Non-iterative phase behavior computation for general compositional problem

Abstract

This paper presents an efficient methodology for the computation of the thermodynamic phase behavior associated with a multi-component multiphase flow in the porous media. The method is based on the interpolation of supporting points for both pressure and composition, adaptively computed in the tie-line space. For the parameterization of displacement curve, associated with the compositional process, only a limited number of supporting points in compositional space are needed, depending on predefined precision. Special techniques are used for the adaptive construction of supporting points, because of the complicated behavior of the solution route in the compositional space. The parameterized compositional space is triangulated using Delaunay tessellation and natural-neighbor interpolation technique is used inside the simplex. The following computation of phase behavior for the composition simulation is an iteration-free procedure and doesn t require any EoS calculations. Based on this method, we developed a new nonlinear formulation for general purpose compositional simulation for both immiscible and miscible displacement. Our numerical experience shows that the nonlinear behavior of the new formulation has some advantages in comparison with the standard approach. The one important advantage of the approach is the possibility for the direct analysis of the system of conservation law in the hyperbolic limit, since we can directly decouple characteristics, driven by thermodynamic behavior, with pressure and directly compute eigenvalues for each supporting simplex. The efficiency and accuracy of the method are demonstrated for several multi-dimensional compositional problems of a practical interest.