An approximate analytical solution for transient gas flows in a vertically fractured well of finite fracture conductivity

An analytical solution in physical variable space is presented for transient gas flows during constant-rate production from a vertically-fractured well in an infinite homogeneous reservoir with finite fracture conductivity. The solution is based on the short-time asymptotic solution and a new approximate transient elliptical flow solution, which covers transient flows from the bilinear flow regime to the pseudo-radial flow regime. The solution covers the well-known asymptotic solutions in both short- and long-time limits of bilinear and pseudo-radial flows. The analytical model provides a practical and reliable engineering tool to evaluate the fractured reservoir properties, which can be programmed using a spreadsheet.