Modeling of unsteady flow around well with hydraulic fracture

At present, hydraulic fracturing technologies are widely used for intensification of oil and gas recovery from reservoirs with hard-to-recover reserves. Modeling the processes of flow through porous reservoirs with hydraulic fractures has beenfairly completely developed in the steady-state flow approximation. Non-stationary processes of pressure distribution are considered as applied to the theory of hydrodynamic well survey methods, in which asymptotically limited intervals of coordinate and time variations are taken into account, i.e., distances of the order of the well radius and time significantly shorter than the characteristic time of the flow through the porous medium. At the same time, in reservoirs with hard-to-recover reserves (low-permeability reservoirs and high-viscosity oils), the duration of unsteady processes of pressure redistribution can be of the same order as the characteristic time of flow through the reservoir. This study presents new analytical solutions to the problem of the redistribution of non-stationary pressure in the vicinity of a well penetrated by a vertical fracture. The scientific novelty of the study lies in the fact that the model used takes into account, first, the fluid compressibility in the fracture and, secondly, the fluid flow not only through the fracture, but also through the porous reservoir. The solutions to the problems are constructed using the Laplace transform technique. In particular cases, the expressions known in literature follow from the solutions obtained. The analytical solutions obtained are analyzed, which makes it possible to determine the main characteristic features of the flow processes of around a porous medium