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Geothermics
j ou rn a l h o m epa ge :w w w. e l s e v i e r . c o m / l o c a t e / g e o t h e r m i c s
The
influence
of
facies
heterogeneity
on
the
doublet
performance
in
low-enthalpy
geothermal
sedimentary
reservoirs
R.A.
Crooijmans
a,∗,
C.J.L.
Willems
a,
H.M.
Nick
a,b,
D.F.
Bruhn
a,caFacultyofCivilEngineeringandGeosciences,DelftUniversityofTechnology,TheNetherlands bTheDanishHydrocarbonResearchandTechnologyCentre,TechnicalUniversityofDenmark,Denmark cHelmholtzCentrePotsdam–GFZGermanResearchCentreforGeosciences,Germany
a
r
t
i
c
l
e
i
n
f
o
Articlehistory:Received28December2015 Receivedinrevisedform26May2016 Accepted3June2016
Availableonline17June2016
Keywords:
Non-isothermalflow Variablefluidproperties Heterogeneity Geothermal Doublet Sedimentaryformation Net-to-Grossratio
a
b
s
t
r
a
c
t
Athree-dimensionalmodelisusedtostudytheinfluenceoffaciesheterogeneityonenergy produc-tionunderdifferentoperationalconditionsoflow-enthalpygeothermaldoubletsystems.Process-based faciesmodellingisutilisedfortheNieuwerkerksedimentaryformationintheWestNetherlandsBasinto constructrealisticreservoirmodelshonouringgeologicalheterogeneity.Afiniteelementbasedreservoir simulatorisusedtomodelthefluidflowandheattransferovertime.Aseriesofsimulationsiscarried outtoexaminetheeffectsofreservoirheterogeneity(Net-to-Grossratio,N/G)onthelifetimeandthe energyrecoveryratefordifferentdischargeratesandtheproductiontemperature(Tmin)abovewhichthe
doubletisworking.Withrespecttotheresults,weproposeadesignmodeltoestimatethelifetimeand energyrecoveryrateofthegeothermaldoublet.ThelifetimeisestimatedasafunctionofN/G,Tminand
dischargerate,whilethedesignmodelfortheenergyrecoveryrateisonlyafunctionofN/GandTmin.
BothlifetimeandrecoveryshowapositiverelationwithanincreasingN/G.Furtherourresultssuggest thatneglectingdetailsofprocess-basedfaciesmodellingmayleadtosignificanterrorsinpredictingthe lifetimeoflow-enthalpygeothermalsystemsforN/Gvaluesbelow70%.
©2016TheAuthors.PublishedbyElsevierLtd.ThisisanopenaccessarticleundertheCCBYlicense (http://creativecommons.org/licenses/by/4.0/).
1. Introduction
Geothermal energy production from deep geological forma-tionshasbeengrowingintheNetherlandssincethefirstdoublets wererealisedin2007(vanHeekeren,2015).Themaintargetsare sedimentaryfluvial reservoirs at depths between2 and 2.5km witha temperature between70 and 90◦C (Bonté et al., 2012). These are so-called low-enthalpy reservoirs, which are mainly used for heating of buildings in the horticultural sector. The sedimentaryfluvialreservoirshavedifferentcharacteristicsfrom conventionalgeothermalinmagmaticsettings.Such characteris-ticsare,forexample,porosity,initialtemperature,permeabilityand heatcapacitythatleadtodifferentgeothermalperformance indi-catorssuchasthelifetimeofthedoublet(howlongthedoublet canproduceeconomically),recovery(producedenergycompared tothetotalamountofavailableenergy)andthedailyenergy pro-duction.Theperformanceindicatorstogetherwiththeoperational costsdeterminetheprofitabilityofthegeothermalsystem.The
∗Correspondingauthor.
E-mailaddress:[email protected](R.A.Crooijmans).
focusofthisstudyisontheperformanceofsuchasystemwhere thelifetimeandtherecoveryaredependentonbothhumanand physicalcontrolledparameters.
Saeidetal.(2015)suggestthatthemostinfluencinghuman con-trolledparameteristhedischargeofthewells.Notsurprisingly, thelargerthedischargethefasterthecoolingofthereservoiris noticeable in theproduction fluid(i.e. theearlierthearrival of thecoldwaterfront).Otherimportanthumancontrolled param-etersareinjectiontemperatureandwellspacing.Thelargerthe difference in temperature between the produced and injected fluid, themoreenergy is extractedfrom thereservoir;and the closerthewellsthefasterthecoldwaterreachestheproduction well.
Themainphysicalcontrolledparametersareporosity,salinity oftheporefluid,initialreservoirtemperature(Saeidetal.,2015), reservoirthicknessandthethicknessofshalelayersinbetweenthe reservoirbodies(Poulsenetal.,2015).Thesalinityoftheporefluid andtheinitialreservoirtemperaturecanbeassumedconstantat reservoirscale.Porosityis,however,stronglyheterogeneousand dependentonthefacies. Faciesaregeologicalbodies formedby sedimentologicalprocesses, whichare dependentonthe paleo-riverbehaviour.Thismakesthedistributionofthefaciesuniquefor
http://dx.doi.org/10.1016/j.geothermics.2016.06.004
eachriverdeposit.Thefacieswithhighporosityandpermeability formthereservoirbodies.
Withintheoilindustrythespatialdistributionandgeometryof thereservoirbodiesiscommonlyinvestigated(Jonesetal.,1995; WillisandTang,2010;Attaretal.,2015).Thegeometryand distri-butioncontrolthereservoirconnectivity,whichistheratioofthe volumeofthelargestconnectedreservoirbodyoverthesumofthe volumeofallreservoirbodies.Theconnectivityiscloselylinked tothenet-to-grossratio(N/G),whichisthenetreservoirvolume versusthetotalvolume(HovadikandLarue,2007).Above50%N/G theconnectivityismorethan95%anditisunlikelythatthisisa sig-nificantuncertainty(King,1990).Forfluvialreservoirsystemsthe connectivityismostsensitivebetween10and20%N/G.The con-nectivityisabout20%forreservoirswithN/Gof10%anditreaches 80%forreservoirsof20%N/G(LarueandHovadik,2006).Thisrange inN/Gisrivertypedependent;forexample,forriverswithhigh sinuositytherangeshiftstolowerN/Gvalues(HovadikandLarue, 2007).
LarueandHovadik(2008)studiedtheeffectofN/Gand con-nectivityonoilrecoveryinadoubletsystem.Forreservoirswith aconnectivityabove95%,theyfoundthatgeologicalparameters suchassinuosityandwidth/thicknessratioofthegeobodiesand theorientationofthewellscomparedtothegeobodieshavea rela-tivelysmalleffectonrecoveryandwaterfloodingefficiency.There isasmalldropinoilrecoverywhentheN/Gdecreasesfrom50%to 20%.Belowthe20%N/Gtheoilrecoverydropsdrasticallyfrom80% toroughly25%(LarueandHovadik,2008).
Inthegeothermalsectordepositionalprocessesandthe build-ingofvarioussedimentologicalarchitecturesarenotcommonly considered when the effect of human controlled and physical parametersonthedoubletperformanceisinvestigated.Simplified geologicalrepresentationsarecommonlyusedsuchas homoge-neousmodels(Saeidetal.,2014)orlayercakemodels(Poulsen et al., 2015; Mottaghy et al., 2011; Deo et al., 2014). In the Netherlandsthesoftwareprogramme‘DoubletCalc’iscommonly usedfor prediction of the doublet performance. Thisfree soft-wareprovided by TNOuses homogeneoussand box modelsto calculatetheobtainedpowerofalow-enthalpygeothermal dou-blet (Mijnlief et al., 2012), assuming that the connectivity and N/Gareboth100%.Studiesintheoil-sector,however,showthat theseparametershaveamajorimpactonthefluidflowpatterns (HovadikandLarue,2007)andtherecovery(LarueandFriedmann, 2005;HovadikandLarue,2007;Larueand Hovadik, 2008).The lessonslearntintheoilindustrysectorprovidesomeinsighton theimportanceoftheuseofdetailedreservoirrepresentationsin ageothermalsystem.Theselessons howevercannotbeapplied directlytogeothermalstudiesbecauseoilisonlyextractedfrom theporevolume,whiletheheatextractedfromgeothermal reser-voirsisobtainedfromthefluidin theporesandfromtherock matrix.
Inthispaperprocess-basedfaciesmodellingisusedtocreate realisticrepresentationsofsedimentaryreservoirs.Over45 rep-resentations,calledreservoirrealisationsarecreatedwithaN/G rangingfrom10to100%.Afiniteelementmethod(FEM)isutilised tosimulatethefluidflowandheattransferprocessesingeothermal doublets.Inthefirstpartofthispaperthemodellingapproachis explainedforboththegenerationofreservoirrealisationsandthe non-isothermalsimulations.Next therelationbetweenN/G and thedoubletperformanceparameters (lifetimeand recovery) is discussed,followedbytheeffectofthedischargerate.Then,the resultsarecombinedtoobtainaso-called‘designmodel’,which estimatesthelifetimeofadoubletandtherecovery.Intheendthe differencebetweenrandomlygeneratedrealisationsandthe reser-voirrealisationsisassessedtohighlighttherelevanceofthefacies basedreservoirrealisationinlow-enthalpygeothermalreservoir modelling.
2. Methodology
2.1. Reservoirmodels
Thisworkconsistsof two main parts:staticgeomodels and dynamicreservoirsimulation.Thestaticgeomodels,withdifferent N/Grangingfrom10to100%,aregeneratedinthreedifferentways: ModelTypeIandIIaremadeutilisingaprocess-basedfacies mod-ellingapproachtodistributedifferentfaciesTypes(i.e.sand,shale); ModelTypeIIIismadeusingarandomfaciesfieldgenerator.The differencebetweenTypeIandIIisthewayinwhichpropertiesare assignedtothesandbodies.InTypeIporosityandpermeabilityare heterogeneouswithinthesandbodieswhereasintheModelType IIsingleaverageporosityandpermeabilityvaluesareassignedfor thesandbodies.Therealisationsarethenemployedfor conduct-ingdynamicsimulations(Fig.1).Theheattransferinthereservoir andtemperatureattheproductionwellarecalculatedovertimeby usingthesoftwarepackageCOMSOLMultiphysicsutilisingafinite elementmethod.Inthebasecase(initial)scenariothedischargeis 100m3/h,theinitialreservoirtemperatureis75◦Candforthebase
casescenariotheproductionstopswhentheproduction temper-aturedropsto74◦C(Minimalproductiontemperature,Tmin).The
declineintheproductiontemperaturecanbeseenasthearrival timeofthecoldwaterfront.Flowandheattransfersimulationsare conductedemployingallthegeneratedreservoirrealisationsfor severalscenarioswithdifferentdischargerates(80,100,120and 140m3/h).Consequently,thelifetimevaluesandtotalheat
recov-eryarecalculatedfordifferentminimalproductiontemperatures (74,72,70and68◦C).
2.1.1. ReservoirmodelTypeI,IIandIII
Process-basedfaciesmodellingsoftwareFlumy(Grappeetal., 2012)isutilisedtogenerate48realisations(depositionalmodels) ofa1km×2km×50mgeothermalreservoirwitharesolutionof 20m×20m×2.5m.Inthisprocess-basedapproach,faciesare dis-tributedmainlybymodellingsedimentologicalprocesses.Lopez etal.(2009)suggestthattheconstructedreservoirmodelsutilising acombinedstochasticandprocess-based approacharerealistic. Thisisbecausethechannelssizesandshapesareexplicitlyrelated tochannelwidth,channeldepth, andavulsionfrequencywithin othercontrollingparameters.Forexample,thelocationofafluvial channelaftertheavulsiondependsonthetopographycreatedby thepreviousflowpathanddepositionofsediment.Notethatwhile theconstructedmodelsarenotconditionedbyinputdatasuchas logsorcoresthegeologicaldataconstrainsrangeofthecontrolling parametersintheprocess-basedmodel.Themethodisexplained indetailinGrappeetal.(2012)andLopezetal.(2009).
Theresulting realisations containsevenTypes of geobodies; pointbars,sandplugs,channellag,crevassesplays,levees,overbank floodplainfines andmud plugs.Thesedimentologicalprocesses dependonparameterssuchasavulsionfrequency,floodfrequency, paleo-channel width and depth, maximum floodplain deposit thicknessandtopographyofthefloodplain.Inallofthegenerated realisationsthepaleoflow,fromthesoutheasttonorthwestis ori-entedparalleltothelongedgeofthereservoirboundary(Fig.1). Thepaleo-channelwidthanddepthconsideredinthisstudyare 40mand 4m, respectively. These values and paleo-flow direc-tionarederivedfromcoreinterpretationsoftheLowerCretaceous NieuwerkerkFormationintheWestNetherlandsBasin(DeVault andJeremiah,2002).Thechoiceoforientingthepaleo-flow direc-tionparallel to thelong-edge increases theconnectivity inthe reservoirrealisationscomparedtoapaleoflowperpendicularto thelongedge.Therangesofprocessparametervaluesusedforthe modellingarederivedfromwellcoredataandpresentedinTable1. Afterthereservoirrealisationsaregenerated,themodelis sim-plifiedbydividingthe7typesofgeobodiesintotwogroups;sand
Fig.1. Schematicofthemodeldomainandthewelllocations.
Table1
Reservoirsandbodygeometries.
Bank-fullflowwidth 40ma
Bank-fullflowdepth 4m Meanderbeltwidth 800–1200ma Single-storysandstonebodythickness 4–5m Single-storysandstonebodywidth 200–400ma Multi-storysandstonethickness 6–20m Multi-storysandstonewidth 100–500 Width/thicknessratiosandstonebodies 16–100b
aDonselaarandOvereem(2008). bPranteretal.(2007).
(channellag,pointbar,sandplug)andshale(crevassesplay,levee, overbankalluvium,mudplug).Thesandgroupisconsideredas reservoir and the shalegroup as non-reservoirand the groups areusedtocalculatetheN/Goftherealisations.Sandstonegrain sizeheterogeneitywithinsandstonebodiesdependsonpaleoflow speed,andtheproximitytothechannelaxisandriverbends.Asa result,thepermeabilityofchannellags,point-barsandsandplugs variesacrosssandstonebodies(WillisandTang,2010).Therefore theheterogeneityofthefaciesin thesandgroupisassumedto becapturedbyusingthesandstonepermeabilitydistributionfrom thecoremeasurements(TNO,1977).Abetadistribution correla-tionfunctionwasusedtogenerateaheterogeneousporosityfield withinthesandgroup.Thedistributioncharacteristicsincluding: mean,standard deviation, skewand kurtosisare equal to0.28, 0.075,0.35 and2.3,respectively.Thepermeabilityofthisgroup isderivedfromaporosity-permeabilityrelationshipobtainedfrom petrophysicaldataofwellMKP-11(TNO,1977):
=0.0633e29.507 (1)
whereisthepermeability[mD]and istheporosity[–].The effectofheterogeneityinthethermalrockpropertiesonheat trans-ferinthegeothermalreservoir isinsignificantcompared tothe heterogeneityintheflowproperties(Mottaghyetal.,2011). There-forethethermalrockpropertiesareconsideredhomogeneousand isotropic.Theporosityandpermeabilityoftheshalegrouparealso assumedtobehomogeneousandisotropic(Table2).
Todeterminetheeffectoftheheterogeneousporosityofthe reservoirbodies,someofthereservoirrealisationsarerebuiltwitha homogeneoussandgroupandnamedasmodelTypeII.Theporosity andpermeabilityofthesandgroupisequaltotheaveragedporosity andpermeabilityofthesandgroupinthereservoirrealisationsof modelTypeI.Thesizeanddistributionofthereservoirbodiesare keptthesame.
Further,tostudytherelevanceofprocess-based facies mod-ellingontheestimationofthelifetimeandenergyproductionof thedoublets,geo-modelrealisations(modelTypeIII)aregenerated
Table2
Listofparametersusedinthedynamicmodel.
Parameter Description Value Dimension
˛L Longitudinaldispersioncoefficient 6.5 m
˛T Transversaldispersioncoefficient 2.2 m
shale Permeabilityoftheshalebodies 5 mD
f Conductivityoftheporefluid 0.7 W/m/K
sand Conductivityofthesandbodies 2.7 W/m/K
shale Conductivityoftheshalebodies 2.0 W/m/K
sand Densityofthesandbodies 2650 kg/m3
shale Densityoftheshalebodies 2600 kg/m3
sand Averageporosityofthesandbodies 0.28 –
shale Porosityoftheshalebodies 0.1 –
Cf Specificheatcapacityoftheporefluid 4200 J/kg/K
Csand Specificheatcapacityofthesandbodies 730 J/kg/K
Cshale Specificheatcapacityoftheshalebodies 950 J/kg/K
L Wellspacing 1000 m
P0 Initialpressure 200 bar
S Salinityoftheporefluid 3 ppm/106
T0 Initialtemperature 348 K
Tinj Injectiontemperature 308 K
withthesandandshalefaciesrandomly(uncorrelated)distributed. Thereservoirbodieshaveaconstantporosityof28%andconstant permeabilityof1000mD.Allotherparametersarekeptconstant asinthemodelTypeI.Thedifferencesinlifetimeandproduction betweenaprocessed-basedfaciesreservoirmodel(TypeI)anda randomrealisation(TypeIII)areameasureoftheimportanceof process-basedmodelsusedingeothermalreservoirsimulations.
2.2. Flowandheattransfermodel
The generated reservoir realisations (Type I, II and III) are employedforheattransferandfluidflowmodelling.Fig.1 illus-tratesthereservoirandthewelllocations(wellspacingis1km). Theinjectionandtheproductionwellshavethesamedischargerate whichremainsconstantovertime.Thetwoouterboundariesatthe shortedgeareassignedaconstantpressure,theothersarenoflow boundaries(Fig.1).TheN/Gatthewellpositions,inalldynamic models,hastoberoughlythesameastheN/Gofthefield,especially forreservoirrealisationswithlowN/G.Insomeofthereservoir realisationsthewellmaynotbeincontactwithanysandbody. Thiswouldincreasethewellpressureandchangetheflow pat-ternswithintherealisation.Inthiswork,themaximumallowable differencebetweenN/Gatthewellsandthereservoirrealisation is2.5%.Toachievethisthedoubletcanbeplacedwithinarangeof 50minthexandydirectionfromtheoriginalwelllocations(Fig.1). Theorientationofthedoubletandthedistancebetweenthewells arekeptconstantinallsimulations.
2.2.1. Governingequations
Heattransferingeothermalsystemscanbedescribedwithtwo mainprocesses: conduction and convection.For a systemwith arigidrock,incompressiblefluidsandlocalthermalequilibrium betweenrockandfluidtheheattransferequationreads:
∂
∂
t(CT)=∇
·(∇
T)−∇
·(fCfuT)+fCfqT∗ (2)
wheretistime[s],Tthetemperature[K],thetotalconductivity tensor[W/(kgK)],fthefluiddensity[kg/m3],Cfthefluidspecific
heatcapacity[J/mK],uDarcyvelocityvector[m/s],andCisthe volumetricheatcapacity,qisexternalsinksandsources[1/s],and
T*referstothetemperatureatsources.Darcyvelocityiscalculated
as:u=−(/)
∇
P.Whereisthedynamicviscosity[Pas]andPis thefluidpressure[Pa].Thefluidpressurefieldcanbeobtainedby solvingthecontinuityequation:∂
f/∂
t+∇
·(fu)=fq.Thetotalthermalconductivityisexpressedas:=eqI+dis.Whereeq is
theequivalentconductivityofthefluidandthematrixandthedis
thethermaldispersiontensor.Thisequivalentconductivityandthe volumetricheatcapacityarebothvolumeaveraged:
eq=(1−)s+f
C=(1−)sCs+fCf
(3) wherethesuffixessand fstandforsolid(shale,sand)andfluid (brine),respectively.
Thermal dispersion has influence on the total conductivity. Thermaldispersioncanbedescribedasafunctionofthefluid veloc-ityandfluidheatproperties.Thethermaldispersiontensorwhich isbasedonthesolutedispersionmodel(Scheidegger,1961),reads:
=(eq+(˛T)|u|)I+fCf(˛L−˛T)uu
|u| (4)
|q|isthemagnitudeoftheDarcyvelocityvectorand˛Land˛Tare
thethermaldispersioncoefficientsinthelongitudinaland transver-saldirection,respectively.
Theporefluidusedinthedynamicmodelisbrine.Thebrine hasaconstantspecificheatcapacity,heatconductivityandsalinity (Table2).Theviscosityofthebrinevarieswithtemperature(T)and
Sthesalinityofthebrine[ppm/106](BatzleandWang,1992)as:
=0.1+0.333S+(1.65+91.9S3)e{−[0.42(S0.8−0.17)2+0.045]T0.8} (5)
Thedensityofthebrinedependsonthetemperature,the pres-sureandthesalinityas:
f =w+S{0.668+0.44S+10−6[300P−2400PS +T(80+3T−3300S3P+47PS)]} (6) where w=1+10−6(−80T−3.3T2+0.00175T3+489P−2TP +0.016T2P−1.3×10−5 T3P−0.333P2−0.002TP2) (7)
ForEqs.(5)–(7),Tisin[◦C]andPin[MPa](BatzleandWang, 1992).
Themodeldomainisdiscretisedby3Dtetrahedraland hex-ahedralfinite elements.In general,discretizationerrors arethe dominantsourcesofnumericalerrorsinsimulations(e.g.Nicketal., 2009).Tominimisethediscretisationerroramaximumfinite ele-mentmeshsizeof20m×20m×2.5mischosen.Theminimum finiteelementmeshsizeis0.5m.Themaximummeshsizeisthe sameastheresolutionofthegeomodels.Thisavoidsporosityand permeability upscaling(averagingpropertiesdue togrid coars-ening)ofreservoir realisations.Saeidetal.(2015) analysedthe discretisationerrorfora similardynamic modelandfoundthat
thechosenmeshsize resultsin anegligible discretisationerror forthefluidandheattransfersimulationsfortherangeofstudied parameters.Inthisstudy,therelativeandabsoluteerrortolerances forflowandheattransportsimulationsaresetto10−5and10−6,
respectively.
2.2.2. Lifetime
Thewatertemperaturecalculatedattheproductionwellisused toobtainthelifetimeofthedoublet.Thelifetimeofthedoublet isdeterminedatthetimewhentheproductionfluidtemperature dropsbelowtheminimalproductiontemperature.The tempera-turelossesinthesurfacefacilitiesandthewellsareneglected.Saeid etal.(2015)illustratedthatthetemperaturelossesinthewells havenegligibleeffectonthetemperatureoftheproductionfluidof ageothermalsystem.
2.2.3. Recoveryandnetenergyproduction
Thecalculatedproductiontemperatureovertimecanbeusedto obtainrecovery,R=Eprod/Etotal.WhereRistherecoveryofthefield
[%],Eprod thecumulativeproduced energy[J]and Etotal thetotal
availableenergy[J].Thecumulativeproducedenergyisdefinedas:
Eprod=
n
i=1
QitifCf(Tprod,i−Tinj), (8)
andthetotalavailableenergyas:
Etotal= m
j=1
{Vjjf,jCf,j(T0−Tinj)+Vj(1−j)s,jCs,j(T0−Tinj)} (9)
wheretisthetimestepincrement,thesubscriptithetimestep,
ntotalnumberoftimesteps,Qthedischarge[m3/s],T
prod,iandTinj
thetemperature[K]oftheproductionfluidandtheinjectionfluid atstepi,respectively.misthetotalnumberoffiniteelements,Vj
thevolumeofthemeshelementjandT0istheinitialtemperature [K].
Theenergyproductionistheproducedenergyminusthepump energythatisrequiredtoinduceapressuredifferencebetweenthe injectionandtheproductionwell:Enet=Eprod−Epump.WhereEpump
istherequiredpumpenergy,assumingtheefficiencyofthepumps isequalto1: Epump= n
i=1 Qti(Pinj−Pprod) (10) 3. Results 3.1. BasecaseWhenapplyingthebasecaseconditionsforthedynamic simula-tionofdifferentrealisationsofmodelTypeIthefollowingfeatures wereobserved:(i)theN/Ghasnoticeableimpactonthelifetime ofthedoubletespeciallyforlowN/Gvalues(Fig.2);(ii)decreasing N/Gresultsindecreasingthelifetime,whichismorepronounced forrealisationswithN/Gsmallerthan40%;and(iii)thecumulative energyproductionshowsthesameresultsastherecovery(Fig.3), buttherecoveryincreasesslightlyfasteratN/Gvalueslargerthan 60%.Sincethedifferencesbetweenrecoveryandthecumulative energyproductionarenegligibleonlytheobtainedrecoveryis dis-cussedinthisstudy.TherecoveryshowsasimilarrelationwithN/G asthelifetime(Fig.3).Notethat40%N/Gisthepointwherethe connectivitystartstodecreasewithlowerN/Gvalues.
Fig.2. LifetimeofthedoubletforQ=100m3/handTmin=74◦Candconnectivity
versusN/G,formodelTypeIrealisations.
Fig.3.TotalenergyproductionandrecoveryversusN/GforQ=100m3/hand
Tmin=74◦CutilisingmodelTypeIrealisations.
Basedontheobtainedlifetimeandrecoveryvaluesforthebase casescenario,thelifetimeandrecoverycanbedescribedas func-tionsofN/G:
LT=˛LTln(N/G) (11)
and
R=ˇRln(N/G) (12)
whereLTisthelifetime[years]andRtherecovery[%].˛LTand˛R
arethefittingparametersforlifetimeandrecovery,respectively. Forthebasecasescenariothefittingparameters˛LT,ˇRand are
equalto4.41,6.35and1.5,respectively.
Thevariationinthetemperaturebreakthroughcurvesobtained atthewellproductionforreservoirrealisations(TypeI)withsimilar N/GvaluesincreasesignificantlywithadecreasingN/G.ForaN/G ofaround50%thebreakthroughtemperaturesarealmostidentical (Fig.4C).AtaN/Gofaround30%thetimeatwhichthe tempera-turestartstodropandthegradientatwhichitdropsstarttodiffer amongtherealisations(Fig.4B).Thedifferencesareeven larger ataN/Garound10%(Fig.4A).Thevariationscanalsobeseenin therequiredenergyforthepump(Fig.5).Ahigherenergy require-mentmeansthatmoreenergyisneededtohavethesamedischarge
implyingthatthesandbodiesattheinjectionwellareless con-nectedtothesandbodiesattheproductionwell.Asaresultthenet energyproducedislessscatteredthanthetotalenergyproduced atverylowN/G.
The difference in the temperature breakthrough curves originatesfromthedifferenceinthecorrespondingmedium config-urations.ReservoirrealisationswithaN/Gof10%inFig.4Aillustrate thatthelocationandgeometryofthesandbodiesdeterminewhich partofthereservoirhasahighpermeabilityzone.Thesegeometries differperrealisation.Somesandbodiesgostraight,whileothersare curvedand/orsplitintwo,whichalsoresultsinisolatedsand bod-iesindifferentlocationsinthedomain.WhentheN/Gincreases thiseffectbecomesless.AtaN/Garound30%therearestillsome continuousshalebodiesseparatingthesands(Fig.4B).Theshales formlowpermeablezonesfunctioningasflowbarriers.For reali-sationsaround50%N/G,thesandbodiesareallconnectedtoeach otherandcoverthewholearea,whichmakestherealisationslook morealike(Fig.4C).
3.2. Effectofdischargeongeothermaldoubletperformance
Asexpected,withincreaseddischargerates,thelifetimeofthe doubletdecreases(Fig.6).Similarly,withincreaseddischarge,the varianceinlifetimeamongrealisations(TypeI)isreduced(Fig.7). Thisisrelatedtothefastdecreaseinlifetimeforreservoirswitha largeN/G.Whenthedischargerategoesfrom60to100m3/h,the
lifetimedecreaseswith∼20yearsforTypeIrealisationswithaN/G of100%,whileataN/Gof10%lifetimedecreaseswith∼10years. Athighdischargerates(Q>200m3/h)anincreaseinthedischarge
hasrathernegligibleeffectonthelifetime,whileatlowdischarge rates(Q=60m3/h)smallchangeshavealargeimpactonthelife
time,10yearsdifferencecomparedwithQ=80m3/h(Fig.7).
Thetypeof relationbetweentheN/Gandlifetime doesnot changefordifferentdischarges,butitaffectsthefittingparameter
˛LT.Thisfittingparameterhasalinearrelationwith1/Q(Fig.8A):
˛LT =˛Q
Q (13)
ˇR=ˇQ
Q ≈constant (14)
where˛Qisthedischargefittingparameter.Thefittingparameter
oftherecovery,ˇR,isbarelysensitivetoincreasing1/Q(Fig.8B)
andthereforetheeffectofdischargeonˇR isneglected.Neither
doesthedischargevariationhaveeffectonthefittingparameter .
3.3. Influenceoftheminimalproductiontemperatureon geothermaldoubletlifetimeandrecovery
Adecreaseintheminimalproductiontemperatureresultsina longerlifetimeandhigherrecovery(Fig.9).Asaresultthefitting parameters˛QandˇRarespecificforeachproductiontemperature.
Thelowertheminimal productiontemperaturethesteeper the relationbetweenparameters˛LTand1/Q(Fig.8C).Thedischarge
fittingparameter˛Q hasa linearrelationwiththetemperature
difference(Fig.8A).Asa resultthecompletecurveforlifetime estimationsbecomessteeper,whichgivesanoverestimationfor reservoirswithaN/Gabove60%.Tocorrectforthisoverestimation thefittingparameters isdefinedasafunctionofT:
˛Q =221T+176 (15)
ˇR=3.04T+2.77 (16)
=−0.115T+1.585 (17)
whereT=T0−Tprod.NotethatthisrelationisbestsuitableforT
Fig.4.ProductiontemperaturedevelopmentforQ=100m3/h,correspondingtodifferentTypeIrealisations(1–9).Claystonegridblocksaretransparent,andconnected
sandstonebodieshavethesamecolour.
Fig.5.(A)TheproducedenergyandthenetproducedenergyversusN/G.(B)PumpenergyrequiredtocreatethepressuredifferenceatthewellsversusN/G(Eq.(10)).
3.4. Homogeneousversusheterogeneousreservoirbodies
Thereservoirrealisationswithhomogeneousreservoirbodies (TypeII)haveaslightlyhigherlifetime,1.6yearsonaveragewith
amaximum of4.2years, thanthatofmodel TypeIrealisations withheterogeneousreservoirbodies(Fig.10).Theoverestimation fallsmostlywithintheuncertaintylevelofthecalculatedlifetimes, whichisrelatedtothereservoirheterogeneity.
Fig.6.LifetimeversusN/Gfordifferentdischargerates(Tmin=74◦C).
3.5. Randomrealisationsversusreservoirrealisations
Utilisingtherandomrealisations(TypeIII)withN/Ghigherthan 70%resultsinlifetimevaluescomparabletothosecalculatedforthe modelTypeIrealisations(Fig.11A).UtilisingmodelTypeIII real-isationsinthedynamicmodelresultsinanoverestimationofthe lifetimeforN/Gvaluesbetween70%and40%,wherethelifetimeis almoststable.Below40%N/Gthelifetimestartstodropincaseof TypeIIIrealisations,butlessthanthatoftheTypeIrealisations.Itis foundthattheconnectivityvaluesofthereservoirforTypeIII real-isationsdropsdrasticallyandreacheszeroforTypeIIIrealisations withN/Glessthen30%,whiletheTypeIrealisationshavea min-imumconnectivityof42%(Fig.11B).Thismeansthattherandom realisations(TypeIII)havereservoirbodiesatthewellswhichare smallandisolated.Theserealisationsdonothaveahighpermeable zonebetweenthewells.Andwithrespecttotheboundary condi-tions,fixeddischarge,thepressuredifferencebetweentheinjector
Fig.7. ThevarianceinobtainedlifetimevaluesforN/Gatdifferentdischargerates andTmin=74◦C.
andproducerincreasessignificantly.Themodelswiththerandom realisations(TypeIII)resultinamuchlowervarianceinlifetime forreservoirswiththesameN/Gvaluewhentheyarecompared tothelifetimevaluesobtainedforthemodelTypeIrealisations (Fig.11).
3.6. Asimpledesignmodel
Withrespecttotheresultsgainedbyemployingthereservoir realisationsTypeI,thelifetimeofareservoircanbeestimatedwith asimplifiedmodelwhentheN/G,dischargeandminimal produc-tiontemperatureareknown.Themodelisdescribedas:
LT=221T+176
Q (ln(N/G))
(−0.115T+1.585)
(18)
R=(3.04T+2.77)(ln(N/G))(−0.115T+1.585) (19)
Fig.8. (A)˛LTversus1/Qfordifferentminimalproductiontemperatures,(B)ˇRversus1/Qfordifferentminimalproductiontemperatures,(C)˛QandˇTversusTand(D) versus1/Q.
Fig.9.(A)Thelifetimeand(B)recoveryversusN/GofmodelTypeIrealisationswithaminimalproductiontemperatureof68,70,72and74◦CforQ=100m3/h.
Fig.10.LifetimeversusN/Gforreservoirrealisationswithheterogeneous(TypeI) andhomogeneous(TypeII)sandbodiesincludingthedifferenceinlifetimebetween them(LT)withQ=100m3/handTmin=74◦C.
Fig.11. LifetimeversustheN/Gofrandomrealisation(TypeIII)andgeological realisation(TypeI)withQ=100m3/handTmin=74◦C.
Fig.12.Thelifetimecalculatedwiththedynamicmodelversusthelifetime esti-matedwiththesimplifieddesignmodel(R2=0.85).Thedatapointsofallheat
transferandflowsimulationsofTypeIareused.
Themodelisonlytestedfor dischargeratesbetween80and 140m3/hand minimal production temperaturevalues downto
68◦C.Moreresearchneedstobedonetocheckifthemodelisvalid forhigherdischargevalues.ThelinearrelationofTandlifetime isfoundnottobevalidforalltemperaturevalues.Thisisbecause below65◦Ctheproductiontemperaturecurveisnolongerlinear (Fig.4),whichindicatesthattheeffectofTonthelifetimeis non-linear.
Theresultsobtainedwiththesimplifiedmodelarecomparable withtheresultscalculatedwiththedynamicmodel(Fig.12).The predictedlifetimevaluesarenotexactlythesameasthoseobtained fromthedynamicmodel.Thisispartlyaresultofthevariancein lifetimeofreservoirmodelswithsimilarN/Gvalues(Fig.11).The effectisfoundtobethesamefortherecovery.
3.7. Animproveddesignmodel
Thesimplifiedmodelworksfine,butitunderestimatesthelife timefordischargesof80and100m3/hwithaminimaltemperature
of74◦C.Themodelalsooverestimatesthelifetimeforreservoir realisation with a N/G above 70% with a minimal production
Fig.13.LifetimeversusN/Gfordifferentdischargesbasedontheimproveddesign model.
temperatureof70and68◦C.Thiscanbeimprovedbysplittingthe modelupinto2regions.Region1hasaN/Grangefrom10to45% andRegion2from45to100%N/G.InRegion1asimilarfunctionis usedasinthesimplifiedmodel,butfittingparametersareadjusted tothisregion(Fig.13).Thefunctionislesscomplex,becausethe fittingparameter isconstant.InRegion2thefunctionisnolonger logarithmic,butlinear.Theimproveddesignmodelisdescribedas:
LT=
⎧
⎪
⎨
⎪
⎩
390+56.9T Q (ln(N/G)) 1.5 for 15<N/G≤45 390+56.9T Q (ln(45)) 1.5+18.7−2.84T Q (N/G−45) for 45<N/G<100 (20) R= (0.75T+5.67)(ln(N/G))1.5 for 15<N/G≤45 (0.75T+5.67)(ln(45))1.5+(0.28−0.035T)(N/G−45) for 45<N/G<100 (21) ThismodeldescribesthelifetimeasafunctionofN/G,QandT,andtherecoveryasafunctionofonlyN/Gand T.Aclear distinctioncanbemadebetweenthetworegions.InRegion1the geologicalparameterN/Gisthemaincontrollingfactoronbothlife timeandrecovery.ThehumancontrolledparameterQ(discharge rate)isthemostinfluentialfactorinRegion2onlifetime,while thehumancontrolledparameterTisthemostinfluentialfactor ontherecovery.
Theimproveddesignmodelpredictsthelifetimemore accu-ratelycompared tothesimplifieddesign model;itimprovesR2
from0.85to0.92(Figs.12and14).Theimproveddesignmodel worksbestforN/Gfrom15to100%,butunderestimatesthelife timeofreservoirswithaN/Garound10%(Fig.14).
4. Discussion
4.1. Basecase–modelTypeI
Theeffectof N/Gonlifetimeand recoverycanbedescribed withnaturallogarithmicrelationsforN/Gvaluesbelow45%and withlinearrelationsforN/Gvaluesabove45%.InRegion1the con-nectivityhasalargervariance,precludingaccuratepredictionof thelifetimeandrecovery.Thevarianceinconnectivityincreases withdecreasingN/G.Thiscouldpartlybeaneffectofthechosen resolutionofthereservoirrealisations(TypeI),whichresultinless accurateconnectivitycalculationsforaN/Gbelow20%.Hovadik andLarue(2007)showedthatincreasingthegeomodelresolution
decreasesvarianceforconnectivityandimprovesconnectivity.This incombinationwiththeeffectofthefaciesdistributionexplains whyitishardertopredictdoubletperformancesoflowN/G reser-voirs;morevariablesplayarole.Forthelinearparttherelations aremoreaccurate.Theconnectivityis100%forallrealisationsand hasthereforenegligibleeffectontheresults.
Thehigher variancein lifetime forlow N/G reservoirs indi-catesthattheaccuracyofthereservoirmodeliscrucial,whichis forhighN/Greservoirswithlowervarianceslessimportant,albeit notnegligible.Theenergyrecoveryshowsthesameeffectasin theoilrecovery;oncetheconnectivitystartstodroptherecovery dropsfast(LarueandHovadik,2008).Theabsolutevaluesofthe recoveriesfromoilandgeothermalenergycannotbecompared directly,becausetherecoveriesaredefinedinadifferentway.In theoilindustrythetotalamountofoilavailableisonlyinthepore ofthereservoirbodies,whilethetotalamountofheatavailableis intheconnectedporesandthematrixofboththereservoirand non-reservoir.Thismeanstheoilcanonlybeproducedfromthe reservoirpart,whileheatcanbeproducedfromthesurrounding lowpermeablelayersbyconduction.Nonetheless,theheat recov-eriesobtainedinthisstudyhavearangefrom15to65%(Fig.3), whichissimilartotheoilrecoveriesreportedbyLarueandHovadik (2008).The differencesbetweenobtainedenergy recoveriesfor realisationswith50and100%N/Garesmall,whichindicatesthat theshalesplayanimportantrole ingeothermaldoublet perfor-manceforreservoirswithN/Glowerthan50%.Asaresult,reservoirs withaN/Gofroughly50%arealmostasefficientasthosewith100% N/G.Noticethattheheatcapacityandconductivityaresimilarfor sandandshale,whichmakesthedifferencesinheatconduction small.
Fig.14.Lifetimeobtainedwiththedynamicmodelversusthelifetimeobtained withtheimproveddesignmodel(R2=0.92).Thedatapointsofallheattransferand
4.1.1. CaseA:discharge
Dischargeaffectsthelifetimeandrecovery,butthedifference inrecoverybetweenadischargeof80and140m3/hissmall
com-paredtothevariance inrecoveryforreservoir simulationswith similarN/G(Fig.3).Thismeansthedischargeratecanbeadjusted totheyearlyenergydemand,withoutinfluencingthecumulative producedenergysignificantlyduringthelifetimeofthedoublet.
Thepressureintheinjectionwellincreaseswithincreasing dis-chargeorwhenthewellisonlyincontactwithsmallisolatedsand bodies.Thispressurecannotbehigherthantherockstrength, oth-erwisethereservoirwillbefractured.Fracturesinthereservoir wouldchangethefluidflowbehavioursignificantly(e.g.Matthä etal.,2010;Nicketal.,2011)andthestatedrelationswouldnotbe applicable.
4.1.2. CaseB:minimalproductiontemperature
Lowerminimalproductiontemperaturesextendthelifetime andrecovery.Whentheproducedtemperaturedeclinesthedaily energyproduceddeclinesaswell,becausethedischargeisconstant. Ifaconstantdailyenergyproductionispreferredthedischargehas toincreasetocompensatefortheproducedwaterwithlower tem-peratures.Thiswilldecreasethelifetimeoftheprojectandspeed upthecoolingoftheproductiontemperature.Thisloopwill accel-eratethewholeprocessandthedifferencesinlifetimewillbeless thanshowninFig.9A.
Thevarianceintheobtainedlifetimeandrecoveryincreases fordecreasingminimalproductiontemperatures(Fig.4).Thisis relatedtothedispersioneffect.Theresultofthis effectismost noticeableafterthecoldwaterfronthasreachedtheproduction well.Thetemperatureoftheproducedwaterdropsmoreslowlyfor asystemwithhigherthermaldispersion.Thisuncertaintyin tem-peraturedropmakesithardertopredictthelifetimeandrecovery forlowerminimalproductiontemperatures.
4.2. Homogeneoussandbodies–modelTypeII
Reservoirrealisationswithhomogeneousreservoirbodiesmay overestimatethelife time upto4 years comparedto reservoir realisations(TypeI)withheterogeneoussands,butinmostcases theoverestimationislessthan1year.Thedifferenceinlifetime betweenhomogeneousandheterogeneoussands iswithintheir uncertaintybounds.Thereforetheintrasand-bodyheterogeneity couldbedisregardedforthelifetimecalculation.
4.3. Randomrealisations–modelTypeIII
Thesimulationswiththerandomrealisationresultinunrealistic required(well)pressurevaluesandinmuchhigherlifetimes com-paredtoreservoirrealisations(TypeI)whenN/Gvaluesarebelow 70%.Theseunrealisticpressurevaluesarerelatedtothefixed dis-chargerateandtheshapeandconnectivityofthereservoirbodies. Randomporosityandpermeabilityfieldshardlyanyrandom real-isationhasaconnectedreservoirbodyfromtheinjectiontothe productionwell,whereasthereservoirrealisationsdohavethis. Asaresultveryhighinjectionwellpressurevaluesareneededto pushthewaterthroughtheshaleinbetweenthesandsinorderto achievetherequireddischargerate.
ArealisticgeologicalmodelisthereforenecessaryforN/Gvalues below40%.Above40%N/Gtheconnectivityplaysonlyasmallrole, asitisalwayslargerthan95%.Thelifetimevaluesobtainedwiththe randomrealisationsareoverestimatedforaN/Gbetween40and 60%.ForN/Gvaluesabove70%,thelifetimeobtainedbytherandom realisationsarecomparablewiththeonesobtainedwithreservoir realisations.Nevertheless,intherandomrealisationsthedifference betweenmaximumandminimumpossiblelifetimesismaximum 5years,whiletheresultsofthereservoirrealisationshowthatthe
differencecanbesignificantlylarger(±10years),whichseemsto bethecaseevenforreservoirsupto70%N/G(Fig.11A).Therefore dynamicreservoirsimulationsshouldbeemployedtocalculatethe risksofanearlycoldwaterbreakthrough,especiallybeforedrilling. Eventhoughitishardtomakeveryaccuratereservoir simu-lationsbeforedrilling,simulationresultswillprovideavaluable rangeofexpectedlifetimes.Thismeansthatthegeologyhasa majorimpactonlifetimeandisasimportantasthehuman con-trolledparameter‘discharge’when estimatingthelifetime ofa low-enthalpygeothermaldoublet.
Whenlayercakemodelsareusedtocalculatethelifetimeone majorassumptionisthatallthereservoirbodiesareconcentrated (i.e.100%connectivity).Thecomparisonoftherandomrealisations withreservoirrealisationsshowsthatitisimportanttoknowthe connectivityofthereservoirbodybetweentheinjectionand pro-ductionwell,notonlyforthelifetime,butforwellpressuretoo. Thismeansthatiftheinjectorispoorlyconnectedtotheproducer, higherpressuresareneededtokeepupthedischarge.Thispressure variesthemostforrealisationbelow45%N/G,whichistheregion wheretheconnectivityvaries(Fig.2).Thepressureincreasesare probablylessnoticeablewhenlayercakemodelsareused.
4.4. Simplifiedandimproveddesignmodel
Thesimplifiedmodelprovidesagoodestimateofthelifetime ofdoubletsproducingfromlow-enthalpygeothermalreservoirs. Themodelisonlydirectlyapplicableforreservoirwithroughly thesameheattransferandflowcharacteristics,wellspacingand reservoirthicknessasusedinthisstudy.Themodelassumesthat allreservoirshavethesametypeofnon-linearrelation,butthe fit-tingparametersareformationspecific.Despitethelimitations,the simplifieddesignmodelcanbeusedforprimarycalculationsfor estimatinglifetimeandrecovery.Itmustbekeptinmind, how-ever,thattheresultsunderestimaterealityforthelowerrangeof N/Gbetween35and50%andoverestimateitforaN/Gabove90% (Fig.2).FortheothervaluesofN/G,thesimplifiedmodelgivesa goodaveragevalue,whenthevarianceinlifetimeandrecovery aretakenintoaccount.
Theimprovedmodelestimatesthelifetimemoreaccuratethan thesimplifiedmodelbydividingthemodelinto2regions:a log-arithmicpartandalinearpart.Thisresolvestheproblemforthe underestimationsandoverestimationsofthesimplifiedmodeland removesthefittingparameter fromtheequation.Thedecreasing accuracyofthesimplifiedmodelduetoanincreasingvarianceinlife timeremainsthesameintheimprovedmodel.Thevariance com-binedwithanunderestimationataN/Gof10%makestheimproved modellessaccurateforreservoirswithaN/Gbelow15%.Thisis, however,noproblemforthetargetsforlow-enthalpygeothermal reservoirsintheNetherlands,sincetheNieuwerkerkFormationhas aN/Gbetween20and50%(DenHartogJager,1996).When apply-ingtheimprovedmodeltothisformationthecalculatedlifetime canstillbebetween21years(N/G=20%)and31years(N/G=31%) forQequalto100m3/handTequalto1◦C.InclusionofN/G
val-uesmeasuredinnearbyfieldsinthestudyareacanhelpnarrowing thisrangeofN/Gandimprovingthelifetimeprediction. Neverthe-lessthisimpliesthataccuratefielddataandreservoirrealisations arenecessaryforaccuratepredictionofthedoubletslifetimeand recovery.
5. Conclusions
Theworkcombinesaprocess-basedmodelwithaflowandheat transfermodel.Theprocess-basedmodeliscapableofgenerating reservoirmodels(TypeIandII)utilisingcoredata.Weshowthatthe lifetimecanbeestimatedwiththedesignmodelforbothRegion1
(N/G>45%)andRegion2(N/G<45%).Wehavedemonstratedthat thedifferenceinlifetimewithinRegion2isrelativelysmallandthe maincontrollingfactoristhedischarge.InRegion1thedependence oflifetimeonN/GislargerthaninRegion2.Thereforesmall over-andunderestimationinN/Ghavealargeimpactonlifetime pre-dictionsinRegion1.Theshalehasapositivecontributiontothe heattransferinthesystem,whichincreasesthepotentialoflower N/Greservoirs.
When using a geological model with randomly distributed facies,firstthelifetimesareoverestimated,especiallyfor reser-voirsinRegion1.Next,thevarianceinlifetimeforreservoirswith thesameN/Gislessthan5yearsformodelTypeIIIreservoirs,while itis10yearswhenprocess-basedfaciesmodelling(TypeI)isused. Thismeansarealisticrepresentationofthefaciesheterogeneity isneededtomakemorereliablepredictionsofthelifetimeofa low-enthalpygeothermaldoublet.
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