Experimental study of the temperature effect on two-phase flow properties in highly permeable porous media: Application to the remediation of dense non-aqueous phase liquids (DNAPLs) in polluted soil

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Philippe, Nicolas and Davarzani, Hossein and Colombano,

Stéfan and Dierick, Malorie and Klein, Pierre-Yves and

Marcoux, Manuel Experimental study of the temperature

effect on two-phase flow properties in highly permeable

porous media: Application to the remediation of dense

non-aqueous phase liquids (DNAPLs) in polluted soil. (2020)

Advances in Water Resources, 146. 103783. ISSN 0309-1708

Official URL:

https://doi.org/10.1016/j.advwatres.2020.103783

Experimental

study

of

the

temperature

effect

on

two-phase

flow

properties

in

highly

permeable

porous

media:

Application

to

the

remediation

of

dense

non-aqueous

phase

liquids

(DNAPLs)

in

polluted

soil

Nicolas

Philippe

_,

_Hossein

_Davarzani

_,

_Stéfan

_Colombano

_,

_Malorie

_Dierick

_,

Pierre-Yves

Klein

_,

_Manuel

_Marcoux

a BRGM (French Geological Survey), 3 avenue Claude Guillemin, 45100 Orléans, France

b Institut de Mécanique des Fluides de Toulouse (IMFT), Université de Toulouse, CNRS, 31400Toulouse, France c REMEA, 22-24 rue Lavoisier, 92000 Nanterre, France

Keywords:

Dense non-aqueous phase liquid Two-phase flow

Capillary pressure-saturation relationship Relative permeability

Thermally enhanced DNAPL recovery

a

b

s

t

r

a

c

t

Theremediationofaquiferscontaminatedbyviscousdensenon-aqueousphaseliquids(DNAPLs)isachallenging problem.CoaltarsarethemostabundantpersistentDNAPLsduetotheirhighviscosityandcomplexity. Pump-ingprocessesleaveconsiderablevolumefractionsofDNAPLsinthesoilanddemandhighoperationalcoststo reachcleaningobjectives.ThermallyenhancedrecoveryfocusesondecreasingDNAPLviscositytoreduce resid-ualsaturation.Theoilindustryhaspreviouslyappliedthistechniquewithgreatsuccessforenhancedoilrecovery applications.However,insoilremediation,highporousmediapermeabilitiesandproductdensitiesmay invali-datethosetechniques.Additionally,theimpactsoftemperatureoncoaltar’sphysicalpropertieshavenotbeen thoroughlydiscussedinavailableliterature.Here,weinvestigatedhowcoaltar’sphysicalproperties,thecapillary pressure-saturationcurveandtherelativepermeabilityoftwo-phaseflowinporousmediadependonthe temper-atureandflowrateexperimentally.Drainageandimbibitionexperimentsunderquasi-static(steady-state)and dynamic(unsteady-state)conditionshavebeencarriedoutat293.15Kand323.15Kina1Dsmallcellfilledwith 1mmhomogeneousglassbeads.Twodifferentpairsofimmisciblefluidshavebeeninvestigated,coaltar-water andcanolaoil-ethanol.Resultsdemonstratedsimilartrendsfortemperatureeffectandvaluesoffluidproperties forbothliquidpairs,whichbacksuptheuseofcanolaoil-ethanoltomodelcoaltar-waterflow.Itwasfoundthat thereisnotemperatureeffectondrainage-imbibitioncurvesorresidualsaturationunderquasi-staticconditions. Indynamicconditions,theDNAPLresidualsaturationdecreasedby16%whenthetemperaturechangedfrom 293.15Kto323.15K.Thisdropwasmainlylinkedtodecreasingviscousfingering,aswellastheappearanceof wettingphasefilmsaroundtheglassbeads.Bothphenomenahavebeenobservedonlyindynamicexperiments. Ahighenoughpumpingflowrateisneededtogeneratedynamiceffectsintheporousmedium.Ethanolandoil’s relativepermeabilitiesalsoincreasewithtemperatureunderdynamicmeasurementconditions.Ourfindings in-dicatethatflowrateisanimportantparametertoconsiderinthermalenhancedrecoveryprocesses.Theseeffects arenottakenintoaccountintheclassicallyusedgeneralizedDarcy’slawformodelingtwo-phaseflowinporous mediawithtemperaturevariation.

1. Introduction

Densenon aqueousphaseliquids(DNAPLs)areliquidsdenserthan waterandslightlysolubleinwater.Duetotheirhighdensity,DNAPLs candeeplysinkintothesubsurfaceuntilreachingalesspermeablelayer andformanon aqueousreservoir.Subsurfacezonescontaminatedby DNAPLsaregenerallyhard todelimitduetosoil heterogeneity,soil dispersion,andthesubstantialdepthofthecontaminationcombined withgravity drivenfingerflow.Thusremediatingthesepollutantsin

∗_{Correspondingauthor.}

E-mailaddress:h.davarzani@brgm.fr(H.Davarzani).

theaquiferisacomplicatedmatter.DNAPLsourcezonesareevenmore problematicbecausetheymaykeepondissolvingtoxiccompoundsinto thegroundwater.Ultimately,futurehealthandenvironmentalproblems canarise,suchasdrinkingwatercontaminationorsoilqualitydegrada tion.

CommonlyreportedDNAPLcontaminantsincludechlorinatedsol vents namely,trichloroethylene(TCE)andtetrachloroethylene(PCE)

that were previously widely used as solventsfor organic materi als(SchwilleandPankow,1988).CoaltarsarealsoanotableDNAPL found in the subsurface and are also more viscous than water. (Brownetal.,2006)havemeasuredcoaltar’sdynamicviscosityonmul tiplesitesandhavefoundthatthecoaltar/waterviscosityratiocanvary between10and106_{(Brownetal.,2006).Thisrangeislinkedtothe}

Nomenclature Symbol Definition Bo Bondnumber( ) Ca Capillarynumber( ) g Gravitationalacceleration(m.s−2₎ K Intrinsicpermeability(m2 ) k_r Relativepermeability( ) hc Capillaryheight(m) L Characteristiclength(m) M Viscosityratio( )

n VanGenuchtenparameter( )

p Pressure(Pa)

p_c Capillarypressure(Pa)

R0 Dropmeanradius(m)

S Saturation( ) S_ir Irreduciblesaturation( ) S_r Residualsaturation( ) T Temperature(K) u Darcyvelocity(m.s−1₎ V_c Characteristicvelocity(m.s−1₎

𝛼 VanGenuchtenparameter(m−1₎

𝛽 Shapefactor( )

𝛾 Interfacialtension(N.m−1₎

𝜇 Dynamicviscosity(Pa.s)

𝜌 Density(kg.m−3)

𝜏 Dynamiccapillaritycoefficient(Pa.s)

Subscripts

Symbol Definition

CT Coaltar

dis Displacedphase

E Ethanol

inv Invadingphase

O Canolaoil

w Wettingphase(ethanolorwater)

W Water

nw Non wettingphase(canolaoilorcoaltar)

chemicalheterogeneityincoaltar.Diagnosisandriskassessmentare hardbecausetheexactcompositionofcoaltarisgenerallynotidenti fiable.Hence,asitepollutedbycoaltarisdifficulttocleanupandthe choiceforanapplicablerecoverymethodhastobemadeonacase by casebasis.

Inourstudy,thefocusisoncoaltarsourcezoneswithhighpollutant concentrations.Pumpinginthesubsurfacethroughproductionwellsis aprimarystepusedinremediationoperations.However,thepumping rateisvery low forDNAPLsandtheremediationcould taketens to hundredsofyears,whichiseconomicallyunsatisfying(USEPA,1996;

RussellandRabideau,2000;KavanaughandKresic,2008;Navy,2008;

Newelletal.,2011).Themost efficientcurrent methodsforremedi atingDNAPLsourcezonesarethermaltreatments(Dingetal.,2019). Generally,temperatureisincreasedtovaporize(McDadeetal.,2005;

Baker et al., 2006; Baston et al., 2010) or even burn (Rein, 2009;

Switzeretal.,2009;Hasanetal.,2015;Scholesetal.,2015)thepol lutant.Thevaporsgeneratedarethencollectedandtreatedwithcar bonactivatedfilters.However,generatinghigh temperaturefieldscan be dangerousfor thenutritionalandbiologicalfunctionsof thesoil. (Papeetal.,2015)haveshownthatevenifacontaminantcanbecom pletelytreatedat773.15K,thesoilisunusableforfutureconstruction orindustrialoperations(O’Carrolletal.,2005;Papeetal.,2015).Asa result,NAPLresidualsaturationislowerinthesoilafterathermallyen hancedprocess.Afterwards,thehighsoiltemperaturecanincreasethe degradationrateofchemicaltreatments(oxidation,surfactantflooding) andbiologicalmethods(bioorphytoremediation)(Melinetal.,1998).

Hot waterfloodingisanothertechniquethathasshownsuccessin treatingviscous NAPLs light ordense contamination.Theidea is toreducethedynamicviscosityoftheNAPLbyincreasingitstemper ature. During pumping,the hot waterwill progressivelyreplace the NAPLandleaveresidualNAPLsaturationinthesoil.Previousauthors haveshownthatinjectinghotwaterincreasestotalNAPLrecoveryvol umesby pumpingprocesses (Fulton andReuter, 1991; Davis, 1997;

O’CarrollandSleep,2007).PumpingaDNAPLphasefromthesubsur facecanberepresentedbyanimbibitionprocessinporousmedia.The DNAPLphaseisprogressivelypushedawayfromthesoilandthewater slowlyfillstheporesleftvacant.Thus,itisimportanttoanalyzeand betterunderstandfluiddisplacementsbeforedrawinganyconclusions. Tocharacterize thebehaviorofthephysical systemcomposed of DNAPL,water,andasolidmatrixisstillanongoingchallengeinfluid mechanics.Currently,modellingisbasedonthetheoryofimmiscible multiphaseflowinporousmedia.Inourcase,DNAPLandwaterarerep resentedastwoseparatephases,andthesoilisanimmobilesolidmatrix inwhichbothliquidsmayflow.Forthistypeofengineeringapplication, thesimultaneousflowofDNAPLandwaterinaporousmediumiscom monlydescribedusingthegeneralizationofDarcy’slawtomultiphase flowforeachphase(MuskatandMeres,1936).

𝒖𝑖=− 𝐾𝑘_𝑟,𝑖(𝑆𝑖 ) 𝜇_𝑖 ∇(𝑝𝑖−𝜌𝑖𝒈 ) (1) whereu_iistheDarcyvelocity(m.s−1_{),gthegravitationalacceleration,}

Kthepermeabilitytensor(m2_),p

ithepressure(Pa),𝜇iand𝜌i respec

tivelythedynamicviscosity(Pa.s)anddensity(kg.m−3_{).Thesubscript}

idesignatesthewaterorDNAPLphase.Themaindifferencebetween Darcy’slawanditsextensiontomultiphaseflowistheadditionofrel ativepermeabilitytermskr,i.Itsignifiesthateachphaseflowsindepen

dentlythroughavirtualporousmediumofpermeabilityKk_r,i(S_i).The DNAPLoccupiesapartofthetotalporespace,dependingonitssatura tion,whichreducesthevolumeofwaterthatcanflowthroughandvice versa.Thisequationgenerallyholdstruewhenthereisnomomentum transferattheinterfaceofbothfluidphases(Whitaker,1986).

Thepresenceofthetwofluidphasesresultsinaninterfacethatissub jectedtointerfacialtensionattheporescale.Thisinterfacealsocausesa pressurediscontinuityatthemacroscale,withrespecttocapillarypres surep_c.Thisissubsequentlydefinedasthedifferencebetweenthepres sureofthenon wettingfluidpnwandthepressureofthewettingfluid p_w.

𝑝_𝑛𝑤−𝑝_𝑤=𝑝_𝑐(𝑆_𝑤) (2)

ImmiscibleDNAPLsflowingintheaquifer canbeassimilatedtoa two phaseflowinporousmedia.Thedimensionlessnumberscontrolling theactualflow patternarerespectivelyBond number(Bo),capillary number(Ca),andviscosityratio(M).Inthecaseoftheimbibitionof awettingphaseinsideaporousmediumsaturatedwithanon wetting phase,thesenumberscanbewrittenas:

𝐵𝑜= (𝜌𝑛𝑤−𝜌𝑤)𝑔𝐿 2 𝛾 (3) 𝐶𝑎= 𝑉𝑐𝜇𝑖𝑛𝑣 𝛾 (4) 𝑀=𝜇𝑖𝑛𝑣 𝜇_𝑑𝑖𝑠 (5)

Lisacharacteristiclength.Inunconsolidatedmedialikeglassbeads,L isoftenchosenequaltothemeanparticlediameter.𝛾istheinterfacial

tensionbetweenbothliquidphases.V_cisacharacteristicvelocityrep resentingtheorderofmagnitudeoftheflowrateinsidethepores.The subscriptsinvanddisrespectivelyrepresenttheinvadinganddisplaced phase.Inthiswork,theDNAPLandwateraretheinvadingphasesdur ingdrainageandimbibition,respectively.Alternatively, theviscosity ratiomaybe replacedby themobilityratio (theratiobetween rela tivepermeabilityandviscosity).Thelatterincludesrelativepermeabil itiesinitscalculationandcanbemoresuitableforrealporousmedia

Table2

Bond,capillarynumbersandviscosityratioassociatedwiththetwo-phaseflowofoil/ethanolandcoaltar/waterbetween293.15K and323.15K.

Liquids Coal tar – water Canola oil-ethanol

T(K) Bo Ca M Bo Ca M 283.15 4.19 ×10 −1 _{5.24 ×10} −5 _{1.48 ×10} −2 _{4.36 ×10} −1 _{5.46 ×10} −5 _{1.32 ×10} −2 293.15 4.16 ×10 −1 _{5.20 ×10} −5 _{1.96 ×10} −2 _{4.66 ×10} −1 _{5.82 ×10} −5 _{1.64 ×10} −2 303.15 4.13 ×10 −1 _{5.16 ×10} −5 _{2.55 ×10} −2 _{4.99 ×10} −1 _{6.23 ×10} −5 _{2.01 ×10} −2 313.15 4.09 ×10 −1 _{5.11 ×10} −5 _{3.26 ×10} −2 _{5.35 ×10} −1 _{6.69 ×10} −5 _{2.43 ×10} −2 323.15 4.05 ×10 −1 _{5.07 ×10} −5 _{4.11 ×10} −2 _{5.77 ×10} −1 _{7.21 ×10} −5 _{2.91 ×10} −2

Density,dynamicviscosity,interfacialtension,andcontactanglere sultswereusedtocalculatetherelevantdimensionlessnumbersrelated toimbibitionexperiments(Table2).Bondnumber,Bo,andviscosityra tio,M,couldbecalculateddirectlywiththemeasuredparameters.The intrinsicvelocitycalculatedwithDarcylawwasusedtocalculateCa numbers.Thepressuredifferenceusedinthisexpressionisthesameas theoneusedinourexperiments.TheresultingdefinitionforCaisthus equivalenttotheoneproposedin(ChatzisandMorrow,1984).Since drainageismostlyastableprocessduetoafavorableviscosityratio, dimensionlessnumberswillbecalculatedinthecaseofimbibition,to verifythevalidityofDarcy’slaw.

Wefoundthebondnumbertobeslightlybelow1duetothesmall differenceindensitybetweenthetwophases.Theflowbetweencoal tar/waterandoil/ethanolin1mmglassbeadscan,therefore,bede scribedbyDarcy’slaw.Oil/ethanolBondnumberincreaseswithtem peraturewhilethatofcoaltar/waterdecreases.Thiscanbeexplained bythefactthatthedensitydifference(𝜌_nw−𝜌_w)increaseswithtem peratureinthecaseofoil/ethanolbutdecreasesforcoaltar/water.The capillarynumberhasbeenfoundtobelowenough(10−5_{)tojustifythat}

capillaryforcesprevailratherthanviscousforcesattheporescale.In addition,no emergenceofviscousfingershasbeennotedduringthe smallpressurestepexperiments.Thuswecanconcludethatmeasure mentsofcapillarypressure saturationinourcasehasbeendonewith respecttohypothesisbehindgeneralizedDarcy’slaw,namelythefact thattheinterfacebetweenbothliquidphasesisrigidandnofingering occurs.

Ithasbeenfoundthatviscosityratio,duringimbibition,decreases byafactor3forcoaltar/waterandafactorof2foroil/ethanol.Here, theinfluenceoftemperatureontheviscosityratiowasnotashighas expected.Thosevariationswerenotsufficienttochange theorderof magnitudeofthedimensionlessvaluesandtochangetheresidualsatu rations.Increasingthetemperaturehastwoconsequencesfortheimbi bitionprocess:increasingtheviscosityratioanddecreasingthecapillary number.Also,itappearsthattheeffectoftemperatureonresidualnon wettingphasesaturationS_r,nwwasalmostnegligibleinbothcases.How ever,previous viscous LNAPL andDNAPL displacementexperiments haveshownthattheinjectionofhotwaterincreasestherecoveryrate ofthecontaminantandreducestheresidualsaturation(Jabbouretal., 1996;O’CarrollandSleep,2007).Theexperimentsaredoneherebyin creasingthecapillarypressurewithsmallpressuresteps.Severalweeks areneededtocompleteadrainageandimbibitioncycleexperiment.The capillarynumbersinourquasi staticexperimentsarestilllow(Ca<<

1),whichcorrespondstoacapillaryfingeringregime.Inthiscase,the displacementstructureiscontrolledbythefluctuationsinthecapillary thresholdpressuresatthedisplacementfront.Thus,theviscosityratio doesnothaveavisibleeffectontheresults.However,forhighinvasion rates,thedependenceonMmaybecomerelevantbecauseoftheviscous dominateddisplacement.

Inaddition,thedimensionlessnumbersbetweencoaltar/waterand oil/ethanolarequiteclose.Consideringthatoilandcoaltarareboth non wettingfluids,thesameresidualsaturationsandcapillarycurves betweenbothfluidpairsshouldbeexpected.Theuseofoil/ethanolas amodelfluidpairistherebyjustified.

4.2. Dynamiceffectontwo phaseflowproperties

Aspreviouslynoted,twopore volumes(PV)wereneededtoreach ethanol irreduciblesaturation. Theinjection of oilfrom the bottom (drainage)intotheporouscolumnsaturatedwithethanolwasfoundto beastableprocessatallflowrates.Duringthisstep,onlyethanolwas producedfromthecelloutletandassoonasoilreachedthecelloutlet, onlyoilwas.Thedisplacementfrontwasstableduetogravityeffects andbecauseoil’sdynamicviscosityishigherthanethanol’s(M>1).

Wesawacompletelydifferent trendfortheinjectionof10PVof ethanolfromthetopofthecell(imbibition).Thefollowingobservations wereobservedforthesmallestflowrate(6mL/min):theinjectionof 10PVofethanollasted38minutes.Onlyoilwasrecoveredduringthe first6minutes(0to1.6PV).Afterthat,ethanolbubblesstartedtoflow outseparatelyfromthesystemuntil10minutes(1.6to2.6PV).Then, ethanolandoilwerebothrecoveredasseparatephasesatthesametime. Inthetubing,oilwasflowingnearthewallswhileethanolwasrecovered nearthecenter(2.6to4PV).Finally,afterpumpingfor15minutes(4 to10PV),onlyethanolwasproducedfortherestoftheinjectionand theoilsaturationdidnotchange.

Thesesaturationchangesduringoilinjection(a)andpumping(b) areshowninFig.9,fordifferentflowratesandtemperaturevalues.

Theerrorbars showthedifferencebetweenthesaturation values calculatedfromtheimagingtechniqueandmassbalance.Forallsatura tionpoints,themaximumsaturationdifferencebetweenbothmethods is0.05(±1mL),whichvalidatestheproposedimagingtechniqueto determineliquidsaturationinsidethecell.AsshowninFig.9a,theirre duciblesaturationS_ir,whasbeenfoundnottodependontheflowrate. Itsvaluevariedbetween0.03(at6mL/min)and0.07(at24mL/min). Also, whenthepumpwasstopped between theinjectionandpump ingsteps,therewasasmalltimewindowwhereasaturation change occurred.Thiseffectwasevenmorenoticeableforalowflowrate.Dur ingthistime,wenoticedsaturationredistributioninsidethecelllikely duetoendeffects.There areindeedlocal saturationgradientsinside thecellatporescalethataremoreimportantindynamicconditions. However,wedo nottakeitintoaccount becausewemostly focused ourstudyonmacroscopiccharacteristicsandmeasurethemeansatura tionoverthewholecell.Conversely,oilpumpingheavilydependson bothflowrateandtemperature(Fig.9b).First,higheroilresidualsat urationswereobtainedforhigherflowrates.Duringtheexperiments, moreethanolfingerssweptalowerareaatahighflowrate.Thisphe nomenonhadalreadybeenobservedandconfirmedby(Doorwarand Mohanty,2015).Consequently,oilsaturationdecreasedataslowerrate eventhoughthepumpingratewashigher.Anotherimportantpointis thatresidualsaturationwasobtainedwithlowerporevolumesforlow flowrates.Almost8PVwereneededtoreachSr,o=0.29at24mL/min

whileonly5PVwereneededwithS_r,o=0.06at6mL/min.Thecom parisonbetweenbothprofilesat12mL/min(oneobtainedat293.15K andtheother323.15K)showsthattemperaturehadtwoeffects.Theoil recoveryratewasincreasedathightemperature.Duringourfluidchar acterization,wenotedthatonlytheviscosityratiodecreasedwithtem perature.Thus,fewerfingersareformedduringtheinjectionofethanol insideoilat323.15K,andahighervolumeofoilisrecoveredfromthe

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