Abstract:
The paper describes a quasi-one-dimensional hyperbolic model of hydraulic fracture growth assuming for the hydraulic fracturing that stress intensity is much higher than fracture resistance. The mode under analysis, which accounts for convective and unsteady terms in the fluid flow equation, is a generalization of the Perkins–Kern–Nordgren local model. It has been proved that the obtained system of differential equations is a quasi-linear strictly hyperbolic system, for which the characteristics were found as well as their correlations. For the case of the Coriolis correction neglect, the Riemann invariants were found. Neglecting the injected fluid leak-off and viscosity, the Riemann waves, similar to simple plane waves in gas dynamics, were defined and their properties were studied. The evolutionism of fracture boundaries was investigated. The initial boundary value problem was set for fracture growth. It has been shown that the neglect of dissipative terms in the presented model allows constructing a simple wave theory analogous to the theory of one-dimensional gas dynamics for isentropic plane waves.
This work was supported by the Ministry of Education and Science of the Russian Federation in the framework of the basic tasks of
the state educational institutions of higher education in 2016 and supported by the Russian Foundation for Basic Research (project no. 14–01–97012 r_povolzh’e_a).
Original article submitted 17/XI/2016 revision submitted – 05/XII/2016
Citation:
A. M. Il'yasov, G. T. Bulgakova, “The quasi-one-dimensional hyperbolic model of hydraulic fracturing”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 20:4 (2016), 739–754
This publication is cited in the following 8 articles:
R. A. Bashmakov, D. A. Nasyrova, Z. R. Khakimova, “Natural Vibrations of Fluid in a Well Connected with the Reservoir by a System of Radial Fractures”, Fluid Dyn, 59:2 (2024), 291
R. A. Bashmakov, D. A. Nasyrova, Z. R. Khakimova, “Natural vibrations of fluid in a well connected with the reservoir by a system of radial fractures”, Izvestiâ Akademii nauk. Rossijskaâ akademiâ nauk. Mehanika židkosti i gaza, 2024, no. 2, 126
V. Sh. Shagapov, G. R. Rafikova, R. A. Bashmakov, Z. Z. Mamaeva, “Analysis of the Collector Characteristics of the Bottomhole Zone of a Stratum Subjected to a Hydraulic Fracturing by the Natural Vibrations of the Liquid Column in a Well”, J Eng Phys Thermophy, 96:2 (2023), 281
R. A. Bashmakov, D. A. Nasyrova, V. Sh. Shagapov, “Natural vibrations of a fluid in a well connected with formation in the presence of a hydraulic fracture”, Fluid Dyn., 56:8 (2021), 1049–1061
I. K. Gimaltdinov, A. M. Il'yasov, “Simulation of the friction pressure loss in the bottomhole zone of a reservoir hydraulic fracture”, Fluid Dyn., 55:1 (2020), 89–102
A. M. Ilyasov, K. R. Kadyrova, V. A. Baikov, I. D. Latypov, “Method for estimating the Young's modulus of a rock using a water hammer”, Neftyanoe Khozyaystvo - Oil Industry, 2019, no. 3, 70–73 (In Russian)
V. A. Baikov, G. T. Bulgakova, A. M. Il'yasov, D. V. Kashapov, “Estimation of the Geometric Parameters of a Reservoir Hydraulic Fracture”, Fluid Dynamics, 53:5, 642–653
A. M. Ilyasov, “Novyi podkhod k opredeleniyu geometricheskikh razmerov treschiny gidrorazryva plasta”, Trudy Instituta mekhaniki im. R. R. Mavlyutova UNTs RAN, 12:1 (2017), 126–134
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