Direct Discretization of the Tie-line Space for Compositional Flow Simulation

We present a new and efficient methodology for the explicit representation of thermodynamic phase behavior associated with multicomponent two-phase flow in porous media. The method is based on interpolation in the discretized tie-line (Γ) space. Since a large number of supporting points may be required needed for direct discretization of the Γ−space, the discretization is performed adaptively during the simulation. A procedure based on the generalization of the octree data structure is proposed for adaptive discretization of the Γ−space, which can be of arbitrary dimension. Then, the tie-lines space is tessellated using Delaunay triangulation and the natural-neighbor interpolation technique is used inside a simplex. It is important to note that the EoS computations need to performed only for a limited number of supporting points and that a different EoS model (or EoS-free model) can be used for different regions of the Γ-space. Based on this method, a new nonlinear formulation for general purpose compositional simulation for both immiscible and miscible displacements is proposed. The representation of the sub-critical space is based on the tie-line (γ) variables; whereas the super-critical space is parametrized using overall compositions as nonlinear unknowns. Variable substitution is based on the parametrized critical tie-line and the Minimal Critical Pressure criterion. Numerical experiments indicate that the proposed approach reduces the cost of the thermodynamic related computations quite substantially compared with the standard methods.