Open AccessEffective media theory with spatial correlation for flow in a fracture
Author(s) -
Walsh Joseph B.,
Brown Stephen R.,
Durham William B.
Publication year - 1997
Publication title -
journal of geophysical research: solid earth
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.67
H-Index - 298
eISSN - 2156-2202
pISSN - 0148-0227
DOI - 10.1029/97jb01895
Subject(s) - renormalization , percolation theory , perturbation theory (quantum mechanics) , statistical physics , mechanics , flow (mathematics) , perturbation (astronomy) , physics , geology , mathematics , conductivity , quantum mechanics
Standard effective media theory, real‐space renormalization, and first‐order perturbation theory all predict that a percolation threshold, where the electrical and hydraulic conductivity become zero, is reached when the area of contact is half of the total area. However, calculations of the flow properties of joints, whether simulated by continuous fields or discretely as a network of resistors, show that flow is maintained at appreciably larger contact areas. This behavior has been termed “channeling” in the literature. We have modified the standard effective media theory by introducing a rudimentary sort of nonrandomness in an attempt to simulate features like topographic hills and valleys. Using this new model, we calculate overestimates and underestimates of electrical and hydraulic conductivity as a function of the separation between the fracture surfaces. The underestimate is found to be very close to the standard effective media theory, real‐space renormalization, and first‐order perturbation theory results. The mean of the overestimate and underestimate is a good approximation to the published values found from calculations of electrical and hydraulic conductivities for simulations of real joints.