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Hydraulic fracture is widely performed to enhance oil and gas production in the development of unconventional reservoirs. This paper proposes a numerical model for the calculation of the unpropped fracture conductivity of shale. This numerical model consists of three basic models, namely, the numerical reconstruction model of fracture morphology, fracture deformation model under closed stress, and fluid flow model. The numerical model can be used to analyze the influencing factors of the unpropped fracture conductivity of shale quantitatively. The results demonstrate that the fracture misalignment of shale is a prerequisite for unpropped fractures with conductivity at high closed stress. Furthermore, the unpropped fracture conductivity of shale decreases exponentially with the increase in closed stress. Moreover, closed stress is the factor having the most significant influence on the unpropped fracture conductivity of shale, followed by roughness and fracture morphology. The negative effect of closed stress can be reduced by increasing the fracture morphology during the fracturing operation. [ABSTRACT FROM AUTHOR]

Unpropped fractures constitute a major part of the fracture network in shale after hydraulic fracturing, and their closure process under in situ stress has a significant effect on the well production. In this study, a 3D simulation method based on core experiments and reverse engineering technology was established to simulate the unpropped fracture surface. A contact and deformation model of rock with a rough boundary and normal stress was constructed to investigate the closure process. The plastic characteristics of shale were taken into account through the embedment of the Drucker–Prager yield criterion. An unpropped fracture closure experiment was conducted for validating the model, and the influence of stress state, mechanical properties, fracture roughness and slippage degree on the closure process was analyzed. Numerical results demonstrate that an unpropped fracture with greater roughness and slippage degree possesses more flow regions and a larger residual width under a low stress state, which decreases rapidly as the normal stress rises because of the small contact area. Young's modulus is considered to have a positive effect on resisting fracture closure and maintaining effective flow regions under a high stress state. For the shale of the deep Longmaxi formation in south Sichuan, China, the simulation results indicate that the unpropped fractures always retain a residual width greater than 0.7 mm under a closure stress of 60 MPa, which is suitable for flow passages of oil and gas in shale. Methods for moderating the closure process were also analyzed. The numerical simulations provide insights on the unpropped fracture closure process under in situ stress, which will be helpful for fracturing design and production prediction of shale wells. • A 3D simulation method was established to simulate the unpropped fracture surface. • A contact and deformation model of rock with a rough boundary and normal stress was constructed. • An unpropped fracture with greater roughness and slippage degree possesses a larger residual width under a low stress. • Young's modulus has a positive effect on resisting the closure of unpropped fracture. [ABSTRACT FROM AUTHOR]