In this paper, a semi-analytical mathematical model of pressure transient analysis (PTA) for multi-wing fractured vertical well (MWFV) in coalbed methane (CBM) reservoir is proposed, which considers the complexity of porous media by fractal geometry, the anomalous diffusion based on fractional calculus and the stress sensitivity represented by the exponential expression. Then through line source theory, dimensionless transformation, Pedrosa transformation, and other methods, the solution of the bottom hole pressure is obtained. At last, the PTA curve is presented by the Stehfest inversion method, and seven flowing regimes are identified. It can be observed that after introducing fractal geometry and fractional calculus, the PTA curve is quite different from the traditional curve in the slope of the derivative curve. The influences of related parameters are discussed, including mass fractal dimension, anomalous diffusion coefficient, number of hydraulic fractures, fracture angle, and stress sensitivity factor. Relevant results can provide better guidance to understand the CBM production performance in MWFV.

本文提出了煤层气（CBM）储层中多翼压裂直井（MWFV）压力瞬态分析（PTA）的半解析数学模型，该模型通过分形几何考虑了多孔介质的复杂性，反常基于分数阶微积分的扩散和由指数表达式表示的应力敏感性。然后通过线源理论、无量纲变换、Pedrosa变换等方法得到井底压力解。最后，利用 Stehfest 反演方法给出了 PTA 曲线，确定了 7 种流态。可以看出，引入分形几何和分数阶微积分后，PTA曲线在导数曲线的斜率上与传统曲线有很大不同。讨论了质量分形维数、反常扩散系数、水力裂缝条数、裂缝角度、应力敏感因子等相关参数的影响。相关结果可为了解 MWFV 中煤层气生产性能提供更好的指导。