A Comparison of Standard Thermodynamic Properties and 2+ 2À Solubility Data for Baryte, Ba (Aq) and SO4 (Aq)

Mineralogical Magazine, November 2014, Vol. 78(6), pp. 1505–1515

OPEN ACCESS

A comparison of standard thermodynamic properties and 2+ 2À solubility data for baryte, Ba (aq) and SO4 (aq)

1,2, 1, 1 2 1 B. Y. ZHEN-WU *, K. DIDERIKSEN *, D. A. BELOVA ,P.J.RAAHAUGE AND S. L. S. STIPP 1 Nano-Science Center, Department of Chemistry, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen OE, Denmark 2 Maersk Oil and Gas A/S, Esplanaden 50, 1263 Copenhagen K, Denmark [Received 24 July 2014; Accepted 3 February 2015; Associate Editor: T. Rinder]

ABSTRACT

The thermodynamic solubility product for baryte, determined at standard conditions, from data in commonly used compilations, was compared with published experimental solubility products for baryte and with the solubility products from databases used by the PHREEQC geochemical speciation code and MultiScale, which is often used by oil companies to predict or describe baryte scaling. The values in the various databases agree well with experimental data (10À10.05À10À9.96;Melcher,1910; Neuman, 1933; Templeton, 1960; Davis and Collins, 1971; Blount, 1977; Felmy et al., 1990), which agree within uncertainty with the values presented in the compilations of Robie et al. (1979), Wagman et al. (1982), Lide (2005), Raju and Atkinson (1988), as well as Nordstrom and Munoz (1994), whose values have the least uncertainty. In solutions of 50% seawater mixed with 50% reservoir formation waters, the data predict baryte supersaturation, both at standard temperature and at the temperatures expected in the reservoir, completely consistent with ﬁeld observations. This provides conﬁdence that the Pitzer approach for activity correction and the database is valid for investigations of baryte precipitation rates in high ionic strength solutions.

2+ 2À KEYWORDS: baryte, barite, BaSO4, barium, Ba , sulfate, SO4 , thermodynamics, standard state, solubility, PHREEQC, MultiScale.

Introduction with respect to calcite (Mackenzie and Andersson, 2013) but is typically undersaturated with respect 2+ BARIUM (Ba ) is common in silicate minerals and to baryte (Chow and Goldberg, 1960). Baryte is released to solution during weathering (Kastner, approaches saturation as depth increases 2À 1999; Hanor, 2000). Sulfate (SO4 ) is the most (Wolgemuth and Broecker, 1970). Although stable and most abundant sulfur species in surface seawater is undersaturated, it often oxidizing environments (Ivanov, 1981). contains pelagic baryte particles, some of which 2+ 2À Consequently, Ba and SO4 concentrations are interpreted to have formed in situ, where the exceed baryte (BaSO4) solubility, resulting in its saturation state locally exceeds its solubility formation in a variety of environments such as in product (Hanor, 2000). The presence of baryte sedimentary basins, at seaﬂoor hydrothermal in sediments provides information about the vents and in anthropogenic environments geological processes that occurred during sedi- (Hanor, 2000). Surface seawater is supersaturated

This paper is published as part of a special issue in * E-mail: Mineralogical Magazine, Vol. 78(6), 2014 entitled [email protected]; [email protected] ‘Mineral–fluid interactions: scaling, surface reactivity DOI: 10.1180/minmag.2014.078.6.17 and natural systems’.

# 2014 The Mineralogical Society

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mentation (Grifﬁth and Paytan, 2012) and the been compiled since the 1930s (Latimer et al., biogeochemical cycles that controlled concentra- 1933; Helgeson, 1969; Robie et al., 1979; tion and behaviour (von Allmen et al., 2010). Wagman et al., 1982; Raju and Atkinson, 1988; Sometimes, baryte occurs as a result of human Nordstrom and Munoz, 1994; Robie and activity, most notably during petroleum produc- Hemingway, 1995; Lide, 2005) and a number tion. For oil production, seawater is often injected of geochemical speciation codes are also into reservoirs but where pore solutions contain available that include databases with baryte dissolved barium, the increase in sulfate concen- solubility constants (Crawford, 1999). One tration that results from seawater injection, example is the open-access computer code precipitates baryte (Jordan et al., 2008). Baryte PHREEQC, which features its own database as scaling can completely block pore throats, well as databases from other sources (Parkhurst decreasing permeability and in some cases, and Appelo, 2013). Another licensed computer destroying the reservoir. code, designed speciﬁcally for predicting scaling Several sets of thermodynamic property data in the oil industry, is MultiScale (Scale Consult, for baryte and aqueous barium and sulfate have 2006).

TABLE 1(contd. opposite). Summary of compiled published stadard-state thermodynamic properties for baryte 2+ 2À (BaSO4) and the free ions barium (Ba ) and sulfate (SO4 ).

2+ ———— BaSO4(s) ———— ————— Ba (aq) ————— o o o o o o S DHf DGf S DHf DGf Reference (J·molÀ1KÀ1) (kJ·molÀ1) (kJ·molÀ1) (J·molÀ1KÀ1) (kJ·molÀ1) (kJ·molÀ1)

Helgeson (1969) 12.6*e À538.35*e 132.21a À1473.19b À1362.19b 9.60b À537.64b À560.74b Robie et al. (1979) 1.68 2.00 2.60 1.70 0.24 0.24 Wagman et al. (1982) 132.2 À1473.2 À1362.2 9.6 À537.64 À560.77 and Lide (2005) Raju and Atkinson 132.2b À1473.19b À1362.31b 9.6b À537.71b À560.93b (1988) Nordstrom and Munoz 128.6c À1468.3c À1356.3c 8.4f À532.5f À555.4f (1994) 2.0 2.5 2.6 2.0 2.5 2.6 Robie and Hemingway 132.2d À1473.6d À1362.5d 8.40f À532.5f À555.4f (1995) 1.6 2.0 2.6 1.00 2.0 2.0

Standard state: 298.15 K, 1 bar and assuming unit activity and 1 molal ionic strength. Reference state for elemental o o o barium and sulfur (orthorhombic) for DHf and DGf is zero at standard state and for S is zero at absolute zero o o o temperature. S : absolute standard molar entropy; DHf : standard enthalpy of formation; DGf : standard Gibbs free o o energy of formation; DSr : change in standard entropy of the reaction; DHr : change in standard enthalpy of the o reaction; DGr : change in Gibbs free energy of the reaction; log K: logarithm of the thermodynamic solubility product. Values given in italic were calculated in the present study. Approach a: calculated change in Gibbs free energy of the reaction using the entropy and enthalpy of the reaction: D o D o D o D o D o D o D o D o o o o Gr = Hr À T Sr , where Hr = Hf,Ba + Hf,SO4 À Hf,BaSO4; Sr = SBa + SSO4 À SBaSO4. Approach b: calculated change in Gibbs free energy of the reaction using formation Gibbs free energy of the o o o o reactants and the product: DGr = DGf,Ba + DGf,SO À DGf,BaSO . 4 4 o Thermodynamic solubility of baryte was determined using: log K = À DGr/(ln(10)RT), where T represents the standard temperature, 298.15 K and R is the molar gas constant, 8.3144621(75) J·molÀ1KÀ1 (NIST, 2014). : expanded uncertainty at the 95% conﬁdence level. *: converted from the original data in cal molÀ1degÀ1 with a thermochemical calorie 4.184 J. Data from: a Kelley and King (1961); b Parker et al. (1971); c Nordstrom and Munoz (1994); d DeKock (1986); e Latimer (1952); f Busenberg and Plummer (1986); g Wagman et al. (1968); h Cox et al. (1989).

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Traditionally, the thermodynamic solubility Thermodynamic properties product at standard state serves as the basis for extrapolation to other conditions. Furthermore, Six thermodynamic compilations that include the modelling of mineral dissolution and precipitation thermodynamic properties for baryte, free barium rates relies on equations that incorporate the and sulfate ions at standard conditions (1 bar, difference between actual activities and those 298.15 K and assuming unit activity and 1 molal expected at equilibrium (Palandri and Kharaka, ionic strength) are summarized in Table 1 (all 2004). Small deviation and inconsistency in uncertainties in this work are reported with two reported values for stability are often ampliﬁed standard deviations). All these data sets were when one seeks to model more complex systems. derived from experimental and theoretical studies, Thus, an internally consistent and accurate set of where the sources have been indicated in the table thermodynamic data is required, especially for footnotes. extrapolating from standard conditions to solutions at reservoir temperature and the ionic Free barium ion, Ba2+ strength of seawater or formation water. The aims of this study were to: (1) assess The only experimental data available for the published thermodynamic data for baryte and the entropy of free barium is from Brown et al.

TABLE 1(contd.).

2+ 2À ——————— BaSO4 (s) =Ba (aq) +SO4 (aq) ——————— 2À ——— SO4 (aq) ————— ———————— a ———————— ——— b ——— o o o o o o o S DHf DGf DSr DHr DGr Log K DGr Log K (J·molÀ1KÀ1) (kJ·molÀ1) (kJ·molÀ1) (J·molÀ1KÀ1) (kJ·molÀ1) (kJ·molÀ1) (kJ·molÀ1)

20.1*g À909.27*g À744.63*g À99.6* 25.7* 55.38 À9.70 20.00g À909.27g À744.63g À102.6 26.3 56.9 À9.96 56.8 À9.95 1.70 0.24 0.24 3.0 2.0 2.2 0.39 2.6 0.46

20.1 À909.27 À744.53 À102.5 26.3 56.9 À9.97 56.9 À9.97

20.1b À909.27b À744.54b À102.5 26.2 56.8 À9.95 56.8 À9.96

18.5h À909.3h À744.0h À101.7 26.5 56.9 À9.97 57.1 À10.00 0.4 0.4 0.4 1.0 0.5 1.8 0.32 1.8 0.32 18.5h À909.3h À744.0h À105.3 31.8 62.4 À10.93 63.1 À11.05 0.8 0.8 0.8 2.0 3.0 3.0 0.53 3.4 0.59

free barium and sulfate ions at standard-state (1936). The entropy of barium was originally conditions and compare them with published obtained (9.2 J·molÀ1·KÀ1) from the heat of the experimental solubility data and with the dissolution, measured on high-purity barium solubility constants used in the databases of chloride dihydrate utilizing high-purity solids. speciation models; and (2) to suggest the most Later recalculations by Latimer et al. (1938) and consistent and accurate parameters for the Ba2+– Kelley and King (1961) derived the same value 2À À1 À1 SO4 –H2O system that can be used as a reliable (9.6 1.2 J·mol ·K ). starting point for geochemical speciation calcula- For the Ba2+ enthalpy of formation, two tions and for predicting solubility relationships in experimental values are available: Fitzgibbon et pure systems. Finally, we used the data to predict al. (1973) and Cordfunke et al. (1990). the saturation state for sulfate minerals from Fitzgibbon et al. determined enthalpy using solutions formed of seawater mixed with forma- calorimetry (À535.3 1.7 kJ·molÀ1)ina tion water, from several reservoirs where baryte solution of Ba2+ made from high-purity metal. scaling had been observed under ﬁeld conditions. Cordfunke et al. calculated the enthalpy of Ba2+

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À1 (À534.75 1.74 kJ·mol )usingtheirmeasured species (Ba(s),O2(g),S(g) or S(s)), resulted in the enthalpy of formation for barium chloride as well same value as that estimated by Kelley and King as the thermodynamic properties for the chloride (1961). ion from Cox et al. (1989). The value For the enthalpy of baryte, the first published (À537.64 kJ·molÀ1) compiled by Parker et al. value is from Latimer (1952; À1465.2 kJ·molÀ1). (1971) and Wagman et al. (1982) is close to the Parker et al. (1971) included this value in their experimental data reported by Fitzgibbon et al. compilation and extrapolated from high-temp- (1973) and Cordfunke et al. (1990). erature data to a standard-state value of The values for entropy and enthalpy for Ba2+ À1466.5 kJ·molÀ1 but no information about published by Helgeson (1969) were taken from newer experimental studies was provided. Later, Latimer (1952). These values are higher than Robie et al. (1979) and DeKock (1986) adjusted those of the other data sets (Table 1). this value slightly (À1473.2 kJ molÀ1). Recently, Finally, a new set of thermodynamic properties Majzlan et al. (2002) determined the enthalpy of for Ba2+, derived from solubility data of witherite, formation using high-temperature oxide melt BaCO3, were proposed later by Busenberg and calorimetry. They obtained values for: synthetic Plummer (1986). They fitted the equilibrium baryte, À1459.7 3.7 kJ·molÀ1, Colorado natural constant of witherite to experimental solubility baryte, À1464.2 3.7 kJ·molÀ1, and South data between 278 K and 353 K, using recalculated Carolina natural baryte, À1464.9 thermodynamic data from carbonate species 3.7 kJ·molÀ1. Values for the two natural presented by Busenberg et al. (1984). samples agree within uncertainty with data presented by Nordstrom and Munoz (1994). Free sulfate ion, SO2À From thermodynamic properties for the barium 4 ion (Busenberg and Plummer, 1986) and solubi- Based on many experimental studies, the entropy lity measurements, Nordstrom and Munoz (1994) o À1 À1 o of sulfate was reported by Latimer et al. (1938; obtained values (S : 128.6 J·mol K ; DHf : 18.4 4.2 J·molÀ1·KÀ1) and, later, by Cox et al. À1468.3 kJ·molÀ1) that are lower than those (1989; 18.50 0.40 J·molÀ1·KÀ1). These values obtained calorimetrically (So: 132.2 J·molÀ1KÀ1; o À1 agree within uncertainty. DHf : À1473.2 kJ·mol ) by the other compila- The entropy of sulfate from Wagman et al. (1968) tions from Table 1. is greater than that from Cox et al. (1989) and also agrees with the above values within uncertainty. Solubility data The enthalpy of formation of sulfate from the six compilations of thermodynamic properties There are many values for the thermodynamic agrees within the uncertainty with the experi- solubility product for baryte. However, some are mental value determined by Johnson and Sunner based on recalculation from data previously (1963; À909.34 0.45 kJ·molÀ1). published in compilations (Egorov and Titova, 1962; Silleń and Martell, 1964; Khodakovsky et Baryte, BaSO al., 1966; Malinin et al., 1969; Smith and Martell, 4 1976; Monnin and Galinier, 1988; Kaasa, 1998), The only experimental data available for baryte and in reports of experiments at temperatures entropy were published by Latimer et al. (1933). other than 298.15 K (Uchameyshvili et al., 1966; They used vacuum bomb calorimetry to measure Schulien, 1987; Jiang, 1996). The results of work the heat capacity on high-purity solids and at non-standard conditions are not reviewed here. originally obtained a value of 131.84 Table 2 presents the thermodynamic solubility 0.07 J·molÀ1·KÀ1. This value was later extra- product for baryte extrapolated to infinite dilution polated to standard conditions by Kelley and King from solubility measurements conducted at (1961; 132.2 0.8 J·molÀ1·KÀ1) using the third standard temperature and pressure. Although a law of thermodynamics, which states that the variety of methods has been used, the values entropy for a pure crystal at absolute zero determined (log K: À10.05 to À9.96) are in temperature should be zero. Later estimates by surprisingly good agreement, where the total DeKock (1986), which included Latimer et al. difference is only 19%. For the more recent (1933) and higher-temperature heat-capacity studies, which use more accurate techniques for measurements and considered two independent determining aqueous ion concentrations, all are baryte formation reactions from the elemental within the limits of experimental error.

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TABLE 2. Published experimental thermodynamic solubility product for baryte extrapolated from solubility data to standard-state conditions: 1 bar, 298.15 K and pure water, i.e. ionic strength (IS = 0).

Reference Analytical method Activity coefficient log K estimation approach

Melcher (1910) Conductivity Pitzer ion interaction –10.00a Neuman (1933) Conductivity Linear relationship between solubility –10.04 and square root of the ionic strength Templeton (1960) Spectroscopy Debye-Hu¨ckel –9.96 Davis and Collins (1971) Liquid scintillation Linear relationship between solubility –9.96 and square root of the ionic strength Blount (1977) X-ray fluorescence Extended Debye-Hu¨ckel –9.98 Felmy et al. (1990) ICP-AES Pitzer ion interaction –10.050.05b*

a : calculated in this study using a mean activity coefﬁcient for BaSO4 of 0.970, which is estimated using PHREEQC Version 3 using the Pitzer.dat. b : accepted value derived from NaClO4 electrolyte background. ICP-AES: Inductively coupled plasma-atomic emission spectroscopy. *: Later documentation on the NONLIN software developed by Felmy gives uncertainties as 1 standard deviation. We assume that the uncertainty in Felmy et al. (1990) is reported at that level.

Comparison of the thermodynamic values but is still off by a quarter of an order of properties and solubility data magnitude. Although the sulfate data from The Gibbs free energy and the thermodynamic Helgeson (1969) are similar to those presented solubility product for baryte dissolution, BaSO4(s) by Robie et al. (1979), he obtained a higher log K 2+ 2À =Ba (aq) +SO4 (aq), were calculated for each because his enthalpy estimate for barium was too compilation presented in Table 1 using two high. approaches: from the entropy and enthalpy data Robie and Hemingway (1995) attempted to (a), and from the Gibbs free energy of formation improve their data by incorporating updated (b). The values for baryte using both approaches, thermodynamic properties for Ba2+ from from the compilations of Robie et al. (1979), Busenberg and Plummer (1986), resulting in Wagman et al. (1982) and Lide (2005), Raju and values that are lower than those reported from Atkinson (1988) and Nordstrom and Munoz other work. Recently, Wolery and Sutton (2013) (1994) agree with each other within their identified discrepancies for the barium properties uncertainty because, with the exception of the between the compilations from Robie et al. (1979) Nordstrom and Munoz (1994) compilation, they and Robie and Hemingway (1995) but they did originate from the same sources. They also agree not explain the origin of the discrepancies. Robie with the thermodynamic solubility product and Hemingway (1995) did not assess the internal determined experimentally from solubility consistency of the data set with baryte and sulfate. measurements (Fig. 1). The estimates of Consequently, the solubility product determined Helgeson (1969) are slightly higher (À9.70), from their data is lower than that of Robie et al. whereas calculations from the data of Robie and (1979). The solubility-data deviations are larger Hemingway (1995) result in significantly lower than those from calorimetric measurements so the values (À10.93 and À11.05). uncertainty associated with the Ba2+ data reported Helgeson (1969) was a pioneer in using by Robie and Hemingway (1995) is greater than computer modelling to estimate consistent sets that reported by Robie et al. (1979). of thermodynamic properties from experimental The compilation from Robie et al. (1979), data for a large number of different elements and derived from calorimetric measurements, is systems to get the overall best fits. His estimate reliable and consistent but contains larger for baryte is reasonably close to the experimental uncertainties than the Nordstrom and Munoz

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FIG. 1. Calculated log K for baryte solubility at the 95% conﬁdence limit, determined from the Gibbs free energy of reaction, derived from two approaches: (a) from enthalpy and entropy (ﬁlled symbols); and (b) from Gibbs free energy of formation (open symbols). Values from Helgeson (1969), Wagman et al. (1982), Lide (2005) and Raju and Atkinson (1988) were reported without uncertainty. The double dotted vertical bar represents the range of experimental values for the logarithm of the thermodynamic solubility product for baryte (log K: À10.05 to À9.96).

(1994) compilation which has also been updated À9.97), the change in standard enthalpy of the 2+ o À1 with Ba data from Busenberg and Plummer baryte reaction (DHr : 26.57 kJ·mol ) and the (1986) and the baryte data were adjusted with analytical expression for the temperature depen- calculations from barium and sulfate thermo- dence have all been adopted from Nordstrom et dynamic properties and baryte solubility. al. (1990), which is based on data reported by Nordstrom and Munoz used a combination of Blount (1977). Three other PHREEQC databases, thermodynamic data derived from a variety of amm.dat, phreeqc.dat and pitzer.dat, also use log experimental methods and generated a consistent K=À9.97. data set for the baryte system after assessing the For llnl.dat, sit.dat, minteq.dat and minteq.v4.dat, internal consistency of the newer and previously it was not possible to track the origin of the baryte existing data. data. In these databases, log K is similar but not the same, À9.9711, À9.97, À9.976 and À9.98. The o first three, llnl.dat, sit.dat and minteq.dat, have DHr Geochemical speciation databases 1 close to 26.57 kJ·molÀ , presented by Nordstrom et For the baryte system, eight of the nine al. (1990), with values of 25.9408 kJ·molÀ1, PHREEQC databases (Parkhurst and Appelo, 26.46 kJ·molÀ1 and 26.28 kJ·molÀ1 . o 2013; Version 3; i.e. amm.dat, llnl.dat, Minteq.v4.dat, however, uses a lower DHr value, minteq.dat, minteq.v4.dat, phreeqc.dat, pitzer.dat, 23 kJ·molÀ1. In conclusion, all of the databases sit.dat and waterq4f.dat), include the species: associated with PHREEQC have very similar log K 2+ + 2À À Ba , BaOH ,SO4 and HSO4 . The database for baryte dissolution at standard temperature but at iso.dat does not include any Ba2+ species. The non-standard temperature, the log K using 2+ 2À MultiScale database includes Ba ,SO4 and minteq.v4.dat would differ markedly. For À HSO4 (Scale Consult, 2006; Version 8). example, at 373.15 K, calculations with wateq4f.dat The origin of the thermodynamic data included and minteq.v4.dat result in log K = À9.53 and in the databases for the common speciation codes À9.17, respectively. is often difficult to track. For wateq4f.dat, the The MultiScale speciation code does not equilibrium constant for baryte dissolution (log K: feature a specific log K at 298.15 K for the

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baryte dissolution reaction such as those asso- and celestite, with one exception, i.e. the llnl.dat ciated with PHREEQC. Rather, it uses only an (log K: À5.6771) for celestite. The uncertainty analytical expression for the temperature depen- determined with data from the Robie et al. (1979) dence adopted from Kaasa (1998), which is based compilation is greater than that obtained with the not only on data from Blount (1977) but also on data of Nordstrom and Munoz (1994). data from Templeton (1960), Jiang (1996) and Malinin et al. (1969). Malinin et al. (1969) Sulfate-mineral solubility predictions in calculated a larger value (À9.72) than reservoir conditions Templeton (1960; À9.96) even though they used the same data source. Blount (1977) pointed out The thermodynamic properties of the free ions that Malinin et al. (1969) overcorrected their and the sulfate minerals published by Nordstrom values by changing the ion-size parameter (a˚)at and Munoz (1994) allow us to evaluate the high temperature. The empirical equation used by likelihood of precipitation from solutions where Kaasa (1998) is the same as PHREEQC but with composition is known. During oil recovery, different analytical coefficients. The log K seawater, which contains sulfate, is injected into calculated at standard temperature using the a reservoir where the formation waters often Kaasa (1998) expression and MultiScale code contain barium (Jordan et al., 2008). The present results in the same value (À9.93), which differs authors used the thermodynamic data to predict slightly from most of the data in the thermo- solubility for baryte, celestite and anhydrite, for a dynamic compilations (Table 1) and those selection of reservoir fluids. We set the calcula- produced from experiments (Table 2) but still tions to mix seawater with formation water in agrees within uncertainty. equal proportions. Figure 2 shows phase diagrams 2+ 2+ 2À 2+ 2+ 2À for the Ba –Ca –SO4 and Sr –Ca –SO4 systems using previously published data, for the temperature of the formation water as well as at Application of thermodynamic properties to standard temperature (data from Yuan et al., other sulfate minerals 1994). We also predicted solubility and plotted Anhydrite (CaSO4) is a common mineral in stability diagrams for seawater mixtures with evaporite deposits, precipitated from highly formation water from several other producing saline brine and celestite (SrSO4) and often reservoirs in the North Sea Basin. In all cases, coexists with baryte (Hanor, 2000). To evaluate baryte precipitation was predicted in 50:50 the robustness of the data in the compilations by mixtures of seawater and formation water, in Robie et al. (1979) and Nordstrom and Munoz horizons where field evidence indicated baryte (1994), values for these minerals were calculated formation. using the thermodynamic data for the minerals It is not possible to plot all of the data on one and for the free ions, Ca2+ and Sr2+. Values set of diagrams. For each formation water, new calculated at standard-state conditions for anhy- diagrams are required because the differences in drite, using data from Robie et al. (1979) are: log composition and ionic strength significantly shift K=À4.15 0.79, from enthalpy and entropy (a) the solubility limits. As temperature increases, the and log K = À4.12 0.76 from Gibbs free baryte stability field decreases, whereas the fields energy (b). Using data from Nordstrom and for anhydrite and celestite increase, as expected, o Munoz (1994), these are log K = À4.41 0.34 from the value of the DHr for dissolution of these from enthalpy and entropy (a) and log K = À4.41 phases (Table 1). From the activities (ax) derived 0.32 from free energy (b). Calculated values for from the PHREEQC geochemical speciation celestite, with data from Robie et al. (1979) are program, and using the pitzer.dat database, we log K = À6.51 0.78, derived from a and log K = made diagrams to represent the mixed water for À6.46 0.70, from b. With data from Nordstrom conditions where temperature was 298 K and and Munoz (1994), log K = À6.63 0.20 (a) and above 350 K. Figure 2 shows that the waters are log K = À6.63 0.26 (b). The results agree within highly supersaturated with respect to baryte, uncertainty with the experimental thermodynamic marginally supersaturated with respect to celestite solubility products, for CaSO4, log K = À4.62 and undersaturated with respect to anhydrite. The 0.03 and for SrSO4, log K = À6.50 0.05, which calculations made with the Pitzer database predict were reported by Smith and Martell (1976) and a significant thermodynamic drive for baryte with all the PHREEQC databases for anhydrite precipitation when sea water mixes with forma-

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2+ 2+ 2À 2+ 2+ FIG. 2. Activity-activity diagram for the Beryl and Forties Field: (a) The Ba –Ca –SO4 and (b) the Sr –Ca – 2À 2À 2À SO4 systems at atmospheric pressure, 298.15 K (with log aSO4 = À3.011) and 372.15 K (with log aSO4 = À2.975) for a solution of equal portions of seawater and Beryl Field formation water. The bold star represents the mixed water composition at 298.15 K (c) and the blue open circle at 372.15 K. (c) and (d) Similar diagrams for the same

2À systems with solubility predicted for temperatures of 298.15 K (with log aSO4 = À3.157; bold star) and 369.15 K 2À (with log aSO4 = À3.088; blue open circle) for a solution of equal portions of seawater and Forties Field formation water (data from Yuan et al., 1994).

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tion water, which is completely consistent with barium chloride dihydrate. The entropy of barium the field observations. ion. Journal of the American Chemical Society, 58, 1758À1759. Busenberg, E. and Plummer, L.N. (1986) The solubility Conclusions of BaCO3(cr) (witherite) in CO2-H2O solutions More recent experimental studies using modern between 0 and 90ºC, evaluation of the association + o methods for determination of aqueous concentra- constants of BaHCO3(aq) and BaCO3(aq) between 5 and 80ºC, and a preliminary evaluation of the tions report a thermodynamic solubility product 2+ for baryte of 10À10.05 to 10À9.96 at standard thermodynamic properties of Ba(aq). Geochimica et conditions. These values agree with those Cosmochimica Acta, 50, 2225À2233. calculated from thermodynamic properties Busenberg, E., Plummer, L.N. and Parker, V.B. (1984) compiled by Robie et al. (1979), Wagman et al. The solubility of strontianite (SrCO3)inCO2-H2O solutions between 2 and 91ºC, the association (1982), Lide (2005), Raju and Atkinson (1988) as constants of SrHCO+(aq) and SrCO0(aq) between 5 well as Nordstrom and Munoz (1994), whose 3 3 and 80ºC, and an evaluation of the thermodynamic values have the smallest uncertainty. 2+ properties of Sr (aq) and SrCO3(cr) at 25ºC and Thermodynamic solubility for baryte at stan- 1 atm total pressure. Geochimica et Cosmochimica dard conditions from PHREEQC databases: Acta, 48, 2021À2035. amm.dat, llnl.dat, minteq.dat, minteq.v4.dat, Chow, T.J. and Goldberg, E.D. (1960) On the marine phreeqc.dat, pitzer.dat, sit.dat and waterq4f.dat, geochemistry of barium. Geochimica et agrees with the more recent experimental data. Cosmochimica Acta, 20, 192À198. The data predict baryte precipitation when Cordfunke, E.H.P., Konings, R.J.M. and Ouweltjes, W. seawater is mixed with formation water from a (1990) The standard enthalpies of formation of 2+ number of reservoirs, reflecting observations in MO(s), MCl2(s), and M (aq, ?) (M= Ba, Sr). The the field. This consistency of the thermodynamic Journal of Chemical Thermodynamics, 22, 991À996. data for high-salinity solutions at typical reservoir Cox, J.D., Wagman, D.D. and Medvedev, V.A. (1989) conditions indicates that the data can be combined CODATA (Committee on Data for Science and with Pitzer calculations of activity coefficients Technology) key values for thermodynamics. and used for further experiments where rates of Hemisphere Republishing Corporation, New York, reaction will be examined. 271 pp. Crawford, J. (1999) Geochemical modelling À A review of current capabilities and future directions. Acknowledgements Swedish Environmental Protection Agency, The authors thank Maersk Oil and the DUC Stockholm, Sweden, SNV Report 262, 39 pp. Partners (Danish Underground Consortium: A.P. Davis, J.W. and Collins, A.G. (1971) Solubility of Møller-Mærsk A/S, Shell, Chevron and the barium and strontium sulfates in strong electrolyte Danish North Sea Fund) for permission to solutions. Environmental Science & Technology, 5, publish this paper. They are grateful to the 1039À1043. NanoGeoScience Research Section for support DeKock, C.W. (1986) Thermodynamic properties of and encouragement and to three anonymous selected metal sulfates and their hydrates. U.S. Bureau of Mines, Information Circular 9081, 59 pp. reviewers, whose comments considerably Egorov, A.M. and Titova, Z.P. (1962) Temperature improved the paper. This work was funded by dependence of solubility products of salts with the European Commission (EC) 7th Framework polyatomic ions. Russian Journal of Inorganic Marie Curie (MC) Initial Training Network (ITN) Chemistry, 7, 141À142. grant called MINSC (Mineral Scale Formation; Felmy, A.R., Rai, D. and Amonette, J.E. (1990) The 290040). solubility of barite and celestite in sodium sulfate: evaluation of thermodynamic data. Journal of References Solution Chemistry, 19, 175À185. Fitzgibbon, G.C., Huber, E.J. Jr. and Holley, C.E. Jr. Blount, C.W. (1977) Barite solubilities and thermo- (1973) The enthalpy of formation of barium dynamic quantities up to 300ºC and 1400 bars. monoxide. Journal of Chemical Thermodynamics, American Mineralogist, 62, 942À957. 5, 577À582. Brown, O.L.I., Smith, W.V. and Latimer, W.M. (1936) Griffith, E.M. and Paytan, A. (2012) Barite in the ocean- The heat capacity and entropy of barium chloride occurrence, geochemistry and paleoceanographic dihydrate from 15 to 300ºK. The heat of solution of applications. Sedimentology, 59, 1817À1835.

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