A Novel Linear Solver for Simulating Highly Heterogeneous Black Oil Reservoirs

Journal of Petroleum Science and Engineering (JPSE)

A great deal of computational power and time is necessary for the simulation of highly heterogeneous fractured reservoirs with complicated geometry. Simulating such largescale complex reservoirs with both minimum time and maximum accuracy has always remained a topic of concern to reservoir simulation engineers worldwide. The currently used linear solvers in well-known commercial simulators that utilize classical methods such as Nested Factorization (NF) and Incomplete LU Factorization (ILU) as their preconditioners, all suffer from severe convergence problems in models with high heterogeneity and/or large number of non-neighbor connections. To overcome such problems, a novel Adaptive Algebraic Multi-grid algorithm (AAMG) is proposed to be used in a constrained pressure residual (CPR) preconditioner, abbreviated as CPR-AAMG, in order to solve the governing discretized three-dimensional partial differential equations. The implemented CPR preconditioner which uses AAMG as the preconditioner for the elliptic pressure equation, and the Blocked ILU for the hyperbolic saturation equations, is a robust way for damping both smooth pressure field and high frequency saturation field errors in giant reservoir models. The findings of the current study illustrate that the developed Biconjugate Gradient Stabilized (BiCG-Stab) solver preconditioned by CPR-AAMG is capable of achieving acceptable results of high efficiency and robustness in the SPE10 project which is renowned as an enormous challenge for linear solvers due to the highly heterogeneous porosity and permeability values. The novelty of the proposed CPR-AAMG preconditioner is its ability to solve three-dimensional black oil models of giant, complex and heterogeneous fractured reservoirs without any convergence problems with reduction in time and required computational power.

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