Thermal conductivity and porosity maps for different materials: A combined case study of granite and sandstone

HAL Id: hal-02457295

https://hal.univ-lorraine.fr/hal-02457295

Submitted on 8 Oct 2020

HAL is a multi-disciplinary open access

archive for the deposit and dissemination of

sci-entific research documents, whether they are

pub-lished or not. The documents may come from

teaching and research institutions in France or

abroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire HAL, est

destinée au dépôt et à la diffusion de documents

scientifiques de niveau recherche, publiés ou non,

émanant des établissements d’enseignement et de

recherche français ou étrangers, des laboratoires

publics ou privés.

Thermal conductivity and porosity maps for different

materials: A combined case study of granite and

sandstone

Sébastien Haffen, Yves Géraud, Michel Rosener, Marc Diraison

To cite this version:

Sébastien Haffen, Yves Géraud, Michel Rosener, Marc Diraison. Thermal conductivity and porosity

maps for different materials: A combined case study of granite and sandstone. Geothermics, Elsevier,

2017, 66, pp.143-150. �10.1016/j.geothermics.2016.12.005�. �hal-02457295�

Thermal

conductivity

and

porosity

maps

for

different

materials:

A combined

case

study

of

granite

and

sandstone

Sébastien

Haffen

_,

_Yves

_Géraud

_,

_Michel

_Rosener

_,

_Marc

_Diraison

a _{GeoRessourceslab.,UMR7359,EcoleNationaleSupérieuredeGéologie,UniversitédeLorraine,CNRS,CREGU,2RueduDoyenMarcelRoubault, Vandœuvre-lès-Nancy,}

F-54501,France b _{TeranovSAS,2RueduDoyenMarcelRoubault,Vandœuvre-lès-Nancy,F-54501,France} c _78,84e _{AvenueEst,Blainville,QcJ7C3T3,Canada} d _{InstitutdePhysique}

duGlobedeStrasbourg(IPGS),UMR7516CNRS-UniversitédeStrasbourg/EOST,5rueRenéDescartes,StrasbourgCedex67084,France Keywords:Thermalconductivitymap, Porositymap, Heterogeneity, Geothermal

a

b

s

t

r

a

c

t

Thankstothermalconductivitymaps,obtainedfromOpticalScanningmethod,and porositymaps, inferredfromthermalconductivitymaps,wehavestudiedpetrophysical heterogeneitiescommonly presentinagraniticandsandstonegeothermalreservoir(fault zoneandpermeablelayers,respectively). Themapsalloweddeterminationofthermal conductivityandporosityvariationtomillimeterresolution,atacorescale.They permittedprecisequantification and determination ofthesize ofpetrophysical heterogeneities(thermalconductivityandporosity)inducedbyrockvariability.

.

1.Introduction

Inthecurrentcontextofcommitmenttosustainableandrenewableenergy, manycountriesworldwidearedevelopinggeothermal energy(Dicksonand Fanelli,2003;Lundetal.,2011;Bertani,2012). Toenhanceandensurethe economicandtechnicalviabilityof theheatexchangeratdepth,itappears importanttoimprovethe knowledgeofthermalandhydraulicpropertiesofthe targeted reservoirandtheirbehaviorsduringtheexploitationperiod(see for exampleBirsch,1966;CermakandRybach,1982;Haeneletal., 1988;Clauserand Huenges1995;Clauser2006;Hartmannetal., 2008).Indeed,theseproperties playamajorroleintheplanningof geothermalinstallationandingeothermal modeling.

Throughageothermalreservoirexchanger,fluidflowsoccurin thefractures and faultsconnectednetworkand indifferent sedimentarylevelsofhigh permeability(Haffenetal.,2013;Siffert etal.,2013).Thesefluidspresent differenttypesofdisequilibrium withrespecttothesurroundingrocks,aswellto temperatureand chemicalcomposition.Indeed,interactionprocessesbetween fluidsandrock,whichoccurovertimeintheporousspaceconnected

tothemainfluidflowzone(masstransferinducedbydissolutionandprecipitation phenomenaormechanicaldisplacementof clayedparticles),canprovokedamageto theheatexchangerby modifyingitspermeabilityandalsoaffectthesurfacepower plant (NortonandKnapp,1977;Norton,1979;SeibtandKellner,2003; Ungemach, 2003;Fritzetal.,2010;Civan,2011;Meieretal.,2014).

Thus,thermalconductivityandporositymapsappeartobetwo keyparameters, sincetheyallowtheimprovementofthetargeted rockcharacterization,notablyfrom information(quantification andsize)aboutpotentialrockheterogeneities.

Variousexperimentaltechniquesallowedthecharacterizationofthethermal conductivityandporosityofrocksamples (ZinsznerandPellerin,2007;Tritt,2004). WedevelopedanewnondestructivemethodbasedonOpticalScanning(Popovetal., 1999), toquicklymapthethermalconductivityandporosityofsamples. Wepresent theacquired2Dthermalconductivitymapsandthe computed2Dporositymaps.

Inthispaper,wepresentresultsfortwokindsofrock:graniteandsandstone,which both have specific structures (fractures and sedimentary heterogeneities, respectively).Theserocksare ofspecialinterestbecause,forcontinentalEurope,high enthalpy geothermaltargetsarelocatedinthedeeppartofthesedimentary basin,its basementanditslowerlevels,includingthebottomof thesedimentarycover,whichis generallysandstone(Genteretal., 2003;Bourquinetal.,2011).

2.Geologicalsettingandthermalconductivity/porosity mapselaboration

2.1.Sampledescription

Theselectedsamplesareexpectedtoillustratetwokindsoffluid flownetworksin deepgeothermaltargets.First,agranitesample affectedbyafracturezonewithquartz infillingattheedgeofan openfractureisakindofstructurecurrentlydescribedin granitic geothermalfields(Géraudetal.,2010).Second,asandstonesample is analyzed,whereasedimentologicalheterogeneitywasinduced bygrainsize variation.

Thegranitesample(K195-4777)wastakenfromtheEPS1 borehole,partofthe deepexperimentalgeothermalsiteofSoultzsous-Forêts(France)intheUpperRhine Graben(Genterand Traineau,1992;Rosener,2007)(Fig.1a).Thesampleislocated approximately 2162 m deep, in a granite zone that corresponds to a silicified/cataclasedhydrothermalalterationfacies(Rosener, 2007).Thisallowsthe differentcompartmenttypicallyencounteredinfaultzonestobestudied:theprotolith, thedamagedzone andthefaultcore(Caineetal.,1996;Géraudetal.,2010;Faulkner et al.,2010).Thesampleisdividedintothreezones(Fig.1a). Zone1correspondstoa damaged zoneand isanalteredzone composedof massiveorangefeldspar (orthoclase)associatedwith alteredfeldspar,somesmallsecondaryquartzandblack mica.It hasanincreaseinporosityduetoanalterationprocessinduced by hydrothermalfluids.Zone2ischaracterizedbyasizableconcentrationofsecondary quartzandhardlyanyalteredfeldspar.It correspondstotheprotolith.Zone3showsa partiallysealedlocalizedquartzfaultcore.

Thesandstonesample(EPS161)alsocamefromtheEPS1borehole(Haffen, 2012)(Fig.2a),andwasextractedatadepthof approximately1214m,fromthe Buntsandsteinsandstonesformation:“GrèsVosgiens”facies(Vernouxetal.,1995;

Bourquin etal.,2006).Thepetrographicfaciescorrespondstoclayedcoating sandstonealternatingwithcleansandstone(seeHaffen,2012; fordetails).Thesample canbedividedintotwozones(Fig.2a):zone 1iscomposedmainlyoffinetoveryfine darkbrowngrainedsandstone,andzone2ismainlymadeofmediumtofinebrown grained sandstone.Asmallfaultismarkedbyagapofapproximately5mm, whichis sealedoffbyextremelythinbariteprecipitation.

2.2.Measurementtechniques:thermalconductivityscanner (TCS)

OpticalScanningmeasurementsperformedwithaTCS(Popov etal.,1999;Popov etal.,2003)deliveralargesetofthermalconductivityvaluesfasterthanclassical laboratorytechniques,suchas withadivided-baroraliningsource(Sassetal.,1971, 1984).The OpticalScanningapparatuscorrespondstoamobileblockcomposedof twotemperaturesensorsoneithersideofaconstantand continuousheatsource.These threefixedelementsarelined-up onthemobileblock,paralleltothemobile displacementaxis.The blockmovesunderarailonwhichthesampletobemeasured

had beenpreviouslyplaced.Heatsourceandtemperaturesensorsmove at the same relative speed (TCS mobile block velocity: 4.99mms−1)

alongthescanningsurface,whichismaintainedataconstantdistancefromboth sensors.Thus,measuringthesampletemperature beforeandafteritsheatingis renderedfeasible.Thesedata,associatedwiththoseofthetwostandardssituated eithersideofthe measuredsampleandhavingathermalconductivityknowntobe closetothatofthesample,allowcalculatingtheabsolutethermalconductivityofthe sampletobecomepossible.Thistechnique thereforepermitstheobtainmentofa profileofthermalconductivityofthesamplealongascanline,witharesolutionof1 mm. Thescanlineisatamaximumof500mm,duetothelengthofthe apparatus,while therelativemeasurementerrorisapproximately 3%ofthemeasuredvalue(Popovet al.,1999).Theroomwheremeasurementswerecarriedoutwaskeptataconstant

temperature (20◦C±1◦C).Duringthemeasurements,theincreaseinsample temperaturewaslimitedto3◦C,rangingfrom20±1◦Ctoamaximumof23±1◦C.Abrief coolingtimewassystematicallyimposed betweentwoscanlinestorestricttheheating ofthesampleand ofthestandards.Thermalconductivityvariationsinducedbythe heatingofthesampleduring themeasurementwere neglected, sinceatthis temperaturerangethethermalconductivityvariation isinferiortothemeasurement error(VosteenandSchellschmidt, 2003).

2.3.Thermalconductivityandporositymap 2.3.1.Method

Thermalconductivityinrocksdependsmainlyonthreeparameters(e.g.

Farouki, 1981; Brigaudand Vasseur1989; Clauserand Huenges, 1995; MidttommeandRoaldset,1998):mineralogical composition,porosityand texture.Otherparameterscanalsocontrolthethermalconductivityofrocksaspore fluidspropertiesand structural/texturalpropertiesof rocksincludingrockanisotropy Theporosityofarock canbeestimated(SchärliandRybach,1982) atconstanttemperatureandpressure, usingcomparisonsbetween thermalconductivityvaluesobtainedforair-and water-saturated samples,whilemineralogyandothermicrostructuralparameters aretakenasbeingconstant.Foreachstate,thegeometricmean modelbasedon mixinglaws(Eq.(1),ClauserandHuenges,1995) isconsidered,asfollows: = × 1− (1) f

where (Wm−1 K−1)istheeffectivethermalconductivity,

f

(Wm−1 K−1) is the thermal conductivity of the fluid (air or water)

1 1

presentintheporosity((−)),andm (Wm− K− )isthethermal conductivityofthesolidmatrix.

Forasample,afirstsetofthermalconductivitymeasurementsunder air-saturatedconditionsandasecondsetofthermal conductivitymeasurementsunder water-saturatedconditionsare necessaryandtheseleadtotheporositycalculation (Eq.(2))asfollows(PribnowandSass,1995;Pribnowetal.,1996;Surmaand Geraud,2003;Haffen,2012):

satdry

= (2)

watair

1 1

wheresat (Wm− K− )isthethermalconductivityofthewater- saturated sample, (Wm−1 _K−1_{) is the thermal conductivity of}

dry

theair-saturatedsample,wat isthethermalconductivityofwater (0.6Wm−1 K−1,ClauserandHuenges,1995)and is the thermal

air conductivity of air (0.02Wm−

1 _K−1_,

Clauser and Huenges, 1995).

Thus,tocalculateporosity,wehaveconsideredasimplifiedcase, without needingtobuildanempiricalmodel(Somerton,1992).Satisfyingresultswere obtainedwiththeappliedmathematicalmodel, basedonamixinglaw(Pribnowet al.,1996;Hartmannetal.,2005).

Thismathematicalmodel(Eq.(2))wasusedtodeterminethe meanporosity valuefrommeasurementsofthethermalconductivityinbothdryandwetsamples. Here,weusetheOpticalScanning methodtomeasurethethermalconductivity. Fromthesemeasurementsandtheexperimentalmeasurementprotocolfirst proposed byRosener(2007),wecanbuilda2Dporositymapfrom2Dthermal conductivitymaps.Thisapproachletusobservemillimeterscale variationsof thermalconductivityandporosityforpluri-decimeter rocksamples.

thewatersaturatedgranitesample;(d)Computedporositymapofthegranitesample. Fig.1.(a)Analyzedsurfaceofthegranitesample;(b)Measuredthermalconductivitymapoftheairsaturatedgranitesample;(c)Measuredthermalconductivitymapof

145

2.3.2.Mapconstruction

Beforemeasurements,surfacesofthesamplesthatweregoing tobe mappedweresawedwithadiamondsawandthesurfaces werecarefully brushedtoremovedust.Sothatallthesurfaceshave thesamealbedoandto avoidinterferencewiththemeasurements theywerepaintedblackwithspray paint,suchthatpaint-crushing thicknesswaslimited.Thenthesampleswere driedat60◦Cuntil theyreachedaconstantweight.Severalhoursbefore startingthe test,thesampleswereplacedinthemeasurementroom,soasto keepthematthermalequilibriumunderdryconditions.

ThesampleswerefirstplacedontheTCSrail,atthebeginning ofthe measurements.Aprofileofthermalconductivitywasthen determinedalonga

scanline(line000),ateachmillimeter(point1, point2,etc.,tothemthpoint). Later,withgreataccuracy,thesampleswereshifted1cmperpendiculartothe measurementaxisand anewprofilewascreated(line010).Themeasurement sequence hasbeendefinedasfollows(Fig.3): line000,line010,line020, line030,etc. line001,line011,line021,line031,etc. line002,line012,line022, line032,etc. line003,line013,line023,line033,etc.

...

untilthesurfaceswerecompletelyscanned.Thissequence wasdevelopedtolimit theheatingofthesample,whichcould

Fig.2.(a)Analyzedsurfaceofthesandstonesample,blackdottedlineindicatesthesealedfault;(b)Measuredthermalconductivitymapoftheairsaturatedsandstone sample;(c)Measuredthermalconductivitymap ofthewatersaturatedsandstonesample;(d)Computedporositymapofthesandstonesample.

Fig.3.(a)Photographofagranitesamplepreparedformeasurement,(b)Schematicrepresentationofthesample’sscannedsurface,indicatingthepositionofthemth measuredpointofthenthmeasuredline.

modifythethermalconductivitywithanincreaseintemperature (e.g.Abdulagatova etal.,2009).Asaresult,eachmeasuredpointis about1mmawayfromtheother measuredpointssurroundingit. Thesedataledtoa2Dthermalconductivitymapof air-saturated samples(nline×mpoint/line)witharesolutionof1mm.

Afterobtainingthefirstthermalconductivitymap,thesamples were water-saturatedbysubmergingthemindistilledwaterinside asealedvacuumchamberfor48 h.Thethermalconductivitymaps forwater-saturatedsampleswerederivedsimilarly totheprevious drytest.Theobjectivewastoaccuratelysuperposethetwomeasured

surfaces:lineXXX(underdryconditions)hadtobeinstrictly thesamepositionas lineXXX’(underwater-saturatedconditions). Tolimittheevaporationrisk,each sample except the measured surfaces waswrapped in plastic film.Weight measurementtests, performedonwater-saturatedsamplesbeforeandafterthermal conductivitymeasurementsindicatedthatwaterlosswaslower than1%.

Thermalconductivitymapscouldbedrawnforeachsample, underair-and water-saturated conditions and a porositymap could be computed fromthese by transformingEq.(2)inthefollowing way(Eq.(3)):

ln(sat)dryi,j

i,j = (3)

wat

wherei,j (−)istheporosityatthemthpointofmeasurementof thenthline,(sat)i,j (Wm− K− )isthethermalconductivityofthe

1 1

water-saturatedsampleatthemthpointofmeasurementofthe nthlineand(dry)i,j (Wm−

K− )thethermalconductivityofthe

1 1

drysampleatthemthpointofmeasurementofthenthline.

2.3.3.Watersaturationtest

Foreachsample,themeanporosityvalueobtainedfromthermal conductivity measurementscouldbecomparedtothetotalporositymeasuredfromthewater saturationtest(Melnyk andSkeet, 1986).This valuewasobtainedfrom an experimentalprotocol basedonthewatersaturationofasampleaftervacuum degassing. Initially,samplesweredriedat60◦Cuntiltheirweightbecameconstant(m1 ing)andwerelaterplacedinavacuumchamberfor 24h(afterthermalconductivity measurementswereperformed ondrysamples).Inthemeantime,distilledwaterwas degassed andthenusedtofillthesamplesbycapillarity.Thelevelofwater inthe sampleswasregularlyadjustedaccordingtothecapillary fringe.Oncetheywere entirelysubmersed,thevacuumwasbrokenandthesamplesretainedinwaterfor24h untiltheyreacha constantweight.Priortothermalconductivitymeasurements being carriedoutonwater-saturatedsamples,thesampleswere weighedtwice:firstly, under water-saturatedconditions(m2 in g) andsecondly,under hydrostatic conditions(m3 ing).Porosity( in%)wascalculatedasfollows(Eq.(4)):

m2 −m1 × 100 (4) m2 −m3

3.Results

UsingTCS,bothair-and-watersaturatedthermalconductivity2Dmapswere obtainedforthegraniteandsandstonesamples. Fromthesemaps,aporosity2D mapwascalculated.Histogramsof thermalconductivityandporositydistribution wereplottedfrom thepreviousmaps,todefinearelationshipbetweenporosityand mineralogy.

Forthetwosamplesanalyzed,statisticaldataofthermalconductivityand porosityaregiveninTable1.Thermalconductivity andporositymapsforthe graniteandsandstonesamplesare presentedinFigs.1and2,respectively. Histogramsofthermalconductivityandporositydistributionforthegraniteand sandstone samplesaregiveninFigs.4and5respectively.Thedistribution of thermalconductivitydependingonporosityisalsogivenin Figs.4and5, respectively,forthegraniteandsandstonesamples.

3.1.Granitesample

ThethreestructuralzonesdescribedinFig.1awereidentifiedonthermal conductivitymapsofthesampleunderbothairandwater-saturatedconditions (Fig.1b,c).Thethermalconductivity values for zone 1 ranged from about 1.80– 3.60Wm−1 K−1 for

the air-saturated sample and from about 2.00–4.25Wm−1 K−1 for

thewater-saturatedsample.Forzone2,thethermalconductivity values ranged from about 3.60–5.00Wm−1 K−1 and from 3.75 to

5.25Wm−1 K−1 for the air- and water-saturated samples, respec-

tively.Thethermalconductivityvaluesforzone3rangedfrom about 3.60–4.90Wm−1

K−1 and from about 3.75–5.50Wm−1 K−1

forthesamesamples.Theporositymap(Fig.1d)indicatesthatthe valuesofzone1 rangedfromzerototen%,thoseofzone2ranged betweenzeroandfive%andthe porosityvaluesofzone3ranged fromzerouptoabouteight%.Thus,thequartz cementationin the matrix (zone2)tended toincrease thelocal thermal conductivity andtodecreasethelocalporosity,whileconverselyfeldspar alterationdecreasedthelocalthermalconductivityandincreasedthe local porosity(zone1).

Histogramsofthermalconductivitydistribution,underbothairand water-saturatedconditionsforthegranitesample(Fig.4a,b) presentedthesamebimodal globaltrend,withtwowell-marked peaksofmeasuredthermalconductivity values.Intheair-saturated case (Fig. 4a), peaks were centered on 2.90 and 4.17Wm−1 K−1,

with a gap of about 1.27Wm−1 K−1. In the water-saturated case

(Fig. 4b), peaks were centered on 3.25 and 4.50Wm−1 K−1, with

a gap of about 1.25Wm−1 K−1. A comparison between thermal

conductivityhistogramsandmapssuggestedthatforbothairandwater-saturated cases,thelowervaluepeakscorresponded tozone1,composedmainlyofmassive feldsparassociatedwith alteredfeldsparandsomesmallsecondaryquartz (theoretical thermal conductivity values: Quartz=7.8Wm−1 _K−1_{, Feldspar-}

Table1

Statisticaldataofthermalconductivityandporosityforthetwostudiedsamples(std.:standarddeviation;m1:weightoftheairsaturatedsample;m2:weightofthewater saturatedsample;m3:weightofthesampleunder

hydrostaticcondition).

Sample Scanned surface

(length×width) (mm)

Thermal conductivity map (W m−1 K−1)

Saturation mean std. min. _max.

Porositymap(%)

mean std. min.

max.

Waterporosity

m1 (g) m2 (g) m3 (g) (%) Granite (K195-4777) 180 × 50 air water 3.49 ± 0.10 3.81 ± 0.11 0.70 0.72 1.84 2.04 6.36 7.08 2.87 ± 0.14 1.52 0.01 9.85 602.80 609.61 374.67 2.90 ± 0.09 (EPS1 6 1) 181×61 4.283.13±±0.130.090.180.23 2.533.59 4.93 9.27±0.46 1.98 0.72 16.22 1048.45 1092.44 649.08 9.92±0.30

147

K=2.3Wm−1 K−1, Clauser and Huenges, 1995; Fjeldskaar et al.,

2009).Atthesametime,peaksofthehighervaluesofthermalconductivity,forboth air-andwater-saturatedcases,corresponded toamixtureofzone2andzone3,both mainlycomposedof quartz.Thegapbetweenthetheoreticalandmeasured thermalconductivityinthesetwozonescanbeexplainedbythe porosityandthe presenceofsmallamountsoffeldsparand mica,whichhavelowerthermal conductivityvaluesthanquartz andcanmodifythecontactbetweengrains

(theoretical thermal conductivity values: Biotite=2.3Wm−1 K−1, air=0.02Wm−1 K−1,

water=0.6Wm−

1 _K−1_{,ClauserandHuenges,1995;Fjeldskaaretal.,}

2009).Thehistogramofporositydistribution(Fig.4c)showsaunimodalglobaltrend (Gaussianshape)withamaximumofcalculated pointsforaporosityvalueofabout 2.60%.Thisbehaviorcanbe explainedbyconstantgapsbetweenpeaksofthermal conductivity, whateverthesaturationcondition.Thesaturationofthesampleby waterprovokedalinearincreaseinthermalconductivityinallthree structuralzonesof thesample.Thedistribution ofthermalconductivity(air-saturatedcondition) dependingontheporosity(Fig.4d)

Fig. 4. Granite sample: (a), (b), distribution of measured thermal conductivity values, in the air and water saturated sample respectively (column width: 0.05Wm−1 K−1);

Fig. 5. Sandstone sample: (a), (b), distribution of measured thermal conductivity values, in the air and water saturated sample respectively (column width: 0.05Wm−1 K−1);

(c)distributionofthecalculatedporosityvalues(columnwidth:0.25%);(d)relationshipbetweencalculatedporosityvaluesandmeasuredthermalconductivityvaluesof theairsaturatedsample.

indicatedaglobalbutnotwell-markeddecreaseofthermalconductivity,whilethe porosityincreased(simplelinearregression: ThetwopeaksobservedinFig.4aandb werealso denotedbyapoorly-markeddecreaseofthermal conductivityanda porosityincrease.Thus,mineralogicaldistributionthroughoutthe sampleplaysamajorroleinthethermalconductivity,whereasthe porosityisless sensitivetomineralogicaldistribution.

Themeanporosity(Table1)calculatedfromthermalconductivitymapsis2.87± 0.14%,closetothewaterporosityvalueof 2.90±0.09%.

3.2.Sandstonesample

ThetwozonesdescribedinFig.2acouldbeidentifiedon thethermalconductivity mapofthedrysample(Fig.2b).Zone 1indicatedthermalconductivityvaluesranging between3.20 and 4.00Wm−1 K−1 whereas zone 2 showed thermal conductivity

values ranging from 2.60 to 3.50Wm−1 K−1. The thermal conduc-

tivitymapofthewater-saturatedsample(Fig.2c)appearedmore homogeneousthan thatofthedrysample.Inzone1,thethermal conductivity values ranged between 4.10 and 5.00Wm−1 K−1

whereasinzone2valueswerecomprisedbetween3.75and 4.80Wm−1 _K−1_{. The} porosity map (Fig. 2d) displayed two main

zoneslocatedatthelevelofthemainstructures(Fig.2a).Zone1had porosityvalues rangingbetweentwoandten%whereastheporosityvalueswerecomprisedbetween nineandfifteen%forzone2. However,thesmallfaultdoesnotappearonthermal conductivity andporositymaps.Thus,thedecreaseinthegrainsize(fromzone 2to zone1)resultedinanincreaseinthethermalconductivity associatedwithadecreasein thelocalporosity.

Forthesandstonesample,histogramsofthermalconductivitydistribution underbothair-andwater-saturatedconditions (Fig.5a,b)presentedthesame unimodalglobaltrend,withone peakofmeasuredthermalconductivityvalues.In theair-saturated case (Fig. 5a), the peak showed a maximum at 2.9Wm−1 _K−1_, while

inthewater-saturatedcase(Fig.5b),theequivalentwasabout 4.25Wm−1 K−1. The comparison between thermal conductivity

histogramsandmapsinair-saturationconditions,suggestedthat thelowervalues ofthermalconductivityinthepeakscorresponded tozone2,composedmainlyof mediumgrains,whereasthehigher valuesofthermalconductivitycorresponded tozone1,composed mainlyoffinegrains.Thesametrendwasless-markedunder water-saturationconditions.Thehistogramofporositydistribution (Fig.5c) showedaunimodalglobaltrend,withamaximumofcalculatedpointsfora porosityvalueofabout10.40%.Thelowervalues inthepeakofporosity correspondedtozone1,whereasthehigher valuescorrespondedtozone2.The globalhighvaluesofporosity inthesampleandthepresenceofaclayedcoating couldexplain thelowthermalconductivitymeasuredunderdryconditions (theoretical thermal conductivity values for Illite grains=1.9Wm−1 K−1,

149

ClauserandHuenges,1995;Fjeldskaaretal.,2009)andtheincrease ofthermal conductivityvaluesunderwater-saturatedconditions (Thegapbetweenthe maximumthermalconductivityunderairor water-saturated conditions is about 1.35Wm−1 K−1). The distri-

butionofthermalconductivity(air-saturatedcondition) depending onthe porosity(Fig.5d)indicatedaglobaldecreaseofthermal conductivitywiththe porosityincrease(simplelinearregression: Thus,thegrainsizevariationin laminae, associatedwithmineralogicalsmall variations,ledtoa modificationinthethermalconductivityand porosity distributionatthe millimeterscale.Thesevariationsseemtobecontinuousatthe core scale.

Themeanporosity(Table1)deducedfromthermalconductivity mapsis9.27± 0.46%,closetotheporosityvalueobtainedfrommass weightduringawater saturationtest:9.92±0.30%.

4.Discussion • Mapconstruction

Thethermalconductivityandporositymapswereobtainedfrom successive measurements,throughthescanningofasamplesaturatedwithbothairandwater. TheTCSallowsmeasurementsof thethermalconductivityprofiletobemade,ata densityofone pointpermillimeter.Fromaprofilecarriedoutateachmillimeter, thecalculationofaporosityvalueforeachmillimetersquareof asamplesurfaceis madepossible.Foreachsampleanalyzed,relativelysimilarporosityvalueshave beendeterminedfromboth thermalconductivityandwatersaturationtests(Table 1).Nevertheless,variationsareobservedandthesecanbeexplainedby the followingthreeparameters:thefirstistheresultofthedifferencebetweenthe volumesinvestigatedbythetwomethods. Theentirevolumeofasampleis analyzedduringwaterporosity measurements,whereasamorelimitedvolume underthescanningsurfaceisanalyzedbythethermalconductivitymeasurements (Popov,1997),wherethevolumeinvestigatedis2.5cmmaximum thick.The secondinvolvesthemodificationofthecontactresistancebetweenthedifferent componentsofarocksampleresulting fromwatersaturationandcouldthusalter thethermalconductivitycharacteristics(e.g.Farouki,1981).Thethirdisinduced bya relativelysignificantgapbetweenthethermalconductivityofthe standards andthatofthesample:alargergapwouldtriggeramore extensivemistakeofthe thermalconductivityvalue.Indeed,forthe granitesample,thermalconductivity variationsbetweentheairandwater-saturatedconditionsarelowandinduceno changein standardswhentheexperimentalvaluesremainclosetostandard ones. Forthesandstonesample,therelativehighporosityofthe materialimpliesa changeinstandardsbetweentheair-andwatersaturatedconditions.Standards usedfortheair-saturatedsample measurementshavearelativelylowthermal conductivityvalue forthewater-saturatedsamplemeasurements.Thisgap induces theunderestimationoftheporosityfromthethermalconductivity measurements.

• Informationaboutsamples

Thegraniteandsandstonesamplesarebothmainlycomposed ofquartzand feldspar.However,thethermalconductivitymaps andhistogramsofthermal conductivitydistributionaredifferent, withabimodaldistributionforthegranite andaunimodaldistributionforthesandstone.Thesefeaturecanbeexplainedby the well-markeddifferenceofthermalconductivitybetweenquartz andfeldspar, associatedwiththesizeofthegrainsinthesamples: coarseinthegraniteandfineto mediuminthesandstone,and bythefactthattheTCScannotindividualizefine grainproperties (lowertoafew-millimetersinscale).

In granite and sandstone samples, the porosity distribution is quite heterogeneous,i.e.therearevariationsinthelocalizationof themost(andthe lesser)porouszones,althoughthedistribution oftheporosityisunimodalinboth cases. In the granite sample, the porosity is controlled by structural

heterogeneities:theporosityis mainlylocatednearthefaultalonggrainbordersin analteredzone wherehydrothermalfluidshavepartiallydissolvedthegrains.In the sandstone sample, the porosity is controlled by sedimentological heterogeneities:theporosityappearsaccordingtoalayered organization.Inside eachlayer,theporosityisquitehomogeneous. Theporosityvariesinfunctionof thefaciesdistributionandiscontrolledbygrainssizeinsideeachband.Thus, porosityvariations, insidebothsamples,arenot extremely‘cut’,thereis progressive transitionbetweenthemostandthelessporouszones,atthescale of thesample.

Inthegranitesample,constantgapsbetweenpeaksofthermal conductivity distribution,whateverthesaturationcondition,were observed.Thesaturationofthe samplebywaterprovokesalinearincreaseinthethermalconductivityinthestructural zonesof thesample.Thus,thepercentageincreaseinthermalconductivity inducedby waterishigherforthepeakcorrespondingtothelower thermalconductivity,i.e.the feldspar-richzone,thantheonecorrespondingtothehigherthermalconductivity,i.e. thequartz-rich zone.

Thethermalconductivityandporositymapspresentvaluesthat areinagreement withotherclassicalmeasurementsperformedon equivalentmaterials,usingthesame orothertechniques(Vernoux etal.,1995;Sizun,1995;SurmaandGéraud,2003; Haffen,2012). Nevertheless,themappingofthesephysicalpropertiesbringsmore information,notablyconcerningthelocationofthemost,orless, porousand conductivezonesinsamples.Thesezonescanbelinked tostructuralandpetrographic featuresandsoleadtotheimprovementoftheknowledgeoffluidandheatexchangesin reservoirs.

5.Conclusion

Fromthermalconductivityandporositymaps,wehaveput forwardtheimpactof petrophysical heterogeneitiescommonly present in a granite and sandstone geothermalreservoirs,i.e.fault zoneandpermeablelayersrespectively.Themaps allowthestudy ofthermalconductivityandporosityvariation,atmillimetric resolutionandatcorescale.Fromtwoscansofasamplesurface,in air-saturated conditionsontheonehand,andinwater-saturated conditionsontheotherhand, porosity maps can be established. These allow precise quantification and determinationofthesizeof thermalconductivityandporosityheterogeneities inducedbyrock heterogeneities.

Acknowledgments

Theauthorswould liketothankEEIGHeatMining andA.Genter (ES Geothermie),thescientificcoordinator,forallowingaccessto thecoresoftheEPS1 borehole.

References

Abdulagatova,Z.,Abdulagatov,I.M.,Emirov,V.N.,2009.Effectoftemperatureand pressureonthe thermalconductivityofsandstone.Int.J.RockMech.Min.Sci. 46,1055–1071.

Bertani,R.,2012.Geothermalpowergenerationintheworld2005–2010update report.Geothermics41, 1–29.

Birsch,F.,1966.Thermalconductivityanddiffusivity.In:Clark,S.P.(Ed.),Handbook ofPhysical Constants,Rev.Eds.,Memoir,Vol.97.GeologicalSocietyofAmerica, pp.97–173.

Bourquin,S.,Péron,S.,Durant,M.,2006.LowerTriassicsequencestratigraphyof thewesternpartofthe GermanBasin(westofBlackForest):Fluvialsystem evolutionthroughtimeandspace.Sediment. Geol.186,187–211.

Bourquin,S.,Bercovici,A.,Lopez-Gomez,J.,Diez,J.B.,Broutin,J.,Ronchi,A.,Durant, M.,Arché,A., Linol,A.,Amour,F.,2011.ThePermian-Triassictransitionandthe onsetofMesozoic sedimentationatthenorthwesternperi-Tethyandomaine scale:palegeographicmapand geodynamicimplication.Paloegeography, Paleoclimatology,Paleoecology299,265–280.

Brigaud,F.,Vasseur,G.,1989.Mineralogical,porosityandfluidcontrolonthe thermalconductivityof sedimentaryrocks.Geophys.J.98,525–542.

Caine,J.S.,Evans,J.P.,Forster,C.B.,1996.Faultzonearchitectureandpermeability structure.Geology 24,1025–1028.

Cermak,V.,Rybach,L.,1982.ThermalConductivityandSpecificHeatofMinerals andRocksIn Landolt-Börnstein,NewSeries,GroupV(1a):Geophysics.

Springer,pp.305–343.

Civan,F.,2011.PorousMediaTransportPhenomena.JohnWiley&Sons,USA (400p.).

Clauser,C.,Huenges,E.,1995.Thermalconductivityofrockandminerals.In: Ahrens,T.J.(Ed.),Rock PhysicsandPhaseRelation-aHandbookofPhysical Constants,Vol.3.AGUreferenceshelf,pp. 105–126.

Clauser,C.,2006.Geothermalenergy.In:Heinloth,K.(Ed.),Landolt-Börnstein, GroupVIII:Advanced MaterialandTechnologies,Vol.3:EnergyTechnology, Subvol.C:RenewableEnergy.Springer, pp.493–604.

Dickson,M.H.,Fanelli,M.,2003.GeothermalEnergy:UtilizationandTechnology (ISBN 92-3-103915-6.221p.).

Farouki,O.,1981.ThermalPropertiesofSoils,CRRELMonograph81-1.USArmy ColdRegion ResearchandEngineering,HanoverNewHampshire,USA(151p.).

Faulkner,D.R.,Jackson,C.A.L.,Lunn,R.J.,Schlische,R.W.,Shipton,Z.K.,Wibberley, C.A.J., Withjack,M.O.,2010.Areviewofrecentdevelopmentsconcerningthe structure,mechanicsand fluidflowpropertiesoffaultzones.J.Struct.Geol.32, 1557–1575.

Fjeldskaar,W.,Christie,O.H.J.,Midttomme,K.,Virnovsky,G.,Jensen,N.B.,Lohne,A., Eide,G.I., Balling,N.,2009.Onthedeterminationofthermalconductivityof sedimentaryrocksandthe significanceforbasintemperaturehistory.Pet. Geosci.15,367–380.

Fritz,B.,Jacquot,E.,Jacquemont,B.,Baldeyrou-Bailly,A.,Rosener,M.,Vidal,O., 2010.Geochemical modellingoffluid–rockinteractionsinthecontextofthe Soultz-sous-Forêtsgeothermalsystem. C.R.Geosci.342(7),653–667.

Géraud,Y.,Rosener,M.,Surma,F.,Place,J.,LeGarzic,E.,Diraison,M.,2010.Physical propertiesof faultzoneswithinagranitebody:exampleofthe Soultz-sous-Forêtsgeothermalsite.C.R.Geosci. 342,566–574.

Genter,A.,Traineau,H.,1992.BoreholeEPS1:AlsaceFrance:preliminary geologicalresultsfrom granitecoreanalysisforHotDryRockresearch.Sci. Drill.3,205–214.

Genter,A.,Guillou-Frottier,L.,Feybasse,J.L.,Nicol,N.,Dezayes,C.,Schwartz,S., 2003.Typologyof potentialhotfracturedrockressoucesineurope.

Geothermics32,701–710.

Haenel,R.,Rybach,L.,Stegena,L.,1988.HandbookofTerrestrialHeat-FlowDensity Determination. KluwerAcademicPublishers,Dordrecht.

Haffen,S.,Géraud,Y.,Diraison,M.,Dezayes,C.,2013.Fluid-flowzonesina geothermalsandstone reservoir:localizationfromthermalconductivityand temperaturelogs,boreholeEPS1 (Soultz-sous-Forêts,France)and3Dmodels. In:Proceedings,Thirty-EighthWorkshoponGeothermal Reservoir Engineering,StanfordUniversity,Stanford,California,February11–13,2013 (SGP-TR-198).

Haffen,S.,2012.CaractéristiquesgéothermiquesDuréservoirGréseuxDu Buntsandsteind’Alsace. Thesis.InstitutdePhysiqueduGlobedeStrasbourg, UniversitédeStrasbourg,Strasbourg,France (391p.InFrench).

Hartmann,A.,Rath,V.,Clauser,C.,2005.Thermalconductivityfromcoreandwell logdata.Int.J.Rock Mech.Min.Sci.42,1042–1055.

Hartmann,A.,Pechnig,R.,Clauser,C.,2008.Petrophysicalanalysisofregional-scale thermal propertiesforimprovedsimulationsofgeothermalinstallationsand basin-scaleheatandfluidflow. InternationalJournalofEarthScienceGR97, 421–433.

Lund,W.J.,Freeston,D.H.,Boyd,T.L.,2011.Directutilizationofgeothermalenergy 2010worldwide review.Geothermics40,159–180.

Meier,D.B.,Gunnlaugsson,E.,Gunnarsson,I.,Jamtveit,B.,Peacock,C.L.,Benning, L.G.,2014.

Microstructuralandchemicalvariationinsilica-richprecipitatesat theHellisheioigeothermal powerplant.Mineral.Mag.78(6),1381–1389.

Melnyk,T.W.,Skeet,A.M.M.,1986.Animprovedtechniqueforthedetermination ofrockporosity. CanadianJournalofEarthScience23,1068–1074.

Midttomme,K.,Roaldset,E.,1998.Theeffectofgrainsizeonthermalconductivity ofquartzsandsand silts.Pet.Geosci.4,165–172.

Norton,D.,Knapp,R.,1977.Transportphenomenainhydrothermalsystems:the natureofporosity.Am. J.Sci.277,913–917.

Norton,D.,1979.Transportphenomenainhydrothermalsystems:the redistributionofchemical componentsaroundcoolingplutons.Bull.Mineral. 102,471–486.

Popov,Y.A.,Pribnow,D.F.C.,Sass,J.H.,Williams,C.F.,Burkhardt,H.,1999. Characterizationofrock thermalconductivitybyhigh-resolutionoptical scanning.Geothermics28,253–276.

Popov,Y.A.,Pohl,J.,Romushkevich,R.,Tertychnyi,V.,Soffel,H.C.,2003.Geothermal characteristics oftheRiesimpactstructure.Geophys.J.Int.154(2),355–378.

Popov,Y.A.,1997.Opticalscanningtechnologyfornondestructivecontactless measurementsof thermalconductivityanddiffusivityofsolidmatters. Brussels,BelgiumIn:ExperimentalHeat

Transfer,FluidMechanicsand ThermodynamicsProceedingofthe4thWorldConference,1, pp.109–117.

Pribnow,D.F.C.,Sass,J.H.,1995.Determinationofthermalconductivityfordeep boreholes.J. Geophys.Res.100,9981–9994.

Pribnow,D.F.C.,Williams,C.F.,Sass,J.H.,Keating,R.,1996.Thermalconductivityof water-saturated rocksfromtheKTBpilotholeattemperatureof25–300◦C.

GeophysicalResearchLetter23,391–394.

Rosener,M.,2007.EtudepétrophysiqueEtModélisationDesEffetsDesTransferts ThermiquesEntre RocheEtFluideDansLeContextegéothermiqueDe Soultz-sous-Forêts.Thesis.Institutde PhysiqueduGlobedeStrasbourg, UniversitéLouisPasteur,Strasbourg,France(207p.InFrench).

Sass,J.H.,Lachenbruch,A.H.,Munroe,R.J.,1971.Thermalconductivityofrocks from measurementsonfragmentsanditsapplicationtoheat-flow determination.J.Geophys.Res. 76,3391–3401.

Sass,J.H.,Stone,C.,Munroe,R.J.,1984.Thermalconductivitydeterminationson solidrock−a comparisonbetweensteadystatedividedbarapparatusanda commercialtransientline-source device.J.Volcanol.Geotherm.Res.20, 145–153.

Schärli,U.,Rybach,L.,1982.Onthethermalconductivityoflow-porosity crystallinerocks. Tectonophysics103,307–313.

Seibt,P.,Kellner,T.,2003.Practicalexperienceinthereinjectionofcooledthermal waterbackinto sandstonereservoirs.Geothermics32,733–741.

Siffert,D.,Haffen,S.,Garcia,M.H.,Géraud,Y.,2013.Phenomenologicalstudyof temperaturegradient anomaliesintheBuntsandsteinformation,abovethe Soultzgeothermalreservoir,usingTOUGH2 simulations.In:Proceedings, Thirty-EighthWorkshoponGeothermalReservoirEngineering, Stanford University,Stanford,California,February11–13,2013(SGP-TR-198).

Sizun,J.P.,1995.ModificationDesStructuresDePorositéDeGrèsLorsDe Transformations pétrographiquesDansLaDiagenèseEtl’hydrothermalisme Thèse.InstitutdeGéologie. Strasbourg,UniversitéLouisPasteur,Strasbourg, France(297p.InFrench).

Somerton,W.H.,1992.ThermalPropertiesandTemperature–relatedBehaviourof Rock/fluidSystem. ElsevierSciencePublishingCompany,NewYork(257p.).

Surma,F.,Geraud,Y.,2003.Porosityandthermalconductivityofthe soultz-sous-Forêtsgranite.Pure Appl.Geophys.160,1125–1136.

Tritt,T.M.,2004.Thermalconductivity,theory,propertiesandapplication.In:Tritt, Terry(Ed.),Physics ofSolidsandLiquids),IncludesBibliographicalReferences andIndex.KluwerAcademic/Plenum Publishers,NewYork(290p.).

Ungemach,P.,2003.Reinjectionofcooledgeothermalbrinesintosandstone reservoirs.Geothermics 32,743–761.

Vernoux,J.F.,Genter,A.,Razin,P.,Vinchon,C.,1995.Geologicalandpetrophysical parametersofa deepfracturedsandstoneformationasappliedtogeothermal exploitation.In:RapportBRGM R38622.EPS-1borehole,Soultz-sous-Forêts, France(70p.,24fig.,5tabl.,3append).

Vosteen,H.D.,Schellschmidt,R.,2003.Influenceoftemperatureonthermal conductivity,thermal capacityandthermaldiffusivityofdifferenttypesof rock.Phys.Chem.Earth28,499–509.

Zinszner,B.,Pellerin,F.M.,2007.AGeoscientist’sGuidetoPetrophysics.IFP Publication,Edition TECHNIP,Paris,France,pp.384p.