Thermodynamic modeling of aqueous Ca2+- Na+ - K+ - Cl- quaternary system

Sheik Tanveer, Chau Chyun Chen

Research output: Contribution to journalArticlepeer-review

18 Scopus citations


We present a comprehensive thermodynamic model for the aqueous Ca2+ - Na+ - K+ - Cl- quaternary system with electrolyte concentrations up to saturation and temperatures up to 473 K. This work is part of a larger effort to develop an engineering thermodynamic model for high salinity produced water in oil and gas production. Built on the thermodynamic framework of symmetric electrolyte Non-Random Two Liquid (eNRTL) theory, the model correlates composition dependency of the solution nonideality with two binary interaction parameters for each of the molecule-electrolyte pairs and the electrolyte-electrolyte pairs present in the system. The model further correlates temperature dependency of the binary parameters through a Gibbs-Helmholtz type equation with three temperature coefficients. We identify the binary parameters and their temperature coefficients for the (Ca2+ Cl-):H2O pair, the (Ca2+ Cl-):(Na+ Cl-) pair and the (Ca2+ Cl-):(K+ Cl-) pair by regressing experimental phase equilibrium, calorimetric and salt solubility data. These binary parameters are then integrated with published binary parameters for other subsystems present in the quaternary system. Together the eNRTL model and the model parameters offer a comprehensive thermodynamic model for the quaternary system; and it shows excellent agreement with literature data for the quaternary system and its subsystems.

Original languageEnglish
Pages (from-to)193-206
Number of pages14
JournalFluid Phase Equilibria
StatePublished - Feb 15 2016


  • Aqueous electrolytes
  • Calcium chloride
  • Electrolyte NRTL model
  • Solubility
  • Thermodynamic properties


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