Numerical experiments with idealised pore space geometries and shear-thinning fluids.

In an endeavour to describe quantitatively the water flow and solute transport in soils and other heterogeneous porous media, various different approaches have been introduced in the past decades, including double porosity, double permeability and other multiple-continua approaches. Recently, a promising methodology to identify experimentally the pore structure of porous media has been proposed, where a discrete distribution of effective pore radii is established based on saturated flow experiments with non-Newtonian (shear-thinning) fluids, as described by Abou Najm and Atallah (2016) and in other works. In this particular concept, the porous media is idealised as a bundle of capillaries with only a reasonably small number of distinct values of their radii. This allows to identify the pore radii and the contributions of the corresponding pore groups to the total flow by performing and evaluating a reasonable number of flow experiments.

In an attempt to understand better the relation of the effective discrete pore radii distribution concept (with a given number of distinct pore radii allowed) to the structure of the porous media, we perform numerical experiments with other idealised geometries of the pore space. The saturated flow experiments with shear-thinning fluids are simulated by finite element method and then, based on the resulting flow, the discrete pore radii distributions are established and compared with the original geometry. For simplicity, we stick to one-dimensional models analogous to Poiseuille or Hagen-Poiseuille flow. The idea is to examine pore size distributions that are continuous rather than discrete, while keeping the advantage of a perfectly controlled and comprehensible idealised geometry. This in-silico approach may later serve as a supporting tool for studying various aspects of the addressed experimental methodology, e.g., in taking into account realistic non-Newtonian rheology, proposing an optimal set of experiments, or contemplating links with solute transport models.