Mixed Variational Problem for a Generalized Darcy--Forchheimer Model Driven by Hydraulic Fracture
DOI:
https://doi.org/10.5890/JVTSD.2023.03.003Abstract
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.References
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