A Stratified Percolation Model for Saturated and Unsaturated Flow Through Natural Fracturesby L. J. Pyrak-Nolte, Purdue Univ, United States,
N. G. W. Cook, Purdue Univ, United States,
L. R. Myer, Purdue Univ, United States,
Abstract: The geometry of the asperities of contact between the two surfaces of a fracture and of the adjacent void spaces determines fluid flow through a fracture and the mechanical deformation across a fracture. Heuristically we have developed a stratified continuum percolation model to describe this geometry based on a fractal construction that includes scale invariance and correlation of void apertures. Deformation under stress is analyzed using conservation of rock volume to correct for asperity interpenetration. Single phase flow is analyzed using a critical path along which the principal resistance is a result of laminar flow across the critical neck in this path. Results show that flow decreases with apparent aperture raised to a variable power greater than cubic, as is observed in flow experiments on natural fractures. For two phases, flow of the non-wetting phase is likewise governed by the critical neck along the critical path of largest aperture but flow of the wetting phase is governed by tortuosity.
Subject Headings: Fluid flow | Hydraulic fracturing | Critical flow | Percolation | Flow resistance | Critical path method | Radioactive wastes | Geometrics
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