Explicit relation between relative permeability and structural parameters in stochastic pore networks

• Published in: Chemical engineering science 1989, Vol.44 (12), p.2967-2977
• Main Authors: Petropoulos, J.H., Petrou, J.K., Kanellopoulos, N.K.
• Format: Article
• Language: English
• Subjects: Chemistry; Colloidal gels. Colloidal sols; Colloidal state and disperse state; Exact sciences and technology; General and physical chemistry
• ISSN: 0009-2509; 1873-4405
• DOI: 10.1016/0009-2509(89)85106-1

It is shown, by suitable use of the effective medium approximation, that the relative permeability of a stochastic network consisting of idealised pores of randomly varying radius, which are progressively constrited and/or blocked, can be expressed analytically as an explicit function of suitable parameters characteristic of pore and network structure as well as the physics of flow. In this manner, it is possible to: (i) gain a much deeper insight into the dependence of relative permeability on the breadth and shape of the pore radius probability distribution as well as the network connectivity, and (ii) greatly simplify the approximate evaluation of the relative permeability of given stochastic networks under suitable conditions. These points are illustrated by a detailed study of the case of (Knudsen) gas relative permeability of cylindrical pore networks, in the presence of an adsorbed and condensed foreign vapour. Results of immediate importance for experimental pore structure analysis, which emerged from this study include the capability of: (i) estimating the network connetivity, and (ii) testing the self-consistency of pore size distributions determined experimentally by conventional vapour sorption isotherm analysis.