Permeability versus conductivity for porous media with wide distribution of pore sizes

Using recent results on random resistor networks, we derive the relation between the permeability and the conductivity of liquid-saturated porous materials, presumably exact in the limit of a wide distribution of pore sizes. This relation also applies to some continuum percolation models, and the range of its universality is discussed. Some discrepancy is found with the previous anlaysis of Katz and Thompson [Phys. Rev. B 34, 8179 (1986)]. Mechanisms are proposed to recover agreement with their experiments. The pore-size parameter {Λ} characterizing surface effects is computed.