The pressure transient behavior of hydraulically fractured wells has been the subject of considerable study over the recent years. Several investigators have presented solutions of the fundamental equations, identified qualitative diagnostic trends and suggested integral techniques. This paper presents a new method to solve the problem of analysis of well test data of the hydraulically fractured well.

The new mathematical model for the vertically fractured well in the dual-porosity and homogeneous reservoirs was founded by using the elliptic flow model and the integral method of conservation mass. The solution for the new model was obtained in real space. The type curves for the vertically fractured well in both homogeneous and dual-porosity reservoirs with and without wellbore storage and skin effect were calculated. In order to consider the wellbore storage and skin effect, the techniques of Laplace numerical transformation and Laplace numeral inversion were used. The special results for homogeneous reservoir have been identified by compared with the results of other authors, such as the infinite conductivity solution of A.C. Gringarten, the finite conductivity solution of H. Cinco-ley and the finite conductivity solution of M.J.Economades which considered the wellbore storage. They all have the same identities. Two field examples are used to illustrate the use of the new method.

The characteristics of the type curves for both homogeneous and dual-porosity reservoir are described. For the dual-porosity reservoir, the type curve presents seven flow periods: the wellbore storage controlled period, the skin effect controlled period, the bilinear flow period, the first transient period, the dual-porosity characteristic flow period, the second transient flow period, and the radial or pseudo-radial flow period.

The solutions have the following advantages: The solution may be used for both homogenous and dual-porosity reservoirs, and for both infinite and finite conductivity vertical fracture. The range of the dimensionless conductivity is from 0.001 to 500. Even more, the type curve is quickly calculated by using this method than any others. The new sets of type curves can be directly used in the oil field.