Porosity and permeability in ternary sediment mixtures

Permeability, k, and porosity, φ, were measured in mixtures of fine, medium, and coarse sand, where the volume fraction of each of the three components was systematically varied. The k was modeled well by the Kozeny-Carman equation for three-component mixtures by using a representative grain size parameter, d, computed by averaging the grain diameters of components recursively, with averaging methods based on whether finer components exist in sufficient volume to fill the pores within coarser components. The φ was modeled well by using linear interpolation with piecewise-planar models. We explored the use of differing numbers of piecewise-planar elements in the model, and illustrate the trade-off between the increased accuracy and the increased data requirements that both come from adding more elements. The k model is a function of both d and φ, but more sensitive to d. The k model gave results consistent with measured values when computed using either measured φ values, or values from any of the φ models.