Simulation of Compositional Reservoir Phenomena on a Distributed-Memory Parallel Computer
Authors: Killough J.E. , Bhogeswara Rao 
Published: December 2007

Summary
Distributed-memory parallel computer architectures parallel computer architectures appear to offer high performance at moderate cost for reservoir simulation applications. In particular, the simulation of compositional reservoir phenomena shows great promise for phenomena shows great promise for parallel applications because of the parallel applications because of the large parallel content of the compositional formulations. This paper focuses on the application of a distributed-memory parallel computer, the iPSC/860, to the solution of two compositional simulations; one based on the Third SPE Comparative Solution problem and another based on a real production compositional model. An improved linear equation solution technique based on multigrid and domain decomposition methods is compared with other techniques in serial and parallel environments. For a hypothetical heterogeneous example, the new technique showed a high degree of parallel efficiency. Finally, results parallel efficiency. Finally, results show that performance of the compositional simulations with a fully parallel simulator is comparable to that of parallel simulator is comparable to that of current mainframe supercomputers.

Introduction
Over the past decade, computer performance has advanced significantly. Current performance has advanced significantly. Current single-processor performance is limited by speed-of-light considerations. These limitations indicate that, to achieve speed ups greater than an order of magnitude above current technology, significant architectural changes must be made. The emerging parallel computer architectures appear to be parallel computer architectures appear to be the most likely avenue for this advancement. Parallel computers have existed for Parallel computers have existed for several decades, but only recently have the architectures and languages allowed these machines to be used for significant work. The parallel machines have three varieties: shared memory, distributed memory, and very long instruction word. Some shared memory machines are the Cray Y-MP 8/32, the IBM 3090 600S/VF, the Sequent Symmetry, and the ETA 10. The CPU's and memories are connected so that all memory is accessible by all CPU's. This is illustrated in Fig. 1, which shows a cross-bar-like connection among the memory banks and CPU's. For the high-performance supercomputers like the Cray X-MP and IBM 3090, this global memory connection can be costly because of the requirement of rapid access to memory. To overcome this difficulty, several distributed-memory architectures have evolved. These are characterized by grids of less-powerful CPU's connected in some fashion for communication of data and synchronization (Fig. 2). One of the most popular of these connection schemes is the hypercube topology. The N-Cube and Intel iPSC/860 use this architecture. Each may have more than 100 processors. Both the N-Cube and Intel are processors. Both the N-Cube and Intel are multiple-instruction, multiple-data computers. Each CPU may execute different sets of instructions on different data. Another emerging distributed-memory, massively parallel computer is the connection machine, parallel computer is the connection machine, which is a single-instruction, multiple-data architecture with up to thousands of processors. All CPU's execute each instruction in processors. All CPU's execute each instruction in lock step with one another. The very-long-instruction-word computer, such as the Multiflow and FPS 264, exploit local parallelism within a user's program. By combining many parallel program. By combining many parallel operations of the functional units of the machine into each instruction, the compiler can achieve significant speedups. Several authors have dealt with the application of parallel computing to petroleum reservoir simulation in shared-memory parallel environments. Scott et al. parallel environments. Scott et al. investigated the parallelization of the coefficient routines and linear equation solvers for a black-oil model on a Denelcor HEP. Chien et al. investigated compositional modeling in parallel on a Cray X-MP 4/16. Barua and Horne applied parallel computing using a nonlinear equation solver for the black-oil case on the Encore Multimax. Killough and Wheeler looked at parallel linear equation solvers on both the Cray X-MP and IBM 3090. Each application involved a shared memory parallel computer. The question still remained as to whether a distributed-memory architecture could be used efficiently for simulation of petroleum reservoirs. More recently, parallelization of reservoir simulators has been accomplished on distributed-memory parallel computers. van Daalen et al. showed a speedup of a factor of 40 on 60 processors on the Transputer-based Meiko computer. Wheeler and Smith showed that black-oil modeling could be performed efficiently on a hypercube. Application of compositional reservoir modeling to the distributed-memory, message-passing Intel iPSC/2 Hypercube was investigated by Killough and Bhogeswara. Simulations using a commercial compositional reservoir simulator (VIP-COMP) showed that high parallel efficiencies could be obtained with a model problem based on the Third SPE problem based on the Third SPE Comparative Solution Project. The key issues in this parallelization involved the data structure of the program, message passing of data among processors, and development of parallel linear equation solvers for the parallel linear equation solvers for the model.