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

[1] 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_h³ ∝ 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.