Opening the Black Box: A Critical and Comparative Investigation of Solvers and Methods in Conventional and Next-Generation Reservoir Simulators

The term “next-generation” has been used related to reservoir simulation within the industry for almost a decade. This paper discusses factors that make next-generation simulators more special and effective than well-known previous methods by outlining the basis as well as the differences between the methods. The conventional reservoir simulator discussed makes use of the fully implicit (FI) and implicit in pressure / explicit in saturation (IMPES) methods. Fully implicit methods are more stable than explicit methods; however, more core memory and computation effort per time step are required when using fully implicit methods. Time truncation errors encountered when large time steps are used and the difficulties with implementation of higher order methods to reduce spatial truncation are some of the drawbacks of fully implicit formulations. Krylov subspace algorithms are the sole option for linear system solvers. The next-generation simulator discussed uses a relaxed volume balance approach, which is better than a mass balance formulation because the volume balance is a local error, and does not accumulate over time. The volume balance is simply the difference between the fluid volume and the pore volume in each grid block in the model, and is the primary convergence criteria in a volume balance model. A review and systematic comparison of solvers and solution methods is provided, such as finite difference methods (FDMs) and finite element methods (FEMs). Finally, the results of runs conducted on the SPE CSP 9 from both “conventional” and next-generation simulators are provided along with a comparison of processing times.