The Porosity and Permeability of Binary Grain Mixtures

Abstract

AbstractThe processes that control binary mixing of two sizes of grains have been investigated theoretically and validated by comparison with experimental data. These seemingly simple experiments are difficult to carry out with the degree of precision needed to test the models. We have developed a methodology allowing porosity and permeability to be measured to within ± 4.415% and ± 4.989% (at a flow rate of 5.13 cm3/s) of each value, respectively. Theoretical considerations recognise mixing processes: (1) an interstitiation process whereby small grains fit between larger grains and (2) a replacement process whereby large grains replace smaller grains and the porosity associated with them. A major result of this work is that the theoretical models describing these two processes are independent of grain size and grain shape. The latter of these two findings infers that the models developed in this work are applicable to any shape of grain or type of packing, providing that a representative porosity of each size of grain pack is known independently, either experimentally or theoretically. Experimental validation has shown that the newly developed relationships for porosity described measurements of porosity for near-ideal binary mixtures extremely well, confirming that porosity is always reduced by binary mixing, and that the degree of reduction depends upon the size of the ratio between the two grain sizes. Calculation of permeability from the packing model has also been done. Six different permeability estimation methods have been used. It was found that the most accurate representations of the experimental permeability were obtained (1) when the exact RGPZ (Revil, Glover, Pezard, Zamora) method was used with the porosity mixing models developed in this work and (2) when the exact RGPZ method was used with the weighted geometric mean to calculate a representative grain size.