Summary
When designing a waterflood, the important aspect of processing rate with respect to pattern selection has not been addressed adequately in the literature. It has not been possible, using the existing analytical background, to determine and compare the flowrate performance of all the patterns for any given rock/fluid (mobility) system. While general two-phase equations exist for the five-spot and line-drive patterns, flow equations for other patterns either have not been presented (e.g., the seven-spot) or are not sufficiently general (e.g., the nine-spot) to apply to all mobility conditions. A general treatment of skin effect also has not been given.
This paper presents a new, comprehensive analytical treatment of pattern flow for isotropic, homogeneous reservoirs that applies to all patterns and mobility conditions. This is made possible by a new equation for the volumetric average reservoir pressure of regularly spaced, repeated patterns. The new formulas demonstrate how the producer/injector ratio (P/I) controls reservoir pressures and flow rates and (for the first time) allow the differences in the flow capacity of patterns to be quantified. The mobility characteristics that control flow rates are described fully by a newly defined total mobility ratio, MT. The form of the new equations allows for modifications for skin effect and reservoir heterogeneity. We show how skin effect can act disproportionately with injectors and producers because of its interaction with P/I and MT.
