(111f) A Multi-Scale Approach to Modeling Aqueous Electrolyte Mixtures at High Pressure

High pressure aqueous electrolyte solutions are important in reservoir simulations for modeling ocean sedimentary carbon sequestration, geological carbon storage in saline aquifers, and groundwater remediation. This work describes a new multi-scale approach to modeling weak and strong aqueous electrolyte solutions using the Gibbs-Helmholtz constrained (GHC) equation of state (EOS) recently proposed by Lucia (2010) in which the Gibbs-Helmholtz equation is used to constrain the energy parameter, a, in cubic equations in the van der Waals family. The resulting new expressions for the energy parameter for pure components and mixtures include internal energies of departure, which are obtained from NTP Monte Carlo simulations in order to correctly account for temperature, pressure and composition effects form a natural bridge between the molecular and bulk phase length scales. This makes the GHC EOS truly predictive.

Adaptation and applications of the multi-scale GHC EOS to weak and strong aqueous electrolyte systems containing salts and mixed salts are described. It is shown that the GHC EOS approach allows the user to model all relevant electrolyte physics (i.e., van der Waals forces, electrostatic forces, mixtures of ions, atoms and/or molecules) at the small length scale and, when done correctly, results in exceptionally good bulk phase densities, phase stability and phase equilibrium predictions. Moreover it removes the need to use either Debye-Huckel or Pitzer theory for modeling electrolyte effects. The computational reliability and efficiency of the multi-scale GHC EOS approach is also discussed with particular attention to the facts that 1) internal energies of departure from NTP Monte Carlo simulations need only be calculated once using small simulation boxes (i.e., small numbers of particles), 2) coarse-graining (i.e., relatively few values of temperature, pressure and composition) can be used, and 3) the resulting internal energies of departure can be used in look-up tables which, together with interpolation formulae, provide fast and reliable communication of information between the molecular and bulk phase length scales.

Numerical results for bulk phase densities, stability and equilibrium for NaCl-H2O, NaCl-KCl-H2O, and NaCl-MgSO4-H2O mixtures are presented over ranges of temperatures, pressures, and compositions relevant to high pressure carbon dioxide storage and are compared to Debye-Huckel theory and Pitzer's approach based on virial expansion and are validated using experimental data. Geometric illustrations are used to elucidate key aspects of our approach.