Transport behavior of a passive solute in continuous time random walks and multirate mass transfer

By M. Dentz, Brian Berkowitz. 2003

248 citations recorded by the source corpus.

Subfields: Civil and Structural Engineering, Environmental Engineering, Physical and Theoretical Chemistry

View Paper: https://www.semanticscholar.org/paper/46c480e3adb1ca32f87891e7bd4f3065425f2c37

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In Civil and Structural Engineering

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In Physical and Theoretical Chemistry

Citations in the corpus

Time and space nonlocalities underlying fractional-derivative models: Distinction and literature review of field applications (2009, methodology): “Previous research [20,47,128] established a connection between CTRW and MRMT models.”
Comparison of alternative models for simulating anomalous solute transport in a large heterogeneous soil column (2009, methodology): “The single-rate MIM and the diffusion models for different geometries are all shown to be the special cases of the multiple-rate MIM model (Haggerty and Gorelick, 1995; Carrera et al., 1998; Haggerty et al., 2000; Dentz and Berkowitz, 2003).”
Impact of velocity correlation and distribution on transport in fractured media: Field evidence and theoretical model (2015, methodology): “…a/mkv r @2cmðr; tÞ @r2 50: (17) It has been shown that the MRMT model is equivalent to CTRW models characterized by uncoupled transition length and time distributions, and to time fractional advection-dispersion models [Dentz and Berkowitz, 2003; Schumer et al., 2003; Benson and Meerschaert, 2009].”
Aquifer operator scaling and the effect on solute mixing and dispersion (2006, background): “…spectrum, the nonFickian plumes (Figure 10) do not display the anomalous (power law) late-time tailing associated with fractal mobile/ immobile and typical continuous time random walk formulations [Berkowitz and Scher, 1997; Berkowitz et al., 2000; Schumer et al., 2003b; Dentz and Berkowitz, 2003].”
Upscaling discrete fracture network simulations: An alternative to continuum transport models (2005, background): “Dentz and Berkowitz [2003] recently extended the CTRW approach to account for retention process that can be described as a multitude of first-order trapping rates that do not vary spatially.”
Diffusion in Porous Media: Phenomena and Mechanisms (2019, methodology): “Likewise, CTRW is connected to time-domain random walk models (Cvetkovic et al. 1996; Delay and Bodin 2001; Painter and Cvetkovic 2005) and multirate mass transfer models (Dentz and Berkowitz 2003).”
Modeling non‐Fickian transport in geological formations as a continuous time random walk (2006, methodology): “1 the transport behavior is Fickian [Dentz and Berkowitz, 2003].”
Perspective on theories of non-Fickian transport in heterogeneous media (2009, background): “Others, such as multirate mass transfer [35] and delayed diffusion [28] models, can be related to the four approaches analyzed in this paper [24,28].”
Pore‐scale intermittent velocity structure underpinning anomalous transport through 3‐D porous media (2014, background): “…mass transfer [Haggerty and Gorelick, 1995], fractional advection-dispersion [Benson et al., 2001], and continuous time random walk (CTRW) models [Berkowitz et al., 2006; Bijeljic and Blunt, 2006], and the equivalence between the models has been shown for certain cases [Dentz and Berkowitz, 2003].”
Non‐Fickian transport in homogeneous unsaturated repacked sand (2004, methodology): “The CTRW model is able to encompass Fickian, single-rate and multiple-rate MIM transport models [Dentz and Berkowitz, 2003].”