Theory and modelling of the effects of grain sorting, compaction & cementation on porosity and permeability

Just how much do sorting, cementation and compaction control the porosity and permeability of rocks? In this work we start with making extremely accurate porosity and permeability measurements on binary grain mixtures, arriving at good agreement between them and theoretical results. 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. The newly developed theoretical framework includes both the interstitiation mixing process and several replacement processes.

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 carried out. 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 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. For mixtures where there is a large difference in grain sizes, permeability (k) varies little for the ranges of mixtures from 28% to 100% of small grains (about 4*k), only increasing significantly as the fraction of small grains falls below 28% to zero (to 2 orders of magnitude in k) because the small grains then only partially occupy the space between the large grains. For mixtures of grains of similar sizes, the situation is remarkably different. The variation in permeability for small grain fractions between 100% and about 28% is much amplified (2 orders of magnitude in k), while the increase in permeability as the fraction of small grains falls from about 28% to zero is similar to the other case, and perhaps slightly less pronounced (about 1.5 orders of magnitude in k). This counterintuitive behaviour is important for the interpretation of how sorting affects permeability, implying a greater spread of permeabilities for rock composed of grains with a small difference in grain size.