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SUMMARY:Diffusion and dispersion with heterogeneous reaction in homogeneou
s porous media: The macroscale models revisited
DTSTART;VALUE=DATE-TIME:20180517T170800Z
DTEND;VALUE=DATE-TIME:20180517T171000Z
DTSTAMP;VALUE=DATE-TIME:20210120T121846Z
UID:indico-contribution-784@events.interpore.org
DESCRIPTION:Speakers: D. Lasseux (CNRS - I2M)\nMass transport combined wit
h heterogeneous reaction in homogeneous porous media is a common process e
ncountered in chemical engineering that is of major concern for many appli
cations ranging from packed bed reactors to porous electrodes. In these sy
stems\, reactants are transported by diffusion (and eventually by advectio
n) inside the pores where chemical reactions take place at the solid-fluid
interfaces. Modelling the macroscopic behavior of these mechanisms is of
prime importance and has been the subject of numerous studies [1\, 2\, 3\,
4]. However\, in almost all the analyses reported in the literature\, the
Kinetic number\, Ki\, referred to as the ratio between the characteristic
time associated to diffusion and the characteristic time associated to re
action at the pore-scale\, is considered to be exceedingly small compared
to unity. Many industrial processes are indeed operating in this range of
Ki\, but this constraint is however not always fulfilled. Under these circ
umstances\, the purpose of the present work is focused on the development
of macroscopic models in a range of Ki ≤1\, relaxing the above mentioned
restriction. \nThe study is focused on single-phase transport of a single
chemical species undergoing a first-order heterogeneous reaction in rigid
and homogeneous porous media. In addition\, the advection problem is assu
med to be decoupled from the transport/reaction mechanisms. Macroscopic mo
dels are derived\, with and without advection\, using the volume averaging
method and the associated closure problems are provided to compute the ef
fective diffusion (or dispersion) and reaction-rate coefficients. In order
to elucidate the impact of the Kinetic number on the coefficients involve
d in the upscaled equations\, a Maclaurin expansion in Ki is carried out\,
yielding models for which the corrections at the successive orders in Ki
and the necessary closure problem to compute them are clearly highlighted
and numerically solved in periodic unit cells. Validations of the macrosco
pic models are carried out from comparisons with direct numerical simulati
ons and a discussion is provided on the impact of the corrections. In part
icular\, it is shown that the impact of the Kinetic number is significant
on the effective reaction-rate coefficient as well as on the convective ma
croscopic term in the average transport equation when the Péclet number i
s non zero but that Ki has a completely negligible contribution to the eff
ective diffusion (or dispersion) tensor.\nKeywords: Diffusion\, Heterogene
ous reaction\, Upscaling\nReferences\n[1] Whitaker S.\, The method of volu
me averaging. Kluwer Academic Publishers\, Dordrecht\, the Netherlands (19
99).\n[2] Ryan\, D.\, Carbonell\, R.G.\, and Whitaker\, S. 1980. Effective
diffusivities for catalyst pellets under reactive conditions. Chemical En
gineering Science\, 35\, 10-16.\n[3] Ochoa-Tapia\, J.A.\, Stroeve\, P.\, a
nd Whitaker\, S. 1994. Diffusive transport in two-phase media: Spatially p
eriodic models and Maxwell's theory for isotropic and anisotropic systems.
Chemical Engineering Science\, 49\, 709-726.\n[4] Le\, T. D.\, Lasseux\,
D.\, Nguyen\, X. P.\, Vignoles\, G.\, Mano\, N.\, and Kuhn\, A. 2017. Mult
i-scale modeling of diffusion and electrochemical reactions in porous micr
o-electrodes. Chemical Engineering Science\, 173\, 153-167.\n\nhttps://eve
nts.interpore.org/event/2/contributions/784/
LOCATION:New Orleans
URL:https://events.interpore.org/event/2/contributions/784/
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