Modeling Longitudinal Dispersion in Variable Porosity Porous Media: Control of Velocity Distribution and Microstructures

Hydrodynamic dispersion process in relation with the geometrical properties of the porous media are studied in two sets of 6 porous media samples of porosity θ ranging from 0.1 to 0.25. These two sets of samples display distinctly different evolutions of the microstructures with porosity but share t...

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Autores principales:	Philippe Gouze, Alexandre Puyguiraud, Thierry Porcher, Marco Dentz
Formato:	article
Lenguaje:	EN
Publicado:	Frontiers Media S.A. 2021
Materias:	dispersion continuous time random walk microstructure velocity distribution pore network Environmental technology. Sanitary engineering TD1-1066
Acceso en línea:	https://doaj.org/article/85b03b083b2b4c558a9c7192947559af
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spelling	oai:doaj.org-article:85b03b083b2b4c558a9c7192947559af2021-11-19T07:30:19ZModeling Longitudinal Dispersion in Variable Porosity Porous Media: Control of Velocity Distribution and Microstructures2624-937510.3389/frwa.2021.766338https://doaj.org/article/85b03b083b2b4c558a9c7192947559af2021-11-01T00:00:00Zhttps://www.frontiersin.org/articles/10.3389/frwa.2021.766338/fullhttps://doaj.org/toc/2624-9375Hydrodynamic dispersion process in relation with the geometrical properties of the porous media are studied in two sets of 6 porous media samples of porosity θ ranging from 0.1 to 0.25. These two sets of samples display distinctly different evolutions of the microstructures with porosity but share the same permeability trend with porosity. The methodology combines three approaches. First, numerical experiments are performed to measure pre-asymptotic to asymptotic dispersion from diffusion-controlled to advection-controlled regime using Time-Domain Random Walk solute transport simulations. Second, a porosity-equivalent network of bonds is extracted in order to measure the geometrical properties of the samples. Third, the results of the direct numerical simulations are interpreted as a Continuous Time Random Walk (CTRW) process controlled by the flow speed distribution and correlation. These complementary modeling approaches allow evaluating the relation between the parameters of the conceptual transport process embedded in the CTRW model, the flow field properties and the pore-scale geometrical properties. The results of the direct numerical simulations for all the 12 samples show the same scaling properties of the mean flow distribution, the first passage time distribution and the asymptotic dispersion vs. the Péclet number than those predicted by the CTRW model. It allows predicting the asymptotic dispersion coefficient D* from Pe = 1 to the largest values of Pe expected for laminar flow in natural environments (Pe≈ 4,000). D∝Pe2−α for Pe≥Pecrit, where α can be inferred from the Eulerian flow distribution and Pecrit depends on porosity. The Eulerian flow distribution is controlled by the distribution of fractions of fluid flowing at each of the pore network nodes and thus is determined mainly by the distribution of the throat radius and the coordination number. The later scales with the number of throats per unit volume independently on the porosity. The asymptotic dispersion coefficient D decreases when porosity increases for all Péclet values larger than 1 due to the increase with porosity of both α and the flow speed decorrelation length.Philippe GouzeAlexandre PuyguiraudThierry PorcherMarco DentzFrontiers Media S.A.articledispersioncontinuous time random walkmicrostructurevelocity distributionpore networkEnvironmental technology. Sanitary engineeringTD1-1066ENFrontiers in Water, Vol 3 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	dispersion continuous time random walk microstructure velocity distribution pore network Environmental technology. Sanitary engineering TD1-1066
spellingShingle	dispersion continuous time random walk microstructure velocity distribution pore network Environmental technology. Sanitary engineering TD1-1066 Philippe Gouze Alexandre Puyguiraud Thierry Porcher Marco Dentz Modeling Longitudinal Dispersion in Variable Porosity Porous Media: Control of Velocity Distribution and Microstructures
description	Hydrodynamic dispersion process in relation with the geometrical properties of the porous media are studied in two sets of 6 porous media samples of porosity θ ranging from 0.1 to 0.25. These two sets of samples display distinctly different evolutions of the microstructures with porosity but share the same permeability trend with porosity. The methodology combines three approaches. First, numerical experiments are performed to measure pre-asymptotic to asymptotic dispersion from diffusion-controlled to advection-controlled regime using Time-Domain Random Walk solute transport simulations. Second, a porosity-equivalent network of bonds is extracted in order to measure the geometrical properties of the samples. Third, the results of the direct numerical simulations are interpreted as a Continuous Time Random Walk (CTRW) process controlled by the flow speed distribution and correlation. These complementary modeling approaches allow evaluating the relation between the parameters of the conceptual transport process embedded in the CTRW model, the flow field properties and the pore-scale geometrical properties. The results of the direct numerical simulations for all the 12 samples show the same scaling properties of the mean flow distribution, the first passage time distribution and the asymptotic dispersion vs. the Péclet number than those predicted by the CTRW model. It allows predicting the asymptotic dispersion coefficient D* from Pe = 1 to the largest values of Pe expected for laminar flow in natural environments (Pe≈ 4,000). D∝Pe2−α for Pe≥Pecrit, where α can be inferred from the Eulerian flow distribution and Pecrit depends on porosity. The Eulerian flow distribution is controlled by the distribution of fractions of fluid flowing at each of the pore network nodes and thus is determined mainly by the distribution of the throat radius and the coordination number. The later scales with the number of throats per unit volume independently on the porosity. The asymptotic dispersion coefficient D decreases when porosity increases for all Péclet values larger than 1 due to the increase with porosity of both α and the flow speed decorrelation length.
format	article
author	Philippe Gouze Alexandre Puyguiraud Thierry Porcher Marco Dentz
author_facet	Philippe Gouze Alexandre Puyguiraud Thierry Porcher Marco Dentz
author_sort	Philippe Gouze
title	Modeling Longitudinal Dispersion in Variable Porosity Porous Media: Control of Velocity Distribution and Microstructures
title_short	Modeling Longitudinal Dispersion in Variable Porosity Porous Media: Control of Velocity Distribution and Microstructures
title_full	Modeling Longitudinal Dispersion in Variable Porosity Porous Media: Control of Velocity Distribution and Microstructures
title_fullStr	Modeling Longitudinal Dispersion in Variable Porosity Porous Media: Control of Velocity Distribution and Microstructures
title_full_unstemmed	Modeling Longitudinal Dispersion in Variable Porosity Porous Media: Control of Velocity Distribution and Microstructures
title_sort	modeling longitudinal dispersion in variable porosity porous media: control of velocity distribution and microstructures
publisher	Frontiers Media S.A.
publishDate	2021
url	https://doaj.org/article/85b03b083b2b4c558a9c7192947559af
work_keys_str_mv	AT philippegouze modelinglongitudinaldispersioninvariableporosityporousmediacontrolofvelocitydistributionandmicrostructures AT alexandrepuyguiraud modelinglongitudinaldispersioninvariableporosityporousmediacontrolofvelocitydistributionandmicrostructures AT thierryporcher modelinglongitudinaldispersioninvariableporosityporousmediacontrolofvelocitydistributionandmicrostructures AT marcodentz modelinglongitudinaldispersioninvariableporosityporousmediacontrolofvelocitydistributionandmicrostructures
_version_	1718420270578925568

Modeling Longitudinal Dispersion in Variable Porosity Porous Media: Control of Velocity Distribution and Microstructures

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