The permeability of a random medium: Comparison of simulation with theory

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Abstract
The results of numerical simulations of the lattice‐Boltzmann equation in three‐dimensional porous geometries constructed by the random positioning of penetrable spheres of equal radii are presented. Numerical calculations of the permeability are compared with previously established rigorous variational upper bounds. The numerical calculations approach the variational bounds from below at low solid fractions and are always within one order of magnitude of the best upper bound at high solid fractions ranging up to 0.98. At solid fractions less than 0.2 the calculated permeabilities compare well with the predictions of Brinkman’s effective‐medium theory, whereas at higher solid fractions a good fit is obtained with a Kozeny–Carman equation.