Simulation of flow and transport in heterogeneous reservoirs containing many wells presents a variety of numerical difficulties. The wells and heterogeneities represent two different types of singularities. In the examples presented, a two dimensional reservoir contains both injection and production wells. Reservoir properties vary in space and are represented as a stochastic process. Flow is simulated by the modified method of characteristics method and hybrids. Areal displacement patterns and production well recovery curves are monitored.

A variety of numerical algorithms are applied to the solution of the equations: strongly implicit procedures, alternating direction methods, multi-griding procedures, pre-conditioned conjugate gradient methods, and domain decomposition. The algorithms are applied separately to three test problems involving (1) mean uniform flow through a heterogeneous media, (2) diverging/converging flow between many wells in a homogeneous media, and (3) flow between many wells in a heterogeneous media. Algorithms which work well in the presence of only one type of singularity, for example test problems (1) or (2), fail in the presence of both singularity types (problem 3). The most robust algorithms for solving problem 3 appear to be particular versions of the preconditioned conjugate gradient method with/without domain decomposition. Adaptive gridding methods may offer another potentially successful approach.

Another aspect of the simulations is the recognition that small fluctuations of permeability located near a well have much more influence on flow and displacement than the same fluctuation located at the midpoint between wells. This issue is explored from several points of view: gridding, domain decomposition, and pseudo-properties.

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