A new method for pressure test analysis of a vertically fractured well producing commingled zones in bounded square reservoirs

Although hydraulically or naturally fractured wells located in stratified bounded reservoirs are common, reliable techniques available to analyze the pressure test data for such reservoirs are lacking. This paper presents a mathematical model that describes the pressure behavior of a vertically fractured well located in a stratified, bounded, square reservoir. The fracture can be either a uniform flux or an infinite conductivity fracture. It was found that the dimensionless pressure function and its derivative and the fractional production rate from the different layers are mainly controlled by the fracture penetration into the formation, and that transmissibility and storativity affect the fractional production rate and the pressure derivative but have little effect on the dimensionless pressure function. Type curves of dimensionless pressure and dimensionless pressure derivative can be used to evaluate the reservoir characteristics. The selection of the appropriate type curve is guided by the behavior of the layer fractional production rate obtained from flow rate survey carried out during well testing. Type curves for uniform flux and infinite conductivity fractures exhibit similar features. Two examples are presented to demonstrate the application of the new method of analysis presented in this paper.