Pore-scale modelling of diffusion in unconsolidated porous structures

A deterministic pore-scale model is used to predict the diffusivity ratio of unconsolidated porous media in which the diffusion process can be regarded as isotropic. The pore-scale model is based on a rectangular representative unit cell concept. A porosity-based weighted average of the two-dimensional and three-dimensional pore-scale models is proposed as a convenient model to predict the effective diffusion coefficient of isotropic systems. The diffusivity ratio of two-dimensionally staggered and non-staggered arrays of anisotropic solid rectangles is computed numerically and an existing weighted average model is applied to verify the numerical data. A particular case of a staggered array of solid squares, for which this weighted average model is no longer adequate, is outlined and the weighted average pore-scale model is proposed instead to predict the diffusivity ratio. The newly proposed pore-scale model and the present numerical results compare favourably with numerical data, experimental data and other predictive measures reported in the literature.