conceptos simulacion de reservorios
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Conceptos basicos de simulacion matematica de reservoriosTRANSCRIPT
SIMULACION MATEMATICA RESERVORIOSSimulación de Reservorios
Un modelo es un conjunto de datos que describen un reservorio
Profundidad, dimensiones, porosidad, espesor, permeabilidad
Densidad de fluidos, viscosidad, solubilidad gas, factores de volumen
Presión de reservorio, presión capilar, permeabilidades relativas
Un simulador es un programa que calcula la distribución de presión y saturación de un reservorio, como función de tiempo.
SIMULADOR VERSUS MODELO DE RESERVORIO
*
Simulators and Models
Through the years, many engineers have referred to simulators and models as though they were the same, which is not true, and can cause confusion. A simulator is a program, generally written in fortran, that is typically leased from one of the major vendors, such as GEOQUEST RESERVOIR TECHNOLOGIES. A model is a set of data used to describe a reservoir, its fluids, wells, etc.
During this course we will be building a model using data provided by the instructor. ECLIPSE 100 is the simulator (or program) we will be using to do this work.
Seferino Yesquen
Simulación de reservorios.- Uso de modelos matemáticos para simular el comportamiento de un reservorio real
INPUT
Calidad de un estudio de simulación = f ( datos ingreso, modelo, simulador )
Ec. de continuidad ( E B M ).
Ec. de flujo de fluidos ( Darcy ).
Ec. de estado. = f (p)
Simulador
OUTPUT
*
Ecuacion de la difusividad, es la combinacion de las principales ecuaciones que describen el proceso fisico del movimiento de fluido dentro del reservorio, convina:
La EBM (continuidad) se basa en la ley de conservación de la materia, que establece que la masa de un sistema cerrado permanece sirmpre constante. La EBM establece que la diferencia entre la cantidad de fluidos iniciales en el yac. Y la cantidad de fluidos remanentes es igual a la cantidad de fluidos producidos.
Para la aplicación del BM se toma en cuenta algunas consideraciones importantes:
Volumen poroso es constante, no existe compactacion ni subcidencia.
El PVT es representativo del yac.
Proceso isotermico
Cw y Cf son despreiables
Se considera equilibrio termodinamico entre entre el gas y el petroleo a presion y temperatura de yac.
(Ecuacion de flujo) La unidad mas comun de la permeabilidad es el Darcy, el cual esta definido como el flujo Q en cm3/s resultante cuando la caida de presion es de 1 atm, aplicada a un lecho de 1cm2 de are transversal A de 1 cm de largo y para un fluido de viscosidad 1Cp
Ecuacion de estado (compresibilidad), describe la relacion volumen-presion o presion – densidad para los fluidos presentes.
Para cada momento, estas tres ecuaciones son combinadas en una unica ecuacion diferencial parcial, luego escritas como ec. Difrenciales finitas, es decir que el yacimiento es visto como una sucesion de bloques y la produccion es dividida en espacios de tiempo, osea discretizar el problema en tiempo y espacio.
Seferino Yesquen
Es necesario DISCRETIZAR las variables espacio y tiempo.
Discretización Espacio : División del reservorio en pequeñas distancias;
z
x
y
Distancia
Es necesario DISCRETIZAR las variables espacio y tiempo.
Discretización Tiempo : División. de historia de producción en intervalos de tiempo
Tiempo
Discretización de las ecuaciones de flujo
Primero la coordenada en X deberá ser dividido en un numero discreto de bloques. Considerando un sistema poroso horizontal en una dimensión, se tiene un sistema de N grid blocks, cada uno de longitud Dx:
Esto es llamado un grid de block centrado, y las propiedades promedios de reservorio se refieren al punto medio del bloque.
1
N
i-1
i
Aproximación por Serie de Taylor
*
Método de Modelaje con diferencias finitas
Se resuelven las ecuaciones par cada celda (grid block) por métodos numéricos para obtener los cambios de PRESION y SATURACION con el TIEMPO
La exactitud de los datos de entrada
Impacta la exactitud de los cálculos del simulador
La ecuación de Difusividad (1 Fase, flujo 1D)
*
1.-
Matrices
In order to solve the mass balance equation for each grid cell, all cells have to be solved at the same time. The reason for this is that in order to determine the flow of fluids into and out of a cell, you need to know what is going on in the surrounding cells. In other words, there has to be consistency between cells. To solve several equations at the same time, it is convenient to use matrices.
Seferino Yesquen
Consideraciones
Metodología de modelado
Recursos:
Cantidad y Calidad
Los resultados deberán estar asociados a una “banda de incertidumbre”
*
Ejemplos de Metas de Estudios en Campos Nuevos
Definir limites internos y externos del reservorio.
Definir net pay, volumen & reservas
Determinar numero optimo de locaciones y configuración de pozos
Optimizar el timing y tamaño de las facilidades de producción
Estimar el potencial de recuperación.
Anticipar la producción futura de fluidos y cambio operacionales.
Determinar los caudales críticos para conning de agua gas.
CLARIDAD DEL PROPOSITO
Ejemplos de Metas de Estudios en Campos Maduros
Monitorear el movimiento de los contactos de fluidos
Evaluar y seguir la productividad de los pozos
Evaluar el comportamiento histórico. Determinar tendencias y anomalías.
Determinar la fuente de la producción de agua y gas. Identificar pozos potenciales para workover.
Monitorear barrido del reservorio. Localizar petróleo by paseado. Perforación infill
Estimar beneficios de procesos de recuperación secundaria y EOR:
Determinar conectividad entre reservorios múltiples.
Cuantificar migración a través de los limites del contrato.
*
Transformación de Datos
Caracterización Geológica
La descripción Geológica deberá identificar los factores claves que afectan el flujo de fluidos en el reservorio.
*
Etapa 2: Caracterización del reservorio
La caracterización de los fluidos define las propiedades físicas de las mezclas de los fluidos en el reservorio y como pueden variar con cambios de P, T y V.
Clasificar el tipo de fluido
Determinar las propiedades de los fluidos.
Describir los mecanismos de producción del reservorio.
Caracterización de los fluidos
Etapa 2: Caracterización del reservorio
El modelo Petro físico define donde están localizados los volúmenes de petróleo, gas y agua, así como es el comportamiento de estos fluidos en la presencia de diferentes tipos de rocas.
Mojabilidad de la roca
SELECCIÓN DEL MODELO
Determine La Dimensionalidad
Use modelos 1D para flujos lineales o radiales en una dirección.
Use modelos 2D para flujos en dos direcciones: Cross sections
*
CONSTRUCCION DEL MODELO
Convirtiendo el Modelo de la Tierra en un Modelo de Simulación.
Control de Calidad de errores y problemas del modelo geológico.
Scalar el modelo
Hacer un Output del modelo en formato del simulador
*
Equilibrar el modelo
AJUSTAR LA HISTORIA
Calibrar el Modelo
Seferino Yesquen
Datos Requeridos
A fin de realizar balance de materia en cada grid block, el simulador necesita saber:
La presión y saturación inicial de cada grid block
La transmisibilidad para el flujo en las direcciones X, Y Z
La producción o inyección de cada grid block
*
Data Requirements
In order to perform a mass balance on each cell, the simulator needs to be able to determine the initial mass of oil, water and gas that exists in each grid block and also be able to determine how much fluid flows in or out of each block.
The initial mass of each fluid is determined from the dimensions, net thickness and porosity of each block, the initial saturation of each fluid within the block, and the fluid density. The fluid densities are determined from PVT data required for each fluid present in the reservoir. The initial saturations are determine from the depth of each block relative to the fluid contacts, relative permeability endpoints, and capillary pressure data.
The flow of fluids in a simulator can be described in general as:
q = T l DF
Here you have a flow rate equal to a transmissibility*mobility*driving force.
The driving force in our case is the potential drop either between two cells or a cell and the well. The initial pressure of each block is determined from the initial pressure at datum, the depth of each block, and initial reservoir fluid gradients. The gradients are determined from the PVT data specified for each fluid initially present in the reservoir.
K
A
L
Volumen de roca = DX*DY*DZ
El punto medio de la celda puede ser calculado
Punto medio = Prof. Tope + DZ/2
Volumen de roca y profundidad de los puntos medios
Dx
Dy
Dz
Bulk Volume and Midpoint Depth
The dimensions and top depth of each grid cell are required by the simulator. The Areal dimension of each cell is taken from the simulation grid. The vertical dimension of each cell is actually the gross thickness assigned from gross thickness maps. The top depth of each grid cell can be assigned from structure maps for each model layer, however, where applicable, most simulators will allow the user to specify the top depth of the reservoir for the first model layer and the simulator will determine the depth of each grid block from the top of the reservoir and gross thickness values.
From these data, the simulator is able to determine the bulk volume of each cell and the midpoint depth of each cell. The cell is actually represented vertically by this mid-cell depth to determine the initial pressure of the block and the angle and distance of flow from one cell to another. Therefore, if this value is incorrect, its effect with regard to these calculations needs to be considered.
Seferino Yesquen
Valores de porosidad, relacion Net-to-gross y espesor neto son asignados a cada celda de los mapas.
EL volumen poral es calculado :
VOLUMEN PORAL: DX*DY*DZ*NTG*PORO
VOLUMEN PORAL
Volumen Poral
Pore Volumes
The porosity and net thickness or net to gross are specified by the user for each grid cell. These values are taken from maps created for each model layer and are used to determine the initial pore volume and, subsequently, initial volumes of oil, water, and gas in each cell. As a result, the net thickness includes all sand that contains fluid expected to add pressure support, regardless of the type of fluid that initially exists in the sand.
It is actually the pore volume that is needed by the simulator. After the pore volume for each cell has been determined, the porosity becomes unimportant.
The net thickness or net to gross values will also be used to determine the net sand thickness used in flow calculations from one cell to another.
Seferino Yesquen
La permeabilidad para cada celda es especificada ya sea de mapas o de correlaciones
La transmisibilidad para cada cara de flujo puede ser calculada.
Transmisibilidad = K A / L
Permeability and Transmissibilities
A transmissibility must be calculated for each flow face in order to determine the flow of fluids between cells. By default, most simulators use what is referred to as a five point finite difference scheme. The five points refer to a cell and the four cells surrounding it, in the horizontal plane. In other words, there is no diagonal flow considered by the simulator. Some simulators have what is referred to as a nine point finite difference scheme which, in its most rigorous form, does consider diagonal flow in the horizontal plane. In a five point finite difference scheme, flow is allowed between a cell, the four cells surrounding it in the horizontal plane, and the cells above and below it. Therefore, transmissibilities are required for each of the six faces of flow, for each cell.
Similarly, a transmissibility for fluid flow between each cell and the well must be determined to calculate flow in and out of each well. These transmissibilities are calculated in general as:
Values for permeability are assigned either from maps or specified using a correlation. In most cases the permeability in the x and y direction are specified to be the same, though most simulators will allow directional permeabilities. The permeability in the vertical direction is usually specified as the horizontal permeability times some factor. These values are used together with the net thickness and perforated thickness to calculate transmissibilities.
There are a variety of transmissibility calculations. These are discussed in Chapter 6 along with different formats for specifying this data.
It is actually the transmissibility that is important for each flow face, for each cell. Once all transmissibilities are determined, the permeability becomes unimportant.
.00707Kh
ln( )+
S
r
e
r
w
K
A
L
Parámetros de Equilibración
El nivel de referencia, presión a este nivel, y los contactos de fluidos son especificados
De estos datos, la presión de petróleo, agua y gas son tabuladas como función de la profundidad.
Estas tablas usan las gradientes de los fluidos tomadas de los datos PVT
*
Equilibration Parameters
For most problems, the reservoir is initialized assuming that the reservoir is in equilibrium. Many problems can arise from poor initialization of pressures and saturations. It is therefore important that the initial pressures, saturations, and capillary pressures are consistent with each other.
Initial Pressures
The initial pressure for each grid cell is determined from the midpoint depth of the block, a datum depth, the initial pressure at datum, and the initial fluid gradients present in the reservoir. We have already seen how the midpoint depth of each block is determined. The initial pressure at datum is specified to the simulator along with the initial oil-water and gas-oil contacts. These parameters are generally referred to as Equilibration or Initialization parameters. The simulator uses this data to determine the initial pressure, for each phase, for each cell.
In ECLIPSE, tables of oil pressure, water pressure, and gas pressure are created as a function of depth. The range of depths is determined from the midpoint depths of each cell and the fluid contacts specified by the user. The pressure at each depth is calculated using the pressure at datum and the appropriate fluid gradients determined from the PVT data. The initial pressure for each cell is then determined from a table look-up process
OWC
P
i
h
Seferino Yesquen
Para celdas que no caen dentro de la zona de transición, las saturación inicial de agua y gas son determinadas de los endpoints de las curvas de permeabilidades relativas.
La saturación de petróleo es siempre determinada de 1-Sw-Sg
Fuera de la zona de transicion
Saturaciones Iniciales: So, Sw, Sg
*
Initial Oil, Water, and Gas Saturations
The initial oil, water, and gas saturations are used to determine the initial volume of fluids in each cell. To rigorously determine these volumes we need to recognize that part of a cell may be in the transition zone and the cell may be cut by a fluid contact.
For those volumes of the cell that do not lie in the transition zone, the initial water and gas saturation are determined from the relative permeability endpoints. This is usually true for all simulators. The lowest water saturation value found in the table is usually assigned to those volumes above the oil-water contact. For volumes below the oil-water contact, in some simulators, the value of water saturation is automatically set to a value of 1.0, however, in ECLIPSE, the value is set to the highest water saturation found in the relative permeability table. Similarly for gas, the values of gas saturation for any volume below the gas-oil contact is set to the lowest value found in the relative permeability table. This value is usually 0.0. The value of gas saturation above the gas-oil contact is set to the highest values found in the table, usually 1-Swc. For those volumes of a cell that are in a transition zone, the saturation is determined from the capillary pressure table. The resulting water and gas saturations are then a pore volume average of the volumes in the transition zone and outside the transition zone. The oil saturation is always calculated as 1-Sw-Sg.
Initialization Runs
It is important for the user to check the initial volumes of oil, water, and gas calculated by the simulator. This is a first step, basic check of the reservoir data. In particular, the initial oil volume should be checked and compared to other estimates of the initial oil in place.
Gas
Oil
Seferino Yesquen
En las zonas de transición, los valores iniciales de Sw y Sg son determinados de una tabla de presión capilar versus Sw ó Sg.
Las presiones capilares son calculadas como la diferencia entre las presiones de las fases.
Saturaciones Iniciales, So, Sw, Sg
En la zona de transición
*
Capillary Pressures
In the simulator, capillary pressures are determined for each grid cell from the phase pressures. The oil-water capillary pressure is calculated as a difference between the oil and water phase pressures. Similarly, the gas-oil capillary pressure is a difference between the oil and gas phase pressures.
Capillary pressures are used to determine the initial fluid saturations for each cell, in the transition zone. A table of water saturation versus capillary pressure is specified by the user, to the simulator. The simulator knows the capillary pressure for each cell and simply determines the water saturation from the table.
Capillary pressure measurements taken in the laboratory are usually not used to specify the initial water saturation distribution in the reservoir. Instead, initial values of water saturation are derived from logs and specified to the simulator. This data is referred to as Pseudo Capillary Pressure data.
Oil Water Contact
Permeability and Transmissibilities
A transmissibility must be calculated for each flow face in order to determine the flow of fluids between cells. By default, most simulators use what is referred to as a five point finite difference scheme. The five points refer to a cell and the four cells surrounding it, in the horizontal plane. In other words, there is no diagonal flow considered by the simulator. Some simulators have what is referred to as a nine point finite difference scheme which, in its most rigorous form, does consider diagonal flow in the horizontal plane. In a five point finite difference scheme, flow is allowed between a cell, the four cells surrounding it in the horizontal plane, and the cells above and below it. Therefore, transmissibilities are required for each of the six faces of flow, for each cell.
Similarly, a transmissibility for fluid flow between each cell and the well must be determined to calculate flow in and out of each well. These transmissibilities are calculated in general as:
Values for permeability are assigned either from maps or specified using a correlation. In most cases the permeability in the x and y direction are specified to be the same, though most simulators will allow directional permeabilities. The permeability in the vertical direction is usually specified as the horizontal permeability times some factor. These values are used together with the net thickness and perforated thickness to calculate transmissibilities.
There are a variety of transmissibility calculations. These are discussed in Chapter 6 along with different formats for specifying this data.
It is actually the transmissibility that is important for each flow face, for each cell. Once all transmissibilities are determined, the permeability becomes unimportant.
.00707Kh
ln( )+
S
r
e
r
w
Permeability and Transmissibilities
A transmissibility must be calculated for each flow face in order to determine the flow of fluids between cells. By default, most simulators use what is referred to as a five point finite difference scheme. The five points refer to a cell and the four cells surrounding it, in the horizontal plane. In other words, there is no diagonal flow considered by the simulator. Some simulators have what is referred to as a nine point finite difference scheme which, in its most rigorous form, does consider diagonal flow in the horizontal plane. In a five point finite difference scheme, flow is allowed between a cell, the four cells surrounding it in the horizontal plane, and the cells above and below it. Therefore, transmissibilities are required for each of the six faces of flow, for each cell.
Similarly, a transmissibility for fluid flow between each cell and the well must be determined to calculate flow in and out of each well. These transmissibilities are calculated in general as:
Values for permeability are assigned either from maps or specified using a correlation. In most cases the permeability in the x and y direction are specified to be the same, though most simulators will allow directional permeabilities. The permeability in the vertical direction is usually specified as the horizontal permeability times some factor. These values are used together with the net thickness and perforated thickness to calculate transmissibilities.
There are a variety of transmissibility calculations. These are discussed in Chapter 6 along with different formats for specifying this data.
It is actually the transmissibility that is important for each flow face, for each cell. Once all transmissibilities are determined, the permeability becomes unimportant.
.00707Kh
ln( )+
S
r
e
r
w
VALIDACION DEL MODELO
Para VALIDAR adecuadamente el Modelo de Reservorios debemos mantener en la mente siempre :
El ajuste de Historia no deberá nunca ser logrado a expensas de modificar parámetros que son físicamente y/o geológicamente errados.
*
Que es ajuste de Historia?
*
Por que ajustar la Historia ?
*
Datos de producción
Distribución de saturación (pozos, de 4D ), …
*
Que parámetros son cambiados para lograr un ajuste de historia?
Permeabilidad (distribución espacial)
Porosidad (volumen poral)
Fallas (transmisibilidad, ubicación)
Otros ????
*
Consideraciones Importantes para hacer predicciones
Los casos de predicciones nunca deben exceder las capacidades del modelo de simulación.
Las predicciones necesitan ser consistentes con las practicas de campo.
Cas siempre la simulación trae consigo una solución no única con incertidumbres inherentes de:
Falta de validación. Ej Reservorios con datos escasos de geología e ingeniería.
*
R1
I1
VAN1
R2
I2
VAN2
R3
I3
VAN3
Simulators and Models
Through the years, many engineers have referred to simulators and models as though they were the same, which is not true, and can cause confusion. A simulator is a program, generally written in fortran, that is typically leased from one of the major vendors, such as GEOQUEST RESERVOIR TECHNOLOGIES. A model is a set of data used to describe a reservoir, its fluids, wells, etc.
(
)
(
)
(
)
(
)
(
)
...
'
'
'
!
Predictive cases, for different total field injection rates
0
2,000
4,000
6,000
8,000
10,000
12,000
14,000
16,000
18,000
20,000
Dec-95
Dec-97
Dec-99
Dec-01
Dec-03
Dec-05
Dec-07
Dec-09
Dec-11
Dec-13
Dec-15
Dec-17
Dec-19
Dec-21
Dec-23
Dec-25
Oil rate -- 200M BWID, delay until 2007
5000 BOPD economic limit
Un modelo es un conjunto de datos que describen un reservorio
Profundidad, dimensiones, porosidad, espesor, permeabilidad
Densidad de fluidos, viscosidad, solubilidad gas, factores de volumen
Presión de reservorio, presión capilar, permeabilidades relativas
Un simulador es un programa que calcula la distribución de presión y saturación de un reservorio, como función de tiempo.
SIMULADOR VERSUS MODELO DE RESERVORIO
*
Simulators and Models
Through the years, many engineers have referred to simulators and models as though they were the same, which is not true, and can cause confusion. A simulator is a program, generally written in fortran, that is typically leased from one of the major vendors, such as GEOQUEST RESERVOIR TECHNOLOGIES. A model is a set of data used to describe a reservoir, its fluids, wells, etc.
During this course we will be building a model using data provided by the instructor. ECLIPSE 100 is the simulator (or program) we will be using to do this work.
Seferino Yesquen
Simulación de reservorios.- Uso de modelos matemáticos para simular el comportamiento de un reservorio real
INPUT
Calidad de un estudio de simulación = f ( datos ingreso, modelo, simulador )
Ec. de continuidad ( E B M ).
Ec. de flujo de fluidos ( Darcy ).
Ec. de estado. = f (p)
Simulador
OUTPUT
*
Ecuacion de la difusividad, es la combinacion de las principales ecuaciones que describen el proceso fisico del movimiento de fluido dentro del reservorio, convina:
La EBM (continuidad) se basa en la ley de conservación de la materia, que establece que la masa de un sistema cerrado permanece sirmpre constante. La EBM establece que la diferencia entre la cantidad de fluidos iniciales en el yac. Y la cantidad de fluidos remanentes es igual a la cantidad de fluidos producidos.
Para la aplicación del BM se toma en cuenta algunas consideraciones importantes:
Volumen poroso es constante, no existe compactacion ni subcidencia.
El PVT es representativo del yac.
Proceso isotermico
Cw y Cf son despreiables
Se considera equilibrio termodinamico entre entre el gas y el petroleo a presion y temperatura de yac.
(Ecuacion de flujo) La unidad mas comun de la permeabilidad es el Darcy, el cual esta definido como el flujo Q en cm3/s resultante cuando la caida de presion es de 1 atm, aplicada a un lecho de 1cm2 de are transversal A de 1 cm de largo y para un fluido de viscosidad 1Cp
Ecuacion de estado (compresibilidad), describe la relacion volumen-presion o presion – densidad para los fluidos presentes.
Para cada momento, estas tres ecuaciones son combinadas en una unica ecuacion diferencial parcial, luego escritas como ec. Difrenciales finitas, es decir que el yacimiento es visto como una sucesion de bloques y la produccion es dividida en espacios de tiempo, osea discretizar el problema en tiempo y espacio.
Seferino Yesquen
Es necesario DISCRETIZAR las variables espacio y tiempo.
Discretización Espacio : División del reservorio en pequeñas distancias;
z
x
y
Distancia
Es necesario DISCRETIZAR las variables espacio y tiempo.
Discretización Tiempo : División. de historia de producción en intervalos de tiempo
Tiempo
Discretización de las ecuaciones de flujo
Primero la coordenada en X deberá ser dividido en un numero discreto de bloques. Considerando un sistema poroso horizontal en una dimensión, se tiene un sistema de N grid blocks, cada uno de longitud Dx:
Esto es llamado un grid de block centrado, y las propiedades promedios de reservorio se refieren al punto medio del bloque.
1
N
i-1
i
Aproximación por Serie de Taylor
*
Método de Modelaje con diferencias finitas
Se resuelven las ecuaciones par cada celda (grid block) por métodos numéricos para obtener los cambios de PRESION y SATURACION con el TIEMPO
La exactitud de los datos de entrada
Impacta la exactitud de los cálculos del simulador
La ecuación de Difusividad (1 Fase, flujo 1D)
*
1.-
Matrices
In order to solve the mass balance equation for each grid cell, all cells have to be solved at the same time. The reason for this is that in order to determine the flow of fluids into and out of a cell, you need to know what is going on in the surrounding cells. In other words, there has to be consistency between cells. To solve several equations at the same time, it is convenient to use matrices.
Seferino Yesquen
Consideraciones
Metodología de modelado
Recursos:
Cantidad y Calidad
Los resultados deberán estar asociados a una “banda de incertidumbre”
*
Ejemplos de Metas de Estudios en Campos Nuevos
Definir limites internos y externos del reservorio.
Definir net pay, volumen & reservas
Determinar numero optimo de locaciones y configuración de pozos
Optimizar el timing y tamaño de las facilidades de producción
Estimar el potencial de recuperación.
Anticipar la producción futura de fluidos y cambio operacionales.
Determinar los caudales críticos para conning de agua gas.
CLARIDAD DEL PROPOSITO
Ejemplos de Metas de Estudios en Campos Maduros
Monitorear el movimiento de los contactos de fluidos
Evaluar y seguir la productividad de los pozos
Evaluar el comportamiento histórico. Determinar tendencias y anomalías.
Determinar la fuente de la producción de agua y gas. Identificar pozos potenciales para workover.
Monitorear barrido del reservorio. Localizar petróleo by paseado. Perforación infill
Estimar beneficios de procesos de recuperación secundaria y EOR:
Determinar conectividad entre reservorios múltiples.
Cuantificar migración a través de los limites del contrato.
*
Transformación de Datos
Caracterización Geológica
La descripción Geológica deberá identificar los factores claves que afectan el flujo de fluidos en el reservorio.
*
Etapa 2: Caracterización del reservorio
La caracterización de los fluidos define las propiedades físicas de las mezclas de los fluidos en el reservorio y como pueden variar con cambios de P, T y V.
Clasificar el tipo de fluido
Determinar las propiedades de los fluidos.
Describir los mecanismos de producción del reservorio.
Caracterización de los fluidos
Etapa 2: Caracterización del reservorio
El modelo Petro físico define donde están localizados los volúmenes de petróleo, gas y agua, así como es el comportamiento de estos fluidos en la presencia de diferentes tipos de rocas.
Mojabilidad de la roca
SELECCIÓN DEL MODELO
Determine La Dimensionalidad
Use modelos 1D para flujos lineales o radiales en una dirección.
Use modelos 2D para flujos en dos direcciones: Cross sections
*
CONSTRUCCION DEL MODELO
Convirtiendo el Modelo de la Tierra en un Modelo de Simulación.
Control de Calidad de errores y problemas del modelo geológico.
Scalar el modelo
Hacer un Output del modelo en formato del simulador
*
Equilibrar el modelo
AJUSTAR LA HISTORIA
Calibrar el Modelo
Seferino Yesquen
Datos Requeridos
A fin de realizar balance de materia en cada grid block, el simulador necesita saber:
La presión y saturación inicial de cada grid block
La transmisibilidad para el flujo en las direcciones X, Y Z
La producción o inyección de cada grid block
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Data Requirements
In order to perform a mass balance on each cell, the simulator needs to be able to determine the initial mass of oil, water and gas that exists in each grid block and also be able to determine how much fluid flows in or out of each block.
The initial mass of each fluid is determined from the dimensions, net thickness and porosity of each block, the initial saturation of each fluid within the block, and the fluid density. The fluid densities are determined from PVT data required for each fluid present in the reservoir. The initial saturations are determine from the depth of each block relative to the fluid contacts, relative permeability endpoints, and capillary pressure data.
The flow of fluids in a simulator can be described in general as:
q = T l DF
Here you have a flow rate equal to a transmissibility*mobility*driving force.
The driving force in our case is the potential drop either between two cells or a cell and the well. The initial pressure of each block is determined from the initial pressure at datum, the depth of each block, and initial reservoir fluid gradients. The gradients are determined from the PVT data specified for each fluid initially present in the reservoir.
K
A
L
Volumen de roca = DX*DY*DZ
El punto medio de la celda puede ser calculado
Punto medio = Prof. Tope + DZ/2
Volumen de roca y profundidad de los puntos medios
Dx
Dy
Dz
Bulk Volume and Midpoint Depth
The dimensions and top depth of each grid cell are required by the simulator. The Areal dimension of each cell is taken from the simulation grid. The vertical dimension of each cell is actually the gross thickness assigned from gross thickness maps. The top depth of each grid cell can be assigned from structure maps for each model layer, however, where applicable, most simulators will allow the user to specify the top depth of the reservoir for the first model layer and the simulator will determine the depth of each grid block from the top of the reservoir and gross thickness values.
From these data, the simulator is able to determine the bulk volume of each cell and the midpoint depth of each cell. The cell is actually represented vertically by this mid-cell depth to determine the initial pressure of the block and the angle and distance of flow from one cell to another. Therefore, if this value is incorrect, its effect with regard to these calculations needs to be considered.
Seferino Yesquen
Valores de porosidad, relacion Net-to-gross y espesor neto son asignados a cada celda de los mapas.
EL volumen poral es calculado :
VOLUMEN PORAL: DX*DY*DZ*NTG*PORO
VOLUMEN PORAL
Volumen Poral
Pore Volumes
The porosity and net thickness or net to gross are specified by the user for each grid cell. These values are taken from maps created for each model layer and are used to determine the initial pore volume and, subsequently, initial volumes of oil, water, and gas in each cell. As a result, the net thickness includes all sand that contains fluid expected to add pressure support, regardless of the type of fluid that initially exists in the sand.
It is actually the pore volume that is needed by the simulator. After the pore volume for each cell has been determined, the porosity becomes unimportant.
The net thickness or net to gross values will also be used to determine the net sand thickness used in flow calculations from one cell to another.
Seferino Yesquen
La permeabilidad para cada celda es especificada ya sea de mapas o de correlaciones
La transmisibilidad para cada cara de flujo puede ser calculada.
Transmisibilidad = K A / L
Permeability and Transmissibilities
A transmissibility must be calculated for each flow face in order to determine the flow of fluids between cells. By default, most simulators use what is referred to as a five point finite difference scheme. The five points refer to a cell and the four cells surrounding it, in the horizontal plane. In other words, there is no diagonal flow considered by the simulator. Some simulators have what is referred to as a nine point finite difference scheme which, in its most rigorous form, does consider diagonal flow in the horizontal plane. In a five point finite difference scheme, flow is allowed between a cell, the four cells surrounding it in the horizontal plane, and the cells above and below it. Therefore, transmissibilities are required for each of the six faces of flow, for each cell.
Similarly, a transmissibility for fluid flow between each cell and the well must be determined to calculate flow in and out of each well. These transmissibilities are calculated in general as:
Values for permeability are assigned either from maps or specified using a correlation. In most cases the permeability in the x and y direction are specified to be the same, though most simulators will allow directional permeabilities. The permeability in the vertical direction is usually specified as the horizontal permeability times some factor. These values are used together with the net thickness and perforated thickness to calculate transmissibilities.
There are a variety of transmissibility calculations. These are discussed in Chapter 6 along with different formats for specifying this data.
It is actually the transmissibility that is important for each flow face, for each cell. Once all transmissibilities are determined, the permeability becomes unimportant.
.00707Kh
ln( )+
S
r
e
r
w
K
A
L
Parámetros de Equilibración
El nivel de referencia, presión a este nivel, y los contactos de fluidos son especificados
De estos datos, la presión de petróleo, agua y gas son tabuladas como función de la profundidad.
Estas tablas usan las gradientes de los fluidos tomadas de los datos PVT
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Equilibration Parameters
For most problems, the reservoir is initialized assuming that the reservoir is in equilibrium. Many problems can arise from poor initialization of pressures and saturations. It is therefore important that the initial pressures, saturations, and capillary pressures are consistent with each other.
Initial Pressures
The initial pressure for each grid cell is determined from the midpoint depth of the block, a datum depth, the initial pressure at datum, and the initial fluid gradients present in the reservoir. We have already seen how the midpoint depth of each block is determined. The initial pressure at datum is specified to the simulator along with the initial oil-water and gas-oil contacts. These parameters are generally referred to as Equilibration or Initialization parameters. The simulator uses this data to determine the initial pressure, for each phase, for each cell.
In ECLIPSE, tables of oil pressure, water pressure, and gas pressure are created as a function of depth. The range of depths is determined from the midpoint depths of each cell and the fluid contacts specified by the user. The pressure at each depth is calculated using the pressure at datum and the appropriate fluid gradients determined from the PVT data. The initial pressure for each cell is then determined from a table look-up process
OWC
P
i
h
Seferino Yesquen
Para celdas que no caen dentro de la zona de transición, las saturación inicial de agua y gas son determinadas de los endpoints de las curvas de permeabilidades relativas.
La saturación de petróleo es siempre determinada de 1-Sw-Sg
Fuera de la zona de transicion
Saturaciones Iniciales: So, Sw, Sg
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Initial Oil, Water, and Gas Saturations
The initial oil, water, and gas saturations are used to determine the initial volume of fluids in each cell. To rigorously determine these volumes we need to recognize that part of a cell may be in the transition zone and the cell may be cut by a fluid contact.
For those volumes of the cell that do not lie in the transition zone, the initial water and gas saturation are determined from the relative permeability endpoints. This is usually true for all simulators. The lowest water saturation value found in the table is usually assigned to those volumes above the oil-water contact. For volumes below the oil-water contact, in some simulators, the value of water saturation is automatically set to a value of 1.0, however, in ECLIPSE, the value is set to the highest water saturation found in the relative permeability table. Similarly for gas, the values of gas saturation for any volume below the gas-oil contact is set to the lowest value found in the relative permeability table. This value is usually 0.0. The value of gas saturation above the gas-oil contact is set to the highest values found in the table, usually 1-Swc. For those volumes of a cell that are in a transition zone, the saturation is determined from the capillary pressure table. The resulting water and gas saturations are then a pore volume average of the volumes in the transition zone and outside the transition zone. The oil saturation is always calculated as 1-Sw-Sg.
Initialization Runs
It is important for the user to check the initial volumes of oil, water, and gas calculated by the simulator. This is a first step, basic check of the reservoir data. In particular, the initial oil volume should be checked and compared to other estimates of the initial oil in place.
Gas
Oil
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En las zonas de transición, los valores iniciales de Sw y Sg son determinados de una tabla de presión capilar versus Sw ó Sg.
Las presiones capilares son calculadas como la diferencia entre las presiones de las fases.
Saturaciones Iniciales, So, Sw, Sg
En la zona de transición
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Capillary Pressures
In the simulator, capillary pressures are determined for each grid cell from the phase pressures. The oil-water capillary pressure is calculated as a difference between the oil and water phase pressures. Similarly, the gas-oil capillary pressure is a difference between the oil and gas phase pressures.
Capillary pressures are used to determine the initial fluid saturations for each cell, in the transition zone. A table of water saturation versus capillary pressure is specified by the user, to the simulator. The simulator knows the capillary pressure for each cell and simply determines the water saturation from the table.
Capillary pressure measurements taken in the laboratory are usually not used to specify the initial water saturation distribution in the reservoir. Instead, initial values of water saturation are derived from logs and specified to the simulator. This data is referred to as Pseudo Capillary Pressure data.
Oil Water Contact
Permeability and Transmissibilities
A transmissibility must be calculated for each flow face in order to determine the flow of fluids between cells. By default, most simulators use what is referred to as a five point finite difference scheme. The five points refer to a cell and the four cells surrounding it, in the horizontal plane. In other words, there is no diagonal flow considered by the simulator. Some simulators have what is referred to as a nine point finite difference scheme which, in its most rigorous form, does consider diagonal flow in the horizontal plane. In a five point finite difference scheme, flow is allowed between a cell, the four cells surrounding it in the horizontal plane, and the cells above and below it. Therefore, transmissibilities are required for each of the six faces of flow, for each cell.
Similarly, a transmissibility for fluid flow between each cell and the well must be determined to calculate flow in and out of each well. These transmissibilities are calculated in general as:
Values for permeability are assigned either from maps or specified using a correlation. In most cases the permeability in the x and y direction are specified to be the same, though most simulators will allow directional permeabilities. The permeability in the vertical direction is usually specified as the horizontal permeability times some factor. These values are used together with the net thickness and perforated thickness to calculate transmissibilities.
There are a variety of transmissibility calculations. These are discussed in Chapter 6 along with different formats for specifying this data.
It is actually the transmissibility that is important for each flow face, for each cell. Once all transmissibilities are determined, the permeability becomes unimportant.
.00707Kh
ln( )+
S
r
e
r
w
Permeability and Transmissibilities
A transmissibility must be calculated for each flow face in order to determine the flow of fluids between cells. By default, most simulators use what is referred to as a five point finite difference scheme. The five points refer to a cell and the four cells surrounding it, in the horizontal plane. In other words, there is no diagonal flow considered by the simulator. Some simulators have what is referred to as a nine point finite difference scheme which, in its most rigorous form, does consider diagonal flow in the horizontal plane. In a five point finite difference scheme, flow is allowed between a cell, the four cells surrounding it in the horizontal plane, and the cells above and below it. Therefore, transmissibilities are required for each of the six faces of flow, for each cell.
Similarly, a transmissibility for fluid flow between each cell and the well must be determined to calculate flow in and out of each well. These transmissibilities are calculated in general as:
Values for permeability are assigned either from maps or specified using a correlation. In most cases the permeability in the x and y direction are specified to be the same, though most simulators will allow directional permeabilities. The permeability in the vertical direction is usually specified as the horizontal permeability times some factor. These values are used together with the net thickness and perforated thickness to calculate transmissibilities.
There are a variety of transmissibility calculations. These are discussed in Chapter 6 along with different formats for specifying this data.
It is actually the transmissibility that is important for each flow face, for each cell. Once all transmissibilities are determined, the permeability becomes unimportant.
.00707Kh
ln( )+
S
r
e
r
w
VALIDACION DEL MODELO
Para VALIDAR adecuadamente el Modelo de Reservorios debemos mantener en la mente siempre :
El ajuste de Historia no deberá nunca ser logrado a expensas de modificar parámetros que son físicamente y/o geológicamente errados.
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Que es ajuste de Historia?
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Por que ajustar la Historia ?
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Datos de producción
Distribución de saturación (pozos, de 4D ), …
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Que parámetros son cambiados para lograr un ajuste de historia?
Permeabilidad (distribución espacial)
Porosidad (volumen poral)
Fallas (transmisibilidad, ubicación)
Otros ????
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Consideraciones Importantes para hacer predicciones
Los casos de predicciones nunca deben exceder las capacidades del modelo de simulación.
Las predicciones necesitan ser consistentes con las practicas de campo.
Cas siempre la simulación trae consigo una solución no única con incertidumbres inherentes de:
Falta de validación. Ej Reservorios con datos escasos de geología e ingeniería.
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R1
I1
VAN1
R2
I2
VAN2
R3
I3
VAN3
Simulators and Models
Through the years, many engineers have referred to simulators and models as though they were the same, which is not true, and can cause confusion. A simulator is a program, generally written in fortran, that is typically leased from one of the major vendors, such as GEOQUEST RESERVOIR TECHNOLOGIES. A model is a set of data used to describe a reservoir, its fluids, wells, etc.
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Predictive cases, for different total field injection rates
0
2,000
4,000
6,000
8,000
10,000
12,000
14,000
16,000
18,000
20,000
Dec-95
Dec-97
Dec-99
Dec-01
Dec-03
Dec-05
Dec-07
Dec-09
Dec-11
Dec-13
Dec-15
Dec-17
Dec-19
Dec-21
Dec-23
Dec-25
Oil rate -- 200M BWID, delay until 2007
5000 BOPD economic limit