Closure of rough surfaces under normal closure stress is investigated in this study. Rough surface closure model presented in this paper is based on surface asperity deformation. The main components of deformation are asperity compression and half-space deformation. Mechanical interaction among asperities which is a consequence of half-space deformation is considered in the model and its impact on the closure behavior is analyzed. Asperities are assumed to be elastic-perfectly-plastic materials and therefore may experience inelastic deformation under closure stress. Modeling results indicate that a significant portion of closure takes place earlier on at low stress levels because there are fewer asperities in contact initially. Asperity inelastic deformation is found to influence rough surface closure with its degree of impact depending on surface profile. A mechanical interaction sensitivity analysis indicates that neglecting interaction among asperities may lead to erroneous results particularly in surfaces with closely spaced asperities. By conducting an analysis on the elastic properties of asperity and half-space we found that the normal stiffness is much more influenced by Young’s modulus of half-space rather than that of asperity.


Acid fracturing is a stimulation technique which is being used in carbonate reservoirs. This technique is considered as an alternative to the well-known propped hydraulic fracturing. Fractures tend to close due to the in-situ stresses acting normal to the plane of fracture. Fracture closure has detrimental effect on the conductivity and therefore, should be prevented. Proppant is widely used in the hydraulic fracturing process and this material serves to keep the fracture open against closure stress. However, the mechanism by which the fracture is being held open is essentially different in acid fracturing technique.

Acid fracturing is a complex process in which acid reacts with rock and removes some parts of it, resulting in two random rough surfaces. Asperities on these surfaces act as pillars to keep the fracture open. Fracture surfaces come into contact after the pump pressure is dissipated. The success of an acid fracturing job depends on how well the asperities withstand the closure stress. Increasing effective stress often reduces the fracture aperture and its conductivity.

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