Physically consistent diffusion in media with memory

Caputo, M. (1999) Physically consistent diffusion in media with memory. Il nuovo cimento C, 22 C (3-4). pp. 253-263. ISSN 1826-9885

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Some data on the flow of fluids in rocks exhibit properties which cannot be interpreted with the classic theory of propagation of pressure and of fluids in media (ROELOFFS E. A., Fault Stability Changes Induced Beneath a Reservoir with Cyclic Variations in Water Level, J. Geophys. Res., 93 (1988) 2107-2124) based on the classic D’Arcy’s law which states that the flux is proportional to the pressure gradient. In order to obtain a better representation of the flow and pressure of fluids in media, the law of D’Arcy was modified introducing instead of the pressure gradient its time derivative of fractional order z (CAPUTO M., The Green function of diffusion of fluids in porous media with memory, Rend. Fis. Acc. Lincei, 9 (1996) 243-250). However, the new law implies a filtering of the pressure gradient with response curves which are singular or nil at zero or infinite frequency. In this note we extend the law of D’Arcy introducing a memory formalism operating on the flow as well as on the pressure gradient which implies a filtering of the pressure gradient without singularities; the properties of the filtering are also described.

Item Type: Article
Additional Information: Paper presented at the “Fourth International Conference on Rare Gas Geochemistry”, Rome, October 8-10, 1997.
Uncontrolled Keywords: Rivers, runoff, and streamflow; modeling, general theory; groundwater; rheology of litosphere and mantle; conference proceedings
Subjects: 500 Scienze naturali e Matematica > 550 Scienze della Terra > 551 Geologia, Idrologia, Meteorologia > 551.9 Geochimica
Depositing User: Marina Spanti
Date Deposited: 18 Sep 2018 14:51
Last Modified: 18 Sep 2018 14:51

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