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 time step-sizes; hence, commonly used in the current mainstream commercial reservoir simulators. In this paper, a CPRtype preconditioner with an adaptive "setup phase" is developed to improve parallel efficiency of petroleum reservoir simulation. Furthermore, we propose a multi-color Gauss-Seidel (GS) algorithm for 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 CUDA implements. Moreover, the proposed algorithm yields good parallel speedup as well as same convergence behavior as the corresponding single-threaded algorithm. In particular, for a three-phase benchmark problem, the parallel speedup of the OpenMP version is over 6.5 with 16 threads and the CUDA version reaches more than 9.5.

An Improved Multi-Stage Preconditioner on GPUs for Compositional Reservoir Simulation

“…We can observe that MSP-GMRES-PJAC-NO has the more number of iterations, our MSP-GMRES-PGS-MC has the least number of iterations (and less time), while MSP-GMRES-PGS-NO's iterations is between MSP-GMRES-PGS-MC and MSP-GMRES-PJAC-NO. This shows that MSP-GMRES-PGS-MC produces the same convergence behavior as the corresponding single-thread algorithm (this conclusion is also confirmed by the OpenMP version [30]).…”

“…In this subsection, we utilize an adaptive SETUP strategy for the MSP preconditioner to improve its parallel efficiency, denoted as ASMSP. As mentioned earlier, this strategy has been employged for the blackoil model by Zhao et al [30]. Assume that the solution objective is A (ι) x (ι) = b (ι) .…”

“…A hybrid approach that combines the Jacobi and GS methods can be applied, but its convergence rate also deteriorates with respect to higher parallelism. In order to overcome the limitations of the traditional red-black GS algorithm, a multi-color GS algorithm based on the coefficient matrix of strong connections has been proposed and analyzed in [30]. This paper proposes a multi-color GS algorithm from the algebraic point of view.…”

“…In this paper, we focus on a GPU-based parallel linear solver for compositional models, which is an extension of the recent work for the blackoil model [30]. To the best of our knowledge, few numerical tests have been done for the algebraic systems arising from the fully implicit discretization of the compositional model in the literature.…”