Some aspects of wetting/dewetting of a porous medium

Abstract

Various features of wetting/dewetting of porous media are examined. The phenomenon of capillary hysteresis is illustrated by a vertical capillary tube which consists of an alternating sequence of convergent—divergent conical sections. A study of the kinetics of wetting of this tube by a liquid shows that when the velocity of the liquid/vapour meniscus is plotted against the height of penetration, it oscillates about the Washburn velocity—distance curve and performs Haines jumps. A general macroscopic equation is derived for the rate of wetting/dewetting of a porous medium having randomly distributed, finely divided particles or pores. Use is made of the Forchheimer equation, which is an extension of Darcy's equation to higher Reynolds numbers. Dissipative energy terms due to internal fluid calculaton and to irreversible movements of the meniscus strongly affect the initial rate of imbibition, but as the wetting progresses the Reynolds number decreases and Washburn's equation prevails. The application of percolation theory to wetting/dewetting phenomena in porous media is studied. The use of percolation theory by Kirkpatrick and Stinchcombe to find the electrical conductivity of inhomogeneous solid mixtures is adapted to determining the permeability of a porous medium to fluid flow. It is also shown how the relation between the “precolation probability” and the concentration of “unblocked” channels or pores can be applied in calculating the capillary pressure—desaturation curve in drainage. In particular, percolation theory predicts that a threshold pressure or break-through pressure is required before a non-wetting fluid can displace a wetting fluid in a porous medium. It is often convenient to use tree-like or branching lattice networks as models of a porous medium, because these are amenable to exact solutions in regard to percolation probability and permeability. The percolation properties of porous medium models which consist of lattice networks of cylindrical channels with a distribution of cross-sections and also of randomly packed rotund particles are examined and their relevance to wetting/dewetting phenomena discussed.