Modeling of unsteady filtration in a formation–hydraulic fracture system

This paper presents the results of modeling of unsteady fluid filtration in the formation penetrated by a well, which intersects a vertical hydraulic fracture throughout the entire thickness of the formation. The model of a bilinear fluid flow in a formation vertical hydraulic fracture system is considered in the case when the horizontal extent of the formation is considered to be infinite, and the fracture is of a finite length. The bilinearity of the flow means that in the formation–fracture system there are two mutually perpendicular fluid flows: from the formation to the fracture and along the fracture to the well. The analytical solution to a system of equations describing fluid filtration in the formation and fracture is obtained using the Laplace transform method. Analyzing the derived solution, main characteristic features of the filtration in the formation–fracture system are determined.