Solutions to and Validation of Matrix-Diffusion Models |
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Authors: | Pekka Kekäläinen Mikko Voutilainen Antti Poteri Pirkko Hölttä Aimo Hautojärvi Jussi Timonen |
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Institution: | (1) Los Alamos National Laboratory, PO Box 1663, Los Alamos, NM 87544, USA;(2) Montgomery and Associates, 1550 East Prince Rd, Tucson, AZ 85719, USA |
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Abstract: | 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. |
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