PERMEABILITY VS. GRAIN SIZE: CORRECTING FOR SORTING

Despite the recognition of the strong correlation between grain size and permeability in granular materials, the complete relationship has eluded the scientific community for more than a century. Current methods for calculating permeability from grain size include large correction factors that need to be empirically determined. The problem with these methods is that they mostly do not adequately account for the effects of sorting (i.e. width of grain-size distribution) on the statistical distribution of pore throat sizes. Weight-based grain-size distributions require correction to numerical frequencies before pore throat diameters can be calculated, and the correction is strongly affected by the standard deviation (i.e. sorting). Once the grain-size distributions are corrected to numerical frequency, a statistical frequency of pore throat diameters and resulting pore throat flow parameters can be calculated. The pore throat mean diameter (in phi units) is m(ψ) = 2.6925 + m(W(d)) + ln(8) ∙ (σ(W(d)))² and the standard deviation is σ(ψ) = σ(W(d))/3, where m(W(d)) is the mean of the weight distribution and σ(W(d)) is the standard deviation of the fine-grained limb of the log-normal weight distribution curve. The permeability of the pore system (in mm) is given by k = c₁ ∙ 2^{-[4 ∙ [c2 ∙ m(ψ) – ln(16) ∙ (σ(ψ))^2]} / [(√3) ∙ 2^{-[2 ∙ m(N(d))]}], where c₁ is a constant that includes all of the geometric elements of the granular medium, c₂ is a constant that relates pore diameter to effective flow diameter, and m(N(d)) is the numerical mean grain size in phi units.