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Archie's Law for the porosity and saturation dependence of electrical conductivity, σ(θ) = aσbϕm(θ/ϕ)n (where σ is electrical conductivity, the subscript b denotes the brine or bulk solution, ϕ is porosity, θ is volume wetness, and a, m, and n are fitting parameters) was recently derived by applying continuum percolation theory to fractal porous media. We have recast Archie's Law in terms of saturation alone to obtain σ(θ) = σ0 (θ − θc)μ, where θc is the critical volume fraction for percolation, and σ0 = aσb/(1 − θc)μ. The value of the exponent, μ = 2.0 for three‐dimensional systems and 1.28 for two, is consistent with theory and simulations. We examined the universality of the exponent's value, and the range of validity of our expression. Drawing on published data, we compared predicted and measured values of σ(θ) across the full range of saturation, and found that the newly derived expression provides good predictions, is robust with respect to secondary effects such as residual salinity and contact resistance, and yields meaningful physical parameters.

Gas‐producing wells in the Barnett Formation show a steep decline from initial production rates, even within the first year, and only 12–30% of the estimated gas in place is recovered. The underlying causes of these production constraints are not well understood. The rate‐limiting step in gas production is likely diffusive transport from matrix storage to the stimulated fracture network. Transport through a porous material such as shale is controlled by both geometry (e.g., pore size distribution) and topology (e.g., pore connectivity). Through an integrated experimental and theoretical approach, this work finds that the Barnett Formation has sparsely connected pores. Evidence of low pore connectivity includes the sparse and heterogeneous presence of trace levels of diffusing solutes beyond a few millimeters from a sample edge, the anomalous behavior of spontaneous water imbibition, the steep decline in edge‐accessible porosity observed in tracer concentrations following vacuum saturation, the low (about 0.2–0.4% by volume) level presence of Wood's metal alloy when injected at 600 MPa pressure, and high tortuosity from mercury injection capillary pressure. Results are consistent with an interpretation of pore connectivity based on percolation theory. Low pore connectivity of shale matrix limits its mass transfer interaction with the stimulated fracture network from hydraulic fracturing and serves as an important underlying cause for steep declines in gas production rates and a low overall recovery rate.