From Darcy Equation to Darcy Paradox
This theoretical paper focuses on the single-phase fluid flow through a granular porous medium. The emphasis is on the Darcy flow regime (without free boundary) of a linear viscous fluid in a saturated, deformable, homogeneous porous medium. The approach is developed at the Darcy scale (also referre...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-03-01
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| Series: | Fluids |
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| Online Access: | https://www.mdpi.com/2311-5521/7/4/120 |
| _version_ | 1797434740940210176 |
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| author | Carmine Di Nucci Daniele Celli |
| author_facet | Carmine Di Nucci Daniele Celli |
| author_sort | Carmine Di Nucci |
| collection | DOAJ |
| description | This theoretical paper focuses on the single-phase fluid flow through a granular porous medium. The emphasis is on the Darcy flow regime (without free boundary) of a linear viscous fluid in a saturated, deformable, homogeneous porous medium. The approach is developed at the Darcy scale (also referred to as macroscale or phenomenological scale). Within this framework, some discrete aspects of the flow model are highlighted, the governing equations are revisited, the thermodynamic state functions are reconsidered, and the Darcy paradox is presented. The Darcy paradox is illustrated for the isoshoric-isothermal flow of a viscous fluid in the liquid state, in a homogenous porous medium. After some remarks about the intrinsic assumption of this kind of flow, the governing equations are reduced to a well-known parabolic equation. According to this equation, infinitesimal pressure disturbances diffuse at an infinite speed. To remove this paradox, a mathematical model, based on the elementary scales method, is employed. |
| first_indexed | 2024-03-09T10:36:47Z |
| format | Article |
| id | doaj.art-ee47bd83cdf142c399e2dba58bda2b35 |
| institution | Directory Open Access Journal |
| issn | 2311-5521 |
| language | English |
| last_indexed | 2024-03-09T10:36:47Z |
| publishDate | 2022-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fluids |
| spelling | doaj.art-ee47bd83cdf142c399e2dba58bda2b352023-12-01T20:53:06ZengMDPI AGFluids2311-55212022-03-017412010.3390/fluids7040120From Darcy Equation to Darcy ParadoxCarmine Di Nucci0Daniele Celli1Environmental and Maritime Hydraulic Laboratory (LIam), Civil, Construction-Architectural and Environmental Engineering Department (DICEAA), University of L’Aquila, 67100 L’Aquila, ItalyEnvironmental and Maritime Hydraulic Laboratory (LIam), Civil, Construction-Architectural and Environmental Engineering Department (DICEAA), University of L’Aquila, 67100 L’Aquila, ItalyThis theoretical paper focuses on the single-phase fluid flow through a granular porous medium. The emphasis is on the Darcy flow regime (without free boundary) of a linear viscous fluid in a saturated, deformable, homogeneous porous medium. The approach is developed at the Darcy scale (also referred to as macroscale or phenomenological scale). Within this framework, some discrete aspects of the flow model are highlighted, the governing equations are revisited, the thermodynamic state functions are reconsidered, and the Darcy paradox is presented. The Darcy paradox is illustrated for the isoshoric-isothermal flow of a viscous fluid in the liquid state, in a homogenous porous medium. After some remarks about the intrinsic assumption of this kind of flow, the governing equations are reduced to a well-known parabolic equation. According to this equation, infinitesimal pressure disturbances diffuse at an infinite speed. To remove this paradox, a mathematical model, based on the elementary scales method, is employed.https://www.mdpi.com/2311-5521/7/4/120single-phase flowsaturated porous mediaclassical continuum thermodynamicselementary scaleslocal thermodynamic equilibrium condition |
| spellingShingle | Carmine Di Nucci Daniele Celli From Darcy Equation to Darcy Paradox Fluids single-phase flow saturated porous media classical continuum thermodynamics elementary scales local thermodynamic equilibrium condition |
| title | From Darcy Equation to Darcy Paradox |
| title_full | From Darcy Equation to Darcy Paradox |
| title_fullStr | From Darcy Equation to Darcy Paradox |
| title_full_unstemmed | From Darcy Equation to Darcy Paradox |
| title_short | From Darcy Equation to Darcy Paradox |
| title_sort | from darcy equation to darcy paradox |
| topic | single-phase flow saturated porous media classical continuum thermodynamics elementary scales local thermodynamic equilibrium condition |
| url | https://www.mdpi.com/2311-5521/7/4/120 |
| work_keys_str_mv | AT carminedinucci fromdarcyequationtodarcyparadox AT danielecelli fromdarcyequationtodarcyparadox |