An Analytical Method for Determining the Bottom-Hole Pressure of Vertical Well With Multiple Fractures

Abstract

Hydraulic fracturing has been a common treatment to enhance well productivity, especially in tight oil and gas reservoirs. Studying the pressure response characteristics of fractured reservoir has been a hot topic due to the significant contribution of fractures to conductivity enhancement. Because of the difficulty in describing the flow problems in vertical fractured well and the lack of related literatures, a novel method to determine the bottom-hole pressure of a vertical well with multiple fractures based on Newman product method is proposed in this paper. First, the physical model and corresponding mathematical model are established. Then, the solution of bottom-hole pressure can be obtained through Laplace transformation. Sequentially, the validations of computational method and computational codes contain are presented. From the view of curve fitting and interpretation results, the calculations in this paper are in good agreement with the previous numerical results and our computation method is reliable. Next, a group of typical curves are generated to analyze the flow regimes. And a series of curves are generated to demonstrate effects of key parameters on curve shape. The results indicate that increasing the fracture wings, fracture intersection angle, and fracture length uniformity can enhance the well productivity. Lastly, a case study is exhibited to show the application of the proposed method.