A multiscale restriction-smoothed basis method for compositional models

Compositional simulation is attractive for a wide variety of applications in reservoir simulation and it is especially valuable when modeling gas injection for enhanced oil recovery. Since the nonlinear behavior of gas injection is sensitive to the resolution of the simulation grid used, it is important to use a fine grid to accurately resolve the gas front and the pressure propagation. Unfortunately, discretizing a compositional flow system with many components on a high-resolution geological model leads to very large and poorly conditioned linear systems, and the high computational cost of solving these systems tends to render field-scale simulations infeasible. An additional challenge is the need for phase-equilibrium calculations, which often represent a large fraction of the computational time when both gas and liquid are present. We present a multiscale solver for compositional three-phase flow problems in which the behavior of the liquid and vapor phases are described by generalized cubic equations of state. The solver relies on a total-mass and overall composition based sequential solution strategy for the flow and transport equations and uses restricted smoothing to compute multiscale basis functions on unstructured grids with general polyhedral cell geometries. The resulting method computes approximate pressure solutions (to within a prescribed residual tolerance) that have conservative fluxes on the reduced computational grid, the original fine-scale grid, or any intermediate partition. The new method is verified against existing compositional simulators on conceptual models and validated on more complex cases represented on both unstructured and corner-point grids with strong heterogeneity, faults, pinched and eroded cells, etc. The resulting implementation is the first demonstrated multiscale method applicable to general compositional problems relevant for the petroleum industry, which includes a cubic equation of state and stratigraphic grids.