Interpretation of Well-Block Pressures in Numerical Reservoir Simulation With Nonsquare Grid Blocks and Anisotropic Permeability

Previous work on the interpretation of well-block pressure (WBP) for a single isolated well is extended to the case of nonsquare grid blocks (∆x ≠ ∆y). Numerical solutions for the single-phase five-spot problem, involving various grid sizes, show that the effective well-block radius (where the actual flowing pressure equals the numerically calculated WBP) is given by ro=0.14 (Δx2+Δy2)½. This relationship is verified by a mathematical derivation for a single well in an infinite grid. The exact value of the constant is shown to be eγ/4, where γ is Euler's constant. Finally, the analysis is extended to include anisotropic permeability, and an expression for the effective well-block radius in terms of Δx, Δy, kx, and ky is derived.