John H. Weare

The prediction of mineral solubilities in natural waters: The Na-K-Mg-Ca-H-Cl-SO4-OH-HCO3-CO3-CO2-H2O system to high ionic strengths at 25°C

The mineral solubility model of Harvie and Weare (1980) is extended to the eight component system, Na-K-Mg-Ca-H-Cl-SO4-OH-HCO3-CO3-CO2-H2O at 25°C to high concentrations. The model is based on the semi-empirical equations of Pitzer (1973) and co-workers for the thermodynamics of aqueous electrolyte solutions. The model is parameterized using many of the available isopiestic, electromotive force, and solubility data available for many of the subsystems. The predictive abilities of the model are demonstrated by comparison to experimental data in systems more complex than those used in parameterization. The essential features of a chemical model for aqueous electrolyte solutions and the relationship between pH and the equilibrium properties of a solution are discussed.

The prediction of mineral solubilities in natural waters: the NaKMgCaClSO4H2O system from zero to high concentration at 25° C

Abstract A chemical model of the seawater system, NaKMgCaClSO 4 H 2 O, is developed for predicting mineral solubilities in brines from zero to high ionic strengths. The calculated solubilities are shown to be in agreement with the experimental data from gypsum saturation ( I m ) to bischofite saturation (I > 20 m). The model utilizes activity coefficient expressions recently developed by Pitzer and co-workers and an algorithm for rapidly identifying the coexisting phases and their composition at equilibrium. The activity coefficient expressions are parameterized using binary and ternary system solubility and osmotic data. The results indicate that a free energy model defined by binary and ternary system data will accurately predict solubilities in more complex systems. The algorithm for solving the general chemical equilibrium problem is briefly discussed. The method can be used to model systems with an arbitrary number of possible non-ideal solution phases. The iterative procedure is guaranteed to converge and has been found to be efficient and easy to implement. Calculated phase diagrams associated with the seawater system are compared to experimental data. Our calculations are within experimental accuracy whereas the prediction of other seawater models are in substantial disagreement with the data even at low concentration. The calculation of evaporation sequences is also briefly discussed and qualitatively compared to field data. The mineral assemblages predicted by this method are in substantially better agreement with core samples than the sequences predicted by phase diagram methods ( Braitsch , 1971), which do not explicitly include the Ca component.

An equation of state for the CH4-CO2-H2O system: I. Pure systems from 0 to 1000°C and 0 to 8000 bar

An equation of state (EOS) for the CH4-CO2-H2O system covering a wide T-P range has been developed. In this article the new EOS is presented and applied to the pure endmembers. The equation is similar to that of Lee and Kesler (1975) and contains fifteen parameters. It is used with a mixing rule in the following article to provide a thermodynamic model for the mixed system. Though the parameters are evaluated from the PVT data in the temperature range from 0 to 450°C for CH4, from 0 to 1000°C for CO2 and H2O, and for pressures from 0 to 3500 bar, comparison of this EOS with a large amount of experimental data in the pure systems indicates that predictions for temperatures and pressures from 0 to 1000°C and 0 to 8000 bar (or slightly above) are very nearly within experimental uncertainty. The EOS can describe both the gas and the liquid phases of the endmember systems with similar accuracy. Fugacity coefficients are derived and compiled. In this paper mixing is considered using ideal mixing based on the endmember fugacities (Amagats rule). It is shown that such an approach leads to quite accurate predictions for high temperatures and low pressures.

The prediction of methane solubility in natural waters to high ionic strength from 0 to 250°C and from 0 to 1600 bar

Abstract A model for the solubility of methane in brines (0–6 m) for temperatures from 0 to 250°C and for pressures from 0 to 1600 bar (or slightly above) is presented. The model is based on Pitzer phenomenology for the liquid phase and a highly accurate equation of state recently developed for the vapor phase. Comparison of model predictions with experimental data indicates that they are within experimental uncertainty. Most experimental data sets are consistent within errors of about 7%. Although the parameters were evaluated from binary and ternary data, the model accurately predicts methane solubility in much more complicated systems like seawater and Salton geothermal brines. Application to fluid inclusion analysis is discussed. Minimum trapping pressures are calculated given the composition and homogenization temperature.

The prediction of borate mineral equilibria in natural waters: Application to Searles Lake, California

Abstract The chemical equilibrium model of Harvie et al . (1984) has been extended to include borate species. The model is based upon the semi-empirical equations of pitzer (1973) and coworkers and is valid to high ionic strength (≈14 m) and high borate concentration. Excellent agreement with the existing emf, isopiestic and solubility data in the system (Na-K-Ca-Mg-H-Cl-SO 4 -CO 2 -B(OH) 4 -H 2 O) is obtained. Calculated mineral solubilities are in general within 10% of their experimental values, even at high ionic strengths. The model was applied to the multicomponent, high ionic strength (I ~ 10) and high borate concentration (B T ~ 0.5 m) Searles Lake evaporite deposit. Utilizing the chemical composition of the interstitial brine, the model predicts equilibrium between the brine and only those minerals which are known to be in contact with the brine. These calculations clearly demonstrate the applicability of the model to high ionic strength, high borate concentration natural waters. The model was also utilized to calculate the mineral sequences which should result from evaporation of the major source of water for Searles Lake, the Owens River. The geochemical conditions necessary for the formation of the most recent mud and saline units are examined. The final results indicate that the mineral sequences found in the most recent saline unit in Searles Lake can be produced by evaporation of a water close in composition to present Owens River water, provided primary dolomite formation is delayed and back reaction between the Parting Mud and the Upper Salt is inhibited.

Equation of state for the NaClH2OCO2 system: prediction of phase equilibria and volumetric properties

An equation of state (EOS) has been developed for the NaClH2OCO2 system which consistently predicts various properties including PVTX, immiscibility or phase equilibria, solubilities, and activities with an accuracy close to that of experimental data from 300 to about 1000°C and 0–6000 bar with NaCl concentrations to about 30 wt% of NaCl (relative to NaCl + H2O) or to about 50 wt% with less accuracy. The EOS predicts that excess volumes can be over 30% of the total volume under some T-P conditions. Adding NaCl to the H2OCO2 system dramatically increases the T-P range of immiscibility. The immiscibility field is minimal around 400–500°C. Above or below this temperature, it expands for a constant pressure. A moderately saline brine can evolve into a very saline brine by phase separation at high temperatures. The presence of NaCl can substantially decrease the activity of H2O and increase that of CO2, thus affecting decarbonation and dehydration reactions. Compared to the EOS of Bowers and Helgeson (1983a), the EOS of this study is more reliable in the calculation of volumetric properties particularly in the low pressure range. In addition, BH EOS cannot predict phase equilibria.

An equation of state for the CH4-CO2-H2O system: II. Mixtures from 50 to 1000°C and 0 to 1000 bar

An equation of state (EOS) for mixtures in the CH4-CO2-H2O system has been developed. The model is based on the highly accurate endmember EOS presented in the previous article and on an empirical mixing rule. The mixing rule is based on an analogy with high order contributions to the virial expansion for mixtures. Comparison with experimental data indicates that the mixed system EOS can predict both phase equilibria and volumetric properties for the binaries with accuracy close to that of the experimental data for a temperature range from 50 to 1000°C and a pressure range from 0 to 1000 bar (or to 3000 bar with less accuracy). For temperatures below the critical point of water, there is very little PVTX (density) data. However, even for temperatures for which sufficient data exists we found that parameterization from PVTX data alone did not lead to a free energy that would accurately predict liquid-vapor equilibria. On the other hand, using this data alone we obtain a free energy that predicts both liquid-vapor equilibria and the PVTX properties of the binaries with roughly experimental accuracy. There are very few data inside the ternary. However, the mixing rule contains third order parameters, which require evaluation from ternary mixtures. For the single temperature for which we have data, the adjustment of one parameter gives good prediction of phase equilibrium in the ternary. The resulting EOS predicts that the presence of a small amount of CO2 can significantly affect the solubility of CH4. The application of this EOS to the study of fluid inclusions is discussed. The presence of CH4 in CO2rich fluid inclusions can significantly affect the predicted trapping pressure.

The prediction of mineral solubilities in natural waters: A chemical equilibrium model for the NaKCaMgClSO4H2O system at temperatures below 25°C☆

Abstract A low temperature thermochemical model for the system NaKCaMgClSO4H2O is presented. Aqueous species and standard chemical potentials of solid-solution reactions are modeled from published data for binary and ternary solutions. The temperature range below 25°C (to near −60°C) is emphasized, although the model parameters are fitted to merge smoothly with those of higher temperature models at temperatures between 25 and 100°C. Binary and ternary specific ion interaction terms vary independently with temperature and are modeled using freezing point depression and mineral solubility measurements. The standard chemical potential of the ice-water reaction is fitted independent of the model (from vapor pressure and free energy data). Remaining standard chemical potentials of solidsolution reactions are fitted along with the specific ion interaction terms. Model predictions are tested against published data for minerals formed and brine compositions obtained by chilling seawater to the eutectic (about −54°C). The model predicts the sequence of solid phases observed to precipitate from chilled seawater (mice-mirabilite-hydrohalite-sylvite-MgCl2 · 12H2Oantarcticite). For all but mirabilite model temperatures are within the uncertainty of the measured temperature. The compositions of brines predicted by the model also closely follow the observed compositions. The model allows accurate predictions of the freezing points of simple and complex solutions in the system. Low temperature phase equilibria and mineral solubilities may also be predicted. The model may be used to determine the composition of brines in fluid inclusions in the multicomponent system based on low temperature phase equilibria.

A general equation of state for supercritical fluid mixtures and molecular dynamics simulation of mixture PVTX properties

Abstract A general Equation of State (EOS), which we previously developed for pure nonpolar systems, is extended to polar systems such as water and to mixtures in this study. This EOS contains only two parameters for each pure component and two additional parameters for each binary mixture (no higher order parameters are needed for more complicated mixture systems). The two mixing parameters can be eliminated for nonaqueous mixtures with a slight loss of accuracy in both total mole volume and in excess volume (or nonideal mixing). Comparison with a large amount of experimental PVTX data in pure systems (including H2O) and in the mixtures, H2O-CO2, CO2-N2, CH4-CO2, and N2-CO2-CH4 results in an average error of 1.6% in density. Comparison with commonly used EOS for supercritical fluids shows that the EOS of this study covers far more T-P-X space with higher accuracy. We believe that it is accurate from supercritical temperature to 2000 K and from 0 to 25,000 bar or higher with an average error in density of less than 2% for both pure members and mixtures in the system H2O-CO2-CH4-N2-CO-H2-O2-H2S-Ar and possibly with additional gases. Comparison with the published simulated data suggests that this EOS is approximately correct up to 300,000 bar and 2800 K. We also simulated the PVTX properties of a number of supercritical fluid mixtures using molecular dynamics (MD) simulation. These results and those of other authors are well predicted by the EOS of this study.

Mineral equilibria in the six-component seawater system, Na-K-Mg-Ca-SO4-Cl-H2O at 25°C. II: Compositions of the saturated solutions

Abstract Using the solubility model developed by Harvie and Weare (1980), the stable mineral-solution assemblages for the six-component system Na-K-Mg-Ca-SO 4 -Cl-H 2 O and its constituent 5-, 4- and 3-component systems at 25°C have been defined. Invariant point maps have been constructed showing the connections by univariant lines. The solubility volumes for all 20 minerals considered are also illustrated. Of the 37 invariant points, only 3 have solutions which are Ca-rich; the remaining 34 can be plotted in the reciprocal system Na-K-Mg-SO 4 -Cl, which is similar to the seawater system, except that the restriction of halite saturation has been removed. Application of these results and implications for the evolution of major brine types are briefly discussed.