JOURNALOF GEOPHYSICALRESEARCH,VOL. 102,NO. B1,PAGES773-783,JANUARY10,1997
Methane hydrate stability in pore water: A simple theoretical approach for geophysical applications Gerald R. Dickens• Departmentof GeologicalSciences,Universityof Michigan,Ann Arbor
Mary S. Quinby-Hunt EnergyandEnvironment Division,LawrenceBerkeleyNationalLaboratory,Berkeley,California
Abstract. Geophysicists haverecentlyexpressed an interestin understanding how porewater composition affectsCH4 hydratestabilityconditionsin the marineenvironment.It haspreviously beenshownin thechemicalengineering literaturethatCH4 hydratestabilityconditionsin electrolytesolutions arerelatedto theactivityof water(aw).Herewe presentadditionalexperimental datain supportof thisrelationship andthenusetherelationship to address issuesrelevantto geophysicists. Pressure andtemperature conditions of CH4 hydratedissociation weredeterminedfor
10solutions containing variable concentrations of CI-,SO4 2-,Br-,Na+,K+, Mg2+,NH4+,and Cu2+.Thereciprocal temperature offset ofCH4hydrate dissociation between theCH4-pure water systemandeachof thesesolutions (andfor otherelectrolytesolutions in literature)is directlyrelatedto thelogarithmof theactivityof water(lnaw).Stabilityconditions for CH4 hydratein any porewatersystemthereforecanbepredictedsimplyandaccurately by calculating lnaw.The effect of salinityvariationandchemicaldiagenesis on CH4 hydratestabilityconditions in the marineenvironmentcanbe evaluatedby determining howtheseprocesses affectlnawof porewater.
Introduction
Clathrate hydrates of methane (CH 4 hydrates) occur naturally in sediment pore space along many continental margins [Kvenvolden, 1988, 1993]. These hydratesexist in a depth zone that is dictatedby pressure-temperature conditions of a CH4-hydrate-waterequilibriumcurve [Kvenvolden,1988, 1993]. BecauseCH4 hydratein the marine enviroment exists in associationwith salinepore watersthat are chemicallydistinct fxomseawater(andpurewater), a presentline of inquiryis the effect that variationsin pore water chemistryhave on the stability conditionsof CHn-hydrate-waterequilibrium curves [Hyndman et al., 1992; Westbrooket al., 1994; Ussler and Pau!l, 1995; Kastner et al., 1995]. The issueis relevant to current geophysicalliterature,inasmuchas it has a directbearing on (1) methodsto estimate the distributionof CH4 hydrate
aw= e RT
(1)
where/•w is the chemicalpotentialof waterin the solution, /• is the chemicalpotentialof pure water, R is the gas constant,and T is temperature(in kelvins), or aw = •rwXw ,
(2)
where •'w is the activitycoefficientof water, and xw is the mole fraction of water in the solution.The aw of an dectrolyte solutioncan be accuratelycalculatedwith severalconstantsand a seriesof equations[e.g., Pitzer, 1991] (see also Appendix 1 of this paper). The reciprocaltemperature offsetbetweenthe CH4-hydratewaterequilibriumcurvein purewaterandthat in an electrolyte [Kvenvolden, 1988; Kvenvolden and Grantz, 1990; solutionshouldbe linearly related to the logarithmof the acMacDonald, 1990; Gornitz and Fung, 1994], (2) use of tivity of water (In aw) of the solutionat a given pressure[cf. bottom-simulatingreflectors (BSRs) to estimate geotherms Pieroen, 1955; Mentenet al., 1981]. This simple theoretical and heat flow [Cande et al., 1987; Minshull and White, 1989; relationshipcan be verified with.limited experimentaldata for Davis et al., 1990; Hyndmanet al., 1992; Brown and Bangs, ar.tificial and actual seawater as well as for solutions 1995], and (3) approachesto modeling hydrate dissociation containingCI', K+, Na+, andCa2+ [deRooet al., 1983; during past climate change[Nisbet, 1990; MacDonald, 1990; Dholabhai et al., 1991; Dickens and Quinby-Hunt, 1994]. Paull et al., 1991; Hatzikiriakos and Englezos,1994;Dickens Here we demonstratethat the relationship is also valid for et al., 1995].
The activityof water( aw) of a solutionis a measureof the effective concentration of water in the solution. It is defined as
additionalsolutionscontainingCI', SO42-,Br-, Na+, K+, Mg2+,NI-I4 +, andCu2+.Thuspressure-temperature conditions that define a CH4-hydrate-waterequilibriumcurve in any pore water can be estimatedby calculatingthe ln aw of the pore
water. 1Now' atDepartment ofEarth Sciences, James Cook University,
Townsville, Australia.
Background
Copyright1997 by the AmericanGeophysicalUnion.
Methanehydrateis restrictedto an uppermost depthzoneof
Papernumber96JB02941. 0148-0227/97/96JB-02941 $09.00
sediment columns in the marine environment. This zone, at 773
774
DICKENS ANDQ IN Y-HUNT:METHANEHYDRATESTABILITYIN POREWATER
any given location, lies between the sediment-waterinterface
hydratewill form and/ordissociate at a lowertemperature at andthesubbottom depthwherethegeotherm intersects a CHn- any given pressure. hydrate-waterequilibriumcurve (Figure 1)[Kvenvoldenand McMenamin, 1980].
Most BSRs on seismicreflectionprofiles are inferredto representan interfacebetweenan overlying zone of CH4 hydrateandan underlying zoneof freeCH4 [e.g.,Singhet al., 1993; Lee et al., 1994; Katzman et al., 1994; Singh and Minshull, 1994]. This interpretation is stronglysupported by recentinvestigations of the OceanDrilling Program(ODP) at the Chile Triple Junction(Leg 141 [Bangset al., 1993;Brown andBangs,1995]),at theCascadia Margin(Leg 146 [MacKay
Most hydrate in the marine environmentcontains>98.5%
CH4 [Kvenvolden, 1993].Thusfor a givengeotherm thedepth rangeoverwhichCH4hydrateis stableandthedepthof a BSR are expectedto dependon porewatercomposition. The effect
of dissolved ionsuponthestabilityrangeof CH4 hydratein themarineenvironment is significant. For example,at a locationwitha waterdepthof 675m, a bottomwatertemperature of 5.5øC,anda geotherm of 0.051øC/mthetotaldepthof the CH4 hydratestabilityzonewouldbe decreased fromapproxi-
mately100 rn to 75 rn if pureCH4 hydratewas formedfrom et al., 1994;Daviset al., 1995]),andat theBlakeRidge(Leg seawater ratherthanpurewater(Figure1). Recentinvestiga164 [Paull et al., 1996;Holbrook et al., 1996]). Thus BSRs tionsat theChileTripleJunction, Cascadia Margin,andBlake are widely believedto be depthcoincidentwith an intersection Ridgeindeedhavedocumented significant shoaling of thehyof a geothermanda CHn-hydrate-water equilibriumcurve. dratestabilityzonefromthatexpected for theCH4-purewater
Pressures andtemperatures that definea CH4-hydrate-water system[Brown and Bangs,1995;Davis et al., 1995;Paull et equilibrium curvein anygivensystemdependon tracegasand al., 1996]. dissolvedion concentrations [Sloan, 1990]. Incorporation of Porewatersin whichCH4 hydrateis formedarecomposi(andpurewater)because tracegases(e.g., CO2, H2S, ethane,andpropane)into the hy- tionallymuchdifferentfromseawater dratelatticedisplacesthe CHn-hydrate-water equilibriumcurve of chemical diagenesis, ionic diffusion and fluid flow. suchthathydratewill form and/ordissociateat a highertem- Therefore it is of interestto investigations of naturalCH4 perature at any given pressure.Addition of dissolved ions to
water shiftsthe CHn-hydrate-water equilibriumcurvesuchthat
hydrateto knowhow variationsin porewatercomposition
affectthepressure andtemperature conditions thatdefineCHnhydrate-waterequilibriumcurves [Hyndmanet al., 1992; Westbrook et al., 1994;UsslerandPaull, 1995;Kastneret al., 1995].
0-0 f''''I''''I''''I',,, 0 Methane-hydrate-water equilibriumcurve
Seawater
Pure water
2.0
200
4.0
-..;•
•
Pieroen[1955]presented a simplerelationship to describe thereciprocal temperature offset(at a givenpressure) between theCH4-hydrate-water equilibrium curveof theCH4-pure water systemandthatof certainCH4-water-alcohol systems:
=/•r-IDIS • IT• lnaw 1 Ta 11'
Hydrotherm 400
(3)
whereAHDIs is theenthalpy of dissociation of CH4hydrate, n is the numberof watermoleculesin the hydrateformula
6.0
(CH4.nH20), R isthegasconstant, andT• andTd arethetem._
8.0
Pure waterSeawater
peratures at whichCH4hydratedissociates in purewaterandin an water-alcohol solution,respectively. The equationis a for-
Geotherm
%
Methane Hydrate Stability Zone
' " -',
10.0
800
-5
I .... 0
I , , , , I , , , , 5
10
derivedfromclassical thermodynamic theorygiventhefollow-
ingassumptions: (1) negligible CH4 exists in water,(2) negligiblewaterexistsin gaseous CH4,(3) AHDI s is constant over 1000
Dissolved ions.• 12.0 ....
malexpression of theHammerschmidt Equation andis easily
smalltemperature ranges,and(4) theeffectof addingalcohol is only to reduceaw. Experimental datawere shownby Pieroen [1955] to verify equation(3) for water-alcohol solutions.
1200 15
Temperature (øC)
Figure 1. The zone of CH4 hydratestability in the marine
Severalauthors[e.g.,Hollisterand Burruss,1976;Menten
et al., 1981;Englezosand Bishnoi,1988;Diamond,1994] havesuggested that,similarto alcohol, theonlyeffectof dis-
environment lies between the sediment-water interface and the
solvedionsuponCH4 hydratestabilityconditions is to reduce
and geothermal gradient (5.5øC + 0.051øC/m below the
tionsof a CH4-hydrate-water equilibrium curvein anygiven
(3) therefore should alsoapplyto electrolyte sointersection of the geothermal gradientand a CHn-hydrate- aw. Equation by Mentenet al. [1981]) andoffersa water equilibrium curve [after Kvenvolden and McMenamin, lutions(as mentioned condi1980].The sediment-water interface(675 rn belowsealevel) very simplemethodto estimatepressure-temperature seafloor) on thisdiagramarethosefor OceanDrillingProgram pore water (note that Englezos and Bishnoi [1988] and (ODP) Site 892 [Westbrooket al., 1994].The depthaxison Dholabhai et al. [1991]haveofferedanalternative, yetrelathisdiagramassumes a hydrostatic pressuregradientof 0.010 tivelyinvolved,statistical thermodynamic method). MPa/m.The CH4-hydrate-water equilibrium curvesfor thepure water and seawatersystemsare from Sloan [ 1990] andDickens
and Quinby-Hunt [1994], respectively.Note that dissolved Approachand Methodof Study ionsshift the CH4-hydrate-water equilibriumcurve suchthat The experimentalportionof this investigationwas dethe zone of CH4 hydratestabilityis shallowerthan would be signed to testtwo relatedhypotheses: (1) thatthereciprocal expected fromconsideration of theCH4-purewatersystem. temperature offsetof CH4 hydratedissociation, 1/T• minus
DICKENSAND QUINBY-HUNT:METHANEHYDRATESTABILITY'IN POREWATER
775
1/T d, for anyelectrolytesolution,is linearlyrelatedto ln aw portedpuritiesin excessof 99.7% exceptCuC12.2H20,which at a givenpressure;and (2) if so, that the "slope"of this rela- has a reportedpurity of 98%. Methaneusedin theseexperitionshipis equivalentto •lms/n. Our experimentalapproach mentswas suppliedthroughAirco Gasesandhasa reportedpuwas as follows. rity in excessof 99.99%. Pressureand temperatureconditionsof CHa-hydrate-water The reciprocal temperatureoffset (at a constantpressure) equilibriumcurvesfor a variety of CHa-water-electrolytesys- andIn aw were determinedfor eachof the 10 electrolytesolutems,including solutions containing SO42',Br', Mg2+,NI-I4+, tions analyzedhere and for those presentedby de Roo et al. andCu2+,weredetermined byusingtheexperimental apparatus[1983], Dholabhai et al. [1991], andDickensand Quinby-Hunt andproceduredescribedby Dickensand Quinby-Hunt[1994]. [1994]. A fourth publishedexperimentaldata set concerning The aboveions were chosenbecausethey are of particularin- C H4 hydrate stability conditions in electrolyte solutions terest to investigationsin the marine environment and be- [Kobayashi et al., 1951] appearsto be (for an unexplained causepreviousexperimentalwork regardingCH4 hydratesta- reason) incorrect [Diamond, 1994] and is not discussedin this bility conditionsin electrolyte solutionshave focusedonly paper. Thevalue1/T• minus1ITd wasdetermined at a conon solutions containing CI', Na+, K+, andCa2+(withtheex- stantpressure,as shownin Figure2. The aw for single-elecception of artificial and actual seawater).Errors in reported trolyte solutions was calculated via the Pitzer technique temperatures andpressuresare within 0.2øC and 0.07 MPa, and previouswork has shownthat our apparatusandproceduregive Table 1. MethaneHydrateDissociationTemperatureat pressures and temperatures for the CHa-hydrate-waterequilib- ConstantPressurefor SolutionsExaminedin This Study rium curveof the CI-I4-purewater systemthat are within analytical precisionof those obtainedby using other apparati and Solution T, K P, MPa procedures[cf. Sloan, 1990; Dickens and Quinby-Hunt,1994]. 268.2 4.21 Note, however, that two recent experimental investigations (A) 1.998 m NaCl + 2.001 m NaCI 269.4 4.90 concerningCH4 hydratestability in electrolytesolutions[de 270.8 5.52 Roo et al., 1983; Dholabhai et al., 1991] have used apparati 272.8 6.89 andproceduresdifferentfrom ours. 273.6 7.72 274.5 8.34 Electrolyte solutionswere preparedby dissolvingknown masses of various salts into 250 ml of deionized water. Masses
of salt were determinedby using a balancewith an accuracy greaterthan0.001 g. Saltsusedin theseexperiments were obtained from Baker (B), Fisher (F), and Mallinkrodt (M) and in-
cludedNaCI(B ), KClfB),MgSO4(M), NaBr(M), MgC12.6H20(F ), NH4CI(B ), Na2SO4(B), andCuC12.2H20(B ). All saltshavere-
(B) 1.000 m NaCI + 1.001 m KCI
(C) 1.001 m KC1
+ 1.000m MõSO4
0.8
ßInP = 30.98 - 8206(1/T) r>.999 ß InP = 30.52 - 7927(1/T) r>.99
1.0
(D) 1.000 m NaBr
1.2
(E) 1.096m MgSO4
1.4
•1.6
(F) 1.001m MgCl2 + 1.000m NHnC1
mmmmmmmmmmmmmmmmmm•mmmmmmm mmmmmmmmmm P = 7.40 MPa
,
(G) 0.889m MgCI2
2.2
2.4
375
370
365
360
355
350
345
(I-I) 1.001m NIt4C1
1/Temperature(K) x 105 Figure 2. The reciprocal absolutedissociationtemperature (I) 0.333m CuC12 varies nearly linearly with the logarithm of pressurefor any
electrolyte solution.The reciprocal temperature offset,1/T•' minus1/Td, produced by dissolved ionsin anelectrolyte solution canbe estimatedat a given pressurefrom leastsquareserror curveequationsthroughexperimentaldata for CH4 hydrate stability in pure water and that in the electrolyte solution. Shown here are experimental data for CH4 hydrate stability conditionsin pure water (compiledby Sloan [1990]) and a 11.74 wt % NaC1 solution [de Roo et al., 1983].
(J) 0.394m Na2SO4
271.3
3.45
274.6 276.3 277.9 279.0 279.5
4.55 5.58 6.76 7.58 7.93
272.3
3.45
274.6
4.27
276.3
5.24
278.6 279.6 279.9
6.69 7.45 7.58
271.8
2.69
275.0 277.5 279.6
3.86 5.03 6.21
280.5
6.89
274.9
3.52
276.7 279.3 281.6 282.3
4.21 5.58 6.89 7.65
269.4 271.0
3.52 4.21
273.8 274.9 275.7
5.58 6.27 6.83
274.4
4.21
275.7 277.1 278.2 279.4
4.83 5.52 6.21 7.10
275.8
4.14
277.3 279.2
4.83 5.86
280.5
6.89
275.1
3.45
277.1 278.2 279.9 281.3
4.14 4.83 5.52 6.55
275.1
3.45
277.1 278.2 280.9 282.1
4.27 4.90 6.21 7.03
776
DICKENSAND QUINBY-HUNF:METHANE HYDRATESTABIIlTY IN POREWATER
(summarized by Pitzer [1991] andin Appendix1). The aw for mixed electrolyte solutionswas calculatedaccordingto the Patwardhan and Kumar [1986] approximation(Appendix 1). This latter approachhas a predictiveaccuracyof within 2% [Patwardhan and Kumar, 1986] and is much simpler than the rigorousion interactionmethodfor determiningaw of mixed electrolyte solutions [Pitzer, 1991; Clegg and Whitfield, 1991]. The Debye-Hiickel parameterand virial coefficients neededfor the above aw calculationswere takenfrom Pitzer [1991] and are for 0.1 MPa and 25øC.The choiceof usingthe Debye-Hilckel parameter and virial coefficients at standard temperatureand pressure(STP) arisesbecausevaluesat lower temperatureand, especially,higher pressureare not well constrainedfor many salts and becausepressure-temperature corrections to these values result in slight (although significant asdiscussed below) changesto aw.
Resultsand Experimental Discussion Pressures and temperatures at whichCH4 hydratedissociates in the 10 CH4-water-electrolyte systemsare reportedin Table 1. The pressure-temperature conditionsthat define the CH4hydrate-waterequilibrium curve for each of theseelectrolyte solutions(Figure 3) as well as thoseof de Roo et al. [1983], Dholabhai et al. [1991], andDickensand Quinby-Hunt[ 1994]
demonstrate that1/7'variesnearlylinearlywithlnP(r2 > 0.99 for all electrolytesolutions).The slope(m) andy intercept(b) for leastsquareserror curve equationsthroughdata in 1/T versus lnP spaceare presentedin Table 2. Table 2 also lists the calculatedIn aw (at STP) for each of the experimentalsolutions and the observedreciprocaltemperatureoffset between the CH4-hydrate-water equilibriumcurveof the CH4-purewater system(compilationof Sloan [1990]) and that of CH4-waterelectrolytesystemsat two pressures, P = 3.32 and 7.40 MPa.
The slopem is not constantfor all solutionsandmay be explained by experimental error. For example, the observed rangein m for the 10 solutionsof this studyis 554 (K), and this range is about that expectedfor our estimatedanalytical errors and number of analyses (0.996) at anypressure spanned by theexperimental data. At pressuresat the limits of the data set, P = 3.32 MPa and
7.40 MPa, the relationshipbetweenthe reciprocaltemperature of dissociationand calculatedIn aw (at STP) canbe described by the followingempiricalequations(Figure4):
I 1 1.I,P=3.32M (4)
lna w+0.00207 =1118(K) T• Td and
lna w +0.00624= 1089(K)I½• 11'P=7.40 MPa, (5) Td
where K is kelvin.
ExperimentalSolutions
(A)1.998 mNaCl +2.001 mKCl
(F)1.001 mMgC12+ 1.000 mNH4Cl
(B)1.000m NaCl+ 1.001m KCl (C) 1.001m KCl+ 1.000m MgSO4
(G)0.889m MgCl2 (H) 1.001mNH4Cl
(D) 1.000 m NaBr
(I) 0.333 m CuCl2
(E)1.096mMgSO 4
(J)0.394mNa2SO4
0.8
0.8
1.0
1.0
1.2
1.2
1.4
1.6
1.8
.1.8 _c2.0 2.2
F
2.0
G
-
2.2
I J 2.4
2.4
375
370
365
360
355
350
345
375
370
365
360
355
350
345
1/Temperature (K)x 105 Figure 3. Methanehydratestabilityconditions(in 1/T versusIn P space)for the 10 solutionsanalyzedin this study.Data for the CHn-purewatersystemare from Sloan [ 1990].
DICKENS ANDQUINBY-HUNT: METHANE HYDRATE STAB• INPORE WATER
777
Table 2.Parameters Describing Experimental Methane Hydrate Stability Conditions inPure Water andMixed Electrolyte Solutions andtheOffset Between Predicted andObserved Methane Hydrate Dissociation Temperature atTwoPressures 1/Tø- l/T, x 10• Experimental Solution
Deionized water
Reference rn
1.096 rnMgSO4 1.001 rnNH4C1 0.889 mMgCI2 0.394 mNazSO4 1.001 rnMgCI2 +1.000 rnNH4CI 0.333 rnCuCI 2
3.32MPa
7.40MPa
-1.34 -1.52
-0.02 0.11
-0.20 -0.28
-7.57 -10.73
-0.28 -0.16
-0.25 -0.27
0.0000
3 3 3 3 3 3 3 3 3 3 3
-7595 -7495 -8144 -8153 -8118 -8113 -8390 -7945 -7971 -7898 -7884
28.86 28.61 31.15 31.41 31.55 31.76 33.00 30.28 30.52 30.48 30.66
-0.0176 -1.35 -0.0322 -2.85 -0.0575 -4.94 -0.0894 -7.72 -0.1281 -10.99 -0.1620 -13.87 -0.1897 -16.25 -0.0329 -3.13 -0.0553 -4.96 -0.0908 -7.90 -0.1205 -10.87
-0.57 -1.93 -4.86 -7.66 -10.89 -13.76 -16.47 -2.81 -4.67 -7.52 -10.47
-7927 -7940 -8449 -8726 -7899
30.52 31.01 33.34 34.74 30.33
-0.0820 -0.1378 -0.1970 -0.2395 -0.0683
-8026 -8301 -7943 -7809 -7748 -7956
30.45 31.51 30.38 29.64 30.02 30.15
-0.0211 -1.60 -0.0325 -2.34 -0.0513 -4.55 -0.0151 -1.29 -0.1034 -9.15 -0.0153•'-1.07
-6.72 -12.29 -17.81 -22.08 -5.49 -4.56 -12.75 -2.54
3 3 4 4 4 4
0.00
7.40MPa
30.98
0.590 rnNaC1 +1.036 rnCaCI2 1.222 mNaC1 +1.073 mCaClz
1.001 rnKCI+ 1.000 rnMgSO4 1.998 rnNaCI +2.001 rnKCI 1.000 rnNaBr
3.32MPa
-8206
2 3
2.276 mNaCI 3.537 mNaCI 4.687 mNaCI 5.427 mNaCI 1.000 mNaCI + 1.001 rnKCI
Inaw
1
Monterey seawater (•33.5%o) Synthetic seawater (•35%o) 0.529 mNaCI 0.546 mNaCI +0.428 rnKCI 0.951 mNaCl +0.747 rnKCI 1.006 rnNaCI + 1.575 rnKCI 1.069 rnNaCI +2.515 rnKCI 2.196 mNaCI +2.064 mKCI 3.330 rnNaCI + 1.392 rnKCI 0.546 rnNaC1 +0.288 rnCaC12 1.128 rnNaC1 +0.297 rnCaC12 1.967 mNaC1 +0.311 rnCaClz 2.030 rnNaC1 +0.641 rnCaCI2
b
-8103 30.72 -0.0180 -1.47 -8343 31.59 -0.0189 -1.36
-8010 30.89 -0.0851 -7.81 -8235 31.96 -0.1191 -10.69
-8084 -7978 -8183
-7.06 -12.62 -17.53 -21.50 -5.87 30.91 -0.0566 -4.71 31.19 -0.1498 -13.03 31.10 -0.0345 -2.56
Tobyrye d- Tpredic•d, øC
0.00
-1.39 -2.45 -4.23 -0.80 -8.57 -0.75
0.03 -0.12 0.02 0.07 0.20 0.31 0.37 -0.28 -0.14 0.03 -0.20 0.07 -0.34 -0.06 -0.17 0.04 0.06 0.14 0.25
0.07 0.29 -0.11 -0.09 -0.06 0.10
0.38 0.36 -0.12 -0.01 0.23 0.41 0.28 -0.29 -0.13 0.19 0.02
0.19 -0.15 -0.21 -0.46 0.17 -0.02 0.33 0.05
-0.02 -0.03 -0.07 0.02 0.27 0.07
References are(1)compilation bySloan [1990], (2)Dickens and Quinby-Hunt [1994], (3)Dholabhai etal.[1991], and (4)deRoo etal.[1983]. The parameters rn(slope) and b(yintercept) arefrom least squares error curve equations through experimental data in1/Tversus logP space (Figure 4),with Tinkelvins, and Pinmegapascals. The activity ofwater (aw)has been calculated according toPitzer [1991] forsingle-salt solutions and Patwardhan andKumar [1986] formixed electrolyte solutions. TheDebye-Htickel parameter and vidalcoefficents used tocalculate
awarefromPitzer [1991] andarefor0.1MPaand25øC.
tThepurity ofthesalt used (-98%) may introduce asignificant error (-0.002) into thecalculation oflnaw.
between The coefficients of 1/T• minus1ITd in the aboveequa- similarfor all electrolytesolutions,the relationship tionsshouldbe equivalent to AHDis/nRif the assumptions1/T• minus1/Td andlnaw at STP(i.e.,theslopein the should be greater thanthatexpected at low behind equation (3) arevalidandlnaw for eachsolution has aboveequations) andtemperature, similarto thatexpected atmoderate beencalculatedcorrectly.Handa [1986] determined via pressure
calorimetry that AHDi s for CH4.(6.0ñ 0.01)H20is 54.2ñ 0.28kJ/mol(at 273K), andthesevalues constrain AHDis/nR forCH4.6.0H20 to between 1079and1093(K). Thecoefficient of equation(5) thereforeis withinthe rangeof
pressure andtemperature, andlessthanthatexpected at high
pressure andtemperature. A variable coefficient of 1/T• minus 1/Td inequations such asthose above reflects theuseofvirial coefficients andDebye-Htickel parameters at STPfor condi-
AHDis/nR determined bycalorimetry, whereas thecoefficienttions other than STP. Agreement between theslopes of linearempirical equations of equation (4) is slightly (butsignificantly) greater thanthis
by range.Theseobservations areexplained in partby pressure- (suchas thoseabove)and the AHDis/nRdetermined calorimetry verifies the assumptions underlying equation (3) temperature effectsoncalculated Inaw. demonstrates thattheonlyeffectof dissolved ions Virial coefficientsfor NaC1 andthe Debye-HOckelparameter andclearly
of CH4hydrate istoreduceaw. The agreement atpressures of0.1and20MPaandtemperatures of0øC,10øC, onthestability
is nearlyconstant overa wide and25øChavebeentabulated by Pitzeret al. [1984].Although alsoimplies(1) that AHDis/n of n and/or (2) thattheaverage hydrate beingformed in thesevaluesarenot current(i.e., vidal coefficients at STP are range has a composition approximating not identicalto thoseof Pitzer [1991]), they canbe usedto the variousexperiments
verification of equation (3) implies evaluate general pressure-temperature effects uponcalculatedCHn.6H20.Furthermore, thatthereis a linearrelationship betweenthe reciprocaltem1haw (Figure 5).Asexemplified bya 2.276m NaC1solution, offset of theCHn-hydrate-water equilibrium curveand theInaw adjusted forpressure andtemperature isslightly less perature pointdepression of icein anyelectrolyte solution thanthatcalculatedat STP whentemperatures andpressures are thefreezing (as alluded to by Menten et al. [1981]). The equation thatdelow.With increasing pressure andtemperature, however, the scribes the temperature depression of ice in an electrolyte Inaw adjusted forpressure andtemperature approaches andsur(relativeto thatin purewater)is similarto equation passes thatcalculated atSTP.Given thatthemagnitude ofthis solution effectisproportional toInaw andassuming thatthiseffectis (3):
778
DICKENSAND QUINBY-H•:
-0.25
METHANEHYDRATESTABILITYIN POREWATER
ß' ' ßI ' ' ' " I " ' ' ' I ' ' ' ' I ' • ' '
ßP=3.32 MPa
/
ß P = 7.40 MPa
-0.20
œorinaccuracy(i.e., the differencein temperature betweenan observedvalue and a value predictedby a linear equation) arisesfrom the rangein rn of experimentalsolutionsand not
fromassumptions behindequation(1) or techniques for calculating In aw (indeed,thereis a moderatecorrelationbetween
inaccuracy andm). As such,anyof theaforementioned explanationsfor theobserved rangein m couldexplaintheinaccuracyof the methodto predictstabilityconditions alongthe CH4-hydrate-water equilibriumcurve.Thereare,however,two
-0.1 5
•
-0.10
important points.If theobserved rangein m principally reflectsexperimental error,thenthe accuracy of usinga linear equation (e.g.,equation (4) or (5)) topredicta CH4 hydrate dis-
Slope ~ AH DIS
sociationtemperatureis better than 0.46øC. Likewise, if the observedrange in m principallyreflectsdifferencesin the -O.05
AHDis of CH4.nH20,thenfora hydrate of a givenAHDi s (and n) theaccuracy of usinga linearequation topredicta CH4hydratedissociation temperatureis betterthan0.46øC. -
0 0
•
,
ß I
-
-5
ß ,,
= I
-10
ß
ß ß ß
I
.
•
I
-15
I
I
I
I
-20
I
I
-25
Methane Hydrate Stability in the Marine Environment
[1/T•-1/Td] x105
The stabilityconditions of CH4 hydrate(assuming a fixed composition, n) in association with any marine pore water temperatureoffset of CH4 hydrate dissociationin an electrolytesolutionandcalculated In aw (according to Patwardhan shouldbe directlyrelatedto activityof theporewater.The inmarineprocesses affectthepressure-temand Kumar [1986] and Pitzer [1991]) of the solutionat two quiryof howvarious conditions of theCH4-hydrate-water equilibrium curve pressures, 3.32 and7.40 MPa.The correlation coefficient (r2) perature betweenthe two parameters exceeds0.996 at anypressure be- [Hyndmanet al., 1992; Westbrooket al., 1994; Ussler and tween3.32 and 7.40 MPa. The slopeof this relationshipis Paull, 1995;Kastneret al., 1995]is therefore a question of 1118(K) at 3.32 MPa and1089(K) at 7.40MPa.Theseslopes how thesesameprocesses affect aw. Two relativelybasic shouldbe equivalent to AHDis/nR,whichis between1079 and scenarios concerning howtheCH4-hydrate-water equilibrium 1093 (K) [Handa, 1986]. curve varies with salinity and chemicaldiagenesisare Figure 4. The relationship betweenthe observedreciprocal
considered here.
In aw =
œ
-
,
(6)
exceptthatAHFus(i)is theenthalpy of fusionforpurewaterto ice (6008J/toolat 273.2K) and T• and Tf arethe fusion (melting)temperatures of ice in purewaterandan electrolyte solution,respectively. Hence,by combining andrearranging
-0.083
''''1''''1''''1''''1''''1''''1''''
-0.082
-0.081
equations (3) and(6) therelationship betweenthe temperature offsetof the CI'I4-hydrate-water equilibriumcurveand that of the ice-waterequilibriumcurvein any electrolytesolution(at
-0.080
constantpressure)is -0.079 ß
T•
Hydrato ZMC/DIS Ic•
This relationship may be of interestto shipboard investigations,inasmuch astheCI-I4-hydrate-water equilibriumcurveof a particularpore watermight be estimatedquicklyfrom the freezingpointof the pore water. A linearequationcanbe usedto predictthe stabilitycondi-
-0.078
'
P = 0.1 MPa
,•
P = 20 MPa
ß
P = 40 MPa
,,.-I..-.I.,..I,.,.I.,.,I,,..I....
-0.077 -5
0
5
10
15
20
25
30
Temperature(øC)
tionsalonga CI-I4-hydrate-water equilibrium curvein anyelec- Figure5. Theeffectof pressure andtemperature uponcalcuaccording to dataof trolytesolution(e.g.,porewaters)providedthatIn aw canbe latedInaw for a 2.276-mNaC1solution lowpressure andtemperature determined. The accuracyof usingthis approach to estimate Pitzeret al. [1984].At relatively for the CH4-hydrate-water equilibrium curve(via lnaw calcula- the In aw of a solutionis slightlylessthanthatcalculated at STP.However,withincreasing pressure tionsaccordingto the techniques of Patwardhanand Kumar thesamesolution andtemperature the In aw of a solutionapproaches and sur[1986]andPitzer [1991])is suchthata linearequation (e.g., passes that calculated for the same solution at STP. Thus the equation(4) or (5)) canpredictthe CH4 hydratedissociation linearrelationship betweenreciprocaltemperature offsetof temperature within0.46•C from thatobserved for anyexperi- CH4 hydratedissociation and calculated1haw at STP mental solutionand at any pressurebetween3.32 and 7.40 (equations (4) and (5)) is slightlydependent on the presMPa (Table2). Moreover,we suggest thattheprimarycause sure/temperature regimeof interest(seetext).
DICKENSAND QUINBY-HUNT: METHANE HYDRATE STABR.1TYIN POREWATER
Table 3a. ApproximateCompositionof 30%00xic and Euxinic Seawaterin Terms of Molarity (M) and Molality (m) Constituent
Ion
Oxic Seawater
Euxinic Seawater
m, mol/kg
M, mol/L
m, mol/kg
CI' Na+
0.48009 0.41182
0.48492 0.41596
0.50700 0.44400
0.51210 0.44847
Mg2+ SO_• •'
0.04685 0.02482
0.04732 0.02507
0.02780 0.00000
0.02808 0.00000
HCO3'
0.00205
0.00207
0.01500
0.01515
0.00909 0.00871
0.00918 0.00880
Br' • Sr•
0.00072 0.oooo6 0.0000•
0.00073 0.o0oo6 0.0000•
NHn+
0.00000
0.00000
Table 4. Calculatedlnaw and TheoreticalMethane Hydrate DissociationTd at 3.32 and 7.40 MPa in Various Salinities of Seawater
M, mol/L
Ca2' K+
0.00600 0.00760
(0.00320) (0.0o006) (0.00004)
0.00600
0.00606 0.00768
0.00323 0.o0oo6 0.0oo04
Seawater Pure water
5%o
10%o 15%o 20%o
25%o
0.00606 309'oo
Molarity concentrationsfor oxic seawaterare extrapolatedfrom Clegg and Whitfield [ 1991], and molarity concentrations for euxinic seawater are from ODP Site 892 [Westbrook
779
et al.,
35%O
1994].
Concentrations for Br', F', andSr2+ are estimatedfor the euxinic 40%o seawater. Boric acid and trace elements are not considered here.
45%o 50%o 55%o 6•oo
Calculatedlnaw 0.0000
-0.0027 -0.0030 -0.0054 -0.0050 -0.0081 -0.0080 -0.0103 -0.0101 -0.0134 -0.0131 -0.0161 -0.0161 -0.0189 -0.0192 -0.0216 -0.0222 -0.0244 -0,0272 -0.0301 -0.0330
(PK) (CW) (PK) (CW) (PK) (CW) (PK) (C-'W) (PK) (CW) (PK) (C-'W) (PK) (CW) (PK) (C%V) (PK) (PK) (PK) (PK)
Tdat 3.32 MPa, øC
Td at 7.40 MPa, øC
2.60
10.53
2.41 2.39 2.23 2.26 2.05 2.05 1.90 1.91 1.69 1.71 1.51 1.51 1.32 1.30 1.14 1.10 0.95 0.76 0.56 0.37
10.33 10.31 10.13 10.16 9.93 9.94 9.77 9.78 9.54 9.56 9.34 9.34 9.14 9.11 8.94 8.89 8.73 8.53 8.32 8.11
In determiningthe ln aw of natural waters it typically is convenientto describethe mixed electrolytesolutionin terms of the component neutralsaltsthat couldbe combinedto make the solution[e.g., Clegg and Whitfield, 1991]. Table 3 gives the compositionof "artificial" seawater at 30%0 salinity in termsof its componentneutral salts(extrapolatedfrom Clegg and Whitfield [1991]) and the lna w of this mixed electrolyte solution (at STP) calculatedby two different methods.The value -0.0161 is estimatedby both a rigorousion interaction method that includes a treatmentfor boric acid [Clegg and Whitfield, 1991] and the Patwardhan and Kumar [1986] approximation(using data of Pitzer [1991]) with no treatment
Using the same approach,CH4 hydrate dissociationtemperatures for seawaterat salinitiesother than 30%0can be easily calculated (Table 4). Note that the predicteddissociationtemperaturesfor 359'00seawateraxeidenticalto thoseextrapolated
forboricacid(because borate species arenotamenable tothis
•om
particularapproach).Using equations(4) and (5)(and the parametersfor the CH4-hydrate-waterequilibrium curve in the CH4-pure water systemfrom Sloan [1990]), we predict that CH4 hydratewill dissociatein 30%0seawaterat 1.51øC at 3.32 MPa and 9.34øC at 7.40 MPa (the significantdigits imply that the accuracyof equations(4) and (5) is better than 0.46øC).
thoseextrapolatedfrom "actual" Monterey Bay 33.5 + 0.5%0 seawaterdata (Table 2). Bacterial methanogenesisof organic matter is believed to be the sourceof CH4 for most marine hydrate [Kvenvolden, 1988, 1993]. Methanogenesis, however,is typically the last of a seriesof organicmatteroxidationpathwaysin the maxine environment[e.g., Froelich et al., 1979]. Prior to methanogenesis,organic matter is degradedby oxic respiration,deni-
Table 3b. ApproximateCompositionof 30%00xic and Euxinic Seawaterin Terms of ComponentNeutral Salts Component Salt
Oxic Seawater, mol/kg
Euxinic Seawater, mol, kg
NaC1
0.36369
0.43200
Na2SO4 NaHCO3
0.02507 0.00207
0.00000 0.01510
NaF KCl KBr
0.00006 0.00807 0.00073
0.00006 0.00600 0.00170
MgCI2 CaC!2 S•rl 2 NH4C1
0.04732 0.00918 0.00008 0.00000
0.02810 0.00606 0.00004 0.00610
NaBr
0.00000
0.00150
lna•,
-0.0161
-0.0169
Calculatedlna• is via the techniques of PatwardhanandKumar[ 1986] and Pitzer [ 1991].
For calculationof lna•, PK refersto the Patwardhan and Kumar [1986] approximation technique, and CW refers to ion interaction
methoddescribedby Clegg and Whitfield[1991]. The CH4 hydrate dissociation temperatures are determinedaccordingto equations(2) and (3) in text.
"artificial"
359'00seawater data and within 0.1øC less than
trification, Fe-Mn oxide reduction, and surfate reduction. Each
of thesereactionssignificantlychangesthe chemicalcompositionof seawatersuchthat in sedimentwheremethanogenesis occurs,porewatersaremarkedlydifferentfrom seawater.They
invar.iably aredepleted in 0 2 andSO42',deficient in Ca2+and Mg2+(viacarbonate precipitation), enricked in NH4+ andvarioustracemetals,andelevatedin Br' (rel,easedfrom organic matter). It is expected, and indeed it has been documented
[Kvenvolden and Kastner,1990;Kastneret al., 1990;Von Breymannet al., 1990; Westbrooket al., 1994;Kastneret al., 1995; Paull et al., 1996], that CH4 hydratein the marine environmentshouldoccurin association with these"euxinic"(0 2
andSO42'depleted) seawater solutions. Table 3a providesmol•ities determinedon shipfor various
ionsin a -30%0euxinicporewaterthatwascollected nearhydratedsediment at ODP site892 [Westbrook et al., 1994]. Table 3a also gives the molalities of these ions. Table 3b gives the approximate concentrationsof componentneutral salts that can form such a solution. Concentrations of Br', F-,
780
DICKENSAND QUINBY-HUNr: METHANE HYDRATE STABI11TYIN POREWATER
andSr2+werenotdetermined onshipforthisporewater;we pH and high pCO2 is an intriguing theoreticalmechanismto thus have assumed molarities
for these ions in accord with
concentrations observedin othereuxinicpore waters[Kastner et al., 1990; Von Breymannet al., 1990] suchthat the sumof
decreasethe stabilityof CH4 hydratein euxinic pore water in
relationto that in oxic seawater(assumingthatpCO2 is sufficienfiylow thatCO2 doesnot enterthe hydratelattice). Previousworkershaveusedexperimental datafor pureCH4NaC1 solutionsin order to estimatepressureand temperature
componentneutral salts can form the solution. Of interest in Table 3 is that the calculatedIn aw of this euxinicporewater is close to the calculatedln aw of a similar salinity seawater conditionsof the CH4-hydrate-waterequilibriumcurve for the solution.Hence the stability conditionsof CH4 hydratein this pure CH4-oxicseawatersystem. For equivalentsalinitysolutions,the In aw of a NaC1solutionis significantlylessthan particular euxinic pore water are similar to those in oxic (in partbecause of SO42- ion interaction seawater, even though the actual compositionof the pore thatof oxicseawater water is significantlydifferent. Note, however,that pore water in seawater). Thus CH4 hydrateis significantlylessstablein compositionsdeterminedon ship are not at in sire pressure- NaC1 solutions than in equivalent salinity seawater (as temperatureconditionsand that "core retrieval" effects on the observed in experimental data and noted in Dickens and chemical compositionof pore water are poorly constrained Quinby-Hunt [1994]). (such as from CO2 degassing during pressure loss; see Recentinvestigations concerningin situ pressuresand teminorganicgeochemistrysection,Sites 994 and 995, Paull et peratures[Brown and Bangs, 1995; Davis et al., 1995] have al. [1996]). shownthat the BSR is at a depth approximatelycoincident conditionsof the A recurringissue in geophysicalliteratureconcernswhich with that expectedfrom pressure-temperature equilibriumcurvefor thepureCH4-seawater CH4-hydrate-waterequilibriumcurveis appropriatefor under- CH4-hydrate-water system[Dickens and Quinby-Hunt, 1994]. Thus Brown and standingthe sedimentaryzone of CH4 hydrateand the depthof that the BSRs [e.g., Hyndman et al., 1992; Westbrooket al., 1994; Bangs [1995] andDavis et al. [1995] have suggested CH4-hydrate-seawater equilibriumcurveis appropriate for unBrown and Bangs, 1995, Kastner et al., 1995; Davis et al., thesedimentary zoneof CI-I4hydrateandthedepth 1995]. It should be clear from the work presentedhere that derstanding Implicit in this suggesthere is no unique answerto this question.A range of CI-I4- of BSRs in the marineenvironment. hydrate-waterequilibrium curves should be expectedin the tion is that the aw of pore water is similarto that of seawater marine environment. The magnitude of this range will be in all marinesedimentthat containsCH4 hydrate.Although dictatedby the naturalvariability of In aw of porewater. this supposition may be correct,it cannotbe rigorouslyevaluTwo general processesare of interestto geophysicistsbeated at presentbecausein situ pore water compositions have causethey may significanfiychangethe ln aw of pore water not yet been determined in sediment with CH4 hydrate. from thatof seawaterandhencethe CH4-hydrate-water equilib- Likewise,it is unclearif (and how) capillaryforcesandvariarium curvefrom that of the seawatersystem.This effectcan be tions in sedimentcompositionaffect pressure-temperature equilibriumcurves[cf. Cha et understoodby consideringthe two basic parametersthat affect conditionsof CH4-hydrate-water ln aw (equation(2)). An increase/decrease in the mole fraction al., 1988; Ouar et al., 1992; Clennell et al., 1995]. of water(Xw) of an electrolytesolutionwill increase/decrease ln aw . Thus processesthat significantlyincrease/decrease the Conclusion salinity of a solution (even without changing the relative The reciprocaltemperature offsetof CH4 hydratedissociaionic distribution)will decrease/increase the stabilityof CH4 hydrate(as discussedaboveand shownin Table 4). Suchpro- tion,1/T• minus 1/Td, is linearly related tolnaw at a given cesses include advection and diffusion of ions that have been pressurefor all electrolyte solutions examined to date. The suggestedto occur in sediment columns with CH4 hydrate "slope"of thisrelationship is equivalentto AHDis/nR.These [Kastner et al., 1990, 1995; Paull et al., 1996]. expectations are predictedfrom classicalthermodynamics and An increase/decrease in the activity coefficient of water provide a simple approachfor determiningstability condi-
equilibriumcurve in any (Yw) of an electrolytesolutionalso will increase/decrease tionsalonga CH4-hydrate-water ln aw. The Yw of an electrolytesolutionis highly dependent givenporewater.This approach(Appendix2) can be usedto on the distribution of dissolved ions within the solution estimate CH4 hydrate stability conditionsin hypothetical affectCH4 (becauseof ion-ion interactions).Thus processesthat change pore watersand to evaluatehow variousprocesses pore water composition (even without changing the mole fractionof water)can affectpressure-temperature conditionsof the CH4-hydrate-water equilibriumcurve.For example,a 0.5 m
hydrate stability conditionsin the marine environment.
Appendix 1: Calculation of the Logarithm of the Activity of Water exchange of SO42'and2Cl' therefore represents a mechanism The logarithmof the activityof water(lnaw) in thispaper
MgSO4 solution(ln aw = -0.0095) has a significantlyhigher Yw than a 0.5 m MgC12 solution(ln aw = -0.0255). Anion that can significantlychangethe stability of CH4 hydratein
was calculatedaccordingto the techniquesof Pitzer [1991] and
pore water.
Patwardhan and Kumar [1986]. They have thoroughly
The processof sulfatereductionshoulddecrease ln aw and CH 4 hydrate stability conditionsin pore water. However, the ln aw of the aforementionedeuxinic pore water is similar to that of equivalentsalinity oxic seawater(Table 3). It is suggested that much of this similarity arises becausesufficient
Ca2+andMg2+havebeenremoved fromtheeuxinicsolution (via carbonateprecipitation) to compensatefor the lack of
discussedthese techniquesthat are summarizedhere for the benefitof thereader.NotethatIn aw for a given solutionalso
canbe determined via relativelyaccessible computer programs (e.g., SOLMINEQ.88[Kharakaet al., 1988])or freezingpoint information(seeequation(6)).
The aw of a solutionis der'reed in equations (1) and(2) (see text).However,for purposes of calculation it is customary to
SO42-(viasulfate reduction). Suppression of carbonate precip- rearrangetheseequationsand introducea new parameter,the itation(andretention of dissolved Ca2+andMg2+)withlow molal osmoticcoefficient(•), that containsthermodynamic
DICKENS ANDQUINBY-HUNT: MEI'HANEHYDRATE STABILITY IN POREWATER expressionsfor chemicalpotentials[e.g., Pitzer, 1991]. Thus the In aw for single-electrolyte solutionsis oftenrewrittenas -18 vm
lna w = ••,
1000
(8)
781
Appendix2: Conditionsof Methane Hydrate Stability in Seawater In this appendixwe demonstratehow the approachdetailed in this paper can be used to determinea CH4-hydrate-water equilibriumcurve for a pore water of given ionic distribution.
The primaryobjectivethereforeis to calculateln aw of the is the molality of the electrolytesolution.For an electrolyte pore water. Once In aw has been calculated,the CH4-hydrateMX with vM positiveionsof chargezM andvx negativeions water equilibriumcurveof the pore water systemcan be easily determinedfrom that of the pure water system(e.g., equations of chargezx the molal osmoticcoefficientis (4) and (5)). The examplepresentedhere is oxic seawaterwith a salinity of 30%o. q)= l +[ZMzxlf q)+m(2VMV x/v)B•Mx Concentrationsof dissolvedions in pore water typically are presented in units of molarity. These concentrations are convertedto units of molality. This conversionis shown in Table 3 for seawaterwith a salinityof 30%0. where f• is anextended Debye-Hiickel termandB•MX and componentneutral salts that can be combinedto give C•x arevirialcoefficients. Theextended Debye-Htickel term theThe total molality of each ion are then determined.For most is water in the marine environmenta relatively small numberof componentsalts (99% of the total (10) ionic distribution.Concentrationsof componentneutral salts whereA• is the Debye-Htlckel parameter, I is the ionic in seawaterwith a salinity of 309'00are given in Table 3. The Patwardhanand Kumar [ 1986] approximationfor mixed strength of the solution,andb is a constant. Valuesfor A• solutions (equation (13))requires thatlnaw of each dependon temperatureand are given by Pitzer [1991]. The electrolyte componentneutral salt be calculatedat the sameionic strength valueforb is 1.2kgl/2/moll/2. Virialcoefficents C?• x aretabulated byPitzer [1991]; virial (I) as that of the given pore water. For the componentneutral saltsin seawaterwith a salinity of 30%o(Table 3), I is 0.6196. coefficents B•MX arecalculated asfollows. Forallelectrolytes The In aw of eachsalt at thisvaluethencanbe calculatedusing MX except2-2 salts, equations(8) through (10) and either equation (11) or (12) (Appendix 1). In the example presentedhere, considerthe (11) B•MXn(0)+n(1)exp(_tx/1/2) component saltsNaC1andCaC12.Tabulatedvalues(at 25øC) where u is the number of ions in the electrolyteformula and m
+m2[2(VMVX)3/2/v]C•Mx, (9)
fq)=-Aq)l 1/2/(l+bll/2),
forB(Nø)C1 , •NaCI' n(1) n(0) •'CaC12 ' and B(•)c12 are0.0765, 0.2664,
where B(M• 0) andBMX O) are parametersspecificto a given
0.4071, and 2.278, respectively[pitzer, 1991]. Thus, at I =
electro-
0.6196, thevirialcoefficients B•ac1 andBCaC12 • (witha =
lyte,anda hasa valueof 2.0kgl/2/mol 1/2(at 25øC).For2-2 2.0 kgl/2/moll/2) are 0.1317 and 0.8790, respectively salts (e.g., MgSO4), (equation (11)).The Debye-Hilckel parameter, A•, is 0.3915at 25øC[Pitzer,1991].Theextended Debye-Hiickel termf• (with b = 1.2 kgl/2/mol 1/2) is therefore-0.1585(equation
(10)).Tabulated values for CNaC1 • andCCaC12 • - (at 25øC) are
+n(2) oMXexp(_ot211/2 ),
(12)
0.00127 and -0.00064, respectively[Pitzer, 1991].Thus,at I
= 0.6196,theosmotic coefficient (q) ofNaC1(UM,ZM,UX,Zx = 1) is0.9236(equation (9)),andtheInaw of NaC1is -0.0206 specific to agiven (equation where B(•, B(•x, andBMX -(2)areparameters (8)).Likewise, •) ofCaC12 (uM,zx = !; ZM,UX= 2) is 2-2 electrolyte andal anda2havevalues of 1.4kgl12/mol 1/2 0.8646,andtheInaw o• CaC12is -0.0096.Usingthesame and12 kgl/2/mol1/2,respectively (at 25øC).Notethatvirial procedure,the ln aw of other componentneutral salts in coefficientparametersdependon temperature[Pitzer, 1991]. seawater(Table 3) at I = 0.6196 are as follows- Na2SO4 = In calculationsfor this paper, virial coefficientparametersat -0.0084; NaHCO3 = -0.0193; NaF =-0.0197; KCI = -0.0200; 25øC were used for all calculationsof In aw becausethesepa- KBr= -0.0202; MgC12 = -0.0098;andSrc12 = -0.0095. rametershave been tabulatedfor 25øC, becausethe approach The contributionof eachcomponentneutralsalt to the total for correctingthe parametersto temperatures otherthan 25øC Inawofthemixed electrolyte solution is•alcula.ted accord•g is relatively involved, and becausethe correctionsare rela- to equation(13). In the examplepresentedhere, consideragain tively minor for the temperature rangeof interest. the componentsaltsNaC1 and CaC12.Concentrations of NaC1 The ln aw for mixed electrolytesolutionswas determined and CaC12in seawaterwith a salinityof 30•0oare 0.36369 and according to thePatwardhanand Kumar [1986] approximation: 0.00918 mol/kg, respectively (Table 3). Concentrationsof
NaC1andCaC12in solutions containing only these saltsat an (13)
ionic strength(I = 0.6196) equivalentto that of seawaterwith a salinity of 30%o are 0.6196 and 0.2065 mol/kg, respec-
tively.Thusthe contributions of NaC! andCaC12'to theto{al ln aw of the example solution are -0.0121 and -0.0004, rewhere mk is the molality of electrolytek in the mixed elec- spectively (above and equation (13)). The contribution of o trolytesolution andrn• andaw,k arethemolality andactivity other componentneutralsalts(Table 3) to the total ln aw of of water (as calculated above) of a solution containingonly seawaterwith a salinity of 30•0oare as follows: Na2SO4 = electrolytek, whichhas the sameionic strengthas that of the -0.0010; NaHCO3 = -0.00006; NaF = -0.000002;KC1 = mixed electrolyte solution. -0.0003;KBr = -0.00002;MgC12=-0.0022; andSrC12 =
782
DICKF..NS AND QUINBY-•:
METHANEHYDRATESTABHATY IN POREWATER
-0.000004. The In aw of seawaterwith a salinity of 309'oo is therefore-0.0161 (equation(13)). The temperature offsetbetweenthe CHn-hydrate-water equilibrium curve of seawaterwith a salinity of 30%oand that of the pure water systemcan be estimatedfrom this calculated In aw. Usingequations(4) and(5), the temperature offsetfor a solutionwith an lna w of-0.0161 is approximately-1.1øCto -1.2øC at a given pressure.For comparison,laboratoryresults indicatethat the temperatureoffsetbetweenthe CHn-hydratewater equilibrium curve of actual seawaterwith a salinity of 33.5%oand that of the pure water systemis -1.1øC [Dickens and Quinby-Hunt,1994]. Acknowledgments. We sincerelythank E. D. Sloan, W. S. Holbrook,M. K. Tivey, andJ'.R. O'Neil for valuablecomments thatimprovedthe qualityof this manuscript.Fundingfor G. Dickenswasprovidedby the U.S. Departmentof Energyunderappointment to Graduate Fellowshipsfor Global Changeadministered by Oak RidgeInstitutefor Scienceand Education(ORISE). Fundingfor M. S. Quinby-Huntwas providedby LaboratoryDirectoryResearchDevelopmentfundsunder contract DE-AC030-76f00098.
References Bangs,N.L.B., D.S. Sawyer,and X. Golovchenko,Free gasat the base of the gas hydratezone in the vicinity of the Chile triple junction, Geology,21,905-908, 1993. Brown, K.M., and N.L. Bangs,Thermal regime of the Chile Triple Junction:Constraintsprovidedby downholetemperaturemeasurementsand distributionof gas hydrate,Proc. OceanDrill. Program Sci. Results,141,259-175, 1995. Cande, S.C., R.B. Leslie, J.C. Parra, and M. Hobart, Interactionbetween the Chile RidgeandChile Trench:Geophysical andgeothermal evidence,J. Geophys.Res.,92, 495-520, 1987. Cha, S.B., H. Ouar, T.R. Wildeman, and E.D. Sloan, A third-surfaceeffect on hydrateformation,J. Phys.Chern.,92, 6492-6494, 1988. Clegg, S.L., and M. Whitfield, Activity coefficientsin naturalwaters,in ActivityCoefficientsin ElectrolyteSolutions,2nd ed., editedby K.S. Pitzer,pp. 279-434, CRC Press,BocaRaton,Fla., 1991. Clennell,M.B., M. Hovland,D. Lysne,andJ.S.Booth,Role of capillary forcesand sedimentwater depletionin the habitatof gas hydrate (abstract), Eos Trans.AGU, SpringMeet. Suppl.,76(16), S164-S165,
Handa, Y.P., Compositions, enthalpies of dissociation, and heat capacitiesin the range 85 to 270 K for clathratehydratesof methane, ethane, and propane, and enthalpy of dissociationof isobutanehydrateas determinedby heat-flowcalorimeter,J. Chem. Thermodyn.,18, 915-921, 1986.
Hatzikiriakos, S.G.,andP. Englezos, Permafrost meltingandstabilityof offshoremethane hydrates subjectto globalwarming,Int. J. Offshore Polar Eng., 4, 162-166, 1994. Holbrook,W.S., H. Hoskins,W.T. Wood,R.A. Stephen,D. Lizarralde, and Leg 164 ScienceParty, Methanehydrateand free gason the Blake Ridge from vertical seismicprofiling, Science,273, 18401843, 1996.
Hollister,L.S.,andR.C. Burmss,Phaseequilibriain fluidinclusions from the KhtadaLakemetamorphic complex,Geochim.Cosmochim. Acta, 40, 163-175, 1976. Hyndman, R.D., J.P. Foucher,M. Yamano, A. Fisher, and Scientific Teamof OceanDrilling ProgramLeg 131, Deep seabottom-simulat-
ing-reflectors: Calibration of thebaseof thehydratestabilityfieldas usedfor heatflow estimates,Earth Planet. Sci. Lett., 109, 289-301, 1992.
Kastner,M., H. Elderfield,J.B. Martin, E. Suess,K.A. Kvenvolden,and
R.E. Garrison,Diagenesisand interstitial-waterchemistryat the Peruviancontinentalmargin:Major constituents and strontiumisotopes,Proc. OceanDrill. ProgramSci.Results,112, 413-440, 1990. Kastner,M., K.A. Kvenvolden,M.J. Whiticar, A. Camerlenghi,and T.D. Lorenson,Relation betweenpore fluid chemistryand gas hydratesassociated with bottom-simulating reflectorsat the Cascadia Margin,sites889 and892, Proc. OceanDrill. ProgramSci.Results, 146 (part 1), 175-187, 1995. Katzman, R., W.S. Holbrook, and C.K. Paull, Combined verticalincidenceand wide-angleseismicstudyof a gashydratezone,Blake
Ridge,J. Geophys. Res.,99, 17,975-17,995,1994. Kharaka, Y.K., W.D. Gunter,P.K. Aggarwal,E.H. Perkins,and J.D. DeBraal, SOLMINEQ.88: A computerprogramfor geochemical modelingof water-rockinteractions,U.S. Geol. Surv.WaterResour. Invest.Rep., 88-4227, 1988. Kobayashi,R., H.J. Withrow,G.B. BtynerWilliams,andD.L. Katz, Gas hydrateformationwith brine and ethanolsolutions,Proc. NGAA, 27, 1951.
Kvenvolden,K.A., Methanehydrate:A major reservoirof carbonin the shallowgeosphere?, Chem.Geol., 71, 41-51, 1988.
Kvenvolden,K.A., Gas hydrates:Geologicalperspective and global
change,Rev. Geophys.,31, 173-187, 1993. Kvenvolden,K.A., and A. Grantz, Gas hydratesof the Arctic Ocean region,in TheArcticOceanRegion,editedby A. Grantz,L. Johnson, andJ.F.Sweeney, pp.539-549,Geol.Soc.Am., Boulder,Colo.,1990. 1995. Kvenvolden,K.A., and M. Kastner, Gas hydratesof the Peruvian Davis, E.E., R.D. Hyndman,and H. Viilinger, Ratesof fluid expulsion Margin, Proc. OceanDrill. ProgramSci. Results,112, 527-526, acrossthe northernCascadiaAccretionaryPrism:Constraintsfrom 1990. new heat flow andmultichannelseismicreflectiondata,J. Geophys. Kvenvolden, K.A., andM.A. McMenamin,Hydratesof naturalgas:A
Res., 95, 8869-8889, 1990. Davis, E.E., K. Becker, K. Wang, and B. Carson,Long-termobservations of pressure and temperature in hole 892B, Cascadia AccretionaryPrism, Proc. OceanDrill. ProgramSci. Results,146, 299-311, 1995. de Roo, J.L., C.J. Peters, R.N. Lichtenthaler,and G.A.M. Diepen, Occurrenceof methanehydrate in saturatedand unsaturatedsolutions of sodium chloride and water in dependenceof temperature andpressure, AIChE J., 29, 651-657, 1983. Dholabhai, P.D., P. Englezos, N. Kalogerakis, and P.R. Bishnoi, Equilibriumconditionsfor methanehydrateformationin aqueous mixed electrolytesolutions,Can. J. Chem.Eng., 69, 800-805, 1991. Diamond,L.W., Salinityof multivolatilefluid inclusiondeterminedfrom clathratehydrate stability, Geochim. Cosmochim.Acta, 58, 19-41, 1994.
Dickens,G.R., andM.S. Quinby-Hunt,Methanehydratestabilityin seawater,Geophys.Res.Lett.,21, 2115-2118, 1994. Dickens, G.R., J.R. O'Neil, D.K. Rea, and R.M. Owen, Dissociation of
methanehydrateas a causeof the carbonisotopeexcursionat the end of the Paleocene,Paleoceanography,10, 965-971, 1995. Englezos,P., andP.R. Bishnoi,Predictionof gashydrateformationconditions in aqueouselectrolyte solutions,AIChE J., 34, 1718-1721, 1988.
Froelich, P.N., G.P. Klinkhammer, M.L. Bender, N.A. Luedtke, G.R.
Heath,D. Cullen,andP. Dauphin,Early oxidationof organicmatter in pelagic sedimentsof the easternequatorial Atlantic: Suboxic diagenesis, Geochim.Cosmochim. Acta,43, 1075-1090,1979. Gomitz,V., andI. Fung,Potentialdistribution of methanehydrates in the world'soceans,GlobalBiogeochem. Cycles,8, 335-347, 1994.
reviewof their geologicoccurrence, U.S. Geol. Surv.Circ., 825, 111, 1980.
Lee, M.W., D.R. Hutchinson, W.F. Agena,W.P. Dillon, J.J.Miller, and B.A. Swift, Seismiccharacterof gas hydrateson the southeastern U.S. continental margin,Mar. Geophys. Res.,16, 163-184,1994. MacDonald,G., Role of methaneclathratesin pastand futureclimates, Clim. Change,16, 247-281, 1990. MacKay, M.E., R.D. Iarrard, G.K. Westbrook,R.D. Hyndman,and ShipboardScientificParty of Ocean Drilling ProgramLeg 146, Origin of bottom-simulating reflectors:Geophysicalevidencefrom the Cascadiaaccretionary prism,Geology,22, 459-462, 1994. Menten,P.D., W.R. Parrish,andE.D. Sloan,Effectof inhibitors on hydrate formation,Ind. Eng. Chern.Process.Des. Der., 20, 399-401, 1981.
Minshull,T., andR. White,Sedimentcompaction andfluidmigration in the Makran AccretionaryPrism, J. Geophys.Res., 94, 7387-7402, 1989.
Nisbet,E.G., The end of the ice-age,Can. J. Earth Sci.,27, 148-157, 1990.
Ouar, H., S.B. Cha, T.R. Wildeman, and E.D. Sloan, The formation of
naturalgashydratesin water-based drillingfluids,Chern.Eng.Res. Der., 70, 48-54, 1992.
Patwardhan,V.S., and A. Kumar, A unified approachfor predictionof thermodynamic propertiesof aqueousmixed-electrolyte solutions, I, Vapor pressureand heat of vaporization,A/ChE J., 32, 1419-1428, 1986.
Paull,C.K., W. UsslerlIl, andW.P. Dillon, Is the extentof glaciation limited by marine gas-hydrates?, Geophys.Res. Lett., 18, 432-434, 1991.
DICKENSANDQUINBY-HUNT: METHANEHYDRATESTABILITYIN POREWATER Paull, C.K., et al., Proceedingsof the Ocean Drilling ProgramInitial Reports,vol. 164, in press,OceanDrill. Program,CollegeStation, Tex., 1996.
Pieroen,A.P., Gashydrates:Approximaterelationsbetweenheatof formarion, composition,and equilibrium temperaturelowering by "inhibitors,"Rec.Tray. Chim.,74,995-1002, 1955. Pitzer, K.S., Ion interactionapproach:Theoryand datacorrelation,in ActivityCoefficients in ElectrolyteSolutions, 2nded.,editedby K.S. Pitzer,pp.75-153,CRC Press,BocaRaton,Fla., 1991. Pitzer,K.S., J.C. Peiper,andR.H. Busey,Thermodynamic propertiesof
783
Ussler, W., llI, and C.K. Paull, Effects of ion exclusionand isotopic fractionationon pore water geochemistryduringgashydrateformationanddecomposition, GeoMar. Left.,15, 37-44, 1995. Von Breymann,M.T., K.-C. Faneis,andA. Camerlenghi, Geochemistry of sedimentsfrom the Peru upwellingarea:Resultsfrom Sites680, 682, 685, and 688, Proc. Ocean Drill. Program Sci. Results,112, 491-504, 1990. Westbrook,G.K., et al., Proceedingsof the Ocean Drilling Program Initial Reports,vol. 146 (part 1), 611 pp., OceanDrill. Program, CollegeStation,Tex., 1994.
aqueous sodiumchloridesolutions, J. Phys.Chem.Ref.Data, 13, 1102, 1984.
Singh,S.C., and T.A. Minshull, Velocity structureof a gashydraterefiector at OceanDrilling ProgramSite 889 from a global seismic waveforminversion,J. Geophys.Res.,99, 24,221-24,233,1994. Singh,S.C., T.A. Minshull,andG.D. Spence,Velocitystructure of gas hydratereflector,Science,260, 204-207, 1993. Sloan,E.D., Jr., ClathrateHydratesof Natural Gases,641 pp., Marcel Dekker, New York, 1990.
G.R. Dickens,Departmentof Each Sciences,JamesCook University of Northern Queensland,Townsville, Queensland4811, Australia. M.S. Quinby-Hunt, Energy and EnvironmentDivision, Lawrence Berkeley National Laboratory, Bldg. 90-2024, 1 Cyclotron Rd., Berkeley,CA 94720. (email:
[email protected]) (ReceivedApril 3, 1996; revisedAugust21, 1996; acceptedSeptember26, 1996.)
