transporte de np en medio poroso

8/12/2019 Transporte de NP en Medio Poroso

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Powder Technology 192 (2009) 195202

Contents lists available at ScienceDirect

Powder Technology

journal homepage: www. el sevier. com/l oca te/ powtec

Experimental study and mathematical model of nanoparticle transport in porous

media

Binshan Ju , Tailiang Fan

School of Energy Resources, Key Laboratory of Marine Reservoir Evolution and Hydrocarbon Accumulation Mechanism, Ministry of Education, China University of Geosciences (Beijing), Beijing

100083, China

a r t i c l e i n f o

Article history:Received 22 August 2008Received in revised form 7 November 2008

Accepted 22 December 2008Available online 7 January 2009

Keywords:NanoparticleOil recoveryWater injectionPorous mediaMathematical model

a b s t r a c t

Two types of polysilicon nanoparticles (PN) were used in oil fields to improve oil recovery and enhance water injection

respectively in this work. The physical properties of the nanoparticles were studied experimentally, and pore characteristics of

sandstone were investigated by mercury injection experiments. The adsorption experiments of lipophobic and hydrophilic

polysilicon nanoparticles (LHPN) were conducted to testify wettability change (from oil wetting to water wetting) of

sandstone surface, and the nanoparticles attached to pore walls were observed bya transmission electron microscope (TEM). A

mathematical model to describe the nanoparticles transport carried by two-phase flow in random porous media was presented

and a numerical simulator was developed to simulate two application examples of the nanoparticles in oil fields. An important

discovery is that water-phase permeabilities of these sandstones increase from 1.6 to 2.1 times of their original values.

However, there are decreases in their absolute permeabilities because of nanoparticle adsorption on pore surfaces and

nanoparticle capture at pore throats. The important parameters such as the distributions of porosities and permeabilities, the

changes in water injection capability and oil recovery are obtained successfully by numerical simulation approach.

Furthermore, the permeabilities obtained from numerical simulation have a good match with experimental data. The

conclusion that polysilicon nanoparticles are effective agents for enhancing water injection capability or improving oil

recovery can be safely drawn.

2009 Elsevier B.V. All rights reserved.

1. Introduction

Nanometer particles have many special physical effects [1]and they can

be made in different ways [25]. Their applications in chemicals, metallurgy,

ceramics, medicines and other fields have been reported frequently in recent

years. Ding and Wen [6]presented a theoretical model for predicting particle

concentration and velocity fields of nanofluids flowing through a pipe. By

contrast, the flow paths in random porous media look like network

interconnected by pore throats and pore bodies. The sandstone in oil

formation can be regarded as a kind of complicated random porous media and

the transport process of nanoparticles carried by fluids in sandstone belongs to

multiphase flow.

As far as it goes, only few papers address the issues of the application ofnanopowders in oilfields to enhance water injection by virtue of changing the

wettability of reservoir rock through their adsorption on porous walls of

sandstones. Ju and Dai [7] reported that one nanometer-scale polysilicon

material could change the wettability of porous surfaces of sandstone and

consequently have effects on the flows of water and oil in oil formation when

the suspension of the nanoparticles is injected into an oil reservoir. There are

only few papers [811]dealing with mathematical modeling of fine particles

migration in formation;

Corresponding author.

E-mail address:[email protected](B. Ju).

0032-5910/$see front matter 2009 Elsevier B.V. All rights reserved.

doi:10.1016/j.powtec.2008.12.017

however, none of which deals with the migration and adsorption of

nanometer-scale materials in porous media.During PN transport in porous media, there is a mass exchange between

the PN on pore framework and the PN in fluids by adhering to pore walls,

detaching from pore walls and blocking at pore throats. In addition, the

covering of PN on pore walls will change the wettability of pore surfaces. To

understand the PN transport behaviors in random porous media, theoretical

and experimental approaches were used in the present investigation and a

mathematical model for predicting PN transport performances and its effects

on two-phase flow behaviors was developed. Two examples, enhancing water

injection capacity of low permeability reservoirs and improving oil recovery

of high permeability reservoirs, were also studied by numerical simulation

approach on the simulator developed in current work.

2. Experimental studies on physical properties of the nanoparticles, random

porous media and flowability with HLPN treatment

2.1. Physical properties of the polysilicon nanoparticles

The PN in this study is a kind of modified ultra-fine powder (see Fig. 1),

which is made from SiO2and an additive. The shape of ananoparticle looks

like an approximate sphere when observed under a TEM and the particle

diameters are from 10 to 500 nm (see Fig. 2).


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196 B. Ju, T. Fan / Powder Technology 192 (2009) 195202

Fig. 3. Particle size distribution curve.Fig. 1. The nanopower in a beaker.

Fig. 3 indicates that the sizes of the particles have a quasi-Gaussian

distribution. The bulk density of the nanopowder is 0.056 g/cm3. According

to wettability of the surface of the polysilicon nanoparticles, they can be

classified into two types: lipophobic and hydrophilic polysilicon nanoparticle

(LHPN) and hydrophobic and lipophilic polysilicon nanoparticle (HLPN).

2.2. Physical properties of random porous media (sandstone)

Sandstone oil and gas reservoir is one major type of reservoirs discovered

by the petroleum companies in the world. Therefore sandstone was selected to

be as an example of random porous media. As we know, sandstone,

composed of grains of different sizes, is porous media deposited under the

combination of consolidation and compaction through a long geological

period. Sandstone contains voids dispersed in a solid matrix and it can be

considered equivalent to a system in which the solid particles and void phases

are randomly dispersed in such a way that both phases form continuous

conducting paths through the medium. Void space is generally known as the

pore space as it is known to consist of randomly distribution pores of various

shapes and sizes. The void spaces in sandstone can be divided into pore

throats (the narrowest segments of pores) and pore chambers (the widestsegments of pores). The sizes of pore throats in sandstone are from 0.5 to 5.0

m, and the size of pore chamber is from 5.0 to 50.0 m [12,13].

In the laboratory, the physical properties of sandstone cores, obtained

from the drilling wells in H.Z.J oil field, China, are studied by mercury

injection experiments. The main data of the sandstone cores used in these

experiments are shown in Table 1. The data obtained by mercury injection

experiments are shown in Fig. 4. It indicates that the radii of most pores fall in

the range of 0.4 to 10 m. The pores of radii less than 0.4 m have little

contribution for mercury permeation.

Fig. 2. The images of polysilicon nanoparticles observed under TEM.

2.3. Experimental studies on the effects of nanoparticles on the physical

properties of the porous media

The experimental data from the above section show that the sizes of

polysilicon particles are from 10100 to 5.010

2 nm, and pore radii of

sandstone are in the range of 6.010

0

6.310

4

nm. In the process of thenanoparticle transport with flow in porous media, a particle larger than a pore

throat may block at the pore throat. Two or more than two particles that sizes

are slightly less than a pore throat may bridge at the pore throat. If the sizes of

particles are far less than pore sizes, the nanoparticles can be adhered to the

pore walls. The theoretical analysis of adsorption is given in the Ref. [7].

Generally, the wettability of polysilicon particles and the wettability of

sandstone pore walls are different. Therefore, the adsorption of polysilicon on

sandstone pore walls leads to wettability change of pore walls. The following

experiments were conducted to study the effects of polysilicon nanoparticles

on the physical properties of the porous media.

2.4. Macroscopic experiment on wettability change

In order to study the wettability change of sandstone surface, themeasurement of wetting angles was conducted. First, a rock slice sawed froma block of sandstone was furbished on ultra-fine sand paper; then, a drop of

water was placed on the rock slice surface and the wetting angle ( 1) wasmeasured; finally, the rock slice was immersed in an aqueous LHPN solution

for 2 h and the wetting angle (2) was measured. Fig. 5(a) indicates that the

wetting angle (1) is much larger than /2, while (b) shows that the wetting

angle (2) after LHPN treatment becomes much smaller than /2. The changein wetting angles indicates the wettability of surface of reservoir rock can bechanged from oil-wet to water-wet by adsorbing LHPN. The image (c) of

wetting angle (3) of the rock immerged in pure water for 2 h shows that 3is

slightly higher than /2. It indicates that the wettability in this case is weakoil-wetting.

2.5. Microscopic adsorption observation under a TEM

Two furbished slices from an oil-wet sand core were first extracted with

benzene, then, one was directly observed under a TEM, the other was

observed under a TEM after it was dipped in an aqueous LHPN solution for 2

h. Fig. 6(a) is an image of sandstone surface without adsorbing LHPN. Fig. 6

(b) shows that the adsorbed LHPN looks like a layer of white frost.

2.6. Experimental study on flowability with HLPN treatment

Dynamic core displacements were conducted to study the fluid flowability

in porous media after treatment with HLPN under the reservoir temperature

and pressure.


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B. Ju, T. Fan / Powder Technology 192 (2009) 195202 197

Table 1The parameters of sandstone cores.

Sandstone core name Depthaof core, m Length of Rock density, Diameter of Porosity,% Permeability, Sedimentarysandstone core, cm g/cm3 sandstone core, cm 103m2 microfacies

RC3-1 2271.9 2.20 2.15 2.496 21.40 352.1 River channel faceSS6-1 2365.1 2.40 2.04 2.495 25.12 150.5 Sand sheet faceDB4-1 2374.4 2.42 2.00 2.495 22.25 79.3 Distal Bar faceaThe depth of core is the location of the core before it was drilled. For instance, RC3-1 core was buried underground 2271.9 m from well head before it was drilled.

The displacement routine for each core is listed in the following steps:

(1) Heat the core holder with core sample up to a constant temperature of

80 C.

(2) Flooded by diesel oil until the flow rate reaches at a constant and the

outflow shows no water.

(3) Flooded by brine until the flow rate reaches at a constant and

the outflow shows no hydrocarbon, then record overall differential

pressure, Pi(=PinPout) and flow rate qiw(ml/s).

(4) Flooded by the suspension of HLPN in diesel oil until 10 pore volumes

(PV) of the suspension pass the core.

(5) Flooded by brine again until the flow rate reaches at a constant

and the outflow shows no diesel oil, then record overall differential

pressure, P (=PinPout) and flow rate qw(ml/s).

As we know, the formation near the wellbore is very important where thepressure drop of the oil-field mainly depletes [6]. The mobile oil in thevicinity of injection well has been displaced by water, so the flow in the poresof the reservoir rock around wellbore can be regarded as single-phase flow.Therefore, the water injectability can be evaluated by comparing the effective

perme-ability of water, Kwb, (= KKrwb), before HLPN treatment, with the

effective permeability of water, Kwa(= KKrwa) after the treatment as long as

the maximum water saturation is reached (only water phase flow). Theeffective permeability of water can be calculated by Darcy's law on condition

that the length (L), cross-sectional area (A) of a core, viscosity of water ( w),

overall differential pressure ( P) and injection rate (qw) are measured.

Kw=q

Aww

PL

:

The parameters of rock cores and experimental results are shown in Table

2. The data inTable 2 show that the effective permeabilities of water after

HLPN flooding are improved 1.6272.136 times for the four cores.

3. Mathematical model to describe the nanoparticle transport process in

random porous media

3.1. Assumptions

The model simulating two-phase displacement is based on the following

assumptions:

(1) The flow is one-dimensional under isothermal condition. The rock and

fluids are supposed to be incompressible.

(2) The porous media is heterogeneous.

(3) The oil and water flows in porous media follow Darcy's law and the

gravity force is neglected.

(4) The nanoparticles are discretized into n size intervals.(5) The viscosity and density of the fluids are constant and oil and water

are Newtonian fluids.

3.2.Transport of fluids in porous media

Since the flows of oil and water in porous media follow Darcy's law, the

continuity equations of oil (o) and water (w) phases for incompressible

Newtonian flow are given by the following equation:

A K P_Sl _ l _= 0 ;l = o;w; 1At x

l

where x is the distance from the inlet of the sand core, t is time, is the

porosity of the porous media, Sl, l and Pl are saturation, viscosity, and

pressure of phase l, respectively, and Kl(=Krl) is the effective permeability ofphase l. The expression [14]for capillary force is

Pc= PoPw= a + bsw=1 + csw; 2

where a, b and c are empirical parameters. swis water saturation.

Fig. 4. Mercury saturation histogram and cumulative permeability contribution curve.


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Fig. 5. Wettability change of sandstone after absorbing LHPN.

3.3. Transport of PN in porous media

Since PN have wettabilities, LHPN exist in the water, and HLPN exist in

the oil phase. Inasmuch as the sizes of PN are in the range of 10 to 500 nm,

Brownian diffusion should be considered. Thus, the continuity equation for

size interval i of PN can be expressed as

AC AC C

_li;l

+ _Sli;l

_

l i;li;l

+ Ri;l= 0; 3Ax At x

x

where i =1,2n.The initial and boundary conditions, respectively, for Eq. (3) are given by

Ci;l= 0;t = 0; 4

Ci;l

=

Ci;l;in

;

x

= 0; 5

where Ci,lis the volume concentration of PN in interval i in phase l, D i,lis the

dispersion coefficient of PN in size interval i in phase l, Ri,lis the net rate of

loss of PN in interval i in phase l, and C i,in is the con-centration of theinterval i of PN in the injected fluids.

3.4. Net loss rate of PN in transport process

The pore spaces in sandstone mainly consist of interconnected pore bodies

and pore throats. For the PN transport carried by fluid stream in the porousmedia, two types of particle retention in the pores may occur: deposition on

pore surfaces and blockage in pore throats. For the retained particles on pore

surfaces, they may desorb for hydrodynamic forces, and then possibly adsorb

on other sites of the pore bodies or get entrapped at other pore throats. By

modifying the Ju and Dai's model [7], Ri,lin Eq. (3) is given by

Ri;l

=

Ai;l

+

Ai;l

; 6At Atwhere i,lis the volume of PN i in contact with phase l available on the pore

surfaces per unit bulk volume of sandstone, i,l is the volume of PN i

entrapped in pore throats from phase l per unit bulk volume of sandstone dueto plugging and bridging.

According to Gruesbeck and Collins [15], there exists a critical velocity

for surface deposition, below which only particle retention occurs and above

which retention and entrainment of PN particles take place simultaneously. A

modified Gruesbeck and Collins's model for the surface deposition is

expressed byA

i;l

d i l

ul

Ci l ;when ulbulc

=_

d;i;;lu

;lCi;l

; e;i;li;lul ulc ;when ulNulc : 7At

The initial condition for Eq. (7) is

i;l= 0;t= 0: 8In Eq. (7), d,i,l and e,i,l are rate coefficients for surface retention and

entrainment respectively of PN in interval i in the phase l, and u lc is the

critical velocity for the phase l to entrain particles.

The rate equation for the entrapment of the particles in interval i in pore

throats in phase l can be written as

Ai;l=

pt;i;l

ul

Ci;l

; 9At

where p,i,lis a constant for pore throat blocking. The initial condition for Eq.

(9) is

i;l= 0;t= 0: 103.5. Change of porosity and absolute permeability

Both PN deposition on the pore surfaces and blocking in pore throats may

lead to the reduction in porosity and permeability. The instantaneous porosity

is expressed by

_= _0_; 11

where denotes the variation of porosity by release and retention of PN inthe porous media, and it is expressed by

_

=

i;l+

i;l

: 12

According to Ju and Dai's model [7], the expression for the instantaneous

permeability due to the deposition and blocking of particles can thus be

written as

K = K0 1f kf+ f _=_0&n; 13

where K0 and 0 are initial permeability and porosity, K and are

instantaneous local permeability and porosity of the porous media, kf is a

constant for fluid seepage allowed by the plugged pores, and f is the fractionof the original cross-sectional area open to flow.

3.6. Evaluation of relative permeability

As we know, the wettability of pore surfaces is the most important factor

to determine the relative permeability of a porous media. The PN retention in

porous media may induce wettability changes and the shape of relative

permeability curve can also be changed. If Vi,lis the

Fig. 6. TEM images of the sandstone surfaces.


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Table 2Parameters of cores and experimental results.

The core Cross-sectional Length of The effective The effective wa wbame area, A, cm2 core, L, cm permeability permeability

measured before measured afterHLPN flooding, HLPN flooding,Kwb, 10

3m

2 Kwa103m2N1 4.91 7.91 4.434 9.471 2.136M1 4.91 7.23 2.133 4.212 1.975M2 4.91 7.62 4.345 8.783 2.021M3 4.91 7.14 1.162 1.891 1.627

size interval i entrapped in pores, the total PN retention volume satis fies the

following equation:

nV = Vi;l: 14

i = 1;l = w;o

Supposing the spherical particles in size interval i touching each other in

the form of point contact and using the real volume of particles as the

denominator, the specific area of the particles in size interval i can be defined

asAt n

3d2 6

sbi= =i i

= : 15V 61ni3di3 diSupposing i,lis the PN volume in interval i adsorbed on the pore

surfaces and is the volume of PN in interval i entrapped in porei,l

throats per unit bulk volume of the porous media. PN adhered to the pore

walls first spread as a single layer, the surface area for particles in interval i is

given by

si=_

i;l+ i;l

_

sbi: 16The total surface area in contact with fluids for all the size intervals of PN

per unit bulk volume of the porous media is calculated by

n n6

s = si= i;l+i;l

_

;

17

i = 1 i = 1;l = w;o_

diwhere is the surface area coefficient. The specific area of a sand core can be

calculated by the following empirical equation [16],

_s= 7000_

rffiffiffiffiffi :

18K

We suppose that the relative permeabilities of water and oil phases are,

respectively, Krwj and Krojat a water saturation, Swj. When s s, the totalsurfaces per unit bulk volume of the porous media are

Table 3Parameters of HLPN used for numerical simulation.

HLPN Diameter HLPN d,i,l, e,i,l, p,i,l, i,l, ulc,composition of HLPN, concentration, cm cm cm cm s cm s

umber nm cm3/cm3C1 40 0.004 0.16 0.3 0.0128 0.00056 0.00046C2 50 0.0065 0.2 0.24 0.02 0.00036 0.00058C3 60 0.009 0.24 0.2 0.0288 0.00025 0.00069C4 70 0.01045 0.28 0.17143 0.0392 0.00018 0.00081C5 80 0.0075 0.32 0.15 0.0512 0.00014 0.00092C6 90 0.005 0.36 0.13333 0.0648 0.00011 0.00103C7 100 0.0035 0.4 0.12 0.08 0.00009 0.00115C8 150 0.002 0.6 0.08 0.18 0.00004 0.00172C9 200 0.00115 0.8 0.06 0.32 0.00002 0.0023C10

300

0.0009

1.2

0.04

0.72

0.00001

0.00345

Fig. 7. Concentration distribution of HLPN particles along the dimensionless distance at

different injection PV.

completely covered by PN adsorbed on pore body surfaces or entrapped in

pore throats, and wettability is determined by PN. However, when s bs, onlypart of the surfaces per unit bulk volume of the porous media is occupied byPN.

When the surfaces per unit bulk volume of the porous media arecompletely occupied by PN, the relative permeabilities of water and oil

phases are taken as Krwj and Kroj respectively; otherwise, the relative

permeabilities of water and oil phases are taken as a linear function of the

surfaces covered by PN, that is, when 0 bs bs, the relative permeabilities ofwater and oil are given by

Krwjp

V= Krwj+

Krwj

V

Krjw

s 19sand

KrojVKrowK

rojp

V= Kroj+ s: 20s

4. The solution method to mathematical model

The overall mathematical model is a nonlinear system that includes the

continuity equations of oil (o) and water (w) phases (Eq. (1)), the convectiondiffusionadsorption equation (Eq. (3)), and a series of auxiliary equations.

The finite-difference method is used for solving the nonlinear equation

system. In this work, the Implicit-Pressure/Explicit-Saturation (IMPES)

technique was used to solve the pressuresaturation equation (Eq. (1)) and an

explicit method was employed to solve the convection-diffusion-adsorption

equation (Eq. (3)). The solving procedures are: first, the pressure

distribution is obtained by solving the mass balance equation; then, the

velocity is calculated by Darcy's law; the PN concentration distribution in

interval i is obtained by solving the convectiondiffusionadsorption Eq. (3);

the new porosity , absolute permeability K, relative permeabilities of oil

and water phases for

Fig. 8. Porosity distribution along the dimensionless distance at different injection PV.


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Table 4Comparisons of permeabilities between experimental and numerical results.

Core name N101A N2B RZ1Before treatment, Kwb, 10

m Experiment 1.400 4.330 1.130

After treatment, Kwa, 103

m2Kwa/Kwb

Numericals 1.378 4.336 1.127Experiment 0.570 9.470 4.100Numericals 0.572 9.480 4.107Experiment 0.407 2.187 3.628Numericals 0.415 2.186 3.644

Fig. 9. Permeability distribution along the dimensionless distance at different injection PV.

each grid are calculated, and then return to the first step if maximum

simulated time is not reached.

5. Application examples and discussion

This section gives two examples concerning oil field development. Since

PN can adhere to sandstone pore walls and change the wettabilities of pore

walls, it can be used in oil field-development to enhance oil recovery. The first

example is that HLPN is used in a low permeability oil reservoir to enhance

water injection capacity. The second one is that LHPN is used in a high

permeability oil reservoir to improve oil recovery.

5.1. Examples 1: Enhancing water injection capacity of a well in a low

permeability reservoir

Water injection into a low permeability reservoir either for pressure

maintenance or for secondary oil recovery is very difficult for the following

conflicts. On one hand, injection rates must be low enough to prevent

formation damages from over pressuring and inducing unwanted fractures.

On the other hand, these rates must be high enough to make the costly fluid

injection process economic. Formation damages caused by clay minerals

(Illite, Kaolinite, Calcium montmorillonite and Sodium montmorillonite)

easily occur in low permeability reservoirs. Although some conventional

stimulations, such as hydraulic fracturing [17,18]and acidizing [19,20], are

used to improve the flow conductivity of low permeability reservoirs, the

stimulations may fail to acquire expected designation for geological

complexity. Wettability of reservoir rock pore walls can be changed into

hydrophobic by HLPN adsorption, which supplies a new approach to enhance

water injection capacity of wells in low permeability reservoirs.

Numerical simulation approach is also used in the present work to study

the transport performances of HLPN in porous media and its effects on

physical characteristics of sandstone. The parameters of

each composition of HLPN used for numerical simulation are shown in Table

3.Fig. 7 gives the distribution of dimensionless concentration of C1 of

HLPN from inlet (dimensionless distance is equal to 0.0) to outlet

(dimensionless distance is equal to 1.0) of the sand core at different injection

PV (1 PV is defined as the total porous volume of the simulation model at

initial time). It indicates that the wave of HLPN concentration travels toward

the outlet and the concentration curves become flatter and flatter with the

increasing injection PV.Figs. 8 and 9 show that both the ratios of porosity (/0) and theratios of

permeability (K/K0) decline with the increasing injection PV. For an injection

volume, the ratios of porosity and permeability are smaller at the vicinity of

inlet than those at the vicinity of outlet. The decrease in porosity andpermeability results from the HLPN adsorption on pore walls and capture inpore throats.

Fig. 10 indicates that water injection capability (Iw/Iw0 = KwKrw/

(KwoKrw0)) doesn't increases linearly with HLPN injection volume. The

water injection capability reaches maximum at injection volume of 1.8 PV, so

the 1.52.0 PV of injection with total concentration of 5 vol.% of HLPN is

recommended to enhance water injection capability for low permeability

oilfields. It is very difficult to measure porosity and permeability of each point

along a sand core by experimental approach; however, the average porosity of

a sand core can be obtained by experiments and the average permeability can

be calculated by Darcy's law when having experimental data. Numerical

results and experimental data are shown in Table 4.

5.2. Examples 2: Improving oil recovery of high permeability reservoirs

It is well known that the water-flood sweep efficiency in a slight water-

wetting reservoir is lower than that in a strong water-wetting one. Since

LHPN has an ability to increase the tendency of strong water-wetting by

adsorption of LHPN on porous surfaces, it can be used to improve oil

recovery in the oil fields flooded by water injection. The following simulation

example is conducted to predict production performance with injection

LHPN. The main parameters used the numerical simulation runs are shown in

Table 5.This example clearly shows how we can use LHPN to enhance oil

recovery. The one-dimensional numerical simulator developed in this work

was used to study flooding performances displaced by LHPN solution of 5.0

vol.%.Fig. 11 shows that the numerical results have good matches with

experimental data. Fig. 12indicates that permeability declines

Fig. 10. The relations between water injection capability (Iw/Iw0) and HLPN injectionvolume Iw/Iw0= KwKrw/(KwoKrw0).

Table 5Parameters for simulation.

Number of grid 40Grid size, dx/m 0.025Cross-sectional area/10

4m

2 5.100Original porosity, 0.254Original permeability/m

2 0.300Original saturation of oil 0.730Viscosity of reservoir oil/mPas 5.100Viscosity of injection water/mPas 0.515Injection rate of water/10

m s

1.500

Production rate of fluid / /10

8

m

3

s

1

1.500


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Fig. 11. The comparison of permeability ratios between experimental and numerical results.

(7) HLPN is suitable for enhancing water injection capacity for lowpermeability reservoirs, and LHPN can be used to improve oil

considerably in the vicinity of injection inlet. The mechanism of this recovery.kind of formation damage caused by LHPN injection is same as that

Nomenclaturecased by HLPN. Fig. 13shows that oil recovery has been improved to aA cross sectional area, m considerable extent from 52.2% to 69.8% after injection of 2.0 PV LHPN.a,b constants for capillary pressure correlations, PaThe recovery is improved 17.6%.c constants for capillary pressure correlationsThe simulation model is one-dimension, so the sweep efficiency is

Ci volume concentration of interval i of PN particles, m m almost up to 100%. In an oil reservoir, the sweep efficiency can be onlyup to 4060% due to heterogeneity and the existence of well pattern Di dispersion coefficient of interval i in oil phase, m s

dead area. Therefore, the recovery is approximately improved 7.04 to di diameter of interval i, m

10.56% in an oil reservoir. f flow efficiency factorK absolute permeability of porous media, m

6. Conclusion Kr relative permeability of porous mediaf constant for fluid seepage allowed by the plugged pores

(1) The experimental data show that the sizes of the nanoparticles in P pressure, Paq injection rate or production rate, m s this study are in the range of 10 to 500 nm, and the diameters ofRi volume changing rate of PN particles in interval i in thethe nanoparticles approximately follow a normal distribution.

(2) The mercury injection tests show that the pore radii of the water phase per unit bulk volume of the porous mediam m

s sandstone fall in the range of 6.06.310 4 nm.

S saturation(3) The change of wetting angles indicates that the wettability ofs total surface area in contact with fluids for all particles of PNsurface sandstone can be changed from oil-wet to water-wet by

per unit bulk volume of the porous media, m m

adsorbing LHPN.sv specific area of sand core, m m

(4) Microscopic adsorption tests imply that these nanoparticles canbe adsorbed on pore surfaces of sandstones and in turn reduce t time, s

u flow velocity, ms the pore radii.wc critical velocity for water phase, ms (5) An important discovery is the sandstones' effective permeabil-

ities of water increase from 1.6 to 2.1 times of their original V total volume of retention of PN per unit bulk volume of theporous media, m m

values in spite of the decease in their absolute permeabilities.i volume of particles i of PN available on pore surfaces per(6) The mathematical model presented in this paper is able to

simulate successfully the transport process of nanoparticles in unit bulk volume of the porous media, m m

i volume of particles i of PN entrapped in pore throats perrandom porous media, and numerical results have good matchwith experimental data. unit bulk volume of the porous media, m m

x distance, m rate constant, m surface area coefficient

porosity of porous media viscosity of fluid, Pas wetting angle

Subscripts0 initial valuec critical value or capillary pressured depositione entrainmentfe flow efficiencyi one compositionpt pore throat

Fig. 12. The distribution of permeability ratio by numerical simulating approach along o oildistance at different injection volume. w water

g. . e re at ons etween o recovery an n ect ng vo ume o .


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SI metric conversion factors1 cm 110 m1m 110 m1 nm 110 m1MPa 110 Pa

1 mPa 1103Pa

Acknowledgments

The authors would like to thank Prof. Zhian Luan, the teachers and

graduates, laboratory of displacement mechanism, U.P.C, East China, for

their partial experimental work. The authors would also like to thank Dr.

Guodong Jin, Institute of Mechanics, Chinese Academy of Sciences, and Dr.

Faisal Qureshi, Department of Physics, to thank Faisal Qureshi, Department

of Physics, Institute of Heavy Ion Physics Peking University, China, for their

proof reading and improving the English expression.

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transporte de np en medio poroso

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