The Use of Numerical Techniques to Analyze the Transient Response of a Reservoir Undergoing Meor...

8/10/2019 The Use of Numerical Techniques to Analyze the Transient Response of a Reservoir Undergoing Meor Process

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INTERNATIONAL JOURNAL OF TECHNOLOGY ENHANCEMENTS AND EMERGING ENGINEERING RESEARCH, VOL 2, ISSUE 7 85ISSN 2347-4289

Copyright 2014 IJTEEE.

The Use Of Numerical Techniques To AnalyzeThe Transient Response Of A ReservoirUndergoing Meor ProcessChukwuma Godwin Jacob Nmegbu, Lotanna Vitus Ohazuruike

Departmentof Petroleum Engineering, Rivers State University of Science and Technology, Port Harcourt, Nigeria;Department of Petroleum Engineering, Rivers State University of Science and Technology,Port Harcourt, Nigeria.Email:[email protected]

ABSTRACT: The development of a three-dimensional, three-phase, multicomponent numerical model to analyse the microbiatransport and fluid flow phenomena in a microbe-flooded reservoir is presented. The multiphase flow equations are solved inmulti cases and in three-dimensional frameworks following the implicit pressure explicit saturation (IMPES) procedure in whichthe solution of the bacteria transport equations is solved implicitly whereas the nutrient transport equation is solved explicitlyThe MEOR model was incorporated into an existing chemical f looding simulator (UTCHEM). The simulation results showed thathe sharp increase of pressure after the microbial flooding is caused by pore plugging and the production of biogenic gas. As thetime increased and water flooding continued, the permeability recovered slightly with the declogging of microbes in the porespace, resulting in a decrease in pressure drop.

Keywords:Transient Response; Nutrient transport; Bacteria transport; Multiphase flow; MEOR Simulation

1INTRODUCTIONMicrobial Enhanced Oil Recovery (MEOR) is a family ofprocesses that involves the use of selected microbes toachieve enhancement of oil production. The microbial systemis carefully designed to produce bioproducts capable of mak-ing positive alterations to the inherent rock and fluid proper-ties. The usefulness of this technology lies in the broad rangeof the bioproducts obtainable and the consequent flexibility itoffers the technology. Also advantageous are the economicattractiveness and the environmental friendliness of the

process. The first suggestion for using MEOR was made asearly as in 1926. The first detailed study of MEOR was con-ducted by Zobell [1],[2],[3]. He observed that sulfate-reducingbacteria led to gradual separation of oil or tar from sand. Studyin this area has been extended by Beck [2] and Updegraff andWren [3].Modeling of these processes often rely on conserva-tion laws, incorporating growth and retention kinetics of bio-mass. A simplified model of this nature was presented byKnapp et al [4]. They predicted porosity reduction as a functionof distance and time. Updegraff [3] used a filtration model inorder to express bacteria transport as a function of pore en-trance size. Similar models were used by Jang et al [5]. In arecent work, Jenneman et al [6] modified the filtration theory torelate permeability with the rate of bacteria penetration. Some

of these models were found to show good agreement withexperimental results. However none of these models incorpo-rates fundamental laws of bacterial deposition, entrainment oradsorption of bacteria to the rock surface [7]. An early paperthat covered all the core phenomena of MEOR and in 3-dimensional formulations was presented by Islam in 1990 [8].It was based on a conventional three phases black oil formula-tion and additional equations to describe these processes [8].The mathematical representation includes equation of speciestransport, microbial growth kinetics, empirical formula for per-meability reduction and continuity equations for pressure andsaturation. He also discussed the problem of scaling up oflaboratory experiments conducted on MEOR processes.Another early work by Zhang et al [9] is a one-dimensional

model, therefore not suited for field application but for coresimulations, nevertheless it has a more advanced formulationof pore-throat plugging and pore surface retention plus asecond growth limiting substrate. However, having a reliablesimulation model is very crucial in todays reservoir engineering for field development, scenario runs and sensitivity studiesetc. For MEOR, it is more important because it is a complexand interdisciplinary topic that cannot be covered with analyti-cal formulas, rules of thumb, charts or whatsoever [10]. Maud-

galya et al [10] in their recommendation have identified anaccurate simulation model as key element for the broad suc-cess and acceptance of MEOR. For recent, large MEOR pilotprojects [11],[12], the application of simulation technology waslimited to streamline simulation. The main task is to identify theflow path between the injectors and producers, combined withtracer test to provide the basis for the selection of injector/producer pattern that is used for the project. It is further abasis for verification and analysis of process, later on whichcan be done for every MEOR project.

2METHODOLOGYThe multiphase flow equations will be solved in multi casesand in three-dimensional frameworks following the implicit

pressure explicit saturation (IMPES) procedure. Also, the solution of the bacteria transport equations will be solved implicitlywhereas the nutrient transport equation will be solved explicitly. To achieve this, the equations are discretized in space. Thissequence is repeated until convergence is achieved for eachtime step.

2.1 Model Development


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2.1.1 AssumptionsThe assumptions made include:a) No mass transfer between oil and waterb) The gas produced as a metabolic by-product can exist

either as a free gas or dissolved gasc) Isothermal reservoir conditionsd) Uniform gridblockse) The fluids are in thermodynamic equilibrium in the reser-

voirf) Multiphase flow, that is, simultaneous oil, water and gas

flow.

2.1.2 Nutrient Transport EquationThe nutrient transport equation in three-dimension is given by:

x Ax CwnKx Krww Bw

wx x + y Ay CwnKy Krww Bw

wy y +

z Az CwnKx Krww Bw

wx z + qw Cwn = t Sw CwnBw +

r

w

1 Cwnt (1)Applying finite difference approximation to the LHS secondorder partial differential equation in the x, y and z directions at

gridpoints i, j, k respectively [13],

x

AxCwn Kx Krw

w

Bw

wx xi,j,k x AxCwn KxKrw

w

Bwxw xi,j,k

(2)Also,x Ax CwnKx Krww Bw

wx xi,j,k= Ax CwnKx Krww Bw x i+1

2,j,k

wx i+1,j,k wx i,j,k Ax CwnKx Krww Bwx i1

2,j,k

wx i,j,k wx i1,j,k (3)

Let

Twxi+

1

2,j,k

=

Ax CwnKx Krw

w

Bw

x

i+12,j,k (4)

Twxi1

2,j,k

= Ax CwnKx Krww Bw x

i12

,j,k

(5)

Hence, (3) becomes

x Ax CwnKx Krww Bw

wx xi,j,k= Twx Cwn i+12,j,kwx i+1,j,k

wx i,j,k Twx Cwn i12

,j,kwx i,j,k wx i1,j,k (6)

From (2), (6) can be written as:

x Ax CwnKx Krw

w Bw xw xi,j,k= Twx Cwn i+1

2,j,kwx i+1,j,k wx i,j,k+ Twx Cwn i1

2,j,k

wx i1,j,k+ wx i,j,k (7)The finite difference approximation to the second order diffe-rential term in y-direction, is derived with similar procedure tothe just presented approximation for the x-direction term, butin this case, we consider gridpoint (i,j,k) with its gridblock-boundaries (i,j-1/2,k) and (i,j+1/2,k) and its neighbouringgrid-blocks (i, j-1,k) and (i,j+1,k) in the y-direction.

The approximation in the y-direction may be expressed as:y Ay CwnKy Krww Bw

wy yi,j,k y Ay CwnKy Krww Bw yw yi,j,k

(8)

y Ay CwnKy Krww Bw yw yi,j,k= Twy Cwn i,j+12,kwy i,j+1,k wy i,j,k+ Twy Cwn i,j1

2,kwy i,j 1,k+ wy i,j,k (9

And the approximation in the z-direction may be expressedas:

z

Az CwnKz Krw

w Bw

wz zi,j,k z

Az CwnKz Krw

w Bw z

w zi,j,k(10)z Az CwnKz Krww Bw zw zi,j,k= Twz Cwn i,j,k+12 wz i,j,k+1

wz i,j,k+ Twz Cwn i,j,k12

wz i,j,k1+ wz i,j,k (11)Let

AC wnKK rww Bw

wi,j,k

x Ax CwnKx Krww Bw xw xi,j,k+y Ay CwnKy Krww Bw yw yi,j,k+ z

Az CwnKz Krw

w Bwzw zi,j,k

(12)Substituting (7), (9) and (11) gives:

ACwn KKrw

w

Bw wi,j,k= Twx Cwn i+1

2,j,k

wx i+1,j,k wx i,j,k+ Twx Cwn i1

2,j,k

wx i1,j,k+ wx i,j,k+ Twy Cwn i,j+1

2,kwy i,j+1,k wy i,j,k

+ Twy Cwn i,j12

,kwy i,j 1,k+ wy i,j,k

+ Twz Cwn i,j,k+12

wz i,j,k+1 wz i,j,k+ Twz Cwn i,j,k12 wz i,j,k1+ wz i,j,k

(13)wherew= water potential and is defined as:w= Pw- wz (14)andPw= Po- Pcow (15)w = Po Pcow wz (16)Substituting (16) and rearranging (13) gives:

AC wnKK rww Bw

Po Pcow wzwi,j,k

=

Twx Cwn i+12

,j,kPox i+1,j,k Pox i,j,k wZi+1,j,kZi,j,k

(Pcowx i+1,j,kPcowx i,j,k+ Twx Cwn i12,j,kPox i1,j,k+ Pox i,j,k

wZi1,j,kZi,j,k (Pcowx i1,j,kPcowx i,j,k+

Twy Cwn i,j+12

,kPoy i,j+1,k Poy i,j,k wZi,j+1,kZi,j,k

(Pcowy i,j+1,kPcowy i,j,k)+ Twy Cwn i,j1

2,kPoy i,j 1,k Poy i,j,k

wZi,j1,k Zi,j,k (Pcowy i,j1,k Pcowy i,j,k) +

Twz Cwn i,j,k+12

Poz i,j,k+1 Poz i,j,k wZi,j,k+1 Zi,j,k (Pcowz i,j,k+1 Pcowz i,j,k)+ Twz Cwn i,j,k1

2

Poz i,j,k1+ Poz i,j,k


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wZi,j,k1 Zi,j,k (Pcowz i,j,k1 Pcowz i,j,k) (17)

Consider the RHS of (1), we have:t

Sw Cwn

Bw+ r

w

1 Cwnt=

1

ttSwCwn

Bw

i,j,k

+r

w

1 1ttCwn i,j,k=

1

tSw Cwn

Bw

i,j,k

n+1 Sw CwnBw

i,j,k

n +

r

w

1 1tCwn n+1 Cwn n(18)

Resolving the Equation gives:1

ttSw CwnBw + rw 1 1

ttCwn = 1t

Bwn Cwnn +

n+1 1Bw

Cwnn Swn tPo+ Bwn+1

Cwnn+1tSw+ 1t Bw

n+1

Swn +

r

w 1 tCwn (19)LetNp =

1

t

Bwn Cwnn + n+1 1Bw Cwnn Swn (20)

Nw =1

t Bwn+1

Cwnn+1 (21)

Nn =1

t Bwn+1

Swn +

r

w

1 (22)Hence, (19) becomes:1

ttSw CwnBw +r

w

1 1ttCwn = NptPo+ NwtSw+NntCwn (23)

The finite difference equation for the nutrient transport mod-el is obtained by combining (17) and (23):

Twx Cwn i+12,j,k Pox i+1,j,k Pox i,j,k wZi+1,j,kZi,j,k (Pcowx i+1,j,kPcowx i,j,k+ Twx Cwn i1

2,j,k

Pox i1,j,k+ Pox i,j,k

wZi1,j,kZi,j,k (Pcowx i1,j,kPcowx i,j,k+

Twy Cwn i,j+12

,kPoy i,j+1,k Poy i,j,k wZi,j+1,kZi,j,k

Pcowy i,j+1,kPcowy i,j,k+ Twy Cwn i,j12

,kPoy i,j 1,k Poy i,j,k

wZi,j1,k Zi,j,k Pcowy

i,j1,k Pcowy i,j,k +Twz Cwn i,j,k+1

2

Poz i,j,k+1 Poz i,j,k wZi,j,k+1 Zi,j,k Pcowz i,j,k+1 Pcowz i,j,k+ Twz Cwn i,j,k1

2

Poz i,j,k1+ Poz i,j,k wZi,j,k1 Zi,j,k Pcowz i,j,k1 Pcowz i,j,k= NptPo+ NwtSw+ NntCwn (24)

If we define xas the set of neighbouringgridblocks asso-ciated with Gridblock (i,j,k) along the x direction:

x= i 1, j, k, i + 1,j, k (25)

Similarly,

y= i, j 1, k, i,j + 1, k (26)

z= i , j ,k1, i,j, k + 1 (27)

Then,

i,j,k=

x

y

z (28)

And

x= n 1, n + 1

y= n nx, n + nx for nx= 1

z= n nxny, n + nynx fornx= ny= 1 (29)

The variable m is the value of at gridblockm i,j,k. Thecoefficient (TwCwn)(i,j,k),m is the (TwCwn) interactions betweengridblock (i,j,k) and its immediate neighboring gridblockm

i,j,k

Using this notation, the implicit finite difference equation in

Gridblock n, in multidimensional space becomes: Twn+1Cwn+1n,m mPon+1 m Pcown+1 wn,mn m zn+1mn

+ qwnn+1Cwn n

n+1

= NpntPon + Nwn tSw+ NnntCwn (30)

2.1.3 Bacteria Transport EquationThe bacteria transport equation is given as:

CwbKK rwAw Bw

w+ qw Cwb = tSww Cwb+ (31)

In three-dimensional coordinates:x CwbKx KrwAxw Bw

wx x + y CwbKy KrwAyw Bwwy y +

z CwbKz KrwAz

w Bw w

z z + qw Cwb = tSwwCwb+ (32)Applying a similar finite difference approximation to that performed on the nutrient transport equation, the bacteria transport equation given above can be written as:Twn+1Cwbn+1m,n m Pon+1 m Pcown+1 wn m Z= BpntPon +BbtCwb n + Bwn tSwn + nt qwsc nn+1 Cwb nn+1 (33)

where

Bp =1

tw Cwb n+ n+1Swn Bb=

1

twn+1Swn Bw =

1

twCwb n+1 (34)2.1.4 Multiphase flow equationsThe model equations for oil, water and gas are given as follows.2.1.4.1 OilThe model equation for oil is given as:

x Ax Kx Kroo Bo

ox x + y Ay Ky Kroo Bo

oy y + z Az Kz Kroo Bo

oz z +

qo = vbt SoBo (35)

Applying the finite difference approximation to the secondorder partial differential term in the x, and z directions at gridpoints (i,j,k) and simplifying results in:

Tooijk = Tox i+12

,j,k

ox i+1,j,k

ox i,j,k

+ Toxi1

2,j,k

ox i1,j,k ox i,j,k

+ Toyi,j+

12

,k oy i,j+1,k oy i,j,k+ Toy

i,j 12

,k

oy i,j 1,k oy i,j,k+ Toz

i,j,k+12

oz i,j,k+1

oz i,j,k

+ Toz

i,j,k12

oz i,j,k+1

oz i,j,k

(36)

where

To=kkroA

o Bo (37)

From the definition of change in fluid potential, the oil equa-tion becomes:


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AK Kroo Bo

Po oZi,j,k

n+1

= CoptPo+ CogtSg+ CowtSw qosc

n+1i,j,k

(38)

Where

Cop = 1

t

Bon+

n+1 1Bo

1 Sgn Swn

Cow = 1

t

Bon+1

Cog = 1t Bon+1

(39)

Writing (38) in a control volume finite difference (CVFD) me-thod, the final oil equation becomes:

Ton,mn+1 m Pon+1 on,mn mZmn

= Cop ntPon + Cog n tSgn + Cow ntSwn qosc nn+1 (40)

2.1.4.2 WaterThe model equation for water is given as:

x Ax Kx Krww Bw

wx x + y Ay Ky Krww Bw

wy y + z Az Kz Krww Bw

wz z +

qwsc = vb tSw

Bw (41)Applying the finite difference approximation to the secondorder partial differential term in the x,y and z directions at grid-points (i,j,k) and simplifying results in:

Tww ijk = Twx i+12

,j,k

wx i+1,j,k

wx i,j,k

+ Twxi1

2,j,k

wx i1,j,k wx i,j,k

+ Twyi,j+

12

,k

wy i,j+1,k

wy i,j,k

+ Twyi,j 1

2,k

wy i,j 1,k wy i,j,k+ Twz

i,j,k+12

wz i,j,k+1

wz i,j,k

+ Twz

i,j,k12 wz i,j,k+1 wz i,j,k

(42)where

Tw =kkrwA

w Bw (43)

From the definition of change in fluid potential, the waterequation becomes:

AK Krww Bw

Po+ Pcow wZi,j,k

n+1

= Cwp tPo+ Cww tSw qw

n+1i,j,k

(44)

Where

Cwp = 1

t

Bwn +

n+1 1Bw

Swn

Cww = 1t Bwn+1

(45)

Writing (45) in a control volume finite difference (CVFD) me-thod, the final water equation becomes:

Twn,mn+1 m Pon+1 + m Pcown+1 wn, mn m Zmn

= Cwp n tPon + Cww n tSwn qwsc nn+1 (46)

2.1.4.3 GasThe model equation for water is given as:

x Ax Kx Krgg Bg

gx +

A x Kx KroRso

o Bo

ox x + y Ay Ky Krgg Bg

gy +

Ay Ky KroRso

o Bo

oy y + z Az Kz Krgg Bg

gz +

A z Kz KroRso

o Bo

oz z + qg+

qoRso = vbt SgBg (47)

From the definition of change in fluid potential, the gas equation becomes:

AK Krgg Bg

Po+ Pcog gZ+AK KroRsoo Bo Po oZi,j,kn+1

=

CgptPo+ CggtSg qgn+1 qon+1Rson+1i,j,k (48)where

Cgp = 1

t

Bo+ n+1 1

Bo Rson + Bo

n+1

Rso 1 Sgn

Swn + 1t

Bbn+ n+1 1Bg Sgn

Cgg = 1

t Bgn+1

Bon+1 Rson+1 (49)

Writing (45) in a control volume finite difference (CVFD) method, the final water equation becomes:

Tgn,mn+1 m Pon+1 + m Pcogn+1 gn,mn m Zmn

+ ToRson,mn+1 m Pon+1 on,mn m Z= Cgp n tPon + Cgg n tSgn qgsc nn+1

(50)whereqgsc n

n+1 = q fgs nn+1 + Rsn

n+1qosc nn+1 + Rsw n

n+1 qwsc nn+1 (51)

2.2 Experimental DataThe pressure response from the simulation was observedbased on the experimental parameters obtained from the coreflood test. In the experiment, 0.1 pore volume of microbial so-lution was introduced into the core. This was followed by theinjection of 0.2 pore volume of nutrient solution and incubatedfor 2 days. After the incubation period, 0.2 pore volume of nu

trient solution was injected after which the core was waterflooded at 1.5cm

3/min. the values of the parameters used in

the simulation are listed in the table below.

TABLE 1CORE PROPERTIES, FLUID AND MICROBIAL SYSTEM

PARAMETERS USED IN THE SIMULATION

Parameters Value

CoreLength, cm 14Width, cm 14

Thickness, cm 9Porosity, % 15

Permeability [kx,ky,kz],md

410, 410, 200

Grid size (x, y, z),cm

1,1,1

Number of grid (x,y,z)axis

14,14,9

FluidInitial oil saturation, % 87Residual water satura-

tion, %13

Initial oil viscosity, cp 19


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Oil compressibility, psi- 0.00014

Initial pressure, psi 28

Water injection rate,cm

3/min

1.5

Oil production rate,cm

3/min

2

Water production rate,cm

3/min

0.53

Gas production rate,cm

3/min

1.0

Bacteria and nutrientBacteria injection rate,

cm3/min

0.5

Injected microbial conc.% pore volume

0.1

Injected nutrient conc. %pore volume

0.2

Diffusion coefficient forbacteria, cm

3/day

5.1

Diffusion coefficient fornutrients, cm

3/day

7.4

Maximum growth rate,day-1

5.3

Decay rate, day-

34Nutrient solution

Beef extract, g/c 1.0Yeast extract, g/c 2.0Peptone, g/c 5.0Sodium Chloride, g/c 5.0

3

RESULTSThe simulator used in this project is known as UTCHEM [14].UTCHEM is a three dimensional chemical flooding simulatorthat incorporates the MEOR model. The solution scheme isanalogous to the implicit pressure explicit hrs saturation (IM-

PES) where the pressure was solved implicitly and saturationswere solved explicitly. A time step of 2 hours was consideredand a no-flow boundary of the core was implemented by set-ting pressure gradient at the boundary interfaces to zero.

TABLE 2PRESSURE AND PRESSURE DROP RESPONSE DUR-

ING CONTINUOUS WATERFLOODING

Pressure, P(psi)

Pressuredrop p = (P-

Pi), psi

Time stept, hr

28.00 0 0

36.00 8 243.00 15 4

45.50 17.5 649.30 21.3 850.60 22.6 10

52.20 24.2 1249.30 21.3 1447.00 19.0 1648.00 20.0 1846.80 18.8 20

45.70 17.7 2245.60 17.6 2444.50 16.5 2643.70 15.7 28

42.80 14.8 3040.80 12.8 32

40.70 12.7 3440.60 12.6 3640.30 12.3 3840.20 12.2 4040.10 12.10 42

40.05 12.05 44

40.02 12.02 4640.01 12.01 48

The graphical plots of the simulation result are presented below.

Fig.1.Pressure in core with time

Fig. 2.Pressure drop in core with time

The simulation results showed that the sharp increase of pressure after the microbial flooding is caused by pore pluggingand the production of biogenic gas. The pore plugging reducesthe rock permeability and the increase of gas saturation de-creases the relative permeability of the oil and water phaseAs the time increases and water flooding proceeds, the permeability recovered slightly with the declogging of microbes inthe pore space. Consequently, a decrease in pressure dropwas observed from the core flood.

4

CONCLUSIONNumerical models of pressure transient response duringMEOR have been presented. It was a logical step to incorpo

0

10

20

30

40

50

60

0 20 40 60

Pre

ssure

(psi)

Time (hrs)

0

5

10

15

20

25

30

0 20 40 60

Pressure

drop,psi

Time (hrs)


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rate a MEOR model into an existing chemical flooding simula-tor. The simulator was run based on the experimental dataand in a three dimensional framework to determine the effectsof pressure drop as water flooding continued, describing thetransient response of the core during the MEOR process. Inaddition, UTCHEM can accommodate a number of substratesaccepters, biotic decay, biomass growth, and biomass at-tachment which are all microbial enhanced oil recovery

processes. Since MEOR reduces or eliminates the need touse harsh chemicals during oil recovery, it is an environmen-tally friendly and economically feasible method of carrying outenhanced oil recovery, amidst recent growing concerns of cer-tain methods like fracturing. Therefore, there is need for spe-cial skills and logical steps to incorporate MEOR into a simula-tor that will describe or analyze the transient response of areservoir during microbial enhanced oil recovery processes.

NOMENCLATUREA = Cross sectional area, ft

2

Ax,Ay,Az= Cross sectional area normal to the x, y and z direc-tions, ft

2

B = Formation volume factor (FVF), bbl/STB

Cwn= Concentration of nutrient in the injected water, lb/ft3Cwb= Concentration of bacteria in the injected water, lb/ft

3

Kr= relative permeability to gas, dimensionlessKx,Ky,Kz= Permeability in the x,y and z directions respectively,mDm = a member of gridblock set nn = number of gridblocksnx,ny,nz= number of gridblocks in the x, y and z directionsP = Pressure, psiPon= Oil pressure for gridblock n, psiPcgo= Gas/Oil capillary pressure, psiPcow=Oil/water capillary pressure,psiq = production rate, scf/DRon= Oil residual in gridblock n, STB/D

Rs= Solution GOR, scf/STBS = saturation, fractiont = time, dayst = time step (= t

n+1- t

n), days

Uf= Darcy flux = gravity, psi/ft = difference operatorn= difference operator in the gridblock domaint= difference operator in the time domain = viscosity, cp = density, lb/ft

3

Tg= Transmissibility = Fluid potential, psi = porosity, fraction

n= set of gridblocks associated with but excluding gridblockn in natural orderingSubscriptsg = gaso = oilw = waterp = phasei = index for blocks in the x direction

j = index for blocks in the y directionm = neighbouringgridblock to gridblock nn = gridblocksc = standard conditionst = time

REFERENCES[1]. C.E. Zobell, Bacterial Release of Oil from Sedimenta

ry Materials, Oil and Gas J., vol. 46, no. 13, pp. 6265, 1974

[2]. J.V. Beck, Penn Grade Progress on use of Bacteriafor Releasing Oil from Sands, Producers Monthly

Sept.13-19, 1947.

[3]. D.M. Updegraff and G.B. Wren, The release of Oifrom Petroleum Bearing Materials by Sulfate-reducingBacteria, Appl. Microbial.,vol.12, pp.309-322, 1954

[4]. R.M. Knapp, M.J. McInerney, D.E. MenzieG.E.Jennemen, The Use of Microorganisms in Enhanced Oil Recovery, Status Report of US DOE Contract, 1982

[5]. K.L. Jang, M.M. Sharma, J.E. Findley, P. Chang andT.F. Yen,An Investigation of the Transport of Bacteriathrough Porous media, Proc. Int. Conf. on Microbia

Enhanced Oil Recovery, Afton, USA, pp.60-70, 1982

[6]. G.E. Jenneman, R.M. Knapp, D.E. Menzie, M.J., McInerney, D.E. Revus, J.B. Clark, D.M. Munnecke,Transport Phenomena and Plugging in BereaSandstone Using Microorganisms, Proc. Int. Conf. onMicrobial Enhanced Oil Recovery, Afton, USA, pp.7175, 1982

[7]. C. Gruesbeck and R.E. Collins, Entrainment Deposition of Fine Particles in Porous Media, SPE J.pp.847-856, Dec. 1982

[8]. M.R. Islam, Mathematical Modeling of Microbial En

hanced Oil Recovery, SPE Res., pp.159, Sept 1990

[9]. X. Zhang, R.M. Knapp, M.J. McInerney, A Mathematical Model for Microbially Enhanced Oil RecoveryProcess, Paper SPE 24202, Presented at theSPE/DOE 8

thSymposium on Enhanced Oil Recovery

Tulsa, Oklahoma, USA, April 22-24, 1992

[10]. S. Maudgalya, R.M. Knapp and M.J. McInerney, Microbial Enhanced Oil Recovery Technologies: A Review of the Past, Present and Future, Paper SPE106978, Presented at the 2007 SPE Production andOperation Symposium, Oklahoma, USA, 31 Mar-3April, 2007

[11]. [11] R.A. Strappa, J.P. De Lucia, M.A. Maure andM.L. Lopez Liopiz, A Novel and Successful MEORPilot Project in a Strong Water-Drive Reservoir Vizeacheras Field, Argentina, Paper SPE 89456, Presented at the 14th SPE/DOE Symposium on Im-proved Oil Recovery, Tulsa, Oklahoma, 17-21 April2004

[12]. [12] A. Maure, F. Dietrich, U. Gomez, J. VallesiM. Irusta, Waterflooding Optimization Using Biotechnology: 2- Years Field Test, La Ventana Field, Argentina, Paper SPE 69652, Presented at the SPE Latin


7/7



American and Caribbean Petroleum Engineering Con-ference, Buenos Aires, Argentina, 25-28 March, 2001

[13]. [13] E. Turgay, J.H. Abou-Kassem and R.K. Gre-gory, Basic Applied Reservoir Simulation, Richardson,Texas:SPE Textbook Series, vol. 7., SPE, , pp.4-6,2001

[14]. [14] Technical Documentation for UTCHEM-9-0,Reservoir Engineering Research Programme, Centrefor Petroleum and Geosystems Engineering, Univ. ofTexas, July 2000

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