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 Matem. Mod., 2017, Volume 29, Number 11, Pages 3–18 (Mi mm3904)

The analytical investigation of hydraulic fracture dynamics according to the incomplete coupling principle

M. M. Ramazanovab, A. V. Karakinbc, V. E. Borisovb

a Institute for Geothermal Problems of the Dagestan Scientific Center RAS
b Keldysh Institute of Applied Mathematics RAS
c Oil and Gas Research Institute RAS

Abstract: In the paper we present a self-similar solution of the coupling problem about slow movement in the hydraulic fracture and corresponding deformation and fluid percolation in the external medium. These movements are generated with fluid uploading into well. The flow in a crack is described with the hydrodynamics Stokes equations in the approach of the lubricating layer. The outer problem is described with the poroelasticity equations. We consider an option of the heterogeneous pressure into a crack in three- and two-dimensions. In the second case one can have the self-similar solution in the analytical form.

Keywords: hydraulic fracture problem, self-similar solution, incomplete coupling principle, equilibrium crack.

 Funding Agency Grant Number Russian Science Foundation 15-11-00021

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English version:
Mathematical Models and Computer Simulations, 2018, 10:3, 322–332

Citation: M. M. Ramazanov, A. V. Karakin, V. E. Borisov, “The analytical investigation of hydraulic fracture dynamics according to the incomplete coupling principle”, Matem. Mod., 29:11 (2017), 3–18; Math. Models Comput. Simul., 10:3 (2018), 322–332

Citation in format AMSBIB
\Bibitem{RamKarBor17} \by M.~M.~Ramazanov, A.~V.~Karakin, V.~E.~Borisov \paper The analytical investigation of hydraulic fracture dynamics according to the incomplete coupling principle \jour Matem. Mod. \yr 2017 \vol 29 \issue 11 \pages 3--18 \mathnet{http://mi.mathnet.ru/mm3904} \elib{http://elibrary.ru/item.asp?id=30462926} \transl \jour Math. Models Comput. Simul. \yr 2018 \vol 10 \issue 3 \pages 322--332 \crossref{https://doi.org/10.1134/S2070048218030110} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85048068471}