Open AccessEquivalent channel network model for permeability and electrical conductivity of fracture networks
Author(s) -
Van Siclen Clinton D.
Publication year - 2002
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 - 10.1029/2000jb000057
Subject(s) - tortuosity , exponent , power law , fracture (geology) , permeability (electromagnetism) , materials science , planar , mechanics , hydraulic conductivity , geotechnical engineering , porosity , geology , geometry , physics , mathematics , soil science , computer science , chemistry , soil water , philosophy , biochemistry , linguistics , statistics , computer graphics (images) , membrane
It is remarkable that the permeability k and electrical conductivity σ of saturated, fractured rock exhibit a power law relationship with exponent r as pressure is applied to the rock. To understand this behavior, the fracture network is viewed as a collection of connected, planar fractures. This allows the construction of algebraic expressions for the transport properties of the fracture network, in which the local effective properties, namely, the hydraulic aperture d h and the electric aperture d e of the representative planar fracture (the “equivalent channel”), are distinguished from the network properties (e.g., fracture connectivity) parameterized by the tortuosity factors τ h and τ e . This “equivalent channel network model” reproduces the observed power law behavior on the conditions that d h 3 ∝ d e r and τ h ∝ τ e r over the range of applied pressures. The first condition is met, as demonstrated by calculations for a variety of simulated planar fractures using the Reynolds equations for fluid and current flow. The value of the exponent r is found to indicate the degree to which the fracture resembles a porous medium but cannot otherwise identify fracture surface or aperture characteristics. No direct evidence currently exists to support the second condition; however, such a power law relationship has been demonstrated elsewhere for simulated porous media.