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A Multi-Level Algebraic Multiscale Solver (ML-AMS) For Reservoir Simulation
- Publisher: European Association of Geoscientists & Engineers
- Source: Conference Proceedings, ECMOR XVI - 16th European Conference on the Mathematics of Oil Recovery, Sep 2018, Volume 2018, p.1 - 12
Abstract
Summary
The Algebraic Multiscale Solver (AMS) is very efficient in handling the highly heterogeneous pressure system that arises from incompressible flow in porous media ( Wang et al., 2014 ). The standard AMS method employs a single auxiliary coarse level on which the original problem can be projected and solved efficiently, given the huge reduction in its original ‘fine’ size. The coarse solution is then projected back to the fine level and its quality can be further enhanced by iteratively applying additional AMS passes until ultimately converging to the exact solution ( Zhou and Tchelepi, 2012 ; Wang et al., 2014 ). However, the efficiency of AMS drops significantly when the problem size becomes extremely large, as the size of the coarse-scale representation of the problem, and, in turn, its solution cost, becomes inevitably large. Thus, in this work, we propose an extension of the standard two-level AMS method: a Multi-Level AMS (ML-AMS) method, which continues to use additional coarser levels recursively as needed to solve the problem more efficiently. The performance of ML-AMS is demonstrated and compared with the standard two-level AMS using 2D and 3D heterogeneous problems derived from the SPE10 benchmark ( Christie et al., 2001 ). For all test cases, ML-AMS is shown to have comparable performance with the two-level AMS, while avoiding the expensive cost of handling the coarse-scale problem with a direct solution method. Since ML-AMS applies the original two-level AMS algorithm recursively, any existing multiscale implementation can be easily extended to use ML-AMS.
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