(440b) Molecular Thermodynamic Model for Aqueous Na+–K+–Mg2+–Ca2+–Cl?/SO42? Quinary Electrolyte Systems

Managing produced water is one of the major challenges in oil and gas production [1]. Produced water can be as much as seven times saline compared to sea water systems, and desalination of this water depends on novel material and process innovations. We present a comprehensive thermodynamic model aimed to support heat and mass balance calculations and predict mineral scale deposition of the saline water. The six major ions that control salinity of the water are: Na⁺, K⁺, Mg²⁺, Ca²⁺, Cl^−, and SO₄^2−. Current investigation focuses on establishing a thermodynamic model for the Na⁺–K⁺–Mg²⁺–Ca²⁺–Cl^− and the Na⁺–K⁺–Mg²⁺–Ca²⁺–SO₄^2− aqueous quinary electrolyte systems. To model the systems, we adopt electrolyte Non-Random Two Liquid theory (eNRTL) for electrolyte solutions [2] which describes concentration dependency of the solution nonideality with two binary interaction parameters for each water-electrolyte and electrolyte-electrolyte pair. Temperature dependency of each binary parameters is further correlated with a Gibbs-Helmholtz type expression with three temperature coefficients representing Gibbs energy, enthalpy, and heat capacity contributions. With the binary parameters and thermodynamic constants of the precipitating salts regressed from phase equilibria, calorimetric and salt solubility data, the model reliably calculates various thermodynamic properties i.e., salt solubility of the quaternary subsystems as well as quinary systems with temperatures from 273.15 to 473.15 K. The model is being extended to cover additional ions such as Sr²⁺, Ba²⁺, and HCO₃^− without losing inherent consistency and it should become a very useful tool for chemical engineering calculations.

Reference:

[1] A. V. García, K. Thomsen and E. H. Stenby, "Prediction of Mineral Scale Formation in Geothermal and Oilfield Operations Using the Extended UNIQUAC Model: Part I. Sulfate Scaling Minerals," Geothermics. 2005, 34(1): 61-97.

[2] Y. Song, C.-C. Chen, “Symmetric Electrolyte Nonrandom Two-Liquid Activity Coefficient Model,” Ind. Eng. Chem. Res. 2009, 48:7788-7797.