Non-Fickian transport and multiple-rate mass transfer in porous media

Brian Berkowitz*, Simon Emmanuel, Harvey Scher

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

77 Scopus citations


Non-Fickian behavior is due to a broad spectrum of rates limiting the solute transport. There are two generic mechanisms that can generate these spectra: the complex flow field of a highly heterogeneous medium and the mass exchange between a mobile phase and a distribution of immobile states. We have developed a physical model that incorporates both of these mechanisms into the continuous time random walk (CTRW) framework. We study their interacting dynamics as a function of the spectra of advective-diffusive transition times and exchange times and the relative separation of their respective time domains. Examples of interacting transport in a dispersive medium with immobile states include tracer migration in a random fracture network with matrix diffusion and transport in a porous medium with adsorption/desorption sites. To date, non-Fickian transport has been quantified effectively using the CTRW in a wide variety of porous and fractured geological formations. The basis of the CTRW framework is the portrayal of transport as a sequence of transition rates (e.g., between pore spaces, fracture intersections) and the incorporation of the full spectrum of these rates into the transport equations. The emphasis herein is on systems in which the time domains of the two different types of spectra are distinguishable, so that a more complete characterization of the transport can be obtained (i.e., rather than lumping all the rates together). Experimental data are analyzed from two of these systems: (1) tracer transport in a fractured shear zone and (2) sorbing species transported through a heterogeneous porous domain. The CTRW framework is found to produce excellent fits to and predictions from the experimental data.

Original languageAmerican English
Article numberW03402
JournalWater Resources Research
Issue number3
StatePublished - Mar 2008
Externally publishedYes


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