At present, the research on productivity of fractured vertical wells at home and abroad is mainly based on the existing seepage model, and the approximate solution is adopted to solve the productivity model. However, the accuracy of the productivity model has certain limitations. In order to correct the productivity equation of fractured vertical well and improve the prediction accuracy of production capacity, based on the previous research, a new productivity model with considering the factors such as fracture, heterogeneity and reservoir shooting degree is obtained from the most basic three-dimensional seepage equation. What's more, the model demonstration and sensitivity analysis are carried out for the fractured straight well productivity equation. The results show that in the early stage of the oil well production, productivity is mainly affected by the length of fractures and the degree of shot blasting, and the optimal fracture length and reasonable degree of reservoir blasting exist. In the middle and late stages of the oil well production, the productivity is mainly affected by fracture orientation, reservoir anisotropy and boundary condition. In the late stage of oil well production, productivity is mainly affected by reservoir width. This method can optimize the hydraulic fracturing parameters and guide the design of fracturing process. It can help to predict and analyze productivity.

In order to solve the problem that the pressure drop curve or the pressure recovery curve made by measured data was not fitting well with the classic model curve in low permeability reservoir, on the basis of previous studies and nonlinear flow of power law model, the method of differential discrete was used to build a quick and precise method for calculating the pressure, and the calculation method of dynamic permeability and conductivity was also investigated in detail. The factor of pressure curve model was analyzed by using control variable method. The result showed that the bigger the powerlaw index was, the greater the bending upwards magnitude of the pressure curve model was; with the coefficient of the wellbore storage and skin factor becoming larger, the reservoir fluid in low permeability reservoir cost more time to flow into steady flow; for closed boundary reservoir, the pressure model curve upturns and the reservoir resolution points were very clear. The pressure curve and the pressure derivative curve intersected. For the constant pressure boundary reservoir, it was on the contrary with the closed boundary reservoir, but after the fluid flows into the quasi steady state of radial flow, model curves were a cluster of parallel inclined lines.

In recent years the multilateral horizontal well plays a more and more important role in the development of low permeability oil and gas reservoir, which is the effective method to exploit shale reservoir and tight sandstone reservoir. In order to further improve the yield, hydraulic fracturing cracks could be used to increase oil and gas production of multilateral horizontal well. Based on the water and electricity resembling principle, the experiment inspected the crack length, osmotic conditions，branch number, the influence of horizontal segment of the openhole and closed conditions. The results show that there existed the optimal length of cracks and the yield of each branch horizontal well was different|there existed yield differences between openhole completion and closure completion under the conditions of the same branch.