Parallel multi-stage preconditioners with adaptive setup for the black oil model

Abstract

The black oil model is widely used to describe multiphase porous media flow in the petroleum industry. The fully implicit method features strong stability and weak constraints on timestep sizes; hence, it is commonly used in current mainstream commercial reservoir simulators. In this paper, a Constrained Pressure Residual (CPR) preconditioner with an adaptive “setup phase” is developed to improve the parallel efficiency of a petroleum reservoir simulation. Furthermore, we propose a multi-color Gauss–Seidel (GS) algorithm for the algebraic multigrid method based on the coefficient matrix of strong connections. Numerical experiments show that the proposed preconditioner can improve the parallel performance for both OpenMP and Compute Unified Device Architecture (CUDA) implements. Moreover, the proposed algorithm yields good parallel speedup as well as the same convergence behavior as the corresponding single-thread algorithm. In particular, for a three-phase benchmark problem (about 3.28 million degrees of freedom), the parallel speedup of the OpenMP version is over 6.5 with 16 threads, and the CUDA version reaches more than 9.5.