Permeability as a Function of the Size Parameters of Unconsolidated Sand

Abstract

The relation between permeability and the size parameters of unconsolidatedsand is approached by considering sands as logarithmic frequency distributionshaving the basic parameters mean size and standard deviation. Sieve separateswere mixed in accordance with the normal logarithmic probability law, so thatthe mean and standard deviation could be varied at will. Experiments wereconducted in which one parameter was kept fixed and the other varied; in thismanner the dependence of permeability on the individual parameters wasevaluated. It was found that permeability can be expressed as the product of apower function of the mean size and an exponential function of the standarddeviation. Introduction: Earlier studies of the effect of size of particles on the permeability ofunconsolidated sand have shown that the permeability varies with the square ofsome average diameter. This was first pointed out by Hazen in 1892 and verifiedby Slichter in 1898. Hazen's mean size was defined as the 10 percentile of thecumulative curve (i.e., size that is smaller than 90 per cent of thedistribution and larger than 10 per cent). Slichter's effective size, on theother hand, was found by Wilsey to agree with the 31 percentile. Fair and Hatchfound that the geometric mean size of sieve separates yielded the same powerfunction; Hulbert and Feben found that the permeability of sieve separatesvaried as the 1.89 power of the median diameter (i.e., the size associated withthe 50 percentile of the cumulative curve). Relatively few studies included the effect of the "sorting" of thesediment on the permeability. It was recognized that the nature of the sizedistribution, in terms of the spread of the particles about the mean, affectsthe permeability, but no systematic investigations of this effect are known tothe writers. Cloud demonstrated that the effect of the grain-size distributionon permeability is definitely measurable. In the present paper the authorsinvestigate this relation analytically, and show that the effects of the sizeparameters on permeability may be predicted for at least a restricted set ofconditions. T.P. 1492