Engineering Reasearch - Permeability as a Function of the Size Parameters of Unconsolidated Sand (Petr. Tech., July 1942)

The relation between permeability and the size parameters of unconsolidated sand is approached by considering sands as logarithmic frequency distributions having the basic parameters mean size and standard deviation. Sieve separates were mixed in accordance with the normal logarithmic probability law, so that the mean and standard deviation could be varied at will. Experiments were conducted in which one parameter was kept fixed and the other varied; in this manner the dependence of permeability on the individual parameters was evaluated. It was found that permeability can he expressed as the product of a power function of the mean size and an exponential function of the standard deviation. Earlier studies of the effect of size of particles on the permeability of uncon-solidated sand have shown that the permeability varies with the square of some average diameter. This was first pointed out by Hazenl in 1892 and verified by Slichter2 in 1898. Hazen's mean size was defined as the 10 percentile of the cumulative curve (i.e., size that is smaller than 90 pel cent of the distribution and larger than 10 per cent). Slichter's effective size, on the other hand, was found by Wilsey3,4 to agree with the 31 percentile. Fair and Hatch6 found that the geometric mean size of sieve separates yielded the same power function; Hulbert and Feben6 found that the permeability of sieve separates varied as the 1.89 power of the median diameter (i.e., the size associated with the 50 percentile of the cumulative curve). Relatively few studies included the effect of the "sorting" of the sediment on the permeability. It was recognized that the nature of the size distribution, in terms of the spread of the particles about the mean, affects the permeability, but no systematic investigations of this effect are known to the writers. Cloud7 demonstrated that the effect of the grain-size distribution on permeability is definitely measurable. In the present paper the authors investigate this relation analytically, and show that the effects of the size parameters on permeability may be predicted for at least a restricted set of conditions. Properties OF Sediments Recent investigations have shown that essentially all the geologically important characteristics of sediments may be expressed in terms of six measurable quanti-tities possessed by each clastic sedimentary particle. These attributes are: (I) size, (2) shape (sphericity), (3) roundness (angularity) , (4) mineralogical composition (density), (5) surface texture, (6) orientation. Each of these characteristics may be defined in several manners. Size may be expressed in terms of sieve mesh, settling velocity, volume, etc. Sphericity is a shape concept introduced by Wadell;8 it is essentially a measure of the ratio of the surface area of an equivalent sphere to the surface area of the particle. The same