The need for accurate well productivity models with arbitrarywell trajectories spurred a revival in analytic solutionmethodology for fluid transport problems. Analyticformulations often depict single phase flow throughout thereservoir. The Babu-Odeh horizontal well solution for a boxshapedreservoir with spatially invariant properties isgeneralized here to allow closed-form solutions forheterogeneous media. A reservoir is decomposed intointeracting regions, each with its own reservoir properties andassociated analytic potential flow solution. Using wellestablishedboundary element techniques, pressure and fluxcontinuity are imposed at selected interface points to solve forthe steady material exchange between regions. Constantpressure and zero flux features (fractures and barriers) areeasily entertained at region boundaries. The 2-D, pseudosteadystate solution for heterogeneous media is embeddedwithin a reservoir performance feedback loop of a powerfulgradient search method to produce a robust optimal in-fill wellplacement algorithm. Utilizing this approach, new criteria aredeveloped concerning optimal placement of vertical wells forprimary production with respect to heterogeneity, asymmetry,and anisotropy. The semi-analytic method has been extendedto 3-dimensional flows to serve as a compute engine for a newgeneration of reservoir management and optimization tools.
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