Abstract: Based on the flow mechanism of hydraulic fractured wells, through integrating linear-flow model and effective well-radius model, a new model of well test analysis for wells with vertical fiacture was established. In the model, wellbore storage, the damage in the wall of fracture and all kinds of boundary conditions are considered. The model is concise in form, has intact curves and computes fast, which may meet the demand of realtime
computation and fast responded well test interpretation. A new method to determine effective well radius was presented, and the correlation between effective well radius and the fracture length, fracture conductivity, skin factor of fracture was given. Matching flow rate or pressure tested, the optimization model that identified formation and fracture parameters was set up. The automatic matching method was presented by synthetically using step by step linear least square method and sequential quadratic programming. At last, the application was also discussed. Application shows that all of these results can analyze and evaluate the fracturing treatment quality scientifically and rationally, instruct and modify the design of
fracturing and improve fracturing design level.

Key words: generalized inverse, critical point, polar decomposition