American Mineralogist, Volume 68, pages 1059-1075, 1983

Calculation of the thermodynamic and geochemical consequences of nonideal mixingin the system H2O-CO2-NaCI on phase relations in geologic systems:

metamorphic equilibria at high pressures and temperatures

TBRese SurBn Bowr,Rsr RNo Henolo C. HelcesoN

Department of Geology and GeophysicsUniversity of California, Berkeley, California 94720

Abstract

Fluid inclusion analyses reported in the literature, together with experimental data andthermodynamic calculations indicate that nonideality in the system H2O-CO2-NaC1 mayhave a profound effect on phase relations in metamorphic processes. High concentrationsof NaCl in the system H2O-CO2-NaCI increase substantially the size of the two-phase(liquid + vapor) region by raising the consolute temperature for a given pressure and ratioof the mole fractions of H2O and NaCl to more than double that in the binary system H2O-CO2. As a consequence, fluid immiscibility may occur at considerable depth duringprogressive metamorphism of siliceous carbonates. The effect of nonideal mixing of H2O,CO2, and NaCl on equilibrium constraints in metamorphic systems can be assessedquantitatively on phase diagrams generated with the aid of a modified Redlich-Kwongequation of state (Bowers and Helgeson, 1983). Diagrams of this kind indicate thatincreasing NaCl concentration results in higher temperatures and/or lower predicted valuesof X66, for equilibrium mineral assemblages than would be true for the binary system H2G-CO2. Transection of various mineral stability fields by saturation lines representingequilibrium between the aqueous phase and calcite, dolomite, or magnesite on logarithmicactivity diagrams is also highly sensitive to the NaCl concentration in the aqueous phase.For example, the assemblage tremolite + dolomite * talc coexists with an H2O-rich fluid at450"C,2 kbar, and NaCl concentrations <l m. However, as the concentration of NaClincreases to -4 m, tremolite is no longer stable in the presence of the fluid phase. Theslopes of isochores for given bulk compositions in the ternary system HzO-COrNaCldecrease substantially with increasing CO2 concentration. The isochores generated fromthe equation of state for the ternary system can be used to calculate pressure correctionsfor fluid inclusion homogenization temperatures. Stability fields for certain mineralassemblages in temperature--composition diagrams for the two-phase (liquid + vapor)region of the system H2O-CO2-NaCI are much smaller than their counterparts in the one-phase region. Furthermore, all univariant curves which cross the consolute compositioncurve on such diagrams exhibit temperature minima. These curves terminate in invariantpoints which are replicated on both sides of the miscibility gap. Subtle changes in NaClconcentration at low to intermediate values of X6e" may result in the appearance of mineralassemblages commonly thought to occur only in the presence of CO2-rich fluids. Failure toaccount for the possible efects of fluid immiscibility on equilibrium mineral assemblagesmay lead to serious errors in interpretation of phase relations in metamorphic rocks.

Introduction

Considerable evidence indicates that aqueous fluids ina wide range of geologic environments contain significantconcentrations of both CO2 and NaCl. The thermody-namic properties of these fluids have been calculated with

'Present address: Division of Geological and Planetary Sci-ences, California Institute of Technology, Pasadena, California9t125.

the aid of a modified Redlich-Kwong (MRK) equation ofstate for the ternary system H2G-CO2-NaCI (Bowers andHelgeson, 1983). The MRK equation of state was appliedto the ternary system by allowing the H2O parameters inthe equation to be functions of NaCl concentration. Theequation was then fit to pressure-volume-temperaturedata reported by Gehrig (1980). The regression parame-ters derived in this manner were used together with agraphic extrapolation procedure to calculate densities,fugacity coefficients, and the compositions of coexisting

0003-004x/83/l I I 2-t 059$02.00 1059

t060 BOWERS AND HELGESON: NONIDEAL MIXING IN HzO-COz-NaCI

phases as a function of pressure at temperatures from350' to 600"C and concentrations of NaCl from 0 to 35wt.% NaCl relative to H2O + NaCl (Bowers and Helge-son, 1983). The purpose of the present communication isto evaluate the efects of compositional variation andimmiscibility in H2O-CO2-NaCI fluids on mineral equilib-ria in geochemical processes at high pressures and tem-peratures. The extent to which such compositional varia-tion and immiscibility occur in hydrothermal systems canbe assessed with the aid offluid inclusion data.

Studies of fluid inclusions in quartz and feldspar ingranitic rocks from trachytic breccias on Ascension Is-land (Roedder and Coombs, 1967) indicate that a 60-70wt.% NaCl fluid unmixed to form an H2O-rich liquid anda CO2-rich vapor between -550" and 700'C. Unmixingalso apparently occurred in fluid inclusions studied byRoedder (1971) in the porphyry ores at Bingham, Utah,between 400'and 700'C. The liquid in these inclusionscontains up to 60 wt.Vo salts and the CO2-rich vapor phasecontains 6-7 wt.Vo salts. In contrast, Barton et al. (1977),in a study of the environment of ore deposition in theCreede Mining District, Colorado, cite fluid inclusionevidence for the unmixing of a I molal NaCl fluid toproduce a CO2-rich vapor at -270"C and 50 bars. Leroyand Poty (1969) and Poty et al. (1974) detected a largerange of Xs6rlXHrs (where X66, and XH,q designate themole fractions of CO2 and H2O, respectively) in a se-ries of fluid inclusions in the uranium deposits in theSaint-Sylvestre granite in the Central Massif in France.Immiscibility apparently occurred in these inclusions at-340-350'C and 700-800 bars. They suggest that theconcentration of uranium in solution is closely related tothe CO2 content, and that the uranium is possibly beingtransported as uranyl carbonate complexes. They furtherpostulate that with decreasing pressure and concomitantunmixing of the fluid phase, the complexes dissociate,causing uranium to precipitate. Similar observations andpostulates have been made by Lyakhov and Popivnyak(1978) and Petrovskaya et al. (1973) in gold deposits inNorthern Buryatia, the Lena region, and several otherlocations in the Soviet Union. Analyses of fluid inclusionsin quartz in the gold-quartz veins in these regions revealvariable amounts of COz and a wide range of homogeniza-tion temperatures, indicating fluid immiscibility. Howev-er, these characteristics are not observed in fluid inclu-sions in the nonproductive zones. Petrovskaya et al.(1973) note that periodic unmixing of the solutions couldhave been caused by abrupt decreases in pressure at theopenings of fissure cavities where the ore depositsformed. Lyakhov and Popivnyak observe maximum im-miscibility in fluid inclusions with homogenization tem-peratures of 210-260'C. They suggest that the pressuredrop and associated degassing of the gold-bearing solu-tions may have contributed to the breakdown of thecomplexes responsible for transporting the gold.

Three recent studies of fluid inclusions indicate thatregions of fluid immiscibility in metamorphic systems

may extend well beyond those exhibited by the binarysystem H2MO2. Examination of fluid inclusions inmatrix quartz crystals from an area of high-grade amphib-olite facies in the Khtada Lake region in British Columbia(Hollister and Bumrss, 1976) indicates that separation ofan H2O-rich liquid and a CO2-rich vapor occurred attemperatures at least 75'C in excess of high-pressureconsolute temperatures in the binary system HzO-COz.Approximately 5-6wt.Vo NaCI is present in the H2O-richliquid in these inclusions. Similarly, Hendel and Hollister(1981) demonstrated by plotting homogenization tempera-tures as a function of the mole fraction of COz thatimmiscibility occurred in fluid inclusions containing 2.6wt.% NaCl relative to H2O + NaCl in quartz veinlets in apelitic schist at temperatures -65'C higher than theconsolute temperatures for pressures between I and 2kbar in the system H2O-CO2. In addition, Sisson et a/.(1981) describe fluid inclusions in quartz segregations in acalcareous psammite and a carbonate schist which exhibitimmiscibility between a brine containing -24 wt.Vo dis-solved solids and a CO2-rich vapor at 600'C and 6.5 kbar.

The observations summarized above leave little doubtthat both NaCl and CO2 may be present in high concen-trations in crustal fluids, and that these fluids may unmixat high temperatures and pressures. Nevertheless, pres-sure corrections applied to fluid inclusion homogeniza-tion temperatures are commonly calculated by assumingthat the pressure-volume-temperature properties of theffuids in the inclusions can be approximated closely bythose of pure H2O. However, even small amounts of CO2or NaCl may alter substantially these properties. Theeffect of such differences on pressure corrections offluidinclusion homogenization temperatures can be assessedwith the aid of the MRK equation of state adduced above.

Pressure corrections for hornogenizationtemperatures of fluid inclusions in the

ternary system HzO-COz-NaCl

Calculated densities of fluids in the ternary systemH2GCO2-NaCI (Bowers and Helgeson, 1983) are shownas isochores on the pressure-temperature diagrams de-picted in Figures 1-5. The solid curves in Figure Irepresent pure H2O, which is designated A in the compo-sition diagram in the upper left corner of the figure. Thedashed curves refer to HzO-COz fluids containing l0moleVo CO2 (solution B). The dot-dash curves correspondto H2GCO2-NaCI fluids with l0 moleVo CO2 and 1.74moleVo NaCl (solution C). Although fluid inclusions con-taining pure H2O homogenize along the equilibrium va-porJiquid saturation curve for the system HzO shown inFigure 1, those with compositions corresponding to solu-tions B and C homogenize along the curves labeled D andE, respectively. Certain areas in the figure are shaded orhachured to emphasize the shift in the slopes of theisochores resulting from addition of CO2 and NaCl. Thiseffect is most pronounced at high temperatures.

The diagrams shown in Figures 2-5 can be used tocalculate pressure corrections for fluid inclusion homog-enization temperatures if the fluid composition is known.Isochores for bulk compositions not shown in thesefigures can be generated from densities taken from tablesor calculated from the MRK equation of state for theternary system H2O-CO2-NaCI given by Bowers andHelgeson (1983).

Phase relations among minerals andH2HO2-NaC| fluids

Jacobs and Kerrick (1981) have demonstrated experi-mentally that compositional variation of fluids in theternary system H2G{O2-NaCI may affect significantlymineral equilibria in metamorphic systems.3 Several ex-amples ofthese effects on dehydration and decarbonationreactions are discussed below. The thermodynamic prop-erties of minerals and H2O employed in the calculationswere generated from equations and data summarized byHelgeson and Kirkham (1974), Helgeson et al. (1978), andHelgeson et al. (1981). Fugacities of H2O and CO2 werecalculated from the MRK equation of state for the ternarysystem H2G-CO7-NaCI using parameters generated byBowers and Helgeson (1983).

Dehydration reactions

Univariant curves representing equilibria among miner-als and a fluid phase are shown in Figure 7. The coexis-tence of muscovite and quartz with andalusite, K-feld-spar, and a fluid is depicted in Figure 7A for variousvalues of X6q, along binary PA-l in Figure 68. Thecurves in Figure 7B refer to fluid compositions alongparabinary PA-2 in Figure 68. Those in Figure 7C are forconstant Xcor: 0.1 and the designated values ofXy.s1,which correspond approximately to molalities of 0, 1,2,

2 The terms liquid and vapor are used in the present communi-cation to designate coexisting phases of higher and lower densi-ties, respectively, in an immiscible region of pressure-tempera-ture-<omposition space. The term fluid is used to designate asingle phase.

3 For the most part, Jacobs and Kerrick's (1981) experimentaldata compare favorably with fluid compositions calculated fromthe MRK equation of state (Bowers and Helgeson, 1983).

l(br

Fig. l. Isochores (designated in g cm-3; for solutioncompositions corresponding to pure HzO (solid curves), 90moleVo H2O and lO moleVo CO2 (dashed curves), and 8E.26moleVo H2O , l0 moleVo CO2, and | .7 4 moleVo NaCl (double doGdash curves)-see text.

and 4, respectively. The long-dash curves in Figure 7represent metastable extensions of the equilibrium curvesinto the sillimanite or kyanite stability fields. The short-dash curves in Figures 78 and C represent the limits ofthe two-phase vapor + liquid immiscible region in theternary system H2O-CO5NaCI.

The equilibrium assemblage represented by the curvesin Figure 7 consists of six components and five coexistingphases in the fluid-phase region of the subsystem H2G-COlNaCl. Of the three degrees of freedom required bythe phase rule, two are constrained by specifying theconcentration of CO2 and NaCl in the fluid, which resultsin the isocompositional univariant curves shown in thediagrams. The intersection of these curves with theboundary of the two-phase liquid + vapor region in thesystem H2GCO2-NaCI is thus invariant at constantcomposition. Note that addition of CO2 and/or NaCl at agiven pressure lowers significantly the equilibrium tem-perature for the dehydration reaction.

Equilibria in the system CaO-MgO-SiOrHzO-CO7NaCl

Phase relations in this system at 2 kbar are shown inFigures 8-13 as a function of temperature and Xss" orNqer, which is defined bya

BOWERS AND HELGESON: NONIDEAL MIXING IN H,O-CO-NaCI

The isochores depicted in Figures 2-5 refer to the bulkcompositions labeled A through P in Figure 6A. Thedashed curves represent the limits of the two-phase vapor+ liquid immiscible region extrapolated from publishedexperimental solubility data by Bowers and Helgeson(1983).2 Note in these figures that the slopes of theisochores decrease only slightly with increasing NaClconcentration at constant Xse, (diagrams A-D in Fig. 2), &but they decrease dramaticaliy with increasing X66" at :constant Xp.61 (diagrams B,F,J,L,N, and P in Figs. 2-51. "AIt can be seen that the limits of the two-phase region shift Eto higher temperatures with increasing NaCl concentra-tion.

( l )

/vs'/r2o olo r.odoo

a N6q, in the present communication corresponds to N6qb/H,6in Bowers and Helgeson (1983).

1062 BOWERS AND HELGESON: NONIDEAL MIXING IN HzO-COrNaCl

.roo 500TEIP€RATURE,'C

400 500TEiIP€RATI,RE. 'C

Fig. 2. Isochores (solid curves, designated in g cm-3) for fluids with the bulk compositions labeled in the lower right corner of eachdiagram. The letters in the upper left corners correspond to the same letters shown in Fig. 6A. The dashed curyes represent the limitsof the miscibility gap in the system HzO4Oz-NaCl.

oEf,

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E

6c,o

U5oa

H

qE

o

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qE

o

uloo

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400 500TEiPERATIJRE. 'C

where

Note that only for the binary system H2O-CO2 is Ng6,equal to Xser. The circled letters shown in Figures 8, 12,and 13 designate fluid compositions and temperaturesrepresented by activity diagrams presented below.

Figure 8 (Walther and Helgeson, 1980) refers to theH2O-CO2 binary, but Figures 9 and l0 represent phaserelations along the pseudobinaries through the ternarysystem H2O-CO2-NaCI designated as PS-l and PS-2 inFigure 6C. It can be seen in Figure 9 that the miscibilitygap in the system HzGCOTNaCI at 2 kbar occupies onlya small part of temperature-X6o2 space above 4fi)"Calong PS-1. As a consequence, none ofthe curves repre-senting mineral equilibria intersects the miscibility gap inFigure 9. Nevertheless, it can be deduced by comparison

ofFigures 8 and 9 that increasing departures from idealityin the fluid with increasing NaCl concentration result inhigher equilibrium temperatures for reactions at lowXsqr. This effect diminishes with increasing X6er.

Invariant point A in Figure 8, which represents theassemblage talc, dolomite, calcite, qvarlz, tremolite, andfluid is displaced to A' in Figure 9. The fluid compositionrepresented by A in Figure 8 corresponds to that desig-nated A in Figure 9. Note that the difference between Aand A' is -4 mole%o CO2, which is of the order of themaximum difference in the positions of correspondingcurves in the H2O-rich regions of Figures 8 and 9.

In contrast to Figure 9, the miscibility gap in the systemH2GCO2-NaCI is a prominent feature of Figure 10,where the consolute temperature reaches -535'C. As aconsequence, seven new invariant points occur in thediagram. It should perhaps be emphasized that curvessuch as those representing equilibrium among talc, for-

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BOWERS AND HELGESON: NONIDEAL MIXING IN H,O-CO-NaCI 1063

sterite, magnesite, and the fluid phase in Figure l0terminate in invariant points at different temperatures oneither side of the miscibility gap. The temperature differ-ence occurs because pseudobinary PS-2 in Figure 6Cdoes not coincide with any of the equilibrium tie linesshown in Figure 6D. As a consequence, no tie lines can bedrawn through the miscibility gap on the plane represent-ed by Figure 10. Similarly, no curve is shown connectingcorresponding invariant points on either side of themiscibility gap because the compositions of the coexistingvapor and liquid phases in this region do not fall on theplane of the paper.

The invariant point labeled A and A' in Figures 8 and 9,respectively, does not appear in Figure l0 because thefigure refers to a fixed value of XN^g1lXHrq and theequilibrium assemblage talc, dolomite, calcite, quartz,and tremolite occurs together with both a liquid and vaporphase along a tie line within the immiscible region of the

400 500TEIIIPERATURE. 'C

system H2GCO2-NaCI. This can be seen in the schemat-ic three-dimensional diagram in Figure ll, where two ofthe curves that meet at invariant point A and A' inFigures 8 and 9 are represented by surfaces in tempera-ture-Xser-XNasl Spaco. The surface bounded byAA'B'BFC in Figure ll represents

3CaMg(COr)z + 4SiO2 + H2O(dolomite) (quartz)

: MgrSrnOro(OH)z + 3CaCOr + 3CO2 (3)(talc) (calcite)

and surfaces AA'D'D and BB'E'E correspond to

2CaMg(COr)z * Mg3SiaO16(OH)2 + 4SiO2(dolomite) (talc) (quartz)

: Ca2Mg5SfuOzz(OH)z + 4COz (4)(tremolite)

q'*H*P ,"-

aco

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Fig. 3. Isochores (solid curves, designated in g cm-3) for fluids with the bulk compositions labeled in the lower right corner of eachdiagram. The letters in the upper left corners correspond to the same letters shown in Fig. 64. The dashed curves represent the limitsof the miscibility gap in the system HzO-COrNaCl.

x^^ .oto""2xNoCt.ootg3

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locl BOWERS AND HELGESONT NONIDEAL MIXING IN HzO-COTNaCI

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Fig. 4. Isochores (solid curves, designated in g cm-3) for fluids with the bulk compositions labeled in the lower right corner of eachdiagram. The letters in the upper left corners correspond to the same letters shown in Fig. 6,{. The dashed curves represent the limitsof the miscibility gap in the system H2O-COr-NaCl.

400 500TEiPERAT(f€ . 'C

Curves AC and AD in Figure 11 correspond to univariantcurves in the plane of the H2O-CO2 binary depicted inFigure 8. The miscibility gap in the system H2O-CO5NaCl is bounded in Figure l l by D'A'B'E'JH.

Univariant curves on phase diagrams like those shownin Figures 8-10, 12, and l3 correspond to the intersectionof pseudobinary or parabinary planes with divariant sur-faces like those in Figure I l. Invariant points such as A inFigure 8 become univariant curves (AA') in the one-phaseregion of the ternary system (Fig. 1l). Note that where aunivariant curve like AA' (which corresponds to thecoexistence of talc, dolomite, calcite, quartz, tremolite,and fluid) intersects the miscibility gap (at A') the curveterminates in an invariant point which is replicated on theopposite side of the immiscible region (at B'). As aconsequence, the invariant assemblage is stable for allbulk compositions along the tie line connecting A' and B'in the immiscible region. The intersection of this tie line

300 400 500 600TEITiPERATWE.'C

(as well as the other tie lines shown in Figure I l) with thepseudobinary represented by Figure l0 is not shown inthe latter figure because the compositions of the coexist-ing vapor and liquid phases do not fall on the plane ofthediagram.

Univariant curve BB' in Figure 11 corresponds to theanalog of AA' in the liquid phase region. The assemblagetremolite + liquid + vapor is stable at temperaturesabove those corresponding to surface D'A'B'E' in Figure11, which consists of liquid-vapor tie lines. At tempera-tures below those represented by this surface, the assem-blage dolomite * talc + quartz + liquid * vaporis stable.At more H2O-rich bulk compositions, talc, calcite, liquid,and vapor coexist at temperatures above those corre-sponding to A'B'A', but dolomite, talc, quartz, liquid,and vapor are in equilibrium below the tie line surfacedenoted by A'B'A'. This trivariant phase region abovethe tie line surface is bounded at higher temperatures by a

, xco2.o'5\ x*1,'oosr

BOWERS AND HELGESON: NONIDEAL MIXING IN H,O-CO-NaCI

400 500TEiPERATI.f,E .'C

rKto 500TETPERAIIfE , 'C

Fig.5. Isochores(sol idcurves,designatedingcm-3)forf luidswiththebulkcomposit ionslabeledinthelowerrightcornerofeachdiagram. The letters in the upper left corners correspond to the same letters shown in Fig. 6,{. The dashed curve s represent the limitsof the miscibility gap in the system H:O-COz-NaCl.

1065

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o5o

H.66

H

6G

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H

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H

divariant surface corresponding to equilibrium amongtalc, calcite, quartz, tremolite, liquid, and vapor, whichextends from the limits of the immiscible region at highertemperatures to tie line A'B'. This surface, as well asother surfaces represented by univariant curves in Fig-ures 8 through l0 were omitted from Figure ll for thesake of clarity.

Figures l2 and l3 correspond to parabinaries throughthe one-phase region of the ternary system H2o-CO5NaCl along PA-2 and PA-3 in Figure 68, respectively. Itshould be emphasized that the positions of the invariantpoints shown in Figure 13 are somewhat uncertain be-cause they lie outside of the compositional region repre-sented by the experimental data array used to generatethe regression parameters in the MRK equation of state.As a consequence, fugacity coefficients had to be extrap-olated (Bowers and Helgeson, 1983) to calculate these

fluid compositions. The parabinary phase diagramsshown in Figures l2 and l3 do not differ significantly fromtheir pseudobinary counterparts in Figures 9 and 10, butthey are perhaps more geologically relevant because theyrepresent fluids with constant concentrations of NaCl.

Activity diagrams are shown in Figure 14, which referto the fluid compositions and temperatures representedby the circled letters in Figures 8, 12, and 13. Thesymbols oyr++ ofid o6u** st&hd for solvation parametersdefined by (Walther and Helgeson, 1980)

oi = 4rro@;-Zint+) (5)

where z1 and Z; refer to the solvation number and chargeof the ith aqueous species. The dashed lines on theactivity diagrams represent fluid saturation with respectto calcite (horizontal lines), magnesite (vertical lines),and dolomite (diagonal lines). Regions of the diagrams

1066

@

corresponding to values of log(ayr**/(oy**-4fu.)) andIog(as^**l(os^**a?^*11 that are greater than those corre-sponding to the dashed saturation lines represent meta-stable equilibria.

It can be deduced from Figures 8, 12, and 13, togetherwith the activity diagrams designated B, D, and F inFigure 14 that the tremolite stability field in the presenceof calcite, dolomite, and a fluid phase becomes smallerand disappears with increasing NaCl concentration at450"C and Nco. : 0.05. Similarly, it can be deduced fromFigures 8, 12, 13, and the activity diagrams annotated C,E, and G in Figure 14 that forsterite becomes metastablein the presence of a fluid phase at 500'C, Nse, = 0.10, andconcentrations of NaCl in excess of X61"q1 - 0.02.

Phase relations in the system CaO-MgO-SiOrH2O-CO2-NaCl at 2 kbar and 500'C are depicted in Figure 15in terms of N6e, and either log(ayr**/(oy***afrr;; orlog(as^**l(oc^..ah-D.Figure l5A, which refers to Xy"s1= 0 (PA-l in Figure 68) was taken from Walther andHelgeson (1980). Figures l5B and 15C refer to parabinaryPA-2 in Figure 68 (XNucr = 0.0193), but Figure l5Drepresents parabinary PA-3 (XNuct = 0.0715). The posi-tions of the invariant points shown in Figure l5D aresomewhat uncertain because extrapolated fugacity coeffi-

IAI

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BOWERS AND HELGESON: NONIDEAL MIXING IN H,O-CO-NaCI

;;-ot @-;o;;-@

D

c%

B c

t4?307r5

or93c% xzo ro 20 5o 40 50 60 70 8o 90 c%

t.q

Fig. 6. Diagram A: Bulk compositions in the ternary system H2O-CO2-NaC| designated by letters A-P in Figures 2-5. Diagram B:Bulk compositions corresponding to binary PA-l and parabinaries PA-2 and PA-3, for which Xx.cr : 0, 0.0193 and 0.0715,respectively. Diagram C: Bulk compositions in the ternary system corresponding to pseudobinaries PS-1, PS-2, and PS-3 for whichNN"cr = 0.0193, 0.0715, and 0.1423. Diagram D: Schematic phase diagram for the ternary slstem H2O-COz-NaCl at a giventemperature and pressure (see text).

cients were used to calculate the fluid compositions(Bowers and Helgeson, 1983). Nevertheless, it can beseen by comparing Figures l5A through D that theinvariant points occur at lower N66" values with increas-ing NaCl concentration.

Phase relations among minerals, liquid' andvapor in the two-phase region of the

ternary system H2G-CO2-NaC|

Correlation of pressure-volume-temperature relationsfor the ternary system H2O-CO2-NaCI with tempera-tures, pressures, and bulk fluid compositions characteris-tic of metamorphic terranes (Sisson et al.,l98l; Hendeland Hollister. 1981: Kreulen, 1980; Crawford et al.,1979;Hollister and Burruss, 1976; among others) indicates thatfluid immiscibility may occur far more commonly inmetamorphic processes than has been generally recog-nized in the past. Because the presence of coexistingliquid and vapor has a dramatic effect on equilibriumtemperatures for dehydration and decarbonation reac-tions, failure to take into account the thermodynamicconsequences of vaporJiquid immiscibility may lead toserious errors in interpreting phase relations in metamor-phic rocks. This can be demonstrated by comparing the

NoCl

:31 ps-z l ps_

BOWERS AND HELGESON: NONIDEAL

temperature-Xso, diagram in Figure 8 (for which Xp"., :0) with the corresponding temperature-Nse" diagram inFigure 16, which represents equilibrium among mineralsin the system CaO-MgO-SiO5H2O-CO2 in the presenceof both liquid and vapor in the two-phase immiscibleregion of the system H2GCO2-NaCI.

The curves shown in Figure 16 represent projections ^from XNugl : I of phase relations on the face of the Amiscibility gap (which corresponds to the surface bound-ed by D'A'B'E'JH in Figure ll) to a temperature-Nqe.plane at XN.cr = 0. As a consequence, the mineralstability fields shown in the figure correspond to those inthe two-phase region of the ternary system H2O-CO1NaCl. Note that each of the univariant curves and invari-ant points on the CO2-rich side of the miscibility gap inFigure 16 are repeated on the H2O-rich side. Eachcorresponding curve or invariant point can be connectedby an isothermal tie line, along which the indicatedmineral assemblages are stable in the immiscible region.For example, invariant points A and B in Figure 16,which represent the coexistence of talc, dolomite, calcite,quartz, tremolite, liquid, and vapor correspond to invari-ant points A' and B' in Figure I I , which are connected bya tie line. Similarly, a given point on a univariant curye onthe Co2-rich side of the miscibility gap, such as b', can beconnected by an isothermal tie line to its H2o-richcounterpart (b) as shown in Figure 17. All but a few suchtie lines have been omitted from Figure 16 for the sake ofclarity, but an example is shown in Figure 17, where thestable mineral assemblages coexisting with liquid + vaporat 525"C are shown along cross section.;f in Figure 16.The letters shown within the large circles in Figure 17denote the limits in the large triangle of the compositionalrange of liquid + vapor for which the assemblagesdesignated in the circled triangles are stable. The lettersin the large triangular cross section in Figure l7 designatethe intersections of univariant curves with the line of thecross section in Figure 16.

It can be deduced from Figure 17 that calc-silicatecompatibilities in the two-phase liquid + vapor region ofthe system H2GCO2-NaCI are highly sensitive to smalldifferences in NaCl concentration. For example, increas-ing XNugl at Nse, : 0.5 from 0.166 by only 0.003 to 0.169changes the stable mineral assemblage from that repre-sented by bb'c'c to that designated as ct'd,d. Because ofthe dual occurrence of each invariant point in Figure 16,the mineral assemblages coexisting with liquid and vaporin regions such as cc'd'd in Figure 17 are stable at anygiven temperature over a wide range of bulk compositionsin the system H2O-CO2-NaCL. Note that in the absenceof high enough NaCl concentrations to cause immiscibil-ity, all of the univariant curves and invariant points onthe H2O-rich side of the phase diagram shown in Figure16 occur at equivalent temperatures and pressures only inthe presence of a single CO2-rich fluid phase. It followsthat fluid inclusion analyses are a requisite for reliableinterpretation of metamorphic phase assemblages.

400 450 500 550TEMPERATURE , OC

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x69r'ol

500 520 540 560 580 600TEMPERATURE.OC

Fig. 7. Diagram A: Univariant dehydration curves for fluidcompositions along the H2O-CO2 binary designated PA-l in Fig.68. Diagram B: univariant dehydration curves for fluidcompositions along parabinary PA-2 in Fig. 68. The labels on thecurves correspond to values of X66r. Diagram C: Univariantdehydration curves for fluid compositions with constant Xcoz=0.1. The labels on the curves correspond to values ofXN"q1, andthe short-dash curves represent the limits of the miscibility gap inthe system HzG{Oz-NaCl (see text).

MIXING IN H.O-CO-NaCI tM7

4

G

9.slr,Gl

3zlrJE,c

I

4

E

6 ,Y J

t r l dI - . , ( l

c r ^( n 'lrJEo-

I

O L350

O L350

3

2

E

dtv

f . ;\., 56anlrJEo-

II

I/

/ ,I t> ti /

,l l

II

II

to9

I

MUSCOVITE+

OUARTZ

550

450

400o.2 o.4 o.8

MOLE FRACTTON COzFig. 8. Temperature-X66, diagram depicting mineral-fluid equilibria in the system CaO-MgO-SiO2-H2O-CO2 at 2 kbar taken

from Walther and Helgeson (1980). The circled letters designate temperatures and fluid compositions represented by activitydiagrams in Fig. 14. CAL - calcite, DOL : dolomite, QTZ = quartz, TREM : tremolite, FORST = forsterite, DIOP = diopside,MAG = magnesite, WOL = wollastonite, ANTHOP = anthophyllite, and ENST = enstatite.

C)o .

td(rfFE 500T.Etrl(L

UJF

ooHzo

o.9Q70.6o.5o'3ol tocoz

Oo .

UJE:)F

EUJ(L

tdF

oo o.r 02NoclorgsHzo.geoz

o.3 0.4 0.5 0.6MOLE FRACTTON COz

o.7 t.ocoz

o.9o.8

Fig. 9. Temperature-X66, diagram depicting mineral-fluid equilibria in the system CaO-MgO-SiO2-H2O{OrNaCl at 2 kbaralong pseudobinary PS-l in Fig. 6C. The dotted invariant point A corresponds to invariant point A in Fig. 8 (see text and caption ofFie. E).

'&ry

oo o.l

BOWERS AND HELGESON: NONIDEAL MIXING IN H2O-CO7-NaC\ t069

NoG16.97,uHzoo.gzgso'3 0.4 o'5 06 0l

MOLE FRACTTON COz

Fig. l0' Temperature-X6o, diagram depicting mineral-fluid equilibria in the system CaO-MgO-SiO2-H2O-CO2-NaCI at 2 kbaralong pseudobinary PS-2 in Fig. 6C. The dot-dash curve represents the limits of the miscibility gap in the system H2O-CO2-NaC| (seetext and caption ofFig. 8).

(Jo .

lrJOEl

kEUJI=lrJF

o.8 0.9 l.ocoz

02

All of the curves in Figure 16 that cross over theconsolute composition curve for the system H2G-CO1NaCl exhibit minima along the face of the miscibility gap.The minima result from the intersection of the miscibilitygap with the divariant surfaces representing the equilibri-um phase assemblages in temperature-XpssFNsq. spoce.In certain cases these minima restrict significaritly therange of temperature and Nqe, over which a givenmineral assemblage is stable in the immiscible region. Forexample, it can be seen in Figure 15 that immiscibilitycauses the univariant curves representing both liquid andvapor coexisting with (l) dolomite, quurtz, talc, andcalcite, (2) talc, calcite, quartz, and tremolite, and (3)talc, calcite, tremolite, and dolomite to exhibit tempera-ture minima between Nco" : 0.2 and Nco. = 0.25. As aconsequence, the sizes oi the stability delds betweenthese curves are drastically reduced from their counter-parts for Xuucr = 0 in Figure 8. Note that as a result ofincreasing XN,ql and concomitant fluid immiscibility,each of the curves in Figure 8 that exhibits a maximum isrepresented by a corresponding curve in Figure 16 thatexhibits two maxima, one each at high and low values ofNser. As a result, mineral assemblages that would other-

wise be stable only at low temperatures in the presence ofan HzO-rich fluid occur at much higher temperatures inthe presence of coexisting liquid and vapor phases.

The effects of immiscibility in the system H2O-CO1

C . . GXcoz*

Fig. ll. Schematic 3-dimensional representation of phaserelations in the system CaO-MgO-SiO2-H2OCOrNaCl at 2kbar (see text and caption of Fig. 8).

tsN

x l-s

:lF5IJ,'.".';1i,,"931 "xI TREM+ilDoL*gFoRsr[ +l3CAL+gCOZ+H2O

I zDoL.tALc.4orzl[+rnell*aco2 |

OOL+TALC+QTZ+ FLUID

1070

(Jo -

lrlEf

kE,Lu(L

Lr,lF

o.3 o.4 0.5*ao,

Fig. 12. Temperature-Nc6, diagram depicting mineral-fluid equilibria in the system CaO-MgO-SiO2-H2O-CO2-NaCI at 2 kbar

along parabinary PA-2 in Fig. 68. The long-dash curve represents the limits of the miscibility gap in the system HzO-COrNaCl (see

text and caption of Fig. 8).

600

NaCl on the activity ratios of ionic species characteristicof mineral equilibria in the system CaO-MgO-SiOrHzO-CO2 can be assessed in Figure 18, where log(avr,tl(ay",*a?11)) is plotted as a function of Nse, in a projectionfrom X11"61 : I of phase relations on the face of themiscibility gap at 500" and 2 kbar to an N6q, - log(avr.-/

loyu-*afi-)) plane at XN"cl : 0. Tie lines (which are notshown for the sake of clarity) can be drawn to connectpoints of equal log(ayr../(oMg**a?Hr)) on either side of themiscibility gap in Figure 18. As in the case of Figure 16,each invariant point appears on opposite sides of theconsolute composition curve. Comparison of Figures l5Cand l8 indicates that immiscibility introduces minima inthe curves representing equilibrium among minerals, va-por, and liquid that are not apparent in the correspondingcurves for coexisting minerals and a single fluid phase.Note also that the solubilities of calc-silicate minerals areincreased significantly in the liquid phase at high NaClconcentrations.

02 o.6 o.7 o.8 o.9

Fig. 13. Temperature-Nsg, diagram depicting mineral-fluidequilibria in the system CaG-MgO-SiOrH2O{OrNaCl at 2kbar along parabinary PA-3 in Fig. 68. The dashed curverepresents the limits of the miscibility gap in the system H2O-CO2-NaCl (see text and caption of Fig. 8).

oo .

|JlEf

k sooEUJ(L=IJF

o.r o.l5*ao,

^ ^ )

,III

I/

(LIQUID+VAPOR)-\ -.r'

- - - - - - - - - - -Yc-? 2 KBi-fsror....oL+4erz+l \

"i -[9111c.ec11.aorz+l \ pA-z

[3TREM+6CO2+zHzO J

'6#

K*'*+sFoRJrl-[*t3CAt*9COr+Xaq I

fzralc*scnl+tnEul /I+DOL+H2O+CO2 l'

/ I 3DoL+4oTz+Hro+l- t - |

I TALC+3CAL+3CO, J, '

I zra PA-3

450

oo5 o.20 0.25

6 5

6 0

5.5

BOWERS AND HELGESON: NONIDEAL MIXING IN HzO-OOrNaCI

LoG(ouo++/(Cuo..ofi . ) )

Fig' 14' Logarithmic activity diagrams for the system Cao-MgO-SiOrH2o-Co2-N aCl at2kbar. The circled letters in the lowerleft comers of the diagrams refer to the temperatuies and fluid compositions with corresponding labels in Figures E, 12, and 13 (see!!10' rne dashed lines represent fluid saturation with respect to calcite (horizonral lines), magnesite (vertical lines), and dolomite(diagonal lines).

l07l

+( \ ' I

o

+o

++o()

I

oo)

+N I

0

o. oI

+oC)

o(9oJ

A I Io++0

- oI

++oo

o(9oJ

6 I ro++o

. c t

++o()

o|9oJ

Concluding remarks

The results of calculations summarized above leavelittle doubt that metamorphic phase equilibria may behighly sensitive to Xpu61 in the fluid. The phase diagramsdiscussed in the preceding pages representing equilibriumamong minerals and a single fluid phase or coexistingliquid and vapor phases in the system H2O-CO2-NaCIillustrate but a few examples of the dramatic conse-quences of nonideality and immiscibility in multicompon-ent crustal fluids on mineral relations in geologic systems.Many mineral assemblages that are stable in the presenceof a fluid over a narrow range of composition in the binarysystem H2O-CO2 may coexist with fluids that exhibit awide range of composition in the ternary system H2O-CO2-NaCl, and vice versa. The fact that separation of aliquid and vapor from a single fluid phase in the ternarysystem can occur at pressures and temperatures in excessof 2 kbar and 550'C suggests that immiscibility may be

responsible for apparent contradictions between phaserelations documented by experiments with fluids in thesystem H2G{O2 and those observed in metamorphicrocks.

Highly saline solutions may be generated from NaCl-poor fluids as a result of immiscibility. For example,decreasing temperature and/or pressure to 5fi)"C and 500bars will result in unmixing of a fluid in which X66,: 0.2,XN.cr : 0.04, and Xg.ro = 0.76 to 14 moleVo liluid inwhich Xg6, : 0.004, XN"cr = 0.18 (-12 molal), and Xs,6= 0.816 coexisting with 86 moleVo vapor in which Xse, :0.735, XN,ql = 0.016, and X11,s : 0.249. This processafords an alternative mechanism to those proposed in thepast to explain the origins of highly saline fluids in diversegeologic environments. These include partitioning ofchlorine gas and chloride complexes of alkalies, alkalineearths, and heavy metals into a magmatic aqueous phasegenerated by retrograde boiling during cooling of a hy-drous magma at intermediate pressures (Burnham and

orz

t072 BOWERS AND HELGESON: NONIDEAL MIXING IN H2O-CO2-NaC|

0.t5 0.20*ao,

Fig. 15. Log(ay***/(oy"*+a2s*)) and log(as.**/( o(:^+-li2*,')) at 2 kbar and 500"C as a function of X9o, and Nc6, in fluids coexisting

with minerals in thJ systeri CaO-MgG-SiOrH2O{OrNaCl along the binary and parabinaries designated as PA- I , PA-2' and PA-3

in Fig. 68 (see text). The long-dash curves in diagrarn. b, C, and D represent the limits of the miscibility gap in the system HzG{Or

NaCl.

6.4

o t Io

. i3 s.za 9A

"3

eo(9oJ

5.8

DN I

o++ctr

. =\t

++ctr

oIoJ

4 4

+(\I -

c'i 4 2

^ @P\ r s

l- ao=

Io9 s.e

ts

*co,

o 02 o.4 0.6 0.8 toNcoz

Ohmoto, 1980). It has also been proposed that highlysaline fluids found in the pore spaces of sandstones mayhave been derived from evaporites, or by filtrationthrough semipermeable shale membranes (Hunt, 1979;Kharaka and Smalley, 1976).

Although the results of the calculations summarizedabove apply to fugitive phases in the system H2O--COrNaCl, they are probably indicative of the consequencesof reactions among minerals and coexisting liquid and

vapor or fluid phases involving HzO, COz, and substantialconcentrations of other electrolytes such as KCl, MgCl2,or CaCl2. Many more experimental studies will be re-quired to assess adequately the effects of these electro-lytes on devolatilization reactions. In the interim, calcula-tions of the kind described above should afford closeapproximation of metamorphic phase relations as a func-tion of XNasl and Nqe" at high pressures and tempera'tures.

I eioesrrtsco".rex2()+22C02 rrTREx l| +mOL+26H+

TREM+3co'++ 2H2o+loco2 r ' 30oL+80T2+6X+

\ ' -- i l*r. .orz+rcc+r

Ii-[ 'z'aotsoroP'6H' j

iar*c'rorz'-' l.FoRST+5C0".6H2o+ I-[

roco2anlc.cool+ox'J

[ 4FoRST+5COr+HrOl'-

[ .s"ec.nr-i -

| PA- 2

,/ zoot,e,hz.l 1| 3xs+++.H2o.. | |

frnex.rcoz.ex'J i(LrourD +vAPoR)---+

Q..."i tt"to'oto'

I :-'."".*-:IaDroP+Me+++2Hzo.2cozl i[drREM.2cAL.2H' I i

IfCAL.2OTZ+Mg'++HZOI[*orop.coz.zx'| ,| zKB

1073

(Jo .

lrj(E:)k sooElrjo-=UJF

450

o.4 o.5 o.6 o.7 o.8 o.9taoz

Fig. 16. Temperature-Nqo, diagram depicting mineral-fluid equilibria in the system CaO-MgO-SiOrH2O-COrNaCl in the two-phase liquid + vapor region ofthe subsystem H2O-CO2-NaCI at 2 kbar (see text). The double-short-dash long-dash horizontal linecorresponds to the trace of the cross-section represented by the large triangular diagram in Fig. 17, which is labeled with the samelower case letters shown above.

si02QTZ

2KB525"C

+ANTHOPENST

FORST

MAG

\\:

'd'

Fig. 17. Cross section ofthe ternary system H2O-CO2-NaC| at 2 kbar and 525'C (large triangle) along the horizontal line labeledf in Fig' 16. The letters shown within the large circles designate the limits in the large triangle of the compositional range of liquid +vapor for which the mineral assemblages shown in the circled triangles are stable (see text).

o 8o 5o.4o.3o.2o.lHzo coz

[zool+TALc+4erz Ilrrner.eco, I

l-lcoT zr3ilAc+ HzO r. TALG + 3COz ] 2KB #

dd'e'e

odb'b

o'oo' ee'f 'f

1074

4.6

4.4

4.2

4.2

3.8

3.6

o.2 0.4 0.6 0.8*ao,

Fig. 18. Log (ay"**/(os"**aL*11 as a function of Nq6, formineral-fluid equilibria in the system CaO-MgO-SiO-HzO-COrNaCl in the two-phase liquid + vapor region of thesubsystem HzO-COu-NaCl at 2 kbar and 500"C (see text).

Acknowledgments

The research reported above represents the second part of thesenior author's Ph.D. dissertation at the University of California,Berkeley. We are indebted to George C. Flowers, R. MikiMoore. Carol J. Bruton. Kenneth J. Jackson, Everett L. Shock,William M. Murphy, John C. Tanger IV, Peter C. Lichtner,Richard O. Sack, Mark S. Ghiorso, Cathy J. Wilson, DaraGilbert, Michael J. O'Leary, Tom Welsh, Laurel B. Goodwin,Mary Gilzean, Joachim Hampel, Mike Ryan, Greg Williams,Korda Cordes, Joan Bossart, Mark L. Bowers, John A. Smegal,and others among our friends and colleagues at Berkeley forhelpful suggestions, assistance, and encouragement during thecourse of this research. Thanks are also due E. Ulrich Franckand the members of the Institut ftir Physikalische Chemie undElektrochemie der Universitiit Karlsruhe in Germany for theirhospitality, assistance, and stimulating discussions during a five-month stay by one of us (T.S.B.). The research project wassupported by the National Science Foundation (NSF grants EAR77-14492 and EAR 8l-15859) and the Committee on Research atthe University of California, Berkeley. Finally, we would like toexpress our appreciation to George H Brimhall, John M. Praus-nitz, John R. Holloway, and John M. Ferry for their constructivereviews of the manuscript and helpful suggestions for improve-ment.

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BOWERS AND HELGESON: NONIDEAL MIXING IN HzO-COrNaCl

+a n I

o++ctr

tJ

++ctl

o(9oJ

thermodynamic and geochemical consequences of nonidealmixing in the system HzO-{OrNaCl on phase relations ingeologic systems: Equation of state for HzO-COrNaCl fluidsat high pressures and temperatures. Geochimica et Cosmochi-mica Acta. 47. 1247-1275.

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Crawford, M. L., Kraus, D. W., and Hollister, L' S. (1979)

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nifu:er Mischungen aus Wasser, Kohlendioxide, und Na-

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o.o

I SQTZ+2CAL+5Mg**.6H20

[ +TREM*zcoa.tox*

6*09

[,Au+M9+++11r.-..-

BOWERS AND HELGESON: NONIDEAL MIXING IN H2O1Oy-NaCI 1075

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Manuscript receiued, August 27, l9E2;acceptedfor publication, April 25, IgBj-