Upscaling solute transport in porous media from the pore scale to dual‐ and multicontinuum formulations

Abstract

[1] We provide pore to Darcy-scale theoretical upscaling of solute transport in porous media and discuss the key theoretical elements underlying double-and multirate mass transfer formulations which are typically adopted to interpret laboratory-and/or field-scale transport experiments. We model pore-scale transport by considering advective and diffusive processes. The resulting mass balance equation is subject to volume averaging relying on an unsteady closure. This leads to a nonlocal in time continuum-scale twoequation transport model, which we compare against existing double-and multirate mass transfer formulations. Coefficients appearing in our upscaled model are expressed as functions of time and pore-scale geometry and velocity distribution. We analyze in detail the scenario associated with two-dimensional flow in a plane channel and discuss the temporal dynamics and the associated asymptotic behavior of the different effective coefficients appearing in the upscaled system of equations. The relative influence of the terms included in the continuum-scale model is quantitatively assessed.Citation: Porta, G., S. Chaynikov, M. Riva, and A. Guadagnini (2013), Upscaling solute transport in porous media from the pore scale to dual-and multicontinuum formulations, Water Resour.

Continuum‐scale characterization of solute transport based on pore‐scale velocity distributions

“…While our conceptual model relies on a simplification of the actual pore space, it enables us to derive simple analytical formulations for the double‐continuum model parameters. Our approach is also consistent with previous findings showing that this simplified geometry can provide powerful guidance for the interpretation of flow and transport phenomena taking place in complex pore spaces [e.g., Davit et al ., ; Orgogozo et al ., ; Wang et al ., ; Porta et al ., ; Dejam et al ., ; Bianchi Janetti et al ., ]. We now discuss the key developments leading to the definition of our effective transport models.…”

“…Parameters of double-continuum models can directly be related to pore-scale features by theoretical studies based on volume averaging [e.g., Davit et al, 2010;Orgogozo et al, 2010;Davit et al, 2012;Soulaine et al, 2013;Porta et al, 2013]. Rigorous application of volume averaging to real porous media requires solving a set of closure problems in a (generally) complex three-dimensional geometry.…”

Impact of space‐time mesh adaptation on solute transport modeling in porous media

“…A key assumption underlying the ADE is that the total dispersion coefficient can be described by the sum of effective diffusion and hydrodynamic dispersion, according to the so‐called Fickian analogy [ Bear and Cheng , ]. Limitations of this modeling option have been identified and discussed on the basis of theoretical arguments, numerical simulations, and experimental evidences, which led to the development of alternative formulations encapsulating effective descriptions of non‐Fickian (or anomalous) transport [see, e.g., Haggerty et al ., ; Levy and Berkowitz , ; Berkowitz et al ., ; Zhang et al ., ; Porta et al ., , and references therein]. These approaches encompass very different modeling perspectives, based on both Lagrangian and Eulerian mathematical formulations and can give rise to local and/or nonlocal (integrodifferential) equations.…”

Reliability of the spherical agglomerate models for catalyst layer in polymer electrolyte membrane fuel cells

“…In the process, a FIB/SEM system was used to obtain the 3D structure of mesoporous samples (Joos et al, 2012;Porta et al, 2013;Siddique and Liu, 2010;Thiele et al, 2011;Wu et al, 2012;Zils et al, 2010). The process involves milling away a slice of the sample as thin as 10~15 nm from the side wall of a trench using FIB, and taking an SEM image of the new surface as illustrated in Figure 1.…”