(69e) Multi-Scale Modeling & Validation of CO2-Water-NaCl Phase Behavior at High Pressure

High pressure carbon dioxide-seawater (or carbon dioxide-brine) mixtures are of interest in geological and deep ocean sedimentary carbon storage. Recently Lucia (2010) has proposed a new multi-scale equation of state (EOS) approach to modeling high pressure phase behavior. In this approach, the Gibbs-Helmholtz equation is used to constrain the energy parameter, a, in cubic equations in the van der Waals family and results in expressions for the energy parameter for pure components and mixtures that include the internal energy of departure. This multi-scale Gibbs-Helmholtz constrained (GHC) EOS approach uses internal energies of departure obtained from NTP Monte Carlo simulations in order to correctly account for temperature, pressure and composition effects and is truly predictive. Preliminary numerical results for high pressure density calculations for carbon dioxide and water are very promising. When compared to experimental data available in the literature, the GHC version of the SRK equation predicts liquid densities within 2% of experimental values. The reason for this excellent agreement is due to the fact that the GHC framework provides an appropriate natural bridge (i.e., the internal energy of departure) between the molecular and bulk phase length scales.

In this work we describe extensions and applications of the multi-scale GHC EOS to electrolyte systems containing carbon dioxide. Specifically, we study the behavior of model mixtures of seawater or brine + carbon dioxide at high pressure comprised of CO2, H2O and NaCl. We show that the GHC EOS approach allows the user to model all relevant 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 phase densities, phase stability and phase equilibrium predictions. We also demonstrate that the multi-scale GHC EOS is computationally reliable and efficient since 1) NTP Monte Carlo simulations need only be performed 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 Monte Carlo simulation results can be used as 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 phase densities, stability and equilibrium for NaCl-H2O and CO2-H2O-NaCl mixtures are presented over a range of temperatures, pressures, and compositions relevant to high pressure carbon dioxide storage and validated using experimental data. Geometric illustrations are used to elucidate key aspects of our approach.