Analytical modeling of one-dimensional diffusion in layered systems with position-dependent diffusion coefficients

Diffusion in stratified porous media is common in the natural environment. The objective of this study is to develop analytical solutions for describing the diffusion in layered porous media with a position-dependent diffusion coefficient within each layer. The orthogonal expansion technique was use...

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Bibliographic Details
Published in:Advances in water resources 2008-02, Vol.31 (2), p.251-268
Main Authors: Liu, G, Si, B.C
Format: Article
Language:English
Subjects:
diffusion
diffusivity
Earth sciences
Earth, ocean, space
equations
Exact sciences and technology
groundwater
Hydrogeology
hydrologic models
Hydrology. Hydrogeology
layered porous media
mathematical models
multi-layer porous media
porous media
simulation models
stratified porous media
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Summary:Diffusion in stratified porous media is common in the natural environment. The objective of this study is to develop analytical solutions for describing the diffusion in layered porous media with a position-dependent diffusion coefficient within each layer. The orthogonal expansion technique was used to solve a one-dimensional multi-layer diffusion equation in which the diffusion coefficient is expressed as a segmented linear function of positions in the porous media. The behavior of the solutions is illustrated using several examples of a three-layer system, with constant diffusion coefficient alpha sub(1) in layer 1 (0
ISSN:0309-1708
1872-9657
DOI:10.1016/j.advwatres.2007.08.008