Transport in Porous Media

, Volume 87, Issue 1, pp 125–149 | Cite as

Solutions to and Validation of Matrix-Diffusion Models

  • Pekka Kekäläinen
  • Mikko Voutilainen
  • Antti Poteri
  • Pirkko Hölttä
  • Aimo Hautojärvi
  • Jussi Timonen
Article

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.

Keywords

Matrix-diffusion Diffusion in porous medium 

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Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  • Pekka Kekäläinen
    • 1
  • Mikko Voutilainen
    • 1
  • Antti Poteri
    • 2
  • Pirkko Hölttä
    • 3
  • Aimo Hautojärvi
    • 4
  • Jussi Timonen
    • 1
  1. 1.Department of PhysicsUniversity of JyväskyläJyväskyläFinland
  2. 2.VTT Research CenterEspooFinland
  3. 3.Laboratory of RadiochemistryUniversity of HelsinkiHelsinkiFinland
  4. 4.Posiva OyOlkiluotoFinland

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