This paper presents an analytical study of transient flow into multiple vertical wells producing from a porous media containing randomly distributed discrete fractures. The model may be used to analyze the production and well test data from tight gas sands and Austin chalk type reservoirs. Both vertical openholes and hydraulically fractured vertical wells are considered. Wells and fractures are randomly distributed. The model dynamically couples the multiple fracture flow models with an analytical reservoir flow model. The analytical model simulates pressure and pressure derivative characteristics of wells and flow distribution along and through both the natural and hydraulic fractures.

The study shows that single or multiple isolated fractures yield negative pseudoskin factors in vertical wells near isolated fractures. The negative pseudoskin factor in unstimulated wells has also been observed in field tests. The negative pseudoskin factor is a function of fracture conductivity, fracture density, length, distance from the wellbore, and azimuth.

Using the model, we demonstrate that the shape of pressure derivative is related to fracture distribution. However, the wellbore pressure derivative response is controlled by the fractures in the near wellbore region.

The result of this study indicate that the conventional analysis, based on the double porosity model such as the Warren and Root model, to predict the storativity ratio of a naturally fractured system is not reliable. Also, the displacement between two semilog straight lines is not necessarily a good indicator of the storativity ratio.

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