Mixed variational problem for a generalized Darcy-Forchheimer model driven by hydraulic fracture

Mixed variational problem for a generalized Darcy-Forchheimer model driven by hydraulic fracture Full article

Conference

Analytical and Numerical Methods in Differential Equations A virtual conference on occasion of the 100th birthday of Academician Nikolai N. Yanenko August 23-27, 2021, Suranaree University of Technology, Nakhon Ratchasima, Thailand.
23-27 Aug 2021 , Тайланд

Journal

Journal of Vibration Testing and System Dynamics
ISSN: 2475-4811 , E-ISSN: 2475-482X

Output data

Year: 2023, Volume: 7, Number: 1, Pages: 15-21 Pages count : 7 DOI: 10.5890-JVTSD.2023.03.003

Authors

Kovtunenko Victor Anatolʹevich ¹

Affiliations

1	Lavrentyev Institute of Hydrodynamics

Funding (1)

Министерство науки и высшего образования Российской Федерации

FWGG-2021-0010

The model of a stationary flow in porous media stemming from hydraulic fracking and accounting for inertial phenomena is considered. The incompressible fluid is modeled by a nonlinear Darcy–Forchheimer (DF) equation under mixed boundary conditions, which are appropriate for a fluid-driven fracture. The classical DF equation is generalized with respect to a growth exponent m and inhomogeneous coefficients. Using mixed variational formulation of the problem for unknown fluid velocity and fluid pressure, the well-posedness theorem is proved for arbitrary m > 1. The developed Lagrange multiplier formalism is advantageous for optimal shape design of fractures.

Kovtunenko V.A.
Mixed variational problem for a generalized Darcy-Forchheimer model driven by hydraulic fracture
Journal of Vibration Testing and System Dynamics. 2023. V.7. N1. P.15-21. DOI: 10.5890-JVTSD.2023.03.003 РИНЦ

Elibrary:

54691548

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