Grain-mixing modelling of the porosity and permeability of binary mixtures

The porosity and permeability of binary mixtures of spherical grains were modelled theoretically and studied empirically against such variables as grain-size, grain-size ratio, grain volume fraction and grain packing. The results confirmed that binary mixing of different-sized grains always results in a porosity loss. The degree of porosity loss was found to be a function of the grain-size ratio. Consequently, the mixture with the highest grain-size ratio of 3 dropped to the lowest minimum porosity of 0.3116 while the mixture with the minimum grain-size ratio of 1.5 experienced the highest minimum porosity of 0.3716. The observed porosities could not be described by some of the existing porosity models including the ideal and fractional packing models due to the assumptions of ideal packing and no-mixing respectively underlying these models. Thus, a corrected fine packing (or replacement) model was developed during this research to incorporate the grain-size ratio effect on porosity. Together with the interstitiation model, the corrected replacement model gave the best fit to the observed porosities. The mixtures' permeabilities could not be modelled by the grain-size/porosity-dependent permeability models because these models tend to mimic the trend of the representative porosity used. The weighted geometric/harmonic mean permeability models (weighted by volume fraction) described the observed permeabilities best.