Molecular thermodynamic modeling of aqueous Na+-K+-Mg2+-Ca2+-SO42− quinary system

A comprehensive thermodynamic model for high salinity produced waters

“…Among the most widely used thermodynamic frameworks for modeling the system are the Pitzer activity coefficient model, the extended UNIQUAC activity coefficient model, and the revised extended UNIQUAC model . As summarized by Tanveer and Chen, the Pitzer models developed by Harvie and Weare, Harvie et al, Spencer et al, and Marion and Farren have shown limited success . However, these models are largely restricted to room temperature conditions and are impractical to apply in process development studies due to the extensive parameterization requirement associated with both the binary and ternary interaction parameters and the large number of temperature dependence coefficients associated with the parameters .…”

“…Tanveer et al reported the parameters for the (Mg 2+ Cl − ):H 2 O pair, the (Na + Cl − ):(Mg 2+ Cl − ) pair, and the (K + Cl − ):(Mg 2+ Cl − ) pair. Though Bhattacharia et al reported the parameters for the (Mg 2+ SO 4 2− ):H 2 O pair, the (Na + SO 4 2− ):(Mg 2+ SO 4 2− ) pair, and the (K + SO 4 2− ):(Mg 2+ SO 4 2− ) pair, these parameters have been updated by Tanveer and Chen to correct the inconsistency in treating the Mg 2+ ion molar heat capacity at the aqueous phase infinite dilution standard state. In addition, Tanveer and Chen further reported the parameters for the (Ca 2+ SO 4 2− ):H 2 O pair, the (Na + SO 4 2− ):(Ca 2+ SO 4 2− ) pair, the (K + SO 4 2− ):(Ca 2+ SO 4 2− ) pair, and the (Mg 2+ SO 4 2− ):(Ca 2+ SO 4 2− ) pair.…”

“…Though Bhattacharia et al reported the parameters for the (Mg 2+ SO 4 2− ):H 2 O pair, the (Na + SO 4 2− ):(Mg 2+ SO 4 2− ) pair, and the (K + SO 4 2− ):(Mg 2+ SO 4 2− ) pair, these parameters have been updated by Tanveer and Chen to correct the inconsistency in treating the Mg 2+ ion molar heat capacity at the aqueous phase infinite dilution standard state. In addition, Tanveer and Chen further reported the parameters for the (Ca 2+ SO 4 2− ):H 2 O pair, the (Na + SO 4 2− ):(Ca 2+ SO 4 2− ) pair, the (K + SO 4 2− ):(Ca 2+ SO 4 2− ) pair, and the (Mg 2+ SO 4 2− ):(Ca 2+ SO 4 2− ) pair. In this work, we identify the parameters for the remaining three electrolyte–electrolyte pairs: the (Mg 2+ Cl − ):(Ca 2+ Cl − ) pair, the (Mg 2+ Cl − ):(Mg 2+ SO 4 2− ) pair, and the (Ca 2+ Cl − ):(Ca 2+ SO 4 2− ) pair.…”

“…The properties of pure water are retrieved from Wagman et al, the saturation vapor pressure of water is calculated using Steam Tables equation‐of‐state, and the vapor phase fugacity of water is calculated with the Redlich–Kwong equation‐of‐state. Summarized in Table S2, standard state thermodynamic properties of the salt crystals, that is, Gibbs energy of formation, enthalpy of formation, and heat capacity, are identified in this work or taken from our earlier works …”

“…To model the aqueous Mg 2+ ‐Cl − ‐SO 4 2− ternary system, we retrieve the binary interaction parameters for the (Mg 2+ Cl − ):H 2 O pair from Tanveer et al and the parameters for the (Mg 2+ SO 4 2− ):H 2 O pair from Tanveer and Chen . This work identifies the binary interaction parameters for the (Mg 2+ Cl − ):(Mg 2+ SO 4 2− ) pair from regression of thermodynamic property data and salt solubility data available for the ternary.…”