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 and characteristics of the fracture geometry, including the length ratio , width ratio , branching angle and level , fracture penetration ratio , asymmetry in the length of fracture wing, and fracture intersection angle 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 , , , and asymmetry in the length of the fracture wing. Furthermore, the productivity of a well intercepted by tree-shaped fractures primarily depends on and , and is almost entirely unaffected by . By contrast, the well productivity gradually decreases with increasing . A tree-shaped fracture significantly enhances the well productivity by 110% (, ), compared with a straight fracture. Finally, we provide an approach to increase the productivity of vertical wells based on the findings of this study.

中文翻译：

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裂缝几何特征及对多裂缝直气井产能影响的研究

垂直压裂井已广泛应用于致密气藏开发。表征水力压裂产生的裂缝的几何形状是影响此类井产能的关键因素。因此，适当地模拟实际裂缝的形状对于准确预测油井产能非常重要。过去该领域的研究倾向于将裂缝简化为直线，但这并不能充分代表裂缝性油藏中遇到的复杂水力裂缝。在本研究中，我们提出了垂直压裂井产能的通用模型，以捕捉气田水力压裂的特征。所提出的模型考虑了多种相关机制，包括克努森滑移、复杂裂缝几何形状的特征以及多个裂缝引起的干扰。我们通过将所提出的模型应用于文献中考虑的一系列案例来验证该模型，并分析检查裂缝数量和裂缝几何特征等关键参数，包括长度比、宽度比、分支角度和水平、裂缝渗透率比值、裂缝翼长度不对称性、裂缝交叉角等。结果表明，裂缝入口与出口之间存在较小的压降。发现油井产能与 、 、 、 以及裂缝翼长度的不对称性呈正相关。此外，被树状裂缝截断的井的产能主要取决于 和 ，几乎完全不受 的影响。相比之下，井产能随着 的增加而逐渐降低。与直裂缝相比，树状裂缝可显着提高井产能 110% (, )。最后，我们根据本研究的结果提供了一种提高直井产能的方法。