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The CPA Equation of State and an Activity Coefficient Model for Accurate Molar Enthalpy Calculations of Mixtures with Carbon Dioxide and Water/Brine

Thermodynamic property calculations of mixtures containing carbon dioxide (CO$_2$) and water, including brines, are essential in theoretical models of many natural and industrial processes. The properties of greatest practical interest are density, solubility, and enthalpy. Many models for density and solubility calculations have been presented in the literature, but there exists only one study, by Spycher and Pruess, that has compared theoretical molar enthalpy predictions with experimental data. In this report, we recommend two different models for enthalpy calculations: the CPA equation of state by Li and Firoozabadi, and the CO$_2$ activity coefficient model by Duan and Sun. We show that the CPA equation of state, which has been demonstrated to provide good agreement with density and solubility data, also accurately calculates molar enthalpies of pure CO$_2$, pure water, and both CO$_2$-rich and aqueous (H$_2$O-rich) mixtures of the two species. It is applicable to a wider range of conditions than the Spycher and Pruess model. In aqueous sodium chloride (NaCl) mixtures, we show that Duan and Sun's model yields accurate results for the partial molar enthalpy of CO$_2$. It can be combined with another model for the brine enthalpy to calculate the molar enthalpy of H$_2$O-CO$_2$-NaCl mixtures. We conclude by explaining how the CPA equation of state may be modified to further improve agreement with experiments. This generalized CPA is the basis of our future work on this topic.