PRESSURE FIELD IN A FORMATION WITH A HYDRAULIC FRACTURE BETWEEN AN INJECTION WELL AND A PRODUCTION WELL
A.I. Filippov1, M.A. Zelenova1, R.R. Gareev1, A.Ya. Davletbaev2, A.F. Kunafin1
1Sterlitamak Branch of Ufa University of Science and Technology, Sterlitamak, Russia
2Ufa University of Science and Technology, Ufa, Russia
Keywords: hydraulic fracture, fluid flow, injection well, production well, asymptotic method, Laplace-Carson integral transform, computational experiment
Abstract
A solution to the problem of the pressure field in an oil and gas reservoir with a hydraulic fracture connecting an injection well and a production well is obtained. The solution is constructed in the Laplace-Carson transform space using an asymptotic method. Analytical expressions for the pressure field in the fracture are derived in the quasi-stationary approximation. An approximate formula for calculating the pressure field in a hydraulic fracture is proposed. Computational experiments are performed using numerical inversion algorithms and the obtained analytical expressions. Spatiotemporal pressure distributions are constructed for realistic values of reservoir and fracture parameters. Based on an analysis of the computational results, the patterns of pressure field formation in a reservoir with a hydraulic fracture are refined. A comparison of the numerical calculations with the analytical relationships shows that the proposed analytical formula provides accuracy sufficient for practical purposes over a time period comparable to the production lifetime of real oil and gas fields.
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