A comparison of standard thermodynamic properties and solubility data for baryte, Ba2+ (aq) and SO4 2– (aq)

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 (10–10.05–10–9.96; 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.


Introduction
BARIUM (Ba 2+ ) is common in silicate minerals and is released to solution during weathering (Kastner, 1999;Hanor, 2000). Sulfate (SO 4 2À ) is the most stable and most abundant sulfur species in oxidizing environments (Ivanov, 1981). Consequently, Ba 2+ and SO 4 2À concentrations exceed baryte (BaSO 4 ) solubility, resulting in its formation in a variety of environments such as in sedimentary basins, at seafloor hydrothermal vents and in anthropogenic environments (Hanor, 2000). Surface seawater is supersaturated with respect to calcite (Mackenzie and Andersson, 2013) but is typically undersaturated with respect to baryte (Chow and Goldberg, 1960). Baryte approaches saturation as depth increases (Wolgemuth and Broecker, 1970). Although surface seawater is undersaturated, it often contains pelagic baryte particles, some of which are interpreted to have formed in situ, where the saturation state locally exceeds its solubility product (Hanor, 2000). The presence of baryte in sediments provides information about the geological processes that occurred during sedi-mentation (Griffith and Paytan, 2012) and the biogeochemical cycles that controlled concentration and behaviour (von Allmen et al., 2010). Sometimes, baryte occurs as a result of human activity, most notably during petroleum production. For oil production, seawater is often injected into reservoirs but where pore solutions contain dissolved barium, the increase in sulfate concentration that results from seawater injection, precipitates baryte (Jordan et al., 2008). Baryte scaling can completely block pore throats, decreasing permeability and in some cases, destroying the reservoir.
Traditionally, the thermodynamic solubility product at standard state serves as the basis for extrapolation to other conditions. Furthermore, modelling of mineral dissolution and precipitation rates relies on equations that incorporate the difference between actual activities and those expected at equilibrium (Palandri and Kharaka, 2004). Small deviation and inconsistency in reported values for stability are often amplified when one seeks to model more complex systems. Thus, an internally consistent and accurate set of thermodynamic data is required, especially for extrapolating from standard conditions to solutions at reservoir temperature and the ionic strength of seawater or formation water.
The aims of this study were to: (1) assess published thermodynamic data for baryte and the free barium and sulfate ions at standard-state conditions and compare them with published experimental solubility data and with the solubility constants used in the databases of speciation models; and (2) to suggest the most consistent and accurate parameters for the Ba 2+ -SO 4 2À -H 2 O system that can be used as a reliable starting point for geochemical speciation calculations and for predicting solubility relationships in pure systems. Finally, we used the data to predict the saturation state for sulfate minerals from solutions formed of seawater mixed with formation water, from several reservoirs where baryte scaling had been observed under field conditions.

Thermodynamic properties
Six thermodynamic compilations that include the thermodynamic properties for baryte, free barium and sulfate ions at standard conditions (1 bar, 298.15 K and assuming unit activity and 1 molal ionic strength) are summarized in Table 1 (all uncertainties in this work are reported with two standard deviations). All these data sets were derived from experimental and theoretical studies, where the sources have been indicated in the table footnotes.

Free barium ion, Ba 2+
The only experimental data available for the entropy of free barium is from Brown et al. (1936). The entropy of barium was originally obtained (9.2 J·mol À1 ·K À1 ) from the heat of the dissolution, measured on high-purity barium chloride dihydrate utilizing high-purity solids. Later recalculations by Latimer et al. (1938) and Kelley and King (1961) derived the same value (9.6 Ô 1.2 J·mol À1 ·K À1 ).
For the Ba 2+ enthalpy of formation, two experimental values are available: Fitzgibbon et al. (1973) and Cordfunke et al. (1990   (À534.75 Ô 1.74 kJ·mol À1 ) using their measured enthalpy of formation for barium chloride as well as the thermodynamic properties for the chloride ion from Cox et al. (1989). The value (À537.64 kJ·mol À1 ) compiled by Parker et al. (1971) and Wagman et al. (1982) is close to the experimental data reported by Fitzgibbon et al. (1973) and Cordfunke et al. (1990).
The values for entropy and enthalpy for Ba 2+ published by Helgeson (1969) were taken from Latimer (1952). These values are higher than those of the other data sets (Table 1).
Finally, a new set of thermodynamic properties for Ba 2+ , derived from solubility data of witherite, BaCO 3 , were proposed later by Busenberg and Plummer (1986). They fitted the equilibrium constant of witherite to experimental solubility data between 278 K and 353 K, using recalculated thermodynamic data from carbonate species presented by Busenberg et al. (1984).
The entropy of sulfate from Wagman et al. (1968) is greater than that from Cox et al. (1989) and also agrees with the above values within uncertainty.
The enthalpy of formation of sulfate from the six compilations of thermodynamic properties agrees within the uncertainty with the experimental value determined by Johnson and Sunner (1963; À909.34 Ô 0.45 kJ·mol À1 ).

Baryte, BaSO 4
The only experimental data available for baryte entropy were published by Latimer et al. (1933). They used vacuum bomb calorimetry to measure the heat capacity on high-purity solids and originally obtained a value of 131.84 Ô 0.07 J·mol À1 ·K À1 . This value was later extrapolated to standard conditions by Kelley and King (1961; 132.2 Ô 0.8 J·mol À1 ·K À1 ) using the third law of thermodynamics, which states that the entropy for a pure crystal at absolute zero temperature should be zero. Later estimates by DeKock (1986), which included Latimer et al. (1933) and higher-temperature heat-capacity measurements and considered two independent baryte formation reactions from the elemental species (Ba (s) , O 2(g) , S (g) or S (s) ), resulted in the same value as that estimated by Kelley and King (1961).
For the enthalpy of baryte, the first published value is from Latimer (1952; À1465.2 kJ·mol À1 ). Parker et al. (1971) included this value in their compilation and extrapolated from high-temperature data to a standard-state value of À1466.5 kJ·mol À1 but no information about newer experimental studies was provided. Later, Robie et al. (1979) and DeKock (1986) adjusted this value slightly (À1473.2 kJ mol À1 ). Recently, Majzlan et al. (2002) determined the enthalpy of formation using high-temperature oxide melt calorimetry. They obtained values for: synthetic baryte, À1459.7 Ô 3.7 kJ·mol À1 , Colorado natural baryte, À1464.2 Ô 3.7 kJ·mol À1 , and South C a r o l i n a n a t u r a l b a r y t e , À1 4 6 4 . 9 Ô 3.7 kJ·mol À1 . Values for the two natural samples agree within uncertainty with data presented by Nordstrom and Munoz (1994).

Solubility data
There are many values for the thermodynamic solubility product for baryte. However, some are based on recalculation from data previously published in compilations (Egorov and Titova, 1962;Sillén and Martell, 1964;Khodakovsky et al., 1966;Malinin et al., 1969;Smith and Martell, 1976;Monnin and Galinier, 1988;Kaasa, 1998), and in reports of experiments at temperatures other than 298.15 K (Uchameyshvili et al., 1966;Schulien, 1987;Jiang, 1996). The results of work at non-standard conditions are not reviewed here. Table 2 presents the thermodynamic solubility product for baryte extrapolated to infinite dilution from solubility measurements conducted at standard temperature and pressure. Although a variety of methods has been used, the values determined (log K: À10.05 to À9.96) are in surprisingly good agreement, where the total difference is only 19%. For the more recent studies, which use more accurate techniques for determining aqueous ion concentrations, all are within the limits of experimental error.

Comparison of the thermodynamic properties and solubility data
The Gibbs free energy and the thermodynamic solubility product for baryte dissolution, BaSO 4(s) = Ba 2+ (aq) + SO 4 2À (aq) , were calculated for each compilation presented in Table 1 using two approaches: from the entropy and enthalpy data (a), and from the Gibbs free energy of formation (b). The values for baryte using both approaches, from the compilations of Robie et al. (1979), Wagman et al. (1982) and Lide (2005), Raju and Atkinson (1988) and Nordstrom and Munoz (1994) agree with each other within their uncertainty because, with the exception of the Nordstrom and Munoz (1994) compilation, they originate from the same sources. They also agree with the thermodynamic solubility product determined experimentally from solubility measurements (Fig. 1). The estimates of Helgeson (1969) are slightly higher (À9.70), whereas calculations from the data of Robie and Hemingway (1995) result in significantly lower values (À10.93 and À11.05). Helgeson (1969) was a pioneer in using computer modelling to estimate consistent sets of thermodynamic properties from experimental data for a large number of different elements and systems to get the overall best fits. His estimate for baryte is reasonably close to the experimental values but is still off by a quarter of an order of magnitude. Although the sulfate data from Helgeson (1969) are similar to those presented by Robie et al. (1979), he obtained a higher log K because his enthalpy estimate for barium was too high. Robie and Hemingway (1995) attempted to improve their data by incorporating updated thermodynamic properties for Ba 2+ from Busenberg and Plummer (1986), resulting in values that are lower than those reported from other work. Recently, Wolery and Sutton (2013) identified discrepancies for the barium properties between the compilations from Robie et al. (1979) and Robie and Hemingway (1995) but they did not explain the origin of the discrepancies. Robie and Hemingway (1995) did not assess the internal consistency of the data set with baryte and sulfate. Consequently, the solubility product determined from their data is lower than that of Robie et al. (1979). The solubility-data deviations are larger than those from calorimetric measurements so the uncertainty associated with the Ba 2+ data reported by Robie and Hemingway (1995) is greater than that reported by Robie et al. (1979).
The compilation from Robie et al. (1979), derived from calorimetric measurements, is reliable and consistent but contains larger uncertainties than the Nordstrom and Munoz We assume that the uncertainty in Felmy et al. (1990) is reported at that level.
(1994) compilation which has also been updated with Ba 2+ data from Busenberg and Plummer (1986) and the baryte data were adjusted with calculations from barium and sulfate thermodynamic properties and baryte solubility. Nordstrom and Munoz used a combination of thermodynamic data derived from a variety of experimental methods and generated a consistent data set for the baryte system after assessing the internal consistency of the newer and previously existing data. À9.97), the change in standard enthalpy of the baryte reaction (DH r o : 26.57 kJ·mol À1 ) and the analytical expression for the temperature dependence have all been adopted from Nordstrom et al. (1990), which is based on data reported by Blount (1977). Three other PHREEQC databases, amm.dat, phreeqc.dat and pitzer.dat, also use log K = À9.97.

Geochemical speciation databases
For llnl.dat, sit.dat, minteq.dat and minteq.v4.dat, it was not possible to track the origin of the baryte data. In these databases, log K is similar but not the same, À9.9711, À9.97, À9.976 and À9.98. The first three, llnl.dat, sit.dat and minteq.dat, have DH r o close to 26.57 kJ·mol À1 , presented by Nordstrom et al. (1990), with values of 25.9408 kJ·mol À1 , 2 6 . 4 6 k J · m o l À1 a n d 2 6 . 2 8 k J · m o l À1 . Minteq.v4.dat, however, uses a lower DH r o value, 23 kJ·mol À1 . In conclusion, all of the databases associated with PHREEQC have very similar log K for baryte dissolution at standard temperature but at non-standard temperature, the log K using minteq.v4.dat would differ markedly. For example, at 373.15 K, calculations with wateq4f.dat and minteq.v4.dat result in log K = À9.53 and À9.17, respectively.
The MultiScale speciation code does not feature a specific log K at 298.15 K for the 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).
baryte dissolution reaction such as those associated with PHREEQC. Rather, it uses only an analytical expression for the temperature dependence adopted from Kaasa (1998), which is based not only on data from Blount (1977) but also on data from Templeton (1960), Jiang (1996) and Malinin et al. (1969). Malinin et al. (1969) calculated a larger value (À9.72) than Templeton (1960;À9.96) even though they used the same data source. Blount (1977) pointed out that Malinin et al. (1969) overcorrected their values by changing the ion-size parameter (å) at high temperature. The empirical equation used by Kaasa (1998) is the same as PHREEQC but with different analytical coefficients. The log K calculated at standard temperature using the Kaasa (1998) expression and MultiScale code results in the same value (À9.93), which differs slightly from most of the data in the thermodynamic compilations (Table 1) and those produced from experiments (Table 2) but still agrees within uncertainty.

Application of thermodynamic properties to other sulfate minerals
Anhydrite (CaSO 4 ) is a common mineral in evaporite deposits, precipitated from highly saline brine and celestite (SrSO 4 ) and often coexists with baryte (Hanor, 2000). To evaluate the robustness of the data in the compilations by Robie et al. (1979) and Nordstrom and Munoz (1994), values for these minerals were calculated using the thermodynamic data for the minerals and for the free ions, Ca 2+ and Sr 2+ . Values calculated at standard-state conditions for anhydrite, using data from Robie et al. (1979) are: log K = À4.15 Ô 0.79, from enthalpy and entropy (a) and log K = À4.12 Ô 0.76 from Gibbs free energy (b). Using data from Nordstrom and Munoz (1994), these are log K = À4.41 Ô 0.34 from enthalpy and entropy (a) and log K = À4.41 Ô 0.32 from free energy (b). Calculated values for celestite, with data from Robie et al. (1979) are log K = À6.51 Ô 0.78, derived from a and log K = À6.46 Ô 0.70, from b. With data from Nordstrom and Munoz (1994), log K = À6.63 Ô 0.20 (a) and log K = À6.63 Ô 0.26 (b). The results agree within uncertainty with the experimental thermodynamic solubility products, for CaSO 4 , log K = À4.62 Ô 0.03 and for SrSO 4 , log K = À6.50 Ô 0.05, which were reported by Smith and Martell (1976) and with all the PHREEQC databases for anhydrite and celestite, with one exception, i.e. the llnl.dat (log K: À5.6771) for celestite. The uncertainty determined with data from the Robie et al. (1979) compilation is greater than that obtained with the data of Nordstrom and Munoz (1994).

Sulfate-mineral solubility predictions in reservoir conditions
The thermodynamic properties of the free ions and the sulfate minerals published by Nordstrom and Munoz (1994) allow us to evaluate the likelihood of precipitation from solutions where composition is known. During oil recovery, seawater, which contains sulfate, is injected into a reservoir where the formation waters often contain barium (Jordan et al., 2008). The present authors used the thermodynamic data to predict solubility for baryte, celestite and anhydrite, for a selection of reservoir fluids. We set the calculations to mix seawater with formation water in equal proportions. Figure 2 shows phase diagrams for the Ba 2+ -Ca 2+ -SO 4 2À and Sr 2+ -Ca 2+ -SO 4 2À systems using previously published data, for the temperature of the formation water as well as at standard temperature (data from Yuan et al., 1994). We also predicted solubility and plotted stability diagrams for seawater mixtures with formation water from several other producing reservoirs in the North Sea Basin. In all cases, baryte precipitation was predicted in 50:50 mixtures of seawater and formation water, in horizons where field evidence indicated baryte formation. It is not possible to plot all of the data on one set of diagrams. For each formation water, new diagrams are required because the differences in composition and ionic strength significantly shift the solubility limits. As temperature increases, the baryte stability field decreases, whereas the fields for anhydrite and celestite increase, as expected, from the value of the DH r o for dissolution of these phases (Table 1). From the activities (a x ) derived from the PHREEQC geochemical speciation program, and using the pitzer.dat database, we made diagrams to represent the mixed water for conditions where temperature was 298 K and above 350 K. Figure 2 shows that the waters are highly supersaturated with respect to baryte, marginally supersaturated with respect to celestite and undersaturated with respect to anhydrite. The calculations made with the Pitzer database predict a significant thermodynamic drive for baryte precipitation when sea water mixes with forma-  Yuan et al., 1994).
tion water, which is completely consistent with the field observations.

Conclusions
More recent experimental studies using modern methods for determination of aqueous concentrations report a thermodynamic solubility product for baryte of 10 À10.05 to 10 À9.96 at standard conditions. These values agree with those calculated from thermodynamic properties compiled by 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 smallest uncertainty. Thermodynamic solubility for baryte at standard conditions from PHREEQC databases: amm.dat, llnl.dat, minteq.dat, minteq.v4.dat, phreeqc.dat, pitzer.dat, sit.dat and waterq4f.dat, agrees with the more recent experimental data.
The data predict baryte precipitation when seawater is mixed with formation water from a number of reservoirs, reflecting observations in the field. This consistency of the thermodynamic data for high-salinity solutions at typical reservoir conditions indicates that the data can be combined with Pitzer calculations of activity coefficients and used for further experiments where rates of reaction will be examined. between 5 and 80ºC, and a preliminary evaluation of the thermodynamic properties of Ba 2+ (aq) . Geochimica et Cosmochimica Acta, 50, 2225À2233. Busenberg, E., Plummer, L.N. and Parker, V.B. (1984) The solubility of strontianite (SrCO 3 ) in CO 2 -H 2 O solutions between 2 and 91ºC, the association constants of SrHCO + 3 (aq) and SrCO 0 3 (aq) between 5 and 80ºC, and an evaluation of the thermodynamic properties of Sr 2+ (aq) and SrCO 3 (cr) at 25ºC and