| Some theoretical problems of solving flowing equations with Finite Element Method(FEM) are studied deeply in this thesis, and some numerical simulations are performed for the flow rate of hydraulically fractured well.1. Equations of finite element method are established systematically in theory, including single phase flow, oil-water two phases flow. The linear equations are resolved by variable band Gauss Method, which enormously reduces the occupation in the computer memories.2. To the transient flow of single phase fluid, the solution of FEM is compared with analytical solution, in respect of planar one-dimension flow, radial flow and three-dimensions flow. It is shown that the FEM and the program provided in the thesis are correct, precise and reliable to solve reservoir problems.3. The configuration of hydraulic fracture is described carefully. The geometry of fracture is assumed as cuneiform, and the permeability changes with only distance, or changes with only time, or changes with distance and time simultaneously, Under the assumption, the well performance is simulated, and the effects of this factors are analyzed.4. The description to curved fracture is implemented and the flow rate is simulated. These results significative to study the effect of complex fracture configuration on hydraulically fractured well.5. A numerical simulator is developed by Fortran 90 , the idea of high modularization and high structuralization are adopted in the program , which has perfect structure and high calculation efficiency, and it is easy to be maintained and be extended.
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