Equivalent channel network model for permeability and electrical conductivity of fracture networks

[1] It is remarkable that the permeability k and electrical conductivity sigma 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 tau(h) and tau(e). This "equivalent channel network model'' reproduces the observed power law behavior on the conditions that d(h)(3) proportional to d(e)(r) and tau(h) proportional to tau(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.