Semi-Analytical Solutions for a Partically Penetrated Well with Wellbore Storage and Skin Effects in a Double-Porosity System with a Gas-Cap

Morteza Dejam
Supervisors: Dr. Hassan Hassanzadeh, Dr. Zhangxin Chen


The subject of pressure transient analysis of double-porosity reservoirs has been studied extensively in the literature. The impacts of the skin factor and wellbore storage coefficient on the results of well tests have been widely investigated. There have been a limited number of studies on the effect of a gas cap on the pressure transient response of fractured formations.

The pressure transient behavior of a partially penetrates well in an infinite-acting double-porosity system with a constant pressure at the top boundary, based on a semi-analytical solution of the 2D diffusivity equation using successive Laplace and modified finite Fourier sine transforms is studied. Both pseudo-steady state and transient formulations for the matrix-fracture exchange term are considered in this 2D double-porosity model. These analytical solutions can be used to generate type curves for the pressure transient analysis of well bores in naturally fractured reservoirs or aquifers with a constant pressure at the top boundary. Sensitivity analyses have been presented for both pseudo-steady state and transient matrix-fracture exchanges to investigate the effects of the interporosity flow coefficient, the storativity ratio, wellbore storage, the skin factor and the perforation interval. The results show that in the presence of wellbore storage, the early period fracture flow can be easily masked and the wellbore storage effect appears as a unit slope line in the derivative plot. The late-period combined matrix and fracture flow is not evident, due to the gas cap effect. Therefore, the two parallel lines observed in the traditional semi-log plot for radial double-porosity models without a gas cap are not apparent in a double-porosity model with a gas cap, and a conventional semi-log analysis is not possible. In addition, it has been shown that it is possible to observe the v-dip in the derivative plot for a weak wellbore storage effect; however, it is not possible to see such a dip when the wellbore storage effect is strong.