Phase diagrams and thermochemical modeling of salt lake brine systems. IV. Thermodynamic framework and program implementation for multicomponent systems

Abstract

This paper is part of a series of studies on the development of a multi-temperature thermodynamically consistent model for salt lake brine systems. The objective of this study is to extend the binary thermodynamic models published in our previous studies to multicomponent systems. A revised general Pitzer–Simonson–Clegg (PSC) gE,∗ equation for multicomponent system is proposed without limitation on the number of components. From the gE,∗ equation, mathematical expressions of the activity coefficient of each component as well as the excess enthalpy and excess heat capacity of the aqueous phase are derived. Based on the multicomponent PSC equations and the CALPHAD-type thermodynamic framework, a generic command-line based program, named ISLEC, was developed for the thermodynamic modeling of aqueous system. The performance of the model and program were tested using three case studies based on typical systems. In the first case study, a temperature-dependent model for a six-component system of Li+-Na+-K+-Mg2+-Ca2+-Cl--H2O was developed based our previous published binary models and the regressed mixing parameters developed in this study. The model well represents the phase equilibrium and activity properties of all 10 sub-ternary systems well over a wide temperature range. These ternary models are generally valid from the lowest eutectic temperature to approximately 373.15 K. For most of the studied ternary systems, the original PSC model is valid for solubility isotherm and phase diagram modeling. However, for the LiCl + KCl + H2O and KCl + CaCl 2+ H2O ternary systems, the revised PSC equations are advantageous in describing the solid-liquid phase equilibria, especially at elevated temperatures. Using the parameters determined in binary and ternary systems, the Li+-Na+-K+-Mg2+-Ca2+-Cl--H2O model system reproduces the phase diagrams of its 10 sub-quaternary and two of its sub-quinary systems (LiCl + NaCl + KCl + MgCl2+H2O and NaCl + KCl + MgCl2+CaCl2+H2O) generally well at various temperatures. However, the reliability of our model predictions of the thermal properties of multicomponent aqueous mixture cannot be assured, and the differences from experimental data are usually large. Thus, the thermal data generated from our model should be used with caution for multicomponent systems. The evaporation and cooling crystallization processes of Dead Sea brine, which is a six-component Li+–Na+–K+–Mg2+-Ca2+-Cl--H2O system, were simulated to test the ISLEC program. The results demonstrate the satisfactory performance of the ISLEC program for solving multiphase equilibria in systems containing at least six components. In the second case study, the PSC equations were applied to model the solubility isotherms in a neutral-solute-containing system: H3BO3+NaCl + H2O. The results are excellent, but additional H3BO3-containing systems should be studied for further validation. In the last case study, mass and energy balance simulations were performed for the process of KCl production using sylvinite as the raw material, thus revealing the applications of ISLEC for process design and simulation.