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On the analysis of brine transport in porous media

Published online by Cambridge University Press:  26 September 2008

C. J. van Duijn ,
L. A. Peletier  and
R. J. Schotting
C. J. van Duijn
Affiliation:
Department of Mathematics, Delft University of Technology, Delft, The Netherlands Mathematical Institute, Leiden University, Leiden, The Netherlands
L. A. Peletier
Affiliation:
Mathematical Institute, Leiden University, Leiden, The Netherlands
R. J. Schotting
Affiliation:
Department of Mathematics, Delft University of Technology, Delft, The Netherlands
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Abstract

An analysis is given of brine transport through a porous medium, which incorporates the effect of volume changes due to variations in the salt concentration. Two specific situations are investigated which lead to self-similarity. We develop the existence and uniqueness theory for the corresponding ordinary differential equations, and give a number of qualitative properties of the solutions. In particular, we present an asymptotic expression for the solution in terms of the relative density difference (ρs−ρf)/ρf. Finally, we show some numerical results. It is found that the volume changes have a noticeable effect on the mass transport only when salt concentrations are large.

Type
Research Article
Information
European Journal of Applied Mathematics , Volume 4 , Issue 3 , September 1993 , pp. 271 - 302
Copyright
Copyright © Cambridge University Press 1993

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