On matrix diffusion: formulations, solution methods and qualitative effects |
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Authors: | Jesús Carrera Xavier Sánchez-Vila Inmaculada Benet Agustín Medina Germán Galarza Jordi Guimerà |
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Institution: | (1) School of Civil Engineering, Universitat Politècnica de Catalunya, E-08034 Barcelona, Spain Fax: +34-3-401-6504, ES |
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Abstract: | Matrix diffusion has become widely recognized as an important transport mechanism. Unfortunately, accounting for matrix diffusion
complicates solute-transport simulations. This problem has led to simplified formulations, partly motivated by the solution
method. As a result, some confusion has been generated about how to properly pose the problem. One of the objectives of this
work is to find some unity among existing formulations and solution methods. In doing so, some asymptotic properties of matrix
diffusion are derived. Specifically, early-time behavior (short tests) depends only on φ
m
2
R
m
D
m
/ L
m
2, whereas late-time behavior (long tracer tests) depends only on φ
m
R
m
, and not on matrix diffusion coefficient or block size and shape. The latter is always true for mean arrival time. These
properties help in: (a) analyzing the qualitative behavior of matrix diffusion; (b) explaining one paradox of solute transport
through fractured rocks (the apparent dependence of porosity on travel time); (c) discriminating between matrix diffusion
and other problems (such as kinetic sorption or heterogeneity); and (d) describing identifiability problems and ways to overcome
them.
Received, October 1997 · Revised, November 1997 · Accepted, December 1997 |
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Keywords: | tracer tests fractured rocks analytical solutions matrix diffusion |
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