Krumbein and Monk found an empirical relationship for the permeability of unconsolidated and as a function of the mean grain diameter (by weight) dW and the standard deviation &sgr;ϕ2(ϕ=-log2 d for d in millimeters). This expression, for lognormal grain size distributions, is k=760dW exp(-1.31&sgr;ϕ) for dW in millimeters, &sgr;ϕ in ϕ units, and k in darcys. Their data have been reanalyzed to express the permeability in terms of the mean grain diameter by number, dN. This representation is a more physical one because the permeability depends upon the number of pores of particular sizes (i.e., upon the number distribution function of the pore sizes). It is expected that the pore size distribution function (by number) is more closely related to the grain size distribution function by number than to the grain size distribution function by weight. It is found that equally good fits of all their data are given by k=665dN2 exp (1.78&sgr;ϕ3)=665dW2exp)-2.88 &sgr;ϕ2 +1.78&sgr;3ϕ) and k=648dN2 (1+2.77&sgr;ϕ3). It was found that the expression k=735dN2 gives permeability values that are accurate to 10% for loose, unconsolidated sands (porosity ≂=40%¿5%) with standard deviation &sgr;ϕ in the range 0≤&sgr;ϕ≤0.5. These results may be applied to porous rocks if Berg's semitheoretical/empirical determination of the permeability variation with porosity is used (for porosities in the range 30%≤n≤45%). An expression for the theoretical variation of permeability with effective confining pressure is also given. |