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

Li Zhao, Chen-Song Zhang, Chun-Sheng Feng, Shi Shu

TL;DR

An efficient multistage preconditioner for the fully implicit compositional flow simulation that achieves good parallel speedup while yielding the same convergence behavior as the corresponding sequential version.

Abstract

The compositional model is often used to describe multicomponent multiphase porous media flows in the petroleum industry. The fully implicit method with strong stability and weak constraints on time-step sizes is commonly used in the mainstream commercial reservoir simulators. In this paper, we develop an efficient multi-stage preconditioner for the fully implicit compositional flow simulation. The method employs an adaptive setup phase to improve the parallel efficiency on GPUs. Furthermore, a multi-color Gauss-Seidel algorithm based on the adjacency matrix is applied in the algebraic multigrid methods for the pressure part. Numerical results demonstrate that the proposed algorithm achieves good parallel speedup while yields the same convergence behavior as the corresponding sequential version.

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

TL;DR

An efficient multistage preconditioner for the fully implicit compositional flow simulation that achieves good parallel speedup while yielding the same convergence behavior as the corresponding sequential version.

Abstract

The compositional model is often used to describe multicomponent multiphase porous media flows in the petroleum industry. The fully implicit method with strong stability and weak constraints on time-step sizes is commonly used in the mainstream commercial reservoir simulators. In this paper, we develop an efficient multi-stage preconditioner for the fully implicit compositional flow simulation. The method employs an adaptive setup phase to improve the parallel efficiency on GPUs. Furthermore, a multi-color Gauss-Seidel algorithm based on the adjacency matrix is applied in the algebraic multigrid methods for the pressure part. Numerical results demonstrate that the proposed algorithm achieves good parallel speedup while yields the same convergence behavior as the corresponding sequential version.
Paper Structure (21 sections, 20 equations, 4 figures, 8 tables, 4 algorithms)

This paper contains 21 sections, 20 equations, 4 figures, 8 tables, 4 algorithms.

Table of Contents

  1. Introduction
  2. Mathematical model and discretization
  3. The compositional model
  4. Discretization method
  5. The choices of primary variables
  6. Finite volume method and backward Euler method
  7. Fully implicit method
  8. Discrete system
  9. Parallel multi-stage preconditioners with adaptive SETUP
  10. Multi-stage preconditioner
  11. MSP with adaptive SETUP
  12. A multi-color GS based on adjacency matrix
  13. Adjacency graph and algorithm principles
  14. Multi-color GS algorithm
  15. Numerical experiments
  16. ...and 6 more sections

Figures (4)

  • Figure 1: The algorithm flow chart of adaptive SETUP.
  • Figure 2: Field oil production rate and average pressure for the modified SPE1 problem on GPUs.
  • Figure 3: Field oil production rate and average pressure of the SPE10 problem on GPUs.
  • Figure 4: Field oil production rate and average pressure of the SPE5 problem on GPUs.

Theorems & Definitions (2)

  • Remark 1
  • Remark 2