numericalsimulationofmicroemulsionfloodingin...

Research ArticleNumerical Simulation of Microemulsion Flooding inLow-Permeability Reservoir

Dongqi Wang 1 Daiyin Yin 1 and Xiangzhu Gong 2

1College of Petroleum Engineering Northeast Petroleum University Daqing 163318 China2Huaqiao University Quanzhou 362021 China

Correspondence should be addressed to Daiyin Yin yindaiyin163com

Received 9 October 2018 Accepted 6 December 2018 Published 21 January 2019

Academic Editor Ajaya Kumar Singh

Copyright copy 2019 Dongqi Wang et al is is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work isproperly cited

Based on the features of microemulsion flooding in low-permeability reservoir a three-dimension three-phase five-componentmathematical model for microemulsion flooding is established in which the diffusion and adsorption characteristics of surfactantmolecules are considered e non-Darcy flow equation is used to describe the microemulsion flooding seepage law in which thechanges of threshold pressure gradient can be taken into account and the correlation coefficients in the non-Darcy flow equationare determined through the laboratory experiments A new treatment for the changes of threshold pressure and the quantitativedescription of adsorption quantity of surfactant and relative permeability curves are presented which enhance the coincidencebetween mathematical model and experiment results e relative errors of main development indexes are within 4 A softwareis programmed based on the model to execute a core-level small-scale numerical simulation in Chaoyanggou Oilfield e fittingrelative errors of the pressure flow rate and moisture content are 325 271 and 254 respectively e results of laboratoryexperiments and numerical simulation showed that microemulsion system could reduce the threshold pressure gradient by0010MPam and injection pressure by 06MPa e biggest decline in moisture content reaches 33 and the oil recovery isenhanced by 108

1 Introduction

With the characteristics of narrow pores large pore-throatratio high irreducible water saturation and serious het-erogeneity the low-permeability reservoirs do not meetDarcyrsquos law anymore and there is threshold pressure gra-dient Compared to the high-pressure of water injection lowwater displacement efficiency and low ultimate recoveryefficiency of water flooding [1ndash4] the surfactant flooding canreduce the threshold pressure gradient and injection pres-sure increase the water injection rate which expands theswept volume reduce the interfacial tension and improvethe displacement efficiency [5ndash8] According to the sur-factant concentration in the injection system the surfactantflooding is divided into active water system (Cs lt 1) andmicroemulsion system (Cs 3sim5) [9ndash13] Because of thepeculiarities of ultra-low interfacial tension and better

mobility control the latter one has become the hotspot inenhanced oil recovery of low-permeability reservoir As themicroemulsion flooding is characterized with high risk andhigh input the numerical simulation of this method shouldbe put to the strategic position e leader in this aspect isthe University of Texas BYUYANHE and POPE whoestablished UTCHEM model [14 15] e biggest draw-back of the models is that the model is unable to considerthe threshold pressure gradient In addition so manyfactors are considered that it is difficult to get the resultsand the calculation accuracy or convergence of the modelis poor [16ndash18] Han introduced the chemical model to theEOS composition simulator module and a fully implicitparallel component chemical flood simulator is estab-lished to improve the calculation speed [19] Howeversince some parameters are difficult to obtain the appli-cability of the model is limited In this paper based on the

HindawiJournal of ChemistryVolume 2019 Article ID 5021473 8 pageshttpsdoiorg10115520195021473

characteristics of the microemulsion flooding a three-dimension three-phase five-component microemulsionflooding mathematical model is established in which thediffusion and adsorption of surfactant molecules thechange of microemulsion viscosity and relative perme-ability are considered e finite difference method is usedto solve the model and simulation accuracy and calcu-lation speed are improved

2 The Non-Darcy Equation in Low-Permeability Reservoir

According to the literature [20] non-Darcy flow equation inlow-permeability reservoir can be expressed as

v K

μnablaPminus ξ1 minus

ξ1ξ2nablaPminus ξ2

1113888 1113889 (1)

e laboratory experiments are carried out to get thevalue of ξ1 and ξ2 e microemulsion system used in theexperiment is made of water SDS light oil n-butanol andsodium chloride e experimental schemes and the valuesof ξ1 and ξ2 under different conditions are shown in Table 1and the seepage velocity-pressure gradient curves are shownin Figure 1

3 The Establishment of MicroemulsionFlooding Mathematical Model

31 (e Assumptions of the Model Generally oil watersurfactant alcohol and inorganic salt are taken into accountin the microemulsion flooding And it is assumed that thereis a three-phase flow involving oil water andmicroemulsionin the reservoir It is considered that the reservoir is an-isotropic and heterogeneous and the reservoir rock andfluids involved in the microemulsion flooding process arecompressible e influences of capillary force and gravityeffect are also included

32 (e Material Balance Equation Considering the diffu-sion of surfactant molecules among each phase and theadsorption on the rock surface the continuity equation ofthe j composition in the i phase is

nabla middot ϕDijnabla ρjCij1113872 11138731113960 1113961minusnabla middot ρjViCij1113872 1113873minus 1113944

m

a1ηaij φij minusφaj1113872 1113873

z

ztϕρjsiCij + ρjaij1113872 1113873minus ρjqiCij

(2)

In above equations i indicates oil water and micro-emulsion phases denoted by o w and m and the value of i

could be 1 2 or 3 j assigning value of 1 2 3 4 or 5represents the compositions of oil water surfactant alcoholand inorganic salt respectively

It is assumed that the mass percentage of water com-position in oil phase Co2 is equal to 0 and the mass per-centage of oil composition in water phase Cw1 is 0 too e

Dij and aij pertaining to oil and water compositions re-spectively are neglected Combining equations (1) and (2) athree-dimensional three-phase and five-compositionmathematical model for microemulsion flooding can beobtained

nabla middot ϕSiρiDijnablaCij1113872 1113873 + 1113944m

i1nabla

⎧⎨

⎩KKriρi

μi

Cij⎡⎣nablapi minus ρignablaH

plusmn ξ1 +ξ1ξ2nablapi minus ξ2

1113888 11138891113891⎫⎬

⎭ z

zt1113944

m

i1ϕSiρiCi( 1113857minus 1113944

m

i1ρiqiCij

(3)

where Dij is the diffusion velocity of j composition in i

phase Cij is the mass percentage of j composition in i phaseand Ci is the comprehensive mass percentage of i phaseincluding the adsorbed terms

33 (e Auxiliary Equation e relationships of saturationamong each phase and mass percentage of j composition ineach phase can be written as

1113944

m

i1Si 1 (4)

1113944

n

j1Cij 1 (5)

e relationship of pressure among each phase is asfollows

pcai pa minuspi (6)

where a 1 2 and 3 and pcai 0 when a i

4 The Treatment of Important Parameters

41 Interfacial Tension Surfactant plays an important role inreducing interfacial tension and improving the flow ability ofcrude oil in the microemulsion system e indoor exper-iments are carried out to get the interfacial tension in dif-ferent surfactant concentrations And the results are shownin Figure 2

It can be seen from Figure 2 that with the increase ofsurfactant concentration the interfacial tension decreasesgreatly But the extent of decrease becomes smaller whenthe surfactant concentration reaches a certain value ereason is that with the increase of surfactant concentrationthe adsorption quantity of surfactant molecules in oil layersalso increases but the increase of effective concentration isnot proportional erefore the relationship betweensurfactant concentration and the interfacial tension couldbe written as

σ Acn cleCMC

σ C cgtCMC1113896 (7)

where the value of coefficients A index n constant C andCMC could be given through the experiments

2 Journal of Chemistry

42 Adsorption e Langmuir adsorption curve is used todescribe the surfactant molecules adsorption in the processof microemulsion ooding in which the eects of saltconcentration surfactant concentration and core perme-ability are considered And the expression is

CiC1 min

CiC1

ai CiC1( )minus CiC1( )( )1 + bi CiC1( )minus CiC1( )( )

(8)

e concentration in the adsorption process is nor-malized by water and the minimum value is got to makesure that the total amount of adsorption is not greater thanthe surfactant concentration Adsorption quantity increasedwith the increase of salt concentration but decreased withthe increase of permeability

ai ai1 + ai2CSE( ) middot kminus05 (9)

where CSE is eective salinity and CSE 16037ξH2O(NsaltNH2O) Adsorption parameters aij and bi can beobtained by tting the adsorption data of surfactant mea-sured indoor

43 Viscosity e viscosity of microemulsion system isrelated to the components and the viscosity of oil and waterIn the process of microemulsion ooding the surfactantmolecules could adsorb onto the interface in the porousmedium And some crude oil would be dissolved into thedisplacement phase under the action of surfactant moleculeswhich changed the microemulsion viscosity To research thechange of microemulsion system viscosity 12mPamiddots salineand 42mPamiddots light oil are used to formulate microemulsionsystem according to dierent oil-water volume ratio ecurve between microemulsion viscosity and oil-water vol-ume ratio is shown in Figure 3

e graph in Figure 3 can be described by the followingformula

μm μw 1 +MK

1minusK( )

n

(10)

where M is the oil-water viscosity ratio K is the oil-watervolume ratio and n is the index which is related to thecharacter and concentration of surfactant e value of theseparameters could be obtained by experiments

44 Relative Permeability Steady-state method is applied todeterminate the relative permeability curves between oil-water and oil-microemulsion in dierent surfactant con-centration And the porous media are natural cores inChaoyanggou Oilelde relative permeability curves underdierent surfactant concentration are shown in Figure 4

Multiphase ow relative permeability could be simulatedby the Corey function And the impact of crude oil

Table 1 e threshold pressure gradient of schemes in dierent surfactant concentrations

Scheme Numberof cores

Length(cm)

Diameter(cm)

Porosity()

Gas permeability(10minus3 μm2)

Surfactantconcentration ()

reshold pressuregradient (MPam) ξ1 ξ2

1 Y1-11 502 250 1216 398 00 00242 001802 minus0006182 Y1-13 497 250 1223 404 10 00217 001668 minus0005023 Y1-14 496 251 1214 406 15 00194 001509 minus0004314 Y1-15 501 250 1223 401 20 00171 001352 minus0003585 Y1-17 502 250 1230 403 25 00159 001306 minus0002846 Y1-18 498 251 1212 396 30 00142 001263 minus000217

000

005

010

Seep

age v

eloc

ity (c

ms

)

015

020

025

0 002 004 006 008 01Pressure gradient (MPam)

Experimental data (Cs = 0)Simulative curve (Cs = 0)Experimental data (Cs = 10)Simulative curve (Cs = 10)Experimental data (Cs = 15)Simulative curve (Cs = 15)


Figure 1 Relationship curve between the seepage velocity andpressure gradient

0001

001

01

Inte

rfaci

al te

nsio

n (m

Nm

)

1

10

100

0 1 2 3 4Surfactant concentration (wt)

Experimental data 1Simulative curve 2


Figure 2 Relationship curve between surfactant concentration andinterfacial tension

Journal of Chemistry 3

entrapment on the relative permeability is taken into ac-count It can be written as

kri k0riS

nii (11)

where k0ri denotes relative permeability endpoints for the iphase which can be obtained through the experiment

Si Si minus Sir

1minus Sir minus Siprimer

Sir min Si SHighir +

SLowir minus SHighir

1 + TiNTi

ni nLowiprimer +

SLowiprimer minus SiprimerSLowiprimer minus S

Highiprimer

nHighi minus n

Lowi( )

(12)

where variables with superscripts High and Low expressedthe values at high and low captured number

45 Phase Equilibrium Constraints Regard the uid in thereservoir as a ternary system including water oil andmicroemulsion And the equilibrium conditions can bedescribed by the equilibrium theory of regular solution forternary system According to the thermodynamic re-lations the spinodal equation for three phases can bewritten as

f1 T p x2 x3( ) μ11μ22 minus μ12( )2 0

f2 T p x2 x3( ) μ22μ33 minus μ23( )2 0

f3 T p x2 x3( ) μ11μ33 minus μ13( )2 0

(13)

Under a certain temperature and pressure condition thechemical potential of each component comply with theGibbsndashDuhem equation

sumk

i1ni dμi 0 (14)

0

2

4

Visc

osity

(mPa

middots)

6

8

10

0 01 02 03 04Oil-water volume ratio

Experimental dataSimulative curve

Figure 3 Relationship curve between viscosity and oil-water volume ratio

0

02

04

06

08

1

20 30 40 50 60 70 80

K rj

Sw ()

Cs = 02

KrwKro

KrmKrom

(a)

KrwKro

KrmKrom

0

02

04

06

08

1K r

j

20 30 40 50 60 70 80Sw ()

Cs = 03

(b)

Figure 4 Relative permeability curves under dierent surfactant concentration


For the three-component system the formulas above canbe written as

n1μ11 + n2μ12 + n3μ13 0

n1μ21 + n2μ22 + n3μ23 0

n1μ31 + n2μ32 + n3μ33 0

(15)

Under the condition of a certain pressure

f T x2 x3( 1113857 x1μ12μ31 + x2μ21μ23 + x3μ31μ23 0

(16)

Moreover T x2 x3 should satisfy the followingequation

Gm T x2 x3( 1113857 z2μ2zn2

21113888 1113889

Tpμ1 n1

0 (17)

Apply the formula above to calculate the content of oilwater and microemulsion and obtain the equilibriumrelationship

M Co

CmN

Cw

Cm (18)

5 The Solution of Model

51(e Solution Steps of the Mathematical Model e finitedifference method is used to solve the mathematical modele solution steps are as follows

(1) Combining equations (3) (4) and (6) for waterphase oil phase and microemulsion phase get thepressure po pw pm

(2) Substituting pressure po pw pm into equation (3) forwater phase to calculate water saturation sw

(3) Combining equation (3) for microemulsion phase(5) for water phase and oil phase and (18) toeliminate relative variables and obtain differentialequation including variable Cw3 then substitutingpressure value po and saturation sw into this dif-ferential equation to calculate concentration Cw3

(4) Applying the same method to get so sm and Co3 Cm3

52 (e Implementation Process of the Mathematical Modele flow chart of implementation process of the Mathe-matical Model is shown in Figure 5

6 Calculation of an Example

e indoor experiments in tablet cores and the corre-sponding core-level small-scale numerical simulation arecarried out to study the microemulsion flooding mecha-nism Block-centered grid system is established on themodel for Cartesian coordinate grid and X and Y di-rections are divided into 21 grids and the grid step length is15 cm ere are 1 production well and 4 injection wells inthe table core and the distance from each injection well tothe production well is 212 cm Mesh dissection in the

model is shown in Figure 6 and the three-dimensionalgeological model is shown in Figure 7 e injection systemis water flooding +microemulsion flooding + subsequentwater flooding

rough numerical simulation the injection pressurecurve and moisture content and oil recovery curves areobtained as shown in Figures 8 and 9 As you can see fromthe figures with the increase of water injection volume theinjection pressure continues to rise and reaches themaximum value at 137MPa after that the pressuregradually reduces to a steady state and keeps at 12MPae theoretical value of oil recovery is 50517 the op-erative value is 51183 and the relative fitting error is1318 Within this stage the water cut rises greatly butslowly as the oil recovery degree e reason is that theinjected water rushes along the high permeability layer dueto the serious heterogeneity and larger thickness of thehigh-permeability layer in the core In the process ofmicroemulsion flooding since the surfactant moleculescould reduce oil-water interfacial tension and change thewettability the injection pressure greatly reduces to037MPa with the theoretical value of 040MPa In thisperiod the oil recovery increases by 1235 while theincrease of water cut is within 10 Some crude oil isdissolved into the microemulsion and the particle sizeincreased which increased the microemulsion apparentviscosity and the injection pressure e larger micro-emulsion particles can plug higher permeability layer ef-fectively and the moisture content reduced sharplyMeanwhile with the high permeability layer plugged theseepage resistance increased and the following injectedmicroemulsion would enter the low-permeable layer atcould decrease the threshold pressure gradient and in-jection pressure in low-permeability layer enlarge sweepvolume of displacement fluid and increase recovery effi-ciency effectively In the subsequent water flooding in-jected water dilutes the microemulsion system which leadsto the decrease of its viscosity and the injection pressureWith the increase of injection volume the viscous effect ofmicroemulsion system is not obvious Due to the ad-sorption of surfactant molecules on the surface in coreporosity and the change of wettability the injectionpressure of water reduces and keeps at about 07MPaAnalysis of the experimental data and the simulative datathrough the entire process the fitting relative errors of thepressure flow rate and moisture content are 325 271and 254 respectively the biggest decline in moisturecontent is up to 33 and the oil recovery is enhanced by108

7 Conclusion

(1) A three-dimension three-phase five-componentmathematical model is established for micro-emulsion flooding in which the adsorption anddiffusion of surfactant molecules are consideredAnd the finite difference method is used to solve themathematical model


(2) Quantitative description for threshold pressuregradient viscosity of the microemulsion and relativepermeability are given and they are used in the

model A numerical simulation software formicroemulsion ooding is developed

(3) Experimental and theoretical calculations showedthat microemulsion system could reduce thresholdpressure gradient 0010MPam and injection pres-sure 06MPa

(4) e biggest reduction of moisture content is33 percentage points and the oil recovery is

Begin

Input experimentalparameters

i = 1

i le time nodes

Y

Read dynamic data

Solve the pressure

Solve the saturation

Solve the concentration

i = i + 1

N

Meet the accuracyrequirements

Y

Output results

N

Check experimentalparameters

End

Enter a static field

Figure 5 e ow chart of implementation process

INJ3INJ1

PROD

INJ2 INJ4

Figure 6 Grid subdivision schemes of the model

Figure 7 ree-dimensional geological model


improved by 108 percentage points the relativeerrors of main development indexes arewithin 4

Data Availability

e data used to support the ndings of this study weresupplied by the corresponding author under license and socannot be made freely available Requests for access to thesedata should be made to the corresponding author

Conflicts of Interest

e authors declare that they have no conicts of interest

Acknowledgments

is work is supported by the Natural Science Foundation ofChina under grant no 51474071 and supported by Northeast

Petroleum University Innovation Foundation For post-graduate no YJSCX2017-006NEPU

References

[1] Y Zhou D Wang Z Wang and R Cao ldquoe formation andviscoelasticity of pore-throat scale emulsion in porous mediardquoPetroleum Exploration and Development vol 44 no 1pp 111ndash118 2017

[2] D-z Ren W Sun H Huang J-x Nan and B Chen ldquoDe-termination of microscopic waterooding characteristics andinuence factors in ultra-low permeability sandstone reser-voirrdquo Journal of Central South University vol 24 no 9pp 2134ndash2144 2017

[3] B Zeng L Cheng and C Li ldquoLow velocity non-linear ow inultra-low permeability reservoirrdquo Journal of Petroleum Scienceand Engineering vol 80 no 1 pp 1ndash6 2011

[4] Y Q Wu J S Li X H Zhang J Zhou and T J LiuldquoNumerical simulation of low-permeability fractured reser-voirs on imbibitionrdquo Advanced Materials Research vol 712-715 pp 792ndash795 2013

[5] J Hou Y Zhang N Lu C Yao and G Lei ldquoA new methodfor evaluating the injection eect of chemical oodingrdquo Pe-troleum Science vol 13 no 3 pp 496ndash506 2016

[6] B Jin H Jiang X Zhang J Wang J Yang and W ZhengldquoNumerical simulation of surfactant-polymer oodingrdquoChemistry and Technology of Fuels and Oils vol 50 no 1pp 55ndash70 2014

[7] C Zheng G Jing J Luo Y Tang Y Liu and Z Zhen ldquoUsinga model to predict the migration and transformation ofchemicals for alkali-surfactant-polymer ooding in soilrdquoEnergy Sources Part A Recovery Utilization and Environ-mental Eects vol 40 no 13 pp 1657ndash1662 2018

[8] G Cheraghian S Kiani N N Nassar S Alexander andA R Barron ldquoSilica nanoparticle enhancement in the emacr-ciency of surfactant ooding of heavy oil in a glass micro-modelrdquo Industrial amp Engineering Chemistry Research vol 56no 30 pp 8528ndash8534 2017

[9] S Khorsandi C Qiao and R T Johns ldquoSimulation ofsurfactantpolymer oods with a predictive and robustmicroemulsion ash calculationrdquo SPE Journal vol 22 no 2pp 470ndash479 2017

[10] C A Carrillo D Saloni L A Lucia M A Hubbe andO J Rojas ldquoCapillary ooding of wood with microemulsionsfrom Winsor I systemsrdquo Journal of Colloid and InterfaceScience vol 381 no 1 pp 171ndash179 2012

[11] Z Jeirani B M Jan B S Ali C H See andW SaphanuchartldquoPre-prepared microemulsion ooding in enhanced oil re-covery a reviewrdquo Petroleum Science and Technology vol 32no 2 pp 180ndash193 2013

[12] T Qin G Javanbakht L Goual M Piri and B TowlerldquoMicroemulsion-enhanced displacement of oil in porousmedia containing carbonate cementsrdquo Colloids and SurfacesA Physicochemical and Engineering Aspects vol 530pp 60ndash71 2017

[13] R Nguele K Sasaki Y Sugai H Said Al-Salim and R UedaldquoMobilization and displacement of heavy oil by cationicmicroemulsions in dierent sandstone formationsrdquo Journal ofPetroleum Science and Engineering vol 157 pp 1115ndash1129 2017

[14] G Asadollahfard A Khodadi and N Javadifar ldquoUTCHEMmodel application for prediction of crude oil removal fromcontaminated sand columnsrdquo Journal of the Geological Societyof India vol 82 no 6 pp 712ndash718 2013

00

03Inje

ctio

n pr

essu

re (M

Pa)

06

09

12

15

0 3 6 9 12 15Injection-pore volume ratio

Experimental dataSimulation curve

Figure 8 e injection pressure curve

0

7

14

21

28

35

0

20

40

60

Moi

sture

cont

ent (

) 80

100

0 4 8 12 16

Oil

reco

very

()

Injection-pore volume ratio

Experimental data (moisture content)Simulative curve (moisture content)Experimental data (oil recovery)Simulative curve (oil recovery)

Figure 9 e moisture content and oil recovery curves


[15] K Aboulghasem Kazemi Nia S Kamy and D MojdehldquoCoupling IPhreeqc with UTCHEM to model reactive flowand transportrdquo Computers and Geosciences vol 82pp 152ndash169 2015

[16] P Zhang D Shen C Fan A Kan and M TomsonldquoSurfactant-assisted synthesis of metal-phosphonate inhibitornanoparticles and transport in porous mediardquo SPE Journalvol 15 no 3 pp 610ndash617 2013

[17] A Lohne and I Fjelde ldquoSurfactant flooding in heterogeneousformationsrdquo in Proceedings of Eighteenth SPE Improved OilRecovery Symposium pp 1ndash19 Society of Petroleum Engi-neers SPE-154178-MS Tulsa OK USA April 2012

[18] N Abou Sayed R Shrestha H K Sarma et al ldquoA newapproach optimizing mature waterfloods with electrokinetics-assisted surfactant flooding in Abu Dhabi carbonate reser-voirsrdquo in Kuwait International Petroleum Exhibition ampConference (KIPC) pp 1ndash20 Society of Petroleum EngineersSPE-163379-MS Kuwait December 2012

[19] C Han M Delshad K Sepehrnoori and G A Pope ldquoA fullyimplicit parallel compositional chemical flooding simulatorrdquoSPE Journal vol 12 no 3 pp 322ndash338 2013

[20] R Yang R Jiang S Liu X Zhang and H Liu ldquoNumericalsimulation of nonlinear seepage in ultra-low permeabilityreservoirsrdquo Acta Petrolei Sinica vol 32 no 2 pp 299ndash3062011


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Submit your manuscripts atwwwhindawicom

characteristics of the microemulsion flooding a three-dimension three-phase five-component microemulsionflooding mathematical model is established in which thediffusion and adsorption of surfactant molecules thechange of microemulsion viscosity and relative perme-ability are considered e finite difference method is usedto solve the model and simulation accuracy and calcu-lation speed are improved

2 The Non-Darcy Equation in Low-Permeability Reservoir

According to the literature [20] non-Darcy flow equation inlow-permeability reservoir can be expressed as

v K

μnablaPminus ξ1 minus

ξ1ξ2nablaPminus ξ2

1113888 1113889 (1)

e laboratory experiments are carried out to get thevalue of ξ1 and ξ2 e microemulsion system used in theexperiment is made of water SDS light oil n-butanol andsodium chloride e experimental schemes and the valuesof ξ1 and ξ2 under different conditions are shown in Table 1and the seepage velocity-pressure gradient curves are shownin Figure 1

3 The Establishment of MicroemulsionFlooding Mathematical Model

31 (e Assumptions of the Model Generally oil watersurfactant alcohol and inorganic salt are taken into accountin the microemulsion flooding And it is assumed that thereis a three-phase flow involving oil water andmicroemulsionin the reservoir It is considered that the reservoir is an-isotropic and heterogeneous and the reservoir rock andfluids involved in the microemulsion flooding process arecompressible e influences of capillary force and gravityeffect are also included

32 (e Material Balance Equation Considering the diffu-sion of surfactant molecules among each phase and theadsorption on the rock surface the continuity equation ofthe j composition in the i phase is

nabla middot ϕDijnabla ρjCij1113872 11138731113960 1113961minusnabla middot ρjViCij1113872 1113873minus 1113944

m

a1ηaij φij minusφaj1113872 1113873

z

ztϕρjsiCij + ρjaij1113872 1113873minus ρjqiCij

(2)

In above equations i indicates oil water and micro-emulsion phases denoted by o w and m and the value of i

could be 1 2 or 3 j assigning value of 1 2 3 4 or 5represents the compositions of oil water surfactant alcoholand inorganic salt respectively

It is assumed that the mass percentage of water com-position in oil phase Co2 is equal to 0 and the mass per-centage of oil composition in water phase Cw1 is 0 too e

Dij and aij pertaining to oil and water compositions re-spectively are neglected Combining equations (1) and (2) athree-dimensional three-phase and five-compositionmathematical model for microemulsion flooding can beobtained

nabla middot ϕSiρiDijnablaCij1113872 1113873 + 1113944m

i1nabla

⎧⎨

⎩KKriρi

μi

Cij⎡⎣nablapi minus ρignablaH

plusmn ξ1 +ξ1ξ2nablapi minus ξ2

1113888 11138891113891⎫⎬

⎭ z

zt1113944

m

i1ϕSiρiCi( 1113857minus 1113944

m

i1ρiqiCij

(3)

where Dij is the diffusion velocity of j composition in i

phase Cij is the mass percentage of j composition in i phaseand Ci is the comprehensive mass percentage of i phaseincluding the adsorbed terms

33 (e Auxiliary Equation e relationships of saturationamong each phase and mass percentage of j composition ineach phase can be written as

1113944

m

i1Si 1 (4)

1113944

n

j1Cij 1 (5)

e relationship of pressure among each phase is asfollows

pcai pa minuspi (6)

where a 1 2 and 3 and pcai 0 when a i

4 The Treatment of Important Parameters

41 Interfacial Tension Surfactant plays an important role inreducing interfacial tension and improving the flow ability ofcrude oil in the microemulsion system e indoor exper-iments are carried out to get the interfacial tension in dif-ferent surfactant concentrations And the results are shownin Figure 2

It can be seen from Figure 2 that with the increase ofsurfactant concentration the interfacial tension decreasesgreatly But the extent of decrease becomes smaller whenthe surfactant concentration reaches a certain value ereason is that with the increase of surfactant concentrationthe adsorption quantity of surfactant molecules in oil layersalso increases but the increase of effective concentration isnot proportional erefore the relationship betweensurfactant concentration and the interfacial tension couldbe written as

σ Acn cleCMC

σ C cgtCMC1113896 (7)

where the value of coefficients A index n constant C andCMC could be given through the experiments



CiC1 min

CiC1


(8)






μm μw 1 +MK

1minusK( )

n

(10)






Length(cm)

Diameter(cm)

Porosity()





000

005

010

Seep

age v

eloc

ity (c

ms

)

015

020

025





0001

001

01

Inte

rfaci

al te

nsio

n (m

Nm

)

1

10

100







kri k0riS

nii (11)


Si Si minus Sir




1 + TiNTi

ni nLowiprimer +


Highiprimer

nHighi minus n

Lowi( )

(12)



f1 T p x2 x3( ) μ11μ22 minus μ12( )2 0

f2 T p x2 x3( ) μ22μ33 minus μ23( )2 0

f3 T p x2 x3( ) μ11μ33 minus μ13( )2 0

(13)


sumk

i1ni dμi 0 (14)

0

2

4

Visc

osity

(mPa

middots)

6

8

10




0

02

04

06

08

1

20 30 40 50 60 70 80

K rj

Sw ()

Cs = 02

KrwKro

KrmKrom

(a)

KrwKro

KrmKrom

0

02

04

06

08

1K r

j

20 30 40 50 60 70 80Sw ()

Cs = 03

(b)




n1μ11 + n2μ12 + n3μ13 0

n1μ21 + n2μ22 + n3μ23 0

n1μ31 + n2μ32 + n3μ33 0

(15)


f T x2 x3( 1113857 x1μ12μ31 + x2μ21μ23 + x3μ31μ23 0

(16)


Gm T x2 x3( 1113857 z2μ2zn2

21113888 1113889

Tpμ1 n1

0 (17)


M Co

CmN

Cw

Cm (18)












7 Conclusion







Begin


i = 1

i le time nodes

Y

Read dynamic data

Solve the pressure



i = i + 1

N


Y

Output results

N


End



INJ3INJ1

PROD

INJ2 INJ4





Data Availability




Acknowledgments



References















00

03Inje

ctio

n pr

essu

re (M

Pa)

06

09

12

15




0

7

14

21

28

35

0

20

40

60

Moi

sture

cont

ent (

) 80

100

0 4 8 12 16

Oil

reco

very

()

















Journal of

Chemistry





Journal of

Volume 2018






Volume 2018




Journal of






Enzyme Research


Journal of



MaterialsJournal of






Na

nom

ate

ria

ls





CiC1 min

CiC1


(8)






μm μw 1 +MK

1minusK( )

n

(10)






Length(cm)

Diameter(cm)

Porosity()





000

005

010

Seep

age v

eloc

ity (c

ms

)

015

020

025





0001

001

01

Inte

rfaci

al te

nsio

n (m

Nm

)

1

10

100







kri k0riS

nii (11)


Si Si minus Sir




1 + TiNTi

ni nLowiprimer +


Highiprimer

nHighi minus n

Lowi( )

(12)



f1 T p x2 x3( ) μ11μ22 minus μ12( )2 0

f2 T p x2 x3( ) μ22μ33 minus μ23( )2 0

f3 T p x2 x3( ) μ11μ33 minus μ13( )2 0

(13)


sumk

i1ni dμi 0 (14)

0

2

4

Visc

osity

(mPa

middots)

6

8

10




0

02

04

06

08

1

20 30 40 50 60 70 80

K rj

Sw ()

Cs = 02

KrwKro

KrmKrom

(a)

KrwKro

KrmKrom

0

02

04

06

08

1K r

j

20 30 40 50 60 70 80Sw ()

Cs = 03

(b)




n1μ11 + n2μ12 + n3μ13 0

n1μ21 + n2μ22 + n3μ23 0

n1μ31 + n2μ32 + n3μ33 0

(15)


f T x2 x3( 1113857 x1μ12μ31 + x2μ21μ23 + x3μ31μ23 0

(16)


Gm T x2 x3( 1113857 z2μ2zn2

21113888 1113889

Tpμ1 n1

0 (17)


M Co

CmN

Cw

Cm (18)












7 Conclusion







Begin


i = 1

i le time nodes

Y

Read dynamic data

Solve the pressure



i = i + 1

N


Y

Output results

N


End



INJ3INJ1

PROD

INJ2 INJ4





Data Availability




Acknowledgments



References















00

03Inje

ctio

n pr

essu

re (M

Pa)

06

09

12

15




0

7

14

21

28

35

0

20

40

60

Moi

sture

cont

ent (

) 80

100

0 4 8 12 16

Oil

reco

very

()

















Journal of

Chemistry





Journal of

Volume 2018






Volume 2018




Journal of






Enzyme Research


Journal of



MaterialsJournal of






Na

nom

ate

ria

ls





kri k0riS

nii (11)


Si Si minus Sir




1 + TiNTi

ni nLowiprimer +


Highiprimer

nHighi minus n

Lowi( )

(12)



f1 T p x2 x3( ) μ11μ22 minus μ12( )2 0

f2 T p x2 x3( ) μ22μ33 minus μ23( )2 0

f3 T p x2 x3( ) μ11μ33 minus μ13( )2 0

(13)


sumk

i1ni dμi 0 (14)

0

2

4

Visc

osity

(mPa

middots)

6

8

10




0

02

04

06

08

1

20 30 40 50 60 70 80

K rj

Sw ()

Cs = 02

KrwKro

KrmKrom

(a)

KrwKro

KrmKrom

0

02

04

06

08

1K r

j

20 30 40 50 60 70 80Sw ()

Cs = 03

(b)




n1μ11 + n2μ12 + n3μ13 0

n1μ21 + n2μ22 + n3μ23 0

n1μ31 + n2μ32 + n3μ33 0

(15)


f T x2 x3( 1113857 x1μ12μ31 + x2μ21μ23 + x3μ31μ23 0

(16)


Gm T x2 x3( 1113857 z2μ2zn2

21113888 1113889

Tpμ1 n1

0 (17)


M Co

CmN

Cw

Cm (18)












7 Conclusion







Begin


i = 1

i le time nodes

Y

Read dynamic data

Solve the pressure



i = i + 1

N


Y

Output results

N


End



INJ3INJ1

PROD

INJ2 INJ4





Data Availability




Acknowledgments



References















00

03Inje

ctio

n pr

essu

re (M

Pa)

06

09

12

15




0

7

14

21

28

35

0

20

40

60

Moi

sture

cont

ent (

) 80

100

0 4 8 12 16

Oil

reco

very

()

















Journal of

Chemistry





Journal of

Volume 2018






Volume 2018




Journal of






Enzyme Research


Journal of



MaterialsJournal of






Na

nom

ate

ria

ls





n1μ11 + n2μ12 + n3μ13 0

n1μ21 + n2μ22 + n3μ23 0

n1μ31 + n2μ32 + n3μ33 0

(15)


f T x2 x3( 1113857 x1μ12μ31 + x2μ21μ23 + x3μ31μ23 0

(16)


Gm T x2 x3( 1113857 z2μ2zn2

21113888 1113889

Tpμ1 n1

0 (17)


M Co

CmN

Cw

Cm (18)












7 Conclusion







Begin


i = 1

i le time nodes

Y

Read dynamic data

Solve the pressure



i = i + 1

N


Y

Output results

N


End



INJ3INJ1

PROD

INJ2 INJ4





Data Availability




Acknowledgments



References















00

03Inje

ctio

n pr

essu

re (M

Pa)

06

09

12

15




0

7

14

21

28

35

0

20

40

60

Moi

sture

cont

ent (

) 80

100

0 4 8 12 16

Oil

reco

very

()

















Journal of

Chemistry





Journal of

Volume 2018






Volume 2018




Journal of






Enzyme Research


Journal of



MaterialsJournal of






Na

nom

ate

ria

ls








Begin


i = 1

i le time nodes

Y

Read dynamic data

Solve the pressure



i = i + 1

N


Y

Output results

N


End



INJ3INJ1

PROD

INJ2 INJ4





Data Availability




Acknowledgments



References















00

03Inje

ctio

n pr

essu

re (M

Pa)

06

09

12

15




0

7

14

21

28

35

0

20

40

60

Moi

sture

cont

ent (

) 80

100

0 4 8 12 16

Oil

reco

very

()

















Journal of

Chemistry





Journal of

Volume 2018






Volume 2018




Journal of






Enzyme Research


Journal of



MaterialsJournal of






Na

nom

ate

ria

ls





Data Availability




Acknowledgments



References















00

03Inje

ctio

n pr

essu

re (M

Pa)

06

09

12

15




0

7

14

21

28

35

0

20

40

60

Moi

sture

cont

ent (

) 80

100

0 4 8 12 16

Oil

reco

very

()

















Journal of

Chemistry





Journal of

Volume 2018






Volume 2018




Journal of






Enzyme Research


Journal of



MaterialsJournal of






Na

nom

ate

ria

ls
















Journal of

Chemistry





Journal of

Volume 2018






Volume 2018




Journal of






Enzyme Research


Journal of



MaterialsJournal of






Na

nom

ate

ria

ls




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