The Use of Vectorization and Parallel Processing for Reservoir Simulation

Abstract

A general purpose reservoir simulator was developed as a vehicle to investigate vectorization and parallel processing on the Cray XMP/48. The simulator can model black oil, compositional and steam injection processes. It includes both fully implicit and IMPES formulations. Microtasking is used for parallel processing in order to maintain the portability of the code. The simulator calculations other than linear equation solution were structured to facilitate vectorization and parallel processing. Several issues concerning parallel processing are discussed. These include task granularity, load balance, synchronization, memory contention, and balance between vectorization and arallel processing. Based on three test problems, the speedup of the calculations due to vectorization ranges from 5.3 to 10. The speedup can be augmented by as much as 3.3 times through parallel processing. The scheme proposed here is general enough to be applicable to other vector and parallel processing computers. Introduction Two factors which are important in simulator utilization are speed and maintainability. Vectorization and parallel processing can significantly improve speed. A general purpose reservoir simulator can improve maintainability by elimimating the need to duplicate routines which are common to many simulators. Although much attention has been paid to applying vectorization in reservoir simulation, little work was done in parallel processing. This work is intended to test the feasibility of using both vectorization and parallel processing in a general purpose reservoir simulator. Although the simulator was developed for a Cray multiprocessor machine, the methodology used in the development is applicable to other multiple and vector processors. This paper is divided into four parts. The first part describes the mathematical formulation and numerical solution procedure for the general purpose simulator. The second part discusses the fundamentals of vectorization and parallel processing. The third part shows how vectorization and parallel processing is applied to the simulator. Finally, the fourth part describes the performance tests and discusses the results of these tests. MATHEMATICAL MODEL AND NUMERICAL SOLUTION PROCEDURE Mathematical Model The mathematical model is formulated to simulate black oil, compositional, and thermal recovery processes. It includes both fully implcit and IMPES formulation. A compositional approach is used to model black oil processes. Darcy's law and instantaneous phase equilibrium are assumed valid. In order to simulate different processes using a single code, mutual solubilities of the components in the mixture have to be distinguished. Mutual solubilities of water and hydrocarbon components are considered unimportant in black oil or compositional processes, but are important for steam injection processes. P. 329^

Vectorization and Parallel Processing of Local Grid Refinement and Adaptive Implicit Schemes in a General Purpose Reservoir Simulator

“…VwJ.tw (ld) In these equations, Zik is the total mass of component i in grid block k. Note that Zik is not based on a per pore volume basis as used by Chien et al 7 In the equations above, t is time, t!.t is difference in time, 6 k is difference in space relative to grid block k, T g is the geometric conductance, Xij is the composition of component i in phase j, k rj is the relative permeability, J.tj is the phase viscosity, Vj is the phase volume, Pj is the phase density, qik is the injection rate of component i in grid block k, Po is the oil phase pressure, Pjo is the pressure difference between phase j and the oil phase. Pjo becomes a gas phase capillary pressure and a negative water phase capillary pressure when j is set to g (the gas phase) and w (the water phase), respectively.…”

Simulation of Compositional Reservoir Phenomena on a Distributed-Memory Parallel Computer

“…Chien et at. 2 investigated compositional modeling in parallel on a Cray X-MP 4/16. Barua and Horne 3 applied parallel computing using a nonlinear equation solver for the black-oil case on the Encore Multimax.…”

Development of a framework for parallel reservoir simulation

“…Since the early days of parallel vector processor systems, development of parallel reservoir simulators has been advancing in tandem with the new technological advancements in parallel computing. Most of the works done in parallel reservoir simulation has been focused in either linear, nonlinear solvers and preconditioners (Barua and Horne, 1989; Briens et al, 1990; Cheshire and Bowen, 1992; Khait, 2009; Killough and Wheeler, 1987; Liu et al, 2000; Scott et al, 1987; Wallis et al, 1991; Yu et al, 2012), new parallel simulator development (Atan et al, 2006; Chien et al, 1987; DeBaun et al, 2005; Dogru et al, 2013; Maliassov et al, 2013; Rutledge et al, 1992; Wheeler and Smith, 1990), or the conversion of nonparallel reservoir simulators (Beckner et al, 2015; Ghori et al, 1995; Kårstad et al, 1988; Killough and Bhogeswara, 1991; Rame and Delshad, 1995; Van Daalen et al, 1989; Wang and Killough, 2014).…”