PhDprojectTHMmodelingofclaystonefromthemolecularscale

L.Brochard,A.Pouya–NavierLab.,EcoledesPontsParisTech

ContextClaystone is a highly heterogeneous material and their finest mineral (clay) is made ofnanometric particles for which the molecular interactions between interstitial water andminerals are essential to theunderstandingof theporo-mechanical behavior. Thepressureofthisboundwater(adsorbed)differverysignificantlyfromtheusualpressure, thedifferenceisgenerally referred to as the disjoining pressure. The disjoining pressure is at the origin ofvariousunusualmechanicalbehaviorsofclays,inparticularthephenomenaofdryingshrinkage,ofthermalcompaction(normallyconsolidatedclays),orofexcesswaterthermalpressurization.The macroscopic consequences are numerous, the most well-known being the desiccationcracking.InthecontextofCIGEO(nuclearwastegeologicalstorageinFrance),variousissuesaredirectly related to the THM behavior of claystone: cracking around galleries, re-saturationaround waste packages, pressurization / compaction under thermal loading etc.. The fineunderstanding of the THM behavior of claystone is therefore an important challenge for thevalidationoftheobservationsandmacroscopicmodels,and,infine,forthedesignandsafetyofthestorage.

However,evaluatingthepropertiesofboundwaterisextremelydifficultfromanexperimentalpoint of view and limited to very well controlled minerals. For about a decade, molecularsimulation has become an interesting alternative to experiment, able to provide realisticestimates of the properties at the nanometric scale. However, the time and length scalesaccessiblearehighlyconstrained(tensofnm/tensofns),sothemolecularsimulationapproachhastobecompletedbyanupscalingapproachtobeapplicabletoclaystone.IntheframeworkoftheANRprojectTEAM2ClayDesicc(2015-2019),afirststepinthatdirectionwasundertakentorelatetheboundwatertothethermalbehaviorofsaturatedclays.Theapproachconsideredusesmolecular simulation to estimates the thermo-mechanicalmoduli of boundwater, and then aporo-mechanical formulation extended to bound water provides an upscaling which can beconfrontedtoexperiment.

The goal of this PhD project is to set up a THMmacroscopic modeling of Callovo-Oxfordianclaystonethattakesintoaccountexplicitlytheunusualpropertiesofboundwater,obtainedbymolecular simulations of representative clays. The project is organized in three parts: 1-molecularsimulation,2-poromechanicalformulation,and3-confrontationtothestateoftheart(modelingandexperiment)

Figure:DisjoiningpressureofwaterinNa-Montmorilloniteobtainedbymolecularsimulation1

MolecularsimulationWe propose to use molecularsimulationtoestablishadatabaseofthe properties of bound water inclay minerals representative of theCallovo-Oxfordian claystone.Previousstudies(inparticularANRTEAM2ClayDesicc)haveprovided firstestimatesandhaveshown in particular that bound water can be fully described only by taking into account 6moduliinsteadof3forusualfluids(compressibility,thermalexpansion,heatcapacity)becausethe high confinement breaks the extensivity of the fluid (otherwise said, the Gibbs-Duhemequationnomoreholds forboundwater).However, these first estimateswereobtained for a

1Honorioetal.(2017)Langmuir,33(44),12766–12776.http://doi.org/10.1021/acs.langmuir.7b03198

modelmontmorilloniteabove thebulkwatersaturationpressure.Wepropose toconsider thecaseofmineralsrepresentativeofCOxinconditionscorrespondingtogeologicalstorage.

Poro-mechanicalformulationTaking into account adsorption in poro-mechanics is an active topic of research,which is notlimited toclaystone2.Recentadvancesmake itpossible to take intoaccountquantitatively theeffect of bound water and its 6 moduli3 . The practical implementation of the extendedporomechanicsisrathersimplebecausethestructureoftheconstitutiveequationsremainsthesameasinusualporo-mechanicsandthusiseasilyintegratedtoexistingcodes.However,ifthemolecular simulation provides the properties of bound water, one has to determine theproperties of the solid skeleton. We propose to calibrate those properties from the inverseanalysis of usual tests (e.g., drained compressibility). In this respect, various experimentalresultsonCOx(fromtheliteratureorfromANDRA)willbeconsidered.

We propose to set up a numerical implementation of this poro-mechanical model base onDiscroc4.Disroc is a finite element codededicated in particular to the simulation of fracturedporousmedia.ItisparticularlyadaptedtothestudyofcrackingundertheeffectofcomplexTHMcouplings: natural fracturing of sedimentary formations and oil/gas reservoirs5, desiccationcrackingofsoils6,crackpropagationundertheeffectof fluid injection7.TheimplementationinDisroc offers the perspective to simulate various issues of interestwith respect to the CIGEOproject,andthustoconfrontthenewmodelingtoexistingmodelsandexperimentalresults.

ConfrontationwiththestateoftheartIn agreementwith ANDRA, themodel developedwill be confronted to the state of the art inorder to assess the influence of addressing bound water explicitly, in contrast with existingapproaches. The situations studiedwill relate in priority on issues for which boundwater isknowntobeattheheartoftheTHMcouplings.

PracticaldetailsandapplicationsTheapplicantsmustholdaMasterofScienceorequivalentinthefieldofmechanicsandphysicsof (geo)-materials, with a strong taste for numerical approaches. Interested applicants areinvited to send a CV, a motivation letter and their transcripts to L. Brochard(laurent.brochard@enpc.fr)orA.Pouya(amade.pouya@enpc.fr)by27March2020.

Localization:Navier lab (https://www.navier-lab.fr) locatedatEcoledesPontsParisTech (6-8avenueBlaisePascal,77455Champs-sur-Marne,France)Advisors:L.Brochard(laurent.brochard@enpc.fr)andA.Pouya(amade.pouya@enpc.fr)Duration:3years,startinginFall2020Funding:applicationforfundingwillbesubmittedintheframeworkofthecallforgrantsoftheAgencenationalepourgestiondesdéchetsradioactifs.FollowingtheeligibilityrulesofANDRA,applicantsmustbe26yearsoldorlessonOctober1st2020andbecitizenoftheEuropeanUnion.

2Brochardetal.(2012)JournaloftheMechanicsandPhysicsofSolids,60(4),606–622.http://doi.org/10.1016/j.jmps.2012.01.0013Brochardetal.(2020)Revisitingthermo-poro-mechanicsunderadsorption:FormulationwithoutassumingGibbs-Duhem

equation,underrevision4Ouraga(2017)Modélisationdelafracturationnaturelledessédiments:impactssurlamodélisationdebassin.PhDthesisENPC.5Disroc(2016)AFiniteElementcodeformodellingcoupledTHMCphenomenainporousfracturedmedia.Fracsima,www.fracsima.com6Vo(2017)ModélisationNumériqueetAnalytiquedelaFissurationdeséchagedesSolsArgileux.PhDthesisENPC.7Jungetal.(2020)FractureClosureMechanismsduringFlowbackfromHydraulicFractureNetworks,inpreparation.

PhDproject

Modelingofthebehaviorofafracturedporousmediumsubmittedtogaspressurization

L.Brochard,A.Pouya–NavierLab.,EcoledesPontsParisTech

ContextIn the context of the Cigéo project, the excavation of underground galleries in the Callovo-Oxfordianclaystoneinducesanetworkof fracturesaroundtheexcavatedzone.Thisfracturingexhibits a typical profile of propagation in mixed I/II mode, which originates from theinstantaneousdischargeoftheclaystoneafterexcavation.ThetopologyandspatialextentoftheinducednetworkoffractureshasbeenwidelystudiedbyANDRA1aroundtheexcavationsoftheLaboratoire Souterrain de Meuse/Haute-Marne (LSMHM). Over long time, this network offracturesisexpectedtoexperienceadditional loadingsbygas(mostlyH2)originatingfromthecorrosionofmetalsused in theenvelopofnuclearwastepackagesand fromwater radiolysis.The accumulation of these gases induces a pressurization that can affect the fractured zone.ANDRA has been investigating the risks associated with gas pressurization since 2003. Inparticular, gas-fracturing testshavebeenperformed inaverticalwelldrilled fromthesurfaceandinwellsdrilledfromtheLSMHM.

ThegoalofthisPhDprojectistosetupanumericalsimulationtoolabletomodelandsimulatethemechanical responseof a fracturedporousmediumsubmitted togaspressurizationwhiletaking into account the peculiar thermo-hydro-mechanical (THM) couplings of claystone. Theproject is organized in three parts: 1- set up of the numerical tool, 2- numerical study underTHMloadingswithgaspressurization,and3-confrontationexperience-simulation.

Setupofthenumericalsimulation

WeproposetosetupthenumericalsimulationbasedonDisroc2.Discrocisafiniteelementcodededicated in particular to the simulation of the fracturedmedia. Cracking is accounted for bycohesivezonemodels,whicharewelladaptedtothemodelingofbrittleandquasi-brittlemedia.ThesemodelsavoidthemainissuesofGriffithmodels:theydonotexhibitstresssingularitiesatcrack tips,andtheycanmodelbothcrack initiationandcrackpropagation.Disrochasalreadybeen used for the study of fracturing in several PhD and research projects in various labsincluding Navier lab. In particular, the propagation of fracture under THM couplings raisesspecific questions that have been addressed in the PhD thesis of Z. Ouraga3dedicated to thenaturalfracturingofsedimentaryformations(oilandgasreservoirs),andofT.D.Vo4dedicatedtothedesiccationcrackingofsoils.Amorerecentresearchwork5investigatedthepropagationoffracturesundertheeffectofafluidinjection(cf.figure).

Thestudyoffracturingduetogaspressurizationrequiresextendingtheseworks,dedicatedtothecaseofa single incompressible fluid, to thecaseofamulti-phase fluid (liquid+gas) inanunsaturated medium. Recent researches at Navier lab make it possible to take into accountquantitatively the effects of adsorption associated with bound water thanks to rigorousthermodynamics formulations of the poro-mechanics under adsorption6 , 7 . The numericalmodeling proposed in this work will aim at integrating these new formulations. The

1Armandetal.(2014)RockMech.RockEng.,47,21-41.doi:10.1007/s00603-012-0339-6.2Ouraga(2017)Modélisationdelafracturationnaturelledessédiments:impactssurlamodélisationdebassin.PhDthesisENPC.3Disroc(2016)AFiniteElementcodeformodellingcoupledTHMCphenomenainporousfracturedmedia.Fracsima,www.fracsima.com4Vo(2017)ModélisationNumériqueetAnalytiquedelaFissurationdeséchagedesSolsArgileux.PhDthesisENPC.5Jungetal.(2020)FractureClosureMechanismsduringFlowbackfromHydraulicFractureNetworks,inpreparation.6Brochardetal.(2012)JournaloftheMechanicsandPhysicsofSolids,60(4),606–622.http://doi.org/10.1016/j.jmps.2012.01.0017Brochardetal.(2020)Revisitingthermo-poro-mechanicsunderadsorption:FormulationwithoutassumingGibbs-Duhemequation,underrevision

implementation of these new poro-mechanical formulations in Disroc is rather simple(analyticalformulationwiththesamestructureasusualporo-mechanics).

NumericalstudyunderTHMloadingswithgaspressurization

TheparametersofthenumericaltoolwillbecalibratedsoastoreproducethebehavioroftheCallovo-Oxfordian claystone. In this respect, various experimental results available in theliterature or obtained in otherANDRAprojectswill be considered. The behaviors of the non-adsorbed fluids (gas, free water) will be accounted for with usual models (ideal gas,incompressible,orempiricalequationof states if these two limit casesprove inappropriate inthe range of temperatures-pressures of interest). The behavior of the bound water will beobtained by crossing experimental data of the THM couplings andmolecular simulation dataavailableintheliterature8.

Thenumerical toolwill thenbeapplied tovarious simple cases inorder toevaluate themainfactorsinfluencingthegasbreakthrough.SpecialattentionwillbededicatedtotheroleofTHMcouplingsspecifictoclaystone(notably:swelling/shrinkageandthermalpressurization).

Confrontationexperience-simulationIn order to evaluate the numerical model, a confrontation with experiment is necessary. InagreementwithANDRA, thenumericalmodelwillbeused tosimulate thegas-fracturing testsperformedatLSMHMorotherlabtestsperformedforANDRAduringthisPhD.The3DaspectswillbeaccountedforwiththefutureversionofDisrocthatshallbereleasedduringthisPhD.

PracticaldetailsandapplicationsTheapplicantsmustholdaMasterofScienceorequivalentinthefieldofmechanicsandphysicsof (geo)-materials, with a strong taste for numerical approaches. Interested applicants areinvited to send a CV, a motivation letter and their transcripts to L. Brochard(laurent.brochard@enpc.fr)orA.Pouya(amade.pouya@enpc.fr)by27March2020.

Localization:Navier lab (https://www.navier-lab.fr) locatedatEcoledesPontsParisTech (6-8avenueBlaisePascal,77455Champs-sur-Marne,France)Advisors:L.Brochard(laurent.brochard@enpc.fr)andA.Pouya(amade.pouya@enpc.fr)Duration:3years,startinginFall2020Funding:applicationforfundingwillbesubmittedintheframeworkofthecallforgrantsoftheAgencenationalepourgestiondesdéchetsradioactifs.FollowingtheeligibilityrulesofANDRA,applicantsmustbe26yearsoldorlessonOctober1st2020andbecitizenoftheEuropeanUnion.

8Honorioetal.(2017)Langmuir,33(44),12766–12776.http://doi.org/10.1021/acs.langmuir.7b03198

Figure:Explicitmodelingofthefracturesinducedbytheinjection of a pressurizedfluidinaporousmedium