1983/06/01 by D.W. Peaceman, Donald W. Peaceman · 911 citations
Chemistry · Engineering · Mathematics · #Anisotropy #Applied mathematics #Block (permutation group theory) #Chemistry #Computer science #Constant (computer programming) #Enhanced Oil Recovery Techniques #Geometry #Grid #Hydraulic Fracturing and Reservoir Analysis #Interpretation (philosophy) #Mathematical analysis #Mathematics #Optics #Permeability (electromagnetism) #Physics #RADIUS #Reservoir Engineering and Simulation Methods
paper · doi:10.2118/10528-pa
published in Society of Petroleum Engineers Journal 23(03), 531-543 (Society of Petroleum Engineers)
crossref issued 1983/06/01 · crossref published 1983/06/01 · crossref published-online 1983/06/01 · crossref published-print 1983/06/01 · openalex publication_date 1983/06/01 · crossref created 2007/12/07 · crossref deposited 2022/02/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/31 · crossref indexed 2026/07/31
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.