The mathematic model of transient flow of finite conductivity vertically fractured well in composite reservoir with arbitrary shape is established and solved by finite element method(FEM).The well bore storage factor and the skin factor are introduced by Laplace transformation and Stethfest inversion.And its typical productivity performance curves are drawn and analyzed.By analysos,it shows that the fractural conductivity,the skin effect and the heterogeneity all have a great effect on the productivity of f...