Finding a regular geometry for an irregular reservoir shape for well performance calculations

The shape and geometry of the reservoir play an important role in well pressure performance calculations by analytical methods. Dietz (1965) reported analytical solutions for a variety of regular shape reservoirs. He presented a table of shape factors for different geometries (circle, square, triangle etc.) and different locations of the well within the reservoir. However, no solution is available for an irregular geometry or for any shape that is not covered in the Dietz shape factor table. This paper presents a method in which a numerical simulator is used for an irregular shape reservoir to obtain an equivalent regular geometry that produces the same well performance as that of the real irregular reservoir. The well can be slanted or horizontal and can be situated anywhere within the reservoir. To do this an optimization routine is used which minimizes the sum squared deviations between the well block pressures as obtained by the numerical simulators for both shapes. Once the nearest regular shape has been identified, well performance calculations can be carried out using an analytical method selected from those presented by Dietz or by the same authors in their recent papers.