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 s tructure 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 q uite 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 behavio r in a corner during imbibition, enables the relationships between cap illary pressure and saturation to be investigated as a function of con tact angle and pore geometry. In this study, a general relationship be tween contact angle, corner angle, liquid saturation, and the curvatur e of a meniscus in the corner of an n-sided tube is derived. For any c orner angle, there is a critical contact angle at which the meniscus b ecomes fiat and the capillary pressure falls to zero. Drainage of poly gonal tubes (having cross-sections such as equilateral triangles and s quares) is analyzed as a function of contact angle using the MS-P theo ry. 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 e xpanding the menisci from the tube corners. For both mechanisms, the c ontact angle is treated as having either zero or finite contact angle hysteresis. Systematic changes in drainage and imbibition capillary pr essure curves with contact angle are obtained. The results are qualita tively consistent with several features of the behavior of natural por ous media, including the effect of wettability on the displacement eff iciency of crude oil by water.