Permeability and effective porosity of porous media

The concept of permeability of porous media is discussed, and a modification of Kozeny's permeability equation to include the effect of effective porosity is introduced. An analytical expression for the specific surface area of a system constructed of randomly placed identical obstacles with unrestricted overlap is derived, and a lattice-gas cellular automaton method is then used to simulate the dependence on porosity of permeability, tortuosity, and effective porosity for a flow of Newtonian uncompressible fluid in this two-dimensional porous substance. The simulated permeabilities can well be explained by the concept of effective porosity, and the exact form of the specific surface area. The critical exponent of the permeability near the percolation threshold is also determined from the simulations.