Solutions to and Validation of Matrix-Diffusion Models

A model transport system is considered in which a pulse of tracer molecules is advected along a flow channel with porous walls. The advected tracer thus undergoes diffusion, matrix-diffusion, inside the walls, which affects the breakthrough curve of the tracer. Analytical solutions in the form of se...

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Bibliographic Details
Published in:Transport in porous media 2011-03, Vol.87 (1), p.125-149
Main Authors: Kekäläinen, Pekka, Voutilainen, Mikko, Poteri, Antti, Hölttä, Pirkko, Hautojärvi, Aimo, Timonen, Jussi
Format: Article
Language:English
Subjects:
Apertures
Asymptotic properties
Channels
Civil Engineering
Classical and Continuum Physics
Diffusion
Earth and Environmental Science
Earth Sciences
Earth, ocean, space
Exact sciences and technology
Exact solutions
Geotechnical Engineering & Applied Earth Sciences
Hydrogeology
Hydrology. Hydrogeology
Hydrology/Water Resources
Industrial Chemistry/Chemical Engineering
Laplace transforms
Mathematical analysis
Mathematical models
Modelling
Porous media
Porous walls
Tracers
Transport
Walls
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Summary:A model transport system is considered in which a pulse of tracer molecules is advected along a flow channel with porous walls. The advected tracer thus undergoes diffusion, matrix-diffusion, inside the walls, which affects the breakthrough curve of the tracer. Analytical solutions in the form of series expansions are derived for a number of situations which include a finite depth of the porous matrix, varying aperture of the flow channel, and longitudinal diffusion and Taylor dispersion of the tracer in the flow channel. Novel expansions for the Laplace transforms of the concentration in the channel facilitated closed-form expressions for the solutions. A rigorous result is also derived for the asymptotic form of the breakthrough curve for a finite depth of the porous matrix, which is very different from that for an infinite matrix. A specific experimental system was created for validation of matrix-diffusion modeling for a matrix of finite depth. A previously reported fracture-column experiment was also modeled. In both cases model solutions gave excellent fits to the measured breakthrough curves with very consistent values for the diffusion coefficients used as the fitting parameters. The matrix-diffusion modeling performed could thereby be validated.
ISSN:0169-3913
1573-1634
DOI:10.1007/s11242-010-9672-y