To predict fracture height in hydraulic fracturing, we developed and solved a hydraulic fracture height mathematical model aiming at high stress and multi-layered complex formations based on studying the effect of plastic region generated by stress concentration at fracture tip on the growth of fracture height. Moreover, we compared the results from this model with results from two other fracture height prediction models (MFEH, FracPro) to verify the accuracy of the model. Sensitivity analysis by case computation of the model shows that the hydraulic fracture growth in ladder pattern, and the larger the fracture height, the more obvious the ladder growth pattern is. Fracture height growth is mainly influenced by the in-situ stresses. Fracture toughness of rock can prohibit the growth of fracture height to some extent. Moreover, the increase of fracturing fluid density can facilitate the propagation of the lower fracture tip.

为了预测水力压裂的裂缝高度，我们在研究裂缝尖端应力集中产生的塑性区对裂缝高度增长的影响的基础上，开发并解决了针对高应力和多层复杂地层的水力裂缝高度数学模型。此外，我们将该模型的结果与其他两个裂缝高度预测模型（MFEH，FracPro）的结果进行了比较，以验证该模型的准确性。通过实例计算的敏感性分析表明，水力裂缝呈阶梯状增长，裂缝高度越大，阶梯状增长规律越明显。断裂高度的增长主要受原位应力的影响。岩石的断裂韧性可以在一定程度上抑制断裂高度的增长。此外，