Local-porosity theory for flow in porous media

Abstract

A recently introduced geometric characterization of porous media based on local-porosity distributions and local-percolation probabilities is used to calculate dc permeabilities for porous media. The disorder in porous media is found to be intimately related to the percolation concept. The geometric characterization is shown to open a possibility for understanding experimentally observed scaling relations between permeability, formation factor, specific internal surface, and porosity. In particular, Kozeny's equation k\ensuremath{\propto}\ensuremath{\varphi}\ifmmode\bar\else\textasciimacron\fi{} $^{\mathit{b}}$ between effective permeability and bulk porosity and the relation k\ensuremath{\propto}${\mathit{F}}^{\mathrm{\ensuremath{-}}\mathit{h}}$ between permeability and formation factor are analyzed. A simple and general consolidation model is introduced. It is based on the reduction of local porosities and emphasizes the general applicability and flexibility of the local-porosity concept. The theoretical predictions are compared with the experimentally observed range for b and h, and are found to be in excellent agreement.