Modified drag theory of permeability

Abstract

A modified version of the drag theory of permeability for a granular porous medium is presented. The technique employs the Brinkman equation to interpolate between the microscopic (Stokes) equation and the macroscopic (Darcy) equation, but differs from previous treatments in that the medium is built up iteratively beginning with the smallest grains. A discussion of the geometry corresponding to this construction is presented. The result for the permeability takes the form of a nonlinear differential equation which may be integrated numerically for a given choice of porosity and grain size distribution. Numerical results for the case of spherical grains with a log‐normal distribution of sizes are presented, and compared to the predictions of the Kozeny equation for the same geometry. It is found that for narrow distributions the present method gives a somewhat higher permeability than the Kozeny equation, but that for wide distributions it gives a lower permeability. It is shown that in the limits of narrow or wide distribution the differential equation for the permeability may be solved explicitly, and it is suggested that in the latter case the result may be exact.