Exergy return on exergy investment analysis of natural-polymer (Guar-Arabic gum) enhanced oil recovery process

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Delft University of Technology

Exergy return on exergy investment analysis of natural-polymer (Guar-Arabic gum)

enhanced oil recovery process

Hassan, Anas M.; Ayoub, M.; Eissa, M.; Musa, T.; Bruining, Hans; Farajzadeh, R.

DOI

10.1016/j.energy.2019.05.137

Publication date

2019

Document Version

Final published version

Published in

Energy

Citation (APA)

Hassan, A. M., Ayoub, M., Eissa, M., Musa, T., Bruining, H., & Farajzadeh, R. (2019). Exergy return on

exergy investment analysis of natural-polymer (Guar-Arabic gum) enhanced oil recovery process. Energy,

181, 162-172. https://doi.org/10.1016/j.energy.2019.05.137

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A

2-D

simulation

study

on

CO

2

soluble

surfactant

for

foam

enhanced

oil

recovery

Yongchao

Zeng

a

,

Rouhi

Farajzadeh

b,c,

*

,

Sibani

L. Biswal

a

,

George

J. Hirasaki

a

RiceUniversity,6100MainSt.,MS-362,DepartmentofChemicalandBiomolecularEngineering,Houston,TX,77005USA b

ShellGlobalSolutionsInternational,2288GSRijswijk,TheNetherlands c

DelftUniversityofTechnology,Delft,2628CN,TheNetherlands ARTICLE INFO

Articlehistory: Received3October2018

Receivedinrevisedform25November2018 Accepted6December2018

Availableonline14December2018 Keywords: Nonionicsurfactant Partitioncoefﬁcient CO2 Foam Gasbreakthrough Mobilitycontrol

Enhancedoilrecovery(EOR) Foamsimulation

ABSTRACT

ThispaperprobesthetransportofCO2solublesurfactantforfoaminginporousmedia.Wenumerically

investigatetheeffectofsurfactantpartitioningbetweentheaqueousphaseandthegaseousphaseon foamtransportforsubsurfaceapplicationswhenthesurfactantisinjectedintheCO2phase.A2-D

reservoir simulation is developed to quantify the effectof surfactant partition coefﬁcient on the displacementconformanceandCO2sweepefﬁciency.Atexture-implicitlocal-equilibriumfoammodelis

embeddedtodescribehowthepartitioningofsurfactantbetweenwaterandCO2affectstheCO2foam

mobilitycontrolwhensurfactantisinjectedintheCO2phase.Weconcludethatwhensurfactanthas

approximatelyequalafﬁnitytoboththeCO2andthewater,thetransportofsurfactantisinlinewiththe

gaspropagationandthereforethesweepefficiencyis maximized.Toohighaffinitytowater(small partitioncoefficient)resultsinsurfactantretardationwhereastoohighaffinitytoCO2(largepartition

coefficient)leadstoweakfoamandinsufficientmobilityreduction.Thisworkshedslightuponthedesign ofwater-alternating-gas-plus-surfactant-in-gas(WAG+S)processtoimprovetheconventionalfoam process with surfactant-alternating-gas (SAG) injection mode during which significant amount of surfactantcouldpossiblydraindownbygravitybeforeCO2slugscatchuptogeneratefoaminsituthe

reservoir.

Introduction

CO2 injectionhassuperiordisplacementefﬁciency wherever

gas contacts oil. It recovers oil by mechanisms of extraction, dissolution,solubilization,andpossiblysomeotherphasebehavior changes[1–3].Asof 2017inUnited States,itproduces 280,000 barrelsofoilperdayaccountingforapproximatelyhalfoftheoil producedbyenhancedoilrecovery(EOR)methodsand6%ofthe totaldomesticoilproduction[4–7].Withnoveltechnologiesbeing developed to capture CO2 from industrial sites, CO2 injection

methodisattractingmoremarketinterests.Howeverduetothe largedensityandviscositycontrastbetweenCO2andthecrudeoil,

thesweepefﬁciencyofCO2ﬂoodislimitedbygravityoverrideand

viscousfingering.Thescenariocouldbeworseifthereservoiris highly heterogeneous or fractured where the fluids of high mobility tendtofingerthrougha preferential pathand leavea largeportionofthereservoirun-swept[2,8–16].

The sweep efﬁciency of CO2 EOR can be improved by the

injectionmodeofwater-alternating-gas(WAG)[17–22].Ideallythe injected water canreduce the relativepermeability of theCO2

phase and therefore delaythe gas breakthrough.However, the improvementcanbelimitedbecauseofphasesegregation.Amore potentwaytoreducethemobilityofCO2istodispersethegasin

aqueousphase withsurfactants [8,23–30]. CO2 Foam inporous

media is a dispersion of CO2 in aqueous phase such that the

aqueousphase(wettingphase)is continuousandatleastsome partoftheCO2(non-wettingphase)ismadediscontinuousbythin

liquid_ﬁlmscalledlamella[31,8,32_–35].Dependingonthereservoir temperatureandpressure,CO2canbeeithergaseous-likeorinthe

supercritical state.Above thecriticaltemperature(31.10C) and pressure(1071psi),gaseousCO2transitionsintosupercriticalstate.

Conventionalnomenclaturereferstosurfactantstabilized super critical CO2 dispersion in water (C/W) as emulsion. Yet, for

simplicity,wedonotdifferentiatethegaseous-CO2foamandCO2

-in-water (C/W)emulsion [36] andonly usethetermCO2 foam

indicatingthatCO2istheinternalphase.Therationaleisthatthe

fundamental principles of interfacialphenomena and transport propertiesasCO2foamtransitionsintoCO2emulsionstillholdthe

* Correspondingauthor.

E-mailaddress:r.farajzadeh@tudelft.nl(R.Farajzadeh).

https://doi.org/10.1016/j.jiec.2018.12.013

JournalofIndustrialandEngineeringChemistry72(2019)133–143

ContentslistsavailableatScienceDirect

Journal

of

Industrial

and

Engineering

Chemistry

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same.Admittedly,asthedensityincreases,CO2startstosolubilize

crude oil. Nevertheless, the compositional change of the oleic phaseduringCO2ﬂooding beyondminimal miscibilitypressure

(MMP)isbeyondthescopeofthispaper.Wemainlyfocusonthe transportofCO2andsurfactantinporousmedia.

Foam can decrease the mobility of CO2 and increase the

apparentviscosityofinjectionﬂuidsbyblockingthecontinuous

gaspath. DispersedCO2 bubblestrapped inthe foamstructure

haveamobilitythatisordersofmagnitudelowerthancontinuous CO2 ﬂow. Therefore foam assisted CO2 injection can effectively

address the issue of poor mobility ratio and improve the volumetricsweepefﬁciency.

Commonlyusedionicsurfactantscanonlybeinjectedinwater becausetheyarenotsoluble inthegas.Thereforetheinjection mode for these surfactants is called surfactant-alternating-gas (SAG). Well-known ionic surfactants have been introduced in detailfromliterature[26,29,37–41].NovelCO2solublesurfactants

include the nonionic exthoxylated alcohols and switchable exthoxylatedamines[27,40,42_–49].Thehydrophobicpartcanbe either alkylphenol or branched/unbranched alkyl [45]. These surfactantscanbeinjectedwithCO2phase.Ifsurfactantisinjected

withCO2,wecallitwater-alternating-gas-plus-surfactant-in-gas

(WAG+S)mode.WAG+Sprocesshasthepotentialtooutperform SAG in different ways. Firstly WAG+S can improve the well injectivity[50]whensurfacefacilitiesswitchfromCO2injectionto

waterinjection.Secondlyifsurfactantisinjectedandtransported in the CO2 phase, it can foam with thewater from secondary

recovery, elongate thegas-water mixing zone and delayphase segregation[27,51–53].

Becausethesurfactantcandissolve inboth theCO2and the

water, it is critical to understand how the partitioning of the surfactantbetweenthetwophasescanaffectthefoamtransportin porousmedia.PartitioncoefﬁcientKsgwisameasureoftheratioin

solubilityofthesurfactantin gaseousandaqueousphases.Itis deﬁned as theratio of thesurfactant concentrationin gaseous phase Csg to that in aqueous phase Csw at thermodynamic

equilibriumasinEq.(1).Insomeliterature,surfactantpartition coefficientisdefinedastheratioofmassfractionratherthanthe concentration. The two definitions of partition coefficient are differentbyafactor thatequalstothedensityratioofthetwo phases,yetrepresentthesameinnature.

Ksgw¼

Csg

Csw ð1Þ

ThevalueofsurfactantpartitioncoefﬁcientKsgwisdependent

onseveralfactors[27,38,54]andcanbeexperimentallymeasured inthelab.Renetal.[53]testedaseriesofdifferentexthoxylated alcoholsanddiscoveredthatthevalueofthepartitioncoefﬁcient oftheseCO2solublesurfactantsvariesinordersofmagnitudewith

respecttothereservoirconditions(from0.02togreaterthan1).In general,thepartitioncoefﬁcientincreasesproportionallywiththe reservoirpressure,whereasdecreasesmoredramaticallywiththe increase inreservoir temperature.Additionally,theKsgw is very

sensitive to surfactant formula and increases with decreasing ethyleneoxide(EO)groups.Thenumberofpropyleneoxide(PO) groupalsoplaysacriticalroleindeterminingsurfactantpartition coefﬁcient.ComparedtoEOgroups,POgroupismorehydrophobic and tends toincrease theKsgw.Unlike nonionicsurfactants, the

partitioncoefﬁcientofswitchablesurfactantisverysensitivetothe reservoirpH.Thisisbecausetheaminegroupcanbeprotonatedin the aqueous phase and the protonation degree increases with decreasingpH.Thispapersystematicallysimulatesthetransportof surfactantandfoamina2-Dhomogeneousreservoirwithdifferent Ksgwvalues.In ourpreviouspaper[51],weestablisheda1-D

2-phase(waterandCO2)home-madefoamsimulatorand

demon-stratedthatwhensurfactantisapproximatelyequallypartitioning betweengaseousphaseandaqueousphase,foamisinfavorforoil displacement in regard with apparent viscosity and foam propagationspeed. In this paper, weextend themodeling toa 2-D3-phase(water,CO2,andoil)systemwithgravityatplay.The

simulation is done using Shell’s in-house Modular Reservoir Simulator(MoReS)[55].Wewillbrieﬂysummarizethe implicit-texture(IT)local-equilibrium(LE)foammodelinSection “Implicit-Nomenclature

Csg Surfactantconcentrationinthegaseousphase(g/L)

Csw Surfactantconcentrationintheaqueousphase(wt

%)

epdry Foammodelparameterthatregulateshow abrupt-lyfoamdriesoutatlimitingwatersaturation epsurf Foammodelparameter,theexponentinFsurfactant

function

epoil Foam model parameter, the exponent in Foil

function

Foil Oildependentfunctioninfoammodel

Fsurfactant Surfactantdependentfunctioninfoammodel

Fwater Water saturation dependent function in foam

model

ﬂoil Foammodelparameterthatsetsthemaximumoil saturationbelowwhichtheoilhasnoimpacton foam

fmoil Foammodelparameterthatsetstheminimumoil saturation above which the oil kills the foam completely

FM Correctionfactorfunctionfor gasphasemobility reductionbyfoam

fmmob Foammodelparameterthatsetsthemaximumgas mobilityreduction

fmsurf Foam model parameter that sets the minimal surfactant concentration above which foam strength is no longer dependent on surfactant concentration

kfrg Relativepermeabilitytogas(foam)

knfrg Relativepermeabilitytogas(nofoam)

ko_rg End-pointrelativepermeabilitytogas kro Relativepermeabilitytooil

korog End-pointrelativepermeabilitytooilwithrespect

togas

korow End-pointrelativepermeabilitytooilwithrespect

towater

krw Relativepermeabilitytowater

korw End-pointrelativepermeabilitytowater

Ksgw Surfactant partition coefﬁcient between gaseous

phaseandaqueousphase ng Coreyexponentforgas

nog Coreyexponentforoilwithrespecttogas

now Coreyexponentforoilwithrespecttowater

nw Coreyexponentforwater

PV Porevolumesinjected Sg Gassaturation

Sgr Residualgassaturation

So Oilsaturation

Sorg Residualoilsaturationtogas

Sorw Residualoilsaturationtowater

Sw Watersaturation

Swc Connatewatersaturation

l

f

rg Mobilityofthegasphaseinpresenceoffoam

l

nf

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texture local-equilibrium foam model”, and review the three-phaserelativepermeabilitymodelinSection“Three-phaserelative permeability model”. We will introduce the 2-D homogeneous modelreservoircreatedforsimulationinSection“2-D Homoge-neousmodelreservoirforsimulation”.InSection“CO2displacing

waterwith differentpartition coefﬁcients”, wewill discuss the effectofpartition coefﬁcientonfoambycomparingthestudied scenariosinwhichcontinuousCO2isinjectedwithsurfactantsof

variedpartitioncoefﬁcientintoanaqueousreservoirtodisplace water.In Section“Casestudy:WAG,SAGand WAG+S”,wewill compare the oil recovery efﬁciency between WAG, SAG and WAG+SmodesandwillshowthatCO2solublesurfactantswith

proper partition coefﬁcient can outperform conventional ionic surfactantsintermsofmobilitycontrolandoilrecoveryefﬁciency by synchronizing the surfactant transport with gas phase propagationina2-Dhomogeneousmodelsystem.

Numericalmodels

Implicit-texturelocal-equilibriumfoammodel

Foamcanlowerthegasphasemobilitybyordersofmagnitude. Yetthewatermobility isproventoremainthesameatagiven watersaturation[56].Apparentviscosity

m

appisusedasameasure

of foam strength in porousmedia. It is deﬁned as normalized pressuregradientrpwithrespecttorockpermeabilitykandtotal superﬁcialvelocity(ug+uw)asshowninEq.(2).

m

app¼

krp

ugþuw ð2Þ

The STARS version of the implicit-texture local-equilibrium model[57,58]implementedheremodiﬁestherelativemobilityto thegasphaseasshowninEq.(3).Thecorrectionfactorforthegas phasemobilityreductionFMisinverselyrelatedtotheproductofa seriesofdependencefunctionsasshowninEq.(4).Theparameter fmmob sets a reference to the maximum foam strength. The dependencefunctionsFsurfactant,Fwater,andFoilareallintherangeof

[0,1].ThesurfactantconcentrationdependencefunctionFsurfactant

andthewatersaturationdependencefunctionFwaterarediscussed

inpreviouspublications[59–62].InSection“Casestudy:WAG,SAG and WAG+S_” where the oil phase is present, function Foil is

introduced to account for the effect of oil on foam. Oil can destabilize foam in porous media by varied mechanisms

[15,25,33,63,64].Inthissimulation,theparameterﬂoilrepresent theoilsaturationbelowwhichoil doesnotaffectfoamstrength andFoilequalsto1,whereastheparameterfmoilrepresenttheoil

saturationabovewhichfoamiscompletelykilledandFoilequalsto

0.TheparameterepoilregulateshowFoildeceasesasoilsaturation

So increases ﬂoil to fmoil. We list the values assigned to the

parametersaforementionedinTable1andshowthe correspond-ing foam apparentviscosityas a function of foam quality (gas

fractionalﬂow ug

ugþuw)andsurfactantconcentrationCswinFig.1.

l

f rg¼

l

nf

rgFM ð3Þ

FM¼₁_þ_f_mmob_F 1

surfactantFwaterFoil ð4Þ

Fsurfactant¼ Csw fmsurf epsurf forCsw<fmsurf 1 forCswfmsurf 8 < : ð5Þ Fwater¼0:5þ

arctan½epdryðSwfmdryÞ

p

ð6Þ Foil¼ 0 forSo>fmoil fmoilSo fmoilfloil epoil forfloil<So<fmoil 1 forSo<floil 8 > > < > > : ð7Þ

Three-phaserelativepermeabilitymodel

Coreymodel[65]isusedtocalculatetherelativepermeability towaterkrwandgasknfrg(nofoam).Itiswell-knownthatformation

wettability plays a critical role in determining the relative permeability curves [66–69]. Without introducing unnecessary complexities, we simply assume strict water-wet formation condition in this paper. Therefore, theparameter krw is onlya

functionofwatersaturationSwandk

nf

rg isonlyafunctionofgas

saturationSg.Inthe3-phasesimulation,lineariso-permisapplied

tocalculatetherelativepermeabilitytooilkroasshowninFig.2.

Intheabsenceofgas,we usethewater-oiltwo-phaseCorey model tocalculatekrobasedonthewater/oilsaturations (thick

greenlineonthebottom);atconnatewatersaturation(thickgreen lineparalleltothesideGas–Oil),weusetheGas–OilCoreymodel tocalculatethekroatSwc.Inthethreephaseregion,thelinear

iso-permmodelassumesthatthesaturations(Sw,Sg,So)onthesame

tieline(straightlinesconnectingthetwothickgreenlines)givethe Table1

STARSfoammodelparameters.

Parameter Value fmmob 500 Fsurfactant fmsurf 0.2wt% epsurf 1 Fwate fmdry 0.25 epdry 500 Foil ﬂoil 0.1 fmoil 0.4 epoil 1.5

Fig.1.Foam apparentviscositymapp calculatedasa functionoffoam quality (fg¼uguþugw)andsurfactantconcentrationCswusingparametersaforementioned

in Table 1.

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samekrovalue.Thethree-phaserelativepermeabilityparameters

arelistedinTable2.

2-DHomogeneousmodelreservoirforsimulation

A2-Dhomogeneousmodelreservoirwithapermeabilityof1 Darcyis created for the simulations in Section“CO2 displacing

waterwithdifferentpartitioncoefﬁcients”and“Casestudy:WAG, SAGandWAG+S”. Themodelreservoiris2000ftinlengthand 200ftinthickness.Initially,thereservoirconditionissetat100bar inpressureand100Cintemperature.Inallcasesstudied,ﬂuids areinjectedat1ft/dayinterstitialvelocity.ThePecletnumbersfor thesurfactantdispersioninbothphases(CO2andwater)areequal

to50forﬁeld-levelsimulation[2].

In Section “CO2 displacing water with different partition

coefﬁcients”,thereservoirisinitially100%saturatedwithwater. CO2isinjectedcontinuouslywithsurfactantofdifferentKsgwvalues

todisplacethewaterasshowninTable3.Theinjectionsurfactant concentrationis2.5g/LCO2atreservoirconditions,1.25timesofthe

fmsurfvalue.InthisSection,wewillfocusontheeffectofsurfactant partitioningbetweenCO2andaqueousphasesonthesurfactant

transport and foam propagation, and investigate the optimal partitioncoefﬁcientthatmaximizesthesweepefﬁciencyofCO2.

InSection“Casestudy:WAG,SAGandWAG+S”,weaddone moredegreeofcomplexitybyintroducingblackoilintothemodel system.ThehypotheticalblackoilhasanAPIgravityof45anda viscosity of 0.4cP under the reservoir condition (100C and 100bar).ThereservoirisinitiallyatanoilsaturationSoi=ð1SwcÞ

and thereservoiris waterfloodedfor 1PV beforeenhanced oil recovery techniques are applied. After the water flooding, the averageoilsaturationisreducedto0.4.WAG,SAG,andWAG+Sare appliedtothewaterfloodedreservoirrespectivelyinCaseA,B,and C.InthisSection,wewillfocusonthecomparisonbetweenthese EORapplications.

Resultsanddiscussion

InthisSection,wewillﬁrstshowtheresultsofcontinuousCO2

injectionwithCO2solublesurfactanttodisplacewaterandthen

comparethevariousEORtechniques,highlightingthebeneﬁtof injectingsurfactantwithCO2andthecriticalroleofKsgw.

CO2displacingwaterwithdifferentpartitioncoefﬁcients

InCaseI,CO2withaCO2solublesurfactantofsmallpartition

coefﬁcient(Ksgw=0.01)isinjectedtodisplacewater.Theinjected

surfactant concentrationis 2.5g/L atreservoir condition. Fig.3

displays the snapshots of the saturation and the surfactant concentrationpro_ﬁleat differentdimensionlesstimes,thetotal porevolumes(PV)ofCO2injected.Itappearsthatthesurfactant

transportisseverelyretardedwithrespecttothegaspropagation. After1PVofinjection,thesurfactantonlypenetratesafairlysmall portionofthereservoir.Thesegregationbetweenthesurfactantand theCO2isbecauseoftheextremelyhighsurfactantafﬁnitytowater.

Uponwatercontact,mostofthesurfactantquicklypartitionsinto theaqueousphase.Thereforethesurfactantaccumulatesinthenear well-boreregionandthesurfactantconcentration inthe waterCswis

predominately higher than that in thegas phase Csg.Once the

surfactantisstrippedofftothewater,theCO2mobilitycontrolis

lost.Consequently,thegasoverridestheupperlayerofthereservoir andstreaksthroughearlyandthesweepofCO2ispoor.

InCaseII,thesurfactantpartitioncoef_ﬁcientissetto1,which meansthatthesurfactanthasequalafﬁnitytoboththeCO2andthe

Fig.2.Schematicofthelineariso-permrelativepermeabilitytooilin3-phaseregion.

Table2

Three-phaserelativepermeabilityparameterstowater,oil,andgas(nofoam). Water–oilrelativepermeabilityparameters

Parameter Symbol Value

Connatewatersaturation Swc 0.10 Residualoilsaturationtowater Sorw 0.40 End-pointrelativepermeabilitytowater korw 0.22 End-pointrelativepermeabilitytooil ko

row 1.0 Coreyexponentforwater nw 4.0 Coreyexponentforoilwithrespecttowater now 2.0 Oil–gasrelativepermeabilityparameters

Parameter Symbol Value

Residualgassaturation Sgr 0.05 Residualoilsaturationtogas Sorg 0.01 End-pointrelativepermeabilitytogas korg 1.00 End-pointrelativepermeabilitytooil korog k

o row Coreyexponentforgas ng 1.7 Coreyexponentforoilwithrespecttogas nog 4.0

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water.Incontactwithwater,thesurfactantconcentrationinthe gasphaseCsgwillbeequaltothatinthewaterCsw.Fig.4showsthe

snapshots of the surfactant distribution along with the phase saturation proﬁle. In this case, the surfactant transport is synchronized with the gas propagation. The surfactant creates foamwiththewaterresiding inthereservoirwhereverthegas sweeps. The foamed gas can effectively mitigate the effect of gravity.Therefore,thesweepefﬁciencyofCO2isgreatlyimproved.

After1PVofCO2injection,mostofthereservoirhasbeenswept.

IncaseIII,thesurfactantpartitioncoefﬁcientisincreasedto50, whichmeansthatthesurfactantpreferstostaywiththeCO2even

Table3

CharacteristicvaluesforsurfactantpartitioncoefﬁcientKsgwforthecasestudiesin bothSection“CO2displacingwaterwith differentpartitioncoefﬁcients”and Section“Casestudy:WAG,SAGandWAG+S”.

Surfactantpartition coefﬁcient

Characteristic value

Remark

SmallKsgw 0.01 Strongafﬁnitytowater UnityKsgw 1.00 Equalafﬁnitytowaterand

CO2

LargeKsgw 50.0 StrongafﬁnitytoCO2

Fig.3. CaseI:ContinuousCO2(withdissolvedsurfactant)injectiontodisplacewaterwithsmallpartitioncoefficientKsgw=0.01(A)Saturationprofileindicatingthatthegas overridesthereservoirandprematurelybreaksthrough;(B)Surfactantconcentrationprofileindicatingthatthesurfactantishighlyconcentratednearthewellandthe transportisretarded.

Fig.4.CaseII:ContinuousCO2(withdissolvedsurfactant)injectiontodisplacewaterwithunitypartitioncoefficientKsgw=1.00(A)Saturationprofileindicatingthatthe sweepofCO2isgreatlyimproved;(B)SurfactantconcentrationprofileindicatingthatthesurfactanttransportissynchronizedwiththeCO2propagation.

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if it is equilibrated with water. At equilibrium, the surfactant concentrationintheCO2Csgwillbealothigherthanthatinthe

waterCsw.FromFsurfactantfunction,itisclearthatfoamstrengthis

directlyrelatedtotheCsw.Therefore,thehighlydilutedsurfactant

concentration in the aqueous phase results in insufﬁcient gas mobility reduction and thefoam is not strong enough toﬁght against the gravity. Consequently, only the upper layer of the reservoirissweptbyCO2.UnlikeCaseIinwhichtheCO2losesits

mobilitycontrolcompletely,inCaseIII,thepoorsweepefﬁciency resultsfromthelackofsurfactantintheaqueousphaseasshown inFig.5.

From the case studies above, we conclude that the foam transportishighlydependentonthesurfactantpartition coef fi-cient.Fig.6comparesthewaterrecoveryefficiencywithrespectto differentpartition coefficient.Before thegas breakthrough,the efficiencyofthewaterrecoveryisproportionaltothevolumeof CO2injected.Thereforethethreewaterrecoverycurvesoverlapin

the beginning. In case of unity (Ksgw=1) and large (Ksgw=50)

partitioncoefﬁcients,mostofthesurfactantiscarriedbytheCO2.

Therefore, after the CO2 breaks through, the water recovery

efﬁciencytendstoleveloffandreachplateau.However,inthecase of small partition coefﬁcient (Ksgw=0.01), the water recovery

efﬁciencykeepsincreasingaftertheCO2breakthrough.Thisisdue

tothepropagationofretardedsurfactantbank.Becauseofthehigh afﬁnityofthesurfactanttotheaqueousphase,waterstripsoffthe surfactant from the CO2 soon after injection. Therefore, the

surfactantfront is left farbehind thegas front. WhentheCO2

reachestheproductionwellatthebreakthroughtime,surfactantis stillpropagatinginthereservoir.Therefore,morefoamisbeing created and the water recovery efﬁciency keeps increasing. However,ittakesmuchmorevolumesofCO2toreachthesame

levelofwaterrecoveryefﬁciencycomparedtothecaseofunity partitioncoefﬁcient.

Insummary,unitypartitioncoefficientissuperiortoeithertoo largeortoosmallpartitioncoefficientintermsofmobilitycontrol andmaximizingsweepefficiency.Whenthesurfactantpartition coefficientistoosmall,thesurfactantwillbehighlyconcentrated nearthewell-bore, andthegasbreaksthroughearly.Too large partitioncoefficientresultinweakfoam,andthefoamstrength mightnotsufficetofightagainstgravityeffect.

Casestudy:WAG,SAGandWAG+S

InthisSection,wewillcomparethreeEORtechniques(CaseA: WAG, Case B: SAG, and Case C: WAG+S) to demonstrate the advantageofusingconventionalfoamandfoamwithCO2soluble

surfactantfor residualoil recovery.Inall cases,thereservoiris waterﬂooded totheremainingoilsaturationof 0.4.In CaseA, WAG,waterslugsandgasslugsarealternativelyinjectedintothe reservoir.Eachcycleconsistsof0.2PVofgasand0.05PVofwater. Inotherwords,theaveragegasfractionalﬂowis0.8.InCaseB,SAG, 0.5wt%oftraditionalsurfactant(onlysolubleinwater)isaddedto theaqueousphasetogeneratefoaminsitu.Alltheotheroperation conditionsarekeptexactlythesameasCaseA.InCaseC,WAG+S, thesameamountofCO2solublesurfactantisinjectedwithCO2

insteadofwater.TheonlydifferencebetweenCaseBandCisthat in Case C, the surfactant is injected with the gas phase and partitionstotheaqueousphasetofoamwithapartitioncoefﬁcient ofunity(Ksgw=1.0).ThefoammodelparametersinCaseBandCare

keptexactlythesame,meaningthatthesurfactantshavethesame foamingcapability.

Fig.7displaysthe3-phasesaturationprofilesnapshotsforthe WAGprocess.Thegasonlyfloodstheupperpartofthereservoir and breaks through during the first gas slug injection. The saturationprofile doesnot changemuch afterthefirst cycleis injected.Duetothedensityandviscositycontrast,theCO2pushes

the oil down.An oil bandis formed below the gaspath way, however,ishardlyproducedduetothepoorgasmobilitycontrol. Foamcaneffectivelymitigatethegravityeffect.Fig.8showsthe resultsofCaseBinwhich0.5wt%surfactant(onlysolubleinwater) isaddedtotheaqueousphase.Gasmobilityissigniﬁcantlyreduced bythegenerationoffoaminsidetheporousmedium.Gas(depicted inred)partiallypenetratesthelowerpartofthereservoirandan oilbankingreenisformedinfrontofthefoam.Theoilisslowly producedfromtheproductionwellontheright.

However, comparing the3-phase saturation profile and the surfactant concentration profile in Fig. 8, it is noticed that significantamountofsurfactantdrainsdownbeforethegasslugs catchesupandiswastedduringthewaterinjectionperiod.Thegas slugoverridesthereservoir;however,thesurfactantslug under-ridesthereservoir.Abetteralternativetoinjectthesurfactantis

Fig.5.CaseIII:ContinuousCO2(withdissolvedsurfactant)injectiontodisplacewaterwithlargepartitioncoefficientofKsgw=50.0(A)Saturationprofileindicatingthatthe foamstrengthisinsufficienttokeepCO2fromoverridingthereservoir;(B)Surfactantconcentrationprofileindicatingthatthesurfactantconcentrationintheaqueousphase ishighlydiluted.

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needed to synchronize the gas propagationand the surfactant transportsuchthatthesurfactantisavailabletomakefoamwhere thegassweeps.

Fig.9displaystheresultswhenthesameamountofsurfactant isinjectedwiththeCO2phaseinsteadofthewater.Thepartition

coefﬁcientbetweenthewater andtheCO2 inthis case isunity

(Ksgw=1.0).Withthefavorablepartitioncoefﬁcient,itisshownthat

thesweepisfurtherimprovedfromtheSAGprocess.Thegasphase carriesthesurfactantanddissolvestherightamounttowaterto generatefoam.Itisnotablethatthegaspenetratesintoaneven largerareainlowerpartofthereservoir.Inaddition,theoilbank accumulated is larger compared to the SAG process. All these improvement is because of the synchronization of the gas propagationandthesurfactanttransport.

However, it is important to point out that the recovery efﬁciency of WAG+S is highly dependent on the partition coefﬁcient.As discussed in Section “CO2 displacing water with

different partition coefficients”, too small partition coefficient results in surfactant transport retardation whereas too large partition coefficient resultsin insufficient foam robustness. As showninFig.10(A),partitioncoefficientofeither0.01or50.0leads topooreroil recovery efficiencycompared toSAG process.The sensitivity of surfactant partition coefficient onoil recovery is displayedin Fig.10(B).The shape ofthe oil recoveryefficiency curve,exhibitingalocalmaximum,isa resultof thecompeting mechanismsbetweenfastersurfactanttransport(largeKsgw)and

higher foam strength (small Ksgw).The surfactant needs to be

transported with the CO2 whereas adequate amount of the

surfactantneedstobedissolvedinthewatertomakethefoam strong.TheoptimizedsurfactantpartitioncoefﬁcientforWAG+S processisunityforthecaseconsideredhere.

TofurtherinvestigatetheWAG+Sprocess,aseriesofsensitivity analysis are conducted with respect to a number of critical reservoir properties suchascrude oil viscosity, Peclet number/ dispersivity, reservoir thickness, and well spacing (distance betweentheinjectionwelland theproductionwell). In allthe sensitivityanalysis,thereservoiriswater-ﬂoodedfor1PVandthen thesameWAG+Sprocessasdescribedabovewithaunitypartition coefﬁcient (Ksgw=1.0) was applied. The overall oil recovery

efﬁciency(crudeoil percentagerecoveredbased ontheoriginal oilinplace(OOIP))isplottedasafunctionofdifferentvariablesas showninFig.11.

Fig.11(A) shows that the overalloil recoveryefficiency is a strongfunctionofthecrudeoilviscosity.Asthecrudeoilviscosity increases,theefficiencyofWAG+Sprocessdecreaseslinearlyasa functionofthelogarithmofthecrudeoilviscosityusingthesame setoffoamparameters.Togeneralizetheobservation,wedefinea new dimensionless variablecalled the oil/foamedgas viscosity ratioasshowninEq.(8).Thenumeratoristhecrudeoilviscosity

m

oilwhereasthedenominatoristhegasviscosity

m

gastimesthe

parameter fmmob. The denominator is a characteristic of the maximum foam strength (gas mobility reduction) that can be Fig.6. Waterrecoveryefficiencycomparisonbetweencasesofvariedsurfactantpartitioncoefficients.Unitypartitioncoefficientissuperiortoeithertoosmallortoolarge partitioncoefficientintermsofwaterrecoveryefficiency.

Fig.7.CaseA:Water-alternating-gas.The3-phasesaturationproﬁleindicatingthatWAGmodehasverylimitedimprovementinoilrecoverycomparedtowaterﬂooding. Y.Zengetal./JournalofIndustrialandEngineeringChemistry72(2019)133–143 139

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expected.It is asimple measureof therelativeviscosityofthe crude oil and foam. It is concluded that stronger foam willbe requiredasthecrudeoilviscosityincreasesinordertoachievea givenoilrecoveryefﬁciency.Yet,itisworthwhiletomentionthat thecrude oils of differentviscosity arelikely tohavedifferent foam-oil interactions. Therefore the parameters in the oil saturationdependentfunctionFoilarelikelytovary.Forsimplicity,

sucheffectisnotincludedinthisanalysis.

Oil=FoamedGasViscosityRatio¼

m

oil

m

gasfmmob ð8Þ

Fig.11(B) showsthe sensitivity analysiswithrespect tothe dispersion. The overall oil recovery efﬁciency is plotted as a function ofboth the Peclet numberand the dispersivityof the surfactantinthereservoir.Itiswelldiscussedintheliterature[2]

that the actual dispersivity of components increases with the characteristiclengthofthesystem.Thereasonbehindisthatthe geologicalformationshaveheterogeneitiesofalllengthscalesand thus mixing at all length scales. However, in this sensitivity analysis,itisfoundthattheefficiencyofWAG+Sprocessishardly affectedbyawidechangeinthedispersivityvalues.Inbothlab scale and reservoir scale dispersion, the overall oil recovery Fig.8. CaseB:Surfactant-alternating-gas.(A)3-phasesaturationprofileindicatingthatthegasmobilityisreducedbyfoaminpresenceofsurfactantandthesweepefficiency isgreatlyimprovedfromWAGinjection.(B)SurfactantconcentrationprofileindicatingthatsignificantsurfactantdrainsbygravitybeforetheCO2slugcatchesup.(For interpretationofthereferencestocolourinthetext,thereaderisreferredtothewebversionofthisarticle.)

Fig.9. CaseC:Water-alternating-gas-plus-surfactant-in-gas.(A)3-phasesaturationproﬁleindicatingthatalargeroilbankisformedandtheoilrecoveryisfurtherimproved fromSAGmode.(B)Surfactantconcentrationproﬁleindicatingthatthesurfactanttransportissynchronizedwiththegasphasepropagation.

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efﬁciencyisalmostinvariantasafunctionofthePecletnumber andthedispersivitylengthscale.Yet,itisworthwhiletopointout thatthePecletnumbercanplayamorepronouncedrolewithsmall partitioncoefﬁcientwhensurfactantishighlyconcentratednear thewellboreregion.Inthatcase,smallPecletnumberhelpsthe

transport/propagation of surfactant species and can potentially improvethesweepefﬁciency.

Fig. 11(C)and(D)showthattheWAG+Sfoamprocessisalsonot very sensitive to the change in reservoir thickness and well spacing. Aslongasstrong foamisgenerated inthepresenceof Fig.10.(A)OilrecoveryefficiencycomparisonbetweenWAG,SAG,andWAG+Swithvariedpartitioncoefficient.(b)SensitivityofsurfactantpartitioncoefficientonWAG+S oilrecoveryefficiency.

Fig. 11.Sensitivityanalysis:(A)Overalloilrecoveryefficiencyasfunctionofcrudeoilviscosityandoil/foamedgasviscosityratio.(B)Overalloilrecoveryefficiencyasfunction ofPecletnumberanddispersityofthesurfactant.(C)Overalloilrecoveryefficiencyasfunctionofreservoirthickness.(D)Overalloilrecoveryefficiencyasfunctionofwell spacing(distancebetweeninjectionandproductionwells).

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crudeoil,theprocessiseffectiveacrossawiderangeofreservoir dimensions.Admittedly,alloursimulationisdoneatinjectionrate constraint.Sparsewellspacing requires higher foaminjectivity whichmightnotbeachievableatreservoirconditions.

Conclusions

WesimulatedthetransportofCO2solublesurfactantinporous

mediaandprobedtheeffectsurfactantpartitioncoefﬁcientonfoam EOR.WeﬁrstlyinjectedCO2withsurfactantofdifferentKsgwvalues

toa100%watersaturatedreservoir.Itisfoundoutthatthesweepof CO2ishighlydependentonKsgwvalues.Similartoourprevious

publicationin1-Dsystem,whenthesurfactanthasequalafﬁnityto boththewaterandthegas,thesweepefﬁciencyisoptimized.A2-D thickhomogeneousreservoirwithresiduallightoilwasthensetup fornumericalsimulationtoprobetheuseofCO2solublesurfactant

for foam EOR.In our case, WAG process hasmarginally better recoveryefﬁciencycomparedtowaterﬂoodingbecauseofthelow density and viscosity of the injected CO2 phase. SAG process

improvesrecoveryefﬁciencybyfoamingthegaswithsurfactant solutionandthereforeprovidingmobilitycontrol.Yet,inthecaseof SAGinjection,signiﬁcantsurfactantiswastedwhenthesurfactant drainswiththewaterbeforethefollowinggasslugcatchesupto foam.AbetteralternativetoSAGisWAG+Sinwhichthesurfactant isdissolvedintheCO2phaseandinjectedwithgasinsteadofwater.

WAG+Scansynchronizethetransportofsurfactantwiththegas phasepropagationwhen thepartition coefficient isaround1.A seriesof sensitivityanalysiswereconductedtounderstandthe efficiencyandrobustnessoftheWAG+Sprocess.Itisfoundthatthe oilrecoveryefficiencyisastrongfunctionofthecrudeoilviscosity ortheoil/foamedgasviscosityratio.However,theefficiencyofthe process is not severely impacted with changes in dispersion, reservoirthickness,and/orwellspacinginourinvestigatedrange.

Conﬂictofinterest

Theauthorsdeclarenoconﬂictofinterest. Acknowledgement

We acknowledge the ﬁnancial support from Shell Global Solutions International (Rijswijk, Netherlands), Rice University ConsortiuminProcessesinPorousMedia(Houston,TX).

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