Unsteady Flow through a Porous Stratum with Hydraulic Fracture

Abstract

At present, the hydraulic fracture technologies are widely used for intensification of oil and gas recovery from reservoirs with hard-to-recover reserves. The simulation of the processes of flow through porous reservoirs with hydraulic fractures is fairly completely developed in the steady-state flow approximation. Unsteady processes of pressure distribution are considered with reference to the theory of hydrodynamic methods of investigations of wells in which asymptotically limited intervals of variations in the coordinates and time, i.e., the distances of the order of the well radius and time much smaller than the characteristic time of the process of flow through the porous medium, are considered. At the same time, in the reservoirs with hard-to-recover reserves (low-permeability reservoirs and high-viscosity oils) the duration of the unsteady processes of pressure redistribution can be of the same order as the characteristic time of flow through the reservoir. In the present study new analytical solutions of the problem of unsteady pressure redistribution in the neighborhood of a well penetrated by a vertical fracture are given. The scientific novelty of the study consists in the fact that, firstly, the fluid compressibility in the fracture and, secondly, the fluid flow not only through the fracture but also through the porous reservoir are taken into account in the model used. The solutions of the problems are constructed using the Laplace transform technique. In particular cases, the expressions well-known in literature follow from the solutions obtained. The analytical solutions obtained which makes it possible to determine the main characteristic features of the processes of flow through a porous medium are analyzed.