Optimal Well Placement in Heterogeneous Reservoirs via Semi-Analytic Modeling

The need for accurate well productivity models with arbitrary well trajectories spurred a revival in analytic solution methodology for fluid transport problems. Analytic formulations often depict single phase flow throughout the reservoir. The Babu-Odeh horizontal well solution for a box-shaped reservoir with spatially invariant properties is generalized here to allow closed-form solutions for heterogeneous media. A reservoir is decomposed into interacting regions, each with its own reservoir properties and associated analytic potential flow solution. Using well-established boundary element techniques, pressure and flux continuity are imposed at selected interface points to solve for the steady material exchange between regions. Constant pressure and zero flux features (fractures and barriers) are easily entertained at region boundaries. The 2-D, pseudo-steady state solution for heterogeneous media is embedded within a reservoir performance feedback loop of a powerful gradient search method to produce a robust optimal in-fill well placement algorithm. Utilizing this approach, new criteria are developed concerning optimal placement of vertical wells for primary production with respect to heterogeneity, asymmetry, and anisotropy. The semi-analytic method has been extended to 3-dimensional flows to serve as a compute engine for a new generation of reservoir management and optimization tools.