(246a) Modeling and Simulation of Subsurface Processes in Oil Recovery and Carbon Storage

Subsurface flow processes are important in oil recovery from shales and tar sands, carbon storage, and the movement of contaminants in ground water basins and typically involve complex physical phenomena that span several time and length scales. These processes are often modeled using coupled mass and energy balance equations along with phase equilibrium relationships to describe multi-phase flows through porous media. Simulation of steady or unsteady-state behavior of subsurface processes, reservoir simulation, includes a wide class of applications where both accurate phase densities and accurate phase equilibrium are essential. In addition, phase stability and phase equilibrium (or multi-phase flash computations) need to be performed quickly and reliably because they often consume a large fraction of the total reservoir simulation time (anywhere from 40 to 50%).

In this talk we describe a novel multi-scale modeling and simulation approach to subsurface processes. The proposed approach combines information from three time and length scales ? the molecular scale, the bulk fluid phase scale, and the reservoir scale. At the molecular length scale we use coarse-grained NTP Monte Carlo simulations to determine internal energies of departure, UD, and create look-up tables of UD as a function of temperature, pressure and composition. This molecular scale information is communicated to the bulk phase length scale via look-up tables and interpolating formulae in order to predict the energy parameter in the new, multi-scale Gibbs-Helmholtz constrained (GHC) cubic equation of state (EOS) developed by Lucia (2009). The GHC EOS is used to compute fluid phase densities and component fugacity coefficients and solution fugacities which, in turn, are used to determine the number and types of phases as well as their corresponding compositions using Gibbs free energy minimization with full analytical partial derivatives. These minimum Gibbs free energy-based multi-phase flash computations are coupled to the reservoir simulator Finite Element Heat & Mass Transfer (FEHM) primarily developed and evolved by Zyvoloski (1975-present) to determine spatial and temporal distributions of vapor and liquid phases and multi-phase flows throughout the reservoir. FEHM uses a control volume finite element formulation of coupled heat and mass balance equations, Newton's method with analytical partial derivatives to solve the nonlinear algebraic equations that come from a discrete representations of the governing partial differential equations, and a pre-conditioned Krylov subspace method (partial LU factorization with GMRES) to solve the linear equations at each Newton step.

A number of interesting numerical examples are presented to demonstrate the efficacy of the proposed multi-scale modeling and simulation approach. We present comparisons of the GHC and SRK equations in the context of reservoir simulations. We also show that the multi-phase flash computations can be streamlined without loss of accuracy to provide very fast and reliable determination of phase behavior, can be readily interfaced with FEHM, and that coupling the GHC EOS with FEHM permits larger integration time steps and reliable simulations covering time horizons of 20 to 100 years.