Capillary Equilibrium in Porous Materials

Abstract

The experimental points which describe capillary pressure curves are determined at apparent equilibria which are observed after hydrodynamic flow has ceased. For most systems, the time required to obtain equalization of pressure throughout the discontinuous part of a phase is prohibitive. To permit experimental points to be described as equilibria, a model of capillary behavior is proposed where mass transfer is restricted to bulk fluid flow. Model capillary pressure curves follow if the path described by such points is independent of the rate at which the saturation was changed to attain a capillary pressure point. A modified suction potential technique is used to study cyclic relationships between capillary pressure and moisture content for a porous mass. The time taken to complete an experiment was greatly reduced by using small samples. Introduction Capillary retention of liquid by porous materials has been investigated in the fields of hydrology, soil science, oil reservoir engineering, chemical engineering, soil mechanics, textiles, paper making and building materials. In studies of the immiscible displacement of one fluid by another within a porous bed, drainage columns and suction potential techniques have been used to obtain relationships between pressure deficiency and saturation (Fig. 1). Except where there is no hysteresis of contact angle and the solid is of simple geometry, such as a tube of uniform cross section, there is hysteresis in the relationship between capillary pressure and saturation. The relationship which has received most attention is displacement of fluid from an initially saturated bed (Fig. 1, Curve Ro), the final condition being an irreducible minimum fluid saturation Swr. Imbibition (Fig. 1, Curve A), further desaturation (Fig. 1, Curve R), and intermediate scanning curves have been studied to a lesser but increasing extent. This paper first considers the nature of the experimental points tracing the capillary pressure curves with respect to the modes and rates of mass transfer which are operative during the course of measurement. There are clear indications that the experimental points which describe these curves are obtained at apparent equilibria which are observed when viscous fluid flow has ceased; and any further changes in the fluid distribution are the result of much slower mass transfer processes, such as diffusion. Unless stated otherwise, this discussion applies to a stable packing of equal, smooth, hydrophilic spheres supported by a suction plate with water as the wetting phase and air as the nonwetting phase. SPEJ P. 15ˆ

Hysteresis and Horizontal Redistribution in Porous Media

“…4 result from u = constant − H (S w ), where the constant is defined by the intersection point with ∂H im or ∂H dr . The hysteretic function H obtained this way gives a close match to the experiments of Morrow and Harris (1965). Having explicit expressions for P im and P dr , for instance the van Genuchten expressions, would result in a (semi) explicit expression for H .…”

“…Moreover, condition (2.7) ensures that scanning curves originating from arbitrary points on ∂H im or ∂H dr remain in H. The question arises how to choose and construct a function H that gives scanning curves close to experimental data and satisfies (2.7) for mathematical consistency. We present a construction that is based on the experiments of Morrow and Harris (1965). Their results for drying and wetting are shown in Fig.…”

“…Here the variables are as in Morrow and Harris (1965): the saturation is unscaled (0 < S wr < S w < 1 − S ar ) and the suction, capillary pressure u in this context, is in cm of water. In the construction of H we use the same variables to get a meaningful comparison.…”

“…This works quite well if the porous medium is going through only a wetting or a drying process. But if there is a switch between the two, then the P c -S w curves span the region between the P im and P dr curves in the form of scanning curves (Morrow and Harris 1965). Typical behaviour is shown in Fig.…”

C Horizon

“…Poulovassilis (1962Poulovassilis ( , 1970a found a good agreement between the predicted and the measured scanning curves for glass beads and sand. Other investigators reported considerable discrepancies between the theory and observations; Topp and Miller (1966), Morrow and Harris (1965), and Bomba and Miller (1967) observed discrepancies for glass-beads medium; Vachaud and Thony (1971), Talsma (1970), and Poulovassilis and Childs (1971) observed them for sand; Topp (1969Topp ( , 1971a observed them for various loam soils. It seems that the measured discrepancies are due partly to the method of measurement because the poorest agreement between theory and measurements has been observed for unsteady-flow experiments.…”