Elastic Liquid Filtration to a Wellbore Through a Perpendicular Crack Formed during Hydraulic Fracturing
V. Sh. Shagapov1, Z. M. Nagaeva1,2, E. P. Anosova2
1Mavlyutov Institute of Mechanics of the Ufa Investigation Center, Russian Academy of Sciences, Ufa, 450054 Russia
2Ufa State Petroleum Technological University, Ufa, 450062 Russia
Keywords: hydraulic fracturing, fracture, oil wellbore, integro-differential equation, analytical solution, pressure distribution, fluid flow
Abstract
The problem of fluid withdrawal (or injection) from a reservoir into a well in the presence of a hydraulic fracture perpendicular to the wellbore in the mode of a constant pressure difference between the wellhead and the reservoir is considered. Analytical solutions are obtained that describe the evolution of pressure in the fracture and fluid flow into the well. Approximate solutions are constructed using the method of successive change of stationary states. The comparison of exact and approximate solutions of problems for determining the pressure fields in the fracture and the volumetric flow rate of fluid from the well into the fracture is carried out and it is shown that they practically coincide (the relative difference does not exceed 1-2%). In this case, the calculation time for approximate solutions is significantly reduced. This contributes to the creation of effective calculation algorithms for transient modes of well operation in reservoirs with complicated reservoir characteristics. The influence of reservoir characteristics of a reservoir and a fracture on the evolution of pressure in the fracture and fluid flow into the well is analyzed.
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