A closure model is developed for rough fractures along with a fluid flow model to predict fracture conductivity decline under normal closure stress. The closure model is based on surface asperity and half-space deformation considering the effect of mechanical interaction among asperities and inelastic deformation. Fracture aperture profile that is obtained from the closure model is then used in the fluid flow model to predict fracture conductivity. Hydraulic conductivity of synthetic surface profiles are compared to investigate the impact of surface pattern on conductivity. Simulation results indicate that considering half-space deformation and mechanical interaction among asperities affect conductivity decline behavior. Different aperture averaging methods are found to result in noticeably different conductivity results. Narrower and deeper channels undergo less conductivity decline compared to wider and shallower channels.
Rough fractures tend to close due to farfield stresses acting on the plane of fracture. Quantification of fracture closure is crucial to predicting hydraulic conductivity behavior. It is, therefore, necessary to study the closure mechanisms in rough surfaces. The concepts of fracture closure and contact mechanics can be applied to acid fracturing and unpropped fracturing which are of great interest in the petroleum industry.
Several attempts have been made to investigate the closure of rough surfaces in contact. The problem of rough surface closure is addressed in many analytical (Greenwood & Williamson 1966, Brown & Scholz 1985), numerical (Hopkins 1991, Pyrak-Nolte & Morris 2000), and experimental (Bandis et al. 1983, Marache et al. 2008) works. It is worth mentioning that the literature is mainly concerned with the elastic contact of rough surfaces.
Hydraulic conductivity of rough surfaces is extensively studied because of its important implications in different branches of science and engineering. The hydraulic conductivity of rough fractures is studied in many experimental and analytical works (Witherspoon et al. 1980, Tsang and Witherspoon 1981, Gong et al. 1998). It is our aim to investigate the impact of fracture closure on fracture conductivity and also study the importance of fracture surface pattern in conductivity decline behavior.