Conductivity in fluid-bearing rocks

The presence of high-conductivity fluids, such as water or partial melt in cracks, pores, and grain boundaries, determines the electrical conductivity of rocks under most conditions in the crust. Archie's law, σ/σ0 = η/r, is usually observed, where the conductivity in the bulk material is σ, that of the fluid is σ0, the porosity is η, and r is usually in the range 1–2. We have modeled conduction in a porous medium with a simple cubic array of 2340 resistors from which resistors were removed at random to simulate a decrease of porosity. Arrays have a relative conductance G/G0 = [(p − po)/(1 − po)]r, where p is the fraction of remaining resistors and po is close to the critical fraction pc, where G = 0. It is shown that the two cases (r = 1 for bond (branch) removal or r = 2 for site (node) removal) can be interpreted as volume changes of porosity with small effect upon crack connectivity in dilatant rocks or as alterations of internal connectivity with porosity in different rocks, respectively.