Effect of contact angle on drainage and imbibition in regular polygonal tubes

Wettability and pore structure are primary factors in determining the capillary behavior of porous media. A key characteristic of the pore structure of real porous media is the angular corners of the pores. As a model of pore structure, angular tubes are much more realistic than the commonly used cylindrical tube model. However, their behavior is quite complicated because contact angle, corner angle, and the meniscus in the corners are all variables. The Mayer and Stowe-Princen (MS-P) theory of drainage, together with a detailed model of meniscus behavior in a corner during imbibition, enables the relationships between capillary pressure and saturation to be investigated as a function of contact angle and pore geometry. In this study, a general relationship between contact angle, corner angle, liquid saturation, and the curvature of a meniscus in the corner of an n-sided tube is derived. For any corner angle, there is a critical contact angle at which the meniscus becomes fiat and the capillary pressure falls to zero. Drainage of polygonal tubes (having cross-sections such as equilateral triangles and squares) is analyzed as a function of contact angle using the MS-P theory. For imbibition, there are two filling mechanisms: the tube can be filled by a meniscus advancing along the tube or it can be filled by expanding the menisci from the tube corners. For both mechanisms, the contact angle is treated as having either zero or finite contact angle hysteresis. Systematic changes in drainage and imbibition capillary pressure curves with contact angle are obtained. The results are qualitatively consistent with several features of the behavior of natural porous media, including the effect of wettability on the displacement efficiency of crude oil by water.