1973 Third Symposium on Numerical Simulation of Reservoir Performance, Houston, Texas January 11–12, 1973. Performance, Houston, Texas January 11–12, 1973


Computer modeling of petroleum reservoirs leads one to the problem of solving large numbers of simultaneous fluid flow equations. The purpose of this paper is to propose a new method for solving these equations and present comparisons between our method and the strongly implicit procedure (SIP) proposed by Stone and others. We have compared the new technique with SIP for a number of two-dimensional, steady state problems in both homogeneous and strongly heterogeneous reservoirs, with reservoir sizes ranging from 100 to 800 blocks. For some heterogeneous cases the ratios of transmission coefficients varied by a ratio of one million to one for testing. Compared to SIP, our method requires less computer storage space, compiles faster, executes up to 2.96 times faster, has no iteration parameter, is easier to program, requires about two-thirds an many cards, and gives excellent agreement in regard to material balance and final values of Pi,j. The method has been applied to problems with from 2 to 16 wells positioned in the reservoir corners, immediately adjacent, in line, and in random positions. Well magnitudes have been allowed to range up to a ratio positions. Well magnitudes have been allowed to range up to a ratio of 10,000 to 1.0 in the same problem. For every problem thus far attempted, the method has converged to the same answers as SIP in less computer time. Based upon our experience with this new method, we feel that the new method is substantially superior to SIP.

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