Adaptive Algebraic Multiscale Solver for Compressible Flow in Heterogeneous Porous Media

Abstract

An adaptive Algebraic Multiscale Solver for Compressible (C-AMS) flow in heterogeneous oil reservoirs is developed. Based on the recently developed AMS [Wang et al., 2014] for incompressible linear flows, the C-AMS extends the algebraic formulation of the multiscale methods for compressible (nonlinear) flows. Several types of basis functions (incompressible and compressible with and without accumulation) are considered to construct the prolongation operator. As for the restriction operator, C-AMS allows for both MSFV and MSFE methods. Furthermore, to resolve high-frequency errors, Correction Functions and ILU(0) are considered. The best C-AMS procedure is determined among these various strategies, on the basis of the CPU time for three-dimensional heterogeneous problems. The C-AMS is adaptive in all aspects of prolongation, restriction, and conservative reconstruction operators for time-dependent compressible flow problems. In addition, it is also adaptive in terms of linear-system update. Though the C-AMS is a conservative multiscale solver (i.e., only a few iterations are employed infrequently in order to maintain high-quality results), a benchmark study is performed to investigate its efficiency against an industrial-grade Algebraic Multigrid (AMG) solver, SAMG [Stuben, 2010]. This comparative study illustrates that the C-AMS is quite efficient for compressible flow simulations in large-scale heterogeneous 3D reservoirs.