Derivation of the Forchheimer law via homogenization
In this paper we derive the Forchheimer law via the theory of homogenization. In particular, we study the nonlinear correction to Darcy's law due to inertial effects on the flow of a Newtonian fluid in rigid porous media. A general formula for this correction term is derived directly from the N...
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| Veröffentlicht in: | Transport in porous media 2001-08, Vol.44 (2), p.325-335 |
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| container_title | Transport in porous media |
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| creator | ZHANGXIN CHEN LYONS, Stephen L GUAN QIN |
| description | In this paper we derive the Forchheimer law via the theory of homogenization. In particular, we study the nonlinear correction to Darcy's law due to inertial effects on the flow of a Newtonian fluid in rigid porous media. A general formula for this correction term is derived directly from the Navier–Stokes equation via homogenization. Unlike other studies based on the same approach that concluded for the nonlinear correction to be cubic in velocity for isotropic media, the present work shows that the nonlinear correction is quadratic. An example is constructed to illustrate our theory. In this example, the analytic solution to the Navier–Stokes equation is obtained and is utilized to show the validity of the quadratic correction. Both incompressible and compressible fluids are considered. |
| doi_str_mv | 10.1023/A:1010749114251 |
| format | Article |
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In particular, we study the nonlinear correction to Darcy's law due to inertial effects on the flow of a Newtonian fluid in rigid porous media. A general formula for this correction term is derived directly from the Navier–Stokes equation via homogenization. Unlike other studies based on the same approach that concluded for the nonlinear correction to be cubic in velocity for isotropic media, the present work shows that the nonlinear correction is quadratic. An example is constructed to illustrate our theory. In this example, the analytic solution to the Navier–Stokes equation is obtained and is utilized to show the validity of the quadratic correction. 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| ispartof | Transport in porous media, 2001-08, Vol.44 (2), p.325-335 |
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| language | eng |
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| subjects | Compressible fluids Computational fluid dynamics Darcys law Earth sciences Earth, ocean, space Exact sciences and technology Exact solutions Fluid flow Homogenization Hydrogeology Hydrology. Hydrogeology Incompressible flow Isotropic media Navier-Stokes equations Newtonian fluids Porous media |
| title | Derivation of the Forchheimer law via homogenization |
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