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DEPRESSURIZATIONUNDERTERTIARYCONDITIONSINTHENEAR-WELLBOREREGION:EXPERIMENTS,VISUALIZATIONAND
RADIALFLOWSIMULATIONS
P.Egermann,S.BaniniandO.Vizika
InstitutFranaisduPtrole(IFP)
ABSTRACT
Depressurizationcanbeaveryinterestingprocesstorecoverhydrocarbonsfromwaterflooded
oil reservoir with high gas-oil-ratio. Most of the published results are related to depletion
experimentsundersecondaryconditions(virginreservoir).Dataaremorescarceundertertiary
conditionsafterwaterflooding[1,2,3].
Thepresentpapertreatstheissueofthedepressurizationundertertiaryconditionsinthenear-
wellbore region. Practically, this has been achieved by combining experimental results,
obtainedonbothcoreandtransparentmicromodel,withradialflowdepletionsimulationsthatare representative of the conditions prevailing in the near-wellbore region. A validated
methodologypreviouslypresented[4]hasbeenusedtodesigntheexperimentsoncore(the
coreundertertiaryconditionswascontinuouslyflushedwithwateratafixedrate,whilethe
pressureattheoutletwasdecreasedtoreproduceadrawdown).Thesaturationprofiles,the
pressuresandthefluidproductionsasafunctionoftimewererecordedinthetwoexperiments
that are presented. From the core experiments, critical gas saturation (Sgc) and relative
permeability (kr) have been determined using a specific simulation code that takes into
accountnucleation,diffusionandmobilizationprocessesrelatedtotheappearanceofthegas
phasefromsolution.Constantdepletionrateexperimentswerealsoconductedonatransparent
micromodeltostudytheprocessofconnectionofthegasphaseundertertiaryconditions.The
specificityofthenear-wellboreregion(highdP/dtand radialflow) was then investigatedby
conductinganumericalexperimentwithradialgeometry.
Itisshownthatgasrelativepermeabilitiesobtainedundertertiaryconditionsarelowerthan
the ones obtained under secondary conditions. This behavior is attributed to the double
connectionprocessthatisneededforthegastogetmobilized:connectionofthedisconnected
oilphaseandconnectionofthegasphaseitself.Thisphenomenonisalsoconfirmedbythe
visualizationexperimentsconductedonmicromodel.Thenumericalexperimentrepresentative
ofthenear-wellboreconditionswitharadialgeometrydemonstratesthatSgcisafunctionof
thedistancetothewellbore,whichcanhavealargeimpactonreservoirsimulationresults.
INTRODUCTION
Depressurization under tertiary conditions is considered as an interesting process to extend
economicallythelifeof maturewaterfloodedreservoirs[5, 6].Thesuccessof theprocess is
mainlydependentontherecoverablefractionofthesolutiongascontainedinthetrappedoil
and on the quantity of incremental oil that is possible to produce consecutively to the
developmentofthegasphase[7].
Realisticestimationsofthistertiaryrecoverycanonlybeachievedwithrelevantvaluesofboth
Sgc (critical gas saturation) and kr (relative permeability). Unfortunately, most of the
published data on depressurization are related to depletion experiments under secondaryconditions and are mainly focused on the evolution of the Sgc value as a function of the
SCA2003-15
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depletion rate (dP/dt). Secondary depressurization has been looked at with coreflood
experiments[8,9,10],withporenetworkmodeling[11],orwithvisualizationontransparent
micromodel[12,13].Theavailableresultsprovethatkrgvaluesunderinternalgasdriveare
verylowevenatsignificantSgvalues.Thistrendwasobservedforbothlightandheavyoils
[14,15].Morerecently,ithasbeenshownthatinternalgasdrivekrgvaluescanbeseveral
ordersofmagnitudelowerthantheexternalgasdrivekrg[4,16].
Data aremore scarceon tertiary depressurization process.Lighthelm et al.[1] have mainly
studiedtheevolutionofSgcasafunctionofdP/dtusingcoresandfluidsfromtheBrentfield.
TheyshowedthatSgcincreaseswithdP/dt(sametrendasundersecondaryconditions),but
theSgcvaluedependsontheinitialsaturationstateforagivencoreandagivensetoffluids.
The connection process of the gas phase under tertiary conditions was also studied in
micromodel by Hawes et al. [17]. Only Grattoni et al. and Naylor et al. [2, 3] tackled
simultaneously the issues of Sgc and kr under tertiary conditions. Grattoni et al. [2, 18]
conducteddepletionexperimentsonamodelporousmediumcomposedoftransparentpacked
beadsthatenabledalsoflowvisualization.Themainresultofthisstudyistheextremelylow
valuesofkrgmeasured,whichwerefoundaround10-5
-10-3
evenat23%Sg.Thisparticular
behaviorwasattributedtotheintermittentflowofgasthatwasobservedexperimentallyduring
thedepletionprocess.Naylor etal.[3] conducted several depletion experiments atdifferent
ratesonrealagedcores.Thekrgcurveswereobtainedbynumericalhistorymatchingtaking
into accountthe specific shapeof the localSg profiles. The results obtainedwere in good
agreementwiththeexistingliterature.SgcincreaseswithdP/dtandkrgvaluesareextremely
low,around10-4
.
Inthispaper,wewillfocusonthetertiarydepressurizationinthenear-wellboreregion.Thispartofthereservoirisparticularlyimportantfor hydrocarbonproductionbecauseitcontrols
the well productivity / injectivity, whereas the far field region accounts for the overall
recovery.MostofthepublisheddepressurizationexperimentsareconductedatafixeddP/dt,
sothatthepressuredropalongthecoreremainsmoderate,evenathighdP/dt.Thismakesthis
kindofexperimentsonlyrepresentativeofthefarfieldregion.Inthefirstpartofthepaper,we
presenttwocorefloodexperiments using a specificdesignand methodology that enablesto
reproducetheconditionsthatprevailinthenearwellboreregion[4]:highpressuregradient.
Theexperimental resultsareinterpreted using a tertiary depletionsimulator. The related kr
curvesarepresentedandcomparedwithotherpublishedresults.Thegasmobilizationprocess
undertertiary conditions is studied in the second part usingvisualizations obtained from a
highpressuremicromodel.Inthethirdandlastpart,thespecificityofthenear-wellboreregionisinvestigatedbyperformingnumerical experiments witharadialgeometry toevaluatehow
theflowingpropertiesvaryasafunctionofthedistancefromthewell.
COREEXPERIMENTS
Rock/fluidsystem
Alltheexperimentswereperformedona Vosgessandstonecore,whosemainpropertiesare
gatheredinTable1.Thischoicewasmainlymotivatedbythehighdegreeofhomogeneityof
thissandstoneandalsobyitsfairabsolutepermeability.
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Table1:Vosgessandstonecoreproperties
PermeabilitymD Porosity% Lengthcm Areacm2
PVcm3
58 24 34.5 14.5 120
ThesamebinarymixtureC1C7wasusedfortheoleicphaseinbothexperiments.Thebubblepointofthemixturewasequalto21bar,whichcorrespondstoamolarfractionofC1equalto
0.107.Thetablehereafterprovidestheassociatedpropertiesin termsof IFTandviscosityat
Pband20C.DatawerederivedfromIFPdevelopedPVTsoftware.
Table2:fluidpropertiesofthebinarymixtureC1C7
Pbbar %C1molar IFTmN/m OilviscositycP Oildensitykg/m3
21 10.7 17.25 0.402 672
Thebrineiscomposedof50g/lNaCland5g/lCaCl2.Thiscompositionprovedtobeefficient
instabilizingclayscontainedinthesandstoneandingettinga goodcontrastbetweentheoilandthewaterphaseduringtheacquisitionoflocalsaturationmeasurements.
Experimentalset-up
It is mainly composedof a Hassler type core holder made with composite material, which
enables acquisitionof localsaturationmeasurementsalongthecore with CT-scanner.In the
inlet,thebinarymixtureorthebrinecanbeinjectedintothecoreatafixedratewithapump.
Downstream,theoutletpressureiscontrolledbyabackpressurevalveremotelyoperatedbya
PC,sothatthedrawdowncanbemonitoredveryeasily.Attheoutlet,adensimeterisused
mainlyduringthecorepreparationtocheckthecoresaturationwiththemixture.Duringthe
experiment,thedensimeterisalsousefultodetecttheveryfirstapparitionofthegasphasedownstream.Fluidsarecollectedintoaseparatorsothatbothliquidsandgasquantitiescanbe
measured.Evolutionoftheoutletpressureisdirectlyrecordedbyapressuregauge.Theinlet
pressureisdeducedfromadifferentialpressure gaugemeasurement.Only thetotalpressure
dropalongthecoreisavailable(nopressureports).Allthedataareautomaticallyrecordedon
aPC.
CTscanner
acquisition
C1C7reservoir
PumpDensimeter
DP
PCAutomaticacquisition
Outletpressurecontrol
Gasometer
Separator
Pressureregulator
Brinereservoir
Figure1:corefloodexperimentalset-up
Experimentalprocedure
Residualoilsaturation(tertiaryconditions)wasestablishedwiththefollowingprocedure: PreliminarysettingofS wiconditionsusingaviscousoil(Marcol52,10cP)
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MisciblefloodingofMarcolbyC7 MisciblefloodingofC7bythebinarymixtureC1C7underpressure(abovePb) SettingofSorwbyinjectionofbrineatfixedrateTheprincipleofthedepletionexperimentisdescribedinearlierpublication[4].Undertertiary
conditions, the brineis injected upstream ata fixed rate with the outlet pressure originally
abovethebubblepoint. Pressureat theoutlet isprogressively decreaseddownto a definedvaluebelowthebubblepointofthemixture.Alltheexperimentswereperformedwitharate
of30cc/htosimulateconditionsinthewellboreofaproductionwell.Thedrawdowncaused
theformationofthegasphasestartinginthedownstreampartofthecore.Transientevolution
ofgassaturationthroughthecoreisfollowedbyCT-scannerandimpactofgasapparitionon
thepressuredropisdetectedontheinletpressurevariations.
Productiondataresults
Twoexperimentswereconducted(M1andM2).Theoutletpressurewasdecreasedbelowthe
bubblepressureintwosteps(17and14bar)inthefirstexperiment,whereasitwasdecreased
directly down to 14 bar in the second experiment. For both experiments, the pressureevolutionsareverysimilarandalsoingoodagreementwithpreviousexperimentsperformed
undersecondaryconditions(Figure2).Atthebeginning,theinletandoutletpressuresremain
parallel.Thispartcorrespondstoaconstantpressuredropalongthecoreduringtheflowof
waterwhentheoutletpressureisabovethebubblepoint(residualoil immobile).Assoonas
thegasappears downstream, thepressure dropincreaseswith increasinggas saturation,and
then it stabilizes, while the outlet pressure is maintained constant (17 or 14 bar). The
experimentalresultsaresummarizedinTable3.
Secondaryconditions
65
70
75
80
85
90
0 2 4 6 8Timehour
Pressurebar
Inletpressure
Outletpressure
Tertiaryconditions
10
15
20
25
30
35
40
0 1 2 3 4
Timehour
Pressurebar
Outletpressure
Inletpressure
17ba rste p 14ba rste p
Figure2:inletandoutletpressureevolutions(secondaryconditionsandM1)
Oneinterestingfeatureconcernstheevolutionoftheinletpressure.Areboundwasmeasured
under secondary conditions and was associated to a recompression along the core
consecutively to the development of the gas phase and its effect on kro (the oil was the
injectedfluid).Theinletpressureonly decreasesorstabilizesundertertiary conditions.This
result suggests that the development of the gas phase has a less pronounced effect on the
permeabilityoftheinjectedfluid(krw).Thismaybeaconsequenceofthetertiaryconditions,
wherethegasappearswithintheoilphase,whichisnonmobileandtrappedinthelargepores
sincetherockiswater-wet.
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Table3:tertiarydepletionexperimentsresults
Exp Sorw% DPwater/oil Step1/DP1 Step2/DP2 KrwatSorw So%OOIP
M1 28.1 6.1bar 17bar/8.7bar 14bar/9.8bar 0.057 42
M2 29.0 6.4bar 14bar/9.1bar 0.054 35
Figure3showstheevolutionofthedifferentialpressureandtheincrementaloilproductionas
afunctionoftime.Inbothexperiments,theappearanceofthegasphasemakesthepressure
dropalongthecoreincrease,andisassociatedwiththeproductionofasignificantquantityof
oil,whichrepresentsaround10%PV(34-42%OOIP).Inthetwostepexperiment(M1),the
break in the slope of the oil production curve strongly suggests that this incremental oil
productionisdirectlyconnectedwiththeextensionofthethree-phaseareaintothecore.
M1
0
2
4
6
8
10
12
14
16
0 1 2 3 4
Timehour
Oilproductioncm3
0
2
4
6
8
10
12
Differentialpressurebar
Experimentaloilproduction
ExperimentalDP
M2
0
2
4
6
8
10
12
14
0 1 2 3 4 5 6
Timehour
Oilproductioncm3
0
1
2
3
4
5
6
7
8
9
10
Differentialpressurebar
Experimentaloilproduction
ExperimentalDP
Figure3:Experimentalpressuredropandoilproduction(M1andM2)
Saturationprofilesresults
Theaboveobservationsmadeontheproductiondataarecompletelyconfirmedbythein-situ
saturation measurements. Figure 4a illustrates the extension of the gas region upstream
dependingontheoutletpressurevalue(17and14bar).TheshapeoftheSgprofilesisvery
typicalwithagassaturationjumpaheadthegasregionfollowedbyalesspronouncedincrease
of Sg. This shape was found common in all experiments and very similar with the results
obtainedundersecondaryconditions[4].AnotherinterestingfeatureconcernstheevolutionoftheSwprofilesduringM1(Figure4b).
TheSwvalueremainsveryuniformandconstantwithinthethree-phaseareasuggestingthat
the non wetting phasesaturation (Sg+So) value isaround 35%, close to the original Sorw
value,whatevertheexperimentalconditions.
17barstep 14barstep
Gasphase
a earance
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0
0.05
0.1
0.15
0.2
0.25
0.3
0 50 100 150 200 250 300 350
Distancefromtheinletmm
Gassaturation%
17barstep:experimentalM1
14barstep:experimentalM1
14barstep:experimentalM2
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0 50 100 150 200 250 300 350
Distancemm
Watersaturation%
Swbeforedepletion
Sw:end17barstep
Sw:end14barstep
Figure4:(a)Sgprofiles(M1andM2);(b)SwprofilesM1
The conservation of the overall non-wetting phase saturation also explains why the
developmentofthegasphasehasalesspronouncedimpactontheinletpressure,andon the
injectedphasepermeabilitythanundersecondaryconditions.
Interpretation
Numericalsimulator
Thein-housedepletioncodethatwasdevelopedtosimulatetheexperimentsundersecondary
conditionswasused[19].ThegeneralstructureofthecodeisremindedinFigure5.Themain
advantagesofthiscodearelistedbelow:
Account of the physical phenomena involved in the gas formation (nucleation,diffusion) Controlofthegasmobilizationprocess.Dependingontheexperimentalconditions,thecodecanhandlebothdispersedorcontinuousgasflow.
Initialization
t=t+dt
Waterrate
Pressureprofile
Nucleation
Bubblegrowth
Gasmobilization Connection Dispersed
Oilsaturation
Solutiongasconcentration
Upstream
Qw
Downstream
Poutlet
Figure5:codearchitecture
Somemodificationshavebeenintroducedintheoriginalcodeinordertotakeintoaccountthe
specificityofthetertiaryconditions.
The pressure drop along the core results from the injection of the water phase(krw(Sg))
The three-phase flow was handled like a pseudo two-phase flow. As the localsaturation measurements showed that the non wetting phase saturation remains
a b
Sgjump
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constantwithinthethree-phaseregion,theoilsaturationineachcellwascalculated
from the gas saturation value using the conservation of the non wetting phase
saturation:
SgSSo NWR = , whereSNWRwaskeptconstantandequalto35%
HistorymatchingA very good agreement was reached between the simulation and the experimental data in
termsofproductiondataandSgprofiles(Figure6),whateverthevalueoftheoutletpressure.
Theconsistencyofthishistorymatchingwasalsocheckedbycomparingtheexperimentaland
the simulated gas production a posteriori. Here again, an excellent matching is obtained
(Figure7a).
0
2
4
6
8
10
12
14
16
0 1 2 3 4
Timehour
Oilproductioncm
3
0
2
4
6
8
10
12
Differentialpressure
bar
Simulatedoilproduction
Experimentaloilproduction
SimulatedDP
ExperimentalDP
0
0.05
0.1
0.15
0.2
0.25
0.3
0 50 100 150 200 250 300 350
Distancefromtheinletmm
Gassaturation%
17barstep:experimental
14barstep:experimental17barstep:simulated
14barstep:simulated
Figure6:historymatchingofM1(productiondataandSgprofiles)
0
50
100
150
200
250
300
350
400
450
500
0 1 2 3 4
Timehour
Gasproductioncm3
Experimentalgasproduction
Simulatedgasproduction
1.E-06
1.E-05
1.E-04
1.E-03
1.E-02
1.E-01
1.E+00
0 0.1 0.2 0.3 0.4 0.5Sg
krg
Tertiarykrg
Secondarykrg
Grattonietal
Drummondetal
Figure7:gasproductionhistorymatching(a)andkrgresults(b)
Krgcurveshape
The tertiary krg curve deduced from the history matching procedure is compared with the
secondarykrgcurvethatwasobtainedon anotherrocksampleinFigure7b[4].Bothcurves
show that the mobility of the gas phase is limited under depletion, but this trend is more
pronounced under tertiary conditions. It suggests that one part of the gas formed into theporousmediumdoesnotparticipateinthegasflowundertertiaryconditions,whichleadstoa
a b
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lowerkrgvalueatagivenSg,comparingtothesecondaryconditionscase.Asthegascomes
fromsolutionwithinthetrappeddisconnectedoil,itissuspectedthattheonepartof thegas
formedinnonaccessibleoilgangliacanmisstheconnectionprocessandexplainthisresult.
Althoughtheexperimentsundertertiaryandsecondaryconditionshavenotbeenconductedon
the same rock, it is interesting to observe that a lower Sgc value is found under tertiary
conditionsforsimilardrawdownrate(evenifkrgarelower).Thismaybeaconsequenceofthewaterwettabilityoftherock,whichfavorstheentrapmentoftheoilphaseinthelargest
pores.Hence,itmakesthegasphaseappearsundertertiaryconditionsintheclassofporesthat
accounts for the porous mediumconnectivity leading to lower Sgc value comparing to the
secondarycase,wherethegasbubblescanbecreatedineveryclassesofpores.
Thetertiarykrgcurveisalsoingoodagreementwiththeotheravailablepublishedresultsfrom
Grattonietal.[2]andNayloretal.[3](correspondingkrgcurveinDrummondetal.[6]).All
curveshaveacommonpartaround10-4
,whichconfirmsthegasmobilityisverylimitedunder
tertiaryconditions,whatevertheexperimentalconditions.
VISUALIZATIONEXPERIMENTS:GASMOBILIZATIONPROCESS
Apressurizedmicromodelwasusedtovisualizethegasmobilizationprocessundertertiary
conditionsandexplainthelowvaluesofkrgmeasuredoncorefloodexperiments.Thegeneral
principleoftheexperimentalset-upispresentedinFigure8.Themicromodelcanbeoperated
up to 100 bar and 60C using a circulating device of the heated confining fluid. The
establishmentofthetertiaryconditionswithC1C7wasachievedusingtheprocedurefollowed
withcorefloodexperiments.Thedepletionwasconductedatfixeddepletionrate(dP/dt)by
closing the inlet valve and decreasing progressively the pore pressure through the back
pressurevalve.
Pressurepumps
(doublebody)
Saphircell
N2
Pressure gauges
Oven
Highpressuremicrodel
(100b,60C)
Accumulator
Monitor
Video
recording
Vizualizationdevice
Transfercells
C1C7
Confining
fluid
Pump
N2
Water
Videocamera
Figure8:Experimentalset-upforMicromodelvisualization
AsequenceofthegasphasedevelopmentisgiveninFigure9.Onthefirstpicture,thegas
bubbles(white)startappearingfromtheoilganglia(blue)disconnectedbythewaterphase
(red).Dependingonthesizeofthegangliaandtheavailablequantityofsolutiongasinthe
vicinity of the bubbles, the growingratecan bevery different from one bubble toanother.
Several connection events between two adjacent bubbles are also observed, whereas somebubblesremaindisconnectedduringthewholeexperiment.Attheendofthesequence,alarge
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gas bubble isobtained, whereas a significantfractionof thegas phase is still disconnected
withinthedisconnectedoilganglia.Fromtheseobservations,thelowvaluesofkrgmeasured
from coreflood experiments can be qualitatively explained by the double mechanism of
connectionneededforthegastogetmobilized:reconnectionoftheoilphaseandconnection
ofthegasitself.Thismechanismisalsoverysimilartowhatisobservedundertertiarygravity
assistedinertgasinjectionasshownbyKantzasetal.[20].
Figure9:Developmentofthegasphaseundertertiaryconditions
RADIALGEOMETRYEFFECTINTHENEARWELLBORE
Principle
Thenearwellboreregionischaracterizedbyahighdrawdownandradialgeometry.Thehigh
drawdown is reproduced in our experiments by injection of the producing fluid at a
sufficiently high rate, but the flow is linear, which makes the pressure gradient (dP/dx)
uniformalongthecore.Astheflowisradialnearthewell,bothdP/dxandU(fluidvelocity)
increasefromthefarfieldtothenearwellboreregion,sotheequivalentdepletionratedP/dt,
equal to UdP/dx, also increases [4]. As the flowing parameters (Sgc, kr) are strongly
dependent on dP/dt, we have designed a numerical laboratory experiment with a radial
geometrytoinvestigatetheevolutionoftheflowingpropertiesasafunctionofthedistance
fromthewell.
Rmax=60cm
Rmin=10cm e=10cm
QoilPhi=20%
Angle=30
Qoil=800cm3/h
Figure10:principleoftheradialnumericalexperiment
Gas
Oil
Water
Connection
events
1 2 3
4
987
65
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The simulations were performed under secondary conditions. The numerical experiment
principle is shown in Figure 10 and is the same as the one followed for the coreflood
experiments. The depletion simulator was first calibrated on an existing experiment with a
linear geometry to fix the parameters controlling the nucleation, the diffusion and the gas
mobilization.ItisworthremindingthatourcodeenablestoevaluatethelocalSgcvaluefrom
thebubble population properties (size,number)anda shape factor totake intoaccountthebubble ramifications for connection criterium. After calibration, the code was slightly
modifiedtohandleradialgeometryandthenumericalexperimentwaslaunched.
Results
Figure11showsthepressureprofileswithbothgeometries.Asexpected,thepressuregradient
dP/dxincreasesneartheoutletwhenaradialgeometryisconsidered,whereasdP/dxremains
uniformalongthecorewithalineargeometry.TheassociatedSgprofileshaveasimilarshape
with a gas saturation jump followed by a less pronounced increase of Sg, whatever the
geometryconsidered(Figure12).Themobilizationofthegasphasecanbedetectedfromthe
break in the slope of the Sg profiles (when the increase is less pronounced). With linear
geometry, the break occurs always at the same saturation, whereas the break is clearly a
functionofthedistancewithradialgeometrysuggestingSgcvaluevariesfromtheoutletpart
ofthecoretotheinlet.
Lineargeometry
70
75
80
85
90
0 100 200 300 400
Distancemm
Pressurebar
Radialgeometry
70
72
74
76
78
80
82
84
86
88
90
0204060
Radiuscm
Pressurebar
Figure11:pressureprofileswithlinearandradialgeometry
Lineargeometry
0.00
0.10
0.20
0.30
0.40
0.50
0 100 200 300 400
Distancemm
Sg
Radialgeometry
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
0102030405060
Radiuscm
Sg
Figure12:Sgprofileswithlinearandradialgeometry
SgclineSgcline
increasingtimeincreasingtime
increasingtime increasingtime
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ThisbehaviorisconfirmedinFigure13,wheretheSgcvaluescalculatedbythecodeineach
cell are plotted as a function of the distance. When a linear geometry is considered, the
calculatedSgcvaluesareveryuniformalongthecore,equalto24%,whichisinlinewiththe
experimental data and the theory(high equivalent dP/dt is constant along the core, several
metersawayfromthewell).
0.10
0.15
0.20
0.25
0.30
0 10 20 30 40
Distancefromtheinletcm(linear)
CalculatedSgc
010203040Radius(cm)
Linearcase
Radialcase
1
10
100
1000
0.10 0.15 0.20 0.25 0.30
Sgc(fraction)
dP/dt(psi/hr)
Radialcase
Linearcase
Figure13:calculatedSgcvaluesalongthecoreinlinearandradialgeometry
When a radial geometry is considered, the calculated Sgc value varies from 26% near the
outlet,wheretheequivalentdP/dtismaximum,downto20%atthegasfront,wherethedP/dt
valueislower.ThecalculatedSgcvaluesareclearlya functionofdP/dt(Figure13)andfall
alongalineartrendinsemi-logscaleasalreadypointedoutbyScherpenisseetal.[9].This
studyconfirmstheroleplayedbytheflowgeometryinthespatialdistributionoftheflowing
propertiesunderdepletion.Whensignificantdrawdownvaluesareobservedinthefield(high
productionratesorheavyoilproduction)thisdependencehaslimitedeffectsontheoverall
field recovery [21]but mayimpacttheproductionperformances significantly andshouldbe
takenintoaccountinreservoirsimulations.
CONCLUSIONS
Itisshownthatthegasrelativepermeabilitycurveobtainedundertertiaryconditionsislower
than theone obtainedunder secondaryconditions.This behavior isattributed tothedouble
connectionprocessthatisneededforthegastogetmobilized:connectionofthedisconnected
oilphaseandconnectionofthegasphaseitself.Thisphenomenonisalsoconfirmedbythe
visualizationexperimentsconductedonmicromodel.Thenumericalexperimentrepresentative
ofthenear-wellboreconditionswitharadialgeometrydemonstratesthatSgcisafunctionof
thedistance,whichcanhavelargeimpactonreservoirsimulationresults.
ACKNOWLEDGEMENTS
ThisworkwaspartlyfundedbyARTEP,a researchassociationbetweenTOTAL,ELF,Gaz
deFranceandIFP.
NOMENCLATURE
dP/dt: depletionrate
dP/dx: pressuregradient
IFT: interfacialtension
kri: relativepermeabilityofphasei
OOIP: oiloriginallyinplace
Pb: bubblepressure
Q: totalinjectionrate
Si: saturationofphasei
Sorw: residualoilsaturationtowaterflood
U: fluidvelocity
REFERENCES
Sgc=6%
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This paper was prepared for presentation at the International Symposium of the Society of Core Analysts held in Pau, France, 21-24 September 2003