A new analytical multi-linear solution for gas flow toward fractured horizontal wells with different fracture intensity

Abstract

This paper presents a new analytical solution to study the interplay between flowing pressure and production rate for horizontal wells completed within stimulated reservoir volumes (SRV) in tight gas reservoirs. Field practice has shown that all fracturing stages are not effective in production; this has been explained through varying fracture intensity inside and outside of SRVs along the well (fully fractured zone, partially activated zone and non-activated zone). Despite the existing solutions, the novelty of this model is in integrated approach to consider fracturing stages with different fracture intensity, consistent with observations in the field. In addition, the presented model considers wellbore storage effects, stress-dependent and non-Darcy flows considering threshold pressure gradient.Implementing the Laplace transform technique, our multi-linear analytical solution is obtained from the diffusivity equation. We validate the analytic solution with field data; our results are consistent with the field observation. A sensitivity analysis is conducted to study impacts of fracture intensity, threshold pressure gradient, compaction, and size of the stimulated reservoir volume (SRV) on appearance of different flow patterns and ultimate well productivity. Our results suggest a relation between SRV aspect ratio and occurrence of various flow patterns when fracture intensity is changing along the well.In practice, this septa-linear flow model is simple, practical and time-efficient for the transient pressure analysis and production prediction. Furthermore, this work is one step forward to make the analytic solutions more realistic by incorporating different fracture intensity of each fracturing stage.