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基于煤层的地质特征,推导了煤层气的非稳态扩散方程,建立了体积压裂水平井井底压力数学模型。通过拉普拉斯变换,引入Lord Kelvin点源解和泊松叠加原理,对数学模型进行了求解,获得了煤层气体积压裂水平井井底压力的瞬时点源函数基本解。根据井底压力特征曲线将非线性流动划分为8个阶段,并分析了水平井长度等参数对不同流动阶段的影响。
Based on the geological characteristics of coal seam, the unsteady diffusion equation of CBM is deduced, and the mathematical model of bottom hole pressure in horizontal fracturing of horizontal well is established. Through the Laplace transform, Lord Kelvin point source solution and Poisson superposition principle were introduced to solve the mathematical model. The basic solution of instantaneous point source function of bottom hole pressure in fractured horizontal well of CBM was obtained. According to the bottom hole pressure characteristic curve, the nonlinear flow is divided into eight stages, and the influence of horizontal well length and other parameters on different flow stages is analyzed.