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

TLDR

Prior studies of well‑block pressure for isolated wells are extended to nonsquare grid blocks. The study aims to extend the analysis to anisotropic permeability. An expression for the effective well‑block radius in terms of Δx, Δy, kx, and ky is derived. Numerical solutions and analytical derivation show that the effective well‑block radius is ro = 0.14(Δx² + Δy²)½, with the constant equal to e^γ⁄4.

Abstract

Abstract 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.