Reservoir Simulation on a Hypercube
- John A. Wheeler (Exxon Production Research Co.) | Richard A. Smith (Exxon Production Research Co.)
- Document ID
- Society of Petroleum Engineers
- SPE Reservoir Engineering
- Publication Date
- November 1990
- Document Type
- Journal Paper
- 544 - 548
- 1990. Society of Petroleum Engineers
- 5.5.8 History Matching, 5.5 Reservoir Simulation, 4.2 Pipelines, Flowlines and Risers, 1.10.1 Drill string components and drilling tools (tubulars, jars, subs, stabilisers, reamers, etc), 4.3.4 Scale, 5.1.8 Seismic Modelling, 5.1.5 Geologic Modeling
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The rapid evolution of parallel computers with distributed memory promises to reduce computer hardware costs by an order of magnitude. To examine the extent to which this promise can be realized in practice, we coded and tested a 3D parallel implicit reservoir simulator for an Intel iPSC/2 hypercube with 16 vector processors. The simulator is based on an oil/water model and does not account for a gas phase. Test results were favorable. A correlation of computation efficiency with problem size and the number of processors demonstrates that up to 96 % of the available CPU time on the hypercube can be used. Such high efficiencies were achieved by developing special algorithms well suited for multiple processors and distributed memory.
General-purpose parallel computers available today for supercomputing applications can be classified into three major architectural groups: shared-memory machines, which allow all processors to access a common central memory; distributed-memory machines, for which each processor has its own local memory and communicates with other processors through a communication network; and hybrids of these two architectures. Shared-memory machines require complex and expensive switching hardware to connect processors to memory, and fundamental physical limitations restrict the number of processors such hardware can support. Many shared memory machines therefore rely on a small number of fast, expensive processors to achieve high aggregate computation speeds. In contrast, the architecture of distributed-memory machines avoids central-memory access bottlenecks and is able to accommodate a large number of processors. Thus, distributed-memory multiprocessors can be built using inexpensive, very-large-scale integrated (VLSI) chip technology to produce machines that are two orders of magnitude cheaper but only an order of magnitude or less slower than shared-memory machines. In addition, rapid progress in VLSI design (see Ref. 3) is expected to increase dramatically both the raw computing power and the cost performance of distributed-memory machines in the near future.
To assess the potential application of distributed-memory machines to reservoir simulation, we coded and tested a parallel implicit reservoir simulator that can solve two-phase (oil/water) problems for 3D reservoirs with irregular geometries. The simulator was designed solely as a research tool to determine how a parallel simulator should be organized, to identify problems inherent in parallel reservoir simulation on distributed-memory machines and to explore solutions, and to assess how distributed-memory machines can be used efficiently. The target machine for the simulator was a 16-node iPSC/2 hypercube distributed-memory multiprocessor from Intel Scientific Computers. Each iPSC/2 node included a pipeline coprocessor for accelerating vector arithmetic and one megabyte each of node and vector memory.
Our approach to developing the simulator was to distribute the entire computation segment of the simulator to each processor and then make each processor responsible for computations on a portion of the reservoir grid. Each processor must then communicate results for grid elements on the boundary of its domain to other processors that share the boundary. This approach is more challenging than parallelizing only selected CPU-intensive portions of a simulator, but we believe that it is necessary to realize the full potential of distributed-memory machines for reservoir simulation. In this paper, we describe the parallel simulator, report on its performance and discuss lessons we learned. A description of the mathematical formulation of the simulator is followed by a section on the parallel linear solver we developed for the simulator. Next, simulator timing results and computation efficiencies are presented. Finally, we discuss some of the problems associated with parallel reservoir simulation and outline the major conclusions drawn from our research.
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