Memory Effects on Nonlinear Temperature and Pressure Wave Propagation in the Boundary between Two Fluid-Saturated Porous RocksReport as inadecuate




Memory Effects on Nonlinear Temperature and Pressure Wave Propagation in the Boundary between Two Fluid-Saturated Porous Rocks - Download this document for free, or read online. Document in PDF available to download.

Advances in Mathematical Physics - Volume 2015 2015, Article ID 532150, 6 pages -

Research Article

Dipartimento di Scienze Statistiche, Sapienza University of Rome, Piazzale Aldo Moro, 00185 Rome, Italy

ISAC-CNR, Via Fosso del Cavaliere 100, 00100 Roma, Italy

Received 31 August 2015; Revised 23 October 2015; Accepted 25 October 2015

Academic Editor: Christian Engstrom

Copyright © 2015 R. Garra et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The evolution of strong transients of temperature and pressure in two adjacent fluid-saturated porous rocks is described by a Burgers equation in an early model of Natale and Salusti 1996. We here consider the effect of a realistic intermediate region between the two media and infer how transient processes can also happen, such as chemical reactions, diffusion of fine particles, and filter cake formations. This suggests enlarging our analysis and taking into account not only punctual quantities but also -time averaged- quantities. These boundary effects are here analyzed by using a -memory formalism-; that is, we replace the ordinary punctual time-derivatives with Caputo fractional time-derivatives. We therefore obtain a nonlinear fractional model, whose explicit solution is shown, and finally discuss its geological importance.





Author: R. Garra, E. Salusti, and R. Droghei

Source: https://www.hindawi.com/



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