Abstract

A new method for formulating finite difference equations for reservoir simulation has been developed. It can be applied throughout the entire simulated reservoir or to local segments. When applied to cells containing vertical, fully penetrating, straight-line wells in a homogeneous reservoir, the resulting equations are equivalent to Peaceman's classical well equations used in most reservoir simulators today. However, when the new finite difference equations are applied to both the well-containing cells, and their neighbors, the accuracy of the simulation improves substantially. The method produces still better accuracy results when applied throughout the reservoir. Unlike the Peaceman correction, the new method also applies to reservoirs containing wells of complex geometry. This includes wells that are closely spaced and wells near reservoir faults and external boundaries. The method results from the incorporation of approximate analytical expressions for the pressure into the reservoir simulator's finite difference equations. By incorporating the “physics” of the flow into the solution, rather than relying on polynomial-based finite difference equations based on Taylor's series, as is usually done, solution accuracy improves. Accuracy is particularly improved around the wells where near-singularities in the pressure occur. Polynomials are incapable of accurately representing singularities.

Degree

College and Department

Ira A. Fulton College of Engineering and Technology; Chemical Engineering

Rights

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