590 0.00659 0.01079 n-C5 0.00680 0.00652 0.00627 0.00600 0.00583 0.00604 0.00682 0.01355 C6 0.01090 0.01023 0.00964 0.00893 0.00839 0.00847 0.00966 0.03245 C7+ 0.08210 0.05641 0.04105 0.02749 0.01912 0.01492 0.01549 0.76750

Z- Factor

PVTSim 1.225 1.068 0.966 0.913 0.904 0.922 0.943 Mod. EOS 1.2380 1.0890 0.9720 0.9130 0.9140 0.9370 0.9600

Experimental 1.2618 1.1105 0.9958 0.9239 0.9029 0.9182 0.9407

Gp (%) PVTSim 0.00000 9.310 21.89 38.620 55.42 71.920 81.270

Mod. EOS 0.00000 9.024 21.744 38.674 55.686 72.146 81.301 Experimental 0.00000 9.512 21.782 38.093 54.800 71.473 80.940

Liquid Dropout (%)

PVTSim 0.0 9.31 22.52 23.52 22.19 20.20 18.85 Mod. EOS 0.0 14.10 19.70 21.60 21.30 20.20 19.30

Experimental 0.0 12.89 19.07 20.92 20.56 19.23 18.13 Conclusions 1. Improved correlations for calculating a(Tc), b, and α(T) of the plus fraction, methane, and nitrogen are presented. 2. The modified PREOS gives hydrocarbon liquid density predictions that are compatible with or better than, the S-K and the A-K

density correlations. 3. The proposed modifications eliminate the need for splitting the heptanes-plus fraction into pseudo-components. 4. The proposed modifications significantly improve the ability of the PREOS to predict the PVT properties of complex

hydrocarbon mixtures.

20 SPE 107331

5. With such significant improvement in the predictive capability of the modified EOS, the equation is recommended for calculating the volumetric behavior of crude oil and condensate systems

Nomenclature a, b, A, B = EOS constants Bo = oil FVF obtained from differential expansion, RB/STB Bob = oil FVF at bubblepoint pressure, RB/STB JL = volume fraction of liquid in expansion cell Gp = volume fraction of gas removed from a laboratory CVE cell kij = binary interaction coefficient between Components i and j m = characteristic constant M = molecular weight, lbm/lbm mol p = pressure, psi pb = bubblepoint pressure, psi pc = critical point, psi ps = saturation pressure, psi R = universal gas constant, 10.73 psia ft3/mol °R Rs = solution GOR obtained from differential expansion, scf/STB T = temperature, °R Tc = critical temperature, °R V = laboratory expansion cell total volume, ft3

VL = volume of liquid in expansion cell, ft3 Vm = molar volume Vs = volume of expansion cell at saturation pressure, ft3

x = mole fraction z = compressibility factor α = correction factor for a γ = specific gravity ρ = density, lbm/ft3 ρob = density at bubblepoint, lbm/ft3

ω = acentric factor Ωa, Ωb = EOS constants Subscripts c = critical i, j = component number mix = mixture o = oil ob = bubblepoint References 1. van der Waals, J.D.: “On the Continuity of the Liquid and Gaseous State,” PhD dissertation, Sigthoff U. Leiden (1873) 2. Peng, D.Y. and Robinson, D.B.: “A New Two-Constant Equation of State,” Ind. & Eng. Chem. (1976) 15, No. 1, 59-64 3. Soave, G.: “Equilibrium Constants from a Modified Redlich-Kwong Equation of State,” Chem. Eng. Sci. (1972) 27, 1197-1203 4. Coats, K.H. and Smart, G.T.: “Application of a Regression Based EOS PVT Program to Laboratory Data,” SPERE (May 1986)

277-99. 5. Wilson, A., Maddox, R.N. and Erbar, J.H.: “C Fractions Affect Phase Behavior,” Oil & Gas J. (Aug. 21, 1978) 76-81 6. Katz, D.L. and Firoozabadi, A.: “Predicting Phase Behavior of Condensates/Crude Oil Systems Using Methane Interaction

Coefficients,” JPT (Nov. 1978) 1649-55; Trans., AIME 265 7. Firoozabadi A., Hekim, Y., and Katz, D.L.: “Reservoir Depletion Calculations for Gas Condensates Using Extended Analyses in

the Peng-Robinson Equation of State,” Cdn. J. Chem. Eng. (1978) 56, 610-15 8. Yarborough, L.: “Application of a Generalized Equation of State to Petroleum Reservoir Fluids,” Equations of State in

Engineering, Advances in Chemistry Series, K.C. Choa and R.L. Robinson (eds.), American Chemical Soc., Washington DC (1979) 182, 385-435

9. Whitson, C.H.: “Characterizing Hydrocarbon Plus Fractions,” SPEJ (Aug. 1983) 683-94 10. Whitson, C.H. and Torp, S.B.: “Evaluating Constant Volume Depletion Data: JPT (March 1983) 610-20

SPE 107331 21

11. Lohrenz, J., Bray, B.G., and Clark, C.R.: “Calculating Viscosities of Reservoir Fluids From Their Compositions,” JPT (Oct. 1964) 1171-76; Trans., AIME 231

12. Katz, D.L.: “Overview of Phase Behavior in Oil and Gas Production,” JPT (June 1983) 1205-14 13. Ahmed, T., Cady, G., and Story, A.: “An Accurate Method of Extending the Analysis of C7+,” paper SPE 12916 presented at the

1984 SPE Rocky Mountain Regional Meeting, Casper, WY, May 21-23 14. Ahmed, T., Cady, G. and Story, A.: “A Generalized Correlation for Characterizing the Hydrocarbon Heavy Fractions,” paper SPE

14266 presented at the 1985 SPE Annual Technical Conference and Exhibition, Las Vegas, Sept. 22-25 15. Kenyon, D. and Behie, G.: “Third SPE Comparative Solution Project: Gas Cycling of Retrograde Condensate Reservoirs,” JPT

(Aug. 1987) 981-97 16. Riazi, M.R. and Daubert, T.E.: “Characterization Parameter for Petroleum Fractions,” Ind. & Eng. Chem. Res. (197) 26, No. 4 17. Petersen, C.S.: “A Systematic and Consistent Approach to Determine Binary Interaction Coefficients for the Peng-Robinson

Equation of State,” SPERE (Nov. 1989) 488-96 18. Standing, M.B. and Katz, D.L.: “Density of Crude Oils Saturated with Natural Gas,” Trans., AIME (1942) 146, 150-65 19. Alani, G.H. and Kennedy, H.T.: “Volumes of Liquid Hydrocarbons at High Temperatures and Pressure,” Trans., AIME (1960)

219, 288-92 20. Ahmed, T.: “Supplement to a Practical Equation of State,” SPE 22219 available from SPE Book Order Dept., Richardson, TX. SI Metric Conversion Factors bbl x 1.589 873 E-01 = m3

ft3 x 2.831 685 E-02 = m3 °F (°F-32)/1.8 =°C lbm x 4.535 924 E-01 = kg psi x 6.894 757 E+00 = kPa

HEPTANES-PLUS CHARACTERIZATION 1

Some phase-behavior applications require the use of an equation ofstate (EOS) to predict properties of petroleum reservoir fluids. Thecritical properties, acentric factor, molecular weight, and binary-in-teraction parameters (BIP’s) of components in a mixture are requiredfor EOS calculations. With existing chemical-separation techniques,we usually cannot identify the many hundreds and thousands of com-ponents found in reservoir fluids. Even if accurate separation werepossible, the critical properties and other EOS parameters of com-pounds heavier than approximately C20 would not be known accu-rately. Practically speaking, we resolve this problem by making anapproximate characterization of the heavier compounds with exper-imental and mathematical methods. The characterization of heptanes-plus (C7) fractions can be grouped into three main tasks.1–3

1. Dividing the C7 fraction into a number of fractions withknown molar compositions.

2. Defining the molecular weight, specific gravity, and boilingpoint of each C7 fraction.

3. Estimating the critical properties and acentric factor of each C7fraction and the key BIP’s for the specific EOS being used.

This chapter presents methods for performing these tasks andgives guidelines on when each method can be used. A unique char-acterization does not exist for a given reservoir fluid. For example,different component properties are required for different EOS’s;therefore, the engineer must determine the quality of a given charac-terization by testing the predictions of reservoir-fluid behavioragainst measured pressure/volume/temperature (PVT) data.

The amount of C7 typically found in reservoir fluids varies from50 mol% for heavy oils to 1 mol% for light reservoir fluids.4

Average C7 properties also vary widely. For example, C7 molec-ular weight can vary from 110 to 300 and specific gravity from0.7 to 1.0. Because the C7 fraction is a mixture of many hundredsof paraffinic, naphthenic, aromatic, and other organic compounds,5

the C7 fraction cannot be resolved into its individual componentswith any precision. We must therefore resort to approximate de-scriptions of the C7 fraction.

Sec. 5.2 discusses experimental methods available for quantify-ing C7 into discrete fractions. True-boiling-point (TBP) distilla-tion provides the necessary data for complete C7 characterization,including mass and molar quantities, and the key inspection data foreach fraction (specific gravity, molecular weight, and boiling point).Gas chromatography (GC) is a less-expensive, time-saving alterna-tive to TBP distillation. However, GC analysis quantifies only themass of C7 fractions; such properties as specific gravity and boil-ing point are not provided by GC analysis.

Typically, the practicing engineer is faced with how to character-ize a C7 fraction when onlyzC7 the mole fraction, ; molecularweight, MC7

; and specific gravity, C7, are known. Sec. 5.3 re-

views methods for splitting C7 into an arbitrary number of sub-fractions. Most methods assume that mole fraction decreases expo-nentially as a function of molecular weight or carbon number. Amore general model based on the gamma distribution has been suc-cessfully applied to many oil and gas-condensate systems. Othersplitting schemes can also be found in the literature; we summarizethe available methods.

Sec. 5.4 discusses how to estimate inspection properties and Tb

for C7 fractions determined by GC analysis or calculated from amathematical split. Katz and Firoozabadi’s6 generalized single car-bon number (SCN) properties are widely used. Other methods forestimating specific gravities of C7 subfractions are based on forc-ing the calculated C7

to match the measured value.Many empirical correlations are available for estimating critical

properties of pure compounds and C7 fractions. Critical propertiescan also be estimated by forcing the EOS to match the boiling point andspecific gravity of each C7 fraction separately. In Sec. 5.5, we reviewthe most commonly used methods for estimating critical properties.

Finally, Sec. 5.6 discusses methods for reducing the number ofcomponents describing a reservoir mixture and, in particular, theC7 fraction. Splitting the C7 into pseudocomponents is particu-larly important for EOS-based compositional reservoir simulation.A large part of the computing time during a compositional reservoirsimulation is used to solve the flash calculations; accordingly, mini-mizing the number of components without jeopardizing the qualityof the fluid characterization is necessary.

The most reliable basis for C7 characterization is experimentaldata obtained from high-temperature distillation or GC. Many ex-perimental procedures are available for performing these analyses;in the following discussion, we review the most commonly usedmethods. TBP distillation provides the key data for C7 character-ization, including mass and molar quantities, specific gravity, mo-lecular weight, and boiling point of each distillation cut. Other suchinspection data as kinematic viscosity and refractive index also maybe measured on distillation cuts.

Simulated distillation by GC requires smaller samples and lesstime than TBP distillation.7-9 However, GC analysis measures onlythe mass of carbon-number fractions. Simulated distillation resultscan be calibrated against TBP data, thus providing physical proper-ties for the individual fractions. For many oils, simulated distillation

2 PHASE BEHAVIOR

Fig. 5.1—Standard apparatus for conducting TBP analysis ofcrude-oil and condensate samples at atmospheric and subat-mospheric pressures (after Ref. 11).

provides the necessary information for C7 characterization in farless the time and at far less cost than that required for a completeTBP analysis. We recommend, however, that at least one completeTBP analysis be measured for (1) oil reservoirs that may be candi-dates for gas injection and (2) most gas-condensate reservoirs.

5.2.1 TBP Distillation. In TBP distillation, a stock-tank liquid (oilor condensate) is separated into fractions or “cuts” by boiling-pointrange. TBP distillation differs from the Hempel and American Soc.for Testing Materials (ASTM) D-158 distillations10 because TBPanalysis requires a high degree of separation, which is usually con-trolled by the number of theoretical trays in the apparatus and thereflux ratio. TBP fractions are often treated as components havingunique boiling points, critical temperatures, critical pressures, andother properties identified for pure compounds. This treatment isobviously more valid for a cut with a narrow boiling-point range.

The ASTM D-289211 procedure is a useful standard for TBPanalysis of stock-tank liquids. ASTM D-2892 specifies the generalprocedure for TBP distillation, including equipment specifications(see Fig. 5.1), reflux ratio, sample size, and calculations necessaryto arrive at a plot of cumulative volume percent vs. normal boilingpoint. Normal boiling point implies that boiling point is measuredat normal or atmospheric pressure. In practice, to avoid thermal de-composition (cracking), distillation starts at atmospheric pressureand is changed to subatmospheric distillation after reaching a limit-ing temperature. Subatmospheric boiling-point temperatures areconverted to normal boiling-point temperatures by use of a vapor-pressure correlation that corrects for the amount of vacuum and thefraction’s chemical composition. The boiling-point range for frac-tions is not specified in the ASTM standard. Katz and Firoozabadi6

recommend use of paraffin normal boiling points (plus 0.5°C) asboundaries, a practice that has been widely accepted.

Fig. 5.2—TBP curve for a North Sea gas-condensate sample il-lustrating the midvolume-point method for calculating averageboiling point (after Austad et al.7).

Cutoff (n-paraffin) boiling point

Midvolume (“normal”) boiling point

Fig. 5.27 shows a plot of typical TBP data for a North Sea sample.

Normal boiling point is plotted vs. cumulative volume percent.

Table 5.1 gives the data, including measured specific gravities and

molecular weights. Average boiling point is usually taken as the val-

ue found at the midvolume percent of a cut. For example, the third

cut in Table 5.1 boils from 258.8 to 303.8°F, with an initial 27.49

vol% and a final 37.56 vol%. The midvolume percent is

(27.4937.56)/2 32.5 vol%; from Fig. 5.2, the boiling point at

this volume is !282°F. For normal-paraffin boiling-point intervals,

Katz and Firoozabadi’s6 average boiling points of SCN fractions

can be used (see Table 5.2).

The mass, mi, of each distillation cut is measured directly during

a TBP analysis. The cut is quantified in moles ni with molecular

weight, Mi, and the measured mass mi, where ni mi"Mi. Volume

of the fraction is calculated from the mass and the density, i (or spe-

cific gravity, i), where Vi mi" i . Mi is measured by a cryoscop-

ic method based on freezing-point depression, and i is measured

by a pycnometer or electronic densitometer. Table 5.1 gives cumula-

tive weight, mole, and volume percents for the North Sea sample.

Average C7 properties are given by

MC7

#Ni 1

mi

#Ni 1

ni

and C7

#Ni 1

mi

#Ni 1

Vi

, (5.1). . . . . . . . . . . . . . . . . . . . . . . . . . . . .

where C7 C7

w with w pure water density at standard

conditions. These calculated averages are compared with mea-

sured values of the C7 sample, and discrepancies are reported as

“lost” material.

Refs. 7 and 15 through 20 give procedures for calculating proper-

ties from TBP analyses. Also, the ASTM D-289211 procedure gives

details on experimental equipment and the procedure for conducting

TBP analysis at atmospheric and subatmospheric conditions. Table

5.3 gives an example TBP analysis from a commercial laboratory.


TABLE 5.1—EXPERIMENTAL TBP RESULTS FOR A NORTH SEA CONDENSATE

Fraction

Upper

Tbi

(°F)

Average

Tbi*

(°F)

mi

(g) i**

Mi

(g/mol)

Vi

(cm3)

ni

(mol)

wi

(%)

xVi

%

xi

%

!wi

%

!xVi

% Kw

C7

C8

C9

C10

C11

C12

C13

C14

C15

C16

C17

C18

C19

C20

C21

208.4

258.8

303.8

347.0

381.2

420.8

455.0

492.8

523.4

550.4

579.2

604.4

629.6

653.0

194.0

235.4

282.2

325.4

363.2

401.1

438.8

474.8

509.0

537.8

564.8

591.8

617.0

642.2

90.2

214.6

225.3

199.3

128.8

136.8

123.8

120.5

101.6

74.1

76.8

58.2

50.2

45.3

427.6

0.7283

0.7459

0.7658

0.7711

0.7830

0.7909

0.8047

0.8221

0.8236

0.8278

0.8290

0.8378

0.8466

0.8536

0.8708

96

110

122

137

151

161

181

193

212

230

245

259

266

280

370

123.9

287.7

294.2

258.5

164.5

173.0

153.8

146.6

123.4

89.5

92.6

69.5

59.3

53.1

491.1

0.940

1.951

1.847

1.455

0.853

0.850

0.684

0.624

0.479

0.322

0.313

0.225

0.189

0.162

1.156

4.35

10.35

10.87

9.61

6.21

6.60

5.97

5.81

4.90

3.57

3.70

2.81

2.42

2.19

20.63

4.80

11.15

11.40

10.02

6.37

6.70

5.96

5.68

4.78

3.47

3.59

2.69

2.30

2.06

19.03

7.80

16.19

15.33

12.07

7.08

7.05

5.68

5.18

3.98

2.67

2.60

1.87

1.57

1.34

9.59

4.35

14.70

25.57

35.18

41.40

48.00

53.97

59.78

64.68

68.26

71.96

74.77

77.19

79.37

100.00

4.80

15.95

27.35

37.37

43.74

50.44

56.41

62.09

66.87

70.33

73.92

76.62

78.91

80.97

100.00

11.92

11.88

11.82

11.96

11.97

12.03

11.99

11.89

12.01

12.07

12.16

12.14

12.11

12.10

Sum 2,073.1 2,580.5 12.049 100.00 100.00 100.00

Average 0.8034 172 11.98

Reflux ratio 1 : 5; reflux cycle 18 seconds; distillation at atmospheric pressure 201.2 to 347°F; distillation at 100 mm Hg 347 to 471.2°F; and distillation at 10 mm Hg 471.2to 653°F.

Vi mi /i /0.9991; ni mi /Mi ; wi 100$mi /2073.1; xVi 100$Vi/2580.5; xi 100$ni /12.049; !wi !wi ; !xVi !xVi ; and Kw (Tbi+460)1/3/i .*Average taken at midvolume point.

**Water 1.

Boiling points are not reported because normal-paraffin boiling-point

intervals are used as a standard; accordingly, the average boiling

points suggested by Katz and Firoozabadi6 (Table 5.2) can be used.

5.2.2 Chromatography. GC and, to a lesser extent, liquid chroma-

tography are used to quantify the relative amount of compounds

found in oil and gas systems. The most important application of

chromatography to C7 characterization is simulated distillation by

GC techniques.

Fig. 5.3 shows an example gas chromatogram for the North Sea

sample considered earlier. The dominant peaks are for normal paraf-

fins, which are identified up to n-C22. As a good approximation for

a paraffinic sample, the GC response for carbon number Ci starts at

the bottom response of n-Ci%1 and extends to the bottom response

of n-Ci. The mass of carbon number Ci is calculated as the area under

the curve from the baseline to the GC response in the n-Ci%1 to n-Ci

interval (see the shaded area for fraction C9 in Fig. 5.3). As Fig. 5.47

shows schematically, the baseline should be determined before run-

ning the actual chromatogram.

Because stock-tank samples cannot be separated completely by

standard GC analysis, an internal standard must be used to relate GC

area to mass fraction. Normal hexane was used as an internal stan-

dard for the sample in Fig. 5.3. The internal standard’s response fac-

tor may need to be adjusted to achieve consistency between simu-

lated and TBP distillation results. This factor will probably be

constant for a given oil, and the factor should be determined on the

basis of TBP analysis of at least one sample from a given field. Fig.

5.5 shows the simulated vs. TBP distillation curves for the Austad

et al.7 sample. A 15% correction to the internal-standard response

factor was used to match the two distillation curves.

As an alternative to correcting the internal standard, Maddox and

Erbar15 suggest that the reported chromatographic boiling points be

adjusted by a correction factor that depends on the reported boiling

point and the “paraffinicity” of the composite sample. This correc-

tion factor varies from 1 to 1.15 and is slightly larger for aromatic

than paraffinic samples.

Several laboratories have calibrated GC analysis to provide simu-

lated-distillation results up to C40. However, checking the accuracy

of simulated distillation for SCN fractions greater than approxi-

mately C25 is difficult because C25 is usually the upper limit for reli-

able TBP distillation. The main disadvantage of simulated distilla-

tion is that inspection data are not determined directly for each

fraction and must therefore either be correlated from TBP data or es-

timated from correlations (see Sec. 5.4).

Sophisticated analytical methods, such as mass spectroscopy,

may provide detailed information on the compounds separated by

GC. For example, mass spectroscopy GC can establish the relative

amounts of paraffins, naphthenes, and aromatics (PNA’s) for car-

bon-number fractions distilled by TBP analysis. Detailed PNA in-

formation should provide more accurate estimation of the critical

properties of petroleum fractions, but the analysis is relatively cost-

ly and time-consuming from a practical point of view. Recent work

has shown that PNA analysis3,19-23 may improve C7 characteriza-

tion for modeling phase behavior with EOS’s. Our experience, how-

ever, is that PNA data have limited usefulness for improving EOS

fluid characterizations.

! "#

Molar distribution is usually thought of as the relation between mole

fraction and molecular weight. In fact, this concept is misleading be-

cause a unique relation does not exist between molecular weight and

mole fraction unless the fractions are separated in a consistent man-

ner. Consider for example a C7 sample distilled into 10 cuts sepa-

rated by normal-paraffin boiling points. If the same C7 sample is

distilled with constant 10-vol% cuts, the two sets of data will not

4 PHASE BEHAVIOR

TABLE 5.2—SINGLE CARBON NUMBER PROPERTIES FOR HEPTANES-PLUS (after Katz and Firoozabadi6)

Katz-Firoozabadi Generalized Properties

Tb Interval*

Lee-Kesler12/Kesler-Lee13

Correlations Riazi14 Defined

Fraction

Number

Lower

(°F)

Upper

(°F)

Average Tb

(°F) (°R) !!"! M

Defined

Kw

Tc

(°R)

pc

(psia)

#

#$

Vc

(ft3/lbm mol) Zc

6 97.7 156.7 147.0 606.7 0.690 84 12.27 914 476 0.271 5.6 0.273

7 156.7 210.0 197.4 657.1 0.727 96 11.96 976 457 0.310 6.2 0.272

8 210.0 259.0 242.1 701.7 0.749 107 11.86 1,027 428 0.349 6.9 0.269

9 259.0 304.3 288.0 747.6 0.768 121 11.82 1,077 397 0.392 7.7 0.266

10 304.3 346.3 330.4 790.1 0.782 134 11.82 1,120 367 0.437 8.6 0.262

11 346.3 385.5 369.0 828.6 0.793 147 11.84 1,158 341 0.479 9.4 0.257

12 385.5 422.2 406.9 866.6 0.804 161 11.86 1,195 318 0.523 10.2 0.253

13 422.2 456.6 441.0 900.6 0.815 175 11.85 1,228 301 0.561 10.9 0.249

14 456.6 489.0 475.5 935.2 0.826 190 11.84 1,261 284 0.601 11.7 0.245

15 489.0 520.0 510.8 970.5 0.836 206 11.84 1,294 268 0.644 12.5 0.241

16 520.0 548.6 541.4 1,001.1 0.843 222 11.87 1,321 253 0.684 13.3 0.236

17 548.6 577.4 572.0 1,031.7 0.851 237 11.87 1,349 240 0.723 14.0 0.232

18 577.4 602.6 595.4 1,055.1 0.856 251 11.89 1,369 230 0.754 14.6 0.229

19 602.6 627.8 617.0 1,076.7 0.861 263 11.90 1,388 221 0.784 15.2 0.226

20 627.8 651.2 640.4 1,100.1 0.866 275 11.92 1,408 212 0.816 15.9 0.222

21 651.2 674.6 663.8 1,123.5 0.871 291 11.94 1,428 203 0.849 16.5 0.219

22 674.6 692.6 685.4 1,145.1 0.876 305 11.94 1,447 195 0.879 17.1 0.215

23 692.6 717.8 707.0 1,166.7 0.881 318 11.95 1,466 188 0.909 17.7 0.212

24 717.8 737.6 726.8 1,186.5 0.885 331 11.96 1,482 182 0.936 18.3 0.209

25 737.6 755.6 746.6 1,206.3 0.888 345 11.99 1,498 175 0.965 18.9 0.206

26 755.6 775.4 766.4 1,226.1 0.892 359 12.00 1,515 168 0.992 19.5 0.203

27 775.4 793.4 786.2 1,245.9 0.896 374 12.01 1,531 163 1.019 20.1 0.199

28 793.4 809.6 804.2 1,263.9 0.899 388 12.03 1,545 157 1.044 20.7 0.196

29 809.6 825.8 820.4 1,280.1 0.902 402 12.04 1,559 152 1.065 21.3 0.194

30 825.8 842.0 834.8 1,294.5 0.905 416 12.04 1,571 149 1.084 21.7 0.191

31 842.0 858.2 851.0 1,310.7 0.909 430 12.04 1,584 145 1.104 22.2 0.189

32 858.2 874.4 865.4 1,325.1 0.912 444 12.04 1,596 141 1.122 22.7 0.187

33 874.4 888.8 879.8 1,339.5 0.915 458 12.05 1,608 138 1.141 23.1 0.185

34 888.8 901.4 892.4 1,352.1 0.917 472 12.06 1,618 135 1.157 23.5 0.183

35 901.4 915.8 906.8 1,366.5 0.920 486 12.06 1,630 131 1.175 24.0 0.180

36 919.4 1,379.1 0.922 500 12.07 1,640 128 1.192 24.5 0.178

37 932.0 1,391.7 0.925 514 12.07 1,650 126 1.207 24.9 0.176

38 946.4 1,406.1 0.927 528 12.09 1,661 122 1.226 25.4 0.174

39 959.0 1,418.7 0.929 542 12.10 1,671 119 1.242 25.8 0.172

40 971.6 1,431.3 0.931 556 12.10 1,681 116 1.258 26.3 0.170

41 982.4 1,442.1 0.933 570 12.11 1,690 114 1.272 26.7 0.168

42 993.2 1,452.9 0.934 584 12.13 1,697 112 1.287 27.1 0.166

43 1,004.0 1,463.7 0.936 598 12.13 1,706 109 1.300 27.5 0.164

44 1,016.6 1,476.3 0.938 612 12.14 1,716 107 1.316 27.9 0.162

45 1,027.4 1,487.1 0.940 626 12.14 1,724 105 1.328 28.3 0.160

*At 1 atmosphere.

**Water 1.

produce the same plot of mole fraction vs. molecular weight. How-ever, a plot of cumulative mole fraction,

Qzi

#ij 1

zj

#Nj 1

zj

, (5.2). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

vs. cumulative average molecular weight,

QMi

#ij 1

zj Mj

#ij 1

zj

, (5.3). . . . . . . . . . . . . . . . . . . . . . . . . . . . . .


TABLE 5.3—STANDARD TBP RESULTS FROM COMMERCIAL PVT LABORATORY

Component mol% wt%

Density

(g/cm3)

Gravity

#API

Molecular

Weight

Heptanes

Octanes

Nonanes

Decanes

Undecanes

Dodecanes

Tridecanes

Tetradecanes

Pentadecanes plus

1.12

1.30

1.18

0.98

0.62

0.57

0.74

0.53

4.10

2.52

3.08

3.15

2.96

2.10

2.18

3.05

2.39

31.61

0.7258

0.7470

0.7654

0.7751

0.7808

0.7971

0.8105

0.8235

0.8736

63.2

57.7

53.1

50.9

49.5

45.8

42.9

40.1

30.3

96

101

114

129

144

163

177

192

330

*At 60°F.

Note: Katz and Firoozabadi6 average boiling points (Table 5.2) can be used when normal paraffin boiling-point intervals are used.

should produce a single curve. Strictly speaking, therefore, molardistribution is the relation between cumulative molar quantity andsome expression for cumulative molecular weight.

In this section, we review methods commonly used to describemolar distribution. Some methods use a consistent separation offractions (e.g., by SCN) so the molar distribution can be expresseddirectly as a relationship between mole fraction and molecularweight of individual cuts. Most methods in this category assume thatC7 mole fractions decrease exponentially. A more general ap-proach uses the continuous three-parameter gamma probabilityfunction to describe molar distribution.

5.3.1 Exponential Distributions. The Lohrenz-Bray-Clark24

(LBC) viscosity correlation is one of the earliest attempts to use anexponential-type distribution for splitting C7. The LBC methodsplits C7 into normal paraffins C7 though C40 with the relation

zi zC6

exp[A1(i% 6) A2(i% 6)2], (5.4). . . . . . . . . . . . .

where i carbon number and zC6 measured C6 mole fraction.

Constants A1 and A2 are determined by trial and error so that

zC7 #

40

i 7

zi (5.5). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Fig. 5.3—Simulated distillation by GC of the North Sea gas-con-densate sample in Fig. 5.2 (after Austad et al.7).

and zC7MC7

#40

i 7

zi Mi (5.6). . . . . . . . . . . . . . . . . . . . . . . .

are satisfied. Paraffin molecular weights (Mi 14i2) are used inEq. 5.6. A Newton-Raphson algorithm can be used to solve Eqs. 5.5and 5.6. Note that the LBC model cannot be used when zC7 zC

6and MC7

MC40. The LBC form of the exponential distribution

has not found widespread application.More commonly, a linear form of the exponential distribution is

used to split the C7 fraction. Writing the exponential distributionin a general form for any Cn fraction (n 7 being a special case),

zi zCnexp A[(i% n)], (5.7). . . . . . . . . . . . . . . . . . . . . . . .

where i carbon number, zCn mole fraction of Cn , and

A constant indicating the slope on a plot of ln zi vs. i. The constantszCn

and A can be determined explicitly. With the general expression

Mi 14 i h (5.8). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

for molecular weight of Ci and the assumption that the distributionis infinite, constants zCn

and A are given by

zCn 14

MCn% 14(n% 1) % h

(5.9). . . . . . . . . . . . . . . . . .

and A ln&1% zCn' (5.10). . . . . . . . . . . . . . . . . . . . . . . . . . .

so that#(

i n

zi 1 (5.11). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Fig. 5.4—GC simulated distillation chromatograms (a) withoutany sample (used to determine the baseline), (b) for a crude oil,and (c) for a crude oil with internal standard (after MacAllisterand DeRuiter9).

(a)

(b)

(c)

6 PHASE BEHAVIOR

Fig. 5.5—Comparison of TBP and GC-simulated distillation fora North Sea gas-condensate sample (after Austad et al.7).

and #(

i n

zi Mi MCn(5.12). . . . . . . . . . . . . . . . . . . . . . . . . . .

are satisfied.

Eqs. 5.9 and 5.10 imply that once a molecular weight relation is cho-

sen (i.e., h is fixed), the distribution is uniquely defined by C7 molec-

ular weight. Realistically, all reservoir fluids having a given C7 mo-

lecular weight will not have the same molar distribution, which is one

reason why more complicated models have been proposed.

5.3.2 Gamma-Distribution Model. The three-parameter gamma

distribution is a more general model for describing molar distribu-

tion. Whitson2,25,26 and Whitson et al.27 discuss the gamma dis-

tribution and its application to molar distribution. They give results

for 44 oil and condensate C7 samples that were fit by the gamma

distribution with data from complete TBP analyses. The absolute

average deviation in estimated cut molecular weight was 2.5 amu

(molecular weight units) for the 44 samples.

The gamma probability density function is

p(M) (M% %)&%1 exp )% *&M% %'"'+,

'&"(&), (5.13). . . . . . . .

where " gamma function and ' is given by

' MC7

% %

& . (5.14). . . . . . . . . . . . . . . . . . . . . . . . . . . . .

The three parameters in the gamma distribution are &, %, and

MC7 The key parameter & defines the form of the distribution, and

its value usually ranges from 0.5 to 2.5 for reservoir fluids; & 1

gives an exponential distribution. Application of the gamma dis-

tribution to heavy oils, bitumen, and petroleum residues indicates

that the upper limit for & is 25 to 30, which statistically is approach-

ing a log-normal distribution (see Fig. 5.628).

The parameter % can be physically interpreted as the minimum

molecular weight found in the C7 fraction. An approximate rela-

tion between & and % is

%! 110

1% &1 4"&0.7' (5.15). . . . . . . . . . . . . . . . . . . . . . . . .

Fig. 5.6—Gamma distributions for petroleum residue (afterBrulé et al.28).

700 to 1,000°F Distillate

1,000 to 1,250°F Distillate

1,200°F Residue

for reservoir-fluid C7 fractions. Practically, % should be consideredas a mathematical constant more than as a physical property, eithercalculated from Eq. 5.15 or determined by fitting measured TBP data.

Fig. 5.7 shows the function p(M) for the Hoffman et al.29 oil anda North Sea oil. Parameters for these two oils were determined by fit-ting experimental TBP data. The Hoffman et al. oil has a relativelylarge & of 2.27, a relatively small % of 75.7, with MC7 198; theNorth Sea oil is described by & 0.82, % 93.2, and MC7 227.

The continuous distribution p(M ) is applied to petroleum frac-tions by dividing the area under the p(M ) curve into sections (shownschematically in Fig. 5.8). By definition, total area under the p(M )curve from % to ( is unity. The area of a section is defined asnormalized mole fraction zi"zC7

for the range of molecularweights Mbi%1 to Mbi. If the area from % to molecular-weightboundary Mb is defined as P0(Mb), then the area of Section i isP0(Mbi)%P0(Mbi%1), also shown schematically in Fig. 5.8. Molefraction zi can be written

zi zC7*P0&Mb i'% P0&Mb i%1

'+ . (5.16). . . . . . . . . . . . . . .

Average molecular weight in the same interval is given by

Mi % &'P1&Mb i'% P1&Mb i%1'

P0&Mb i'% P0&Mb i%1' , (5.17). . . . . . . . . . .

where P0 QS, (5.18). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

and P1 Q&S% 1&', (5.19). . . . . . . . . . . . . . . . . . . . . . . . . . .


Fig. 5.7—Gamma density function for the Hoffman et al.29 oil(dashed line) and a North Sea volatile oil (solid line). After Whit-son et al.27

& 2.273% 75.7MC7

198.4

& 0.817% 93.2MC7

227

where Q e%y y& "(&), (5.20). . . . . . . . . . . . . . . . . . . . . . . . .

S #(

j 0

y j*-jk 0

(& k)+%1

, (5.21). . . . . . . . . . . . . . . . . . .

and y Mb% %

'. (5.22). . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Note that P0(Mb0 %) P1(Mb0 %) 0.

The summation in Eq. 5.21 should be performed until the last

term is 1$10%8. The gamma function can be estimated by30

"&x 1' 1 #8

i 1

Ai xi , (5.23). . . . . . . . . . . . . . . . . . . . .

where A1 %0.577191652, A2 0.988205891, A3 %0.897056937,

A4 0.918206857, A5 %0.756704078, A6 0.482199394, A7 %0.193527818, and A8 0.035868343 for 0.x.1. The recurrence

formula, "(x1) x"(x), is used for x1 and x1; furthermore,

"(1) 1.

The equations for calculating zi and Mi are summarized in a short

FORTRAN program GAMSPL found in Appendix A. In this simple

program, the boundary molecular weights are chosen arbitrarily at

increments of 14 for the first 19 fractions, starting with % as the first

lower boundary. The last fraction is calculated by setting the upper

molecular-weight boundary equal to 10,000. Table 5.4 gives three

sample outputs from GAMSPL for & 0.5, 1, and 2 with % 90 and

MC7 200 held constant. Fig. 5.9 plots the results as log zi vs. Mi.

The amount and molecular weight of the C26 fraction varies for

each value of &.

The gamma distribution can be fit to experimental molar-distribu-

tion data by use of a nonlinear least-squares algorithm to determine

&, %, and '. Experimental TBP data are required, including weight

fraction and molecular weight for at least five C7 fractions (use of

more than 10 fractions is recommended to ensure a unique fit of mod-

el parameters). The sum-of-squares function can be defined as

F&&, % , '' #N%1

i 1

(Mi)2, (5.24). . . . . . . . . . . . . . . . . . . . . . .

where Mi (Mi)mod% (Mi)exp

(Mi)exp

. (5.25). . . . . . . . . . . . . . . . . .

Subscripts mod and exp model and experimental, respectively. This

sum-of-squares function weights the lower molecular weights more

than higher molecular weights, in accordance with the expected accu-

racy for measurement of molecular weight. Also, the sum-of-squares

function does not include the last molecular weight because this mo-

lecular weight may be inaccurate or backcalculated to match the mea-

sured average C7 molecular weight. If the last fraction is not in-

cluded, the model average molecular weight, (MC7)mod % &',

can be compared with the experimental value as an independent

check of the fit.

A simple graphical procedure can be used to fit parameters & and

% if experimental MC7 is fixed and used to define '. Fig. 5.10

shows a plot of cumulative weight fraction,

Qwi #i

j 1

wi , (5.26). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

vs. the cumulative dimensionless molecular-weight variable,

Q*M i

QM i% %

MC7% %

. (5.27). . . . . . . . . . . . . . . . . . . . . . . . . . .

Table 5.5 and the following outline describe the procedure for deter-

mining model parameters with Fig. 5.10 and TBP data.

1. Tabulate measured mole fractions zi and molecular weights Mi

for each fraction.

2. Calculate experimental weight fractions, wi (zi Mi)

/ (zC7MC7), if they are not reported.

3. Normalize weight fractions and calculate cumulative normal-

ized weight fraction Qw i .

4. Calculate cumulative molecular weight QM i from Eq. 5.3.

5. Assume several values of % (e.g., from 75 to 100) and calculate

Q*M i for each value of the estimated %.

6. For each estimate of %, plot Q*M i vs. Qwi on a copy of Fig. 5.10

and choose the curve that fits one of the model curves best. Read the

value of & from Fig. 5.10.

7. Calculate molecular weights and mole fractions of Fractions i

using the best-fit curve in Fig. 5.10. Enter the curve at measured val-

ues of Qwi , read Q*M i , and calculate Mi from

Mi % &MC7% %' Qwi% Qwi%1

*&Qwi"Q*M i'% &Qwi%1"Q*

M i%1'+ .

(5.28). . . . . . . . . . . . . . . . . . .

Fig. 5.8—Schematic showing the graphical interpretation of areas under the gamma densityfunction p(M) that are proportional to normalized mole fraction; A area.

P0&Mbi'% P0

&Mbi%1'

Mbi

A P0&Mbi' A P0

&Mbi%1'

Mbi%1

p(M)

A zi"zC7

8 PHASE BEHAVIOR

TABLE 5.4—RESULTS OF GAMSPL PROGRAM FOR THREE DATA SETS WITH DIFFERENT

GAMMA-DISTRIBUTION PARAMETER &

!###!& 0.5 !###!& 1.0 !###!& 2.0

Fraction

Number

Mole

Fraction

Molecular

Weight

Mole

Fraction

Molecular

Weight

Mole

Fraction

Molecular

Weight

1 0.2787233 94.588 0.1195065 96.852 0.0273900 99.132

2 0.1073842 110.525 0.1052247 110.852 0.0655834 111.490

3 0.0772607 124.690 0.0926497 124.852 0.0852269 125.172

4 0.0610991 138.758 0.0815774 138.852 0.0927292 139.038

5 0.0505020 152.796 0.0718284 152.852 0.0925552 152.963

6 0.0428377 166.819 0.0632444 166.852 0.0877762 166.916

7 0.0369618 180.836 0.0556863 180.852 0.0804707 180.883

8 0.0322804 194.848 0.0490314 194.852 0.0720157 194.859

9 0.0284480 208.857 0.0431719 208.852 0.0632969 208.841

10 0.0252470 222.864 0.0380125 222.852 0.0548597 222.826

11 0.0225321 236.870 0.0334698 236.852 0.0470180 236.814

12 0.0202013 250.875 0.0294699 250.852 0.0399302 250.805

13 0.0181808 264.879 0.0259481 264.852 0.0336535 264.797

14 0.0164152 278.883 0.0228471 278.852 0.0281813 278.790

15 0.0148619 292.886 0.0201167 292.852 0.0234690 292.784

16 0.0134879 306.888 0.0177127 306.852 0.0194514 306.778

17 0.0122665 320.890 0.0155959 320.852 0.0160543 320.774

18 0.0111762 334.892 0.0137321 334.852 0.0132017 334.770

19 0.0101996 348.894 0.0120910 348.852 0.0108204 348.766

20 0.1199341 539.651 0.0890834 466.000 0.0463166 420.424

Total 1.0000000 1.0000000 1.0000000

Average 200 200 200

For all three cases % 90 and MC7 200.

Mole fractions zi are given by

zi zC7 &Qw i

Q*M i

%Qw i%1

Q*M i%1

' . (5.29). . . . . . . . . . . . . . . . . . .

For computer applications, Qwi and Q*M i can be calculated exactly

from Eqs. 5.16 through 5.23 with little extra effort.

MC7

Fig. 5.9—Three example molar distributions for an oil samplewith =200 and %=90, calculated with the GAMSPL program(Table A-4) in Table 5.4.

MC7 200

90

Mb 14 2.0

0.5

1.0

Fig. 5.11 shows a Q*M i% Qwi match for the Hoffman et al.29 oil

with % 70, 72.5, 75, and 80 and indicates that a best fit is achievedfor % 72.5 and & 2.5 (see Fig. 5.12).

Although the gamma-distribution model has the flexibility oftreating reservoir fluids from light condensates to bitumen, mostreservoir fluids can be characterized with an exponential molar dis-tribution (& 1) without adversely affecting the quality of EOS pre-

MC7

Fig. 5.10—Cumulative-distribution type curve for fitting exper-imental TBP data to the gamma-distribution model. Parameters& and % are determined with held constant.

1.0

0.0

0.8

0.6

0.4

0.2

0.0 0.2 0.4 0.6 0.8 1.0

Cumulative Normalized Mole Fraction, Qzi

( )

( )


TABLE 5.5—CALCULATION OF CUMULATIVE WEIGHT FRACTION AND

CUMULATIVE MOLECULAR WEIGHT VARIABLE FOR HOFFMAN et al.29 OIL

Q*Mi

Component

i zi #!zi# Mi ziMi $!ziMi$ Qwi QMi % 70 % 72.5 % 75 % 80 % 85

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

0.0263

0.0234

0.0235

0.0224

0.0241

0.0246

0.0266

0.0326

0.0363

0.0229

0.0171

0.0143

0.0130

0.0108

0.0087

0.0072

0.0058

0.0048

0.0039

0.0034

0.0028

0.0025

0.0023

0.0091

0.0263

0.0497

0.0732

0.0956

0.1197

0.1443

0.1709

0.2035

0.2398

0.2627

0.2799

0.2941

0.3072

0.3180

0.3267

0.3338

0.3396

0.3444

0.3483

0.3517

0.3545

0.3570

0.3593

0.3684

99

110

121

132

145

158

172

186

203

222

238

252

266

279

290

301

315

329

343

357

371

385

399

444

2.604

2.574

2.844

2.957

3.497

3.882

4.570

6.067

7.371

5.093

4.079

3.596

3.466

3.008

2.526

2.152

1.811

1.582

1.351

1.196

1.039

0.963

0.926

4.049

2.604

5.178

8.021

10.978

14.475

18.357

22.928

28.995

36.366

41.458

45.538

49.134

52.600

55.607

58.133

60.285

62.097

63.679

65.031

66.227

67.265

68.228

69.154

73.203

0.036

0.071

0.110

0.150

0.198

0.251

0.313

0.396

0.497

0.566

0.622

0.671

0.719

0.760

0.794

0.824

0.848

0.870

0.888

0.905

0.919

0.932

0.945

1.000

99.0

104.2

109.6

114.8

120.9

127.2

134.2

142.5

151.7

157.8

162.7

167.0

171.2

174.9

178.0

180.6

182.9

184.9

186.7

188.3

189.8

191.1

192.5

198.7

0.225

0.266

0.308

0.348

0.396

0.445

0.499

0.563

0.634

0.682

0.720

0.754

0.787

0.815

0.839

0.859

0.877

0.893

0.907

0.919

0.931

0.941

0.952

1.000

0.210

0.251

0.294

0.335

0.384

0.434

0.489

0.555

0.627

0.676

0.715

0.749

0.782

0.811

0.836

0.857

0.875

0.891

0.905

0.918

0.929

0.940

0.951

1.000

0.194

0.236

0.280

0.322

0.371

0.422

0.478

0.546

0.620

0.669

0.709

0.744

0.778

0.808

0.832

0.854

0.872

0.889

0.903

0.916

0.928

0.939

0.950

1.000

0.160

0.204

0.249

0.293

0.345

0.398

0.457

0.526

0.604

0.655

0.697

0.733

0.769

0.799

0.825

0.847

0.867

0.884

0.899

0.913

0.925

0.936

0.948

1.000

0.123

0.169

0.216

0.262

0.316

0.371

0.433

0.506

0.586

0.640

0.683

0.722

0.758

0.791

0.818

0.841

0.861

0.879

0.894

0.909

0.921

0.933

0.945

1.000

Total 0.3684 198.7 73.203

dictions. Whitson et al.27 proposed perhaps the most useful applica-tion of the gamma-distribution model. With Gaussian quadrature,their method allows multiple reservoir-fluid samples from a com-mon reservoir to be treated simultaneously with a single fluid char-acterization. Each fluid sample can have different C7 propertieswhen the split is made so that each split fraction has the same molec-ular weight (and other properties, such as , Tb , Tc, pc, and $), while

Fig. 5.11—Graphical fit of the Hoffman et al.29 oil molar distribu-tion by use of the cumulative-distribution type curve. Best-fitmodel parameters are &=2.5 and %=72.5.

1.0

0.0

0.8

0.6

0.4

0.2

0.0 0.2 0.4 0.6 0.8 1.0

Cumulative Normalized Mole Fraction, Qzi

70

75

80

65!

"

X

the mole fractions are different for each fluid sample. Example ap-plications include the characterization of a gas cap and underlyingreservoir oil and a reservoir with compositional gradient.

The following outlines the procedure for applying Gaussianquadrature to the gamma-distribution function.

1. Determine the number of C7 fractions, N, and obtain thequadrature values Xi and Wi from Table 5.6 (values are given forN 3 and N 5).

2. Specify % and &. When TBP data are not available to determinethese parameters, recommended values are % 90 and & 1.

3. Specify the heaviest molecular weight of fraction N (recom-mended value is MN 2.5MC7

). Calculate a modified '* term,'* &MN% %'"XN.

Fig. 5.12—Calculated normalized mole fraction vs. molecularweight of fractions for the Hoffman et al.29 oil based on the bestfit in Fig. 5.11 with &=2.5 and %=72.5.

10 PHASE BEHAVIOR

TABLE 5.6—GAUSSIAN QUADRATURE FUNCTION

VARIABLES, X, AND WEIGHT FACTORS, W

X W

Three Quadrature Points (plus fractions)

1

2

3

0.415 774 556 783

2.294 280 360 279

6.289 945 082 937

7.110 930 099 29$10%1

2.785 177 335 69$10%1

1.038 925 650 16$10%2

Five Quadrature Points (plus fractions)

1

2

3

4

5

0.263 560 319 718

1.413 403 059 107

3.596 425 771 041

7.085 810 005 859

12.640 800 844 276

5.217 556 105 83$10%1

3.986 668 110 83$10%1

7.594 244 968 17$10%2

3.611 758 679 92$10%3

2.336 997 238 58$10%5

Quadrature function values and weight factors can be found for other quadrature numbers

in mathematical handbooks.30

4. Calculate the parameter (.

( exp& &'*

MC7% %% 1' . (5.30). . . . . . . . . . . . . . . . . . .

5. Calculate the C7 mole fraction zi and Mi for each fraction.

zi zC7*Wi f (Xi)+,

Mi % '* Xi ,

and f(X) (X)&%1

"(&)

&1 ln ('&

(X. (5.31). . . . . . . . . . . . . . . . . .

6. Check whether the calculated MC7 from Eq. 5.12 equals themeasured value used in Step 4 to define (. Because Gaussian quad-rature is only approximate, the calculated MC7 may be slightly inerror. This can be corrected by (slightly) modifying the value of (,and repeating Steps 5 and 6 until a satisfactory match is achieved.

When characterizing multiple samples simultaneously, the valuesof MN , %, and '* must be the same for all samples. Individual samplevalues of MC7

and & can, however, be different. The result of thischaracterization is one set of molecular weights for the C7 frac-tions, while each sample has different mole fractions zi (so that theiraverage molecular weights MC7 are honored).

Specific gravities for the C7 fractions can be calculated withone of the correlations given in Sec. 5.4 (e.g., Eq. 5.44), where thecharacterization factor (e.g., Fc) must be the same for all mixtures.The specific gravities, C7

, of each sample will not be exactly re-produced with this procedure (calculated with Eq. 5.37), but the av-erage characterization factor can be chosen so that the differencesare very small (00.0005). Having defined Mi and i for the C7fractions, a complete fluid characterization can be determined withcorrelations in Sec. 5.5.

$

5.4.1 Generalized Properties. The molecular weight, specific grav-ity, and boiling point of C7 fractions must be estimated in the ab-sence of experimental TBP data. This situation arises when simulateddistillation is used or when no experimental analysis of C7 is avail-able and a synthetic split must be made by use of a molar-distributionmodel. For either situation, inspection data from TBP analysis of asample from the same field would be the most reliable source of M,, and Tb for each C7 fraction. The next-best source would be mea-sured TBP data from a field producing similar oil or condensate fromthe same geological formation. Generalized properties from a pro-ducing region, such as the North Sea, have been proposed.31

Katz and Firoozabadi6 suggest a generalized set of SCN proper-ties for petroleum fractions C6 through C45. Table 5.2 gives an ex-tended version of the Katz-Firoozabadi property table. Molecular

weights can be used to convert weight fractions, wi, from simulateddistillation to mole fractions,

zi wi"Mi

#Nj 7

wj "Mj

. (5.32). . . . . . . . . . . . . . . . . . . . . . . . . . . . .

However, the molecular weight of the heaviest fraction, CN, is notknown. From a mass balance, MN is given by

MN wN

&wC7"MC7'%#

N%1

i 7

&wi"Mi'

, (5.33). . . . . . . . . . . .

where Mi for i 7,…, N%1 are taken from Table 5.2. Unfortunately,the calculated molecular weight MN is often unrealistic because ofmeasurement errors in MC7 or in the chromatographic analysis andbecause generalized molecular weights are only approximate. BothwN and MC7 can be adjusted to give a “reasonable” MN, but cautionis required to avoid nonphysical adjustments. The same problem isinherent with backcalculating MN with any set of generalized molec-ular weights used for SCN Fractions 7 to N%1 (e.g., paraffin values).

During the remainder of this section, molecular weights and molefractions are assumed to be known for C7 fractions, either fromchromatographic analysis or from a synthetic split. The generalizedproperties for specific gravity and boiling point can be assigned toSCN fractions, but the heaviest specific gravity must be backcalcu-lated to match the measured C7 specific gravity. The calculated Nalso may be unrealistic, requiring some adjustment to generalizedspecific gravities. Finally, the boiling point of the heaviest fractionmust be estimated. TbN can be estimated from a correlation relatingboiling point to specific gravity and molecular weight.

5.4.2 Characterization Factors. Inspection properties M, , and Tb

reflect the chemical makeup of petroleum fractions. Some methodsfor estimating specific gravity and boiling point assume that a par-ticular characterization factor is constant for all C7 fractions.These methods are only approximate but are widely used.

Watson or Universal Oil Products (UOP) Characterization Fac-tor. The Watson or UOP factor, Kw, is based on normal boiling point,Tb , in °R and specific gravity, .32,33

Kw1T1"3

b

. (5.34). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Kw varies roughly from 8.5 to 13.5. For paraffinic compounds,Kw 12.5 to 13.5; for naphthenic compounds, Kw 11.0 to 12.5;and for aromatic compounds, Kw 8.5 to 11.0. Some overlap in Kw

exists among these three families of hydrocarbons, and a combina-tion of paraffins and aromatics will obviously “appear” naphthenic.However, the utility of this and other characterization factors is thatthey give a qualitative measure of the composition of a petroleumfraction. The Watson characterization factor has been found to beuseful for approximate characterization and is widely used as a pa-rameter for correlating petroleum-fraction properties, such as mo-lecular weight, viscosity, vapor pressure, and critical properties.

An approximate relation2 for the Watson factor, based on molecu-lar weight and specific gravity, is

Kw! 4.5579 M 0.15178 %0.84573. (5.35). . . . . . . . . . . . . . . . . .

This relation is derived from the Riazi-Daubert14 correlation formolecular weight and is generally valid for petroleum fractions withnormal boiling points ranging from 560 to 1,310°R (C7 throughC30). Experience has shown, however, that Eq. 5.35 is not very ac-curate for fractions heavier than C20.

Kw calculated with MC7 and C7 in Eq. 5.35 is often constant

for a given field. Figs. 5.13A and 5.13B7 plot molecular weight vs.

specific gravity for C7 fractions from two North Sea fields. Data

for the gas condensate in Fig. 5.13A indicate an average

KwC7 11.9900.01 for a range of molecular weights from 135 to

150. The volatile oil shown in Fig. 5.13B has an average

KwC7 11.9000.01 for a range of molecular weights from 220 to


Fig. 5.13A—Specific gravity vs. molecular weight for C7 frac-tions for a North Sea Gas-Condensate Field 2 (after Austad et al.7).

Molecular Weight, MC 7+

255. The high degree of correlation for these two fields suggests ac-

curate molecular-weight measurements by the laboratory. In gener-

al, the spread in KwC7 values will exceed 00.01 when measure-

ments are performed by a commercial laboratory.

When the characterization factor for a field can be determined,

Eq. 5.35 is useful for checking the consistency of C7 molecular-

weight and specific-gravity measurements. Significant deviation in

KwC7, such as 00.03 for the North Sea fields above, indicates pos-

sible error in the measured data. Because molecular weight is more

prone to error than determination of specific gravity, an anomalous

KwC7 usually indicates an erroneous molecular-weight measure-

ment. For the gas condensate in Fig. 5.13A, a C7 sample with spe-

cific gravity of 0.775 would be expected to have a molecular weight

of !141 (for KwC7 11.99). If the measured value was 135, the

Watson characterization factor would be 11.90, which is significant-

ly lower than the field average of 11.99. In this case, the C7 molec-

ular weight should be redetermined.

Eq. 5.35 can also be used to calculate specific gravity of C7 frac-

tions determined by simulated distillation or a synthetic split (i.e.,

when only mole fractions and molecular weights are known). As-

suming a constant Kw for each fraction, specific gravity, i, can be

calculated from

i 6.0108 M 0.17947

iK%1.18241

w . (5.36). . . . . . . . . . . . . . . . .

Kw must be chosen so that experimentally measured C7 specific

gravity, (C7)exp, is calculated correctly.

&C7'

exp

zC7MC7

#Ni 1

&zi Mi"i'. (5.37). . . . . . . . . . . . . . . . . . . . .

The Watson factor satisfying Eq. 5.37 is given by

Kw *0.16637C7A0

zC7MC7

+%0.84573

, (5.38). . . . . . . . . . . . . . .

where A0 #N

i 1

zi M0.82053

i. (5.39). . . . . . . . . . . . . . . . . . . . . .

Fig. 5.13B—Specific gravity vs. molecular weight for C7 frac-tions for a North Sea Volatile-Oil Field 3B(after Austad et al.7).

Molecular Weight, MC 7+

Fig. 5.14—Specific gravity vs. molecular weight for constant val-ues of the Jacoby aromaticity factor (solid lines) and the Watsoncharacterization factor (dashed lines). After Whitson.25

Ja

Kw

Jacoby Correlation(Aromaticity Factor, Ja)

Present Correlation(Watson Factor, Kw)

Boiling points, Tbi, can be estimated from Eq. 5.36.

Tbi (Kwi)3. (5.40). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Unfortunately, Eqs. 5.36 through 5.40 overpredict and Tb at mo-

lecular weights greater than !250 (an original limitation of the

Riazi-Daubert14 molecular-weight correlation).

Jacoby Aromaticity Factor. The Jacoby aromaticity factor, Ja , is

an alternative characterization factor for describing the relative

composition of petroleum fractions.34 Fig. 5.142 shows the original

Jacoby relation between specific gravity and molecular weight for

several values of Ja . The behavior of specific gravity as a function

of molecular weight is similar for the Jacoby factor and the relation

for a constant Kw. However, specific gravity calculated with the

Jacoby method increases more rapidly at low molecular weights,

flattening at high molecular weights (a more physically consistent

behavior). A relation for the Jacoby factor is

Ja % 0.8468 &15.8"M'

0.2456% &1.77"M'(5.41). . . . . . . . . . . . . . . . . .

12 PHASE BEHAVIOR

Fig. 5.15—Specific gravity vs. carbon number for constant val-ues of the Yarborough aromaticity factor (after Yarborough1).

or, in terms of specific gravity,

0.8468 % 15.8M Ja &0.2456 % 1.77

M'. (5.42). . . . . .

The first two terms in Eq. 5.42 (i.e., when Ja 0) express the relation

between specific gravity and molecular weight for normal paraffins.

The Jacoby factor can also be used to estimate fraction specific

gravities when mole fractions and molecular weights are available

from simulated distillation or a synthetic split. The Jacoby factor

satisfying measured C7 specific gravity (Eq. 5.37) must be calcu-

lated by trial and error. We have found that this relation is particular-

ly accurate for gas-condensate systems.27

Yarborough Aromaticity Factor. Yarborough1 modified the

Jacoby aromaticity factor specifically for estimating specific gravi-

ties when mole fractions and molecular weights are known. Yarbo-

rough tries to improve the original Jacoby relation by reflecting the

changing character of fractions up to C13 better and by representing

the larger naphthenic content of heavier fractions better. Fig. 5.15

shows how the Yarborough aromaticity factor, Ya , is related to spe-

cific gravity and carbon number. A simple relation representing Ya

is not available; however, Whitson26 has fit the seven aromaticity

curves originally presented by Yarborough using the equation

i exp*A0 A1 i%1 A2 i A3 ln(i)+ , (5.43). . . . . . . . . .

where i carbon number. Table 5.7 gives the constants for Eq. 5.43.

The aromaticity factor required to satisfy measured C7 specific

gravity (Eq. 5.37) is determined by trial and error. Linear interpola-

tion of specific gravity should be used to calculate specific gravity

for a Ya value falling between two values of Ya in Table 5.7.

Søreide35 Correlations. Søreide developed an accurate specific-

gravity correlation based on the analysis of 843 TBP fractions from

68 reservoir C7 samples.

i 0.2855 Cf (Mi % 66)0.13. (5.44). . . . . . . . . . . . . . .

Cf typically has a value between 0.27 and 0.31 and is determined for

a specific C7 sample by satisfying Eq. 5.37.

5.4.3 Boiling-Point Estimation. Boiling point can be estimated

from molecular weight and specific gravity with one of several cor-

relations. Søreide also developed a boiling-point correlation based

on 843 TBP fractions from 68 reservoir C7 samples,

Tb 1928.3% &1.695$ 105'M%0.03522 3.266

$ exp *% &4.922$ 10%3'M% 4.7685

&3.462$ 10%3'M+ , (5.45). . . . . . . . . . . . . . . . . . . . .

with Tb in °R.

Table 5.8 gives estimated specific gravities determined with the

methods just described for a C7 sample with the exponential split

given in Table 5.4 (& 1, % 90, MC7 200) and C7

0.832.

The following equations also relate molecular weight to boiling

point and specific gravity; any of these correlations can be solved

for boiling point in terms of M and . We recommend, however, the

Søreide correlation for estimating Tb from M and .

Kesler and Lee.12

M *% 12, 272.6 9, 486.4 (4.6523% 3.3287)Tb+

) &1% 0.77084% 0.020582'

$ *&1.3437% 720.79T%1b'$ 107+T%1

b,

)&1% 0.80882 0.022262'

$ *&1.8828% 181.98T–1b'$ 1012+T%3

b, . (5.46). . . . . . . .

Riazi and Daubert.14

M (4.5673$ 10%5)T 2.1962

b%1.0164. (5.47). . . . . . . . . . . .

American Petroleum Inst. (API).36

M &2.0438$ 102'T 0.118

b1.88 exp&0.00218Tb% 3.07' .

(5.48). . . . . . . . . . . . . . . . . . . .

Rao and Bardon.37

ln M (1.27 0.071Kw) ln& 1.8Tb

22.31 1.68Kw

' .(5.49). . . . . . . . . . . . . . . . . . . .

Riazi and Daubert.18

M 581.96T 0.97476

b6.51274 exp*&5.43076$ 10%3'Tb

% 9.53384 &1.11056$ 10%3'Tb+ . (5.50). . . . . . . . .

TABLE 5.7—COEFFICIENTS FOR YARBOROUGH AROMATICITY FACTOR CORRELATION1,26

Ya A0 A1 A2 A2

0.0 %7.43855$10%2 %1.72341 1.38058$10%3 %3.34169$10%2

0.1 %4.25800$10%1 %7.00017$10%1 %3.30947$10%5 8.65465$10%2

0.2 %4.47553$10%1 %7.65111$10%1 1.77982$10%4 1.07746$10%1

0.3 %4.39105$10%1 %9.44068$10%1 4.93708$10%4 1.19267$10%1

0.4 %2.73719$10%1 %1.39960 3.80564$10%3 5.92005$10%2

0.6 %7.39412$10%3 %1.97063 5.87273$10%3 %1.67141$10%2

0.8 %3.17618$10%1 %7.78432$10%1 2.58616$10%3 1.08382$10%3


TABLE 5.8—COMPARISON OF SPECIFIC GRAVITIES WITH CORRELATIONS BY USE OF

DIFFERENT CHARACTERIZATION FACTORS

C7 0.832

i for Different Correlations With Constant Characterization

Factor Chosen To Match

Fraction zi Mi Kw 12.080 Ja 0.2395 Ya 0.2794 Cf 0.2864

1 0.1195 96.8 0.7177 0.7472 0.7051 0.7327

2 0.1052 110.8 0.7353 0.7684 0.7286 0.7550

3 0.0926 124.8 0.7511 0.7849 0.7486 0.7719

4 0.0816 138.8 0.7656 0.7981 0.7660 0.7856

5 0.0718 152.8 0.7789 0.8088 0.7813 0.7972

6 0.0632 166.8 0.7913 0.8178 0.7951 0.8072

7 0.0557 180.8 0.8028 0.8253 0.8075 0.8161

8 0.0490 194.8 0.8136 0.8318 0.8189 0.8241

9 0.0432 208.8 0.8238 0.8374 0.8294 0.8314

10 0.0380 222.8 0.8335 0.8423 0.8391 0.8380

11 0.0335 236.8 0.8426 0.8466 0.8482 0.8442

12 0.0295 250.8 0.8514 0.8505 0.8567 0.8500

13 0.0259 264.8 0.8597 0.8539 0.8646 0.8554

14 0.0228 278.8 0.8677 0.8570 0.8722 0.8604

15 0.0201 292.8 0.8753 0.8598 0.8793 0.8652

16 0.0177 306.8 0.8827 0.8623 0.8861 0.8697

17 0.0156 320.8 0.8898 0.8646 0.8926 0.8740

18 0.0137 334.8 0.8966 0.8668 0.8988 0.8782

19 0.0121 348.8 0.9033 0.8687 0.9048 0.8821

20 0.0891 466.0 0.9514 0.8805 0.9468 0.9096

Total 1.0000 200.0 0.8320 0.8320 0.8320 0.8320

Thus far, we have discussed how to split the C7 fraction into

pseudocomponents described by mole fraction, molecular weight,

specific gravity, and boiling point. Now we must consider the prob-

lem of assigning critical properties to each pseudocomponent. Criti-

cal temperature, Tc; critical pressure, pc; and acentric factor, $, of

each component in a mixture are required by most cubic EOS’s.

Critical volume, vc, is used instead of critical pressure in the Bene-

dict-Webb-Rubin38 (BWR) EOS, and critical molar volume is

used with the LBC viscosity correlation.24 Critical compressibility

factor has been introduced as a parameter in three- and four-constant

cubic EOS’s.

Critical-property estimation of petroleum fractions has a long his-

tory beginning as early as the 1930’s; several reviews22,25,26,39,40

are available. We present the most commonly used correlations and

a graphical comparison (Figs. 5.16 through 5.18) that is intended

to highlight differences between the correlations. Finally, correla-

tions based on perturbation expansion (a concept borrowed from

statistical mechanics) are discussed separately.

The units for the remaining equations in this section are Tb in °R,

TbF in °F Tb%459.67, Tc in °R, pc in psia, and vc in ft3/lbm mol.

Oil gravity is denoted API and is related to specific gravity by

API 141.5/%131.5.

5.5.1 Critical Temperature. Tc is perhaps the most reliably corre-

lated critical property for petroleum fractions. The following criti-

cal-temperature correlations can be used for petroleum fractions.

Roess.41 (modified by API36).

Tc 645.83 1.6667*&TbF 100'+

% &0.7127$ 10%3'*&TbF 100'+2

. (5.51). . . . . . . . . . .

Kesler-Lee.12

Tc 341.7 811 (0.4244 0.1174)Tb

(0.4669% 3.2623) $ 105T%1b . (5.52). . . . . . . . . . . .

Cavett.42

Tc 768.07121 1.7133693TbF

% &0.10834003$ 10%2'T 2

bF

% &0.89212579$ 10%2'APITbF

&0.38890584$ 10%6'T 3

bF

&0.5309492$ 10%5'APIT2

bF

&0.327116$ 10%7'2APIT

2

bF. (5.53). . . . . . . . . . . . . . .

Riazi-Daubert.14

Tc 24.27871T 0.58848

b 0.3596. (5.54). . . . . . . . . . . . . . . . . .

Nokay.43

Tc 19.078T 0.62164

b 0.2985 . (5.55). . . . . . . . . . . . . . . . . . . .

5.5.2 Critical Pressure. pc correlations are less reliable than Tc cor-relations. The following are pc correlations that can be used for pe-troleum fractions.

Kesler-Lee.12

ln pc 8.3634% 0.0566

% *&0.24244 2.2898 0.11857

2'$ 10%3+Tb

14 PHASE BEHAVIOR

Fig. 5.16—Comparison of critical-temperature correlations forboiling points from 600 to 1,500°R assuming a constant Watsoncharacterization factor of 12.

*&1.4685 3.648 0.47227

2'$ 10%7+T2

b

% *&0.42019 1.69772'$ 10%10+T3

b . (5.56). . . . .

Cavett.42

log pc 2.8290406 &0.94120109$ 10%3'TbF

% &0.30474749$ 10%5'T 2

bF

% &0.2087611$ 10%4'APITbF

&0.15184103$ 10%8'T 3

bF

&0.11047899$ 10%7'APIT2

bF

% &0.48271599$ 10%7'2APITbF

&0.13949619$ 10%9'2APIT

2

bF. (5.57). . . . . . . . . . .

Riazi-Daubert.14

pc &3.12281$ 109'T%2.3125b 2.3201 . (5.58). . . . . . . . . . . . .

5.5.3 Acentric Factor. Pitzer et al.44 defined acentric factor as

$1% log &p*v

pc' % 1, (5.59). . . . . . . . . . . . . . . . . . . . . . . .

where p*v vapor pressure at temperature T 0.7Tc (Tr 0.7).

Practically, acentric factor gives a measure of the steepness of the

vapor-pressure curve from Tr 0.7 to Tr 1, where p*v/pc 0.1 for

$ 0 and p*v/pc 0.01 for $ 1. Numerically, $!0.01 for meth-

ane, !0.25 for C5, and!0.5 for C8 (see Table A.1 for literature val-

ues of acentric factor for pure compounds). $ increases to 1.0 for

petroleum fractions heavier than approximately C25 (see Table 5.2).

The Kesler-Lee12 acentric factor correlation (for Tb/Tc0.8) is

developed specifically for petroleum fractions, whereas the correla-

tion for Tb/Tc0.8 is based on an accurate vapor-pressure correla-

tion for pure compounds. The Edmister45 correlation is limited to

pure hydrocarbons and should not be used for C7 fractions. The

three correlations follow.

Fig. 5.17—Comparison of critical-pressure correlations for boil-ing points from 600 to 1,500°R assuming a constant Watsoncharacterization factor of 12.

Fig. 5.18—Comparison of acentric factor correlations for boilingpoints from 600 to 1500°R assuming a constant Watson charac-terization factor of 12.

Lee-Kesler.13 (Tbr Tb/Tc0.8).

$ – ln&pc"14.7' A1 A2 T%1

br A3 ln Tbr A4 T 6

br

A5 A6 T%1br A7 ln Tbr A8 T 6

br

,

(5.60). . . . . . . . . . . . . . . . . . . .

where A1 %5.92714, A2 6.09648, A3 1.28862, A4 %0.169347, A5 15.2518, A6 %15.6875, A7 %13.4721,and A8 0.43577.

Kesler-Lee.12 (Tbr Tb/Tc0.8).

$ % 7.904 0.1352Kw% 0.007465K2w

8.359Tbr (1.408% 0.01063Kw)T%1br . (5.61). . . . . . .

Edmister.45

$ 37

log&pc"14.7'*&Tc"Tb

' % 1+% 1. (5.62). . . . . . . . . . . . . . . . . . . . .


5.5.4 Critical Volume. The Hall-Yarborough46 critical-volume

correlation is given in terms of molecular weight and specific grav-

ity, whereas the Riazi-Daubert14 correlation uses normal boiling

point and specific gravity.

Hall-Yarborough.46

vc 0.025M 1.15%0.7935. (5.63). . . . . . . . . . . . . . . . . . . . . .

Riazi-Daubert.14

vc &7.0434$ 10%7'T 2.3829

b%1.683. (5.64). . . . . . . . . . . . .

Critical compressibility factor, Zc, is defined as

Zc pcvc

RTc, (5.65). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

where R universal gas constant. Thus, Zc can be calculated directly

from critical pressure, critical volume, and critical temperature. Reid

et al.40 and Pitzer et al.44 give an approximate relation for Zc.

Zc! 0.291% 0.08$. (5.66). . . . . . . . . . . . . . . . . . . . . . . . .

Eq. 5.66 is not particularly accurate (grossly overestimating Zc for

heavier compounds) and is used only for approximate calculations.

5.5.5 Correlations Based on Perturbation Expansions. Correla-

tions for critical temperature, critical pressure, critical volume, and

molecular weight have been developed for petroleum fractions with

a perturbation-expansion model with normal paraffins as the refer-

ence system. To calculate critical pressure, for example, critical

temperature, critical volume, and specific gravity of a paraffin with

the same boiling point as the petroleum fraction must be calculated

first. Kesler et al.47 first used the perturbation expansion (with n-al-

kanes as the reference fluid) to develop a suite of critical-property

and acentric-factor correlations.

Twu48 uses the same approach to develop a suite of critical-prop-

erty correlations. We give his normal-paraffin correlations first,

then the correlations for petroleum fractions.

Normal Paraffins (Alkanes).

TcP Tb*0.533272 &0.191017$ 10%3'Tb

&0.779681$ 10%7'T 2

b% &0.284376$ 10%10'T 3

b

(0.959468$ 102)

&0.01Tb'13+%1

, (5.67). . . . . . . . . . . . . . . . . .

pcP (3.83354 1.19629&0.5 34.8888&

36.1952&2 104.193&4)2, (5.68). . . . . . . . . . . . . . .

vcP [ 1% (0.419869% 0.505839&% 1.56436&3

% 9481.7&14)]%8

, (5.69). . . . . . . . . . . . . . . . . . . . . . . . .

P 0.843593% 0.128624&% 3.36159&3

% 13749.5&12 , (5.70). . . . . . . . . . . . . . . . . . . . . . . . . . . .

and Tb exp(5.71419 2.71579)% 0.28659)2

% 39.8544)%1% 0.122488)%2)

% 24.7522) 35.3155)2 , (5.71). . . . . . . . . . . . . . . . .

where & 1%Tb

TcP

(5.72). . . . . . . . . . . . . . . . . . . . . . . . . . . .

and ) ln MP . (5.73). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Paraffin molecular weight, MP, is not explicitly a function of Tb , andEqs. 5.67 through 5.73 must be solved iteratively; an initial guessis given by

MP!Tb

10.44% 0.0052Tb

. (5.74). . . . . . . . . . . . . . . . . . . . .

Twu claims that the normal-paraffin correlations are valid for C1

through C100, although the properties at higher carbon numbers areonly approximate because experimental data for paraffins heavierthan approximately C20 do not exist. The following relations areused to calculate petroleum-fraction properties.

Critical Temperature.

Tc TcP&1 2fT

1% 2fT

'2,

fT T*% 0.362456

T 0.5

b

&0.0398285% 0.948125

T 0.5

b

'T+,and T exp[5(P% )]% 1. (5.75). . . . . . . . . . . . . . . . . .

Critical Volume.

vc vcP&1 2fv

1% 2fv

'2,

fv v*0.466590

T 0 .5

b

&% 0.182421 3.01721

T 0.5

b

'v+,and v exp*4&2

P% 2'+% 1. (5.76). . . . . . . . . . . . . . . . . .

Critical Pressure.

pc pcP& Tc

TcP

'&VcP

Vc

'&1 2fp

1% 2fp

'2,

fp p*&2.53262% 46.1955

T 0.5

b

% 0.00127885Tb'

&% 11.4277 252.14

T 0.5

b

0.00230535Tb'p+,and p exp[0.5(P% )]% 1. (5.77). . . . . . . . . . . . . . . . .

Molecular Weight.

ln M ln MP&1 2fM

1% 2fM

'2,

fM M*|x|&% 0.0175691 0.193168

T 0.5

b

'M+,x 0.012342% 0.328086

T 0.5

b

,

and M exp[5(P% )]. (5.78). . . . . . . . . . . . . . . . . . . . .

Figs. 5.16 through 5.18 compare the various critical-property cor-relations for a range of boiling points from 600 to 1,500°R.

5.5.6 Methods Based on an EOS. Fig. 5.1928 illustrates the impor-tant influence that critical properties have on EOS-calculated proper-ties of pure components. Vapor pressure is particularly sensitive tocritical temperature. For example, the Riazi-Daubert19 critical-tem-perature correlation for toluene overpredicts the experimental value

16 PHASE BEHAVIOR

Fig. 5.19—Effect of critical temperature on vapor-pressure pre-diction of toluene with the PR EOS; AAD absolute average devi-ation (after Brulé et al.28).

Tc underpredicted← →Tc overpredicted

Deviation From Experimental Value, %

by only 1.7%. Even with this slight error in Tc, the average error invapor pressures predicted by the Peng-Robinson49 (PR) EOS is 16%.The effect of critical properties and acentric factor on EOS calcula-tions for reservoir-fluid mixtures is summarized by Whitson.26

In principle, the EOS used for mixtures should also predict the be-havior of individual components found in the mixture. For purecompounds, the vapor pressure is accurately predicted because allEOS’s force fit vapor-pressure data. Some EOS’s are also fit to satu-rated-liquid densities at subcritical temperatures. The measuredproperties of petroleum fractions, boiling point, and specific gravitycan also be fit by the EOS, as discussed later.

For each petroleum fraction separately, two of the EOS parame-ters (Tc; pc; $; volume-shift factor, s; or multipliers of EOS constantsA and B) can be chosen so that the EOS exactly reproduces exper-imental boiling point and specific gravity. Because only two inspec-tion properties are available (Tb and ), only two of the EOS parame-ters can be determined. Whitson50 suggests fixing the value of $with an empirical correlation and adjusting Tc and pc to match nor-mal boiling point and molar volume (M/) at standard conditions.Critical properties satisfying these criteria are given for a wide rangeof petroleum fractions by the PR EOS and the Soave-Redlich-Kwong (SRK) EOS.22,23 A better (and recommended) approach forcubic EOS’s is to use the volume-shift factor s (see Chap. 4) to matchspecific gravity or a saturated liquid density and acentric factor tomatch normal boiling point.

Other methods for forcing the EOS to match boiling point andspecific gravity have also been devised. Brulé and Starling51 pro-posed a method that uses viscosity as an additional inspection prop-erty of the fraction for determining critical properties. This ap-proach proved particularly successful when applied to the BWREOS for residual-oil supercritical extraction (ROSE).28

% & '

We recommend the following C7 characterization procedure forcubic EOS’s.

1. Use the Twu48 (or Lee-Kesler12) critical property correlationfor Tc and pc .

2. Choose the acentric factor to match Tb; alternatively, use theLee-Kesler12/Kesler-Lee13 correlations.

3. Determine volume-translation coefficients, si, to match specificgravities; alternatively, use Peneloux et al.’s52 correlation for the SRKEOS22,23 or Jhaveri and Youngren’s53 correlation for the PR EOS.49

When measured TBP data are not available, a mathematical splitshould be made with either (1) the gamma distribution (default

& 1, % 90) with Gaussian-quadrature or equal-mass fractions or(2) the exponential distribution (Eq. 5.7). Specific gravities shouldbe estimated with the Søreide35 correlation (Eq. 5.44), choosing Cf

to match measured C7 specific gravity (Eq. 5.37). Boiling pointsshould be estimated from the Søreide correlation (Eq. 5.45).

For the PR EOS, we recommend the nonhydrocarbon BIP’s givenin Chap. 4 and the modified Chueh-Prausnitz54 equation for C1

through C7 pairs,

kij A234

1%& 2v1"6ci

v1"6cj

v1"3ci v1"3

cj

'B256, (5.79). . . . . . . . . . . . . . . .

with A 0.18 and B 6.

5.6.1 SRK-Recommended Characterization. Alternatively, thePedersen et al.55 characterization procedure can be used with theSRK EOS.

1. Split the plus fraction Cn (preferably n10) into SCN frac-tions up to C80 using Eqs. 5.7 through 5.11 and h %4.

2. Calculate SCN densities i (i i /0.999) using the equation i A0A1 ln(i), where A0 and A1 are determined by satisfying theexperimental-plus density, n, and measured (or assumed) densi-ty, n%1 ( 6 0.690 can be used for C7).

3. Calculate critical properties of all C7 fractions (distillationcuts from C7 to Cn%1 and split SCN fractions from Cn through C80)using the correlations

Tc 163.12 86.052 ln M 0.43475M% 1877.4M

,

ln pc % 0.13408 2.5019 208.46M

% 3987.2M2

,

and mSRK 0.48 1.574$% 0.176$2

0.7431 0.0048122M 0.0096707

% &3.7184$ 10%6'M2. (5.80). . . . . . . . . . . . . . . . . .

Note that the use of acentric factor is circumvented by directly calcu-lating the term m used in the & correction term to EOS Constant A.

4. Group C7 into 3 to 12 fractions using equal-weight fractionsin each group; use weight-average mixing rules.

5. Calculate volume-translation parameters for C7 fractions tomatch specific gravities; pure component c values are taken fromPeneloux et al.52

6. All hydrocarbon/hydrocarbon BIP’s are set to zero. SRK BIP’sgiven in Chap. 4 are used for nonhydrocarbon/hydrocarbon pairs.

The two recommended C7 characterization procedures out-lined previously for the PR EOS and SRK EOS are probably the bestcurrently available (other EOS characterizations, such as the Re-dlich-Kwong EOS modified by Zudkevitch and Joffe,56 and somethree-constant characterizations should provide similar accuracybut are not significantly better). Practically, the two characterizationprocedures give the same results for almost all PVT properties (usu-ally within 1 to 2%). With these EOS-characterization procedures,we can expect reasonable predictions of densities and Z factors (01to 5%), saturation pressures (05 to 15%), gas/oil ratios and forma-tion volume factors (02 to 5%), and condensate-liquid dropout(05 to 10% for maximum dropout, with poorer prediction of tail-like behavior just below the dewpoint).

The recommended EOS methods are less reliable for predictionof minimum miscibility conditions, near-critical saturation pressureand saturation type (bubblepoint or dewpoint), and both retrogradeand near-critical liquid volumes. Improved predictions can be ob-tained only by tuning EOS parameters to accurate PVT data cover-ing a relatively wide range of pressures, temperatures, and composi-tions (see Sec. 4.7 and Appendix C).

' () *))

The cost and computer resources required for compositional reser-voir simulation increase substantially with the number of compo-


nents used to describe the reservoir fluid. A compromise between

accuracy and the number of components must be made accordingto the process being simulated (i.e., according to the expected effect

that phase behavior will have on simulated results). For example, a

detailed fluid description with 12 to 15 components may be neededto simulate developed miscibility in a slim-tube experiment. With

current computer technology, however, a full-field simulation withfluids exhibiting near-critical phase behavior is not feasible for a

15-component mixture. The following are the main questions re-garding component grouping.

1. How many components should be used?2. How should the components be chosen from the original fluid

description?3. How should the properties of pseudocomponents be calculated?

5.7.1 How Many and Which Components To Group. The numberof components used to describe a reservoir fluid depends mainly on

the process being simulated. However, the following rule of thumbreduces the number of components for most systems: group N2 with

methane, CO2 with ethane, iso-butane with n-butane, and iso-pen-tane with n-pentane. Nonhydrocarbon content should be less than

a few percent in both the reservoir fluid and the injection gas if anonhydrocarbon is to be grouped with a hydrocarbon.

Five- to eight-component fluid characterizations should be suffi-cient to simulate practically any reservoir process, including (1) reser-

voir depletion of volatile-oil and gas-condensate reservoirs, (2) gascycling above and below the dewpoint of a gas-condensate reservoir,

(3) retrograde condensation near the wellbore of a producing well,and (4) immiscible and miscible gas-injection. Coats57 discusses a

method for combining a modified black-oil formula with a simplifiedEOS representation of separator oil and gas streams. The “oil” and

“gas” pseudocomponents in this model contain all the original fluidcomponents in contrast to the typical method of grouping where each

pseudocomponent is made up of only selected original components.Lee et al.58 suggest that C7 fractions can be grouped into two

pseudocomponents according to a characterization factor deter-mined by averaging the tangents of fraction properties M, , and Ja

plotted vs. boiling point.

Whitson2 suggests that the C7 fraction can be grouped into NH

pseudocomponents given by

NH 1 3.3 log(N% 7), (5.81). . . . . . . . . . . . . . . . . . . . .

where N carbon number of the heaviest fraction in the original

fluid description. The groups are separated by molecular weights MI

given by

MI MC7&MN"MC

7'1"NH

, (5.82). . . . . . . . . . . . . . . . . . .

where I 1,..., NH . Molecular weights, Mi, from the original fluiddescription (i 7,..., N) falling within boundaries MI%1 to MI are in-

cluded in Group I. This method should only be used when C7 frac-tions are originally separated on a carbon-number basis and for N

greater than !20.Li et al.59 suggest a method for grouping components of an origi-

nal fluid description that uses K values from a flash at reservoir tem-perature and the “average” operating pressure. The original mixture

is divided arbitrarily into “light” components (H2S, N2, CO2, and C1

through C6) and “heavy” components (C7). Different criteria are

used to determine the number of light and heavy pseudocompon-ents. Li et al. also suggest use of phase diagrams and compositional

simulation to verify the grouped fluid description (a practice that wehighly recommend).

Still other pseudoization methods have been proposed60,61; Schlij-

per’s61 method also treats the problem of retrieving detailed composi-tional information from pseudoized (grouped) components. Behrens

and Sandler62 suggest a grouping method for C7 fractions basedon application of the Gaussian-quadrature method to continuous

thermodynamics. Although a simple exponential distribution isused with only two quadrature points (i.e., the C7 fractions are

grouped into two pseudocomponents), Whitson et al.27 show that

the method is general and can be applied to any molar-distributionmodel and for any number of C7 groups.

In general, most authors have found that broader grouping of C7as C7 through C10, C11 through C15, C16 through C20, and C21 issubstantially better than splitting only the first few carbon-numberfractions (e.g., C7, C8, C9, and C10). Gaussian quadrature is recom-mended for choosing the pseudocomponents in a C7 fraction;equal-mass fractions or the Li et al.59 approach are valid alternatives.

5.7.2 Mixing Rules. Several methods have been proposed for calcu-lating critical properties of pseudocomponents. The simplest andmost common mixing rule is

)I

#i7I

zi)i

#i7I

zi

, (5.83). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

where )i any property (Tc, pc, $, or M) and zi original mole frac-tion for components (i 1,..., I) making up Pseudocomponent I. Av-erage specific gravity should always be calculated with the assump-tion of ideal solution mixing.

I

#i7I

zi Mi

#i7I

&zi Mi"i' . (5.84). . . . . . . . . . . . . . . . . . . . . . . . . . .

Pedersen et al.55 and others suggest use of weight fraction insteadof mole fraction. Wu and Batycky’s63 empirical mixing-rule ap-proach uses both the molar- and weight-average mixing rules anda proportioning factor, F, to calculate pcI, TcI, and $I.

)I #i7I

*i)i , (5.85). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

where )I represents pcI, TcI, and $I and *i average of the molar andweight fractions,

*i F)izi (1% F))i wi

and wi zi Mi

#Nj 1

zj Mj

, (5.86). . . . . . . . . . . . . . . . . . . . . . . . . . . . .

with 0.F.1.A generalized mixing rule for BIP’s can be written

kIJ #i7I

#j7J

*i*j kij , (5.87). . . . . . . . . . . . . . . . . . . . . . . . .

where *i is also given by Eq. 5.86.On the basis of Chueh and Prausnitz’s54 arguments, Lee-Kesler13

proposed the mixing rules in Eqs. 5.88 through 5.92.

vcI *18#i7I

#j7J

zi zj&v1"3

ci v1"3

cj'3+"&#

i7I

zi'2

, (5.88). . .

TcI * 18vcI

#i7I

#j7J

zi zj&Tci Tcj

'1"2&v1"3ci v1"3

cj'3+

/&#i7I

zi'2

, (5.89). . . . . . . . . . . . . . . . . . . . . . . . . . . .

$I &#i7I

zi$i'"&#i7I

zi', (5.90). . . . . . . . . . . . . . . . . . .

ZcI 0.2905% 0.085$I , (5.91). . . . . . . . . . . . . . . . . . . . . .

and pcI ZcI RTcI

vcI. (5.92). . . . . . . . . . . . . . . . . . . . . . . . . . . . .

18 PHASE BEHAVIOR

TABLE 5.9—EXAMPLE STEPWISE-REGRESSION PROCEDURE FOR PSEUDOIZATION

TO FEWER COMPONENTS FOR A GAS CONDENSATE FLUID UNDERGOING DEPLETION

Original

Component

Number

Original

ComponentStep 1 Step 2 Step 3 Step 4 Step 5

1 N2 N2C1* N2C1 N2C1 N2C1CO2C2* N2C1CO2C2

2 CO2 CO2C2* CO2C2 CO2C2 C3i-C4n-C4

i-C5n-C5C6*

C3i-C4n-C4

i-C5n-C5C6

3 C1 C3 C3 C3i-C4n-C4* F1 F1

4 C2 i-C4 i-C4n-C4* i-C5n-C5C6* F2 F2F3*

5 C3 n-C4 i-C5n-C5* F1 F3

6 i-C4 i-C5 C6 F2

7 n-C4 n-C5 F1 F3

8 i-C5 C6 F2

9 n-C5 F1 F3

10 C6 F2

11 F1 F3

12 F2

13 F3

Regression Parameters

kij 1, 9, 10, and 11 1, 7, 8, and 9 1, 5, 6, and 7 1, 3, 4, and 5 1, 3, and 4

%a 1 4 3 1 3

%b 1 4 3 1 3

%a 2 5 4 2 4

%b 2 5 4 2 4

*Indicates the grouped pseudocomponents being regressed in a particular step.

Lee et al.58 and Whitson2 consider an alternative method for cal-culating C7 critical properties based on the specific gravities andboiling points of grouped pseudocomponents.

Coats57 presents a method of pseudoization that basically elimi-nates the effect of mixing rules on pseudocomponent properties.The approach is simple and accurate. Coats requires the pseudoizedcharacterization to reproduce exactly the volumetric behavior of theoriginal reservoir fluid at undersaturated conditions. This isachieved by ensuring that the mixture EOS constants A and B areidentical for the original and the pseudoized characterizations. First,pseudocritical properties ( pcI, TcI, and $I) are estimated with anymixing rule (e.g., Kay’s64 mixing rule). Then %aI and %bI are deter-mined to satisfy the following equations.

%aI

*#i7I

#j7J

zi zj aiaj&1% kij

'+"&#i7I

zi'2

&R2T 2

cI"pcI'&I(TrI,$I)

and %bI

&#i7I

zi bi'"&#i7I

zi'&RTcI"pcI

''I(TrI,$I), (5.93). . . . . . . . . . . . . . . .

where ai %ai

R2T2ci

pci&i (Tri,$i)

and bi %bi

RTci

pci'i(Tri,$i) . (5.94). . . . . . . . . . . . . . . . . . . . .

%ai and %bi may include previously determined corrections to thenumerical constants %o

a and %ob. This approach to determining

pseudocomponent properties, together with Eq. 5.87 for kI J, is sur-prisingly accurate even for VLE calculations. Coats also gives an

analogous procedure for determining pseudocomponent vcI for theLBC24 viscosity correlation.

Coats’ approach is preferred to all the other proposed methods. Itensures accurate volumetric calculations that are consistent with theoriginal EOS characterization, and the method is easy to implement.

5.7.3 Stepwise Regression. A reduced-component characterizationshould strive to reproduce the original complete characterizationthat has been used to match measured PVT data. One approach toachieve this goal is stepwise regression, summarized in the follow-ing procedure.

1. Complete a comprehensive match of all existing PVT data witha characterization containing light and intermediate pure compo-nents and at least three to five C7 fractions.

2. Simulate a suite of depletion and multicontact gas-injectionPVT experiments that cover the expected range of compositions inthe particular application.

3. Use the simulated PVT data as “real” data for pseudoizationbased on regression.

4. Create two new pseudocomponents from the existing set ofcomponents. Use the pseudoization procedure of Coats to obtain%aI and %bI values, and use Eq. 5.87 for kI J.

5. Use regression to fine tune the %aI and %bI values estimatedin Step 4; also regress on key BIP’s, such as (N2C1)%C7,(CO2C2)%C7, and other nonzero BIP’s involving pseudocom-ponents from Step 4.

6. Repeat Steps 4 and 5 until the quality of the characterizationdeteriorates beyond an acceptable fluid description. Table 5.9shows an example five-step pseudoization procedure.

In summary, any grouping of a complete EOS characterizationinto a limited number of pseudocomponents should be checked toensure that predicted phase behavior (e.g., multicontact gas injec-tion data, saturation pressures, and densities) are reasonably closeto the predictions for the original (complete) characterization. Step-wise regression is the best approach to determine the number and


properties of pseudocomponents that can accurately describe a res-ervoir fluid’s phase behavior. If stepwise regression is not possible,standard grouping of the light and intermediates (N2C1,CO2C2, i-C4n-C4, and i-C5n-C5) and Gaussian quadraturefor C7 (or equal-mass fractions) is recommended; a valid alterna-tive is the Li et al.59 method. The Coats57 method (Eqs. 5.93and 5.94) is always recommended for calculating pseudocompon-ent properties.

!

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20 PHASE BEHAVIOR

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30, 459.

" # $ %

ft3/lbm mol 6.242 796 E!02"m3/kmol F ( F!32)/1.8 " C F ( F459.67)/1.8 "Kpsi 6.894 757 E00"kPa R 5/9 "K

This paper was prepared for presentation at the 2007 SPE International Student Paper Con-test at the SPE Annual Technical Conference and Exhibition being held in Anaheim, California, 11-14 November, 2007. This paper was selected for presentation by merit of placement in a regional student paper contest held in the program year preceding the International Student Paper Contest. Contents of the paper, as presented, have not been reviewed by the Society of Petroleum Engineers and are subject to correction by the author(s). The material, as presented, does not necessar-ily reflect any position of the Society of Petroleum Engineers, its officers, or members.

Abstract A compositional simulator uses an Equation of State (EOS) to predict the pressure-volume-temperature (PVT) behavior of gas and crude oil fluids, which are very complex hydrocarbon mixtures.

In a hydrocarbon mixture, the critical properties (critical pressure “Pc”, critical temperature “Tc” and accentric factor “ω”) must be given for each component. These properties are well known for pure compounds (like methane, ethane, etc.), but nearly all naturally occurring gas and crude oil fluids con-tain some heavy fractions that are not well defined. These heavy fractions are lumped and called the “plus-fraction” (C7+). There arises the need of adequately characterizing these undefined plus fractions in terms of their critical properties.

This work presents a correlation for the critical properties of the plus-fraction C7+ needed in the characterization of crude oil fluid samples for a compositional simulator using Peng-Robinson’s1 EOS. The correlation is a function of the frac-tion’s molecular weight (MW).

Twenty (20) PVT laboratory tests made in black oil fluid samples taken from fields of the Neuquén Basin (Argentina) were utilized for the adjustment of the bubble point (Pb), gas – oil ratio (GOR), constant composition expansion pressure-volume relation (PV) and differential expansion curves (Rs, Bo and ρo) of the compositional simulator.

A comparative study was performed against the Riazi-Daubert’s2 correlation. The correlation here presented gives better results than those of Riazi-Daubert’s correlation and also gives excellent liquid density predictions when there are high MW hydrocarbons present in the fluid. Introduction One of the biggest existing problems when using a composi-tional simulator is the lack of good critical properties estima-tion for the heavy fraction of the fluid.3 Furthermore, for the characterization of the fraction few data are available, usually MW, SG and normal boiling point (Tb). For this correlation MW and SG were utilized, as both are habitually given or can be obtained from the molar composition of the fluid.

There are various methods for the characterization of heavy fractions: Riazi-Daubert, Kessler-Lee4, Twu5 and Sta-mataki-Magoulas6. This study only compares to Riazi and Daubert, since it is the one mostly used in the industry; Stama-taki-Magoulas is presented as a better alternative to Twu and Kessler-Lee, but its performance was deficient, consequently these last three studies are discarded from the comparison.

The trigger of this work was that estimations generated from the Riazi-Daubert’s correlation were not close enough to the PVT laboratory tests, and fraction parameter’s adjustment was very time consuming in the simulator. A correlation was created that could solve this problem, giving closer results to laboratory curves and as a consequence, less time spent in the critical parameter’s adjustment. Equation of State Today Peng-Robinson EOS (PR-EOS, 1976) is one of the most widely used EOS in the chemical and petroleum indus-try. It is superior when considering liquid density predictions to the Soave-Redlich-Kwong EOS (SRK-EOS, 1972), al-though all cubic EOS experience difficulties in the liquid den-sity calculations, which brings to the application of certain modifications to these equations. We have used two modifica-tions presented below. The EOS is presented here:

2 22m m m

RT aPV b V bV b

α= −

− + − (1)

2 2

0.457235528921 c

c

R Ta

P= (2)

0.077796073904 c

c

RTb

P= (3)

( ) 21 1 rTα κ⎡ ⎤= + −⎣ ⎦ (4)

20.37464 1.54226 0.26992κ ω ω= + − (5)

For the application of EOS in mixtures (this is the case of

petroleum fluids), certain mixture rules must be utilized. In this study the quadratic mixture rule is used, since it is the simplest:

SPE-113026-STU (Student 6)

Heavy Fraction C7+ Characterization for PR-EOS Gastón Fondevila Sancet, Buenos Aires Institute of Technology

2 SPE Student Paper

( )1ij i j ija a a k= − (6)

2i j

ij

b bb

+= (7)

Binary interaction parameters kij of the Eq. 6 were ob-

tained from Nishiumi’s7 correlation. EOS Modifications In our case the compositional simulator utilizes two modifica-tions: Twu-Coon-Cunningham8 and Twu-Tilton-Bluck9. Twu-Coon-Cunningham. This modification considers a new relation of the attraction term: the α parameter, temperature and accentric factor dependent. They propose the next equa-tions:

( ) ( ) ( )( )0 1 0α α ω α α= + − (8)

( ) ( )0 0.171813 1.77634exp 0.125283 1r rT Tα − ⎡ ⎤= −⎣ ⎦ (9)

( ) ( )1 0.607352 2.20517exp 0.511614 1r rT Tα − ⎡ ⎤= −⎣ ⎦ (10)

Twu-Tilton-Bluck. Presents a volume-change factor for im-proving the liquid density predictions. They propose the fol-lowing equations:

, ,s CEOS s RAc v v= − (11)

( )2 71 1

,

Trcs RA RA

c

RTv Z

P

⎡ ⎤+ −⎢ ⎥⎣ ⎦⎛ ⎞

= ⎜ ⎟⎝ ⎠

(12)

CEOS i iv v x c= − ∑ (13)

Where: vs,CEOS = volume of saturated liquid calculated by a cubic EOS. vs,RA = volume of saturated liquid calculated by Rackett’s equation (Eq. 12). ZRA = Rackett’s parameter (see Table 3). In the case of pseudo-components, the value of ZRA is equal to the critical compressibility factor Zc. Riazi-Daubert Correlation Riazi-Daubert’s correlation utilizes MW and SG as heavy fraction parameters. They propose the same type of equation for all the physical properties, varying only the coefficients in each particular case. For calculating the accentric factor, Ri-azi-Daubert uses the Edmister’s10 correlation. The proposed relationship is next:

( )expb caMW SG dMW eSG f MW SGθ = + + ⋅⎡ ⎤⎣ ⎦ (14)

Where: θ = some physic property. a-f = coefficients for each physic property (Table 1).

The Edmister’s correlation for the accentric factor is Pc and Tc dependent. Is given by:

( )log 14.73 17 1

c

c b

PT T

ω = −−

(15)

TABLE 1 – Riazi and Daubert’s coefficients

θ Tc Pc Tb a 544.4 45203 6.77857 b 0.2998 -0.8063 0.401673 c 1.0555 1.6015 -1.58262 d -0.00013478 -0.0018078 0.00377409 e -0.61641 -0.3084 2.984036 f 0.0 0.0 -0.00425288

PVT Data A selection of twenty (20) PVT studies was realized in the Neuquén-Basin, mostly Black-Oil samples from these reser-voirs: Centenario, Mulichinco, Petrolífera, Quintuco, Sierras Blancas and Tordillo. The samples posses an API range be-tween 30 and 60, a GOR range between 50 and 250 m3/m3 and a C7+ mole % range between 25% and 50%. Their character-istics are given in Table 4 and their heavy fraction properties are given in Table 5. Methodology The compositional simulator utilized is the software UniTest© (property of DeltaP®). It uses the PR-EOS with the modifica-tions previously presented, the quadratic mixing rule and the Nishiumi’s binary interaction parameters. The outputs of the simulator are the following curves:

- Solution gas – oil ratio (Rs), DE. - Oil formation volume factor (Bo), DE. - Oil density (ρo), DE. - Pressure – volume relation (PV), CCE.

DE stands for Differential Expansion and CCE stands for

Constant Composition Expansion. The software has an optimization function for comparing

the laboratory data with the output of the simulator, varying parameters selected by the user and adjusting the data set by the “least squares” method. This function was used to adjust the density curve, varying the plus-fraction MW and obtaining an array of “adjusted MW” (called MW*).

SPE Student Paper 3

Each crude oil sample was represented by a composi-tional model of the reservoir fluid. This model is defined by the mole composition of: Nitrogen (N2), Carbon Dioxide (CO2), Methane (CH4) through Hexane (C6H14); the critical properties of these elements were obtained from Reid11 and are presented in Table 3. Lastly the pseudo-component (which represents the heptanes plus-fraction of the fluid, in this case C7+) is defined with the correlation presented next. Proposed Correlation First a simple curve matching, using the previously presented software function, between the compositional simulator and PVT tests data, varying the critical properties of the C7+, was tried. The results were not promising: an excellent matching for each sample was accomplished, but there was no relation-ship encountered between the MW and SG with the critical properties, the matching took several minutes of computer calculations and no physical meaning or explanation was taken into account.

Then it was decided to try something simpler: the Reid’s known critical properties of pure compounds between n-C7 and n-C20. The reason is that for this set of black oil samples, the MW of the heptanes plus fraction is between the MW n-C7 and n-C20, so it is not radical to think the C7+ as an “average” compound between these two.

A relationship was established between the MW and the critical properties using the data set provided by Reid. The functions for obtaining Pc (Eq. 16) and Tc (Eq. 17) from MW were working well but the ω obtained brought some problems: for samples with high MW of the C7+, the ω was greater than unity and the vapor pressures obtained by the EOS at low temperatures diverged to infinity. So it was decided to represent the accentric factor using the correlation proposed by Edmister (Eq. 15). This decision is based on the fact that the values of calculated accentric factors are less than unity and the previous problem disappears.

Using Edmister’s correlation for the ω calculation brings us an additional problem: the normal boiling point temperature Tb needs to be measured or obtained from the heavy fraction. For solving this inconvenient it was also appealed to Reid’s data set and a relation between Tb and Tc was found (Eq. 18).

The correlation for the C7+ is presented next:

( )[ ] 82.82 653exp 0.007427cP psia MW= + − (16)

( )[ ] 778.5 383.5ln 4.075cT R MW= − + − (17)

( )1.869[ ] 194 0.001241 [ ]b cT R T R= + (18)

The results of using this correlation in the compositional simulator are promising: in all the samples the bubble point is very close to the PVT value so the matching is sometimes not needed, and also the PV, Rs and Bo curves are very close to their PVT values. Graphics of the previous equations are pre-sented in Figure 1 to Figure 3.

But here arises another problem: the liquid density curves calculated by the simulator are far beyond from the laboratory measured curves, although the PV, Rs and Bo curves are adjusted. The solution: match the oil density curve given by the simulator varying the MW of the plus-fraction. This new MW is called the “adjusted MW” (MW*) and is only used for calculating the oil density in the simulator. A relation between MW* and MW (Eq. 19) was found:

( )* 39.44 47.47exp 0.006701MW MW= + (19)

This equation is presented in Figure 4.

Correlation Comparison The comparison of both correlations was done using the rela-tive average error RAE, calculated between the PVT data points and the output points of the simulator, for each correla-tion. Table 2 presents the RAE comparison between the two correlations, Table 6 and Table 7 shows the RAE of Pb, GOR, PV, Rs, Bo and ρo for each sample. The relative aver-age error (RAE) is given by:

1 calc data

data

x xRAE

N x−

= ∑ (20)

Where: N = number of data points xcalc = calculated variable xdata = known data variable

TABLE 2 – RAE Comparison

RAE

This Work RAE

Riazi-Daubert Pb 2.29% 3.43%

GOR 7.37% 11.10% PV 1.42% 1.47% Rs 9.24% 12.59% Bo 2.24% 2.20% ρo 1.50% 12.63%

In Figure 5 and Figure 6 the comparisons between cal-

culated and real values of Pb and GOR are presented, respec-tively. From Figure 7 to Figure 26 the PVT and simulated curves of the following samples can be appreciated: Sample 1 (GOR = 250 m3/m3, m% C7+ = 26%), Sample 6 (GOR = 180 m3/m3, m% C7+ = 33%), Sample 10 (GOR = 130 m3/m3, m% C7+ = 38%), Sample 15 (GOR = 76 m3/m3, m% C7+ = 44%), Sample 20 (GOR = 50 m3/m3, m% C7+ = 51%). The PVT properties presented are PV, Rs, Bo and ρo. The contrast in oil density predictions between this correlation and RD can be clearly seen, showing that this work gives better oil density prediction performance.

4 SPE Student Paper

Conclusions This work presents a new set of correlations for obtain-

ing the critical properties of a pseudo-component repre-senting the heptanes plus fraction C7+ of a crude oil fluid. These correlations are function of the fraction’s MW.

A plus-fraction’s MW adjustment function is presented for improving the liquid density predictions of the simu-lator. This function shows to be a solution to the problem of the cubic EOS when predicting liquid densities in res-ervoirs fluids with high content of heavy hydrocarbons.

This work is compared to the Riazi-Daubert’s correla-tion: the two correlations performed equally when pre-dicting the PV and Bo curves; in the calculation of the Rs curve this work obtained better results than the other. In oil density calculations, this work demonstrates very good predictions, better than the previous correlation.

Future Work Recommendations Add to the adjustment, phase envelope curves obtained

in the laboratory, since the simulator can generate this type or curves. This point should be taken into considera-tion because the adjustments are realized at constant tem-perature, equal to reservoir temperature, having as a re-sult an infinite number of phase diagrams that coincide in the same isotherm, and the user must be careful when ex-trapolating to other temperatures.

The data base of this study should be enlarged with a large number of samples, and from more fields: Golfo San Jorge, Noroeste, Cuyo and Austral–basin. Also cor-relations for different types of fluid should be created: volatile oil and gas–condensate.

Enlarge this work with the study of more heavy frac-tions: C10+ and C20+. Also the effect of dividing the heavy fraction in various pseudo-components with a determined distribution of molecular weights and compositions should be studied. In this point it should be taken into ac-count the computer power needed, because with more components used, the time of calculations increase expo-nentially.

Acknowledgments I want to express my most sincerely gratefulness to all the people that have helped me to do this work: Rubén Caligari, Petrobras Energía SA. For granting

me the access to the PVT laboratory information needed.

Marcelo Crotti, InLab. For his excellent predisposition in helping me with the selection of the information and the PVT tests.

Juan A. Rosbaco, ITBA. For being my mentor in this work and for the excellent person that he is.

Miguel Schindler, DeltaP. For letting me use the soft-ware UniTest®. Also for helping me evaluate certain theory aspects of this study.

Nomenclature Bo = oil formation volume factor CCE = constant concentration expansion DE = Differential expansion EOS = equation of state GOR = gas – oil ratio, m3/m3 kij = binary interaction coefficient, kij = kji MW = molecular weight P = pressure, Pa Pb = bubble point, kg/cm2 Pc = critical pressure, psia PR = Peng-Robinson PV = pressure – volume ratio PVT = pressure – volume – temperature R = universal gas constant, 8.3143 J mol-1 K-1 RAE = relative average error, % RD = Riazi and Daubert Rs = solution gas – oil ratio, m3/m3

SG = specific gravity relative to water at 1 atm and 60 °F T = temperature, K Tb = normal boiling point temperature, R Tc = critical temperature, R Tr = reduced temperature, where Tr = T / Tc Tres = reservoir temperature, ºC Vm = molar volume, m3 Zc = critical compressibility factor ZRA = Rackett’s parameter Greek letters ρo = oil density, g/cm3 ω = accentric factor References 1. Peng, D.Y. and Robinson, D.B.: “A New Two-Constant

Equation of State”, Ind. and Eng. Chem. Fund. (1976) 15, No. 1, 59-64.

2. Riazi, M. R., Daubert, T. E., “Characterization Parame-ters for Petroleum Fractions”, Ind. Eng. Chem. Res., 1987, Vol. 26, No. 24, pp. 755-759.

3. Whitson, C.H.: “Effect of C7+ Properties on Equation-of-State Predictions”, 1982 SPE Annual Technical Con-ference and Exhibition, SPE 11200.

4. Kesler, M.G. and Lee, B.I.: “Improve Prediction of En-thalpy of Fractions”, Hydrocarbon Processing (1976) 55, 59.

5. Twu, C.H.: “An internally Consistent Correlation for Predicting the Critical Properties and Molecular Weights of Petroleums and Coal-Tar Liquids”, Fluid Phase Equi-libria (1984) 16, 137.

6. Stamataki, S.K. and Magoulas, K.G., “Characterization of Heavy Undefined Fractions”, 2001 SPE International Symposium on Oilfield Chemistry, SPE 64996.

7. H. Nishiumi and T. Arai, “Generalization of the Binary Interaction Parameter of the Peng-Robinson Equation of State by Component Family”, Fluid Phase Equilibria (1988), 42, 43-62.

SPE Student Paper 5

8. Twu, C.H., Coon, J.E. and Cunningham, J.R., “A New Generalized Alpha Function for a Cubic Equation of State. Part 1: Peng-Robinson EOS”, Fluid Phase Equi-libria (1995), Volume 105, Number 1.

9. Twu, C.H., Tilton B. and Bluck D., “The Strengths and Limitations of Equations of State Models and Mixing Rules”.

10. Edmister, W.C., “Applied Hydrocarbon Thermodynamic, Part 4: Compressibility Factors and Equations of State”, Petroleum Refiner, April 1958, Vol. 37, pp. 173-179.

11. Reid, R.C., Prausnitz, J.M. and Poling, B.E.: “The Prop-erties of Gases and Liquids”, McGraw-Hill Companies; 4th edition (April 1987).

SI Metric Conversion Factors GOR: m3/m3 x 35.31467 = scf/stb Pressure: kg/cm2 x 14.22334 = psia Temperature: °C x 1.8 + 32 = °F Density: g/cm3 x 62.42796 = lb/ft3

Appendix In the Tables 6 and 7, GF stands for this work (author’s name) and RD stands for Riazi-Daubert.

TABLE 3 – Reid’s Critical Properties

Element MW Pc [psia]

Tc [R] ω ZRA

C1 16.0 666 343 0.0115 0.2892 C2 30.1 707 550 0.0908 0.2808 C3 44.1 616 666 0.1454 0.2766 n-C4 58.1 551 766 0.1928 0.2730 i-C4 58.1 528 735 0.1756 0.2754 n-C5 72.2 489 846 0.2510 0.2684 i-C5 72.2 490 829 0.2273 0.2717 C6 86.2 437 914 0.2957 0.2635 C7 100.2 397 973 0.3506 0.2604 C8 114.2 361 1024 0.3978 0.2571 C9 128.3 334 1071 0.4437 0.2543 C10 142.3 306 1109 0.4902 0.2507 C11 156.3 285 1150 0.5349 0.2499 C12 170.3 264 1185 0.5622 0.2466 C13 184.4 250 1216 0.6231 0.2473 C14 198.4 235 1245 0.6797 0.2430 C15 221.4 220 1272 0.7060 0.2418 C16 226.4 206 1297 0.7418 0.2388 C17 240.5 191 1320 0.7699 0.2343 C18 254.5 176 1341 0.7895 0.2275 C19 268.5 197 1397 0.8270 0.2278 C20 282.6 161 1381 0.9070 0.2281

TABLE 4 – PVT Samples Properties

Sample API GOR [m3/m3]

Tres

[ºC] Pb

[kg/cm2] Sample 1 50.8 249.9 90.0 150.11 Sample 2 47.7 213.1 82.6 146.59 Sample 3 38.0 208.8 105.0 241.53 Sample 4 41.2 204.8 73.9 269.70 Sample 5 60.2 185.4 81.7 69.10 Sample 6 57.2 181.2 81.2 127.00 Sample 7 31.8 163.6 95.6 253.39 Sample 8 42.8 138.1 156.0 198.83 Sample 9 34.9 130.7 86.7 201.48 Sample 10 47.9 129.5 62.5 161.71 Sample 11 35.7 128.2 63.9 159.20 Sample 12 31.7 88.1 61.7 163.73 Sample 13 33.4 85.8 63.0 141.28 Sample 14 32.5 77.9 54.0 140.43 Sample 15 32.4 75.8 59.8 135.30 Sample 16 35.1 75.2 91.5 113.60 Sample 17 35.2 72.7 70.0 111.92 Sample 18 31.8 64.6 52.0 121.39 Sample 19 41.4 57.8 76.0 66.51 Sample 20 32.8 50.2 59.0 82.08

TABLE 5 – C7+ Properties of Samples

Sample MW SG x

[mole %] Sample 1 163.4 0.797 26.13% Sample 2 170.3 0.799 27.82% Sample 3 224.5 0.844 28.97% Sample 4 218.7 0.829 27.55% Sample 5 144.4 0.779 29.52% Sample 6 136.7 0.773 32.62% Sample 7 256.8 0.870 30.67% Sample 8 217.5 0.821 38.54% Sample 9 241.2 0.861 36.50% Sample 10 182.8 0.801 38.52% Sample 11 234.9 0.859 36.05% Sample 12 272.1 0.879 40.98% Sample 13 238.2 0.871 41.70% Sample 14 251.5 0.873 45.35% Sample 15 266.8 0.875 44.19% Sample 16 236.7 0.865 47.30% Sample 17 223.9 0.863 48.45% Sample 18 268.5 0.879 46.57% Sample 19 221.0 0.836 52.60% Sample 20 255.5 0.878 50.93%

6 SPE Student Paper

TABLE 6 – RAE of Pb, GOR and PV

Pb [%] GOR [%] PV [%] Sample GF RD GF RD GF RD

Sample 1 2.1 4.6 5.5 4.6 1.5 1.4 Sample 2 4.3 5.9 0.5 0.6 1.4 1.2 Sample 3 0.4 0.6 14.2 18.3 0.9 0.9 Sample 4 3.0 2.0 3.8 7.1 0.9 0.9 Sample 5 1.1 4.3 20.2 17.9 1.9 1.7 Sample 6 0.0 5.1 3.2 4.5 1.7 1.3 Sample 7 0.6 3.1 11.8 18.3 1.1 1.6 Sample 8 1.6 0.0 15.6 17.7 2.9 2.6 Sample 9 5.5 6.7 11.7 17.3 2.0 2.2 Sample 10 1.5 1.8 3.9 3.1 1.1 1.1 Sample 11 5.8 3.2 5.9 11.8 1.4 1.5 Sample 12 3.7 8.8 7.5 15.2 2.5 2.9 Sample 13 0.1 2.0 5.1 19.9 1.4 1.6 Sample 14 2.3 1.5 3.7 10.9 1.3 1.6 Sample 15 0.1 4.0 5.6 0.4 1.2 1.5 Sample 16 1.6 1.8 8.8 15.3 1.2 1.2 Sample 17 0.3 0.2 3.2 10.3 1.0 1.1 Sample 18 0.4 4.6 1.7 10.1 1.5 1.9 Sample 19 6.0 6.0 10.3 14.5 0.6 0.7 Sample 20 5.2 2.4 5.2 4.1 0.8 0.9

TABLE 7 – RAE of Rs, Bo and ρo

Rs [%] Bo [%] ρo [%] Sample GF RD GF RD GF RD

Sample 1 9.5 9.7 2.0 2.5 1.5 5.6 Sample 2 5.1 5.7 2.3 2.3 1.8 6.5 Sample 3 17.9 21.7 3.4 5.3 1.3 11.0 Sample 4 8.0 10.8 1.7 1.1 2.0 9.4 Sample 5 21.6 19.8 8.8 8.6 0.8 3.9 Sample 6 2.0 3.8 1.2 1.6 1.6 3.3 Sample 7 16.3 21.2 1.4 3.4 1.6 16.4 Sample 8 15.3 18.1 1.9 2.9 2.5 8.6 Sample 9 14.2 19.2 1.0 1.4 1.2 15.3 Sample 10 4.5 3.6 3.0 2.7 3.3 5.4 Sample 11 11.5 16.0 1.2 1.5 1.5 13.6 Sample 12 5.3 10.6 2.7 1.2 0.9 21.4 Sample 13 3.0 4.0 3.6 1.9 1.5 17.0 Sample 14 4.9 10.8 1.9 0.6 0.7 17.9 Sample 15 7.4 13.5 2.0 0.6 1.0 19.7 Sample 16 11.4 17.7 0.8 1.9 0.8 15.0 Sample 17 5.3 11.2 0.9 0.9 0.7 13.8 Sample 18 2.9 9.7 1.9 0.6 0.7 20.7 Sample 19 15.2 19.2 1.3 2.2 3.5 9.8 Sample 20 3.7 5.3 1.7 0.6 1.0 18.3

MW

50 100 150 200 250 300 350

Pc [p

sia]

100

150

200

250

300

350

400

450

Figure 1. Pc vs MW from Reid, Eq. 16.

MW

50 100 150 200 250 300 350

Tc [R

]

900

1000

1100

1200

1300

1400

1500

Figure 2. Tc vs MW from Reid, Eq. 17.

Tc [R]

900 1000 1100 1200 1300 1400 1500

Tb [R

]

600

700

800

900

1000

1100

1200

Figure 3. Tb vs Tc from Reid, Eq. 18.

Pc = 82.82 + 653exp(–0.007427MW)

R2 = 0.9966

Tc = –778.5 + 383.5ln(MW – 4.075)

R2 = 0.9989

Tb = 194 + 0.001241Tc1.869

R2 = 0.9999

SPE Student Paper 7

MW

120 140 160 180 200 220 240 260 280 300

MW

*

140

160

180

200

220

240

260

280

300

320

340

360

Figure 4. MW* vs MW, Eq. 19.

Pb [kg/cm2]

50 100 150 200 250 300

Pb [k

g/cm

2 ]

50

100

150

200

250

300

PVT DataPb This Work Pb Riazi-Daubert

Figure 5. Comparison of predicted bubble points.

GOR [m3/m3]

50 100 150 200 250 300

GO

R [m

3 /m3 ]

50

100

150

200

250

300

PVT DataGOR This Work GOR Riazi-Daubert

Figure 6. Comparison of predicted gas – oil ratios.

Pressure [kg/cm2 abs]

50 100 150 200 250 300

Rel

ativ

e Vo

lum

e

0.90

0.95

1.00

1.05

1.10

1.15

1.20

1.25

1.30

PVTThis WorkRiazi-Daubert

Figure 7. CCE PV relation, Sample 1.


0 50 100 150 200 250 300

Rs

[m3 /m

3 ]

0

50

100

150

200

250

300


Figure 8. DE Rs curve, Sample 1.


0 50 100 150 200 250 300

Bo

[m3 /m

3 ]

1.0

1.2

1.4

1.6

1.8

2.0

2.2


Figure 9. DE Bo curve, Sample 1.

MW* = 39.44 + 47.47exp(0.006701MW)

R2 = 0.9957

GOR = 250 m3/m3 mole % C7+ = 26%

GOR = 250 m3/m3 mole % C7+ = 26%

GOR = 250 m3/m3 mole % C7+ = 26%

8 SPE Student Paper


0 50 100 150 200 250 300

ρo [g

/cm

3 ]

0.50

0.55

0.60

0.65

0.70

0.75

0.80


Figure 10. DE Oil Density curve, Sample 1.


50 100 150 200 250 300

Rel

ativ

e Vo

lum

e

0.90

0.95

1.00

1.05

1.10

1.15

1.20

1.25

1.30




0 50 100 150 200 250 300

Rs

[m3 /m

3 ]

0

50

100

150

200

250




0 50 100 150 200 250 300

Bo

[m3 /m

3 ]

1.0

1.2

1.4

1.6

1.8

2.0




0 50 100 150 200 250 300

ρo [g

/cm

3 ]

0.50

0.55

0.60

0.65

0.70

0.75




50 100 150 200 250

Rel

ativ

e Vo

lum

e

0.95

1.00

1.05

1.10

1.15

1.20

1.25

1.30



GOR = 250 m3/m3 mole % C7+ = 26%

GOR = 180 m3/m3 mole % C7+ = 33%

GOR = 180 m3/m3 mole % C7+ = 33%

GOR = 180 m3/m3 mole % C7+ = 33%

GOR = 180 m3/m3 mole % C7+ = 33%

GOR = 130 m3/m3 mole % C7+ = 38%

SPE Student Paper 9


0 50 100 150 200 250

Rs

[m3 /m

3 ]

0

20

40

60

80

100

120

140

160




0 50 100 150 200 250

Bo

[m3 /m

3 ]

1.0

1.1

1.2

1.3

1.4

1.5

1.6




0 50 100 150 200 250

ρo [g

/cm

3 ]

0.55

0.60

0.65

0.70

0.75

0.80

0.85




50 100 150 200 250

Rel

ativ

e Vo

lum

e

0.95

1.00

1.05

1.10

1.15

1.20




0 50 100 150 200 250

Rs

[m3 /m

3 ]

0

20

40

60

80

100




0 50 100 150 200 250

Bo

[m3 /m

3 ]

1.00

1.05

1.10

1.15

1.20

1.25

1.30



GOR = 130 m3/m3 mole % C7+ = 38%

GOR = 130 m3/m3 mole % C7+ = 38%

GOR = 130 m3/m3 mole % C7+ = 38%

GOR = 76 m3/m3 mole % C7+ = 44%

GOR = 76 m3/m3 mole % C7+ = 44%

GOR = 76 m3/m3 mole % C7+ = 44%

10 SPE Student Paper


0 50 100 150 200 250

ρo [g

/cm

3 ]

0.55

0.60

0.65

0.70

0.75

0.80

0.85

0.90




0 50 100 150 200 250 300

Rel

ativ

e Vo

lum

e

0.95

1.00

1.05

1.10

1.15

1.20

1.25

1.30




0 50 100 150 200 250 300

Rs

[m3 /m

3 ]

0

10

20

30

40

50

60




0 50 100 150 200 250 300

Bo

[m3 /m

3 ]

1.00

1.05

1.10

1.15

1.20

1.25




0 50 100 150 200 250 300

ρo [g

/cm

3 ]

0.60

0.65

0.70

0.75

0.80

0.85

0.90



GOR = 76 m3/m3 mole % C7+ = 44%

GOR = 50 m3/m3 mole % C7+ = 51%

GOR = 50 m3/m3 mole % C7+ = 51%

GOR = 50 m3/m3 mole % C7+ = 51%

GOR = 50 m3/m3 mole % C7+ = 51%

Chequeo PVT(Resumen Apunte de Rafael Cobeñas)

Petrofísica y Fluidos de Reservorio

G. Fondevila

Chequeo de Consistencia y Validación de Datos de un Informe PVT

• ¿Por qué es necesario realizarlo?:– En la etapa de caracterización de un

reservorio nuevo (o no conocido), es de vital importancia obtener datos confiables, ya que luego el reservorista utiliza a diario información del fluido, que debe ser coherente y representativa.

Esquema de Trabajo

• Balance de Masa:– Balance de Masa Global– Balance de Masa por Etapas– Balance de Masa Composicional

• Gráficos de Control– Log K VS Tb– Hoffman– Bashbush

• Chequeos Generales de Parámetros• Simulación Termodinámica

Balance de Masa

• Balance de Masa Global:– Chequea que la densidad de la muestra medida sea

consistente con la calculada mediante los valores reportados de:

• Densidad de TNK• Gravedad específica de los gases liberados en cada etapa

de separación.• Relación de gas producido por etapa (Rs).• Factor volumétrico de Formación del Petróleo (Bo).

• Balance de Masa por Etapas:– Ídem anterior, excepto…– Se va chequeando etapa por etapa de la liberación.

Balance de Masa Global (1)

• En este chequeo se suman las masas correspondientes a las salidas de los efluentes en cada etapa de la liberación diferencial junto con la masa de petróleo residual.

• La masas total dividida por el volumen en fondo dede resultar igual a la densidad de la muestra en fondo.

• Asumiendo que el volumen residual a condiciones de tanque es Vtk, entonces la masa de líquido residual (m_res) resulta igual a:

m_res = dens_res . Vtk

Balance de Masa Global (2)

• La masa de gas en la iésima de la liberación diferencial es igual a:

mgasi = (Rs

i-1 – Rs

i) . densgas

i . Vtk

• Por lo que, la masa total del sistema resulta:

m = Σ [(Rsi-1 – Rs

i) . densgas

i] . Vtk + dens_res . Vtk

• Y el volumen total a presión de burbuja y temperatura de reservorio:

V = Vtk . Bodb

• Entonces la densidad a esas condiciones es:

dens_Pb = ( Σ [(Rsi-1 – Rs

i) . densgas

i] + dens_res ) / Bodb

Balance de Masa

• Balance de Masa Composicional:– En cada etapa de la liberación uno tiene el

dato de la fracción molar de cada componente tanto en la fase líquida como gaseosa.

– Se puede calcular las constantes de equilibrio para cada componente en cada etapa (presión) y compararles con valores de referencia.

Esquema de Trabajo




Gráficos de Control

• Constantes de Equilibrio VS Temperatura de Ebullición:– En una determinada etapa de la liberación (ya

sea flash o diferencial) uno puede calcular para cada elemento la constante de equilibro “K” (fracción molar en fase gaseosa “xi” / fracción molar en fase líquida “yi”).

– Luego se grafica en escala semi-log K vs Tb. La misma debe tender a una línea recta.

K vs Tb


• Gráfico de Hoffman (1952):– Nuevamente para una determinada etapa de

liberación (presión), se grafica en escala semi-log:

• Absisas: Función especial de Hoffman que depende de la inversa de la Temperatura del Ensayo y de la Temperatura de Ebullición del componente i. f_Hoffman = b * (1/Tbi - 1/T)

• Ordenadas: El producto Constante de Equilibrio del componente i por Presión (Ki * P).

– Debe aproximarse a una línea recta.

Gráfico de Hoffman


• Bashbush (1981):– El método consiste en la aplicación de un

balance de masa a los moles del fluido original presente en la celda a presión de saturación.

– El objetivo es obtener la composición molar del líquido, que junto con la composición molar del gas (cromatografía), nos permite calcular las constantes de equilibrio para cada componente en cada etapa de la liberación.

Bashbush

Esquema de Trabajo




Chequeo de Parámetros

• Entre todos los parámetros de un ensayo PVT existen interdependencias.

• Aunque estas interdependencias parezcan coherentes, no es suficiente para indicar que los resultados obtenidos sean representativos.

• En esta etapa tiene mayor peso la experiencia del analista.

• Algunos ejemplos:– Valores anómalos de expansión térmica.– Curva Bo con concavidad errónea.– Curva de viscosidad (P > Pb) no muestra la pendiente

esperada.– Las constantes de equilibrio se entrecruzan.– Etc…

Esquema de Trabajo




Simulación Termodinámica

• El objetivo es hallar un modelo que represente el comportamiento PVT del fluido de reservorio.

• Como vimos anteriormente, uno tiene dos opciones para evaluar el modelo:– Utilizar correlaciones para los parámetros críticos del

pseudo-componente que representa a la fracción pesada.

– Ajustar con los datos PVT el modelo variando los parámetros críticos del pseudo-componente que representa a la fracción pesada

• Luego del ajuste uno puede corroborar la coherencia de los datos.

Ejemplo: Modelo Petróleo Volatil

Chequeo PVT

Hipótesis de Alta y Baja Volatilización

Objetivo

• Es simplemente otro método para poder chequear la

consistencia de un PVT.

• Consiste en utilizar la composición del Fluido de

Reservorio Recombinado y plantear dos hipótesis:

– Alta Volatilidad

– Baja Volatilidad

• En cada caso se calcula el Bob y el Rsb.

• El Bob y Rsb del informe PVT debe estar dentro del

intervalo obtenido:

– Bob (min) < Bob (informe PVT) < Bob (max)

– Rsb (min) < Rsb (informe PVT) < Rsb (max)

Hipótesis

• Alta Volatilización: consideramos que los moles de los componentes más livianos (<C4) al bajar la presión pasan todos a la fase gaseosa. Luego progresivamente vamos repartiendo las fracciones molares en cada fase hasta considerar que los componentes pesados (>C10) están solamente en la fase líquida.

• Baja Volatilización: consideramos que los moles de los componentes más livianos (<C2) al bajar la presión pasan todos a la fase gaseosa. Luego progresivamente vamos repartiendo las fracciones molares en cada fase hasta considerar que los componentes pesados (>C6) están solamente en la fase líquida.

Ejemplo de Hipótesis

Componente Fase Gas Fase Líquida

C1 100% 0%

C2 100% 0%

C3 80% 20%

C4 80% 20%

C5 60% 40%

C6 60% 40%

C7 20% 80%

C8 20% 80%

C9 0% 100%

C10 0% 100%

C11 0% 100%

Componente Fase Gas Fase Líquida

C1 100% 0%

C2 100% 0%

C3 60% 40%

C4 60% 40%

C5 20% 80%

C6 20% 80%

C7 0% 100%

C8 0% 100%

C9 0% 100%

C10 0% 100%

C11 0% 100%

Alta Volatilización Baja Volatilización

Ejemplo de TP

1. Planteo las Hipótesis

A B C D E

Comp

Fluido de

Reservorio

[%molar]

Gas Liq Gas Liq

C1 28 100% 0% 100% 0%

C2 10 100% 0% 100% 0%

C3 8 80% 20% 60% 40%

C4 8 80% 20% 60% 40%

C5 6 60% 40% 20% 80%

C6 6 60% 40% 20% 80%

C7 8 20% 80% 0% 100%

C8 8 20% 80% 0% 100%

C9 10 0% 100% 0% 100%

C10 10 0% 100% 0% 100%

Alta Volatilización Baja Volatilización

Ejemplo de TP

2. Calculo Moles de Líquido y Gas para cada Hipótesis

A B C D E A x C A x E A x B A x D

Comp

Fluido de

Reservorio

[%molar]

Gas Liq Gas LiqAlta

[moles]

Baja

[moles]

Alta

[moles]

Baja

[moles]

C1 28 100% 0% 100% 0% 0,0 0,0 28,0 28,0

C2 10 100% 0% 100% 0% 0,0 0,0 10,0 10,0

C3 8 80% 20% 60% 40% 1,6 3,2 6,4 4,8

C4 8 80% 20% 60% 40% 1,6 3,2 6,4 4,8

C5 6 60% 40% 20% 80% 2,4 4,8 3,6 1,2

C6 6 60% 40% 20% 80% 2,4 4,8 3,6 1,2

C7 8 20% 80% 0% 100% 6,4 8,0 1,6 0,0

C8 8 20% 80% 0% 100% 6,4 8,0 1,6 0,0

C9 10 0% 100% 0% 100% 10,0 10,0 0,0 0,0

C10 10 0% 100% 0% 100% 10,0 10,0 0,0 0,0

Alta Volatilización Baja Volatilización Moles del Líquido

[mol]

Moles del Gas [mol]

Ejemplo de TP

A B C D E A x C A x E A x B A x D A x C A x E A x B A x D

Comp

Fluido de

Reservorio

[%molar]

Gas Liq Gas LiqAlta

[moles]

Baja

[moles]

Alta

[moles]

Baja

[moles]

Alta

[moles]

Baja

[moles]

Alta

[moles]

Baja

[moles]

C1 28 100% 0% 100% 0% 0,0 0,0 28,0 28,0 0,00 0,00 0,46 0,56

C2 10 100% 0% 100% 0% 0,0 0,0 10,0 10,0 0,00 0,00 0,16 0,20

C3 8 80% 20% 60% 40% 1,6 3,2 6,4 4,8 0,04 0,06 0,10 0,10

C4 8 80% 20% 60% 40% 1,6 3,2 6,4 4,8 0,04 0,06 0,10 0,10

C5 6 60% 40% 20% 80% 2,4 4,8 3,6 1,2 0,06 0,09 0,06 0,02

C6 6 60% 40% 20% 80% 2,4 4,8 3,6 1,2 0,06 0,09 0,06 0,02

C7 8 20% 80% 0% 100% 6,4 8,0 1,6 0,0 0,16 0,15 0,03 0,00

C8 8 20% 80% 0% 100% 6,4 8,0 1,6 0,0 0,16 0,15 0,03 0,00

C9 10 0% 100% 0% 100% 10,0 10,0 0,0 0,0 0,25 0,19 0,00 0,00

C10 10 0% 100% 0% 100% 10,0 10,0 0,0 0,0 0,25 0,19 0,00 0,00

ΣΣΣΣ 40,8 52,0 61,2 50,0

Composición Líquido

[%molar]

Composición Gas

[%molar]

Alta Volatilización Baja Volatilización Moles del Líquido

[mol]

Moles del Gas [mol]

3. Totalizo Moles de Líquido y Gas, calculo Composición Molar de ambos

Ejemplo: %C2 líquido = Moles C2 líquido / Σ Cn Moles Líquido

Cálculo de Parámetros PVT• Podemos calcular los parámetros PVT Bo y Rs a través de la composición de los fluidos:

• Tener cuidado con las unidades, siempre chequear consistencia.

• Donde:– X: Fracción molar total del líquido.

– Y: Fracción molar total del gas.

– ρCSliq: Densidad del líquido de TNK a CS (utilizar composición del líquido)

– ρPb: Densidad del fluido en el punto de burbuja (utilizar composición total)

– PMliq: Peso Molecular del líquido de TNK (utilizar composición del líquido)

– PMFres: Peso Molecular del fluido en el punto de burbuja (utilizar composición total)

– R: Constante universal de los gases (0.082 lt atm / K mol)

– Pcs: Presión a condición estándar (1 atm)

– Tcs: Temperatura a condición estándar (60 °F)

• Utilizando las definiciones de los parámetros PVT:

– Bo = Vol liq fondo (fluido de reservorio) / Vol liq CS (comp liquido)

– Rs = Vol gas disuelto CS (comp gas) / Vol liq CS (comp liquido)

• Podemos desarrollar las ecuaciones anteriores. Practicar el desarrollo de las mismas utilizando las siguientes relaciones:

– Vol liq = nro moles liq x PM liq / dens liq = nro moles x Σ xi . PMi / Σ xi . Densi

– Vol gas = nro moles gas x R x T / P

• Para cada hipótesis calculamos Bo y Rs, así obtenemos un intervalo. Los valores informados en el PVT deberían estar dentro del mismo.

Pb

liq

CS

liq

Fres

PM

PM

XBo

ρ

ρ1=

CSliq

CS

liq

CS

PPM

RT

X

YRs

ρ

=

fluid os 2012

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