Investigation into contributions of fracture geometry characterization and interference to productivity of multi-fractured vertical gas well

Vertically fractured wells have been widely used to develop tight gas reservoirs. Characterizing the geometry of fractures created by hydraulic fracturing is a key factor influencing the productivity of such wells. Appropriately modeling the shapes of actual fractures is thus important for accurately predicting the well productivity. Past research in the area has tended to simplify fractures into straight lines, but this does not adequately represent the complex hydraulic fractures encountered in fractured reservoirs. In this study, we propose a generalized model for the productivity of a vertically fractured well to capture the characteristics of hydraulic fractures in gas fields. The proposed model accounts for several relevant mechanisms, including Knudsen slippage, characteristics of complex fracture geometry, and interference caused by multiple fractures. We validate the proposed model by applying it to a series of cases considered in the literature, and analytically examine key parameters such as the fracture number Nf and characteristics of the fracture geometry, including the length ratio a, width ratio b, branching angle theta and level n, fracture penetration ratio l0re, asymmetry in the length of fracture wing, and fracture intersection angle phi et al. The results show that there is a small drop in pressure between the inlet and outlet of the fracture. The well productivity is found to be positively associated with Nf, l0re, phi, and asymmetry in the length of the fracture wing. Furthermore, the productivity of a well intercepted by tree-shaped fractures primarily depends on a and n, and is almost entirely unaffected by b. By contrast, the well productivity gradually decreases with increasing theta. A tree-shaped fracture significantly enhances the well productivity by 110% (a = 0.9, n = 3), compared with a straight fracture. Finally, we provide an approach to increase the productivity of vertical wells based on the findings of this study.