Resistance jumps in mercury injection in porous media

Recent experiments by A. H. Thompson, A. J. Katz, and R. A. Raschke [Phys. Rev. Lett. 58, 29 (1987)] have demonstrated that, when mercury is injected into a porous material, the electrical resistance of the sample decreases in a stepwise manner, with a power-law distribution of step sizes. Here we present computer simulations and a theoretical analysis of this process based on the model of invasion percolation. The simulations are consistent with the prediction that the number N of resistance steps greater in size than a given ΔR should scale as (ΔR${)}^{\mathrm{-}\lambda }$, with λ given in terms of the conduction exponent t and correlation-length exponent ν by 3ν/(t+3ν). This gives λ∼0.58, somewhat smaller than the experimental value 0.81 given by Thompson, Katz, and Raschke. It is argued that neither the resistance jumps themselves nor the hysteresis and long relaxation times observed in the experiment provide evidence against the application of percolation theory to fluid displacement in porous media. From the viewpoint of computer simulation, it is suggested that measurement of the exponent λ may be a good way of obtaining the value of the conduction exponent t.