Modeling of capillary pressure in horizontal rough-walled fractures in the presence of liquid bridges

Abstract

Capillary continuity between adjacent matrix blocks through formation of liquid bridge controls the recovery factor of gravity drainage process in fractured reservoirs. However, stability of liquid bridges as well as related capillary pressure in horizontal rough fractures is not well discussed in the available literature. In this work, new models of rough-walled fracture are developed and the role of roughness size and frequency on formation of liquid bridge and fracture capillary pressure are investigated. The Young-Laplace equation is numerically solved to characterize the liquid bridge formed in the proposed models of rough fractures. Critical fracture aperture for a range of liquid saturations, various roughness models and wettability conditions, is computed. Moreover, an expression is proposed to predict critical fracture aperture as a function of liquid saturation and contact angle for different models of rough fracture. Thereafter, as an interesting result, variation of fracture capillary pressure with liquid saturation, fracture aperture and wettability is evaluated for different models of rough fractures. It has been found that the trend of obtained fracture capillary pressure is similar to a typical matrix capillary pressure curve. The results also revealed that fracture capillary pressures as high as 1 psi (6.9 KPa) are viable when liquid saturation in the fracture is low (<5%) and fracture is sufficiently thin. Increasing wettability to liquid phase decreases the critical fracture aperture and enhances the fracture capillary pressure. At last, a semi-empirical model for capillary pressure as a function of effective fracture aperture, fracture roughness, contact angle and liquid saturation is proposed. The findings of this work help to better understand how liquid bridge stability and fracture capillary pressure may change in rough-walled horizontal fractures.