Formulation and solution of compositional displacements in tie-simplex space

Abstract

We describe an Adaptive Compositional Space Parametrization (ACSP) method for compositional flow simulation. The method is based on casting the nonlinear governing equations, including those that describe the thermodynamic phase equilibrium, in terms of the tie-simplex (tie-lines for two-phase flow) space. The tie-simplex compositional space, which is a function of composition, pressure, and temperature, is then discretized using a limited number of tie-simplexes. The coefficients in the governing system of equations, including the composition, density, and mobility of the phases, are computed using multilinear interpolation in the discretized space. ACSP is different from the CSAT (Compositional Space Adaptive Tabulation) approach, which we have evolved over the last few years. In CSAT, the tie-line (tie-simplex) information, which is stored and updated adaptively, is used to accelerate the equation-of-state (EOS) computations in standard (e.g., natural variables) compositional reservoir simulators. This is why CSAT was used primarily to essentially replace the phase-stability test in the natural-variables formulation, but not the flash procedure. In ACSP, on the other hand, the full mathematical statement is cast in tie-simplex space and consistent discretization is applied directly. The ACSP framework is supplemented with a new tie-line based flash procedure that avoids the use of the Rachford-Rice equation. Thus, ACSP replaces all the standard EOS computations (phase-stability and flash). A grid refinement study of the ACSP method shows that the discrete formulation is convergent; more importantly, even for highly nonlinear near-miscible displacements, the number of tie-simplex needed is small.