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A simple predictive model of quartz solubility in water–salt–CO2 systems at temperatures up to 1000 °C and pressures up to 1000 MPa
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Geochimica et Cosmochimica Acta 73 (2009) 1597–1608 www.elsevier.com/locate/gca
A simple predictive model of quartz solubility in water–salt–CO2 systems at temperatures up to 1000 °C and pressures up to 1000 MPa Nikolay N. Akinfiev a, Larryn W. Diamond b,* a
Institute of Geology of Ore Deposits, Petrography, Mineralogy and Geochemistry RAS, Staromonetnyi per. 35, Moscow 119017, Russia b Rock–Water Interaction Group, Institute of Geological Sciences, University of Bern, Baltzerstrasse 3, Bern CH-3012, Switzerland Received 7 July 2008; accepted in revised form 15 December 2008; available online 25 December 2008
Abstract Knowledge of the solubility of quartz over a broad spectrum of aqueous fluid compositions and T–P conditions is essential to our understanding of water–rock interaction in the Earth’s crust. We propose an equation to compute the molality of aqueous silica, mSiO2ðaqÞ , mol(kg H2O)1, in equilibrium with quartz and water–salt–CO2 fluids, as follows: log mSiO2 ¼ AðT Þ þ BðT Þ log
18:0152 þ 2 log xH2 O V H2 O
Here A(T) and B(T) are polynomials from Manning’s (GCA 58 (1994), 4831) equation for quartz solubility in pure water, and xH2 O and V H2 O stand for the mole fraction and effective P partial molar volume of H2O in the fluid, respectively. The value of V H2 O is computed from the relation V mix ¼ xH2 O V H2 O þ xs V s , where Vmix is the molar volume of the fluid mixture (in cm3 mol1), and xs and Vs denote the mole fraction and the intrinsic volume of the solute, s, respectively. Values of Vmix may be obtained from experimental data on the fluid mixture or from a reliable equation of state for the mixture. Adoption of the Vs values VNaCl = 30.8 cm3 mol1 and V CO2 = 29.9 cm3 mol1 permits satisfactory prediction of quartz solubility both in binary and ternary aqueous systems. In lieu of experimental data Vs can be estimated from pure substance properties: the intrinsic volumes of molten salts yield Vs for the electrolyte components, whereas the excluded volumes of gas species in Redlich–Kwong–Soave-type equations of state yield Vs for the volatiles. The accuracy of our density model is only slightly inferior to the empirical regressions that experimentalists have used to interpolate their measurements of quartz solubility. The strength of our model lies in its ability to predict trends in quartz solubility in fluid mixtures over an extremely wide range of T–P–xs conditions relevant to the Earth’s crust, including conditions hitherto unexplored experimentally. This success is attributable to our model having only one adjustable parameter per solute. Ó 2008 Elsevier Ltd. All rights reserved.
1. INTRODUCTION Quartz is ubiquitous in the Earth’s crust and at elevated temperatures its dissolution- and precipitation behaviour limits the amount of silica that can be transported in hydro-
*
Corresponding author. Fax: +41 31 6314843. E-mail address: [email protected] (L.W. Diamond).
0016-7037/$ - see front matter Ó 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.gca.2008.12.011
thermal fluids. Knowledge of the solubility of quartz is therefore crucial to our understanding of countless geochemical processes. Owing to this importance, numerous studies have been carried out on the solubility of quartz in water at elevated temperatures and pressures, starting with Kennedy (1950), Morey and Hesselgesser (1951), Khitarov (1956) and Kitahara (1960), among others. These early studies have been reviewed and interpreted by Walther and Helgeson (1977). More recent investigations have refined
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the available data and have extended the range of experimental temperature–pressure conditions up to 1000 °C and 2000 MPa (Manning, 1994). Thus, the solubility of quartz has been found to increase with temperature and pressure, except for a restricted T–P region at low pressures in the vicinity of the critical point of water, where the solubility shows retrograde behaviour. While the above studies provide a solid basis for the case of pure water, to understand fully the behaviour of quartz in natural fluids it is necessary to estimate its solubility in complex mixtures containing volatile species, such as CO2, and other dissolved mineral components, especially the alkali and alkaline earth halides. The solubility of quartz in NaCland NaCl–CO2-solutions at hydrothermal conditions has been reported by Khitarov (1956), Kitahara (1960), Anderson and Burnham (1967), Novgorodov (1977), Hemley et al. (1980), Fournier et al. (1982), Xie and Walther (1993), Newton and Manning (2000), and Shmulovich et al. (2001, 2006). These studies have revealed that dissolved silica behaves in a rather intriguing way. Whereas the presence of CO2 in the fluid always lowers silica solubility, the presence of the salt causes more complex effects. At low temperatures (0–250 °C) and at the saturation pressure of water, admixture of salt produces the salting-out phenomenon, lowering silica solubility. However, as temperature approaches the critical point of water, salting-out is superseded by a salting-in effect (Xie and Walther, 1993). Similar behaviour has been experimentally demonstrated at supercritical conditions of H2O (Newton and Manning, 2000). As an example (Fig. 1), at 700 °C, lowering the pressure from 1500 to 435 MPa not only progressively lowers quartz solubility but it also weakens the salting-out effect (the isobars become shallower). When pressure is reduced even further, to below 400 MPa, admixture of moderate amounts of NaCl (up to a mole fraction, xNaCl, of about 0.1) enhances SiO2 solubility in comparison to pure H2O. Moreover, it can be
seen that the 200 MPa isobar of SiO2 solubility vs. salt concentration passes through a maximum: the salting-in effect at low xNaCl switches to salting-out at high salt concentrations. Anderson and Burnham (1967) and Shmulovich et al. (2006) found similar solubility enhancement in KCl solutions. The intent of the present study is to develop a simple predictive model that reproduces this unusual behaviour of quartz solubility over a wide range of T, P and fluid compositions. In this context, ‘‘simple” means that the model ideally has only a small number of empirical fitting parameters. We strive to minimize this number for two reasons. First, if a simple model is successful, its parameters are more likely to carry real physical meaning, and hence they may provide more insight into the solubility phenomenon, pointing the way to fruitful avenues of research. Second, a model with few parameters normally has more predictive power outside the region of available experimental data. Although several published models (discussed below) describe the experimental database for salt- and gas-bearing solutions, they are all essentially empirical in nature, and hence they cannot be expected to extrapolate reliably. On the other hand, the predictive advantages of a simple model often come at the price of accuracy. It will be seen that, for certain fluid P–T–x conditions, this is also the case for the model we present here. The procedure we follow begins with a model of quartz solubility in pure water, the next step being to account for the influence of salts and volatiles on the model parameters. Before presenting our model we review the earlier attempts in the literature on which our model is based, first for pure water and then for mixed gas-salt solutions. Our final model correctly reproduces trends in quartz solubility over a wide range of conditions and fluid compositions relevant to the Earth’s crust. 2. MODELS OF QUARTZ SOLUBILITY IN PURE WATER
700 °C
0.8
Novgorodov, 1977 Manning, 1994 Newton & Manning, 2000
mSiO2 / mol·kg-1
1500 MPa
0.6 1000 MPa
0.4
435 MPa 200 MPa
0.2 150 kbar
0 0
0.1
0.2
0.3
xNaCl
0.4
Two different approaches to the thermodynamic description of aqueous species are currently employed in modern hydrothermal geochemistry: electrostatic models (Fuoss, 1958; Ryzhenko, 1981) and density models (Anderson et al., 1991). Both approaches have been applied with some success to the solubility of quartz, as explained below. The first approach takes account of electrostatic interactions between aqueous dissolved species and the surrounding solvent (H2O) molecules. Within the framework of the well-known HKF model (Helgeson et al., 1981), the solvation term of the chemical potential of ionic species is defined by the Born equation (Born Von, 1920; Helgeson and Kirkham, 1976):
0.5
Fig. 1. Experimental data on quartz solubility (expressed as SiO2 molality, mSiO2 ) in H2ONaCl solutions versus mole fraction of NaCl (xNaCl) at 700 °C and on isobars between 150 and 1500 MPa. Points correspond to the experimental data. Lines are drawn to illustrate trends.
loj;solv ¼ xj
1 1 ; e
ð1Þ
where e represents the static dielectric permittivity of the solvent and xj is the absolute Born coefficient of the jth aqueous species. For aqueous silica, Walther and Helgeson (1977) retrieved a value of xSiO2(aq) = 0.1291 105 cal
Computation of quartz solubility in H2O–salt–CO2 systems
mol1 [=0.5402 105 J mol1] from their regression of available experimental data on quartz solubility, based on the following equilibrium: SiO2ðquartzÞ $ SiO2ðaqÞ ;
ð2Þ
where the properties of aqueous silica, SiO2(aq), do not depend on the explicit structure of the dissolved silica. These same data were later regressed with the revised HKF equation of state (EoS) (Tanger and Helgeson, 1988) to obtain the full set of state parameters for SiO2(aq) (Shock et al., 1989). The resulting description indicates that, within the framework of the adopted EoS, the data are properly described within experimental error. The second major modelling approach, known as the density model, is based on the empirical observations (traced back to works of Franck (1961) and Styrikovich (1969)) that the standard-state chemical potential of a solute is proportional to the decadic (base 10) logarithm of the density of pure water. Thus, the logarithm of the reaction constant of interest may be parameterized by an equation of the form log K ¼ AðT Þ þ BðT Þ log qoH2 O ;
ð3Þ
where A(T) and B(T) are temperature-dependent polynomials, and log qoH2 O stands for the base-10 logarithm of the density of pure water in gcm3. Eq. (3) is independent of the choice of standard state because any choice made for K is automatically incorporated in the proportionality coefficients A and B. The physical reason for the correlation between log K and log qoH2 O is still unexplained, and so the density model remains physically less well-grounded than the electrostatic one. Nevertheless, its simplicity and the dependence of log K only on temperature and qoH2 O make Eq. (3) ideal for thermodynamic calculation of chemical potentials of aqueous species at high T–P conditions. Fournier and Potter (1982) and Manning (1994) regressed the available quartz solubility data according to the density model in terms of the dissolution reaction (2). For the remainder of this study we adopt the polynomials of Eq. (3) for log K ¼ logðmoSiO2ðaqÞ Þ given by Manning (1994): 5764:2 1:7513 106 þ T T2 8 2:2869 10 T3
AðT Þ ¼ 4:2620
1006:9 3:5689 10 ; þ T T2
binary mixtures of H2O and non-polar gases (Sommerfeld, 1967; Novgorodov, 1975; Walther and Orville, 1983) in the studies of Schott and Dandurand (1987), Xie and Walther (1993), and Akinfiev and Zotov (1999). The decrease in solubility of the SiO2 solid phases in the presence of non-polar CO2 in the fluid is accounted for by reducing the dielectric permittivity of the mixture, emix, and by assigning a positive value to the Born parameter for SiO2(aq). The predicted and experimental solubilities are in fair agreement over a geochemically important range of P–T–xgas conditions, i.e. up to 700 °C, 500 MPa and 0.35 mole fraction of non-polar gas (Fig. 10 in Akinfiev and Zotov, 1999), but at more extreme conditions agreement is poor (e.g. at 800 °C and 1000 MPa; Table 1). Nevertheless, this approach is attractive because it does not require any additional empirical parameters beyond those for the initial SiO2–H2O subsystem. Based on the above studies we have attempted to expand the electrostatic approach to the H2O–salt systems. The guiding idea, suggested by Xie and Walther (1993), was to account for the SiO2 salting-out effect at high pressures by the presence of free ions in solution, which lower emix of the mixed fluid (Helgeson et al., 1981). On the other hand, at low pressures, where ions are mostly associated in ion pairs with high dipole moments, the presence of the salt should increase emix of the fluid mixture and thereby enhance quartz solubility. Details of our computational procedure, which are similar to that of Xie and Walther (1993) and of Akinfiev and Zotov (1999), are not given here as this simple model was found to be incapable of explaining the maximum in SiO2 solubility vs. salt content at low pressures. 3.2. Silica solvation in mixed fluids The above obstacles have forced researchers to abandon predictive models for the time being in favour of more complex empirical approaches that afford accurate interpolation of measured quartz solubilities in mixed aqueous fluids. The first step in these approaches is to rewrite the quartz dissolution reaction with explicit regard to solvation: SiO2ðquartzÞ þ nH2 O $ SiO2 ðH2 OÞnðaqÞ ;
ð3aÞ
5
BðT Þ ¼ 2:8454
1599
ð3bÞ
where T is in K. These polynomials are simpler than those of Fournier and Potter (1982) and they accurately reproduce the measured quartz solubilities over a much wider range in pressure and temperature, from 25 °C and 0.1 MPa to 1000 °C and 1000 MPa.
where n is the solvation number of the aqueous silica complex. Abbreviating the aqueous silica complex to SiO2(aq), the equilibrium constant for reaction (4) now becomes
Table 1 Comparison of experimental and predicted quartz solubilities in H2O–CO2 mixtures at 800 °C and 1000 MPa. xCO2
3. MODELS OF QUARTZ SOLUBILITY IN MIXED FLUIDS 3.1. Electrostatic models for mixed fluids The electrostatic approach has been successfully employed to describe experimental data on SiO2 solubility in
ð4Þ
0.185 0.337 0.499 0.503 0.676
mSiO2 (mol kg1 H2 O ) Experimental (Newton and Manning, 2000)
‘‘Electrostatic” model (Akinfiev and Zotov, 1999)
‘‘Density” model (This study)
0.594 0.340 0.209 0.163 0.112
0.419 0.206 0.068 0.066 0.013
0.676 0.365 0.152 0.148 0.036
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log K ¼ log aSiO2ðaqÞ n logðaH2 O Þ:
ð5Þ
Assuming ideal behaviour of the components as a first approximation we set aSiO2ðaqÞ ¼ mSiO2ðaqÞ and, ignoring the mole fraction of H2O bound in the complex, we assume aH2 O ¼ xH2 O . Eq. (5) can now be rewritten for silica solubility as log mSiO2ðaqÞ ¼ log K þ n logðxH2 O Þ: ð6Þ This relation shows that a decrease in the mole fraction of H2O in the fluid will lower SiO2 solubility, qualitatively in accord with the observed salting-out effect at high salt contents. Writing Eqs. (4)–(6) in this way to take account of the existence of SiO2(H2O)n molecules in the aqueous environment is justified by several experimental observations. In situ Raman spectroscopic measurements on silicic acid at conditions up to 800 °C at 425 MPa and up to 600 °C at 820 MPa demonstrate a unique frequency of Si–OH stretching that matches the theoretically calculated frequency of an Si(OH)4 molecule (Zotov and Keppler, 2002). Thus, the dominant form of dissolved silica up to the stated experimental conditions has the molecular stoichiometry Si(OH)4 (i.e. with n = 2). This conclusion is corroborated by quantum chemical calculations on silicic acid in the gaseous and aqueous phases at ambient conditions (Rustad and Hay, 1995; Sefcik and Goddard, 2001) and by experiments on the stoichiometry of gaseous silica at high temperatures (1200 °C) and low H2O pressures (0.01–0.1 MPa) (Hasimoto, 1992). Above 560 MPa at 700 °C the Raman spectra of Zotov and Keppler (2002) indicate gradual polymerisation of dissolved silica, leading to mixed populations of Si(OH)4 monomers and H6Si2O7 dimers, for which n decreases smoothly with P and T. 3.3. Setchenow-type fits for mixed fluids To describe the salting-in effect in relatively dilute salt solutions at low to moderate pressures an empirical approach similar to the Setchenow-type relationship is usually employed to fit the experimental data: mSiO2ðaqÞ ¼ bmsalt : ð7Þ log o mSiO2ðaqÞ Here mSiO2ðaqÞ and moSiO2ðaqÞ stand for silica solubilities in salt solution and in pure water, respectively, msalt is the molality of the salt and b is the salt-dependent constant known as the Setchenow coefficient. Thus, the overall equation for quartz solubility at a given T–P point may be written as ð8Þ log mSiO2ðaqÞ ¼ log moSiO2ðaqÞ þ n logðxH2 O Þ þ bmsalt : Eq. (8) has been successfully exploited to fit experimental data on quartz solubility in several studies. Walther and Orville (1983) treated H2O–CO2 mixtures and Shmulovich et al. (2001, 2006) modelled H2O–salt–CO2 solutions over a wide T–P range. Nevertheless, this approach suffers from drawbacks. According to the fitting, the number of structurally bonded water molecules, n, varies irregularly with T and P,
whereas in reality it should vary smoothly. Also, the Setchenow coefficient is described by sets of polynomial functions that are individually valid over very restricted P–T–x conditions. So in practice both of these parameters are empirical and their form makes it difficult to extrapolate the experimental trends to conditions outside the realm of the measured data. 3.4. Density models of mixed fluids To enable calculation of quartz solubility in aqueous NaCl solutions Fournier (1983) modified the successful density model for quartz solubility in pure water. Fournier started from Eq. (6), subsequently supposing xH2O to be proportional to the density of free water, qf, i.e. water not tightly bound in hydration shells around the salt ions (e.g. Bockris and Reddy, 1998, p. 69). The expression for SiO2(aq) concentration in the saline solution thus becomes ! qf o ; log mSiO2ðaqÞ ¼ log mSiO2ðaqÞ þ n log o qH2 O where qoH2 O is the density of pure H2O and where hmNaCl qf ¼ qF 1 ; 55:51
ð9Þ
in which q is solution density, F stands for the weight fraction of H2O in the solution, and h denotes the average hydration number of the salt. Despite the fact that it describes SiO2 solubility in H2O– NaCl solutions fairly well, the model of Fournier (1983) should be viewed as essentially empirical. We point out that the assumption that xH2 O is proportional to the density of free water is not yet grounded in a clear physical explanation. Moreover, the hydration number, h, is presumably a complex function of P, T and xNaCl, but in the final expression (Eq. (9)) for log mSiO2ðaqÞ given by Fournier (1983) the hydration number is set to zero. 4. NEW DENSITY MODEL FOR MIXED FLUIDS Building on the model of Fournier (1983) we now take the generalized density approach and adapt it to mixed aqueous fluids. In our new formulation we also start from expression (3), adopting the polynomials of Manning ((3a), (3b)) for the solubility of quartz in pure water. However, in contrast to earlier studies, we assume that aqueous silica has the stoichiometry of orthosilicic acid, H4SiO4, in solution, so the dissolution reaction is cast in the form of Eq. (4) with a constant value of n = 2 at all temperatures and pressures. Newton and Manning (2006) recently had success in modelling activities in the H2O–NaCl–SiO2 system at elevated P–T using n = 2. The basic premise of our model is that silica solubility is mainly controlled by short-range interaction with ambient water molecules, while the effects of other dissolved aqueous species are negligible. Thus, the value of mSiO2ðaqÞ shall depend on the mean distance between water molecules in the fluid. Accordingly, in terms of the density model we write the master equation as
Computation of quartz solubility in H2O–salt–CO2 systems
log mSiO2 ¼ AðT Þ þ BðT Þ log
M H2 O þ n log xH2 O : V H2 O
ð10Þ
30 Newton, Manning, 2000 Shmulovich et al., 2006
V mix ¼ xH2 O V
þ
X
xNaCl·VNaCl / cm3·mol-1
Here M H2 O = 18.0152 g mol1 is the molar mass of H2O, xH2 O as above stands for the mole fraction of H2O in the fluid, A(T) and B(T) are polynomials (3) from Manning (1994), and V H2 O denotes a new parameter that we call the effective partial molar volume of H2O in the fluid. We propose to calculate the latter from the following equation: H2 O
ð11Þ
xs V s ;
where Vmix is the known molar volume of the fluid (in cm3 mol1), and xs and Vs denote the mole fraction and intrinsic volume of the solute s, respectively. Fig. 2 illustrates Eq. (11) and distinguishes the effective and intrinsic molar volumes, as used here, from the more familiar partial and apparent molar volumes. For quartz dissolution in pure water, xH2 O 1 and V H2 O V oH2 O , thus Eq. (11) reverts to the initial form of Manning (1994). For a binary mixture, xs ¼ 1 xH2 O , so Eq. (10) becomes V mix ¼ xH2 O V H2 O þ ð1 xH2 O ÞV s :
1601
20 Oversat.
y = 30.8·x
10
0
0
0.2
0.4
0.6
0.8
xNaCl Fig. 3. Product of xNaClVNaCl versus mole fraction of salt, xNaCl, generated from quartz solubility data in the binary H2O–NaCl system. Symbols correspond to the experimental data used in the fitting procedure, spanning the temperature and pressure regions from 400 to 800 °C and from 200 to 1000 MPa. Line corresponds to the retrieved intrinsic volume of the salt, VNaCl, equal to 30.8 ± 1.3 (2r) cm3 mol1. Details are given in the text.
ð12Þ
The intrinsic volume of the solute, Vs, is therefore the only empirical parameter of the model, although in the discussion below we suggest that it may have definite physical meaning, and hence ultimately predictable values. Eqs. (10) and (12) were used to find the best fit for Vs for the binary mixtures H2O–NaCl and H2O–CO2 using available experimental data on quartz solubility. Volumes of the mixtures, Vmix, at given T–P–xs values were calculated according to the EoS of Anderko and Pitzer (1993) and of Duan et al. (1995) for H2O–NaCl and H2O–CO2, respectively. Figs. 3 and 4 indicate that the product xsVs is nearly
linearly dependent on the mole fraction of the solute, xs, although experimental data in the H2O–CO2 binary are rather scattered. For the H2O–NaCl subsystem, experimental data with high xNaCl were assigned preferential weight in the fitting procedure. It should be noted that the set of experimental data used in the fitting spans a wide range of temperatures (400–800 °C) and pressures (200– 1000 MPa).
32 VNaCl intrinsic
H2O–NaCl 500 °C 500 MPa
Vm / cm3·mol–1
30
* +
2
x Na
VNaCl partial φ
VNaCl apparent
O
=
26
·V H 2 x H 2O
x
)
11
V mi
.(
24
Eq
φ
VH O partial
a
Cl
28
VH O apparent 22 2 VH* O effective
·V N
ic
ns
tri
in Cl
V mix
20
2
18 0
0.2
0.4
0.6
x NaCl
0.8
1
Fig. 2. Example of how Eq. (11) is used to obtain the effective molar volume of H2O (V H2 O ). Thick curve labelled Vmix shows the molar volume of H2O–NaCl mixtures between xNaCl = 0 and xNaCl = 0.24 at 500 °C and 500 MPa, calculated with the Anderko and Pitzer (1993) EoS. The application of Eq. (11) is illustrated for a specific solution composition of xNaCl = 0.2 (open dot). Extrapolation of the line that joins the intrinsic molar volume of NaCl (VNaCl intrinsic) with Vmix at xNaCl = 0.2 yields the effective partial molar volume of H2O (V H2 O ) at xNaCl = 0. Geometric definitions of the corresponding partial and apparent molar volumes (not used in our model) are shown for comparison. Note that the thick Vmix curve closely overlaps the long-dash–short-dash line that joins the apparent molar volumes.
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H2O-NaCl
40 Novgorodov, 1975 Walther, Orville, 1983 Newton, Manning, 2000 Shmulovich et al., 2006
500 °C mSiO2 / mol·kg-1
0.15 20
2
2
xCO ·VCO / cm3·mol-1
30
0.20
10
Shmulovich et al., 2006 200 MPa 500 MPa 900 MPa Halite saturation
0.10
Oversat.
0.05
y = 29.9·x 0
0
0
0.2
0.4
0.2
0.4
0.6
0.6
xCO2 mSiO2 / mol·kg-1
Fig. 4. Product of xCO2VCO2 versus mole fraction of CO2 (xCO2) generated from quartz solubility data in the binary H2O–CO2 system. Symbols correspond to the experimental data used in the fitting procedure, spanning temperature from 500 to 800 °C and pressure from 200 to 1000 MPa. Line corresponds to the retrieved intrinsic volume of CO2, VCO2, equal to 29.9 ± 3.4 (2r) cm3 mol1. Details are given in the text.
700 °C
0.8
0.6
Newton, Manning, 2000 200 MPa 435 MPa 1000 MPa
0.4
0.2
5. RESULTS AND DISCUSSION 0
0.2
0.4
0.6
1.6
Shmulovich et al., 2006 200 MPa 500 MPa 900 MPa Newton, Manning, 2000 1000 MPa
800 °C 1.2
mSiO2 / mol·kg-1
The slopes of the fitted lines in Figs. 3 and 4 yield values at the 2r confidence level of 30.8 ± 1.3 and 29.9 ± 3.4 cm3 mol1 for the intrinsic volumes of NaCl and CO2, respectively. These values were subsequently used with Eqs. (10) and (12) to calculate quartz solubility in H2O–NaCl and H2O–CO2 fluids. Figs. 5 and 6, plotted with linear concentration scales, illustrate the quality of the model description by comparison with the available experimental data. We note that two of the experiments reported by Shmulovich et al. (2006) for H2O–NaCl solutions at 500 °C (their runs 151 and 161) were inadvertently conducted under conditions in which halite was stable (based on the P–T–x locus of the halite solidus according to Chou (1987) and Koster van Groos (1991)). The two data therefore do not represent quartz solubility in the reported bulk fluid composition and we have distinguished them accordingly (filled symbols) in Figs. 3 and 5. However, the two values do seem to provide reasonable estimates of quartz solubility on the halite liquidus (projection of the filled symbols in Fig. 5 onto the dotted saturation curve). Overall it can be seen that the trends in the measurements are well reproduced by our model predictions, and that the accuracy of the model is mostly within the experimental uncertainties, except at high pressures (at and above 900 MPa) and high temperatures. Even at these extreme conditions the maximum deviation in absolute terms is small, less than 0.1 molal. The empirical Setchenow-type equations of Shmulovich et al. (2006) generally provide a more accurate description of their experiments, although the difference in some of the CO2–H2O mixtures is minimal. In contrast to our model, which is based on one equation
0.8
0.4
0
0.2
xNaCl
0.4
0.6
Fig. 5. Quartz solubility in H2O–NaCl fluids at 500, 700 and 800 °C. Symbols indicate experimental data at the specified pressure. Small filled dots at xNaCl = 0 mark solubility in pure water according to Manning (1994). Two filled data symbols at 500 °C denote experiments inadvertently conducted under conditions of halite oversaturation (cf. dotted halite saturation curve based on Chou (1987) and Koster Van Groos (1991)). Dashed curves are Setchenow-type models of Shmulovich et al. (2006). Continuous curves are predictions of our density model (Eqs. (10) and (12)) with VNaCl = 30.8 cm3 mol1.
for all P–T–xs conditions, the equations of Shmulovich et al. (2006) require n and b parameters (in Eq. (8)) that are specific to each P–T point and to each binary H2O–salt fluid system.
Computation of quartz solubility in H2O–salt–CO2 systems
H2O-CO2 0.20
Walther, Orville, 1983 200 MPa
mSiO2 / mol·kg-1
600 °C 0.15
0.10
0.05
0
0.2
0.4
0.6
0.6
Novgorodov, 1975 300 MPa 500 MPa
mSiO2 / mol·kg-1
700 °C 0.4
0.2
0
0.2
0.4
0.6
1.5
Shmulovich et al., 2006 200 MPa 500 MPa 900 MPa Newton, Manning, 2000 1000 MPa
mSiO2 / mol·kg-1
800 °C 1.0
0.5
0
0.2
xCO2
0.4
0.6
Fig. 6. Quartz solubility in H2O–CO2 fluids at 600, 700 and 800 °C. Symbols indicate experimental data at the specified pressure. Filled dots at xCO2 = 0 mark solubility in pure water according to Manning (1994). Dashed curves are Setchenow-type models of Shmulovich et al. (2006). Continuous curves are predictions of our density model (Eqs. (10) and (12)) with VCO2 = 29.9 cm3 mol1.
Figs. 5 and 6 show that the presence of CO2 in the fluid consistently reduces SiO2 solubility, whereas the presence of NaCl may cause either salting-in or salting-out, as mentioned above. Specifically, quartz solubility is most markedly enhanced by the presence of NaCl under conditions where pure water has low density (200 MPa isobars in
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Fig. 5). This effect can be rationalised in terms of the basic premise of our model: the behaviour of aqueous silica is governed mainly by its short-range interaction with ambient water molecules. At low water densities, addition of the salt causes a noticeable contraction of the fluid volume (Anderko and Pitzer, 1993), reducing the mean distance between interacting molecules, enhancing hydration and thereby increasing SiO2 solubility. This behaviour is therefore similar to the effect of isothermally increasing pressure in pure water, as shown by the increased solubilities for the 435, 500, 900 and 1000 MPa isobars in Fig. 5. In contrast to the low density region, addition of NaCl at high water densities tends to expand the molar volume of the binary mixture (Anderko and Pitzer, 1993; e.g. see trend of Vmix curve in Fig. 2), thereby increasing the average distance between water molecules and decreasing SiO2 solubility. The variable influence of NaCl on solution volume is attributable to its properties as an electrolyte, i.e. to its variable degree of dissociation and hydration as a function of P, T and concentration. It therefore follows that addition of CO2, which is essentially a non-electrolyte, always tends to expand the fluid volume, consequently diminishing hydration and lowering SiO2 solubility. The empirical parameters of our model—the intrinsic volumes of the solutes NaCl and CO2—can be interpreted as having definite physical meaning. It is notable that the retrieved value of VNaCl = 30.8 cm3 mol1 is very close to the molar volume of undercooled NaCl melt, 30.2 cm3 mol1, given in Morachevsky (1971). Also the retrieved value of VCO2 = 29.9 cm3 mol1 is close to the excluded volume of CO2, bCO2 = 29.7 cm3 mol1, which appears in the family of Redlich–Kwong–Soave cubic EoS (Poling et al., 2001). This close similarity in values suggests that the intrinsic volume we have defined may correspond to an irreducible volume for the component (perhaps equivalent to the sum of volumes of the major species) in solution. In the case of CO2, which dissociates to only a small extent, this analogy seems plausible. For NaCl, however, which is known to exhibit a huge range in its degree of dissociation, a constant excluded volume for all P– T–x conditions is harder to imagine. Again, it may represent the sum of volumes of all NaCl species in solution. Whatever the ultimate explanation of the physical significance of the intrinsic volume, the residual volume of the solution (which we have termed the effective partial volume of H2O, V H2 O ) seems to represent the influence of H2O molecules that are able to interact with aqueous silica in the same way as they do in the H2O–SiO2 system. From this point of view, our V H2 O is analogous to the ‘‘free water” originally sought by Fournier (1983) in the density model for H2O–NaCl solutions. In view of the close similarity between intrinsic volumes and excluded volumes pointed out above, we suggest that, in lieu of other experimental data, first-order estimates of intrinsic volumes of salts may be obtained from volumetric data on molten salts. Similarly, the intrinsic volumes of gases may be estimated from the b parameters used in cubic EoS for volatiles. To illustrate this approach for a different system we have calculated quartz solubility in H2O–KCl solutions. A value
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of VKCl = 45.5 cm3 mol1 was assumed according to the volume of the molten salt given in Morachevsky (1971). Volumetric properties of the mixture were calculated using the extension of the Duan et al. (1995) EoS given by Bakker et al. (1996). The results are only semi-quantitative (Fig. 7) but the qualitative trends of the few experimental data are reproduced by the model. Fig. 8 illustrates how our new model predicts the influence of different solutes on quartz solubility in a fluid of moderate density. It is obvious that, at any given T–P–xs
H2O-KCl 1.2
800 °C 500 MPa
mSiO2 / mol·kg-1
1.0 0.8 0.6 0.4 0.2
0
0.1
0.2
0.3
xKCl
0.4
0.5
0.6
Fig. 7. Quartz solubility in H2O–KCl fluid at 800 °C and 500 MPa. Open symbols indicate experimental data of Shmulovich et al. (2006). Filled dot at xCO2 = 0 marks solubility in pure water according to Manning (1994). Line corresponds to the model predictions (Eqs. (10) and (12)) with VKCl = 45.5 cm3 mol1.
mSiO2 / mol·kg-1
0.12
500 °C 200 MPa
0.08
KCl
NaCl
0.04
CO2
0
0.1
0.2
0.3
0.4
0.5
0.6
xs Fig. 8. Predicted quartz solubilities, mSiO2, versus mole fraction of the solute, xs, for H2O–KCl, H2O–NaCl, and H2O–CO2 fluids at 500 °C and 200 MPa.
point, KCl causes the strongest salting-in effect at low xs. This result is corroborated by the experimental data of Anderson and Burnham (1967) and Shmulovich et al. (2006). Our approach may be easily applied to mixed fluid systems. For instance, for the ternary H2O–NaCl–CO2 system, Eq. (11) is written as xH2 O V H2 O ¼ V mix xNaCl V NaCl xCO2 V CO2 :
ð13Þ
Adopting the previously retrieved values of VNaCl = 30.8 cm3 mol1 and VCO2 = 29.9 cm3 mol1 and using the Duan et al. (1995) EoS for Vmix of the ternary system, values of mSiO2ðaqÞ can be calculated directly from master Eq. (10). Fig. 9 shows that the predicted values of mSiO2ðaqÞ are in fair concordance with the experimental data at 800 °C and 500 MPa, although the experimental data are in fact highly scattered, precluding detailed comparison. It should be noted that the mole fractions of NaCl and CO2 in the fluid each cover relatively wide ranges from 0 to 0.3. The predictive success of the proposed model depends strongly on the reliability of the EoS employed for the fluid mixtures. It is to be emphasized that the values retrieved in this study for the intrinsic volume parameters specifically depend on the fluid densities generated by the Anderko and Pitzer (1993) and Duan et al. (1995) EoS. Both these EoS are strictly applicable only to pressures up to 500 MPa. Although their extrapolation to higher pressures is generally well behaved, there is a lack of experimental data to test the accuracy of the extrapolations. The tendency of our model to overestimate SiO2 solubility at pressures above 600 MPa may be due to a tendency of the EoS to underestimate fluid volumes at extreme pressures. At 700 °C and 1500 MPa, for example, the EoS predicts the volume of pure water to be 18.46 cm3 mol1, compared to 17.15 cm3 mol1 according to the equation for pure water by Wagner and Pruß (2002). Similarly, some of the discrepancies between the experimental data and the model description for the H2O–KCl system (Fig. 7) may be caused by the approximate nature of the employed EoS. In addition, the reliability of the Anderko and Pitzer (1993) EoS for H2O–NaCl is limited at low temperatures where NaCl is predominantly dissociated. Nevertheless, as can be seen from Fig. 10, our model describes quartz solubilities quite well at relatively low temperatures (300–500 °C) and pressures (20–50 MPa), where the Anderko and Pitzer (1993) EoS is still applicable. As the Anderko and Pitzer (1993) EoS cannot be applied at temperatures below 320 °C, another EoS must be used for low temperature predictions. Table 2 shows a comparison between the few experimental data on quartz solubility in H2O–NaCl solutions at low temperatures and the model predictions based on the EoS by Archer (1992), which is valid up to 320 °C. Although a systematic shift could be expected owing to the use of another EoS, the model continues the same trend visible at somewhat higher temperatures (Fig. 10): the solubilities tend to be slightly underestimated but the correct pressure effects on salting-in and salting-out are reproduced. While there are numerous studies of alkali-complexing of aqueous silica (e.g. Anderson and Burnham, 1967;
Computation of quartz solubility in H2O–salt–CO2 systems
H2O-CO2-NaCl xCO2 0.3
0.2
0.1
0
0.6
xH2O = 0.7
800 °C
mSiO2 / mol .kg-1
500 MPa 0.4
0.2 Shmulovich et al., 2006 Eq. 8, Shmulovich et al., 2006 Eq. 9, This study
0 0.1
0
xNaCl
0.2
0.3
Fig. 9. Quartz solubility in ternary H2O–CO2–NaCl fluids at 800 °C and 500 MPa with xH2O = 0.7. The values of xNaCl and xCO2 vary inversely, their sum being equal to 0.3. Symbols indicate experimental data. Dashed curve is Setchenow-type model of Shmulovich et al. (2006). Continuous curve is prediction of our density model (Eqs. (10) and (13)) with VCO2 = 29.9 cm3 mol1 and VNaCl = 30.8 cm3 mol1.
Anderson and Burnham, 1983; Walther and Orville, 1983), we have not invoked such complexing to model quartz solubility within the CO2–H2O–NaCl system in the P–T–x range under consideration. This is not to say that such complexing is unimportant. Indeed, its future incorporation into our model may lead to improved accuracy. Nevertheless, we have found that the maxima in solubility that occur as a function of aqueous chloride concentration under cer-
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tain isobaric, isothermal conditions (e.g. Figs. 5, 7 and 8) are readily explained by the density of the solvent water under those conditions, without recourse to alkali-complexation. This contrasts with the solubility behaviour of wollastonite and corundum in chloride solutions (Newton and Manning, 2006). These minerals display solubility maxima in NaCl solutions at 800 °C and 1000 MPa, which Newton and Manning (2006) showed unequivocally to be due to complexing. We reiterate that the accuracy of our density model is only slightly inferior to the empirical regressions that experimentalists have used to interpolate their measurements of quartz solubility. Presumably the accuracy of master Eq. (10) could be improved by substituting the mole fraction of H2O, xH2 O , by its activity, aH2 O . Fig. 11 illustrates this for H2O–NaCl mixtures at 800 °C and 1000 MPa. Application to Eq. (10) of the activity model of Aranovich and Newton (1996), which invokes complete dissociation of NaCl and ideal mixing of the resulting three components (H2O, Na+ and Cl), leads to significant underestimation of the experimental solubilities (dashed curve in Fig. 11). In contrast, assuming 50% association of NaCl and ideal mixing yields a good fit to the data (thin continuous curve in Fig. 11). However, exactly the same good fit results if we assume complete dissociation and ideal mixing according to Aranovich and Newton (1996), plus a new arbitrary value of n = 1.7. These example calculations demonstrate that there is scope for improving the accuracy of our model, but at present it is not clear how to apportion the corrections realistically between the fluid volume, the activity of H2O and the number of bonded H2O molecules, n. Molecular modelling suggests that the speciation of aqueous NaCl at elevated conditions is a sensitive function of P, T and NaCl concentration (e.g. Sherman and Collings, 2002; Bondarenko et al., 2006). It therefore appears overly simplistic to assign a fixed degree of association or a fixed value of n to a wide range of conditions. Evans (2007) recently described the effect of chloride solutions on quartz
Table 2 Comparison of quartz solubilities calculated in this study and experimental values in H2O–NaCl solutions at temperatures below 320 °C. Archer’s (1992) EoS was used to predict molar volumes of the mixtures for our Eq. (12). T (°C)
P (MPa)
mNaCl (mol kg1 H2 O )
mSiO2 (mol kg1 H2 O ) experimental
Source of experimental data
mSiO2 (mol kg1 H2 O ) calculated
200 200 300 300
100 100 100 100
0.51 4.40 0.51 4.40
0.00537 0.00372 0.01479 0.01318
Hemley et al. (1980)
0.00459 0.00438 0.01387 0.01381
250 250 250 300 300 300
100 100 100 100 100 100
1.56 3.205 4.99 1.56 3.205 4.99
0.01175 0.01096 0.00871 0.01862 0.01698 0.01514
Ganeyev (1975)
0.00827 0.00816 0.00797 0.01399 0.01395 0.01371
0.17 0.17 0.17 1.29 1.29 1.29
0.00960 0.01044 0.01094 0.01057 0.01183 0.01595
Kitahara (1960)
0.00886 0.01027 0.01156 0.00934 0.01114 0.01317
280 300 320 280 300 320
6.3 8.7 11.3 6.1 8.0 10.3
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a
H 2O-NaCl Saccocia, Seyfried,1990 Fournier et al., 1982 Xie, Walther, 1993
350 °C
50 MPa
0.015 0
1
2
3
mNaCl / mol·kg
mSiO 2 / mol·kg -1
b 0.020
0.015
4
-1
0.8
800 °C, 1000 MPa
mNaCl = 0
0
350 °C 10
20
30
50
Pressure / MPa
c mSiO2 / mol·kg -1
1.2
0.4
mNaCl = 4
0.010
0.030
Newton & Manning, 2000 Eq. 9 This study Eq. 9 + 50% ass. + ideal mix or Eq. 9 + 0% ass. + n = 1.7 Eq. 9 + H2O (A&N 1996)
1.6
0.020
mSiO2 / mol·kg-1
mSiO 2 / mol·kg -1
0.025
50 MPa
mNaCl = 1.86
0.020
mNaCl = 0.83 0.010 300
400
500
Temperature / ºC Fig. 10. Quartz solubility in H2O–NaCl fluids in the relatively low temperature, low density range as a function of (a) NaCl molality at 350 °C, 50 MPa, (b) pressure at 350 °C and NaCl molalities of 0 and 4 mol kg1 H2 O , and (c) temperature at constant pressure of 50 MPa for two NaCl molalities of 0.83 and 1.86 mol kg1 H2 O . Symbols indicate experimental data at the specified temperature. Lines correspond to the model predictions (Eqs. (10) and (12)) using VNaCl = 30.8 cm3 mol1 and using the Anderko and Pitzer (1993) EoS for the H2O–NaCl binary. (See above-mentioned reference for further information).
solubility by fitting the degree of association and of alkali– silica complexing to an activity model, with n fixed at 3. However, this multiparametric approach (two fit parameters for each binary system at each P–T point) leads to predictions of similar accuracy to our simple model. Even the poorer performance at very high and very low pressures is common to both models. Further efforts to improve the accuracy of our model may have to be tied to additional solubility experiments. The available experimental measurements are often quite scattered, and even beyond this scatter, the experimental methods themselves may be subject to systematic uncertainties. The required degree of modelling accuracy is also an
0.2
xNaCl
0.4
0.6
Fig. 11. Performance of simple modifications of our model in predicting quartz solubility in H2O–NaCl mixtures at 800 °C and 1000 MPa. Filled dot at xNaCl = 0: quartz solubility in pure water according to Manning (1994). Thick continuous curve: our Eq. (10) without modification. Dashed curve: our Eq. (10) plus the activity model of Aranovich and Newton (1996), which assumes complete dissociation of NaCl and ideal mixing. Thin continuous curve: our Eq. (10) plus 50% association of NaCl plus ideal mixing. The same thin continuous curve is obtained from Eq. (10) plus the fully dissociated activity model of Aranovich and Newton (1996) plus the assumption that n = 1.7.
issue for consideration, because the variations in quartz solubility as a function of solute concentration at fixed T and P are simply not that great. Where the solute is NaCl (the most common electrolyte in aqueous solutions in the Earth’s crust), quartz solubility varies by significantly less than an order of magnitude (<1 molal) over most compositions prevalent in nature. Solutions containing CO2 show greater variations in silica concentrations, but for these systems the experimental measurements are the most scattered. Our model should be rigorously tested for a wider range of electrolytes on the basis of reliable experimental data on fluid densities. Nevertheless, it already seems clear that, besides reproducing available experimental solubilities with good accuracy, our model is able to predict trends in quartz solubility in fluid mixtures over an extremely wide range of T–P–xs conditions. This is clearly because the model has only one adjustable parameter per solute, and because that parameter, which we equate with the intrinsic volume, seems to have real physical meaning. 6. COMPUTER CODE To facilitate calculation of quartz solubility in CO2– H2O–NaCl–KCl fluids at T > 320 °C, the new model (Eqs. (10) and (11)) has been coded into the EoS of Anderko and Pitzer (1993) and Duan et al. (1995). The numerical versions of these EoS are as corrected and computationally executed by Bakker (2003). The resulting programme package, named LonerAP, is maintained by Ronald Bakker and
Computation of quartz solubility in H2O–salt–CO2 systems
may be downloaded free of charge from the following website: http://fluids.unileoben.ac.at/Computer.html. ACKNOWLEDGMENTS This work was supported by Russian Foundation for Basic Research grant (05-05-66811) and by Swiss National Science Foundation grant 200020–111834 to L.W. Diamond. The authors are very grateful to Kirill Shmulovich for fruitful discussions and for providing us with pre-publication experimental results on quartz solubility. We are also indebted to Ronald Bakker for the opportunity to use his package Fluids (Bakker, 2003) for computation of the volumetric properties of mixed fluids. We thank Greg Anderson, Craig Manning and an anonymous journal reviewer for their careful and insightful reviews of the manuscript.
REFERENCES Akinfiev N. and Zotov A. (1999) Thermodynamic description of equilibria in mixed fluids (H2O-non polar gas) over a wide range of temperature (25 to 700 °C) and pressure (1 to 5000 bars). Geochim. Cosmochim. Acta 63, 2025–2041. Anderko A. and Pitzer K. S. (1993) Equation-of-state representation of phase equilibria and volumetric properties of the system NaCl– H2O above 573 K. Geochim. Cosmochim. Acta 57, 1680–1687. Anderson G. M. and Burnham C. W. (1967) Reaction of quartz and corundum with aqueous chloride and hydroxide solutions at high temperatures and pressures. Am. J. Sci. 265, 12–27. Anderson G. M. and Burnham C. W. (1983) Feldspar solubility and the transport of aluminum under metamorphic conditions. Am. J. Sci. 283-A, 283–297. Anderson G. M., Castet S., Schott J. and Mesmer R. E. (1991) The density model for estimation of thermodynamic parameters of reactions at high temperature and pressure. Geochim. Cosmochim. Acta 55, 1769–1779. Aranovich L. Y. and Newton R. C. (1996) H2O activity in concentrated NaCl solutions at high pressures and temperatures measured by the brucite-periclase equilibrium. Contrib. Mineral. Petrol. 125, 200–212. Archer D. G. (1992) Thermodynamic properties of the NaCl + H2O system II. Thermodynamic properties of NaCl(aq), NaCl2H2O(cr), and phase equilibria. J. Phys. Chem. Ref. Data 21, 793–829. Bakker R. J. (2003) Package FLUIDS 1. Computer programs for analysis of fluid inclusion data and for modelling bulk fluid properties. Chem. Geol. 194, 3–23. Bakker R. J., Dubessy J. and Cathelineau M. (1996) Improvements in clathrate modeling. I: The H2O-CO2 system with various salts. Geochim. Cosmochim. Acta 60, 1657–1681. Bockris J. O. M. and Reddy A. K. N. (1998) Modern Electrochemistry 1: Ionics, Second ed. Plenum, New York, p. 769. Bondarenko G. V., Gorbaty Y. E., Okhulkov A. V. and Kalinichev A. G. (2006) Structure and hydrogen bonding in liquid and supercritical aqueous NaCl solutions at a pressure of 1000 bar and temperatures up to 500 degrees C: a comprehensive experimental and computational study. J. Phys. Chem. A 110(11), 4042–4052. Born Von M. (1920) Volumen und Hydratationswarme der Ionen. Zeitschr. Physik 1, 45–48. Chou I.-M. (1987) Phase relations in the system NaCl–KCl–H2O. III: Solubilities of halite in vapor-saturated liquids above 445 °C and redetermination of phase equilibrium properties in the system NaCl-H2O to 1000 °C and 1500 bars. Geochim. Cosmochim. Acta 51, 1965–1975.
1607
Duan Z., Møller N. and Weare J. H. (1995) Equation of state for the NaCl–H2O–CO2 system: prediction of phase equilibria and volumetric properties. Geochim. Cosmochim. Acta 59, 2869– 2882. Evans K. (2007) Quartz solubility in salt-bearing solutions at pressures to 1 GPa and temperatures to 900 °C. Geofluids 7, 451–467. Fournier R. O. (1983) A method of calculating quartz solubilities in aqueous sodium chloride solutions. Geochim. Cosmochim. Acta 47, 579–586. Fournier R. O. and Potter, II, R. W. (1982) An equation correlating the solubility of quartz in water from 25 °C to 900 °C at pressures up to 10,000 bars. Geochim. Cosmochim. Acta 46, 1969–1973. Fournier R. O., Rosenbauer R. J. and Bischoff J. L. (1982) The solubility of quartz in aqueous sodium chloride solution at 350 °C and 180 to 500 bars. Geochim. Cosmochim. Acta 46, 1975–1978. ¨ berkritisches Wasser als elektrolytisches Franck E. U. (1961) U Lo¨sungsmittel. Angew. Chem. 73, 309–322. Fuoss R. M. (1958) Ionic association. III. The equilibrium between ion pairs and free ions. Am. Chem. Soc. J. 80, 5059–5061. Ganeyev I. G. (1975) Solubility and crystallization of silica in chloride. Doklady Academii Nauk SSSR 224, 248–250. Hasimoto A. (1992) The effect of H2O gas on volatilities of planetforming major elements: I. Experimental determination of thermodynamic properties of Ca-, Al-, and Si-hydroxide gas molecules and its application to solar nebula. Geochim. Cosmochim. Acta 56, 511–532. Helgeson H. C. and Kirkham D. H. (1976) Theoretical predication of the thermodynamic properties of aqueous electrolytes at high pressures and temperatures. III. Equation of state for aqueous species at infinite dilution. Am. J. Sci. 276, 97–240. Helgeson H. C., Kirkham D. H. and Flowers G. C. (1981) Theoretical prediction of the thermodynamic behavior of aqueous electrolytes at high pressures and temperatures. IV. Calculation of activity coefficients, osmotic coefficients and apparent molal and standard and relative molal properties to 600 C and 5 kb. Am. J. Sci. 281, 1249–1516. Hemley J. J., Montoya J. W., Marinenko J. W. and Luce R. W. (1980) Equilibria in the system Al2O3–SiO2–H2O and some general implications for alteration-NOT/mineralization processes. Econ. Geol. 75, 210–228. Kennedy G. C. (1950) A portion of the system silica-water. Econ. Geol. 45, 629–653. Khitarov N. I. (1956) The 400 °C isotherm for the system H2O– SiO2. Am. J. Sci. 260, 501–521. Kitahara S. (1960) The solubility of quartz in water at high temperatures and high pressures. Rev. Phys. Chem. Jpn. 30, 109–114. Koster van Groos A. F. (1991) Differential thermal analysis of the liquidus relations in the system NaCl–H2O to 6 kbar. Geochim. Cosmochim. Acta 55, 2811–2817. Manning C. E. (1994) The solubility of quartz in the lower crust and upper mantle. Geochim. Cosmochim. Acta 58, 4831–4839. Morachevsky A. G. (1971) Handbook on the melt salts V. 1. Electroconductivity, density and viscosity of individual melt salts. Leningrad. Khimiya Publishers. 168 p (in Russian). Morey G. W. and Hesselgesser J. M. (1951) The solubility of quartz and some other substances in superheated steam at high pressures. Am. Soc. Mech. Eng. Trans. 73, 864–875. Newton R. C. and Manning C. E. (2000) Quartz solubility in H2O– NaCl and H2O–CO2 solutions at deep crust-upper mantle pressures and temperatures: 2–15 kbar and 500–900 °C. Geochim. Cosmochim. Acta 64, 2993–3005.
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Newton R. C. and Manning C. E. (2006) Solubilities of corundum, wollastonite and quartz in H2O–NaCl solutions at 800 °C and 10 kbar: Interaction of simple minerals with brines at high pressure and temperature. Geochim. Cosmochim. Acta 70, 5571–5582. Novgorodov P. G. (1975) Quartz solubility in the H2O–CO2 mixture at 700 °C and 3 and 5 kbar pressures. Geokhimiya N 10, 1484–1489 (in Russian). Novgorodov P. G. (1977) On the solubility of quartz in H2O + CO2 and H2O + NaCl at 700 °C and 1.5 kb pressure. Geochem. Int. 14(4), 191–193. Poling B., Prausnitz J. M. and O’Connell J. P. (2001) The Properties of Gases and Liquids, fifth ed. McGraw-Hill, New York. Rustad J. R. and Hay B. P. (1995) A molecular dynamics study of solvated orthosilicic acid and orthosilicate anion using parameterized potentials. Geochim. Cosmochim. Acta 59, 1251–1257. Ryzhenko B. N. (1981) Thermodynamics of Equilibria in Hydrothermal Solutions. Nauka Publishers, Moscow (in Russian). Saccocia P. J. and Seyfried Jr., W. E. (1990) Talc-quartz equilibria and the stability of magnesium chloride complexes in NaCl– MgCl2 solutions at 300, 350, and 400 °C, 500 bars. Geochim. Cosmochim. Acta 54, 3283–3294. Schott J., Dandurand J. L. (1987) Prediction of the thermodynamic behavior of aqueous silica in aqueous complex solutions at various temperatures. In Chemical Transport in Metasomatic Processes (ed. H. C. Helgeson), pp. 733–754. Sefcik J. and Goddard, III, W. A. (2001) Thermochemistry of silicic acid deprotonation: comparison of gas-phase and solvated DFT calculations to experiment. Geochim. Cosmochim. Acta 65, 4435–4443. Shmulovich K. I., Graham C. M. and Yardley B. W. D. (2001) Quartz, albite and diopside solubilities in H2O–NaCl and H2O– CO2 fluids at 0.5–0.9 GPa. Contrib. Mineral. Petrol. 141, 95–108. Shmulovich K. I., Yardley B. W. D. and Graham C. M. (2006) The solubility of quartz in crustal fluids: experiments and general equations for salt solutions and H2O–CO2 mixtures at 400– 800 °C and 0.1–0.9 GPa. Geofluids 6, 154–167.
Sherman D. M. and Collings M. D. (2002) Ion association in concentrated NaCl brines from ambient to supercritical conditions: results from classical molecular dynamics simulations. Geochem. Trans. 3(11), 102–107. Shock E. L., Helgeson H. C. and Sverjensky D. A. (1989) Calculation of the thermodynamic and transport properties of aqueous species at high pressures and temperatures: standard partial molal properties of inorganic neutral species. Geochim. Cosmochim. Acta 53, 2157–2183. Sommerfeld R. A. (1967) Quartz solution reaction: 400–500 °C, 1000 bars. J. Geophys. Res. 72, 4253–4257. Styrikovich M. A. (1969) Vapor solutions. Vestn. Akad. Nauk SSSR. 39(12), 70–77 (in Russian). Tanger J. C. and Helgeson H. C. (1988) Calculation of the thermodynamic and transport properties of aqueous species at high pressures and temperatures: revised equations of state for standard partial molal properties of ions and electrolytes. Am. J. Sci. 288, 19–98. Wagner W. and Pruß A. (2002) The IAPWS formulation 1995 for the thermodynamic properties of ordinary water substance for general and scientific use. J. Phys. Chem. Ref. Data 31, 387–535. Walther J. V. and Helgeson H. C. (1977) Calculation of the thermodynamic properties of aqueous silica and the solubility of quartz and its polymorphs at high pressures and temperatures. Am. J. Sci. 277, 1315–1351. Walther J. V. and Orville P. M. (1983) The extraction-quench technique for determination of the thermodynamic properties of solute complexes: application to quartz solubility in fluid mixtures. Am. Mineral. 68, 731–741. Xie Z. X. and Walther J. V. (1993) Quartz solubilities in NaCl solutions with and without wollastonite at elevated temperatures and pressures. Geochim. Cosmochim. Acta 57, 1947–1955. Zotov N. and Keppler H. (2002) Silica speciation in aqueous fluids at high pressures and temperatures. Chem. Geol. 184, 71–82. Associate editor: Zhenhao Duan
Geochimica et Cosmochimica Acta 73 (2009) 1597–1608 www.elsevier.com/locate/gca
A simple predictive model of quartz solubility in water–salt–CO2 systems at temperatures up to 1000 °C and pressures up to 1000 MPa Nikolay N. Akinfiev a, Larryn W. Diamond b,* a
Institute of Geology of Ore Deposits, Petrography, Mineralogy and Geochemistry RAS, Staromonetnyi per. 35, Moscow 119017, Russia b Rock–Water Interaction Group, Institute of Geological Sciences, University of Bern, Baltzerstrasse 3, Bern CH-3012, Switzerland Received 7 July 2008; accepted in revised form 15 December 2008; available online 25 December 2008
Abstract Knowledge of the solubility of quartz over a broad spectrum of aqueous fluid compositions and T–P conditions is essential to our understanding of water–rock interaction in the Earth’s crust. We propose an equation to compute the molality of aqueous silica, mSiO2ðaqÞ , mol(kg H2O)1, in equilibrium with quartz and water–salt–CO2 fluids, as follows: log mSiO2 ¼ AðT Þ þ BðT Þ log
18:0152 þ 2 log xH2 O V H2 O
Here A(T) and B(T) are polynomials from Manning’s (GCA 58 (1994), 4831) equation for quartz solubility in pure water, and xH2 O and V H2 O stand for the mole fraction and effective P partial molar volume of H2O in the fluid, respectively. The value of V H2 O is computed from the relation V mix ¼ xH2 O V H2 O þ xs V s , where Vmix is the molar volume of the fluid mixture (in cm3 mol1), and xs and Vs denote the mole fraction and the intrinsic volume of the solute, s, respectively. Values of Vmix may be obtained from experimental data on the fluid mixture or from a reliable equation of state for the mixture. Adoption of the Vs values VNaCl = 30.8 cm3 mol1 and V CO2 = 29.9 cm3 mol1 permits satisfactory prediction of quartz solubility both in binary and ternary aqueous systems. In lieu of experimental data Vs can be estimated from pure substance properties: the intrinsic volumes of molten salts yield Vs for the electrolyte components, whereas the excluded volumes of gas species in Redlich–Kwong–Soave-type equations of state yield Vs for the volatiles. The accuracy of our density model is only slightly inferior to the empirical regressions that experimentalists have used to interpolate their measurements of quartz solubility. The strength of our model lies in its ability to predict trends in quartz solubility in fluid mixtures over an extremely wide range of T–P–xs conditions relevant to the Earth’s crust, including conditions hitherto unexplored experimentally. This success is attributable to our model having only one adjustable parameter per solute. Ó 2008 Elsevier Ltd. All rights reserved.
1. INTRODUCTION Quartz is ubiquitous in the Earth’s crust and at elevated temperatures its dissolution- and precipitation behaviour limits the amount of silica that can be transported in hydro-
*
Corresponding author. Fax: +41 31 6314843. E-mail address: [email protected] (L.W. Diamond).
0016-7037/$ - see front matter Ó 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.gca.2008.12.011
thermal fluids. Knowledge of the solubility of quartz is therefore crucial to our understanding of countless geochemical processes. Owing to this importance, numerous studies have been carried out on the solubility of quartz in water at elevated temperatures and pressures, starting with Kennedy (1950), Morey and Hesselgesser (1951), Khitarov (1956) and Kitahara (1960), among others. These early studies have been reviewed and interpreted by Walther and Helgeson (1977). More recent investigations have refined
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the available data and have extended the range of experimental temperature–pressure conditions up to 1000 °C and 2000 MPa (Manning, 1994). Thus, the solubility of quartz has been found to increase with temperature and pressure, except for a restricted T–P region at low pressures in the vicinity of the critical point of water, where the solubility shows retrograde behaviour. While the above studies provide a solid basis for the case of pure water, to understand fully the behaviour of quartz in natural fluids it is necessary to estimate its solubility in complex mixtures containing volatile species, such as CO2, and other dissolved mineral components, especially the alkali and alkaline earth halides. The solubility of quartz in NaCland NaCl–CO2-solutions at hydrothermal conditions has been reported by Khitarov (1956), Kitahara (1960), Anderson and Burnham (1967), Novgorodov (1977), Hemley et al. (1980), Fournier et al. (1982), Xie and Walther (1993), Newton and Manning (2000), and Shmulovich et al. (2001, 2006). These studies have revealed that dissolved silica behaves in a rather intriguing way. Whereas the presence of CO2 in the fluid always lowers silica solubility, the presence of the salt causes more complex effects. At low temperatures (0–250 °C) and at the saturation pressure of water, admixture of salt produces the salting-out phenomenon, lowering silica solubility. However, as temperature approaches the critical point of water, salting-out is superseded by a salting-in effect (Xie and Walther, 1993). Similar behaviour has been experimentally demonstrated at supercritical conditions of H2O (Newton and Manning, 2000). As an example (Fig. 1), at 700 °C, lowering the pressure from 1500 to 435 MPa not only progressively lowers quartz solubility but it also weakens the salting-out effect (the isobars become shallower). When pressure is reduced even further, to below 400 MPa, admixture of moderate amounts of NaCl (up to a mole fraction, xNaCl, of about 0.1) enhances SiO2 solubility in comparison to pure H2O. Moreover, it can be
seen that the 200 MPa isobar of SiO2 solubility vs. salt concentration passes through a maximum: the salting-in effect at low xNaCl switches to salting-out at high salt concentrations. Anderson and Burnham (1967) and Shmulovich et al. (2006) found similar solubility enhancement in KCl solutions. The intent of the present study is to develop a simple predictive model that reproduces this unusual behaviour of quartz solubility over a wide range of T, P and fluid compositions. In this context, ‘‘simple” means that the model ideally has only a small number of empirical fitting parameters. We strive to minimize this number for two reasons. First, if a simple model is successful, its parameters are more likely to carry real physical meaning, and hence they may provide more insight into the solubility phenomenon, pointing the way to fruitful avenues of research. Second, a model with few parameters normally has more predictive power outside the region of available experimental data. Although several published models (discussed below) describe the experimental database for salt- and gas-bearing solutions, they are all essentially empirical in nature, and hence they cannot be expected to extrapolate reliably. On the other hand, the predictive advantages of a simple model often come at the price of accuracy. It will be seen that, for certain fluid P–T–x conditions, this is also the case for the model we present here. The procedure we follow begins with a model of quartz solubility in pure water, the next step being to account for the influence of salts and volatiles on the model parameters. Before presenting our model we review the earlier attempts in the literature on which our model is based, first for pure water and then for mixed gas-salt solutions. Our final model correctly reproduces trends in quartz solubility over a wide range of conditions and fluid compositions relevant to the Earth’s crust. 2. MODELS OF QUARTZ SOLUBILITY IN PURE WATER
700 °C
0.8
Novgorodov, 1977 Manning, 1994 Newton & Manning, 2000
mSiO2 / mol·kg-1
1500 MPa
0.6 1000 MPa
0.4
435 MPa 200 MPa
0.2 150 kbar
0 0
0.1
0.2
0.3
xNaCl
0.4
Two different approaches to the thermodynamic description of aqueous species are currently employed in modern hydrothermal geochemistry: electrostatic models (Fuoss, 1958; Ryzhenko, 1981) and density models (Anderson et al., 1991). Both approaches have been applied with some success to the solubility of quartz, as explained below. The first approach takes account of electrostatic interactions between aqueous dissolved species and the surrounding solvent (H2O) molecules. Within the framework of the well-known HKF model (Helgeson et al., 1981), the solvation term of the chemical potential of ionic species is defined by the Born equation (Born Von, 1920; Helgeson and Kirkham, 1976):
0.5
Fig. 1. Experimental data on quartz solubility (expressed as SiO2 molality, mSiO2 ) in H2ONaCl solutions versus mole fraction of NaCl (xNaCl) at 700 °C and on isobars between 150 and 1500 MPa. Points correspond to the experimental data. Lines are drawn to illustrate trends.
loj;solv ¼ xj
1 1 ; e
ð1Þ
where e represents the static dielectric permittivity of the solvent and xj is the absolute Born coefficient of the jth aqueous species. For aqueous silica, Walther and Helgeson (1977) retrieved a value of xSiO2(aq) = 0.1291 105 cal
Computation of quartz solubility in H2O–salt–CO2 systems
mol1 [=0.5402 105 J mol1] from their regression of available experimental data on quartz solubility, based on the following equilibrium: SiO2ðquartzÞ $ SiO2ðaqÞ ;
ð2Þ
where the properties of aqueous silica, SiO2(aq), do not depend on the explicit structure of the dissolved silica. These same data were later regressed with the revised HKF equation of state (EoS) (Tanger and Helgeson, 1988) to obtain the full set of state parameters for SiO2(aq) (Shock et al., 1989). The resulting description indicates that, within the framework of the adopted EoS, the data are properly described within experimental error. The second major modelling approach, known as the density model, is based on the empirical observations (traced back to works of Franck (1961) and Styrikovich (1969)) that the standard-state chemical potential of a solute is proportional to the decadic (base 10) logarithm of the density of pure water. Thus, the logarithm of the reaction constant of interest may be parameterized by an equation of the form log K ¼ AðT Þ þ BðT Þ log qoH2 O ;
ð3Þ
where A(T) and B(T) are temperature-dependent polynomials, and log qoH2 O stands for the base-10 logarithm of the density of pure water in gcm3. Eq. (3) is independent of the choice of standard state because any choice made for K is automatically incorporated in the proportionality coefficients A and B. The physical reason for the correlation between log K and log qoH2 O is still unexplained, and so the density model remains physically less well-grounded than the electrostatic one. Nevertheless, its simplicity and the dependence of log K only on temperature and qoH2 O make Eq. (3) ideal for thermodynamic calculation of chemical potentials of aqueous species at high T–P conditions. Fournier and Potter (1982) and Manning (1994) regressed the available quartz solubility data according to the density model in terms of the dissolution reaction (2). For the remainder of this study we adopt the polynomials of Eq. (3) for log K ¼ logðmoSiO2ðaqÞ Þ given by Manning (1994): 5764:2 1:7513 106 þ T T2 8 2:2869 10 T3
AðT Þ ¼ 4:2620
1006:9 3:5689 10 ; þ T T2
binary mixtures of H2O and non-polar gases (Sommerfeld, 1967; Novgorodov, 1975; Walther and Orville, 1983) in the studies of Schott and Dandurand (1987), Xie and Walther (1993), and Akinfiev and Zotov (1999). The decrease in solubility of the SiO2 solid phases in the presence of non-polar CO2 in the fluid is accounted for by reducing the dielectric permittivity of the mixture, emix, and by assigning a positive value to the Born parameter for SiO2(aq). The predicted and experimental solubilities are in fair agreement over a geochemically important range of P–T–xgas conditions, i.e. up to 700 °C, 500 MPa and 0.35 mole fraction of non-polar gas (Fig. 10 in Akinfiev and Zotov, 1999), but at more extreme conditions agreement is poor (e.g. at 800 °C and 1000 MPa; Table 1). Nevertheless, this approach is attractive because it does not require any additional empirical parameters beyond those for the initial SiO2–H2O subsystem. Based on the above studies we have attempted to expand the electrostatic approach to the H2O–salt systems. The guiding idea, suggested by Xie and Walther (1993), was to account for the SiO2 salting-out effect at high pressures by the presence of free ions in solution, which lower emix of the mixed fluid (Helgeson et al., 1981). On the other hand, at low pressures, where ions are mostly associated in ion pairs with high dipole moments, the presence of the salt should increase emix of the fluid mixture and thereby enhance quartz solubility. Details of our computational procedure, which are similar to that of Xie and Walther (1993) and of Akinfiev and Zotov (1999), are not given here as this simple model was found to be incapable of explaining the maximum in SiO2 solubility vs. salt content at low pressures. 3.2. Silica solvation in mixed fluids The above obstacles have forced researchers to abandon predictive models for the time being in favour of more complex empirical approaches that afford accurate interpolation of measured quartz solubilities in mixed aqueous fluids. The first step in these approaches is to rewrite the quartz dissolution reaction with explicit regard to solvation: SiO2ðquartzÞ þ nH2 O $ SiO2 ðH2 OÞnðaqÞ ;
ð3aÞ
5
BðT Þ ¼ 2:8454
1599
ð3bÞ
where T is in K. These polynomials are simpler than those of Fournier and Potter (1982) and they accurately reproduce the measured quartz solubilities over a much wider range in pressure and temperature, from 25 °C and 0.1 MPa to 1000 °C and 1000 MPa.
where n is the solvation number of the aqueous silica complex. Abbreviating the aqueous silica complex to SiO2(aq), the equilibrium constant for reaction (4) now becomes
Table 1 Comparison of experimental and predicted quartz solubilities in H2O–CO2 mixtures at 800 °C and 1000 MPa. xCO2
3. MODELS OF QUARTZ SOLUBILITY IN MIXED FLUIDS 3.1. Electrostatic models for mixed fluids The electrostatic approach has been successfully employed to describe experimental data on SiO2 solubility in
ð4Þ
0.185 0.337 0.499 0.503 0.676
mSiO2 (mol kg1 H2 O ) Experimental (Newton and Manning, 2000)
‘‘Electrostatic” model (Akinfiev and Zotov, 1999)
‘‘Density” model (This study)
0.594 0.340 0.209 0.163 0.112
0.419 0.206 0.068 0.066 0.013
0.676 0.365 0.152 0.148 0.036
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log K ¼ log aSiO2ðaqÞ n logðaH2 O Þ:
ð5Þ
Assuming ideal behaviour of the components as a first approximation we set aSiO2ðaqÞ ¼ mSiO2ðaqÞ and, ignoring the mole fraction of H2O bound in the complex, we assume aH2 O ¼ xH2 O . Eq. (5) can now be rewritten for silica solubility as log mSiO2ðaqÞ ¼ log K þ n logðxH2 O Þ: ð6Þ This relation shows that a decrease in the mole fraction of H2O in the fluid will lower SiO2 solubility, qualitatively in accord with the observed salting-out effect at high salt contents. Writing Eqs. (4)–(6) in this way to take account of the existence of SiO2(H2O)n molecules in the aqueous environment is justified by several experimental observations. In situ Raman spectroscopic measurements on silicic acid at conditions up to 800 °C at 425 MPa and up to 600 °C at 820 MPa demonstrate a unique frequency of Si–OH stretching that matches the theoretically calculated frequency of an Si(OH)4 molecule (Zotov and Keppler, 2002). Thus, the dominant form of dissolved silica up to the stated experimental conditions has the molecular stoichiometry Si(OH)4 (i.e. with n = 2). This conclusion is corroborated by quantum chemical calculations on silicic acid in the gaseous and aqueous phases at ambient conditions (Rustad and Hay, 1995; Sefcik and Goddard, 2001) and by experiments on the stoichiometry of gaseous silica at high temperatures (1200 °C) and low H2O pressures (0.01–0.1 MPa) (Hasimoto, 1992). Above 560 MPa at 700 °C the Raman spectra of Zotov and Keppler (2002) indicate gradual polymerisation of dissolved silica, leading to mixed populations of Si(OH)4 monomers and H6Si2O7 dimers, for which n decreases smoothly with P and T. 3.3. Setchenow-type fits for mixed fluids To describe the salting-in effect in relatively dilute salt solutions at low to moderate pressures an empirical approach similar to the Setchenow-type relationship is usually employed to fit the experimental data: mSiO2ðaqÞ ¼ bmsalt : ð7Þ log o mSiO2ðaqÞ Here mSiO2ðaqÞ and moSiO2ðaqÞ stand for silica solubilities in salt solution and in pure water, respectively, msalt is the molality of the salt and b is the salt-dependent constant known as the Setchenow coefficient. Thus, the overall equation for quartz solubility at a given T–P point may be written as ð8Þ log mSiO2ðaqÞ ¼ log moSiO2ðaqÞ þ n logðxH2 O Þ þ bmsalt : Eq. (8) has been successfully exploited to fit experimental data on quartz solubility in several studies. Walther and Orville (1983) treated H2O–CO2 mixtures and Shmulovich et al. (2001, 2006) modelled H2O–salt–CO2 solutions over a wide T–P range. Nevertheless, this approach suffers from drawbacks. According to the fitting, the number of structurally bonded water molecules, n, varies irregularly with T and P,
whereas in reality it should vary smoothly. Also, the Setchenow coefficient is described by sets of polynomial functions that are individually valid over very restricted P–T–x conditions. So in practice both of these parameters are empirical and their form makes it difficult to extrapolate the experimental trends to conditions outside the realm of the measured data. 3.4. Density models of mixed fluids To enable calculation of quartz solubility in aqueous NaCl solutions Fournier (1983) modified the successful density model for quartz solubility in pure water. Fournier started from Eq. (6), subsequently supposing xH2O to be proportional to the density of free water, qf, i.e. water not tightly bound in hydration shells around the salt ions (e.g. Bockris and Reddy, 1998, p. 69). The expression for SiO2(aq) concentration in the saline solution thus becomes ! qf o ; log mSiO2ðaqÞ ¼ log mSiO2ðaqÞ þ n log o qH2 O where qoH2 O is the density of pure H2O and where hmNaCl qf ¼ qF 1 ; 55:51
ð9Þ
in which q is solution density, F stands for the weight fraction of H2O in the solution, and h denotes the average hydration number of the salt. Despite the fact that it describes SiO2 solubility in H2O– NaCl solutions fairly well, the model of Fournier (1983) should be viewed as essentially empirical. We point out that the assumption that xH2 O is proportional to the density of free water is not yet grounded in a clear physical explanation. Moreover, the hydration number, h, is presumably a complex function of P, T and xNaCl, but in the final expression (Eq. (9)) for log mSiO2ðaqÞ given by Fournier (1983) the hydration number is set to zero. 4. NEW DENSITY MODEL FOR MIXED FLUIDS Building on the model of Fournier (1983) we now take the generalized density approach and adapt it to mixed aqueous fluids. In our new formulation we also start from expression (3), adopting the polynomials of Manning ((3a), (3b)) for the solubility of quartz in pure water. However, in contrast to earlier studies, we assume that aqueous silica has the stoichiometry of orthosilicic acid, H4SiO4, in solution, so the dissolution reaction is cast in the form of Eq. (4) with a constant value of n = 2 at all temperatures and pressures. Newton and Manning (2006) recently had success in modelling activities in the H2O–NaCl–SiO2 system at elevated P–T using n = 2. The basic premise of our model is that silica solubility is mainly controlled by short-range interaction with ambient water molecules, while the effects of other dissolved aqueous species are negligible. Thus, the value of mSiO2ðaqÞ shall depend on the mean distance between water molecules in the fluid. Accordingly, in terms of the density model we write the master equation as
Computation of quartz solubility in H2O–salt–CO2 systems
log mSiO2 ¼ AðT Þ þ BðT Þ log
M H2 O þ n log xH2 O : V H2 O
ð10Þ
30 Newton, Manning, 2000 Shmulovich et al., 2006
V mix ¼ xH2 O V
þ
X
xNaCl·VNaCl / cm3·mol-1
Here M H2 O = 18.0152 g mol1 is the molar mass of H2O, xH2 O as above stands for the mole fraction of H2O in the fluid, A(T) and B(T) are polynomials (3) from Manning (1994), and V H2 O denotes a new parameter that we call the effective partial molar volume of H2O in the fluid. We propose to calculate the latter from the following equation: H2 O
ð11Þ
xs V s ;
where Vmix is the known molar volume of the fluid (in cm3 mol1), and xs and Vs denote the mole fraction and intrinsic volume of the solute s, respectively. Fig. 2 illustrates Eq. (11) and distinguishes the effective and intrinsic molar volumes, as used here, from the more familiar partial and apparent molar volumes. For quartz dissolution in pure water, xH2 O 1 and V H2 O V oH2 O , thus Eq. (11) reverts to the initial form of Manning (1994). For a binary mixture, xs ¼ 1 xH2 O , so Eq. (10) becomes V mix ¼ xH2 O V H2 O þ ð1 xH2 O ÞV s :
1601
20 Oversat.
y = 30.8·x
10
0
0
0.2
0.4
0.6
0.8
xNaCl Fig. 3. Product of xNaClVNaCl versus mole fraction of salt, xNaCl, generated from quartz solubility data in the binary H2O–NaCl system. Symbols correspond to the experimental data used in the fitting procedure, spanning the temperature and pressure regions from 400 to 800 °C and from 200 to 1000 MPa. Line corresponds to the retrieved intrinsic volume of the salt, VNaCl, equal to 30.8 ± 1.3 (2r) cm3 mol1. Details are given in the text.
ð12Þ
The intrinsic volume of the solute, Vs, is therefore the only empirical parameter of the model, although in the discussion below we suggest that it may have definite physical meaning, and hence ultimately predictable values. Eqs. (10) and (12) were used to find the best fit for Vs for the binary mixtures H2O–NaCl and H2O–CO2 using available experimental data on quartz solubility. Volumes of the mixtures, Vmix, at given T–P–xs values were calculated according to the EoS of Anderko and Pitzer (1993) and of Duan et al. (1995) for H2O–NaCl and H2O–CO2, respectively. Figs. 3 and 4 indicate that the product xsVs is nearly
linearly dependent on the mole fraction of the solute, xs, although experimental data in the H2O–CO2 binary are rather scattered. For the H2O–NaCl subsystem, experimental data with high xNaCl were assigned preferential weight in the fitting procedure. It should be noted that the set of experimental data used in the fitting spans a wide range of temperatures (400–800 °C) and pressures (200– 1000 MPa).
32 VNaCl intrinsic
H2O–NaCl 500 °C 500 MPa
Vm / cm3·mol–1
30
* +
2
x Na
VNaCl partial φ
VNaCl apparent
O
=
26
·V H 2 x H 2O
x
)
11
V mi
.(
24
Eq
φ
VH O partial
a
Cl
28
VH O apparent 22 2 VH* O effective
·V N
ic
ns
tri
in Cl
V mix
20
2
18 0
0.2
0.4
0.6
x NaCl
0.8
1
Fig. 2. Example of how Eq. (11) is used to obtain the effective molar volume of H2O (V H2 O ). Thick curve labelled Vmix shows the molar volume of H2O–NaCl mixtures between xNaCl = 0 and xNaCl = 0.24 at 500 °C and 500 MPa, calculated with the Anderko and Pitzer (1993) EoS. The application of Eq. (11) is illustrated for a specific solution composition of xNaCl = 0.2 (open dot). Extrapolation of the line that joins the intrinsic molar volume of NaCl (VNaCl intrinsic) with Vmix at xNaCl = 0.2 yields the effective partial molar volume of H2O (V H2 O ) at xNaCl = 0. Geometric definitions of the corresponding partial and apparent molar volumes (not used in our model) are shown for comparison. Note that the thick Vmix curve closely overlaps the long-dash–short-dash line that joins the apparent molar volumes.
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H2O-NaCl
40 Novgorodov, 1975 Walther, Orville, 1983 Newton, Manning, 2000 Shmulovich et al., 2006
500 °C mSiO2 / mol·kg-1
0.15 20
2
2
xCO ·VCO / cm3·mol-1
30
0.20
10
Shmulovich et al., 2006 200 MPa 500 MPa 900 MPa Halite saturation
0.10
Oversat.
0.05
y = 29.9·x 0
0
0
0.2
0.4
0.2
0.4
0.6
0.6
xCO2 mSiO2 / mol·kg-1
Fig. 4. Product of xCO2VCO2 versus mole fraction of CO2 (xCO2) generated from quartz solubility data in the binary H2O–CO2 system. Symbols correspond to the experimental data used in the fitting procedure, spanning temperature from 500 to 800 °C and pressure from 200 to 1000 MPa. Line corresponds to the retrieved intrinsic volume of CO2, VCO2, equal to 29.9 ± 3.4 (2r) cm3 mol1. Details are given in the text.
700 °C
0.8
0.6
Newton, Manning, 2000 200 MPa 435 MPa 1000 MPa
0.4
0.2
5. RESULTS AND DISCUSSION 0
0.2
0.4
0.6
1.6
Shmulovich et al., 2006 200 MPa 500 MPa 900 MPa Newton, Manning, 2000 1000 MPa
800 °C 1.2
mSiO2 / mol·kg-1
The slopes of the fitted lines in Figs. 3 and 4 yield values at the 2r confidence level of 30.8 ± 1.3 and 29.9 ± 3.4 cm3 mol1 for the intrinsic volumes of NaCl and CO2, respectively. These values were subsequently used with Eqs. (10) and (12) to calculate quartz solubility in H2O–NaCl and H2O–CO2 fluids. Figs. 5 and 6, plotted with linear concentration scales, illustrate the quality of the model description by comparison with the available experimental data. We note that two of the experiments reported by Shmulovich et al. (2006) for H2O–NaCl solutions at 500 °C (their runs 151 and 161) were inadvertently conducted under conditions in which halite was stable (based on the P–T–x locus of the halite solidus according to Chou (1987) and Koster van Groos (1991)). The two data therefore do not represent quartz solubility in the reported bulk fluid composition and we have distinguished them accordingly (filled symbols) in Figs. 3 and 5. However, the two values do seem to provide reasonable estimates of quartz solubility on the halite liquidus (projection of the filled symbols in Fig. 5 onto the dotted saturation curve). Overall it can be seen that the trends in the measurements are well reproduced by our model predictions, and that the accuracy of the model is mostly within the experimental uncertainties, except at high pressures (at and above 900 MPa) and high temperatures. Even at these extreme conditions the maximum deviation in absolute terms is small, less than 0.1 molal. The empirical Setchenow-type equations of Shmulovich et al. (2006) generally provide a more accurate description of their experiments, although the difference in some of the CO2–H2O mixtures is minimal. In contrast to our model, which is based on one equation
0.8
0.4
0
0.2
xNaCl
0.4
0.6
Fig. 5. Quartz solubility in H2O–NaCl fluids at 500, 700 and 800 °C. Symbols indicate experimental data at the specified pressure. Small filled dots at xNaCl = 0 mark solubility in pure water according to Manning (1994). Two filled data symbols at 500 °C denote experiments inadvertently conducted under conditions of halite oversaturation (cf. dotted halite saturation curve based on Chou (1987) and Koster Van Groos (1991)). Dashed curves are Setchenow-type models of Shmulovich et al. (2006). Continuous curves are predictions of our density model (Eqs. (10) and (12)) with VNaCl = 30.8 cm3 mol1.
for all P–T–xs conditions, the equations of Shmulovich et al. (2006) require n and b parameters (in Eq. (8)) that are specific to each P–T point and to each binary H2O–salt fluid system.
Computation of quartz solubility in H2O–salt–CO2 systems
H2O-CO2 0.20
Walther, Orville, 1983 200 MPa
mSiO2 / mol·kg-1
600 °C 0.15
0.10
0.05
0
0.2
0.4
0.6
0.6
Novgorodov, 1975 300 MPa 500 MPa
mSiO2 / mol·kg-1
700 °C 0.4
0.2
0
0.2
0.4
0.6
1.5
Shmulovich et al., 2006 200 MPa 500 MPa 900 MPa Newton, Manning, 2000 1000 MPa
mSiO2 / mol·kg-1
800 °C 1.0
0.5
0
0.2
xCO2
0.4
0.6
Fig. 6. Quartz solubility in H2O–CO2 fluids at 600, 700 and 800 °C. Symbols indicate experimental data at the specified pressure. Filled dots at xCO2 = 0 mark solubility in pure water according to Manning (1994). Dashed curves are Setchenow-type models of Shmulovich et al. (2006). Continuous curves are predictions of our density model (Eqs. (10) and (12)) with VCO2 = 29.9 cm3 mol1.
Figs. 5 and 6 show that the presence of CO2 in the fluid consistently reduces SiO2 solubility, whereas the presence of NaCl may cause either salting-in or salting-out, as mentioned above. Specifically, quartz solubility is most markedly enhanced by the presence of NaCl under conditions where pure water has low density (200 MPa isobars in
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Fig. 5). This effect can be rationalised in terms of the basic premise of our model: the behaviour of aqueous silica is governed mainly by its short-range interaction with ambient water molecules. At low water densities, addition of the salt causes a noticeable contraction of the fluid volume (Anderko and Pitzer, 1993), reducing the mean distance between interacting molecules, enhancing hydration and thereby increasing SiO2 solubility. This behaviour is therefore similar to the effect of isothermally increasing pressure in pure water, as shown by the increased solubilities for the 435, 500, 900 and 1000 MPa isobars in Fig. 5. In contrast to the low density region, addition of NaCl at high water densities tends to expand the molar volume of the binary mixture (Anderko and Pitzer, 1993; e.g. see trend of Vmix curve in Fig. 2), thereby increasing the average distance between water molecules and decreasing SiO2 solubility. The variable influence of NaCl on solution volume is attributable to its properties as an electrolyte, i.e. to its variable degree of dissociation and hydration as a function of P, T and concentration. It therefore follows that addition of CO2, which is essentially a non-electrolyte, always tends to expand the fluid volume, consequently diminishing hydration and lowering SiO2 solubility. The empirical parameters of our model—the intrinsic volumes of the solutes NaCl and CO2—can be interpreted as having definite physical meaning. It is notable that the retrieved value of VNaCl = 30.8 cm3 mol1 is very close to the molar volume of undercooled NaCl melt, 30.2 cm3 mol1, given in Morachevsky (1971). Also the retrieved value of VCO2 = 29.9 cm3 mol1 is close to the excluded volume of CO2, bCO2 = 29.7 cm3 mol1, which appears in the family of Redlich–Kwong–Soave cubic EoS (Poling et al., 2001). This close similarity in values suggests that the intrinsic volume we have defined may correspond to an irreducible volume for the component (perhaps equivalent to the sum of volumes of the major species) in solution. In the case of CO2, which dissociates to only a small extent, this analogy seems plausible. For NaCl, however, which is known to exhibit a huge range in its degree of dissociation, a constant excluded volume for all P– T–x conditions is harder to imagine. Again, it may represent the sum of volumes of all NaCl species in solution. Whatever the ultimate explanation of the physical significance of the intrinsic volume, the residual volume of the solution (which we have termed the effective partial volume of H2O, V H2 O ) seems to represent the influence of H2O molecules that are able to interact with aqueous silica in the same way as they do in the H2O–SiO2 system. From this point of view, our V H2 O is analogous to the ‘‘free water” originally sought by Fournier (1983) in the density model for H2O–NaCl solutions. In view of the close similarity between intrinsic volumes and excluded volumes pointed out above, we suggest that, in lieu of other experimental data, first-order estimates of intrinsic volumes of salts may be obtained from volumetric data on molten salts. Similarly, the intrinsic volumes of gases may be estimated from the b parameters used in cubic EoS for volatiles. To illustrate this approach for a different system we have calculated quartz solubility in H2O–KCl solutions. A value
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of VKCl = 45.5 cm3 mol1 was assumed according to the volume of the molten salt given in Morachevsky (1971). Volumetric properties of the mixture were calculated using the extension of the Duan et al. (1995) EoS given by Bakker et al. (1996). The results are only semi-quantitative (Fig. 7) but the qualitative trends of the few experimental data are reproduced by the model. Fig. 8 illustrates how our new model predicts the influence of different solutes on quartz solubility in a fluid of moderate density. It is obvious that, at any given T–P–xs
H2O-KCl 1.2
800 °C 500 MPa
mSiO2 / mol·kg-1
1.0 0.8 0.6 0.4 0.2
0
0.1
0.2
0.3
xKCl
0.4
0.5
0.6
Fig. 7. Quartz solubility in H2O–KCl fluid at 800 °C and 500 MPa. Open symbols indicate experimental data of Shmulovich et al. (2006). Filled dot at xCO2 = 0 marks solubility in pure water according to Manning (1994). Line corresponds to the model predictions (Eqs. (10) and (12)) with VKCl = 45.5 cm3 mol1.
mSiO2 / mol·kg-1
0.12
500 °C 200 MPa
0.08
KCl
NaCl
0.04
CO2
0
0.1
0.2
0.3
0.4
0.5
0.6
xs Fig. 8. Predicted quartz solubilities, mSiO2, versus mole fraction of the solute, xs, for H2O–KCl, H2O–NaCl, and H2O–CO2 fluids at 500 °C and 200 MPa.
point, KCl causes the strongest salting-in effect at low xs. This result is corroborated by the experimental data of Anderson and Burnham (1967) and Shmulovich et al. (2006). Our approach may be easily applied to mixed fluid systems. For instance, for the ternary H2O–NaCl–CO2 system, Eq. (11) is written as xH2 O V H2 O ¼ V mix xNaCl V NaCl xCO2 V CO2 :
ð13Þ
Adopting the previously retrieved values of VNaCl = 30.8 cm3 mol1 and VCO2 = 29.9 cm3 mol1 and using the Duan et al. (1995) EoS for Vmix of the ternary system, values of mSiO2ðaqÞ can be calculated directly from master Eq. (10). Fig. 9 shows that the predicted values of mSiO2ðaqÞ are in fair concordance with the experimental data at 800 °C and 500 MPa, although the experimental data are in fact highly scattered, precluding detailed comparison. It should be noted that the mole fractions of NaCl and CO2 in the fluid each cover relatively wide ranges from 0 to 0.3. The predictive success of the proposed model depends strongly on the reliability of the EoS employed for the fluid mixtures. It is to be emphasized that the values retrieved in this study for the intrinsic volume parameters specifically depend on the fluid densities generated by the Anderko and Pitzer (1993) and Duan et al. (1995) EoS. Both these EoS are strictly applicable only to pressures up to 500 MPa. Although their extrapolation to higher pressures is generally well behaved, there is a lack of experimental data to test the accuracy of the extrapolations. The tendency of our model to overestimate SiO2 solubility at pressures above 600 MPa may be due to a tendency of the EoS to underestimate fluid volumes at extreme pressures. At 700 °C and 1500 MPa, for example, the EoS predicts the volume of pure water to be 18.46 cm3 mol1, compared to 17.15 cm3 mol1 according to the equation for pure water by Wagner and Pruß (2002). Similarly, some of the discrepancies between the experimental data and the model description for the H2O–KCl system (Fig. 7) may be caused by the approximate nature of the employed EoS. In addition, the reliability of the Anderko and Pitzer (1993) EoS for H2O–NaCl is limited at low temperatures where NaCl is predominantly dissociated. Nevertheless, as can be seen from Fig. 10, our model describes quartz solubilities quite well at relatively low temperatures (300–500 °C) and pressures (20–50 MPa), where the Anderko and Pitzer (1993) EoS is still applicable. As the Anderko and Pitzer (1993) EoS cannot be applied at temperatures below 320 °C, another EoS must be used for low temperature predictions. Table 2 shows a comparison between the few experimental data on quartz solubility in H2O–NaCl solutions at low temperatures and the model predictions based on the EoS by Archer (1992), which is valid up to 320 °C. Although a systematic shift could be expected owing to the use of another EoS, the model continues the same trend visible at somewhat higher temperatures (Fig. 10): the solubilities tend to be slightly underestimated but the correct pressure effects on salting-in and salting-out are reproduced. While there are numerous studies of alkali-complexing of aqueous silica (e.g. Anderson and Burnham, 1967;
Computation of quartz solubility in H2O–salt–CO2 systems
H2O-CO2-NaCl xCO2 0.3
0.2
0.1
0
0.6
xH2O = 0.7
800 °C
mSiO2 / mol .kg-1
500 MPa 0.4
0.2 Shmulovich et al., 2006 Eq. 8, Shmulovich et al., 2006 Eq. 9, This study
0 0.1
0
xNaCl
0.2
0.3
Fig. 9. Quartz solubility in ternary H2O–CO2–NaCl fluids at 800 °C and 500 MPa with xH2O = 0.7. The values of xNaCl and xCO2 vary inversely, their sum being equal to 0.3. Symbols indicate experimental data. Dashed curve is Setchenow-type model of Shmulovich et al. (2006). Continuous curve is prediction of our density model (Eqs. (10) and (13)) with VCO2 = 29.9 cm3 mol1 and VNaCl = 30.8 cm3 mol1.
Anderson and Burnham, 1983; Walther and Orville, 1983), we have not invoked such complexing to model quartz solubility within the CO2–H2O–NaCl system in the P–T–x range under consideration. This is not to say that such complexing is unimportant. Indeed, its future incorporation into our model may lead to improved accuracy. Nevertheless, we have found that the maxima in solubility that occur as a function of aqueous chloride concentration under cer-
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tain isobaric, isothermal conditions (e.g. Figs. 5, 7 and 8) are readily explained by the density of the solvent water under those conditions, without recourse to alkali-complexation. This contrasts with the solubility behaviour of wollastonite and corundum in chloride solutions (Newton and Manning, 2006). These minerals display solubility maxima in NaCl solutions at 800 °C and 1000 MPa, which Newton and Manning (2006) showed unequivocally to be due to complexing. We reiterate that the accuracy of our density model is only slightly inferior to the empirical regressions that experimentalists have used to interpolate their measurements of quartz solubility. Presumably the accuracy of master Eq. (10) could be improved by substituting the mole fraction of H2O, xH2 O , by its activity, aH2 O . Fig. 11 illustrates this for H2O–NaCl mixtures at 800 °C and 1000 MPa. Application to Eq. (10) of the activity model of Aranovich and Newton (1996), which invokes complete dissociation of NaCl and ideal mixing of the resulting three components (H2O, Na+ and Cl), leads to significant underestimation of the experimental solubilities (dashed curve in Fig. 11). In contrast, assuming 50% association of NaCl and ideal mixing yields a good fit to the data (thin continuous curve in Fig. 11). However, exactly the same good fit results if we assume complete dissociation and ideal mixing according to Aranovich and Newton (1996), plus a new arbitrary value of n = 1.7. These example calculations demonstrate that there is scope for improving the accuracy of our model, but at present it is not clear how to apportion the corrections realistically between the fluid volume, the activity of H2O and the number of bonded H2O molecules, n. Molecular modelling suggests that the speciation of aqueous NaCl at elevated conditions is a sensitive function of P, T and NaCl concentration (e.g. Sherman and Collings, 2002; Bondarenko et al., 2006). It therefore appears overly simplistic to assign a fixed degree of association or a fixed value of n to a wide range of conditions. Evans (2007) recently described the effect of chloride solutions on quartz
Table 2 Comparison of quartz solubilities calculated in this study and experimental values in H2O–NaCl solutions at temperatures below 320 °C. Archer’s (1992) EoS was used to predict molar volumes of the mixtures for our Eq. (12). T (°C)
P (MPa)
mNaCl (mol kg1 H2 O )
mSiO2 (mol kg1 H2 O ) experimental
Source of experimental data
mSiO2 (mol kg1 H2 O ) calculated
200 200 300 300
100 100 100 100
0.51 4.40 0.51 4.40
0.00537 0.00372 0.01479 0.01318
Hemley et al. (1980)
0.00459 0.00438 0.01387 0.01381
250 250 250 300 300 300
100 100 100 100 100 100
1.56 3.205 4.99 1.56 3.205 4.99
0.01175 0.01096 0.00871 0.01862 0.01698 0.01514
Ganeyev (1975)
0.00827 0.00816 0.00797 0.01399 0.01395 0.01371
0.17 0.17 0.17 1.29 1.29 1.29
0.00960 0.01044 0.01094 0.01057 0.01183 0.01595
Kitahara (1960)
0.00886 0.01027 0.01156 0.00934 0.01114 0.01317
280 300 320 280 300 320
6.3 8.7 11.3 6.1 8.0 10.3
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a
H 2O-NaCl Saccocia, Seyfried,1990 Fournier et al., 1982 Xie, Walther, 1993
350 °C
50 MPa
0.015 0
1
2
3
mNaCl / mol·kg
mSiO 2 / mol·kg -1
b 0.020
0.015
4
-1
0.8
800 °C, 1000 MPa
mNaCl = 0
0
350 °C 10
20
30
50
Pressure / MPa
c mSiO2 / mol·kg -1
1.2
0.4
mNaCl = 4
0.010
0.030
Newton & Manning, 2000 Eq. 9 This study Eq. 9 + 50% ass. + ideal mix or Eq. 9 + 0% ass. + n = 1.7 Eq. 9 + H2O (A&N 1996)
1.6
0.020
mSiO2 / mol·kg-1
mSiO 2 / mol·kg -1
0.025
50 MPa
mNaCl = 1.86
0.020
mNaCl = 0.83 0.010 300
400
500
Temperature / ºC Fig. 10. Quartz solubility in H2O–NaCl fluids in the relatively low temperature, low density range as a function of (a) NaCl molality at 350 °C, 50 MPa, (b) pressure at 350 °C and NaCl molalities of 0 and 4 mol kg1 H2 O , and (c) temperature at constant pressure of 50 MPa for two NaCl molalities of 0.83 and 1.86 mol kg1 H2 O . Symbols indicate experimental data at the specified temperature. Lines correspond to the model predictions (Eqs. (10) and (12)) using VNaCl = 30.8 cm3 mol1 and using the Anderko and Pitzer (1993) EoS for the H2O–NaCl binary. (See above-mentioned reference for further information).
solubility by fitting the degree of association and of alkali– silica complexing to an activity model, with n fixed at 3. However, this multiparametric approach (two fit parameters for each binary system at each P–T point) leads to predictions of similar accuracy to our simple model. Even the poorer performance at very high and very low pressures is common to both models. Further efforts to improve the accuracy of our model may have to be tied to additional solubility experiments. The available experimental measurements are often quite scattered, and even beyond this scatter, the experimental methods themselves may be subject to systematic uncertainties. The required degree of modelling accuracy is also an
0.2
xNaCl
0.4
0.6
Fig. 11. Performance of simple modifications of our model in predicting quartz solubility in H2O–NaCl mixtures at 800 °C and 1000 MPa. Filled dot at xNaCl = 0: quartz solubility in pure water according to Manning (1994). Thick continuous curve: our Eq. (10) without modification. Dashed curve: our Eq. (10) plus the activity model of Aranovich and Newton (1996), which assumes complete dissociation of NaCl and ideal mixing. Thin continuous curve: our Eq. (10) plus 50% association of NaCl plus ideal mixing. The same thin continuous curve is obtained from Eq. (10) plus the fully dissociated activity model of Aranovich and Newton (1996) plus the assumption that n = 1.7.
issue for consideration, because the variations in quartz solubility as a function of solute concentration at fixed T and P are simply not that great. Where the solute is NaCl (the most common electrolyte in aqueous solutions in the Earth’s crust), quartz solubility varies by significantly less than an order of magnitude (<1 molal) over most compositions prevalent in nature. Solutions containing CO2 show greater variations in silica concentrations, but for these systems the experimental measurements are the most scattered. Our model should be rigorously tested for a wider range of electrolytes on the basis of reliable experimental data on fluid densities. Nevertheless, it already seems clear that, besides reproducing available experimental solubilities with good accuracy, our model is able to predict trends in quartz solubility in fluid mixtures over an extremely wide range of T–P–xs conditions. This is clearly because the model has only one adjustable parameter per solute, and because that parameter, which we equate with the intrinsic volume, seems to have real physical meaning. 6. COMPUTER CODE To facilitate calculation of quartz solubility in CO2– H2O–NaCl–KCl fluids at T > 320 °C, the new model (Eqs. (10) and (11)) has been coded into the EoS of Anderko and Pitzer (1993) and Duan et al. (1995). The numerical versions of these EoS are as corrected and computationally executed by Bakker (2003). The resulting programme package, named LonerAP, is maintained by Ronald Bakker and
Computation of quartz solubility in H2O–salt–CO2 systems
may be downloaded free of charge from the following website: http://fluids.unileoben.ac.at/Computer.html. ACKNOWLEDGMENTS This work was supported by Russian Foundation for Basic Research grant (05-05-66811) and by Swiss National Science Foundation grant 200020–111834 to L.W. Diamond. The authors are very grateful to Kirill Shmulovich for fruitful discussions and for providing us with pre-publication experimental results on quartz solubility. We are also indebted to Ronald Bakker for the opportunity to use his package Fluids (Bakker, 2003) for computation of the volumetric properties of mixed fluids. We thank Greg Anderson, Craig Manning and an anonymous journal reviewer for their careful and insightful reviews of the manuscript.
REFERENCES Akinfiev N. and Zotov A. (1999) Thermodynamic description of equilibria in mixed fluids (H2O-non polar gas) over a wide range of temperature (25 to 700 °C) and pressure (1 to 5000 bars). Geochim. Cosmochim. Acta 63, 2025–2041. Anderko A. and Pitzer K. S. (1993) Equation-of-state representation of phase equilibria and volumetric properties of the system NaCl– H2O above 573 K. Geochim. Cosmochim. Acta 57, 1680–1687. Anderson G. M. and Burnham C. W. (1967) Reaction of quartz and corundum with aqueous chloride and hydroxide solutions at high temperatures and pressures. Am. J. Sci. 265, 12–27. Anderson G. M. and Burnham C. W. (1983) Feldspar solubility and the transport of aluminum under metamorphic conditions. Am. J. Sci. 283-A, 283–297. Anderson G. M., Castet S., Schott J. and Mesmer R. E. (1991) The density model for estimation of thermodynamic parameters of reactions at high temperature and pressure. Geochim. Cosmochim. Acta 55, 1769–1779. Aranovich L. Y. and Newton R. C. (1996) H2O activity in concentrated NaCl solutions at high pressures and temperatures measured by the brucite-periclase equilibrium. Contrib. Mineral. Petrol. 125, 200–212. Archer D. G. (1992) Thermodynamic properties of the NaCl + H2O system II. Thermodynamic properties of NaCl(aq), NaCl2H2O(cr), and phase equilibria. J. Phys. Chem. Ref. Data 21, 793–829. Bakker R. J. (2003) Package FLUIDS 1. Computer programs for analysis of fluid inclusion data and for modelling bulk fluid properties. Chem. Geol. 194, 3–23. Bakker R. J., Dubessy J. and Cathelineau M. (1996) Improvements in clathrate modeling. I: The H2O-CO2 system with various salts. Geochim. Cosmochim. Acta 60, 1657–1681. Bockris J. O. M. and Reddy A. K. N. (1998) Modern Electrochemistry 1: Ionics, Second ed. Plenum, New York, p. 769. Bondarenko G. V., Gorbaty Y. E., Okhulkov A. V. and Kalinichev A. G. (2006) Structure and hydrogen bonding in liquid and supercritical aqueous NaCl solutions at a pressure of 1000 bar and temperatures up to 500 degrees C: a comprehensive experimental and computational study. J. Phys. Chem. A 110(11), 4042–4052. Born Von M. (1920) Volumen und Hydratationswarme der Ionen. Zeitschr. Physik 1, 45–48. Chou I.-M. (1987) Phase relations in the system NaCl–KCl–H2O. III: Solubilities of halite in vapor-saturated liquids above 445 °C and redetermination of phase equilibrium properties in the system NaCl-H2O to 1000 °C and 1500 bars. Geochim. Cosmochim. Acta 51, 1965–1975.
1607
Duan Z., Møller N. and Weare J. H. (1995) Equation of state for the NaCl–H2O–CO2 system: prediction of phase equilibria and volumetric properties. Geochim. Cosmochim. Acta 59, 2869– 2882. Evans K. (2007) Quartz solubility in salt-bearing solutions at pressures to 1 GPa and temperatures to 900 °C. Geofluids 7, 451–467. Fournier R. O. (1983) A method of calculating quartz solubilities in aqueous sodium chloride solutions. Geochim. Cosmochim. Acta 47, 579–586. Fournier R. O. and Potter, II, R. W. (1982) An equation correlating the solubility of quartz in water from 25 °C to 900 °C at pressures up to 10,000 bars. Geochim. Cosmochim. Acta 46, 1969–1973. Fournier R. O., Rosenbauer R. J. and Bischoff J. L. (1982) The solubility of quartz in aqueous sodium chloride solution at 350 °C and 180 to 500 bars. Geochim. Cosmochim. Acta 46, 1975–1978. ¨ berkritisches Wasser als elektrolytisches Franck E. U. (1961) U Lo¨sungsmittel. Angew. Chem. 73, 309–322. Fuoss R. M. (1958) Ionic association. III. The equilibrium between ion pairs and free ions. Am. Chem. Soc. J. 80, 5059–5061. Ganeyev I. G. (1975) Solubility and crystallization of silica in chloride. Doklady Academii Nauk SSSR 224, 248–250. Hasimoto A. (1992) The effect of H2O gas on volatilities of planetforming major elements: I. Experimental determination of thermodynamic properties of Ca-, Al-, and Si-hydroxide gas molecules and its application to solar nebula. Geochim. Cosmochim. Acta 56, 511–532. Helgeson H. C. and Kirkham D. H. (1976) Theoretical predication of the thermodynamic properties of aqueous electrolytes at high pressures and temperatures. III. Equation of state for aqueous species at infinite dilution. Am. J. Sci. 276, 97–240. Helgeson H. C., Kirkham D. H. and Flowers G. C. (1981) Theoretical prediction of the thermodynamic behavior of aqueous electrolytes at high pressures and temperatures. IV. Calculation of activity coefficients, osmotic coefficients and apparent molal and standard and relative molal properties to 600 C and 5 kb. Am. J. Sci. 281, 1249–1516. Hemley J. J., Montoya J. W., Marinenko J. W. and Luce R. W. (1980) Equilibria in the system Al2O3–SiO2–H2O and some general implications for alteration-NOT/mineralization processes. Econ. Geol. 75, 210–228. Kennedy G. C. (1950) A portion of the system silica-water. Econ. Geol. 45, 629–653. Khitarov N. I. (1956) The 400 °C isotherm for the system H2O– SiO2. Am. J. Sci. 260, 501–521. Kitahara S. (1960) The solubility of quartz in water at high temperatures and high pressures. Rev. Phys. Chem. Jpn. 30, 109–114. Koster van Groos A. F. (1991) Differential thermal analysis of the liquidus relations in the system NaCl–H2O to 6 kbar. Geochim. Cosmochim. Acta 55, 2811–2817. Manning C. E. (1994) The solubility of quartz in the lower crust and upper mantle. Geochim. Cosmochim. Acta 58, 4831–4839. Morachevsky A. G. (1971) Handbook on the melt salts V. 1. Electroconductivity, density and viscosity of individual melt salts. Leningrad. Khimiya Publishers. 168 p (in Russian). Morey G. W. and Hesselgesser J. M. (1951) The solubility of quartz and some other substances in superheated steam at high pressures. Am. Soc. Mech. Eng. Trans. 73, 864–875. Newton R. C. and Manning C. E. (2000) Quartz solubility in H2O– NaCl and H2O–CO2 solutions at deep crust-upper mantle pressures and temperatures: 2–15 kbar and 500–900 °C. Geochim. Cosmochim. Acta 64, 2993–3005.
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N.N. Akinfiev, L.W. Diamond / Geochimica et Cosmochimica Acta 73 (2009) 1597–1608
Newton R. C. and Manning C. E. (2006) Solubilities of corundum, wollastonite and quartz in H2O–NaCl solutions at 800 °C and 10 kbar: Interaction of simple minerals with brines at high pressure and temperature. Geochim. Cosmochim. Acta 70, 5571–5582. Novgorodov P. G. (1975) Quartz solubility in the H2O–CO2 mixture at 700 °C and 3 and 5 kbar pressures. Geokhimiya N 10, 1484–1489 (in Russian). Novgorodov P. G. (1977) On the solubility of quartz in H2O + CO2 and H2O + NaCl at 700 °C and 1.5 kb pressure. Geochem. Int. 14(4), 191–193. Poling B., Prausnitz J. M. and O’Connell J. P. (2001) The Properties of Gases and Liquids, fifth ed. McGraw-Hill, New York. Rustad J. R. and Hay B. P. (1995) A molecular dynamics study of solvated orthosilicic acid and orthosilicate anion using parameterized potentials. Geochim. Cosmochim. Acta 59, 1251–1257. Ryzhenko B. N. (1981) Thermodynamics of Equilibria in Hydrothermal Solutions. Nauka Publishers, Moscow (in Russian). Saccocia P. J. and Seyfried Jr., W. E. (1990) Talc-quartz equilibria and the stability of magnesium chloride complexes in NaCl– MgCl2 solutions at 300, 350, and 400 °C, 500 bars. Geochim. Cosmochim. Acta 54, 3283–3294. Schott J., Dandurand J. L. (1987) Prediction of the thermodynamic behavior of aqueous silica in aqueous complex solutions at various temperatures. In Chemical Transport in Metasomatic Processes (ed. H. C. Helgeson), pp. 733–754. Sefcik J. and Goddard, III, W. A. (2001) Thermochemistry of silicic acid deprotonation: comparison of gas-phase and solvated DFT calculations to experiment. Geochim. Cosmochim. Acta 65, 4435–4443. Shmulovich K. I., Graham C. M. and Yardley B. W. D. (2001) Quartz, albite and diopside solubilities in H2O–NaCl and H2O– CO2 fluids at 0.5–0.9 GPa. Contrib. Mineral. Petrol. 141, 95–108. Shmulovich K. I., Yardley B. W. D. and Graham C. M. (2006) The solubility of quartz in crustal fluids: experiments and general equations for salt solutions and H2O–CO2 mixtures at 400– 800 °C and 0.1–0.9 GPa. Geofluids 6, 154–167.
Sherman D. M. and Collings M. D. (2002) Ion association in concentrated NaCl brines from ambient to supercritical conditions: results from classical molecular dynamics simulations. Geochem. Trans. 3(11), 102–107. Shock E. L., Helgeson H. C. and Sverjensky D. A. (1989) Calculation of the thermodynamic and transport properties of aqueous species at high pressures and temperatures: standard partial molal properties of inorganic neutral species. Geochim. Cosmochim. Acta 53, 2157–2183. Sommerfeld R. A. (1967) Quartz solution reaction: 400–500 °C, 1000 bars. J. Geophys. Res. 72, 4253–4257. Styrikovich M. A. (1969) Vapor solutions. Vestn. Akad. Nauk SSSR. 39(12), 70–77 (in Russian). Tanger J. C. and Helgeson H. C. (1988) Calculation of the thermodynamic and transport properties of aqueous species at high pressures and temperatures: revised equations of state for standard partial molal properties of ions and electrolytes. Am. J. Sci. 288, 19–98. Wagner W. and Pruß A. (2002) The IAPWS formulation 1995 for the thermodynamic properties of ordinary water substance for general and scientific use. J. Phys. Chem. Ref. Data 31, 387–535. Walther J. V. and Helgeson H. C. (1977) Calculation of the thermodynamic properties of aqueous silica and the solubility of quartz and its polymorphs at high pressures and temperatures. Am. J. Sci. 277, 1315–1351. Walther J. V. and Orville P. M. (1983) The extraction-quench technique for determination of the thermodynamic properties of solute complexes: application to quartz solubility in fluid mixtures. Am. Mineral. 68, 731–741. Xie Z. X. and Walther J. V. (1993) Quartz solubilities in NaCl solutions with and without wollastonite at elevated temperatures and pressures. Geochim. Cosmochim. Acta 57, 1947–1955. Zotov N. and Keppler H. (2002) Silica speciation in aqueous fluids at high pressures and temperatures. Chem. Geol. 184, 71–82. Associate editor: Zhenhao Duan