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Effective transport dynamics in porous media with heterogeneous retardation properties
Author(s) -
Dentz Marco,
Castro Adolfo
Publication year - 2009
Publication title -
geophysical research letters
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.007
H-Index - 273
eISSN - 1944-8007
pISSN - 0094-8276
DOI - 10.1029/2008gl036846
Subject(s) - continuous time random walk , random walk , statistical physics , porous medium , scale (ratio) , constant (computer programming) , distribution (mathematics) , mass transfer , length scale , physics , mechanics , mathematical analysis , mathematics , geology , porosity , computer science , statistics , geotechnical engineering , quantum mechanics , programming language
We study a transport model that is characterized by a spatially distributed retardation coefficient. The latter accounts for linear instantaneous mass transfer between a mobile and immobile phases as well as instantaneous equilibrium adsorption. Using a Lagrangian framework we upscale the local scale transport problem to an observation scale that is much larger than the variation scale of spatial heterogeneity. The derived effective Lagrangian transport equation describes the effective particle motion as a random walk in space‐time, or in other words, a continuous time random walk, which is characterized by a joint transition length and time distribution. The transition time distribution is obtained by an exact map from the spatial distribution of retardation coefficients. The effective model compares well with numerical simulations of the small scale transport problem. For broad disorder distributions transport is highly non‐Fickian and an (constant) effective retardation coefficient may not exist at practically relevant time and length scales.