Numerical estimation of electrical conductivity in saturated porous media with a 2-D lattice gas

A 2-D lattice gas is used to calculate the effective electrical conductivit y of saturated porous media as a function of porosity and conductivity rati o R-c between the pore-filling fluid and the solid matrix for various micro scopic structures of the pore space. The way the solid phase is introduced allows the porosity phi to take any value between 0 and 1 and the geometry of the pore structure to be as complex as desired. The results an presented in terms of the formation factor F = sigma(w)/sigma(r), with a, the effect ive conductivity of the saturated rock and a,. the conductivity of the flui d. It is shown that the formation factor F as a function of the porosity ph i follows a power law F = a phi(-m), equivalent to the empirical Archie's l aw The exponent in varies with the microgeometry of the pore space and coul d therefore reflect the microstructure at the macroscopic scale. The prefac tor a of the power law however, is close to 1 regardless of the microstruct ure. For a given microgeometry of the Fore space, the variation of the resi dual electrical conductivity of the solid matrix induced by a finite conduc tivity ratio R-c does not significantly influence the variation of the effe ctive conductivity of the fluid-solid binary mixture unless the porosity is low.