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Wang Zhikai, Cheng Linsong, Cao Renyi, Wang Jin, Jia Pin, Wang Xuanru. Semi-analytical method for unstable pressure of 3D fracture network. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(8): 2246-2256. DOI: 10.6052/0459-1879-21-183
 Citation: Wang Zhikai, Cheng Linsong, Cao Renyi, Wang Jin, Jia Pin, Wang Xuanru. Semi-analytical method for unstable pressure of 3D fracture network. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(8): 2246-2256. DOI: 10.6052/0459-1879-21-183

SEMI-ANALYTICAL METHOD FOR UNSTABLE PRESSURE OF 3D FRACTURE NETWORK

• Due to the influence of in-situ stress and fracturing technology, the distribution of hydraulic fracture network in highly deviated wells is complex with different inclined directions, different distribution forms and different penetration degrees. In this paper, the fracture surface is discretized into several rectangular micro elements to realize the effective characterization of fracture morphology. The seepage process is divided into two stages: matrix flow to fracture and fracture flow to wellbore. The numerical solution of unsteady seepage in discrete fracture surface is constructed by using finite difference method, and the analytical solution of unsteady seepage in matrix is constructed by combining closed boundary source function and superposition principle. The solution of the unstable pressure of the 3D fracture network is obtained by coupling the numerical solution of flow in fracture and the analytical solution of flow in matrix. Based on the integral mean value theorem, a solution method of point source and special line source instead of surface source is proposed to solve the seepage in matrix. The feasibility and applicable conditions of this method are analyzed, which can ensure the accuracy of the model and improve the calculation efficiency. The research shows that the point source function area fraction method can accurately solve the bottom hole pressure dynamic of 3D pressure fracture network in the matrix, but the calculation is quite inefficient. The point source and special line source approximate surface source method based on the integral mean value theorem can greatly improve the calculation efficiency, and can achieve higher accuracy when the fracture micro element division is more precise (the dimensionless side length of micro element is less than 0.15). Based on this model, the flow regimes and related sensitivity analysis are analyzed. The results show that the fracture conductivity, fracture dip angle, fracture height and fracture interval have great influence on the typical well test curves of highly deviated wells. Fracture dip angle and fracture interval mainly affect the pressure and pressure derivative curve from linear flow to early radial flow, especially when the fracture height is small, the pressure derivative has backflow phenomenon.

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