2014 Rice Oil & Gas HPC

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Slow convergence of iterative linear solvers for physical problems with jump or discontinuous coefficients is a well-known challenge for parallel computation. While many papers focus on the finite element (FE) method with an overlapping Schwarz or similar preconditioner for elliptic problems (e.g., Graham and Scheichl 2008), literature with respect to reservoir simulations is limited to steady-state porous media flow with FE (Vuik et al., 2001; Cliffe et al., 2000), or considers two-phase flow, but applies multi-level domain decomposition and finite differences (Kees et al., 2003). However, there are reservoir simulations using either two-stage preconditioners (Aksoylu et al., 2007; Klie et al., 2009) or overlapping Schwarz (Usadi et al., 2007). We consider, instead, the case of non-overlapping, block Jacobi for two-point-flux-approximation finite-volume reservoir simulation. With increased industrial use of HPC for reservoir simulations, significant abnormalities in performance behavior are seen when different HPC configurations are selected. This has been theorized to be partition-induced solver degradation. We construct simple test cases to clearly illustrate the effect and, dependent on the inclusion of both high and low permeability regions inside a subdomain, verify a 20% difference in the average iteration count for linear solutions of the Jacobian. We also consider realistic cases. For a 3D unstructured grid reservoir model with one-hundred-thousand grid cells, we create two identical partitions except for one cell: a nearly vertical stack of cells with high transmissibility connections to each other are split between partitions either above or below this pivotal cell. This small change resulted in a 1.7X increase in computational time due to a similar increase in total linear iterations. Experimentation on a 3-million-cell unstructured grid with as many as 1024 partitions showed a range of 2X in total linear iterations over the course of the simulation. These results show that robust industrial application of HPC for reservoir simulation requires partitioning that is load balanced, communication minimizing and encapsulates local flow patterns. A transmissibility-weighted graph partitioner has been developed that mitigates the performance variability seen in these test cases.