Influence of wettability variations on dynamic effectsin capillary pressureDenisM. OCarroll,1Kevin G. Mumford,2Linda M. Abriola,3and Jason I.Gerhard1Received 29 September 2009; revised 23 February 2010; accepted 16 March 2010; published 3 August 2010.[1] Traditional continuumbased multiphasesimulators incorporatea capillarypressuresaturationrelationship that assumes instantaneousattainmentof equilibriumfollowing adisturbance.This assumption may not be appropriatefor systemswhere the capillarypressure is a function of the rateof change of saturation,a phenomenon referred to asdynamic capillary pressure. Previous studies have investigated the impact of soil and fluidproperties on dynamic effects in capillary pressure; however, the impact of wettability onthis phenomenonhas not been investigated to date. In this study, twophase multistepoutflow(MSO) experiments conducted in chemically treated sands with differentequilibrium contact angles were used to investigate the influence of wettability variationson dynamic effects in capillary pressure during displacement of water by tetrachloroethene(PCE). Data from the MSO experimentswere modeled with a multiphase flowsimulator that includes dynamic effects and were also analyzed through comparisons withtheoreticalmodel predictions for interfacemovement in a single capillarytube. Resultsshowed thata faster approach to equilibrium,characterizedby smaller fitted dampingcoefficients,occurred in sands with largerequilibrium contact angles. Dampingcoefficients for sands with an operational contact angle greater than 80 were found to bean order of magnitude smaller than those with an operational contact angle less than 65.These results suggestthat it may be possible to neglect dynamic effectsin capillarypressure in systems that approach intermediatewet conditions but that these effects will beincreasinglyimportant in more waterwet systems.Citation: OCarroll,D. M., K. G. Mumford, L. M. Abriola, andJ. I. Gerhard (2010), Influence of wettabilityvariationsondynamic effects in capillary pressure, Water Resour. Res., 46, W08505, doi:10.1029/2009WR008712.1. Introduction[2] Continuumbased multiphase flow simulators used topredict the migration of nonaqueous phase liquids (NAPLs)in porous media commonly incorporate a constitutive expres-sion relating capillary pressure and saturation (PcS). Theserelationships have been shown to be a function of the rate ofchange in saturation [e.g., Topp et al., 1967; Smiles et al.,1971; Vachaud et al., 1972; Stauffer, 1978; Hassanizadehet al., 2002; Berentsenet al., 2006; Sakaki et al., 2010],whichcreatesanonuniquenessinPcSrelationshipsthat isnot related to hysteresis (flow reversals). This dependence onthe flow conditions has been attributed to dynamic effects incapillary pressure [Kalaydjian, 1987; Hassanizadeh andGray, 1990]. Anumber of expressionsthat aresimilar inmathematical formhavebeenproposedtomodel thenon-uniqueness associated with dynamic effects, includingdynamic capillary pressure [Stauffer, 1978; Barenblatt andGilman, 1987; Kalaydjian, 1987; Hassanizadeh and Gray,1990]. These expressions incorporate a finite relaxationtimerequiredforasystem toreturntoanequilibriumstatefollowingadisturbance. Therelationshipemployedinthisstudy is expressed as [Hassanizadeh and Gray, 1993]:Pdc Psct 0sw0t. 1wherePcdisthedynamiccapillarypressure,Pcsisthestaticcapillary pressure, Sw is the water saturation, t is time, and tisamaterial coefficient, oftenreferredtoasthedampingcoefficient [Hassanizadeh and Gray, 1993]. In this study thestatic capillarypressure (Pcs) is definedas the differencebetween the nonaqueous and aqueous phase pressures (Pn Pw)whenthereisnochangeinfluidsaturation. Dynamiccapillarypressure(Pcd) isthedifferencebetweenthenon-aqueous and aqueous phase pressures measured at any time.Thestaticanddynamiccapillarypressuresareonlyequiv-alent at equilibrium (i.e., when Sw/t = 0). Static capillarypressure, however, can provide a reasonable approximationof dynamiccapillarypressurefor systemsthat reestablishequilibriumquickly(i.e., t 0).Theassumptionof t=0,andaninstantaneous returntoequilibrium, is implicit incommonmultiphaseflowsimulatorsthat employconstitu-tive relationships basedonequilibriumcapillarypressuremeasurements. This assumptionmaybeinappropriatefor1Department of Civil and Environmental Engineering, University ofWesternOntario, London, Ontario, Canada.2DepartmentofCivil Engineering, QueensUniversity, Kingston,Ontario,Canada.3School ofEngineering,TuftsUniversity, Medford, Massachusetts,USA.Copyright2010 by the American Geophysical Union.00431397/10/2009WR008712WATER RESOURCES RESEARCH, VOL. 46, W08505, doi:10.1029/2009WR008712, 2010W08505 1of 13systems where high rates of saturation change are expected,suchas for water infiltrationintodrysoil [Hassanizadehet al., 2002], arapidreleaseof densenonaqueousphaseliquidintoawater saturatedsoil, or CO2sequestrationindeep subsurface systems.[3] Dynamic effects in capillary pressure have beeninvestigatedinmultiple laboratory[e.g., Stauffer, 1978;Hassanizadeh et al., 2002; Manthey et al., 2004; OCarrollet al., 2005b; Berentsenet al., 2006; Botteroet al., 2006;Sakaki et al., 2010] and modeling [e.g., Dahle et al., 2005;Mantheyetal.,2005;Dasetal.,2007;MirzaeiandDas,2007; Juanes, 2008] studies; however, the underlyingmechanisms and controlling parameters remain unclear.These investigations suggest that the magnitude of thedynamic effects can be related to fluid properties (viscosity,density,andinterfacialtension),porousmediumproperties(intrinsic permeability, porosity, and poresize distribution),watersaturation, andthesizeofthesystemunderconsid-eration. Some of these studies have proposed functionalrelationshipsforthedampingcoefficient, basedonexperi-mental [Stauffer, 1978] or modeling [Das et al., 2007] work.Many of the modeling investigations have consideredmacroscopic contributions to dynamic effects, includingviscous fingering[Das et al., 2007], macroscopichetero-geneities [Mantheyet al., 2005], andboundarypressures[Manthey et al., 2005]. Other studies, however, have exploredthe contributions of smallerscale phenomena, including finescale heterogeneities [Mirzaei and Das, 2007], forces actingatliquidliquidandliquidsolidinterfaces[HassanizadehandGray, 1993], and dynamic contact angles [Friedman,1999; Wildenschild et al., 2001; Hassanizadeh et al., 2002;Mantheyet al., 2008]. To date, however, the impact ofwettabilityvariationsondynamiceffectsincapillarypres-surehasnotbeenexplored.WhilethetheorypresentedbyHassanizadeh and Gray [1993] implicitly incorporateswettabilitybyincludingforcesactingat liquidliquidandliquidsolid interfaces, these investigators did not explicitlyexamine the influence of wettability.[4] Wettability, the tendency of one fluid to spread on oradhereto a solidsurfacein thepresenceofanother immis-ciblefluid[Craig, 1971], istypicallyrepresentedbythecontact angle 0, the angle made by a fluidfluid interface incontact withasolidsurface[HiemenzandRajagopalan,1997]. InaNAPLwatersolidsystem, thesolidsurfaceisreferredtoasstronglywaterwetfor0approaching0andstrongly NAPLwet for0 approaching 180. Solid surfacesin systems where 60 < 0 < 130 are typically referred to asintermediate wet [Morrow, 1976]. Contact angles here refertoequilibriumcontact anglesmeasuredthroughthewaterphase. Althoughit isoftenassumedthat 0=0inmanyporous media systems, where silica is the dominant material[Anderson, 1986], this assumption may be inappropriate formaterials that donot exhibit stronglywaterwet behaviorsuch as calcite, dolomite, coal, and talc [e.g., Anderson, 1986;Gooddy et al., 2002], materials coated with natural organicmaterial[e.g., Abriola etal.,2005;Ryder and Demond,2008],or surfacesthat have been exposed tosurfactantsorNAPLs [e.g., Treiber et al., 1972; Barranco and Dawson,1999; Lord et al., 2000; Harrold et al., 2001; Dwarakanathet al., 2002; Lordet al., 2005; HsuandDemond, 2007;Ryder and Demond, 2008]. Laboratory experiments andtheoretical studies haveshownPcSrelationships tobeafunction of wettability; lower entry pressures and lowercapillary pressures have been observed at intermediatesaturations during drainage and imbibition for both uniformlyandfractionallywetmediathatarecharacterizedbylargercontact angles [e.g., Morrow, 1976; Anderson, 1987a;Bradford and Leij, 1995; Bradford et al., 1997; Ustohal et al.,1998; OCarroll et al., 2005a; Hwang et al., 2006; GladkikhandBryant, 2007]. Thesestudies, however, havetypicallyquantified the PcS relationship under equilibriumconditions.[5] Undernonequilibrium(i.e., movinginterface)condi-tions, thecontact betweenthefluidsandthesolidcanbecharacterizedbyadynamiccontact angle0d, whichisnotnecessarily equal to the equilibriumcontact angle [e.g.,Weisbrod et al., 2009]. The dynamic contact angle is asso-ciated with the dependence of the contact angle on thevelocity of the contact line [Hoffman, 1975; Dussan, 1979;de Gennes, 1985], the line that defines the intersection of thetwofluidphasesandthesolid. Thisconcept differsfromwhat is commonly referred to as contact angle hysteresis, thedependence of the contact angle onthe directionof thecontact line movement. The dynamic contact angle has beenshown to decrease with increasing velocity during drainageand increase with increasing velocity during imbibition[e.g., Dussan, 1979]. The fundamental disagreement betweenconventional hydrodynamic theory, which assumes a noslipcondition at the fluidsolid boundary, and the existence of amovingcontactlinehasinspiredsubstantialresearchrelat-ingtothedynamicsofwettingprocesses, andtodynamiccontact angles in particular (see recent reviews by Blake[2006] andRalstonet al. [2008]). The dynamic contactanglehasbeenrelatedtothecontact linevelocityandthestatic(i.e.,equilibrium)contactanglethroughvariousfunc-tional relationships [e.g., Blake and Haynes, 1969; Hoffman,1975; Voinov, 1976; Cox, 1986; ZhouandSheng, 1990;BrochardWyart and de Gennes, 1992]. The approachesused to generate these relationships can be generally dividedintotwocategories: hydrodynamicandmolecular kinetic.Hydrodynamic approaches emphasize energy dissipation dueto viscous effects in a wedge of liquid near the contact line,and molecularkinetic approaches emphasize a friction forcedue to molecularscale adsorption of the advancing fluid anddesorption of the receding fluid at the contact line [BrochardWyart and de Gennes, 1992; Blake, 2006; Ralston et al.,2008].[6] Friedman[1999] hypothesizedthat dynamiccontactanglescouldaccountfordynamiceffectsincapillarypres-sure. That worksuggested that decreased contact anglesproduced during dynamic drainage would yield higher watersaturations, at a given capillary pressure, when compared tothoseproducedduringequilibriumdrainage. Friedman[1999] suggested that the dynamic effects produced bydynamiccontact angleswerelikelytobemoresignificantfor NAPLgassystemsthanwaterair systemsbecauseofthe lower interfacial tension. The work of Wildenschild et al.[2001] andHassanizadehet al. [2002] supports dynamiccontact angles as a plausible mechanismcontributing todynamiceffectsincapillarypressurebutsuggeststhatitislikely to be more significant in NAPLwater systems than inwatergas systems, where equilibriumcontact angles areexpected to be larger. In a recent theoretical study by BlakeandDeConinck[2004],thecombinedeffectofwettabilityand dynamic contact angle on contact line displacement wasOCARROLLET AL.: WETTABILITY EFFECTS IN CAPILLARY PRESSURE W08505 W085052 of 13investigated. Using a molecularkinetic approach, theyshowed that the contact line will move more slowly duringdrainage or imbibition in systems with a smaller equilibriumcontact angle, all otherconditionsbeingthesame. Onthebasis ofthese results,it is hypothesizedthat the wettabilityofporousmediasystemswillinfluencedynamiceffectsincapillary pressure.[7] Multistep outflow (MSO) experiments have beenproposedas a rapid methodto obtainporous media consti-tutive relationships. In a MSO experiment, a packed columnis subjected to successive increases in pressure at the columninletandthecumulativeoutflowismeasured.Anumericalsolution of Richards equation for airwater systems, ormultiphase flow equations for any twofluid system, is thenused to match observed outflow response. This approach hasbeenusedtorapidlyestimate PcSandkrSconstitutiverelationship parameters in airwater and NAPLwater systems[Kool et al., 1985; Parker et al., 1985; Eching and Hopmans,1993; Eching et al., 1994; van Dam et al., 1994; Liu et al.,1998; Chenet al., 1999; HwangandPowers, 2003]. Theestimationof theseparameters is basedonthebest fit tocumulative outflow data. The approach to steady state, how-ever, is frequently modeled to be more rapid than observed[e.g., Chenetal., 1999;Schultzetal., 1999;Hwang andPowers, 2003]. Recently, MSO experiments have also beenused to estimate the damping coefficient related to dynamiceffects in capillary pressure [OCarroll et al., 2005b]. In thatstudy, incorporationof equation1intothegoverningdif-ferential equations resulted in a better fit to observed outflow,particularlyfor thenonequilibriumportionof theoutflowcurve, than alternative model fits obtained assuming validityof equilibriumcapillarypressureandrelativepermeabilityrelations(t=0). Equilibriummodelfitswerenearlyiden-tical when the capillary pressuresaturation and relativepermeabilitysaturationrelationsweredecoupled, introduc-ingfouradditional relativepermeabilityfittingparameters.These modeling results suggest that dynamic capillaryeffects wereparticularlyimportant tocapturingtheMSOdata.[8] In this paper the influence of wettability variations ondynamic effects in capillary pressure is explored through theanalysisoftheresultsofMSOexperiments, conductedontreated sands characterizedby differentequilibriumcontactangles. MSO data are modeled with a numerical multiphaseflowsimulator that includes dynamic effects [OCarrollet al., 2005b]. Differencesbetweenexperimentsareeval-uatedinthecontext of atheoretical relationshipbetweendynamiceffects andwettabilitybasedoninterfacemove-ment in a single capillary tube.2. Conceptual Model Based on a Single CapillaryTube Model[9] Althoughasinglecapillarytubedoesnotadequatelyrepresent the complexity of a real porous medium, relation-ships defined at the pore scale can provide insight intoprocessesthat manifest asmacroscalebehavior, includingcapillarypressurehysteresis[Morrow,1976],forcesactingat fluid interfaces [Hassanizadeh and Gray, 1993], andfluidfluid interfacial area [Cary, 1994]. Dahle et al. [2005]usedamodelderivedfora singlecapillarytube toprovideinsight into dynamic effects in capillary pressure for aconstant equilibrium contact angle. They used the Washburnequation [Washburn, 1921] to develop an analogous expres-sion to equation 1, thereby elucidating possible relationshipsbetweenthedampingcoefficient (t) andpropertiesof themedium and fluids. Thisstudyfollows themethodology ofDahleet al. [2005] but employs amodifiedformof theWashburnequation[e.g., BlakeandDeConinck, 2004]toincorporate dynamic contact angles and their relationship towettability.[10] Capillaryflowoftwoimmisciblefluidsinasinglecylindrical pore can be described by the Washburn equation[Washburn, 1921]:DP 212 cos 0r8j1l1j2l2r2dl1dt_ _. 2where DP is an externally applied pressure, r is the radius ofthe capillary tube, g12 is the interfacial tension between fluids1and2, 0isthecontactangle(measuredthroughfluid1),m1 and m2 are the viscosities of fluids 1 and 2, respectively,and l1 and l2 are the lengths of the tube occupied by fluids 1and 2, respectively, as shown in Figure 1. Fluid 1 is taken tobe the wetting fluid and fluid 2 the nonwetting fluid.Equation 2 has been expressed in terms of the viscosities ofboth fluids [Adamson, 1982] and can be simplified bydefiningalengthaveragedviscosityasj j1l1j2l2L3[Dahle et al., 2005], where L = l1 + l2 is the total length ofthecapillarytube,toyieldDP 212 cos 0r8jLr2dldt_ _. 4wherethesubscript onl1hasbeenremoved(i.e., l =l1).Equation 4 is typically applied using a constant contactangle, taken to be the static contact angle [Washburn, 1921;Blake and De Coninck, 2004; Dahle et al., 2005; Ralston et al.,2008]. However, equation4canalsobeappliedusingthedynamic contact angleDP 212 cos 0dr8jLr2dldt_ _; 0d fdldt. 0_ _5[Martic et al., 2003; Blake and De Coninck, 2004; Lee andLee,2007]. Several relationships have beenproposedforFigure 1. Schematic representation of a capillary tube con-taining a wetting fluid 1 and a nonwetting fluid 2, where thedotted line represents the fluidfluid interface at equilibriumandthesolidlinerepresentsthefluidfluidinterfaceinmotion during drainage.OCARROLL ET AL.: WETTABILITYEFFECTS IN CAPILLARY PRESSURE W08505 W085053 of 130d= f (dl/dt,0), based on hydrodynamic and molecularkinetic approaches [e.g., Blake and Haynes, 1969; Hoffman,1975; Voinov, 1976; Cox, 1986; ZhouandSheng, 1990;BrochardWyart and de Gennes, 1992].[11] A general form of the relationship used in the hydro-dynamic approach, which emphasizes energy dissipationdue to viscous effects in a wedge of liquid near the contactline, is03d03m 9Ca lnLMLm_ _ _ _6[Blake, 2006], where Ca is the capillary number (Ca = Um1/g12), U is the velocity of the contact line (U = dl/dt), LM is amacroscopiclengthscale,Lmisamicroscopiclengthscalethatdefinesasliplengthorcutofflength[Ralstonetal.,2008], and 0m is a microscopic contact angle typically takento be equal to the static contact angle.[12] Inthemolecularkineticapproach,themovementofthe contact line is assumed to depend on the displacement offluidmoleculesbetweenadsorptionsiteswithinthethreephase (fluidfluidsolid) region at the contact line [BrochardWyart anddeGennes, 1992]. Thecharacteristicfrequencyand distance between these displacements are used to defineacoefficientofcontactlinefriction,whichthenrelatesthedynamic contact angle and the contact line velocityU 12cos 0 cos 0d7[Blake,2006],where zisacoefficientofcontactlinefric-tion. Blake and Haynes [1969] successfully applied themolecularkinetic approach to describe the dynamic contactangles for a benzenewater interface ina glass capillarytreatedwithtrimethylchlorosilane. Thevalueof zisgivenby u expDg*s`2kBT_ _8[BlakeandDeConinck, 2004], whereDgs*isthespecificactivation energy of wetting, l is the average distancebetweendisplacements, kBistheBoltzmannconstant, andTis temperature. b = m1u1/l3for gasliquid systems, and b =m1m2u1u2/hl3for liquidliquid systems, where u is themolecular volume and h is Plancks constant (see Blake andHaynes[1969] for further discussionof molecularkineticparameters). Inthemolecularkineticapproach, themicro-scopic contact angle changes with velocity and is equal to thedynamic contact angle. Note that U = dl/dt < 0 for drainagehere, as l refers to the length of tube occupied by the wettingfluid and 0d < 0 for drainage.[13] Blake[2006]alsosummarizedworkbyBrochardWyart anddeGennes[1992]whoproposedthefollowingexpression that combines both hydrodynamic and molecularkinetic approaches:U 12cos 0 cos 0d 6j10dlnLMLm_ _. 9Equations 6, 7, and 9 have all been used to describe dynamiccontact angles; however, a single preferred approach has notbeen recognized due, in part, to the ability of each model toprovide adequate fits toexperimental data [Blake, 2006;Ralston et al., 2008]. Equations 6, 7 and 9 have typically beenapplied to gasliquid systems [e.g., Martic et al., 2003; Lunatiand Or, 2009], and little information is available concerningthe values of key parameters (e.g., LM, Lm, and z) for appli-cation to liquidliquid systems. However, equation 7 offers anadvantage for use in this study because the value of z has beenlinked to wettability for use in gasliquid systems [Blake andDe Coninck, 2004] and may offer the opportunity for similarlinks in liquidliquid systems. Ranabothu et al. [2005] foundthat a molecularkinetic model was able to provide better fitsto experimental dynamic contact angle data when comparedto the hydrodynamic model for simple fluids (includingwater). However, for polydimethylsiloxane oils, their resultssuggestedthat neither themolecularkineticnor hydrody-namic model adequately represented observed dynamiccontact anglebehavior for therangeof contact velocitiestested. Thus, althoughthemolecularkineticapproachwasselected for the present study, the range of fluids to which itcan be applied is still a subject of investigation. A combina-tion of equations 5 and 7 gives a modified Washburn equationDP 212rcos 0 12dldt_ _ _ _8jLr2dldt_ _10[e.g., Martic et al., 2003; Blake and De Coninck, 2004] andrearrangement givesdldt2r 8jLr2_ _1DP 212 cos 0r_ _. 11Similar expressions could be derived using other approachestodescribe the dynamic contact angle, but modificationswould be required to accommodate two liquids [e.g., Cox,1986]. Althoughexpressionstoestimatezinliquidliquidsystems have not been established [Blake and De Coninck,2004], expressionsderivedfor gasliquidsystemssuggestthat zwill begreaterforsystemscharacterizedbysmallerequilibriumcontact angles[BlakeandDeConinck, 2004].That is, systems with a smaller equilibriumcontact angles willexperience greater resistance to movement of the contact line.[14] Following the approach of Dahle et al. [2005],equation 11 can be considered as a porescale analogue to thecontinuumscalerateofchangeinsaturation, asexpressedby manipulating equation 10sw0t t 1Pdc Psc. 12Here Pcdis analogous to DP, Pcsis analogous to 2g12cos0/r,and tisanalogous to (2z/r + 8mL/r2) in equation 11. Notethat,fornegligiblecontactlinefriction(z0), tisanalo-gousto8mL/r2, aspresentedbyDahleet al. [2005]. Fornonnegligible contact line friction (z > 0), the analogysuggests that twill be a function of not only porous media(r), fluid (m), and scale (L) properties but also the strength ofinteractions between the fluids and the solid (z).[15] On the basis of the above discussion, a dampingcoefficientfor a single capillarytube is defined asttube 2r 8jLr2_ _. 13OCARROLLET AL.: WETTABILITY EFFECTS IN CAPILLARY PRESSURE W08505 W085054 of 13Equation 13 is a newexpression presented here to linkthe previously presented equation 11 for capillary tubes(developedthroughpreviouslypresentedequations25, 7,8, and 10) to equation 1 used to model macroscopic porousmedia. Arelationship between z and 0 is required toinvestigate the effect of wettability variations on ttube usingequation13. ExpressionsforDgs*inliquidliquidsystemsarenotavailableintheliterature[BlakeandDeConinck,2004]. The workof adhesion[WA=g12(1+cos0)] hasbeensuccessfullyusedtoapproximateDgs*ingasliquidsystems [Blake and De Coninck, 2002] and is assumed hereto be a reasonable firstorder estimate for liquidliquidsystems. Blake and De Coninck [2002] do not report atheoretical basis for equating Dgs*and WA but were able tocloselymatchexperimental results usingthis assumption,which provides empirical support for the use of thisassumptionhere. SubstitutingWAfor Dgs*inequation8yields u exp121 cos 0`2kBT_ _14It isimportant toemphasizethat equations11and12areonlyanalogous, andtheunits of t andttubearenot thesame. To facilitate the comparison of theoretical ttubevalueswiththose calculated from the experiments presentedin section 4, dimensionless values of ttube/ttube(0 = 83) werecalculated usingequations13and14andarepresentedinFigure 2 for L/r = 1. Airwater values were calculated usingg12 = 72mN/m, u1=3.01029m3, l=0.36nm[BlakeandDeConinck, 2002], T = 298 K, and m1 = m. PCEwatervalues were calculated using g12 = 47.5 mN/m [Demond andLindner, 1993], u1 = 3.0 1029m3, u2 = 1.7 1029m3, l =0.55 nm, T = 298 K, m1 = m, and m2= 0.0009 kg/ms [PankowandCherry,1996].Thevaluesof u1and u2wereapproxi-mated based on density and molecular weight, and the l valueof 0.55 nm used for the PCEwater calculations is the esti-mated size of a PCE molecule based on l3 u2 [Blake andDe Coninck, 2004]. A reference value of ttube(0 = 83) waschosen to correspond to operative contact anglesin the ex-periments conducted during this work, as discussed insection 3.2. It is implicitly assumed that ttube/ttube(0 = 83)will behave in a similar manner as t/t(0 = 83). The curvesin Figure 2 showthat larger damping coefficients areexpected for smallerequilibrium contact angles.Accordingto equation 1, larger damping coefficients will result ingreaterdynamiceffectsincapillarypressure. Thisanalysissuggeststhat tvaluesinwaterwet systems(approaching0 =0)coulddifferbyanorderofmagnitudewhencom-pared to intermediatewet systems (approaching 0 = 90).[16] It is important to note that the magnitude of thettube/ttube(0 =83) value inFigure 2is sensitive tothechoice of l, the value of which is not clear for liquidliquidsystems [Blake and De Coninck, 2004]. For example, usinga lvalue based on water instead of PCEchanges themaximumttube/ttube(0 =83) value for PCEwater fromapproximately22.1 to3.7.Similarly, ttube/ttube(0=83)isalso sensitive to L/r. For example, increasing L/r by an orderof magnitude lowered the maximumttube/ttube(0 =83)valuefor PCEwater from22.1to21.8andfor airwaterfrom 5.2 to 2.1.3. Materials and Methods3.1. Fluids and Porous Media[17] All MSOand equilibriumexperiments were con-ducted using laboratory grade (99%) tetrachloroethene (PCE)(Aldrich Chemical, Milwaukee, WI) and MilliQ water, withpropertieslistedinTable1.ThecolumnsforallMSOandequilibrium experiments were packed with a mixture of F35F50F70F110 Ottawa sand (US Silica, Ottawa, IL), with amean grain size of 0.026 cm, and a uniformity index of 2.79[OCarroll et al., 2005a]. The same sand was used byOCarroll et al. [2005b] toinvestigatedynamiceffectsincapillary pressure in waterwet sand.[18] Abatch of the sand was treated with a 5%(by volume)solution of octadecyltrichlorosilane (OTS) (ICNBiomedicalsInc, Aurora, OH)inethanol [Andersonet al., 1991]. Twoadditional batches of the sand were treated by immersing thesandina5%(byvolume)solutionofRhodorsilSiliconate51T(RDS) (RhodiaSilicones, RockHill, SC) inMilliQwater and lowering the pH below 8 [Fleury et al., 1999]. ThetwobatchesofRDStreatedsandwerepreparedseparately(referredtohereasbatchesAandB),whichmayhavere-sulted in the development of different surface properties, asdiscussed in section 4.1.[19] The wettingconditions producedbythe OTSandRDS treatments were evaluated by OCarroll et al. [2005a]by measuringadvancingandreceding contact angles onsmooth quartz slides (Fisher Scientific, Pittsburg, PA) treatedusingthesameproceduresusedforthesands.Thecontactanglesweremeasuredusingtheaxisymmetricdropshapeanalysis technique [Cheng et al., 1990; Lord et al., 1997] asdescribed by OCarroll et al. [2005a]. The measured valuesofthewaterrecedingcontact anglesarelistedinTable2.ThesemeasuredcontactanglessuggestthattheOTStreat-ment produced an organicwet surface on the slides, and theRDS treatment produced an intermediatewet surface on theTable 1. Fluid PropertiesProperty WateraPCEbDensity (kg/m3) 999 1630Viscosity(Ns/m2) 1.12 1039.0 104aMunson et al.[1990].bPankow and Cherry [1996].Figure 2. Dimensionlessdamping coefficientfora singlecapillary tube as a function of the equilibrium contact anglefor airwater and PCEwater systems.OCARROLL ET AL.: WETTABILITYEFFECTS IN CAPILLARY PRESSURE W08505 W085055 of 13slides according to the contact angle classification ofMorrow [1976].3.2. Equilibrium Drainage Experiments[20] Four equilibriumdrainage experiments were con-ducted: one using RDStreated sand frombatch A, twousing RDStreated sand frombatch B, and one usingOTStreated sand, referred to here as EQRDSA, EQRDSB1, EQRDSB2, and EQOTS, respectively.Results fromEQRDSB2 were previously reported by OCarroll et al.[2005a]. ThereplicateexperimentsEQRDSB1andEQRDSB2 were performed on subsamples of the same treatedsand but represent different packings. Primary drainagecapillary pressuresaturationdata were measuredusingapressure cell system based on the design of Salehzadeh andDemond[1999]. DrysandfromtheOTSor RDSbatcheswere packed into a column (length =1.27 cmand ID=2.54 cm),flushedwithcarbondioxide, andflushedwith200porevolumes of deaired MilliQ water to begin each experimentat 100%water saturation [OCarroll et al., 2005a]. The sandsineachoftheequilibriumdrainageexperimentsweresub-samples of the sands used in the MSO experiments, to facil-itate comparison between the results obtained using the smallpressure cell system and those from the larger MSO columns.[21] An operative contact angle was calculated usingLeverett scaling for each of the equilibrium drainage experi-ments. The operative contact angle is defined as the contactangle required to scale the van Genuchten PcS curve, fit towaterwet (i.e., 0 = 0) sand data, to measured drainage datafor the treated sands. van Genuchten model parameters andoperative contact angles were fitted by minimizing thesquare difference between measured and fit water saturationat a given capillary pressure. These operative contact anglesrepresent equilibrium receding contact angles that are char-acteristic of each porous medium and include the effects ofboththeOTSor RDStreatment andtheporous mediumsurface. In this work, all drainage curves were fit with vanGenuchten [1980] PcS expressions [OCarroll et al., 2005b].3.3. Multistep Outflow(MSO) Experiments[22] ThreeMSOexperimentswereconducted:oneusingRDStreated sand from batch A, one using RDStreated sandfrombatchB,andoneusingOTStreatedsand,referredtohere as MSORDSA, MSORDSB, and MSOOTS,respectively. The experiments were conducted using theapproachdescribedbyOCarroll et al. [2005b]. DrysandfromtheOTSorRDSbatcheswaspackedintoacustomdesignedaluminumcolumn(length=9.62cmandID=5.07cm), flushedwithcarbondioxide, andthenflushedwithaminimumof 30porevolumes of deairedMilliQwater to completely saturate the column. PCE flowed from aconstant pressurereservoir intothebottomof thecolumnthroughaPCEwet PTFEmembrane(0.45mmporesize;Pall Corporation, Ann Arbor, MI), displacing water from thetopof thecolumnthroughawaterwet nylonmembrane(0.45 mmporesize;PallCorporation,AnnArbor,MI)andinto a reservoir with an overflow weir.[23] Fluid flowwas induced by imposing a fixed airpressureabovethePCEintheconstantpressurereservoir.Water andPCEpressures were measuredinthetopandbottomcolumn end plates, respectively, using pressuretransducers(MicroSwitch,Freeport, IL).The PCE pressurewas increasedin a seriesofsteps(between1.0 and 8.6 cmH2O)duringeachexperiment;9stepswereusedinMSORDSA, 4stepsinMSORDSB, and10stepsinMSOOTS(Table3). Steadystatewasnot necessarilyachievedprior to the initiation of subsequent steps. Each experimentwas stopped when additional pressure increases did notresult in significant additional water outflow, at which pointit was assumed that residual water saturation had beenachieved.3.4. Numerical Model[24] A1D, fullyimplicit, pointcentered, fullycoupledfinite difference multiphase flowsimulator was used toanalyze the MSO experimental results [OCarroll et al.,2005b]. The development of the model is discussed byOCarroll et al. [2005b], and essential elements are presentedTable 2. Contact Angles Measured Through the Aqueous PhaseaTreatmentRecedingContactAngle onGlass SlidebOperative ContactAngle DuringDrainageBasedon PcS ScalingcRhodorsilSiliconate51T (RDS) 66.4 (4.4) 64.4 (1.7)d,82.3 (1.4)eOctadecyltrichlorosilane(OTS) 137.6 (18.0) 83.4 (0.7)aStandard deviation inparentheses.bOCarrollet al.[2005a].cInterfacialtension was equivalentin all systems(41 mN/m).dCalculated by scaling waterwet PcS fit tomatch EQRDSA data.eCalculatedbyscalingwaterwetPcSfittomatchEQRDSB2data[OCarrollet al., 2005a].Table 3. Pressure Steps EmployedDuring MSO ExperimentsStep No. Time (h)PCE Pressureat Bottomof Column(cm H2O)Change inPCEReservoirPressure(cm H2O)ColumnAveragedEffectiveWaterSaturation at Startof Pressure StepMSORDSA1 0 41.8 2.6 1.002 0.1 44.9 3.0 0.983 0.5 47.3 2.5 0.964 12.4 49.2 1.9 0.615 16.1 52.1 3.0 0.496 38.8 55.1 3.0 0.217 45.3 61.9 6.8 0.148 61.5 67.9 6.0 0.029 66.2 75.9 8.0 0.00MSORDSB1 0 46.8 3.9 1.002 0.03 48.4 1.6 0.983 22.3 53.4 4.9 0.034 33.9 59.0 5.6 0.00MSOOTS1 0 34.8 1.4 1.002 0.7 35.7 1.0 0.953 4.1 36.9 1.2 0.874 16.8 40.0 3.0 0.805 25.6 41.8 1.8 0.346 27.4 44.7 2.9 0.247 40.3 47.5 2.8 0.108 41.6 52.0 4.6 0.049 42.5 56.8 4.8 0.0110 43.1 65.4 8.6 0.00OCARROLLET AL.: WETTABILITY EFFECTS IN CAPILLARY PRESSURE W08505 W085056 of 13here for clarity. Thegoverningequationfor the aqueousphaseiscSw0,w0Pw0Pw0t_ _c,w0Sw0Psc0Psc0t_ _00z`w0Pw0z,wg_ _ _ _.15where cis porosity, rwis water density, lw=kw/mwiswatermobility, mwisthewaterviscosity, kw=kkrwisthewater permeability, k is the intrinsic permeability, krwisthe water relative permeability, g is gravity, and z is the spatialdimension.In the governing equationfor the NAPL phase,the NAPL phase pressure is expanded in terms of the aqueousphase and dynamic capillary pressures (Pn=Pcd+Pw).DefiningPcdusingequation1givesanexpressionintermsofPcsandPwc 0,n0Pn0PscPw_ _0tc,n0Sn0Psc0Psc0t_ _00z`n0PscPw_ _0z00zt 0Sw0Psc0Psc0t_ _,ng_ _ _ _. 16where rn is NAPL density, Sn is NAPL saturation, ln = kn/mnis NAPL mobility, mn is the NAPL viscosity, kn = kkrn is theNAPLpermeability, andkrnistheNAPLrelativeperme-ability. Inthis expansion, dynamic effects in the NAPLcompressibilityterm are ignored. Static capillarysaturationrelations were represented by a van Genuchten [1980] PcSfunction (VG)Psc 1cS1,me1_ _1,n. 17where a, m, and n are the van Genuchten model parameters,Se = (Sw Sr)/(1 Sr) is the effective water saturation, and Sristheresidual water saturation. Relativepermeabilitywasexpressed by the Burdine [1953] relationshipkrw S2e1 1 S1,me_ _m_ _ and 18krn 1 Se 21 S1,me_ _m. 19where m=12/n. The relative permeabilitysaturationexpressionswerenotvariedasafunctionofsystemwetta-bility during this study. The appropriateness of this approachwas confirmed by observing that use of wettabilitymodifiedrelativelypermeabilityfunctionsfortheMSOOTSexperi-ment hada veryminor impact onthe magnitude of thedamping coefficient estimated through inverse modeling(furtherdiscussed in section 4.4).[25] The damping coefficient (t) has sometimes beentreated as a constant for the modeling of dynamic effects [e.g.,Hassanizadehetal.,2002].However,itiswidelybelievedthat t = t(Sw) [Hassanizadeh et al., 2002; Dahle et al., 2005;Mantheyet al., 2005; OCarroll et al., 2005b; Berentsenet al., 2006; Mirzaei and Das, 2007], although the form ofthis function remains under investigation [Berentsen et al.,2006]. In this study the following functional formwasassumed [OCarroll et al., 2005b]:t ASeA. 20where the constant Ais a fitting parameter. The use ofequation20waspreviouslyfoundtosignificantlyimprovethe ability of the numerical simulator to fit outflow data fromMSO experiments in waterwet media compared to the useof aconstant tvalue[OCarroll et al., 2005b]. Althoughexperimental studies support the use a saturation dependentt [e.g., Manthey et al., 2004; Sakaki et al., 2010], theassumption of a linear form needs further study.[26] TheMSOexperimentsweresimulatedusingacol-umndomaindiscretizedwith145nodesinavariablegridspacing. A maximum grid spacing of 103m was located atthe center of the domain, and a minimum grid spacing of 8 106m was located near the column boundaries. A dynamictimestepadjustment algorithmwasemployedusingtimesteps between 1012and 10 s.[27] Bestfitstoobserveddatawereobtainedbyvaryingthree parameters (Sr, a, and n) for the t = 0 simulations andfour parameters (Sr, a, n, and A) for the t 0 simulations tominimize the rootmeansquare error based on the differencebetweenmeasuredandpredictedvaluesof thecumulativewater outflow (RMSEQ). The PcS parameters derived fromfitting the MSO data were then used to generate PcS curvesfor comparison to PcS data obtained fromindependentTable 4. NumericalModel ParametersParameter MSORDSA MSORDSB MSOOTSInput parametersSand permeability at Sw =1(m2) 1.08 10111.23 10111.11 1011Nylon membrane permeability atSw =1 (m2) 3.48 10156.48 10156.62 1015Teflon membranepermeability at Sw =Sr (m2) 7.12 10142.77 10144.70 1014Porosity 0.311 0.319 0.301Fittingparameters and RMSE (t= 0)a (cm H2O)16.35 1021.38 1012.25 101n 7.17 8.0 4.42Sr0.24 0.0 0.14RMSEQ1.50 2.08 1.05RMSES1.72 1013.56 1011.69 101Fittingparameters and RMSE (t 0)a (cm H2O)16.69 1021.50 1012.28 101n 6.61 8.0 4.74Sr0.24 0.0 0.17A (kg/ms) 3.43 1072.76 1063.74 106RMSEQ0.57 1.20 0.70Reduction in RMSEQ compared to t= 0 fit (%) 62% 42% 33%RMSES1.51 1013.34 1011.60 101OCARROLL ET AL.: WETTABILITYEFFECTS IN CAPILLARY PRESSURE W08505 W085057 of 13equilibriummeasurements. Sand and membrane intrinsicpermeability, measured independently according to themethod of OCarroll et al. [2005b], were inputs for the modelandarelistedinTable4.Itisimportanttonotethatthe tvalues obtained in the study, calculated using equation 20 andfittedAvalues, represent smallscale(i.e., local) dampingcoefficients [OCarroll et al., 2005b; Berentsen et al., 2006].Thisisincontrasttootherstudiesthathavereportedmac-roscopic tvalues based on averaging pressures and satura-tions over length scales of 3 to 100 cm [Manthey et al., 2005;Das et al., 2007; Mirzaei and Das, 2007].4. Results and Discussion4.1. Equilibrium Drainage Experiments[28] Capillary pressure/saturation data from the four equi-libriumdrainageexperimentsareshowninFigure3,alongwithdatafromanequivalent experiment previouslycon-ducted in the same size fraction of waterwet sand [OCarrollet al., 2005b], referredtohere as EQWW. ExperimentswiththeRDSandOTStreatedsandsexhibiteddecreasedcapillarypressuresat all effectivesaturationvalues, com-pared to those in the waterwet sand. This decrease in capil-lary pressure, at a given water saturation, is consistent withother experiments conducted on nonwaterwet material[e.g., Morrow, 1976; Anderson, 1987a; Bradford and Leij,1995; Bradford et al., 1997; Ustohal et al., 1998; OCarrollet al., 2005a;Hwangetal., 2006]andsupportstheexpec-tationthatlessenergy, characterizedbytheareaunderthePcS curve [Leverett, 1941], is required for drainage in suchmaterials[DonaldsonandAlam,2008].Capillarypressure/saturationdatafor thetwoRDStreatments aredistinctlydifferent. Sands fromthese two experiments were fromdifferent batches leading to these observed differences.Becausethesamesandtreatment procedurewasusedforboth batches, it is unclear why each batch yielded differingwettabilitybehavior. Forthetreatmentsusedinthisstudy,the OTStreated sand had the largest operative contact angle(Table2). Thisisqualitativelyconsistent withthecontactangles measured on glass slides, where the OTStreatedslides alsoexhibitedthe largest contact angle. However,fitted contact angles exhibit two important discrepancieswiththose measuredonglass slides. First, the operativecontact angle for the OTStreated sand falls within the rangefor an intermediatewet system (i.e., 60 130) that wassug-gested by the glass slide measurement. This discrepancy waspreviously noted by OCarroll et al. [2005a], who stated thattheoperativecontactangleof0 90wasconsistentwiththe negligible capillary pressure behavior observed during theinfiltration of PCE into OTStreated sand [OCarroll et al.,2004].InOCarrolletal.[2004],useofanoperativecon-tact angle greater than 90 for OTStreated sand in thenumerical simulator led to results that were inconsistent withexperimental sandboxbehavior. Second, thetwoseparateRDS treatments (A and B) did not produce similar operativecontact angles; treatment Bproducedanoperativecontactangle similar to the OTS treatment. As discussed above, thecause of the discrepancy in operative contact angles betweenthe two separate RDS treatments is unknown.4.2. Multistep Outflow (MSO) Experiments[29] TheoutflowresponsefromthethreeMSOexperi-ments is shown in Figure 4 as cumulative outflow(Q)Figure3. Comparisonofequilibriumdrainagemeasurements(symbols)andvanGenuchtencurves(lines)derivedfromparameteroptimizationinthesimulationofmultistepoutflowdata,assumingnodynamiceffects. ParametersderivedfromMSOdatasimulationsincorporatingdynamiceffects, asdescribed by equations 1 and 20, produced similar van Genuchten curves, which are not shown for clarity.OCARROLLET AL.: WETTABILITY EFFECTS IN CAPILLARY PRESSURE W08505 W085058 of 13versus time. Although the results from MSORDSB appeartohaveresultedfromasinglepressurestep, fourpressuresteps were used. The majority of the water outflow occurredduringthesecondstep, withthenext stepbeinginitiated22.3hintotheexperiment (Table3). Eachof theexperi-ments exhibits aninitiallyrapidincreaseinoutflow, fol-lowedbyaslower approachtozerooutflow(i.e., steadycumulative outflow), subsequent to each step change in thePCE boundary pressure. Previous studies of waterwetmedia have shown that the slow approach to zero outflow isindicative of dynamic effects incapillarypressure if therelative permeability to each phase is not small (i.e., atintermediate fluidsaturations) [OCarroll et al., 2005b].[30] Direct comparisons of the approach rate to zerooutflowamongtheMSOexperimentsisnoteasilyaccom-plished using Figure 4 due to the different magnitudes of thepressure steps, the different magnitudes of the outflowresponseproduced, andthedifferent watersaturationcon-ditions when the pressure steps were initiated. To facilitate acomparisonoftheexperimentaldata, theoutflowresponsefrom one pressure step in each experiment was chosen. Theoutflowresponsesselectedwerethosethat achievednearsteadycumulativeoutflow(Q/t 0)beforetheinitiationofthenext pressurestepandtookplaceat effectivewatersaturationsof Se0.4toSe0.8. Onthebasisof thesecriteria, the selected curves represent reasonably similarconditions. While the achievement of Q/t 0 is notrequired for the determination of PcS parameters by inversemodeling, its attainment facilitates the direct comparisonamong MSO experimentsby allowing the normalization ofthe outflowas described below. The effective water sa-turations,and those listedinTable3, arecolumnaveragedvaluesbasedonthecumulativeoutflowduringtheexperi-ment. The selected outflow responses (Figure 5) have beenshiftedsuchthat t =0correspondstotheinitiationofthepressurestep(referredtohereas relativetime), andnor-malizedtothecumulativechangeinoutflow,suchthattheinitialnormalized outflowis zero, and the final normalizedoutflowis 1, orQN Q QiQf Qi. 21whereQNisthenormalizedcumulativeoutflow, Qisthecumulative outflow at any time, Qi is the cumulative outflowat the initiation of the pressure step, and Qf is the cumulativeoutflowimmediately prior to the initiation of the nextpressure step. Inaddition tothe MSOexperiments con-ducted in this study, selected outflow responses from waterwet experiments (referred to here as MSOWWAandMSOWWB)[OCarrolletal.,2005b]arealsoplottedinFigure5for comparison. TheoutflowstepselectedfromMSOWWA (step 4) resulted from a PCE pressure changeof 6.84cmof water andproducedadecreaseineffectivewatersaturationfrom0.48to0.14. ForMSOWWB, theselectedstep(step6)resultedfromaPCEpressurechangeof 4.53cmof water andproducedadecreaseineffectivewater saturationfrom 0.73 to 0.52.[31] The scaled outflow curves in Figure 5 reveal that zerooutflowwasapproachedfasterintheexperimentswiththeOTStreated sand than with the waterwet sand. This fasterapproach is consistent with a decrease in dynamic capillarypressure effects associated with a larger equilibrium contactangle,asdiscussedinsection2.However,itcouldalsobeattributedtoanincreaseinrelativepermeability, aslargercontact anglesallowthedrainageof water throughlargerpores. The outflow response in the RDStreated sand variedconsiderably between the experiments conducted usingmaterial from batches A and B. The response in MSORDSA was similar to the waterwet experiments, but the responsein MSORDSB was similar to the experiments with OTStreated sand. The similar behavior of the MSORDSB andMSOOTS experiments is consistent with their similarequilibriumdrainagePcScurves(Figure3)andthecorre-spondinglysimilar operative contact angles of 82.3 and83.4, respectively. The faster response in MSORDSB andMSOOTS is consistent with the theory presented in section2, where decreased dynamic effects are expected for systemscharacterized by larger equilibrium contact angles.4.3. Numerical Simulations[32] TheMSOexperimental datawerefirst fit usingthemodel describedinsection3.4, usingthevanGenuchtenBurdinePcSkrrelationships, and t=0(i.e., nodynamiccapillary pressure effects). This is representative of theconventional approach for modeling multiphase flow, wherePcsis achieved instantaneously following a disturbance to asystem at equilibrium [Hassanizadeh and Gray, 1993]. Thebest fitsimulationresultsforthe t=0caseareplottedinFigure4. Datafromthemultistepoutflowexperiments(symbols) compared to best fit numerical simulations (lines)assuming(a)nodynamiceffectsand(b)dynamiceffectsdescribedbyequations 1and20. The measureddata inFigures 4a and4bare the same, andonlyselecteddatapoints(approximatelyevery60thpoint)havebeenplottedfor clarity.OCARROLL ET AL.: WETTABILITYEFFECTS IN CAPILLARY PRESSURE W08505 W085059 of 13Figure 4a, and the best fit values of the parameters are listedinTable4alongwiththeRMSEQvalues. Thesimulatedoutflowcurvesforeachoftheexperimentsfailstocapturethe approach rate to zero outflow and the steady cumulativeoutflow value. Simulated curves tend to exhibit a more rapidapproach to steady cumulative outflow and achieve a lowercumulativeoutflowplateauasthesystemreachesequilib-rium. Similar differences havebeenobservedfor simula-tions of MSO outflow data during the drainage of waterwetsands[Chenetal.,1999;Schultzetal.,1999;HwangandPowers, 2003;OCarrolletal., 2005b]. Ithasbeenprevi-ously reported that this slower approach to zero outflow in aPCE/water/quartzsandsystemcouldnot bematchedbyasimulatorthatneglectsdynamiceffects[OCarrolletal.,2005b]. The lower steadycumulative value obtained in thesimulations is a consequence of the rootmeansquare errorminimizationprocedure, whereminimizationoftheobjec-tivefunctioncauses themodel toundershoot theplateauwhile overshooting its rate of approach. The differencesbetween the observed and simulated values is more apparentin data fromMSORDSAthan fromMSORDSBor MSOOTS, but the differences are generally less than those reportedfor MSO experiments in waterwet sands [OCarroll et al.,2005b].[33] Fit values of the PcS function parameters using t = 0were used to generate PcS curves using equation 17 for eachofthe threesands and are compared to data fromthe equi-librium drainage experiments in Figure 3. Also included, forcomparison, is the PcS curve for the waterwet sand gener-ated using parameters fit using inverse modeling to data fromMSOWWA[OCarroll et al., 2005b]. The rootmeansquare errors for the PcS curves were calculated based on thedifferencebetweenthemeasuredandVGmodelgeneratedvalues of Se (RMSES) and are listed in Table 4. The RMSESwas based on differences in Se rather than Pc to reduce theimportanceofdataat highandloweffectivewatersatura-tions and increase the importance of data in the intermediateeffectivewater saturationrange[OCarroll et al., 2005b].The VG PcS functions based on fits to the MSO data usingt=0weregenerallyconsistent withthestaticPcSmea-surements, despite the inability of the multiphase flowsimulator to fit the outflow data using t = 0. Note that, in theequilibriumcapillarypressure/saturationexperiments, largedecreases in water saturation were observed following a smallincreaseincapillarypressure, whentheoperativecontactanglewaslarge. TheVGPcScurvesgeneratedfromtheMSOapproach, however, donot conformtotheseabruptchanges inwater saturation following small increases incapillary pressure. Nevertheless, the saturation levels athigher capillary pressures are consistent with the staticmeasurements. Thus,this analysis indicatesthat PcS func-tions fit using MSOdata without considering dynamiceffectsincapillarypressurecanyieldPcScurvesthat areingoodagreement (i.e., similar capillarypressureat 50%effective water saturation) withindependent PcSexperi-ments for a broad range of wettability conditions.[34] MSO experimental data were next fit using the sameapproachasdescribedabove(i.e.,fittingVGparameters aand n as well as residual water saturation) and assuming t 0(equation20)toinvestigatewhetherdynamiceffectscouldimprove the fit. The best fit simulation results are plotted inFigure 4b, and the best fit values of the parameters are listedinTable4. Theinclusionof tasalinear functionof Sesignificantly improved the fits to the MSO data. TheRMSEQ values for MSORDSA, MSORDSB, and MSOOTSdecreasedby62%, 42%, and33%, respectively. Inaddition, the simulationresults providedmuchbetter fitstotheapproachtozerooutflowandthemagnitudeofthesteady cumulative outflow (Figure 4b). Previous workdemonstratedthatamodelingapproachthatdecoupledthecapillary pressure and relative permeability constitutiverelationships, adding three additional fitting parameters,Figure 5. Selected, scaledoutflowstepsfromthemultistepoutflowexperimentsinRDSandOTStreatedsand, comparedtooutflowstepsfrompreviouslyconductedmultistepoutflowexperimentsinwaterwet sand[OCarroll et al., 2005b].OCARROLLET AL.: WETTABILITY EFFECTS IN CAPILLARY PRESSURE W08505 W0850510 of 13produced nearly identical agreement between the numericalmodel and experimental MSO data [OCarroll et al., 2005b].Thus, this alternative modeling approach was not consideredherein.[35] Only relatively small differences exist between the fitvalues of the PcS function parameters for t= 0 and t 0(Table4). TheresultingPcScurves aresimilar tothoseshown in Figure 3 and, thus, a separate set of curves is notshown. Theseresultsdemonstratethat thestaticPcSdatacanalsobe well matchedusingthe fit parameter valuesbasedont 0simulations, as indicatedbythe similarRMSES values calculated for the t = 0 and t 0 parameterfits (Table 4).4.4. Effect ofContactAngleontheDampingCoefficient (t)[36] The RMSEoptimized A values differed significantlyamongexperiments(Table4).MSORDSA,characterizedby the lowest operative contact angle of these experiments,hadaRMSEoptimizedvalueof A=3.43107kg/ms.Thisliesbetween thevaluesof A= 5.64 107kg/msandA=1.99 107kg/ms reported for waterwet material[OCarroll et al., 2005b]. The MSORDSB and MSOOTSexperiments, with higher operative contact angles, hadRMSEoptimized values of A = 2.76 106kg/ms and A =3.74 106kg/ms, respectively.[37] It is important to examine whether discrepanciesbetweenobservedandsimulatedcumulativewateroutflowcan be attributed in part to the selected relative permeabilityfunctions, which determine the rate of fluid flowand,therefore, the transient drainage of a twofluid system. Theselectionof wettingandnonwettingfluidsusedtoassigntheserelativepermeabilityfunctionsbecomesincreasinglyambiguous as a systemapproaches an operative contactangle of 90, as was the case for the OTSandRDSBexperiments. It is possible that the faster approach to steadystate observed in these experiments, and the correspondinglysmaller tvalues, weredueinparttotheincreasedperme-abilityof the treatedsandtoNAPL, associatedwiththeincreasedoperativecontactangle.Totestthesensitivityofthe A values to the relative permeability expressions used inthemultiphaseflowsimulator, theMSOOTSexperimentwas also simulated with the wettability of the fluids reversed.That is, water permeabilitywascalculatedusingthenon-wetting phase relative permeability expression (equation 19),and the NAPL permeability was calculated using the wettingphase relative permeability expression (equation 18). This isexpected to bound the dynamic behavior, based upon theo-retical [e.g., Bradfordet al., 1997]andexperimental [e.g.,Anderson, 1987b]workthat hasshownthat waterrelativepermeabilitytends toincreaseandNAPLrelativeperme-ability to decrease as wettability changes from waterwet toNAPLwet. Resultsofsimulationsemployingthisrelativepermeability reversal revealed that the newRMSEoptimizedvalue of A = 1.83 106kg/ms was not significantly different,based on a 95% confidence limit, from the former value ofA=3.74106kg/ms. Thisresult demonstrates that thechoiceof wettingfluiddidnot affect themagnitudeoftdeterminedusingthesimulations.[38] The t values, based on equation 20 and the A valuesinTable4, for MSORDSA(operativecontact angleof64.4),andthoseofthetwopreviouslyreportedwaterwetsandexperiments, areanorder of magnitudegreater thanthosefor MSORDSBandMSOOTS(operativecontactanglesof82.3and83.4,respectively).Thistrendiscon-sistent with the values presented in Figure 2 for a PCEwatersystem, wherettube/ttube(0=83) increasesasthesystembecomes more water wetting. Here it is expected that ttube/ttube(0 = 83) behaves in a similar manner as t/t(0 = 83).Whiletheobservedincreaseintwithdecreasingequilib-riumcontact angleis consistent withFigure2, thesmalldifference between the t values for MSORDSAand the twopreviously waterwet sands is not. For example, based on theoperativecontact anglesandtrendspresentedinFigure2,t values for MSORDSAshould be approximately 3times larger than the tvalues for MSORDSB and MSOOTS[0=64.4, ttube/ttube(0=83) =3.0] andapproxi-mately 4 times less than those in the waterwet system [0 =34.4, ttube/ttube(0 = 83) = 11.9]. This suggests that whilethecapillarytubemodel providesqualitativeinsight, it isinsufficient to provide a quantitative analogy to actual porousmedia in this context. Overall, however, the increase inexperimentallydeterminedtvalueswithdecreasingequi-librium contact angle is consistent with the conceptual modelpresented in section 2 and the expectation of increaseddynamiccapillarypressureeffectswithdecreasedequilib-rium contact angle.5. Summary and Conclusions[39] Aseries of MSOexperiments conducted in 1Dcolumns was used to explore the influence of wettability ondynamic effects incapillarypressure. These effects werequalitativelycomparedtoatheoreticalmodelbasedontheconsiderationof dynamic contact angles duringinterfacemovement in a single capillary tube. The dynamic responsein the cumulative column outflow was found to be faster inexperiments in an OTStreated sand, characterized by ahigher operative contact angle, thaninexperiments con-ductedinwaterwet or RDStreatedsands. As has beenreportedfor waterwet sands [OCarroll et al., 2005a], anumerical model using traditional constitutive relationships,which neglect dynamic effects (t= 0), failed to adequatelyfit the dynamic outflow data. However, the discrepancy waslesspronouncedinexperimentsusingRDSandOTSsandwith higher operative contact angles. Despite the poorerrepresentationofoutflowdatawhenassuming t=0, PcSfunction parameters estimated through inverse modelingwere consistent with equilibriumexperiments, regardlessof wettability. Includingdynamiceffectsinthenumericalsimulations, using a damping coefficient that is a linearfunction of effective water saturation (t = ASe + A), greatlyimprovedthenumerical fit tothemeasuredMSOoutflowdata. These fits yielded damping coefficient values formaterial withequilibriumcontact angles greater than80that were an order of magnitude less than those for materialwith equilibriumcontact angles less than 65.[40] The MSO experiment results reported here show thatanincreasedequilibriumcontact angle produceda fasterapproachtosteadystate duringdrainage, a reduceddis-crepancybetweenobservedandsimulatedoutflowvaluesusing t = 0 and smaller t values as a function of saturation.Thesepreviouslyunreportedeffectsareconsistentwiththemodel presentedhere basedoninterface movement inasingle capillary tube, which predicts increased dampingOCARROLL ET AL.: WETTABILITYEFFECTS IN CAPILLARY PRESSURE W08505 W0850511 of 13coefficients with decreasing equilibrium contact anglebased on dynamic contact angles. While the consideration ofdynamic contact angles alone does not explain all ob-servations related to dynamic capillary pressure effects, thismodel does help to explain observations of this study relatedto wettability. These results suggest that dynamic effects incapillary pressure are likely not only a function of material,fluid, and scale properties but also depend on the interactionof the fluids and solid and that this interaction may be largelyresponsible for localscale dynamic capillary pressure effects.Furthermore, thetheoretical andexperimental results pre-sented here suggest that it may be possible to neglectdynamic effects in systems that approach intermediatewetting conditions but that they will be increasinglyimportant formorewaterwet systems. Theunderstandingof dynamic effects in capillary pressure and the implicationsof includingthose effects innumerical simulators wouldbenefit from additional experiments in materials of differingwettability, theoretical texpressionsthat incorporatewet-tability at the REVscale (e.g., application of the molecularkinetic approach at the macroscopic scale and developing afunctional relationship between t(Sw) and operative contactangle), and fieldscale simulations that include dynamiceffects.[41] Acknowledgments. Thisresearch wassupported bygrantDEFG0796ER14702,EnvironmentalManagementScienceProgram,OfficeofScienceandTechnology,OfficeofEnvironmentalManagement,U.S.Department of Energy (DOE), and by the Natural Sciences and EngineeringResearch Council (NSERC) of Canada through a Strategic Grant (OCarroll/Gerhard) and a Postdoctoral Fellowship (Mumford). 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