Application of Algebraic Multigrid in Fully Implicit Massive Reservoir Simulations

Abstract

Algebraic Multigrid (AMG) methods have proven to be efficient when numerically solving elliptic Partial Differential Equations (PDE). In reservoir simulation, AMG is used together with the Constrained Pressure Residual (CPR) method to solve a partially decoupled pressure system. Recently, effort has been focused on improving the robustness of the AMG-CPR solver. This paper presents the performance of different AMG-CPR strategies for massive reservoir models. In addition, a solver selection analysis is conducted, proving that dynamic selection of solvers has the potential of increasing the overall efficiency and robustness of the simulation. Numerous decoupling/preconditioning algorithms exist and have been shown to influence the pressure matrix properties, some resulting in matrices more suitable to the characteristics favorable to AMG. Several decoupling/preconditioning strategies are investigated, such as Alternate Block Factorization (ABF), Quasi-IMPES (QI), and Dynamic Rowsum (DRS). The extracted pressure matrix could be suitable or unsuitable for AMG, depending on the matrix row sum, the diagonal signs, and the signs of the off-diagonal values. The advantage of using AMG as a preconditioner is demonstrated by running the SPE10 case. The recommended AMG settings that result in the optimal performance for SPE10 are shared. A speedup is seen of up to 4X when using AMG with optimal settings versus the default solver in the in-house reservoir simulator with the improvement range depending on the number of processors used. SPE10 is a highly heterogeneous model resulting in matrices favorable for AMG, i.e., pressure decoupling produces positive definite pressure matrices, which is not necessarily representative of industry models. A comparison is then made with a selection of models with a wide range of characteristics and finally an examination of the convergence behavior of key industry cases with different decoupling strategies is presented. The overall convergence behavior of the pressure and full system are shown and the top decoupling algorithms for the particular models are discussed. Finally, the applicability and performance gain of selectively using AMG during a run is demonstrated. Recent developments have been made in regard to AMG methods, but their applicability in a wide range of massive real cases is yet to be explored. In this work, different decoupling methods are tested, the AMG behavior on real field massive models is analyzed, the scalability is investigated, and AMG is selectively activated during a simulation run shedding light on the potential of future work entailing the use of Artificial Intelligence (AI) to dynamically select the optimal solver choice.