Modeling Phase Behavior in Complex Systems Using the Gibbs-Helmholtz Constrained Equation of State

Abstract

Modeling the phase and thermo-physical behavior of multi-component fluid systems using a cubic equation of state (EOS) is important for many industrially relevant applications. For example, simulations involving hydrocarbon recovery or carbon dioxide sequestration in geological formations rely on thermodynamic models to determine the phase behavior and density of the relevant reservoir fluid mixture. Accurate models for the density phase behavior of these fluids is required to make reliable predictions of the hydrocarbon production capability, or the carbon sequestration capacity of a given formation. Cubic EOS models have remained the industry standard in thermodynamic modeling for fluid phase behavior for the last 50 years, probably due to the relative ease with which these models can be implemented and generally acceptable accuracy for many systems. However, the current models include empirical parameters that are regressed to pure component saturated liquid density and saturation pressure data, as well as binary (and higher order) mixture composition data. Conducting experiments to collect pure component data for the regression of EOS parameters can be expensive, especially at elevated temperatures and pressures. Further, collecting mixture data over the entire composition space at varying temperatures and pressure quickly becomes intractable (especially for mixture of three or more components). Clearly, a cubic EOS model which requires less data for the regression of parameters is desirable. The multi-scale Gibbs-Helmholtz constrained (GHC) equation of state (EOS) is an innovative approach to EOS modeling which uses molecular scale information about the component(s) of interest to calculate bulk scale EOS parameters. More specifically, the molecular attraction parameter (‘a’) in the two parameter Soave-Redlich-Kwong (SRK) EOS is calculated as a function of temperature using an expression derived from the Gibbs-Helmholtz equation (a classical thermodynamic relationship). Further, the GHC expression for the attraction parameter incorporates molecular level information using results of isobaric-isothermal Monte Carlo (NPT-MC) molecular simulations. In this work, some aspects of the GHC EOS performance and thermodynamic consistency are investigated. Further, novel modeling frameworks are developed for the application of the GHC EOS to systems capable of forming simple structure I (sI) gas hydrates and molecular salts. Finally, the GHC EOS is incorporated into a fully compositional and thermal reservoir simulator. The GHC EOS is then used as the thermodynamic model for the underlying reservoir fluid in novel reservoir simulations relevant to enhanced oil recovery, carbon sequestration, and groundwater contamination modeling.