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This paper discusses the issue of non-uniqueness of the permeability of aporous medium with a random structure. The permeability range for 12,000realizations of a random porous structure is examined using arecently-developed modelling approach, which results in up to two orders ofmagnitude permeability variations in low porosities. These findings arecompared with previous results for 13,000 realizations with a scaled-down size,and it is shown that the permeability histogram does not converge towards anarrower spectrum using larger domain sizes. The similarity between advectivetransport in an ensemble of porous media and a random walk phenomenon, acceptedin the literature, is revisited and the inadequacy of the assumptions employedis discussed. It is shown that the conventional definition of advectivetransport in a porous medium, which is generally assumed to follow Hadamard'sdefinition of well-posedness, cannot be realised. The reconstruction of aporous structure from macroscopic parameters is in itself an ill-posed inverseproblem. To clarify this issue, explaining the ontic and epistemicidentifications of a porous medium, it is discussed that while onticidentification cannot be employed for transport analysis, epistemicidentification leads to non-unique solutions. It is finally suggested that aparadigm shift is required for better formulation of the transportcharacteristics of porous media.

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