Éditeur(s) : HAL CCSD American Geophysical Union
Résumé : International audience
Both flow field heterogeneity and mass transfer between mobile and immobile domains have been studied separately for explaining observed anomalous transport. Here we investigate non-Fickian transport using high-resolution 3-D X-ray microtomographic images of Berea sandstone containing microporous cement with pore size below the setup resolution. Transport is computed for a set of representative elementary volumes and results from advection and diffusion in the resolved macroporosity (mobile domain) and diffusion in the microporous phase (immobile domain) where the effective diffusion coefficient is calculated from the measured local porosity using a phenomenological model that includes a porosity threshold ( inline image) below which diffusion is null and the exponent n that characterizes tortuosity-porosity power-law relationship. We show that both flow field heterogeneity and microporosity trigger anomalous transport. Breakthrough curve (BTC) tailing is positively correlated to microporosity volume and mobile-immobile interface area. The sensitivity analysis showed that the BTC tailing increases with the value of inline image, due to the increase of the diffusion path tortuosity until the volume of the microporosity becomes negligible. Furthermore, increasing the value of n leads to an increase in the standard deviation of the distribution of effective diffusion coefficients, which in turn results in an increase of the BTC tailing. Finally, we propose a continuous time random walk upscaled model where the transition time is the sum of independently distributed random variables characterized by specific distributions. It allows modeling a 1-D equivalent macroscopic transport honoring both the control of the flow field heterogeneity and the multirate mass transfer between mobile and immobile domains.
ISSN: 0043-1397

hal-01278285
https://hal.archives-ouvertes.fr/hal-01278285
DOI : 10.1002/2015WR017645

Éditeur(s) : HAL CCSD Elsevier
Résumé : International audience
We study diffusion in a heterogeneous medium that is characterized by spatially varying diffusion properties from a random walk point of view. We show that an inhomogeneous continuous time random walk (CTRW) with a spatially variable exponential transition time distribution solves the spatially discretized heterogeneous diffusion equation. This demonstrates the equivalence of the widely used time-domain random walk (TDRW) scheme and spatially inhomogeneous CTRW and at the same time provides a demonstration of the formal equivalence of the TDRW particle formulation and the heterogeneous diffusion equation. Based on this equivalence, we develop a TDRW method for heterogeneous diffusion under spatially variable multirate mass transfer properties. We discuss the implementation of these schemes and study the diffusion behavior in the presence of traps that are characterized by a truncated power-law trapping time distribution.
ISSN: 0309-1708

hal-00767566
https://hal.archives-ouvertes.fr/hal-00767566
DOI : 10.1016/j.advwatres.2012.07.015

Éditeur(s) : HAL CCSD American Geophysical Union
Résumé : International audience
We derive a general formulation of the time domain random walk (TDRW) approach to model the hydrodynamic transport of inert solutes in complex geometries and heterogeneous media. We demonstrate its formal equivalence with the discretized advection-dispersion equation and show that the TDRW is equivalent to a continuous time random walk (CTRW) characterized by space-dependent transition times and transition probabilities. The transition times are exponentially distributed. We discuss the implementation of different concentration boundary conditions and initial conditions as well as the occurrence of numerical dispersion. Furthermore, we propose an extension of the TDRW scheme to account for mobile-immobile multirate mass transfer. Finally, the proposed TDRW scheme is validated by comparison to analytical solutions for spatially homogeneous and heterogeneous transport scenarios.
ISSN: 0043-1397

hal-01356319
https://hal.archives-ouvertes.fr/hal-01356319
DOI : 10.1002/2015WR018511