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
Mathematical Simulation of Using a Combination of Mesh and Porous Materials as a Phase Separator
