A Thermodynamic Model for the Solubility Prediction of Barite, Calcite, Gypsum, and Anhydrite, and the Association Constant Estimation of CaSO₄⁽⁰⁾ Ion Pair up to 250 °C and 22000 psi

Mineral solubility predictions are critical for estimating scaling risks at conditions of high temperature, pressure, and ionic strength (IS) in mixed electrolytes which occur in various industrial processes. On the basis of the Pitzer theory, this study establishes a thermodynamic model to predict the solubilities and scaling risks of barite, calcite, gypsum, and anhydrite under these extreme conditions. This study combines the related equilibrium constants, virial coefficients, and the solubilities of these minerals from 0 °C to 250 °C, from 14.7 psi to 22000 psi, with up to 6 mol NaCl/kg H₂O with or without mixed electrolytes to determine the temperature and pressure dependences of the following virial coefficients for Ca²⁺–SO₄^2–, Ba²⁺–SO₄^2–, Ba²⁺–Cl^–, Na⁺–SO₄^2–, and Ca²⁺–Br^– binary interactions used in the Pitzer theory. Using these virial coefficients, the solubilities of these four minerals can be accurately predicted with no apparent temperature, pressure, or IS bias in solutions under the extreme conditions. The association constants (<i>K</i>_assoc) for CaSO₄⁽⁰⁾ ion pairs calculated from the β_CaSO₄⁽²⁾ values derived in the model match well with experimental measurements at 25 °C and 1 atm, and show similar temperature and pressure dependence with those calculated from the Fuoss ion pair association theory and those listed in SOLMINEQ. 88

Development and Application of a New Theoretical Model for Additive Impacts on Mineral Crystallization

Additives play an important role in crystallization controls in both natural and industrial processes. Due to the lack of theoretical understanding of how additives work, the use and design of additives in various disciplines are mostly conducted empirically. This study has developed a new theoretical model to predict the additive impacts on crystallization based on the classical nucleation theory and regular solution theory. The new model assumes that additives can impact the nucleus partial molar volume and the apparent saturation status of the crystallization minerals. These two impacts were parametrized to be proportional to additive concentrations and vary with inhibitors. As a practical example, this new model has been used to predict barite induction times without inhibitors from 4 to 250 °C and in the presence of eight different scale inhibitors from 4 to 90 °C. The predicted induction times showed close agreement with the experimental data published previously or produced in this study. Such agreement indicates that this new theoretical model can be widely adopted in various disciplines to evaluate mineral formation kinetics, elucidate mechanisms of additive impacts, predict minimum effective dosage (MED) of additives, and guide the design of new additives, to mention a few

Calcite and Barite Solubility Measurements in Mixed Electrolyte Solutions and Development of a Comprehensive Model for Water-Mineral-Gas Equilibrium of the Na-K-Mg-Ca-Ba-Sr-Cl-SO₄‑CO₃‑HCO₃‑CO₂(aq)‑H₂O System up to 250 °C and 1500 bar

Calcite and barite are two of the most common scale minerals that occur in various geochemical and industrial processes. Their solubility predictions at extreme conditions (e.g., up to 250 °C and 1500 bar) in the presence of mixed electrolytes are hindered by the lack of experimental data and thermodynamic model. In this study, calcite solubility in the presence of high Na₂SO₄ (i.e., 0.0407 m Na₂SO₄) and barite solubility in a synthetic brine at up to 250 °C and 1500 bar were measured using our high-temperature high-pressure geothermal apparatus. Using this set of experimental data and other thermodynamic data from a thorough literature review, a comprehensive thermodynamic model was developed based on the Pitzer theory. In order to generate a set of Pitzer theory virial coefficients with reliable temperature and pressure dependencies which are applicable to a typical water system (i.e., Na-K-Mg-Ca-Ba-Sr-Cl-SO₄-CO₃-HCO₃-CO₂-H₂O) that may occur in geochemical and industrial processes, we simultaneously fit all available mineral solubility, CO₂ solubility, as well as solution density. With this model, calcite and barite solubilities can be accurately predicted under such extreme conditions in the presence of mixed electrolytes. Furthermore, the 95% confidence intervals of the estimation errors for solution density predictions are within 4 × 10^–4 g/cm³. The relative errors of CO₂ solubility prediction are within 0.75%. The estimation errors of the saturation index mean values for gypsum, anhydrite, and celestite are within ±0.1 and that for halite is within ±0.01, most of which are within experimental uncertainties