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A robust upscaling of the effective particle deposition rate in porous media
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Boccardo, Gianluca, Crevacore, Eleonora, Sethi, Rajandrea and Icardi, Matteo (2018) A robust upscaling of the effective particle deposition rate in porous media. Journal of Contaminant Hydrology, 212 . pp. 3-13. doi:10.1016/j.jconhyd.2017.09.002 ISSN 0169-7722.
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Official URL: https://doi.org/10.1016/j.jconhyd.2017.09.002
Abstract
In the upscaling from pore to continuum (Darcy) scale, reaction and deposition phenomena at the solid–liquid interface of a porous medium have to be represented by macroscopic reaction source terms. The effective rates can be computed, in the case of periodic media, from three-dimensional microscopic simulations of the periodic cell. Several computational and semi-analytical models have been studied in the field of colloid filtration to describe this problem. They typically rely on effective deposition rates defined by complex fitting procedures, neglecting the advection-diffusion interplay, the pore-scale flow complexity, and assuming slow reactions (or large Péclet numbers). Therefore, when these rates are inserted into general macroscopic transport equations, they can lead to several conceptual inconsistencies and significant errors. To study more accurately the dependence of deposition on the flow parameters, in this work we advocate a clear distinction between the surface processes (that altogether defines the so-called attachment efficiency), and the pore-scale processes. With this approach, valid when colloidal particles are small enough, we study Brownian and gravity-driven deposition on a face-centred cubic (FCC) arrangement of spherical grains, and define a robust upscaling based on a linear effective reaction rate. The case of partial deposition, defined by an attachment probability, is studied and the limit of perfect sink is retrieved as a particular case. We introduce a novel upscaling approach and a particularly convenient computational setup that allows the direct computation of the asymptotic stationary value of effective rates. This allows to drastically reduce the computational domain down to the scale of the single repeating periodic unit. The savings are ever more noticeable in the case of higher Péclet numbers, when larger physical times are needed to reach the asymptotic regime and thus, equivalently, much larger computational domain and simulation time would be needed in a traditional setup. We show how this new definition of deposition rate is more robust and extendable to the whole range of Péclet numbers; it also is consistent with the classical heat and mass transfer literature.
Item Type: | Journal Article | ||||||||
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Subjects: | Q Science > QA Mathematics | ||||||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||
Journal or Publication Title: | Journal of Contaminant Hydrology | ||||||||
Publisher: | Elsevier | ||||||||
ISSN: | 0169-7722 | ||||||||
Official Date: | May 2018 | ||||||||
Dates: |
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Volume: | 212 | ||||||||
Page Range: | pp. 3-13 | ||||||||
DOI: | 10.1016/j.jconhyd.2017.09.002 | ||||||||
Status: | Peer Reviewed | ||||||||
Publication Status: | Published | ||||||||
Access rights to Published version: | Restricted or Subscription Access | ||||||||
Date of first compliant deposit: | 3 October 2017 | ||||||||
Date of first compliant Open Access: | 17 March 2019 | ||||||||
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