Canadian MinerologistVol. 29, pp.767-790 (1991)

H2O-CO2 MIXTURES: A REVIEW OF P-V-T-X DATAAND AN ASSESSMENT FROM A PHASE-EOUILIBRIUM POINT OF VIEW

URS K. MADER'Department of Geological Sciences, The University of British Columbia, Voncouver, British Columbia V6T 284

ABSTRAcT

A resolution is suggested among inconsistenciesbetween and within data sets, including P-V-T-Xmeasurements, phase-equilibrium experiments and equa-tions of stale for H2O-CO2 mixtures. The P-V-T-X dataof Franck & Tcidheide (1959) are inconsistent with dataobtained by Greenwood (1973) and Gehrig (1980), andcannot be reconciled with measured phase-equilibria inH2O-CO2 fluid mixtures. The data of Greenwood andGehrig are in loose agreement, but extend only to 600bars and do not constrain activities at higher pressures.The correction for chemical association proposed by deSantis el ol. (1974) and adopted by Holloway (1977) andBowers & Helgeson (1983) does not appear to be justified.Resolution of the inconsistencies among phase-equi-librium studies will require further experiments andadjustments of thermophysical propenies of mineralssimultaneously with firs of the mixing propefties of thefluid phase. A procedure is developed for the use ofexperimental phase-equilibrium constraints to put limitson the fugacities of components in the fluid mixture. Itis concluded that the data-base available is not yetadequate to derive a reliable equation of state forH2O-CO2 mixtures. Future work must include P-V-T-Xmeasurements to at least l0 kbar and phase-equilibriumstudies to further constrain deviations from ideal mixingand to resolve inconsistencies among existing measure-ments.

Keywords: water - carbon dioxide mixtures, fluids,thermophysical properties, thermodynamic properties,equations of state, phase equilibria.

SoMMAIRE

Cet arricle porte sur une r6conciliation parmi lesincompatibilit6s internes aux banques de donn€es et entrecelles-ci, portant sur les mesures P-V-T-X, les exp6-riences sur les 6quilibres de phases, et les dquations d'6tatpour les m€langes H2O-CO2. Les donn€es de typeP-V-T-X publi6es par Franck & T6dheide (1959) neconcordent pas avec les donndes de Greenwood (1973) etde Gehrig (1980), et sont irreconciliables avec les €quilibresde phases mesur€s impliquant une phase fluide mixte

"Present address: Geological Survey of Canada, 601Booth Street, Ottawa, Ontario KIA 0E8.

H2O-CO2. Les donndes de Greenwood et Gehrigconcordent grosso modo, mais ne ddpassent pas 600 bars,et ne contraignent aucunement les activit6s i pressionsplus 6lev€es. La correction pour l'association chimiquepropos€e par de Santis et al. (1974) et adoptde parHolloway (1977) er par Bowers et Helgeson (1983) nesemble pas justifi6e. Une r6solution des incompatibilitdsparmi les rdsultats des dtudes des 6quilibres de phasesndcessitera de nouvelles exp6riences et des ajustementsaux propridtds thermophysiques des mindraux, en m€metemps qu'aux propri€tds de mdlange dans la phase fluide.Un protocole est 6tabli pour appliquer les contraintes des6quilibres de phases afin d'dtablir des limites sur lesfugacit6s des composantes du m6lange dans la phasefluide. La banque de donn€es n'est pas encore ad6quatepour d6river une 6quation d'6tat fiable pour les mdlangesH2O-CO2. Les travaux futurs devront inclure des mesuresdes propri6tds P-V-T-X jusqu'ir au moins l0 kbar, et denouvelles 6tudes des dquilibres de phases afin decontraindre davantage les 6carts a I'idealitd dans lemdlange et de resoudre les incompatibilit€s parmi lesdonndes existantes.

(Traduit par la Rddaction)

Mots-clds: m6langes d'eau et d'oxyde carbonique, fluides,propri6t6s thermophysiques, propri6t6s thermodyna-miques, 6quations d'6tat, dquilibres de phases.

INTRODUCTION

C-O-H fluids are important in the study ofmetamorphism, fluid inclusions, properties ofmagmas, and evolution of oil and gas. Much ofour present knowlege of H2O-CO2 mixtures atelevated pressures and temperatures was establishedduring the late 1960s and early 1970s, and wasstimulated by the study of progressive metamor-phism of impure limestones.

Theoretical and experimental contributions com-bined with constraints from field observations wereprovided by Greenwood (1967a, b, 1969, 1973),Skippen (1971), Johannes (1969), Eugster &Skippen (1967), Trommsdorff (1972), Tromms-dorff & Evans (1974), Metz (1967, 1970), amongmany more. About a decade earlier, P-V-T-Xmeasurements on H2O-CO, mixtures were ex-

767

768 THE CANADIAN MINERALOGIST

tended to 2 kbar pressure (Franck & Tddheide1959), and the t\ryo-phase region was mapped to 3.5kbar (Tddheide & Franck 1963, Takenouchi &Kennedy 1964). Spectroscopic ddta and measure-ments of dielectric permittivity were collected inKarlsruhe by Kruse (1975) and Holzapfel & Franck(1966). Equations of state for fluid mixturessuitable for the computation of phase equilibria ingeological systems were developed by Holloway(1917), Flowers (1979) and by Kerrick & Jacobs(1981). Continued efforts have steadily increasedthe experimental data-base (e.g., Sterner & Bodnar1991, Chernosky & Berman 1991) and supple-mented field occurrences of low-variance mineralassemblages coupled with measured compositionsof minerals (e.9., Bucher-Nurminen 1988). Withthe availability of fast microcomputers and im-proved thermodynamic data-bases (e.g., Berman1988), efforts have been made most recently tocompute petrogenetic grids for metacarbonaterocks (Carmichael 1991, Connolly & Trommsdorffl99 l ) .

In light of these continued efforts, it isappropriate to critically examine the very founda-tions of thermophysical properties of HrO-CO,mixtures, namely P-V-T-X measurements, equa-tions of state and experimentally determinedphase-equilibria. The purpose of this paper is tohelp focus on the most important measurementsneeded to improve and resolve the numerousinconsistencies.

THE SYSTEM CO2-H2O

The system CO2-H2O has three components, C,H, O, and contains numerous species: CO2, H2O,CO, 02, H2, CHa, H2CO3, complex hydrocarbons,and the condensed phases graphite, diamond andclathrate hydrates. Despite the existence ofnumerous species, it is possible to take astoichiometric approach for the binary join H2O-CO2, which considers only two species, CO2 andH2O. The experimental data, however, on whichthe equation is calibrated, must be known tocontain only those two species. The bulk composi-tion of the fluid may be displaced from the binaryjoin if the fugacity of one or more species isbuffered, or sources or sinks for C-H-O speciesexist. This is particularly significant in the casewhere graphite or diamond is stable (e.g., Skippen& Marshall 1991, Ulmer & Luth l99l). Gain or lossof hydrogen is the most common problem en-countered in experimental studies. It may be solvedby buffering the fugacity of hydrogen at a very lowpartial pressure, removing likely sources or sinksfor hydrogen, and keeping experimental rundurations as short as possible. Experimentally

measured volumes of COr-H2O mixtures maysuffer from oxygen loss due to the oxidation of thesteel pressure vessel or from hydrogen loss due todiffusion or formation of metal hydrides. Undersufficiently oxidizing conditions, methane,hydrogen and carbon monoxide are present only intrivial amounts, and a binary CO2-H2O fluidconsists chiefly of the species CO2 and H2O (e.g.,Holloway 1987, Eugster & Skippen 1967).

The two-phase region of the COr-H2O binarysystem is encountered geologically under conditionsup to lower-greenschist-grade metamorphism. Thecritical curve that bounds the two-phase regionextends from the critical point of pure H2O(374,15"C, 221.3 bar) to a temperature minimum(266-269'C, 2000-2450 bar, 0.37 < X(CO2)<0.43), and then probably to higher temperatureswith increasing pressure and increasing X(COz)(T6dheide & Franck 1963, Takenouchi & Kennedy1964, Sterner & Bodnar 1991). The lower branchof the critical curve extends from the critical pointof pure CO2 (31.05"C, 73.86 bar) to a lower criticalend-point at somewhat higher temperature andpressure. Equations of state designed for thecomputation of phase equilibria at temperaturesbelow the critical point of water must thereforeaccount for the two-phase region.

CoxsrnarNrs oN EeUATIoNS oF SrATE FRoMTHsonv AND ExPERIMENT

It is fair to state that the problem of theprediction of P-V-T properties of fluids and theirmixtures is not so much due to the lack of theoriesand models, but to the lack of our ability to assesstheir relative merits. Models based on firstprinciples are not yet sufficiently developed to testequations of state, and the body of experimentaldata is not large enough to distinguish between theextrapolation properties of the numerous semi-em-pirical equations. As a consequence, the computa-tion of properties of fluid mixtures relies heavilyon experimentally measured quantities, semi-em-pirical equations of state, and, in many cases,arbitrarily chosen rules for the mixing of end-mem-ber fluids.

The exact shape of the intermolecular potentialas a function of temperature and pressure is notknown, nor are the potentials resulting from theirmutual interaction in mixtures. For this reason.most equations of state applicable to real systemsare based on macroscopic models, with parametersrelated to the dominant intermolecular forces ofattraction and repulsion. Examples are the virial-type equations, the van der Waals equation and theRedlich-Kwong (Redlich & Kwong 1949) equationwith its numerous modifications.

WATER - CARBON DIOXIDE MIXTURES 769

The behavior of mixtures of gases may in somecases be described by equations in which theparameters are formed by some combination of theparameters for the pure gases. However, theequations must be mathematically and physicallycompatible. These "mixing rules" may be inde-pendent of the nature of the end-member gases inthat they simply account for geometrical effectsupon mixing. If one or more of the end-membergases deviate substantially from ideal behavior,mixing rules may be adjusted for nongeometricaleffects upon mixing, such as induced dipole effects,polarizability, strong electronic interactions andchemical association (e.9., Prausnitz et al. 1986),In most cases, only a two-body interactionparameter is developed to account for these effects.The requirement that equations of the end-membergases be compatible puts severe constraints on thepossibility of introducing modifications to eitherend member to fit experimental data. Severalequations intended for geological applications havebeen fit piecewise to data in order to keep equationssimple [e.g., Bottinga & Richet (1981) for COr;Holloway (1977, l98l) for H2O; Saxena & Fei(1987) for H2O and COr; Powell & Holland (1985)and Holland & Powell (1990) for the logarithm ofthe fugacity of H2O and CO2l. The tradeoff in thisapproach is the introduction of discontinuities tothe thermodynamic functions derived from theseequations of state.

An important point that is easily underestimatedis the dependency of the parameters in the equationof state on the mathematical form of the equationitself. The same rules of mixing applied to a vander Waals equation and a Redlich-Kwong equationwill result in different excess properties for amixture, even though the physical justification andthe underlying assumptions may be identical.Increased flexibility to fit measured volumes maybe introduced by making the attractive term or therepulsive term more flexible. Thus, an equationwith a simple hard-sphere repulsive term can mimicincreased compressibility at high pressure byintroducing a volume (or pressure) dependency onthe attractive term (e.g., the equation of Kerrick &Jacobs). The quality of fit to observed data aloneimplies nothing about the physical meaning of thevariation of the parameters with P, V and T, orabout the correctness of the mixing rules.

The number of parameters in an equation ofstate is not always correlated with the goodness offit to data. In most equations, one or moreparameters, such as the excluded volume, are fixedprior to regression to measured volumes (e.9.,Kerrick & Jacobs 1981, Holloway 1977). For someof the mathematically more complex equations, asimultaneous fit of all Darameters is not oossible

owing to problems with numerical stability duringoptimization (e.9., Bottinga & Richet l98l). Anequation with few parameters fit simultaneously,such as the five-parameter equation presented byMiider & Berman (1991) for COr, may achieve afit comparable to a ten-parameter equation, suchas that proposed by Kerrick & Jacobs (1981). Amany-parameter equation may not extrapolatewell, particularly if the parameters are combinedempirically, for example in a power-series expan-sion.

Carbon dioxide

Raman spectroscopic measurements to 490'Cand 2.5 kbar (Kruse 1975) indicate no significantchanges in the spectrum from dataat low densities.Not much is known about the extent of dissocia-tion, ionization, or dimerization of pure COt athigh temperatures and very high densities.

Water

Whereas the peculiar nature and properties ofwater compared to other liquids are well known(e.g., Franks 1972-1984, vols. I-VII), it is not wellunderstood how these properties change withincreasing pressure and temperature. Insight isgained from experimental measurements of P-V-Tproperties, dielectric permittivity, Raman andinfrared spectroscopy, thermodynamic properties,and, more recently, from simulations usingmolecular dynamics (see also Tddheide 1972).

Water at low pressures and temperatures isdominated by hydrogen bonding, which leads to ahighly structured liquid dominated by tetrahedrallycoordinated molecules with an open structuresimilar to that in the corresponding solid, ice-I. Thehydrogen bond persists to high pressures in ice(e.9., ice-VII at pressures >21 kbar), with anincrease in density due to distortion of theframework. The relatively low compressibility ofliquid water despite the open framework indicatesthat the structure dominated by the hydrogen bondmay persist to high pressure in the fluid state aswell. There is evidence that water starts to assumecompressibilities like those of unstructured liquidsat a pressure between 4 and 8 kbar (Franck 1981).

The tetrahedrally coordinated network probablydoes not persist to high temperatures at lowpressures. Spectroscopic data indicate that atsupercritical conditions, H2O has lost many of itsstructured characteristics. Supercritical water is,however, still polar in nature, which is importantfor its ability to interact with other species. No dataare available on structural changes as a function oftemperature at high pressures. At very high

770 THE CANADIAN MINERALOGIST

temperature and pressure (100-200 kbar), watermay be largely an ionic fluid, in view of theobserved monotonic increase of the ion productwith pressure and temperature (Holzapfel & Franck1966, Mitchell & Nellis 1979, and discussion inFranck l98l).

Recent progress in simulations based onmolecular dynamics (Brodholt & Wood, 1990) at adensity of I g,/cm3 and temperatures up to 2100"C(38 kbar) leads 1o reasonable agreement withmeasured volumes and transport properties. Thisapproach may allow testing of intermolecularpotential formulations and equations of state in thenear future. Results of numerical simulations aloneare not yet accurate enough for the purpose ofthermodynamic computations.

The Haar et al. (1984) equation used to expressthe thermodynamic properties of supercriticalwater by Berman (1988) and in this study is thoughtto be reliable to at least 2500 K and 30 kbar. Theequation is based on a formulation of theHelmholtz free energy as a function of temperatureand density. The theoretical model and its empiricalextensions obey the first and second laws ofthermodynamics and thus allow for computationof any thermodynamic function by differentiation.The equation is consistent with virtually allexperimental observations. Most recently, theproperties of H2O in the critical region have beenaddressed by Johnson & Norton (1991).

Mixtures of water and cqrbon dioxide

As a first approximation, inferences fromP-V-T-X measurements about interactions be-tween CO2 and H2O may be tested against whatlimited spectroscopic and other data exist. Fromthe strong depression of the critical compositioncurve to lower temperatures compared to watermixed with an inert gas (e.9., argon, Greenwood196l), one might expect strong chemical associationup to at least 400oC and 4 kbar. The positivedeviation of the volume from ideality on mixing,stemming from dispersion forces, may be reducedor even reversed by slrong chemical association.Greenwood's (1969) P-V-T-X measurements indi-cate distinct negative volumes of mixing attemperatures above 600'C and pressures below300-400 bat (e.g., see below, in Fig. 7). This wouldindicate that chemical association remains sig-nificant beyond 800oC, but decreases with increas-ing pressure. Franck & T0dheide (1959) interpretedtheir P-V-T-X measurements in terms of devia-tions from a van der Waals equation of state with"geometric" rules of mixing and estimated themaximum amount of chemical association in termsof carbonic acid. De Santis et al. (1974) used these

data to formulate a temperature-dependent equi-librium constant (CO2 + H2O + H2CO, that isincorporated into their modified Redlich-Kwongequation of state and adopted by Holloway (1977),Flowers & Helgeson (1983) and Bowers & Helgeson(1983). The P-V-T-X data by Franck & T6dheideare considered suspect for reasons explained below,and the de Santis et al. (1974) correction is notjustified.

Infrared absorption and Raman spectroscopy onfluids at elevated temperature and pressure are rare,owing to obvious technical difficulties arising fromthe use of sapphire windows. The data availableup to 2-3 kbar (Kruse 1975, and summary byFranck l98l) only show a weak band on a Ramanspectrum at low temperatures, which may beassigned to carbonic acid. Spectra at highertemperatures and pressures lack clear evidence forchemical association. Read's (1975) measurementson electrical conductance suggest at least somechemical association up to the limits of hisexperiments at 250"C and 2 kbar.

ExrsrrNc EeuerroNs oF SrATE

In many early applications to geologicalproblems, water and carbon dioxide have beenassumed to mix ideally (e.g., Eugster & Skippen1967, Greenwood 1967b) owing to the lack ofconstraints on nonideality, This may result indistorted topologies in phase diagrams over a widerange of temperature, pressure and fluid composi-tion. The mosl commonly used equations of statethat predict P-V-T-X properties of H2O-CO2mixtures include that of Kerrick & Jacobs (1981)and the Holloway (1977) - Flowers (1979) equation,which are both modifications of the equation ofRedlich & Kwong (1949). Holloway's equations arebased on work by de Santis et al. (1974). Powell& Holland (1985) and Holland & Powell (1990)fitted a polynomial function for the logarithm ofthe fugacity to data computed with existingequations of state. The mixture is modeled by asubregular, asymmetrical solution-model for theactivities, which are fitted to values computed withthe Kerrick & Jacobs equation. Shmulovich el a/.(1980) presented a virial equation and used aMargules formulation to model the excess volumeof mixing as a function of composition, from whichthey derived the fugacities. Spycher & Reed (1988)devised a pressure-explicit virial equation ap-plicable to calculations of hydrothermal boiling,with upper limits at I kbar and 1000"C. Connolly& Bodnar (1983) presented a modified Redlich-Kwong equation for the range 0-10 kbar and100-1000oC, designed for applications to fluid-in-clusion studies. Sterner & Bodnar (1991) derived a

WATER - CARBON DIOXIDE MIXTURES 771

three-coefficient Margules expansion for the excessvolume of mixing from their measurements onsynthetic fluid-inclusions between 2 artd 6 kbar and400 to 700"C. Tabulations of P-V-T-X propertiesand fugacities of CO2-H2O mixtures were offeredby Franck & Tddheide (1959), Greenwood & Barnes(1966), Greenwood (1969, 1913), Ryzhenko &Volkov (1971), Wood & Fraser (1977), Shmulovichet al, (1980), and Sterner & Bodnar (1991). Recentreview articles on equations of state for fluidsinclude those by Ferry & Baumgartner (1987) andHolloway (1987).

THsnrraonvNaMlc RELATIoNSHIPSFOR FLUID MIXTUNES

Whereas most standard texts cover the subjectadequately (Prausnitz et q|.1986, Chatterjee 1991,

Wood & Fraser 1977, Anderson 1977, Skippen &Carmichael 1977), they do not provide thenecessary details relevant to this treatment of thephase-equilibrium experiments. The thermody-namic notation used here is summarized in Table 1.

In order to derive simple expressions for theexcess properties of a mixture (e.9., partial molarexcess volume V"), the fugacity coefficient yi of acomponent in a mixture is best related to its purestate at temperature and pressure of interest, whichyields:

1P 2P

I u"(P,ndP =lx, I v.,(T)itP =J r r * 7 J l bs ( 1 )

Dw]-'tt(P,T,xr)'i

The activity of a component with respect to thesame state becomes ai = XiI. Equation I also

TABLE 1. NOTATION FOR THERMODYNAMIC EQUATIONS

P pressureT absolute temperature in KelvinAnG Gibbs potential of a reactiong Gibbs potential of a reaction diminished by the "R?ln/

terms of the fluid speciesCp heat capacity at constant pressure

a isobaric expansivity

I isothermal compressibility

Uo molar volume of pure component d

U partial molar volume of component i in a mixture

V^ molar volume of a mixture

i' molar volume of a mechanical (ideal) f luid mixture

U molar excess volume of a mixtureV", partial molar excess volume of component i in a mixture

X; mole fraction of component i in a mixture

f; fugacity of component i in a mixture

f: fugacity of pure component i''li fugacity coefficient of component i relative to ideal

mixing at pressure and temperature of interestai activity of component I in a mixture relative to its pure

state at pressure and temperature of interestvi stoichiometric coefficient of component a in a reaction

R gas constant

Superscript * refers to a variable at some standard state

Superscript id refers to a variable in a state of ideal mixing

Superscript exP refers to an experimentally measured variable

'772

*T

V""

url

T,NU.^

Lv;

THE CANADIAN MINERALOCIST

F xr ---Fx"-.|BA

Paofi = Ptotol = cot[tta'nt

experimentaldaturn

i ideal

III

Ezo Xerp Xia

Qoz

Frc. 2. Schematic diagram of a single fluid speciesequilibrium. The experimentally determined equi-librium curve and the computed curve assuming idealmixing in the fluid phase are shown as a thick lineand a thin line, respectively.

The volume integral of the partial molar excessvolume with respect to pressure for this case isobtained from equation l:

1P rldx?* I UJT).]P =.ffilnftp =

Jr bsr ^a (5)

ETltl;(P,7,XqP).

P-V_T_X PROPERTIES CONSTRAINED BYPHess-Eeurr-TBRIUM DATA

From the requirement for a reaction at equi-librium that ApGez be equal to 0, it follows thateach experimental half-bracket leads to an in-equality, ARGP,T d 0 or ARGer > 0, dependingwhether products or reactants are stable, respec-tively. Provided reliable thermodynamic data forall solid phases are available, each measuredhalf-bracket of an equilibrium involving a fluidmixture will put an inequality constraint on thefugacities of the fluid species by combining theabove inequalities with equation 3:

nT ,, Gil u xid - ?*4 h t(f:!- xf ) )--? '\- .f1o(Po'n,2ur; ,l

i e1r*,r-; - g1l",Cu;, (6)

where the "less than" refers to the case whereproducts are stable. The combined bounds frommany experimental half-brackets will confine anequation of state within feasible limits with respectto measured phase-equilibria. This fact may be usedto test existing equations of state or to constrainadjustable parameters of a new equation usingtechniques of numerical optimization. Details ofthis method are outlined by Berman et ol. (1986),and applied to the derivation of an equation ofstate for pure CO2 by Miider & Berman (1991).

T

Frc. 1. Ceometrical interpretationexcess volume in a binarvcomponents A and B.

of the partial molarfluid mixture with

implies the approximate equality of unit pressureand unit fugacity. A simple geometric interpreta-tion of the partial molar excess volume in atwo-component mixture is provided in Figure l.

In order to relate an experimentally determinedphase-equilibrium position at F"p, Zexp, )(exp to ahypothetical reference-position assuming idealmixing at Pd, Td and Xd, one formulates first theGibbs potential of the reaction for both states:

AnG = 0 = g(P.-P, f'r)lvt,W,Sl, El, (Cplt, or, 9rl

*T**rd]ff

and an analogous equation with f andf at statesPd, ?td and Xd. SubscriptT denotes alt species (solidor fluid) that take part in the reaction, k relates tosolid phases only, and I is the subscript for allgaseous species. The function I contains allcontributions to the Gibbs potential from the solidphases and the contributions from the fluid specieswith the exception of the volume integral (RT ln fterm). Equation 2 and its analog are combined toobtain the general expression:

ggq,r'p)_g(Pta,t'd)=

rl ", (*. rrl. _ n*r" ffi). r3t

Figure 2 is an example of the special case whereonly one fluid component in the mixture takes partin a reaction. The deviation from ideality in anisobaric-isothermal section simplifies to:

4iA,#=ar(P,r,xiP)=xld= (4)?r(P,

", Xf'D)XtrP.

(2\

WATER - CARBON DIOXIDE,MIXTURES 773

The validity of this approach hinges on theavailability of accurate thermophysical propertiesof minerals and pure fluids, as well as P-V-T-Xmeasurements and phase-equilibrium experiments.Improvements on equations of state can onlyproceed in conjunction with improvements to theexperimental data-base. Carefully documented as-semblages of natural minerals can provide addition-al constraints and are the ultimate test inapplications of computed phase-equilibria to rocks.

Thermophysical properties of minerals that aredependent on fluid properties by virtue of theavailable phase-equilibrium data must be fittedsimultaneously with fluid properties in order tomaintain self-consistency and to avoid the propaga-tion of systematic errors into fluid properties.Whereas there is some circularity in this process, itis anticipated that every new experimental datumof high quality will guide the numerical best fittoward consistency with all available data.

P-V-T-X Dere oN HP-CO2 MIxTURES

Figures 3 to 7 compare measured excess volumesof mixing with volumes computed by severalequations of state. Parameters for equations ofstate and computer codes for their evalution wereobtained from the following sources: Kerrick &Jacobs (1981), Jacobs & Kerrick (1981a), Holloway(1981) and a computer code obtained by writtencommunication from J.R. Holloway (July, 1990).The van der Waals equation was evaluated usingthe following parameters and mixing rules: a(H2O): 55.0 x 105, ,(H20) : 30.3, a(CO) : 36.8 x105, b(co, : 43,0, Qmix = X(HzO)2a(HzO) +X(co )2 o(Co ) + 2x(Wo) x(co )'/ o(Hzo)a{QoJ'and D*o = 6I(HzO)X(H2O) + -b(CO)X(CO)' inunits iif Kelvin, bar, and cm3/mol. A positivepressure spike at 2l0bar (Figs. 3A-E) in the curvescomputed with the Kerrick & Jacobs equation isthe result of nonconvergence of the iterativeroot-finding procedure coded by Jacobs & Kerrick(1981a). These erroneous volumes do not affectcompuled fugacity coefficients for a pressure above250 bar since the volume integration is performedalgebraically, but volumes between 325 arrd cq.4l5oC cannot be computed reliably below apressure of 250 bars.

Measured volumes are represented by smootheddata provided by the individual authors whereprimary measurements are not reported or do notplot into the selected figures (e.g., Franck &Tddheide 1959, Greenwood 1973, Gehrig 1980,Sterner & Bodnar l99l). Only a representativeamount of data is plotted to avoid rendering graphsillegible. The data of Franck & Tddheide above 1.4kbar are not included in the figures owing to large

uncertainties compared to the small effect onvolume of mixing at high pressures. Theseuncertainties are the result of not reporting P-V-Tdata on the pure fluids. For the computation ofthe excess volume below 1.4 kbar, the data on thepure gases of Kennedy (1954) and Holser &kennedy (1958, 1959) were used; Franck &Tddheide stated that these agree to within l9o oftheir measurements. The same procedure had to beadopted for the data of Gehrig (1980), whoreported data on mixtures between 0'l <X(CO2)<b.9, but none for the pure fluids. Error bars inFigures 3-7 represent my best estimate of uncer-tainty, except for measurements by Sterner &Bodnar (lgtl), where experimental precision isdepicted.

The most striking feature apparent from inspec-tion of Figures 3-7 is the substantial inconsistencyamong the data sets of Franck & Tddheide (1959)'Greenwood (1973), Gehrig (1980) and Shmulovichet ql. (1979,1980). There is reasonable agreement'although not within stated experimental uncertain-ties, between the data of Greenwood (1973) andGehrig (1980) (Figs. 4, 5). The Kerrick & Jacobs(1981) equation of state, which reproduces ex-perimentally measured phase-equilibria quite well(Berman 1988, Jacobs & Kerrick l98lb' anddiscussion below), loosely approximates the databy Greenwood and Gehrig between 400 and 600'C(Figs. 3-6). I conclude that the volumes measuredby Franck & Tddheide are most likely in error'pirticularly at pressures below I kbar, and shouldnot be used. Their volumes are systematicallysmaller than those measured by Greenwood, Gehrigand Schmulovich et a/. It is not possible to relatethe apparently erroneous measurements of Francka tOaneiOe to a single cause. The most likelyproblems in the experimental method that lead tounderestimated volumes are thermal gradients overvolumes of connections, or determination of thevolume of the pressure vessel by the mercurymethod, or creep of Bridgman seals.

Shmulovich et al. (1979,1980) measured volumesof several fluid compositions at 400 and 500"Cbetween 0.15 and 5.7 kbar (Figs. 3' 5). Measure-ments by Shmulovich et al. (1979) at 400 and 500'Cand 400-5700 bar show excess volumes significantlylarger than data by Shmulovich et ol. (1980) andFranck & T6dheide, with the exception of goodagreement in the region of overlap with data byGreenwood and Gehrig at 500-600 bar (Fig' 5). At400'C and 150-200 bar, the excess volumes ofShmulovich et al. (1979) are smaller than thosemeasured by Gehrig (Fig. 3). Excess volumesmeasured by Shmulovich et al. (1979) above 700bar pressure at 700'C (Figs. 5,{, B) are difficult toreconcile with theory or phase-equilibrium data.

t t 4 TTIE CANADIAN MII..ItsRALOGI'ST..

Excess volume (cm3/mole)

( D a@U I ;-l

rD -

5 ;9 )a

o

;

Xc)oIU

6 S' ; - 4 9 9 9

Ftc. 3. Pressure ,e.i'srs excess molar volume diagrams (A, B, C, D) and fluid composition yelsr.t^r excess molar volumediagrams (E, F) of H2O-CO2 mixrures at 400oC. See text for discussion.

q

ia

ir

9

.Nc)

>ro> 3

$$i$ *ii$E f6 ! . S oj. .

_S L

Bts*Edu

itl5I$$ss$$$. - F

A

$E

I o.. ' $

in i$$iris$ $i$- i$rt esss

-.F \o

iE

!tlsI{$s$s;$tr\ i i. - F

r\

Su$n

>rtra>

$$$[$$ii$*

\q)oCJ

q)aq)

0!)

Ia>3 I $r3Yss6'i Q xs - Fs $ 6

bs qi \

$

G*..\ \o\o \,l

\ct

:-

!>

TI

IO>

r ii l s$$

is$$$i$sE ;ii ;u€: Q:t

I

il,

: a

\c>ocJ

Ic>o

oaa, fif$ls;

ilt :iti 3

l$$ si$*$qs esu. - F \ os

iE

775WATER. CARBON DIOXIDE MIXTURES

Excess volume (cm3/mole)

FIG. 4. Pressure yersus excess molar volume diagrams (A, B, C, D) and fluid composition vers''t excess molar volume

diagrams (E, F) of H2O-CO2 mixtures at 450'C. See text for discussion'

C\Io()

X

ct

9

ci

o

$[B$E*os5r

:e:!"s

: o

$58€f ."iISrF$uF I<

!"s\o

si- S r

3* "P F\l?

$ iis5$ ritEE: Ii

6 BfI; TET3

.,<ogx

(s-o

o:fo@o

IL

.a

Fi- v

9 $

$ q\S

5.9 $$:Eli |i$Eso<o

(ocil l

3e.X

s)c)to\s

$t- \ l .

slss:.$'insi l i

(lriq

:R :O \ {\ - \''sXR3*oiststso<a

\tc;l l

3ox$)ct!o\$

5i$ €r$

:*$ i$ii;i IlisEso<a

o s E 6 o o p r 6

r > ,u ,

>moo: I

;$iilliI

I$EsG\\

7'76 THE CANADIAN MINEIIALOCIST

Excess volume (cm3/mole)o N E o e E

-t

oC'CNco

ctg)-

-

P

;.,P

P.

Ftc. 5. Pressure v?rsrs excess molar volume diagrams (A, B, C, D) and fluid composition yelsal excess molar volumediagrams (E, F) of H2O-CO2 mixrures ar 500oC. See rexr for discussion.

I

P

Eo

I

!t

!5

t

P

t\) =

3P

I

-

7E *$*s

i I I o.o.&s I$ f$$t$

*$!riiFssll l$$I'is$ $::$$'g *.ir*:*$S

i EEsEEE

('rc)c!CJ

x6eIpN

F--€- A

1g;- l r\..F+f){

\.. FOt+tsi 4I*...."'1;He

/ >a>o

i il $i$$s x$ Ix$.1:ii i$"sts.$ su3E

o E 6 6 - E ; - E ;

('l

aoc:

c)aoI!J

itlst$$s*- : l A

$ss. - Fs

}E

iil l$$ls$ $$-iS * l G *s \o: \o\o

i'.* *s

}E

l \: \i'--{-i*

:i t---l-+- |

: t: T

! / ,; / t

#,t

WATER - CARBON DIOXIDE MIXTURES

Excess volume (cm3/mole)

777

o

oloIX

ct

ct

'd< N o c l T ?

r { T f

l-

(U-o

ofaao

IL

6 € < d o c . { y f 6 € < N o q { A P

Frc. 6. Pressure yersas excess molar volume diagrams (A, B, C, D) and fluid composition versrs excess molat volume

diagrams (E, F) of H2O-CO2 mixtures at 600oC. See lext for discussion.

. o

ct

€'ci,e,

€ , " !

,e,

o\O\ O\\ o i

*s:3 3 *:d 'i\ - ' -8 0 a

ii*s E 6oo<

s;srs- s r

€ N

9 N 3

i:s! l$$isl l i

c,

'ct

.'q

'c5

'€t

-d

-9

a8CAF j o

c)a;' o

\ F

t€\es)o$d ( oIa\3I\o

sESi l :

- B r, s NP N g

i:s$:!$RsIi

s

$i- \ n

's r\9N' |3:o \ s

;:ss:$$nsIi

o\

c\ c'\\ g i

- t s5{i

p :s

8.0 , . )

$i $u { 6oo<

c;tl

3gx

€t

8Ro(o

O

g\

g\ o\q O i

- € :R-: i

:FE8 s oB!!$r;oo<

:i l l

- lo ' lgx

tC|r

pqI(om

$!- \ .

8 NP N J 3

i:s$:$$Rsili

!I sg i

. s rA N9l'.,3

iis$:.$$Esi l i

(tri Fc\ o\\ ! \

E

- \ f

ili, t a a

s:ioo<

@ o s * o * 6 0 6

;

X6atlpt\

>ao

!33i i !a o 8x * SF a i< \ !- &\r ts$*G .lc \o

b

itlsI$$sss;iF \ i i

" \ FA

i$

6 6 A S O N A O €

it lsxl$ssS$$" - F6

lE

itlsI$rsrs;it \ i i. - F|\

is

>oog$$E*EA t a ' 8* * $X o ix N . ut F \ o

5.*oG-\ ob\ ! n

\o

Ip6

>ao

$s$EsEo o t* * SR {,.*a s \ o53d

.F

G*\o \oh ! n€

778 THE CANADIAN MINERALOCIST

Excess volume (cm3/mole); & i N

T](D@aco

ctg)

Ftc. 7. Pressure versrs excess molar volume diagrams (A, B, C, D) and fluid composition versr.r excess molar volumediagrams (E, F) of H2O-CO2 mixtures at 700 and 800"C. See text for discussion.

o o a N o E A e e o

moo

ril $sI$.iist $SrFF \ d

" - F|.!r6 Ra

daoO

Na

g

L

I

P

!r.

b

ar

xC,oI\) !tl

sIt$R$s;$tr \ i i. t Fs

}E

9

I

P

WATER - CARBON DIOXIDE MIXTURES 779

Greenwood (1969, 1973) measured negativevolumes of mixing at temperatures above 600oCand pressures below 300-400 bar (Fig. 7). If thesemeasurements are correct, significant chemicalassociation must occur in order to reverse thepositive volume-effect resulting from dispersionforces alone. The Holloway - Flowers equation,which accounts for formation of carbonic acid (deSantis e/ a/. 1974), does not represent Greenwood's(1973) data well in this region.

Sterner & Bodnar (1991) derived excess volumesof mixing from measurements on synthetic fluidinclusions in quartz (2-6 kbar, 400-700'C, 0.125<X(CO, <0.875). Only data at 2kbar are shownin Figures 3 and 5-7. The authors computed idealvolumes with the Haar et al, (1984) equation ofstate for water and the equation of Shmonov &Shmulovich (1974) for carbon dioxide. Excessvolumes were inferred to be positive, smaller than1.3 cm3lmol, with the exception of slightly negativeexcess volumes for water-rich compositions at 600and 700'C. Uncertainties are difficult to assessbecause of the lack of sufficient measurements onpure fluids determined by the same method.Uncertainties of 2-30/o in the measurements ofShmonov & Shmulovich (1974) on pure CO2(Miider & Berman l99l) will lead to uncertaintiesin the excess volumes of the mixtures that are ofthe same magnitude as the excess volumes themsel-ves. The important conclusion remains thatfugacity coefficients up to at least l0 kbar and700oC are dominated by relative large deviationsfrom ideal mixing at pressures below 2 kbar.

The Kerrick & Jacobs (1981) equation is mostcompatible with the P-V-T-X data of Greenwood(1973), Gehrig (1980) and Shmulovich et al. (1980),and most phase-equilibrium data between 450 and700oC (see below). The Holloway (1977, 1981) -Flowers (1979) equation is constrained to agree withdata by Franck & Tddheide (1959), but underes-timates deviations from ideal mixing compared tomost other da1a.

CoNsrnatNrs oN AcTIvITY -COMPOSITION RELATIONSHIPS

As an alternative approach to P-V-T-X meas-urements, one can determine directly activity-com-position relationships by the use of fugacity sensorsand buffering techniques. Joyce & Holloway (1987,1989) buffered the fugacity of HrO and analyzedthe fluid mixture to obtain equilibrium X(H2O) at2 kbar fluid pressure and 550-850oC and observednear-ideal activities for HrO. Chou & Williams(1977, 1979a, b) used a hydrogen fugacity sensorand reported negative deviations from ideality atX(CO) >0.4, 2-6 kbar and 600 and 700'C. A

re-evaluation of the technique revealed that thedata in the 1979 paper are incorrect and thatdeviations from ideal mixing are positive over theentire range of composition (Chou & Cygan 1990).Note that Sterner & Bodnar (1991) measurednegative excess volumes on mixing for water-richcompositions at these pressures and temperatures(see above).

Walter (1963c), Shmulovich & Kotova (1980) andZiegenbein & Johannes (1982) constrained thefugacity of CO2 in a H2O-CO2 mixture fromexperimentally measured phase-equilibria. Theresults are limited by the consideration of a singleequilibrium, which leads to curves of activity versasfluid composition at constant pressure that arepolythermal, i.e., the temperature is rising withincreasing X(CO). Eggler et ol. (1979) placedconstraints on the deviation from ideal mixing at26 kbar using experiments performed in a piston-cylinder apparatus.

PHASE.EQUILIBRIUM DATA

INvot-vtNc H2O-CO2 MIxruREs

Whereas the body of experimental data includingH2O-CO2 mixtures is substantial, there are severalincompatibilities among experimental studies of thesame equilibrium (Table 2). One reason for this isthat such experiments are technically difficult tocontrol. There are ample possibilities for errors thatremain undetected. This places obvious difficultieson selection of experiments that place reasonableconstraints on the deviation from ideal mixing ofthe fluid phase.

The following is a summary of problems withinthe experimental data-base, as well as the ther-modynamic data-base that Berman (1988) derivedfrom these experiments (see also Berman 1988).Numbered phase-equilibria are keyed to Table 2.

Phase equilibria with the most disturbinginconsistencies between studies that examine thesame reaction include calcite + andalusite +quartz + anorthite + CO2 (3), calcite + quartzr: wollastonite + CO2 (l), wollastonite + calcite+ anorthite + grossular + CO2 (5), and calcite+ quartz + tremolite + diopside + H2O + CO2(26). Equilibria that show only a discrepancybetween experiment and thermodynamic data ofBerman (1988) include dolomite + tremolite +calcite + forsterite + CO2 + H2O Q1), quartz +dolomite + Hp + calcite + talc + CO2 (29)'magnesite + talc + forsterite + H2O + CO2 (31)'magnesite + quartz + H2O e talc + CO2 Q2)'muscovite + quartz : sanidine + andalusite +H2O (40), and rutile + quartz + calcite + titanite+ CO2 (46). Experiments by Manning & Bohlen(1991) corroborate the thermodynamic data for

780 THE CANADIAN MINERALOGIST

TABLE 2. EXPERIMENTAL STUDIES OF PHASE EQUILIBRIA INVOLVING HZO-COZ MIXTURES

System or Equil ibr ium No Author P[kbar ] r fc l x(co2) 888 TD PH

Ca-Si-C-O * HzO

cal+Qtz:= wo*coz

pure CO2

Ca-AI-Si-C-O * HzO

Zi&Jo,7A 2,4,6Gr,67a L,2Ja&Ke,81b 6Ha&Tu,56 0.3-3

580-850 0.2-0.8 8500-720 0.0-0.9 8870 0.8-0.9 8570-800 - 11

GZJ

(i)-

Cal+Ky+Qtz := An*COz

Cal+And+Qtz:= An*COz

An+Cal+Qtz:= Grs*COzWo*Cal+An r= Grs*COz

An*Cal+Crn:= Gh+COlpure CO2An*Cal ;+ Grs*Gh*COzAn*Cal ;= Grs*Crn*COz

Grs+Cal*Crn + Gh+CO2An*Cal := Wo*Gh*COepure CO2Grs*Cal ;+ Wo+Gh*COz

Ca-Al-Si-C-H-O

2 Ke&Gh,79 6Ja&Ke,81b 6

3 Ke&Gh,79 2Ja&Ke,81b 2Ch&Be,91 1,2

4 Go&Gr,7l 25 Ho,74 L,4

sh,78 1,2,4,6Go&Gr,7l 2

6 Ho,74 1sh,74 0.5-0.7

7 Ho,74 I8 Ho,74 I,4

Ke&Gh,79 29 Ho,74 1,410 Ho,74 1

sh,74 0.5-0.711 Ho,74 1

550-570 0.7450-580 0.0-0.8410-450 0.5370-450 0.1-0.7340-410 0.5-0.8530-570 0.1710-840 0.1-0.5610-730 0.0-0.3580-850 0.0-0.4760-840 0.2-0.6780-860719-880 0.1-0.7750-840 0.1-0.2680-710 0.1700-840 0.0-0.2760-900 0.4-0.9830-890730-800 0.1-0.2

88I8

8999101 110101010101110

(i)+i+ cBi+ cB

KG,JK

i+i+ GG

s

(i)-

(i)-

Zo*COz:= Cal*An*H:O

Cal+Prl+H2O:= Lws*Qtz*CO:

Ca-Mg-Si-C-O + H2O

e (i)+9

L2

13

St&Ni,72 2,5Al&Fa,82 5Ni,72 4,7

430-670 0.0-0.3480-650 0.1-0.3310-390 0.0

Cal+Ak =: Mer*COzFo*Di+Cal ;+ Mtc*COzpure CO2Fo*Cal + Mtc*Per*COzpure CO2Di+Cal := Ak*COzpure CO2Qtz+Dol =r Di+CO2

Dol+Qtz+Tlc + Tr*COzDi+Dol =: Fo+Cal*COz

t4 2h,77 115 2h,77 I

Wa,63a 0.1-0.516 2h,77 I

Wa,63b 0.1-0.7L7 2h,77 I

Wa,63a 0.1-0.718 51,75 L,2

Ja&Ke,81b 5Eg&Ke,81 6

19 Eg&Ke,8l 620 Ka&Me,80 1,3,5,10

790-950 0.0-0.2680-850 0.0-0.3720-880730-930 0.0-0.2750-900740-880 0.1-0.4720-930420-540 0.9570-580 0.7600-630 0.8480-560 0.1-0.2530-870 0.9

24242524 (i)-25 i-24252626262626

WATER - CARBON DIOXIDE MIXTURES 781

TABLE 2 . CONTINUED

System or Equilibrium No Author P [kbar] T f Cl X(CO2) 888 TD P

Ca-Mq-Si-C-H-O

Qtz+Tfc+Cal := Tr+H:O+COz 2l 51,75 2 47A470 0.5 26Cal+Tr = Dol+Di+HzO+CO: 22 51,75 5 640 0.5-0.8 26Dol+Tlc = Fo+Di+HzO+CO: 23 Sk,71 1,2,2.6 500-590 0.7-0.8 26Cal+Qtz+Tlc r= Di+HzO+COz 24 Sk,71 1,2,3 430-550 0.5-0.6 26Dol+Qtz+HzO + Cat*Tr*COz 25 51,75 2 460-500 0.8-0.9 27

Eg&Ke,8l 6 490-600 0.1-0.7 21Cat+Qtz+Tr + Di+HzO+COz 26 Me,70 1,5 430-660 0.0-0.6 27 i+ S

s1,75 1,5 460-650 0.F0.9 27 M

Dol+Tr;= Fo+Cal*HzO*COr 27 Me,67,76 0'5,1 430-550 0.0-0.8 27 i+Cal*Tr + Fo+Di+HzO+COz 28 Ch&Be,86a 1 520-570 0.1-0.5 27Dol+Qtz+HzO + Cal+Tlc*COz 29 Me&Wi,63 2 440-510 0.3-0.9

Go&Gr,70 L,2 390-520 0.2-0.9 28 i+Me&Pu,70,71 L,2,3,5 390-590 0.1-0.9 28 i(1)+sk,71 1,2 410-460 0.5-0.6 28 i(1)+Eg&Ke,8l 6 440-560 0.0-0.3 28

Me-Si-C-O * HzO

Mgs*En = Fo*CO: 30 Jo,69 2 560-580 0.9-1.0 35E1,79 26 1000-1180 0.3-1.0

Ms-Si-C-H-O

Mgs+Tlc :+ Fo*HzO*COz 31 Gr,67b 7,2 480-580 0.1-0.8 34 i*+ JJo,69 0.5,1,2,4,7 470-670 0.1-0.7 34 i*A G

Mgs+Qtz*HzO := Tlc*cOz 32 Jo,69 t,2,4,7 330-620 0.0-0.9 34 i-

Mts+Tlc+H2O r= Ctl+CO2 33 Jo,69 I,2,4 330-480 0.0-0.1 35 (i)-Mgs+Ctl F: Fo+HzO+CO2 34 Jo,69 1,2,4 440-480 0.0-0.1 35Mgs*Ath = En+HzO*COu 35 Jo,69 2 530-560 0.9-1.0 35

Ms-Al-Si-C-H-O

Caf+Chl + DilFo+Spl*HzO+COz 36 Ch&Be,86a L,2,4 550-690 0.1-0.7 33Dol*chl + Fo+cal+5pl*Hzo*coz 37 wk,80 1,2,3 540-620 0.7-0.8 33 i+

Ch&Be.86a 1,2 540-630 0.1-0.7 33Mgs*Chl + Fo+Spl*HzO*COz 38 Ch&8e,86b,89 1,2,3,4 530-670 0'2-0'7 34

Na-Al-Si-H-O * COr

Pg + Ab*Crn*H2Opure H2O

39 Sv.83 r 460-510 0.1-0.4 40cj,70 r-7 520-670 - 37

K-AI-Si-H-O * Coz

Ms+Qtz = Sa*And*HzO 40 5v,83pure H2O

450-510 0.2-0.5 40 r-Ev,65 L4 490-680 - 39Ah,70 1-4 560-690 - 39K e , 7 2 2 6 0 0 - 6 4 0 - 3 9Cj&Jo,74 0.5-5 530-720 - 39

K-Ca-Al-Si-C-H-O

Cal+Ms+Qtz:= Sa+An*HzO*COz 4t He,73 2,4,5,6,7 440420 0.1-0.9 40Cal+Ms+Qtz + Zo*Kfs*HzO+COz 42 Jo&.Qr,72

782

TABLE 2. CONTINUED

THE CANADIAN MINERALOGIST

System or Equil ibr ium No Author P[kba r ] T f c l x(co2) B88 TD PH

K-Mg-Al-Si-H-O + CO2

Phl+Qtz = EnlSa*HzOpure H2O

K-Ca-Mg-Al-Si-C-H-O

43 8o,83 5Wo,76 0.4-0.5Wn&Do,77 0,5

780-800 0.6-0.7 41750-800 - 42820-850 - 42

i- WDi - w

Phl+Qtz+Cal = 5a*Tr*H:O*COr

Dol+Kfs+HzO = Phl+Cal+COz

Ca-Ti-Si-C-O * HrO

Ho,73 2,4,6He,75 2,4Pu&Jo,74 2Pu,78 4,6

500-650 0.1-0.7450-520 0.6-0.7420-540 0.1-0.9460-650 0.1-0.9

45

4 l4114t41

(i)+(i)+

Rt+Qtz+Cal = Ttn+COz 46 Ja&Ke,81b 2,6 420-620 0.1-0.8 45 i(2)+

Key: Numbers in column 'No'are used in the text. Column '888' indicates the igure number of Berman (1988).Notation for column 'TD' which indicates the consistency with the thermodynamic data base of Berman (1988):inconsistent ('i'); slightly inconsistent, within uncertainties of the mineral properties or fluid properties ['(i)']; numbers inparenthesesspecify pressure at which inconsistenciesare observed; experiments are at too high temperatures comparedto Berman (1988) (+); experiments are at too low temperatures compared to Berman (t9S8) (-); includes revisedmagnesite properties of Mider & Berman (1991) (*); Column 'PH' specifies inconsistencies amongst studies of thesame equilibrium. The one-letter abbreviations key to the authors within the same group. Abbreviations for mineralsare those of Kretz (1983). Abbreviations for authors: Allen & Fawcett 19S2 (Al&Fa), Althaus et, al. t970 (Ah), Bohlenet aI. 7983 (Bo), Chernosky & Berman 1986a, b, 1989, 1991 (Ch&Be), Chatterjee 1970 (Ct, Chatterjee & Johannes197a (Cj&Jo), Eggert & Kerrick 1981 (Eg&Ke), Eggler el aL t979 (El), Evans 1975 (Ev), Gordon & Greenuood 1970,1971 (Go&Gr), Greenuood 1967a, b (Gr), Harker & Tutt le 1956 (Ha&Tu), Hewitt 1973, 1975 (He), Hoschek 1973,1974 (Ho), Jacobs & Kenick 1981b (Ja&Ke), Johannes 1969 (Jo), Ki ise & Metz 1980 (Ka&Me), Kerrick 1972 (Ke),Kenick & Ghent 1979 (Ke&Ge), Metz 1967, 1970,L976 (Me), Metz & Puhan, 1970, 1971 (Me&Pu), Metz & Winkler1963 (Me&Wi), Nitsch 1972 (Ni), Puhan 1978 (Pu), Puhan & Johannes 197a (Pu&Jo), 5hmulovich 1974, 1978 (5h),Shvedenkov eJ a/. 1983 (5v), Skippen 1971 (Sk), Slaughter et al. Lg75 (51), Stone & Nitsch 1972 (St&Ni), Walter1963a, b (Wa), Widmark 1980 (Wk), Wones & Dodge 1977 (Wn & Do), Wood 1976 (Wo), Zharikov et al. L977(Zh), Ziegenbein & Johannes $7a (Zi&Jo).

titanite suggested by Berman (1988), who could notfit the measurements at2kbar on equilibrium (46).Revised properties of magnesite (Trommsdorff &Connolly 1990, Mdder & Berman 1991) result innew inconsistencies with equilibria (37, 38) thatwere consistent with the Berman (1988) data-base.All these discrepancies cannot be explained solelyby deviations of the properties of the fluid mixturefrom those computed from the Kerrick & Jacobs(1981) equation of state, and thus must reflecterrors in experiments or thermodynamic data onthe solid phases.

Slight inconsistencies that indicate possible

negative deviations from ideal mixing in the fluidphase at temperatures above 750-800oC at I kbarpressure include brackets on equilibria in theCa-Al-Si system (6, 7, 10, I l) and in the Ca-Mg-Sisystem (14, 15, 16). Consideration of the calciteI-IV transition at approximately 800"C willenhance these inconsistencies. Thermodynamicproperties of the calcite polymorphs are not wellconstrained at present (Miider & Berman 1991).Negative deviations from ideal mixing are consis-tent with Greenwood's (1969) measured negativevolumes on mixing at 700 and 800'C (Fig. 7).

At temperatures below 430oC, where deviations

WATER - CARBON DIOXIDE MIXTURES 783

P-V-T-X data are notfrom ideal mixing become most pronounced,constraints from phase-equilibrium data are not inaccord. New data on the reaction calcite +andalusite + quartz + anorthite + CO2 (3)(Chernosky & Berman 1991) seem to agree with theKerrick & Jacobs (1981) equation, whereas data ondolomite + quartz ;. calcite + talc + CO2 Q9)demand more positive deviations from ideality.Data on reaction (32) cannot be reconciled withexisting constraints on the minerals involved. TheKerrick & Jacobs (1981) equation appears to yieldreasonable deviations from ideal mixing at theselow temperatures. The equation cannot be utilizedbelow 325'C for mathematical reasons.

CoNcr-usloNs AND FuruRE WoRK

I conclude that at present, insufficient ex-perimental data and inadequate theoretical founda-tions are available on which to build a constrainedempirical model that allows one to computefugacities of H2O-CO2 mixtures over the range ofpressure and temperature of interest to petrologists.The de Santis e/ al. (1974) correction for chemicalassociation used by Holloway (1977) and Bowers& Helgeson (1983) is not supported by availableexperimental data. The Kerrick & Jacobs (1981)equation of state yields the most reasonablefugacity coefficients, even at temperatures as lowas 350-400'C.

The existing body of data is sufficiently extensivethat with some effort, the experimental data-baseshould be amenable to the proposed approach. Thefollowing problems or lack of data deserveparticular attention.

P-V-T-X dato

Inconsistensies among existing sets of. P-V-T-Xmeasurements must be resolved, and the range ofpressure must be increased to at least l0 kbar bya complete series of P-V-T-X measurements,including pure H2O and pure CO2. A determinationof the exact shape of the Z.*""r, versas P humpbelow 2 kbar pressure is crucial.

Phase-equilibrium dsta

(a) Several inconsistencies amongst studies onphase-equilibria involving H2O-CO2 mixtures needto be resolved in order to permit refinement ofthermophysical properties of solid phases, whichwill then provide better constraints on the fluidmixture.

(b) Phase-equilibria involving H2O-CO2 mix-tures can be utilized to constrain deviations from

(c) There are very few constraints from phase-equilibrium data on the activity of H2O in aH2O-CO2 mixture.

Minerql properties

More extensive measurements are needed on heatcapacity, expansivity, and compressibility of mag-nesite, calcite, brucite and talc.

Theoreticsl work

None of the equations of state available for fluidmixtures at higher pressures and temperatures areapplicable to subgreenschist metamorphic conditions because they do not account for the two-phaseregion.

The concluding paragraphs are devoted tospecific experimental projects that are aimed atconstraining the mixing properties of the fluidphase and at improving on the thermodynamicdata-base for solid phases.

5 magnesite + I talc + 4forstefite + 1H2O+ 5 C O 2

Experimental brackets by Greenwood (1967) andhalf-brackets by Johannes (1969) constrain theequilibrium position tightly at 1 and 2 kbar (Fig.8), but are difficult to reconcile with the ther-modynamic data-base of Berman (1988) and therevised enthalpy of magnesite (Miider & Berman1991). Ifthese data are accurate, then some mineralproperties must show temperature dependencies(e.g., heat capacity, expansivity) that are verydifferent from the Berman (1988) data-base' or thedeviations from the Kerrick & Jacobs (1981)equation of state are larger than estimated atpresent. New brackets on this equilibrium wouldresolve these inconsistencies and place constraintson the deviation from ideal mixing in the fluidphase.

Equilibria involving margarite

This project would aim to provide constraintson the activity of H2O in a H2O-CO2 mixture in atemperature range where deviations from idealityare expected to be significant (Fig. 9). Equilibriawith margarite in pure HrO have been studied byJenkins (1984), Storre & Nitsch (1974), Nitsch etal. (1981), Chatterjee et al. (1984), and Chatterjee(1974). The two equilibria suitable for study in afluid mixture are: I margarite + I quartz + I

ideal mixing whereavailable.

. '. cot

nso*Sfr-(-

o q \ 1 2 k b a r

A Johanne.e (1969) l, 4 fbu

. {\C tr Johaues (1969) 0.5, 2, ? kbar

5 NgS '

Q Greenwood (1967) I kbar

O creeoreood (1967) 2 tba

784 THE CANADIAN MINERALOGIST

i-: ,rn

= t tn

q

d00

^ 600

o { {nk

- - -

=ko 500

FI

-(DF{ 4JO

x(c0,)Ftc. 8. Fluid composition yersas temperature phase

diagram of the equilibrium magnesite + talc =forster i te + H2O + CO2at0.5, l ,2 ,4and7kbar.Filled symbols depict experimental charges with thereactant-stable phase assemblage, open symbols depictproduct-stable charges. Curves were computed withthe Kerrick & Jacobs (1981) equation of srate, rhethermodynamic data of Berman (1988), and magnesiteproperties revised by Miider & Berman (1991). See textfor discussion of inconsistencies. The diagram wascomputed with GEO-CALC (Brown et al. 1988).

andalusite + I anorthite + I H2O and I margarite+ I anorthite + I corundum + I H2O. Therangeaccessible to experimentation at a fluid pressure of2 kbar spans 400-500'C and 0.1 < X(CO) < 0.7.

Equilibria at pressures greater than 15 kbar

Such studies, performed in a solid-media ap-paratus, would aim to constrain deviations fromideal mixing in the fluid phase at pressures notaccessible by P-V-T-X mesurements (e.9., Eggleret al. 1979). The obvious disadvantages are thesmall volume of sample and the difficulty incontrolling fluid composition, speciation in thefluid phase and diffusion of hydrogen at hightemperatures. Because only the relative displace-ment from the equilibrium in the presence of thepure fluid is sought, some of the uncertaintiesarising from extrapolation of thermodynamicproperties cancel. In order to resolve deviationsfrom ideal mixing in the fluid phase, the bestprecision possible has to be achieved, which isabout t 5 K for piston-cylinder work. Feasible

X(COJ at P = 2000 bat

Frc. 9. Fluid composition versrs temperature phasediagram of equilibria involving margarite, andalusite,corundum, quartz, anorthite, H2O and CO2 at2kbarpressure. The solid curves were computed with theKerrick & Jacobs (1981) equation of state andlhermodynamic data of Berman (1988). Dashed curveswere computed assuming ideal mixing in the fluidphase. Reactions with zoisite or grossular that modifythe diagram at very water-rich compositions are notshown. The diagram was produced with GEO-CALC(Brown el a/. 1988).

studies include the reactions: 2 diaspore €corundum + H2O (580'C at 20 kbar), forsterite+ tremolite +senstatite + 2diopside + H2O(650'C at 20 kbar), talc + forsterite + enstatite+ H2O (700'C at 20 kbar), talc + 3 enstatite +quartz + H2O (800'C at 20 kbar), brucite ..periclase + H2O (950"C at 20 kbar), magnesite +quartz + enstatite + CO2 (900'C at 20 kbar),magnesite + enstatite + forsterite + CO2 (1100'Cat 20 kbar), and calcite + quartz + wollastonite+ CO2 (1350'C at 20 kbar).

ACKNOWLEDGEMENTS

The author is indebted to Hugh J. Greenwood(University of British Columbia) and Robert G.Berman (Geological Survey of Canada) for supportand advice during his Ph.D. research. Hugh alsoensured completion of my Ph.D. on time by settingsail and venturing into new dimensions, exploringfluid properties. For that, and much more, I thankhim. Financial support by NSERC to Greenwood(67-4222) and Berman (OGP 0037234) for part of

- Kerrick & ,lacobs (1981) equqtion of state- tdeal mixitg

this project is acknowledged. J.R. Holloway kindlysupplied computer codes for the evaluation of hisequation of state. The manuscript was improved atvarious stages by R.G. Berman, H.J. Greenwoodand T.H. Brown. Terry Gordon provided stimulusby organizing an exciting "Greenwood Sym-posium" during the Vancouver 1989 GAC-MACAnnual Meeting. The comments made by E.L.Johnson, R.F. Martin and an anonymous reviewerwere constructive and helpful.

REFERENCES

AlleN, J.M. & Fawcrrr, J.J. (1982): Zoisite -anorthite - calcite stability relations in H2O-CO2fluids at 5000 bars: an experimental and SEMstudy. "/. Petrol. 23, 215-239.

ALrHaus, E., KanorrE, E., Nrrscn, K.H. & WrNrlen,H.G.F. (1970): An experimental re-examination ofthe upper stability of muscovite plus quartz. NealesJahrb. Mineral. Monotsh., 325-336.

ANoensoN, G.M. (1977): Fugacity, activity, and theequilibrium constant. .Ir? Application of Ther-modynamics to Petrology and Ore Deposits (H.J.Greenwood, ed.\. Mineral. Assoc. Con., ShortCourse Handbook 2, 17-37.

BrnueN, R.G. (1988): Internally-consistent ther-modynamic data for minerals in the system Na2O-K2O-CaO-MgO-FeO-Fe2O3-SiO2-TiO2-H2O-CO,.J. Petrol. 29. M5-522.

-, ENct, M,, GnrrNwooo, H.J. & BnowN, T,H.(1986): Deviation of internally-consistent ther-modynamic data by the technique of mathematicalprogramming, a review with application to thesystem MgO-SiO2-H2O. J. Petrol. 27, 133l-1364.

Bour-rN, S,R., BosrrcHrn, A.L., Well , V.J. &CLrvrNs, J.D. (1983): Stability of phlogopite -quartz and sanidine - quartz: a model for meltingin the lower crust. Contrib. Mineral. Petrol. E3.270-277.

BorrrNGA, Y. & RrcuEr, P. (1981): High pressure andtemperature equation of state and calculation ofthermodynamic properties of gaseous carbondioxide. Am. J. Sci. 281. 615-660.

Bowrns, T.S. & HrLcesoN, H.C. (1983): Calculationof the thermodynamic and geochemical consequen-ces of nonideal mixing in the system H2O-CO2-NaCl on phase relations in geologic systems:equation of state for H2O-CO2-NaCI fluids at highpressures and temperatures. Geochim. Cos-mochim. Acta 27, 124'I-1275,

BnooHolr, J. & Wooo, B. (1990): Molecular dynamicssimulations of water at high temperatures and

WATER - CARBON DIOXIDE MIXTURES

CHarrrure,stability(oH)zl.753-767.

pressures. Trans. Am. Geophys. Union (EOS) 11,621 (abstr.).

BnowN, T.H., Bsnrr.reN, R.C. & PEnrtNs, E.H. (1988):GEO-CALC: software package for calculation anddisplay of pressure - temperature - compositionphase diagrams using an IBM or compatiblepersonal computer. Comp. Geosci. 14, 279-289,

Bucuen-NunptrNrN, K. (1988): Metamorphism ofultramafic rocks in the central ScandinavianCaledonides. Nor. Geol. Unders., Spec. Publ. 3,86-95.

Cenprrcsapl, D.M. (1991): Univariant mixed-volatilereactions: pressure - temperature phase diagramsand reaction isograds. Can. Mineral. 29, 7 4l-7 54.

785

N.D. (1974): Synthesis and upperlimit of 2M-margante, CaAl2[Al2Si2OtoSchweiz. Mineral. Petrogr. Mitt. 54,

(1970): Synthesis and upper stability ofparagonite. Contrib. Mineral. Petrol. 27, 244-257.

(1991): Applied Mineralogical Thermody-namics : Selected Topics. Springer-Verlag, Berlin.

& JoHlNNrs, W. (1974): Thermal stability andstandard thermodynamic properties of synthetic2M-muscovite, KAl2[Alsi3or0(oH)2]. contrib.Mineral. Petrol. 48, 89-l 14.

& LrnrNEn, H. (1984): The systemCaO-AI2O3-SiO2-H2O: new phase equilibria data'some calculated phase relations, and theirpetrological applications. Contrib. Minerol. Petrol.88, l -13.

Curnnosrv, J.V. & BenuaN, R.G. (1986a): Thestability of clinochlore in mixed volatile, H2O-CO2fluid. Trons. Am. Geophys. Union (EOS) 67,407(abstr.).

-&- (1986b): Experimental reversal of theequilibrium: clinochlore + 2 magnesite : 3forsterite + spinel + 2CO2 + 4H2O. Trons. Am.Geophys. Union (EOS) 67, 1279 (abstr.).

&- (1989): Experimental reversal of theequilibrium: clinochlore + 2magnesite = 3forsterite + spinel + 2COz + 4H2Oandrevisedthermodynamic properties for magnesite. Am. J.Sci. 2E9,249-266.

(1991): Experimental reversal of theequilibrium andalusite * calcite * quartz =anonhite + CO2. Can. Minerol. 29,791-802.

CHou, I-MrNc & Cvcex, R.J. (1990): Quantitativeredox control and measurement in hydrothermalexoeriments. /n Fluid-Mineral Interaction: A

786 THE CANADIAN MINERALOGIST

Tribute to H.P. Eugster (R.J. Spencer & I-MingChou, eds.). The Geochemical Soc., Spec. Publ.2 , 3 - t 5 .

- & Wrnraus, R.J. (1977): Activity of H2O inCO2-H2O at 600oC and pressure to 8 kilobars.Geol, Soc. Am,, Abstr. Programs 9,928.

& - (1979a): Activity of H2O inSoc. Am.,supercritical CO2-H2O fluids. Geol.

Abstr. Programs ll, 401.

& - (1979b): The activity of H2O insupercritical fluids: H2O-CO2 at 600oC and 700oCat elevated pressures. Proc. Xth Lunar Planet. Sci.Conf.,201-203.

CoNNoLLv, J.A.D. & BooNen, R.J. (1983): A modifiedRedlich-Kwong equation of state ior H2O-CO2mixtures: application to fluid inclusion studies.Trans. Am. Geophys. Union (EOS) 64, 350(abstr.).

& Tnouusponrr, V. (1991): Petrogenetic gridsfor metacarbonate rocks: pressure - temperaturephase diagram projection for mixed-volatile sys-tems. Contrib. Mineral. Petrol. 108,93-105.

Eccrlr, R.G. & KEnnrcx, D.M. (1981): Metamorphicequilibria in the siliceous dolomite system: 6 kbarexperimental data and geologic implications.Geochim. Cosmochim. Acta 45, 1039-1049.

Eccr-rn, D.H., KusHrno, I. & Hor-r-owav, J.R. (1979):Free energies of decarbonation reactions at mantlepressures. l. Stability of the assemblage forsterite- enstatite - magnesite in the system MgO-SiO2-CO2-H2O to 60 kbar. Am. Mineral. 64,288-293.

Eucsrrn, H.P. & Srrmru, G.B. (1967): Igneous andmetamorphic reactions involving gas equilibria. /nResearches in Geochemistry 2 (P.H. Abelson, ed.).John Wiley & Sons, New York (492-520).

EveNs, B.W. (1965): Application of a reaction-ratemethod to the breakdown equilibria of muscoviteand muscovite plus quartz. Am. J. Sci. 263,647-667.

Fennv, J.M. & BauvcenrNrn, L. (1987): Ther-modynamic models of molecular fluids at theelevated pressures and temperatures of crustalmetamorphism. 1n Thermodynamic Modeling ofGeological Materials: Minerals, Fluids and Melts(I.S.E. Carmichael & H.P. Eugster, eds.). Rev.Mineral. l7 , 323-365.

FLowens, G.C. (1979): Correction of Holloway's(1977) adaptation of the modified Redlich-Kwongequation of state for calculation of the fugacitiesof molecular species in supercritical fluids ofgeologic interest. Contrib. Minerol. Petol. 69,3 15-3 I 8.

& HrLcrsoN, H.C. (1983): Equilibrium andmass transfer during progressive metamorphism ofsiliceous dolomites. Am. J. Sci. 283, 230-286,

Fnercr, E.U. (1981): Survey of selected non-ther-modynamic properties and chemical phenomena offluids and fluid mixtures. .ln Chemistry andGeochemistry of Solutions at High Temperatureand Pressure (D.T. Rickard & F.E. Wickman,eds.). P&ls. Chem. Earth 13-14, 65-88.

& TooHeroe , K. (1959): ThermischeEigenschaften iiberkritischer Mischungen von Koh-lendioxyd und Wasser bis zu 750'C und 2000 atm.Z. Phys. Chem., Neue Folge 22,232-245.

FneNrs, F., ed. (1912-1984): Woter, a ComprehensiveTreatise (volumes l-7). Plenum Press, New York.

Grunrc, M. (1980): Phasengleichgewichte und PVT-Daten terniirer Mischungen aus Wasser, Kohlen-dioxid und Natriumchlorid bis 3 kbar und 550"C.Dissertation, Hochschulverlag, Freiburg, Cer-many.

GonooN, T.M. & GnEENwooD, H.J. (1970): Thereaction: dolomite + quartz + water = talc rcalcite + carbon dioxide. Am. J. Sci. 268, 225-242.

(1971): The stability of grossularitein H2O-CO2 mixtures. Am. Mineral. 56, 1614-l 688.

GnrrNwooo, H.J. (1961): The system NaAlSi2O6-H2O-argon: total pressure and water pressure inmetamorphism. J. Geophys. Res. 66, 3923-3946.

(1967a): Wollastonite stability in H2O-CO2mixtures and occurrence in a contact-metamorphicaureole near Salmo, British Columbia, Canada.Am. Mineral. 52, 1669-1680.

(1967b): Mineral equilibria in the systemMgO-SiO2-H2O-CO2. In Researches inGeochemistry 2 (P.H. Abelson, ed.). John Wiley& Sons, New York (542-567).

- (1969): The compressibility of gaseous mixturesof carbon dioxide and water between 0 and 500bars pressure and 450' and 800'C. Am. J. Sci.267-4. t9l-208.

(1973): Thermodynamic properties of gaseousmixtures of H2O and CO2 between 450oC and800oC and 0 to 500 bars. Am. J. s,ci .273.561-571.

& BenNrs, H.L. (1966): Binary mixtures ofvolatile components. /z Handbook of PhysicalConstants (S.P. Clark, Jr., ed.). Geol. Soc. Am.,Mem. 97,385-400.

Haan, L., GeLLacuEr, J.S. & Krn, G.S. (1984):NBS/NRC Steam Tables. Thermodynamic and

WATER - CARBON DIOXIDE MIXTURES 787

Transport Properties and Computer Progroms forVapor ond Liquid States of Woter in SI Units.Hemisphere Publishing Co., Washington, D.C.

Hamrn, R.I. & TurrrB, O.F. (1956): Experimentaldata on the P(CO)-T curve for the reaction: calcite+ quafiz + wollastonite + carbon dioxide.,4m.J. Sci. 254,239-256.

Hrwrrr, D.A. (1973): Stability of the assemblagemuscovite - calcite - qvartz. Am. Mineral. 58'785-79t.

(195): Stability of the assemblage phlogopite

FORTRAN programs for a new equation of statefor H2O, CO2 and their mixtures at supercriticalconditions. Comp. Ceosci. 7 , l3l'143.

&- (198 1b): Devolatilization equilibriain H"O-CO' and H2O-COr-NaCl fluids: anexperilrnental-and thermodynamic evaluation atelevated pressures and temperatures. Am. Mineral'66. n35-1153.

JrNrrrs, D.M. (1984): Upper-pressure slability ofsynthetic margarite plus quartz. Contib. Minerol'Petrol. 88,332-339,

JoHeNNns, W. (1969): An experimental investigationof the'system MgO-SiO2-H2O-CO2. Am. J. Sci'267, r083-lr%.

JoHlrsoN, J.W. & NonroN, D. (1991): Criticalphenomena in hydrothermal systems: state, ther-modynamic, electrostatic, and transport propertiesof Aro in the critical region. Am. J. Sci. 291'541-U8.

Jovcr. D.B. & Hot-t-owav, J.R. (1987): Activity -

composition relations for H2O in the systemH.O-CO,-NaCI at high P and T bY a newt"6hniqu6. Trans. Am. Geophys. Union (EoS) 68,450-451 (abstr.;.

- calcite - quartz. Am. Mineral. 60,391-397.

Hollexo, T.J.B. & PoweLL, R. (1990): An enlargedand updated internally consistent thermodynamicdataset with uncertainties and correlations: thesystem K2O-Na2O-CaO-MgO-MnO-FeO-F9O3-Al2O3-TiO2SiO 2-C-H2-O2. f . Metamorph. Geol.8.89-124.

Hor-r-owev, J.R. (1977): Fugacity and activity ofmolecular species in supercritical fluids. /n Ther-modynamics in Geology (D.G. Fraser, ed.). D.Reidel, Dordrecht, Holland (161-1 8l).

(1981): Compositions and volumes of s19e1:al fluids in the earth's crust. .In Fluidcritical flu

Inclusions: Applications to Petrology (L.S. Hol-lister & M.L. Crawford, eds.). Mineral. Assoc.Can., Short Course Hondbook 6, 13-38.

(1987): Igneous fluids. .In ThermodynamicModeling of Geological Materials: Minerals, Fluidsand Melts (I.S.E. Carmichael & H.P. Eugster'eds.). Rev. Mineral. l7,2l l-233.

Holsrn. W.T. & KrNNEov, G.C. (1958): Properties ofwater. IV. Pressure - volume - temperaturerelations of water in the range 100-400'C and100-1400 bars. Am. J. Sci. 256,744-753.

&- (1959): ProPerties of water. V.

cients for H2O in H2O-CO2-NaCI fluids. .Irans'Am. Geophys. Unioi (EoS) 70,495-496 (abstr.).

KAse, H.-R. & Mrrz, P' (1980): Experimentalinvestigation of the metamorphi,sm of siliceousdolomltes. IV. Equilibrium data for the reaction:I Diopside + 3 Dolomite .' 2 Forsterite + 4Calcit6 + 2 COz. Contrib. Mineral. Petrol. 73,15 l -159.

KrNNeoY, G.C. (1954): Pressure - volume - tempera-ture relations in CO2 at elevated temperatures andpressures. Am. J. Sci. 252, 225'241.

KEnntc*, D.M. ( I 972) : Experimental -determination of

muscovite + quaftz stability with Ps2o ( Ptotal."Am. J. Sci. 272, 946-958'

&- (1989): Experimental activity coeffi-

& Gnrwr, E.D. (19?9)l P-T-Xg62 relations of

Pressure - volume - temperature 1elali91s of waterin the range 400-1000'C and 100-1400 bars. Am.J. !c i .257,71-77.

HoLzepruL, W. & Fnaxcr, E.U. (1966): Leitfiihigkeitund lonendissoziation des Wassers bei 1000"C und100 kbar. Berlin. Bunsenges. Phys. Chem. 70,I 105- l I 12.

HoscHrr, G. (1973): Die Reaktion Phlogopit + Calcit+ Quarz = Tremolit + Kalifeldspat + H2O +CO2. Contrib. Mineral. Petrol. 39,231-237.

(1974): Gehlenite stability in the systemMineral.CaO-A12O3-SiO2-H2O-CO2. Contrib.

Petrol. 47. ,45-254.

equilibria in the system: CaO-Al2O3-9LOz-9Ori,O. In Problems in Physico-Chemical Petrology(V-.A. Zakirov, V.I' Finarev * Y.Sr-[gttq"^t\t]'ids)). Academy of sciences of the USSR 2' 32'52,

& Jecoss, G.K. (1981): A modified Redlich-Kwong equation for H2O, CO2, and H2O-CO2mixtures at elevated pressures and temperatures.Am. J. Sci. 281, 735-767.

Knrrz, R. (1983): Symbols for rock-forming minerals.Am. Mineral. 6E, 277 -279.Jacoss, G.K. & Krnntcr, D.M. (l98la): APL and

788 THE CANADIAN MINERALOOIST

KnusE, R. (1975): Ramon-Spektroskopische Unter-suchungen and CO2-H2O Mischungen bis 490"Cund 2500 bar. Ph.D. thesis. Universitiit Karlsruhe.Karlsruhe, Germany.

MADER, U.K. & BERMAN, R.G. (1991): An equationof state for carbon dioxide to high pressure andtemperature. Am. Mineral. 76, 1547-1559.

MeNNrNc, C.E. & BoHr-rr, S.R. (1991): The reactiontitanite + kyanite = anorthite + rutile and titanite- rutile barometry in eclogites. Contrib. Mineral.Petrol. 109, l-9.

Mrrz, P. (1967): Experimentelle Bildung von Forsteritund Calcit aus Tremolit und Dolomit. Geochim.Cosmochim. Acta 31. 1517-1532.

(1970): Experimentelle Untersuchung derMetarnorphose von kieselig dolomitischenSedimenten. II. Die Bildungsbedingungen desDiopsids. Contrib. Mineral. Petrol. 28, 221-250.

(1976): Experimental investigation of themetamorphism of siliceous dolomites. III. Equi-librium data for the reaction: I tremolite + lldolomite + 8 forsterite + 13 calcite + 9 CO2 +I H2O for the total pressures of 3000 and 5@0bars. Contrib. Minerol. Petrol. 58, 137-148.

& PuHar, D. (1970): Experimentelle Unter-suchung der Metamorphose von kieselig dolomitis-chen Sedimenten. I. Die Gleichgewichtsdaten derReaktion 3 Dolomit + 4 Quarz + I H2O + ITalk + 3 Calcit + 3 CO2 fiir die Gesamtgasdruckevon 1000, 3000 und 5000 Bar. Contrib. Mineral.Petrol. 26,302-314.

&- (1971): Konektur zur Arbeit"Experimental Untersuchung der Metamorphosevon kieselig dolomitischen Sedimenten. I. DieGleichgewichtsdaten der Reaktion 3 Dolomit + 4Quarz + I H2O :: I Talk + 3 Calcit + 3 CO2fiir die Gesamtgasdrucke von 1000, 3000 und 5000Bar'. Contrib. Mineral. Petrol.3l. 169-170.

& Wu.n<len, H.G.F. {1963): ExperimentelleGesteinsmetamorphose. VII. Die Bildung von Talcaus kieseligem Dolomit. Geochim. Cosmochim.Acta 27, 431-457.

MrrcHrLL, A.C. & NELLrs, W.J. (1979): WaterHugoniot measurements in the range 30 to 220GPa. In High Pressure Science and Technology. 1.Physical Properties and Material Synthesis, 6thAIRAPT Conference (K.D. Timmerhaus & M.S.Barber, eds.). Plenum Press, New York(428-434).

Nrrscu, K.-H. (1972): Das P-T-X662-Stabilitatsfeldvon Lawsonit, Contrib. Mineral. Petrol, 34.lt6-t34.

telle Bestimmung der Gleichgewichtsdaten derReaktion I Margarit + I Quarz :r I Anorthit +1 Andalusit/Disthen + | H,O. Fortschr. Mineral.59. 139-140.

PowrLL, R. & Hor-r-aNo, T.J.B. (1985): An internallyconsistent thermodynamic dataset with uncertain-ties and correlations. l. Methods and a workedexample. J. Metamorph. Geol. 3, 327'342.

PneusNrrz. J.M.. LIcsTENTHALER, R.N. & DrAzrvroo, E. G. (l 986): Mo lecu lar The rmodynomicsof Fluid-Phase Equilibria (2nd ed.). Prentice-HallInc., Englewood Cliffs, New Jersey.

PuHaN, D. (1978): Experimental study of the reaction:dolomite + K-feldspar + H2O + phlogopite rcalcite + CO2 at the total gas pressure of4000 and6000 bars. Neues Jahrb. Mineral. Monatsh.,tt0-127.

& JonlxNrs, W. (1974): ExperimentelleUntersuchung der Reaktion Dolomit +Kalifeldspat + H2O +Phlogopit + Calcit + CO2.Ein Methodenvergleich. Contrib. Mineral. Petrol.48 ,23-3 t .

Rren, A.J. (1975): The first ionization constant ofcarbonic acid from 25 to 250'C and to 2000 bar.J. Sol. Chem. 4,53-70.

ReoLrcH, O. & Kwouc, J.N.S. (1949): On thethermodynamics of solutions. V. An equation ofstate. Fugacities of gaseous solutions. Chem. Rev,u.233-2M.

RvzurNro, B.N. & VoLrov, V.P. (1971): Fugacitycoefficients of some gases in a broad range oftemperatures and pressures. Geochem, Internat. E,468-48 l.

De SeNrrs, R., Bnerovrlo, G.J.F. & Pneusurrz, J.M.(1974): Thermodynamic properties of aqueous gasmixtures at advanced pressures. Indust. Eng,Chem. Proc. Des. Devel. 13,374-371 .

SaxpNe, S.K. & FEI, Y. (1987): Fluids at crustalpressure and temperatures. I. Pure species. Cor-trib. Mineral. Petrol. 95, 370-37 5.

Surr,roNov, V.M. & SHMULovtcu, K.I. (1974): Molalvolumes and equation of state of CO2 at tempera-tures from 100-1000'C and pressures from 2000-10000 bars. Dokl. Acad. Sci. USSR, Eorth Sci.Sect. 217 , 206-209.

SMULovrcH, K.I. (1974): Phase equilibria in the systemCaO-AI2O3-SiO2-CO2. Geochem. Intern. lL(4),883-887.

(1978): Stability limits of grossular and

sroRRE, B. & rornen, u. (1e8r): Experimen- u':3t:;:';;#I.'f,8, i*;l;tem up to 6 kbar'

WATER - CARBON DIOXIDE MIXTURES 789

& Korova, N.P. (1980): Influence ofelectrolytes on the activity of CO2 in supercriticalaqueous solutions. Dokl. Akad. Nauf SSSR 253,952-956 (in Russ.).

SuvoNov, V.M., Mezun, V.A. & KeLrNrcHEv,A.G. (1980): P-V-T and activity concentrationrelations in the H2O-CO2 system (homogeneoussolutions). Geochem. Intern. 17(6), 123-139.

-,- & ZHertnov, I.V. (1979): P-V-Tmeasurements in hydrous systems at high pressureand temperature. In Experimental ResearchMethods for Hydrothermal Solutions (A.A.Godikov, ed.). Nauka, Novosibirsk (81-89) (inRuss.).

SuvrorNrov, G.Y., SHvnorNrova, S.V., Desurvsrtt,Y.A. & Ker-rNrN, D.V. (1983): Phase equilibria inthe sytem containing muscovite, paragonite.alkaline feldspars, H2O. and CO2. Sov. Geol.Ceophys. 24, 428-436.

SrrereN, G.B. (1971): Experimental data for reactionsin siliceous marbles. J. Geol. 79,457-481.

& CanvrcHasl, D.M. (1977): Mixed-volatileequilibria. In Application of Thermodynamics toPetrology and Ore Deposits (H.J. Greenwood,ed.). Mineral. Assoc. Conadq, Short CourseHandbook 2, 109-125.

& Mensrnll, D.D. (1991): The metamorphismof granulites and devolatilization of the litho-sphere. Can. Mineral. 29, 693-705.

SleucHrpn, J., Krnnrcr, D.M. & War-1, V.J. (1975):Experimental and thermodynamic study of equi-libria in the system CaO-MgO-SiO2-H2O-CO2.Am. J. Sci. 275,143-162.

Srycurn, N.F. & REro, M.H. (1988): Fugacitycoefficients of H2, CO2, CHa, H2O and ofH2O-CO2-CH4 mixtures: a virial equation treat-ment for moderate pressures and temperaturesapplicable to calculations of hydrothermal boiling.Geochim. Cosmochim. Acta 52, 739-7 49.

SrrnNrn, S.M. & BooNER, R.J. (1991): Synthetic fluidinclusions. X. Experimental determination ofP-V-T-X properties in the CO2-H2O system to 6kb and 700"C. Am. J. Sci.29l, l -54.

Sronnr, B. & Nrrscu, K.-H. (1972): Die Reaktion 2Zoisit + I CO2 r. 3 Anorthit + I Calcit + IH2O. Contrib. Mineral. Petrol. 35, l-10.

&- (1974): Zur Stabilitat von Margaritim System CaO-AI2O3-SiO2-H2O. Contrib.Mineral. Petrol. 43, l-24.

TereNoucur, S. & KruNrov, G.C. (1964): The binary

system H2O-CO2 at high temperatures and pres-sures. Am. J. Sci. 262, 1055-1074.

TOouEror, K. (1972): Water at high temperatures andpressures. InWater, a Comprehensive Treatise. I.The Physics and Physical Chemistry of Water (F.Franks, ed.). Plenum Press, New York (463-514).

- & Fr.aNcr, E.U. (1963): Das Zweiphasengebietund die kritische Kurve im System Kohlendioxid-Wasser bis zu Drucken von 3500 bar. Z. Phys.Chem., Neue Folge 37 , 387-401.

Tnouvsnonrr, Y. (1972\: Change in T-X duringmetamorphism of siliceous dolomitic rocks of theCentral Alps. Schweiz. Mineral. Petrogr. Mitt.52,567-5',1l.

& CoNNor-lv, J.A.D. (1990): Constraints onphase diagram topology for the system CaO-MgO-SiO;CO2-H2O , Contrib. Mineral. Petrol. 104, l'7.

& Evnns, B.W. (1974): Alpine metamorphismof peridotitic rocks. Schweiz. Mineral. Petrogr.Mitt. 54,333-352.

Ururn, P. & LurH, R.W. (1991): The graphite-CoHfluid equilibrium in P, T, f62 space. An experimen-tal determination to 30 kbar and 1600"C. Contrib.Mineral. Petrol. 106, 265-272.

WalrEn, L.S. (1963a): Experimental studies onBowen's decarbonation series. I. P-T univariantequilibria of the "monticellite" and "akermanite"reactions. Am. J. Sci. 261,488-500.

(1963b): Experimental studies on Bowen'sdecarbonation series. II. P-T univariant equilibriaof the reaction: forsterite + calcite = monticellite+ periclase + CO2. Am. J. !ci.261,773-779.

(1963c): Data on the fugacity of CO2 inH2O. Am. J. Sci. 261,mixtures of CO2 and

I 5 1 -156.

Wrnnenr, E.T. (1980): The reaction chlorite +dolomite: spinel + forsterite + calcite + carbondioxide + water. Contrib. Mineral. Petrol. 72,t75-t79.

WoNrs, D.R. & DoDcr, F.C.W. (1977): The stabilityof phlogopite in the presence of quartz anddiopside. .lz Thermodynamics in Geology (D.G.Fraser, ed.). D. Reidel, Dordrecht, Holland(229-247).

Wooo, B.J. (1976): The reaction phlogopite + quartz: enstatite + sanidine + H2O. Progr, Exp.Petrol. Not. Environ. Res. Council ll, 17-19.

& FnnsEn, D.G. (1977): Elementary Ther-Oxford Universitymodynamics for Geologists.

Press, Oxford, U.K,

790 THE CANADIAN MINERALOGIST

ZHentrov, V.A., Snuulovtcu, K.I. & Bularov, V.K.(1977): Experimental studies in the system CaO-Mgo-et cir-sio2-co2-H2o and conditions ofhiJtr temierature metairorphism. Tectono p hys. 43,r45-162.

ZrecENrrtN, D. & JoHeNNrs, W. (1974): Wollastonit-bildung aus Quarz und Calcit bei Pf : 2' 4 und 6kb. Fortschr. Mineral. 44,77-79.

& - (1982): Activities of CO2 in

Pressure Researches in Geoscience (W. Schreyer'

suoercritical COr-HrO mixtures, derived fromhigh-pressure mineral equilibrium data. ,In High-

ed.). E. Schweizerbart'sche Verlagsbuchhandlung'Stuttgart, GermanY (493-500).

Received Januory 4, 1991, revised monuscript acceptedSeptember 7, 1991.