  We describe two efficient methods of estimating the fluid permeability of
standard models of porous media by using the statistics of continuous Brownian
motion paths that initiate outside a sample and terminate on contacting the
porous sample. The first method associates the "penetration depth" with a
specific property of the Brownian paths, then uses the standard relation
between penetration depth and permeability to calculate the latter. The second
method uses Brownian paths to calculate an effective capacitance for the
sample, then relates the capacitance, via angle-averaging theorems to the
translational hydrodynamic friction of the sample. Finally, a result of
Felderhof is used to relate the latter quantity to the permeability of the
sample. We find that the penetration depth method is highly accurate in
predicting permeability of porous material.
