| The finite-difference techniques used in reservoir simulation result in many independent calculations, which are amenable to parallel execution. In reservoir simulation, much of the parallel programming literature is on investigations using supercomputers.;Parallel execution could be performed during each time step, therefore an increase in the time step size would increase the areas that were suitable for parallel execution. The Laplace transform was applied to the simulation of a one-dimensional oil-water model with the aim of increasing the time step size. The model simulated was a two-dimensional, two-phase, black oil model with a fully-implicit formulation. The simulator was parallelized using monitors as macros to synchronize calculations. The time-consuming parts of the calculations, matrix generation and matrix solution, were parallelized. The performance of the simulator was measured by the speed up, which is defined as the ratio of the sequential execution time of the simulator to the multiprocessing execution time of the simulator.;The speed ups of the matrix generation time increased almost linearly, ranging from 3.5 to 4.0 for four processes and 7.0 to 7.9 for eight processes. The parallelized matrix solver, Gaussian elimination, resulted in low speed ups of 2.8 for four processes and 3.9 for eight processes. The low values were largely caused by a large synchronization time due to the small granularity of the procedure. However, the simplicity in programming Gaussian elimination permitted a study of the overall parallelization of a simulator without major reprogramming. In the investigations on the application of the Laplace transform to simulation, the time step size did not show improvement in Laplace space. A favorable result of this approach was that, during breakthrough, the transform method needed fewer iterations than the real time simulation and, thus indicating a reduction in the sequential portion. The maximum ratio of the number of iterations in real time space to the number of iterations in Laplace space was 4.55.;In this study, a 32-Mbyte, 12-processor parallel computer was used. The effects of types of table look-ups, number of processes, granularity, load balancing and program structure were studied. |
