Éditeur(s) : HAL CCSD American Geophysical Union
Résumé : International audience
This paper presents a multicontinuum approach to model fractal temporal scaling of catchment response in hydrological systems. The temporal scaling of discharge is quantified in frequency domain by the transfer function HðxÞ, which is defined as the ratio between the spectra of catchment response and recharge time series. The transfer function may scale with frequency x as HðxÞ x2b. While the classical linear and Dupuit models predict exponents of b52 and b51, observations indicate scalings with noninteger exponents b. Such behaviors have been described by multifractal models, which, however, often lack a relation to the medium characteristics. We revisit and extend the classical linear Dupuit aquifer models and discuss their physical meanings in the light of the resulting aquifer dynamics. On the basis of these classical models, we derive a multicontinuum approach that provides physical recharge models which are able to explain fractal behaviors with exponents 1=2 < b < 2. Furthermore, this approach allows to link the fractal dynamics of the discharge process to the physical aquifer characteristics as reflected in the distribution of storage time scales. We systematically analyze the catchment responses in the proposed multicontinuum models, and identify and quantify the time scales which characterize the dynamics of the catchment response to recharge.
ISSN: 0043-1397

insu-00952537
https://hal-insu.archives-ouvertes.fr/insu-00952537
https://hal-insu.archives-ouvertes.fr/insu-00952537/document
https://hal-insu.archives-ouvertes.fr/insu-00952537/file/russian.pdf
DOI : 10.1002/2013WR014255

Éditeur(s) : HAL CCSD Elsevier
Résumé : The correct characterization of the effective reactive transport dynamics is an important issue for modeling reactive transport on the Darcy scale, specifically in situations in which reactions are localized, that is when different reactions occur in different portions of the porous medium. Under such conditions the conventional approach of homogenizing only the porous medium chemistry is not appropriate. We consider here reactive transport in a porous medium that is characterized by mass transfer between a mobile and a distribution of immobile regions. Chemical and physical heterogeneities are reflected by distributions of kinetic reaction rate constants and residence times in the immobile zones. We derive an effective reactive transport equation for the mobile solute that is characterized by non-local physical mass transfer and reaction terms. Specifically, chemical heterogeneity is upscaled in terms of a reactive memory function that integrates both chemical and physical heterogeneity. Mass transfer limitations due to physical heterogeneity yield effective kinetic rate coefficients that can be much smaller than the volumetric average of the local scale coefficients. These results help to explain and quantify the often reported discrepancy between observed field reaction rate constants and the ones obtained under well mixed laboratory conditions. Furthermore, these results indicate that transport under physical and chemical heterogeneity cannot be upscaled separately.
ISSN: 0169-7722

hal-00617674
https://hal.archives-ouvertes.fr/hal-00617674
DOI : 10.1016/j.jconhyd.2010.06.002