一种已压裂页岩气水平井的产量预测新方法

水平井加多段压裂已成为页岩气藏的主要开发模式，针对压裂后的页岩气藏具有人工裂缝、天然裂缝及纳米
级孔隙等多种流动空间，开展了渗流数学模型的建立与求解研究。通过等效简化构建了三线性渗流模型，考虑了具有
解吸吸附作用的基质空间线性渗流、以等效天然裂缝为主的裂缝网络空间线性渗流、等效主裂缝内的线性渗流。对
三重渗流分别建立了极坐标空间和拉普拉斯空间下的数学模型，并对数学模型进行求解，得出单井气藏的产能公式和
井底压力公式。应用所建立模型，对实际压裂水平井的产能进行了求解，与实际产量进行对比，表明利用文中方法建
立的模型及解析解进行产能预测分析是可行的。

A New Productivity Prediction Method for Fractured Horizontal Wells in Shale Gas Reservoirs

Horizontal wells with hydraulic fracturing are going to be the main method of shale gas production. Fractured shale
gas reservoirs have a variety of seepage patterns due to lots of the natural or artificial fracture and nano-scale pore. Establishment
and solution of percolation mathematical model has a strong theoretical and practical value. Equivalent simplified three linear
flow model is constructed，which includes matrix space linear seepage with desorption and adsorption，mainly equivalent natural
fracture of fracture network space linear seepage，linear seepage within the main fracture. Under the polar coordinate space
and the Laplace space，we established mathematical models for triple seepage model，and solved them. Finally，we developed
single well productivity formula of gas reservoir and bottom hole pressure formula. By applying the established model and the
analytical solution，a fractured horizontal well productivity has be calculated. Compared with the actual production，the result
shows that analytical solution based on the model can forecast production capacity.