Conceptual modeling of temperature effects on capillary pressure in dead-end pores

Abstract

The effect of temperature on the liquid–gas interface and consequently on the capillary pressure in unsaturated dead-end pores is conceptually modeled in this paper. Trapping of non-wetting fluid (e.g., air) in the dead-end pores impacts the capillary pressure–saturation relationship and affects the continuous flow of wetting fluids. In the dead-end pore, which is assumed to be a simple vertical cylindrical capillary tube with one end closed and the other end open to the liquid body, the dependence of solid–liquid and solid–air interfacial tensions on temperature and its subsequent effects on the contact angles are deduced. A non-linear ordinary differential equation, using the Young–Laplace equation, in terms of a contact-angle-sensitive temperature function is derived and numerically solved using the fourth order Runge–Kutta method. This temperature function is used to obtain the capillary pressure–temperature relationship for a solid–liquid–air capillary system. Two example problems, first a glass–water–air capillary system and second a polytetrafluoroethylene–n-hexadecane–air capillary system, are solved here. A linear decrease in capillary pressure with temperature is observed, suggesting that entrapped air affects capillary pressure in dead-end pores. A similar linear decrease in capillary pressure, consistent with experimental observations, is observed for open-end pores.