On non-uniqueness issues related to the permeability of a porous medium with a random porous structure

Abstract

This paper discusses the issue of non-uniqueness of the permeability of a porous medium with a random structure. The permeability range for 12,000 realizations of a random porous structure is examined using a recently-developed modelling approach, which results in up to two orders of magnitude permeability variations in low porosities. These findings are compared with previous results for 13,000 realizations with a scaled-down size, and it is shown that the permeability histogram does not converge towards a narrower spectrum using larger domain sizes. The similarity between advective transport in an ensemble of porous media and a random walk phenomenon, accepted in the literature, is revisited and the inadequacy of the assumptions employed is discussed. It is shown that the conventional definition of advective transport in a porous medium, which is generally assumed to follow Hadamard's definition of well-posedness, cannot be realised. The reconstruction of a porous structure from macroscopic parameters is in itself an ill-posed inverse problem. To clarify this issue, explaining the ontic and epistemic identifications of a porous medium, it is discussed that while ontic identification cannot be employed for transport analysis, epistemic identification leads to non-unique solutions. It is finally suggested that a paradigm shift is required for better formulation of the transport characteristics of porous media.