(302a) Accurate Representation of EoS Related Non-Linearities for Compositional Flow Simulation

We present an efficient methodology for the computation of the thermodynamic phase behavior associated with multi-component multiphase flow in porous media. The method is based on interpolation for both pressure and composition based on supporting point in the tie-line space. For the parameterization of displacement curve associated with compositional process we need only limited number of supporting points in compositional space, depending on predefined precision. We use special techniques for the adaptive construction of supporting points, because of the complicated behavior of the solution route in the compositional space. The parametrized compositional space is triangulated using Delaunay tessellation and natural-neighbor interpolation technique is used inside simplex. The 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. The analysis of the approach detect potential problem such as discontinuity of phase behavior on the boundary of triangle (simplex). These discontinuity is similar to one associated with piece-wise linear interpolation of PVT properties for Black-Oil problem. However, our numerical experience shows that there are no disadvantages in nonlinear behavior associated with this type of discontinuities. The additional advantages of the approach is the possibility of direct analysis of the hyperbolic limit for the system since we can directly decouple it with pressure and compute eigenvalues for the characteristics driven by thermodynamic behavior, independently for each triangle. The efficiency and accuracy of the method is demonstrated for several multi-dimensional compositional problems of practical interest.