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Matem. Mod., 2017, Volume 29, Number 6, Pages 115–134 (Mi mm3861)  

This article is cited in 1 scientific paper (total in 1 paper)

The incomplete coupling problem of hydraulic fracturing equations

A. V. Karakinab, M. M. Ramazanovca, V. E. Borisova

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

Abstract: We consider a problem of evolution of the state of poroelastic media coupled with slow motions of the viscous fluid inside hydraulic fracture in 3D setting. The fluid flow is induced by injection of fluid into the fracture. The fluid flow is described using Reynolds lubrication equations. External poroelasric media is governed by Biot poroelasticity equations. We analyze interplay of the different geomechanical processes in the media and the fracture using asymptotic framework. As a result, it is shown that the complete coupled problem can be reduced to the three one-way coupled problems which can be solved sequentially. The approach allows to analyze certain process related to the hydraulic fracture analysis as well as some other ones. At the same time the approach provides theoretical background for construction of new physically-based iterative and preconditioning techniques suitable for solution of the complete coupled problem.

Keywords: hydraulic fracture problem, poroelastic medium, equilibrium crack, incomplete coupling principle.

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


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English version:
Mathematical Models and Computer Simulations, 2018, 10:1, 45–58

Bibliographic databases:

Received: 03.10.2016

Citation: A. V. Karakin, M. M. Ramazanov, V. E. Borisov, “The incomplete coupling problem of hydraulic fracturing equations”, Matem. Mod., 29:6 (2017), 115–134; Math. Models Comput. Simul., 10:1 (2018), 45–58

Citation in format AMSBIB
\Bibitem{KarRamBor17}
\by A.~V.~Karakin, M.~M.~Ramazanov, V.~E.~Borisov
\paper The incomplete coupling problem of hydraulic fracturing equations
\jour Matem. Mod.
\yr 2017
\vol 29
\issue 6
\pages 115--134
\mathnet{http://mi.mathnet.ru/mm3861}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3665418}
\elib{http://elibrary.ru/item.asp?id=29207731}
\transl
\jour Math. Models Comput. Simul.
\yr 2018
\vol 10
\issue 1
\pages 45--58
\crossref{https://doi.org/10.1134/S2070048218010076}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85042558798}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. M. M. Ramazanov, A. V. Karakin, V. E. Borisov, “The analytical investigation of hydraulic fracture dynamics according to the incomplete coupling principle”, Math. Models Comput. Simul., 10:3 (2018), 322–332  mathnet  crossref  elib
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