Research for Unsteady Seepage Flow of Asymmetrical Fractured Vertical Wells in Coalbed

Abstract

In this study, based on Green function and Laplace transformation, a pressure transient analysis semi-analytical evaluation model which can be used for coalbed reservoirs of finite conductivity asymmetrically fractured vertical well was established. The mathematical model considers asymmetrically fracture and finite conductivity. Fick law was used to describe gas diffusion in spherical matrix and Lagrange function was used to depict the unsteady desorption of coalbed gas. The influences of related parameters, such as artificial fracture conductivity, asymmetry factor, storativity ratio, cross-flow factor, dimensionless drainage radius and so forth, on the seepage flow were analyzed by using the established model. The results show that The percolation process include 6 stages (a) artificial fracture flow with the effect of wellbore storage effect; (b) transition flow; (c) linear flow between matrix and artificial fracture; (d) cross-flow between matrix and fracture in double medium fractures; (e) the pseudoradial flow stage of whole system; (f) closed boundary flow. Artificial fracture conductivity has great impact on whole production cycle. With the artificial fracture conductivity increases, the raise of capacity is very significant, especially for the production period after the influence of wellbore storage effect. Asymmetry factor is also important to whole production cycle. The bigger asymmetry factor is, the lower capacity is. Storativity ratio and cross-flow factor influence the degree and occurrence time of cross-flow between matrix and ________________________ Ming Li, Desheng Zhou, Xiong Liu, Chaoneng Zhao, Department of Petroleum Engineering, Xi'an Shiyou University, Xi'an 710065, China 261 fractures respectively. The smaller storativity ratio is, the more observer cross-flow is. The smaller cross-flow factor is, the earlier cross-flow will happen. The dimensionless drainage radius has only an effect on the later production. The smaller dimensionless drainage radius is, the earlier the closed boundary flow will happen.