Thermodynamic modeling of electrolyte solutions: Bridging classical macroscopic models and molecular simulations

Electrolyte solutions are ubiquitous in many industrial, environmental, pharmaceutical, and geothermal processes. The crucial key in the design, optimization, and simulations of the processes involving electrolytes is the availability of comprehensive and versatile thermodynamic models. Correlative-based classical macroscopic thermodynamic models have been extensively applied for identifying the solution chemistry, as well as predicting various phase equilibria and calorimetric properties of ionic solutions. Obtaining these properties are essential for conducting mass and energy balance calculations while carrying out process simulations. The widespread use of the correlative thermodynamic models is due to their simplicity and rapid computational time. Among them, the electrolyte Non-Random Two-Liquid (eNRTL) model, introduced in the early 1980s, has been successfully applied in modeling varieties of electrolyte systems, from simple aqueous binary to multicomponent solutions. The model relates the excess Gibbs free energy of a solution to the liquid structure with a set of adjustable binary interaction parameters that are quantified by regressing them to a wide range of experimental data. Once these adjustable parameters are obtained, the thermophysical properties required for process simulations can be readily calculated. Therefore, the first step toward helping the engineers implement efficiently the eNRTL model into their simulations is to build up a comprehensive and reliable database of the model parameters. Part of this dissertation is attributed to the development of frameworks for several electrolyte systems to predict accurately the thermodynamic properties of vapor-liquid, liquid-liquid, and solid-liquid equilibria, over wide ranges of concentrations and temperatures. It is shown that the predictions provided by the eNRTL model compare well with the reported experimental data for model systems including HCl-H2O binary, aqueous BaCl2 solution, and the multicomponent solution of Na+-Ba2+-Cl--SO42--H2O. Though employing the original eNRTL in its correlative form is straightforward to use, there exist a number of drawbacks associated with the current state-of-the-art that could potentially hinder the process simulations. Some examples of which include the lack of available experimental data or the absence of accurate reports of the data uncertainties. Especially, if too many adjustable parameters are fitted to a limited number of data points, the resulting regressed parameters will not be well-determined. The physical significance of the adjustable parameters is another long-standing debate, the lack of which would raise concerns about the credibility of the predictions beyond the range of the reported experimental data. It is worth mentioning that the regression procedures typically fail to result in a unique set of parameters, thereby selecting the physically meaningful parameters would require substantial experience and ‘manual tuning’. To overcome these issues yet exploiting the rapid and accurate predictions provided by eNRTL, a novel theoretical framework is established to bridge the classical thermodynamic model and molecular simulations from a statistical mechanical approach. By revisiting the statistical mechanics of two-liquid theory, the binary interaction parameters of eNRTL are expressed as functions of the liquid structure and energy information quantities of the solutions. These quantities are then obtained from the molecular dynamics simulations and potential of mean force free energy calculations. Several electrolyte systems including the aqueous NaCl, BaCl2, SrCl2, CaCl2, and MgCl2 solutions are selected for the validation of the approach. The results for the binary interaction parameters, together with the predictions of the phase equilibria properties from the MD simulations are in satisfactory agreement with those obtained from the regression. It is demonstrated, for the first time, that the eNRTL model can be rendered completely predictive, circumventing the inherent shortcomings associated with correlation. The established method, with further refinement and improvement, can be broadly utilized for rapid predictions of the thermodynamic properties in industrial process design.