Anomalous transport in laboratory‐scale, heterogeneous porous media

By Brian Berkowitz, Harvey Scher, S. Silliman. 2000

331 citations recorded by the source corpus.

Subfields: Civil and Structural Engineering, Environmental Engineering

View Paper: https://www.semanticscholar.org/paper/8648478140e0f3e3b90eb47da5bb7227bdaac8c7

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In Civil and Structural Engineering

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Citations in the corpus

An inverse time-dependent source problem for a time-fractional diffusion equation (2016, positive): “The time fractional diffusion equations arise when replacing the standard time derivative with time fractional derivatives and can be used to describe superdiffusion and subdiffusion phenomena [2, 19, 29, 30].”
Comparison of alternative models for simulating anomalous solute transport in a large heterogeneous soil column (2009, methodology): “The CTRW has been used to quantify laboratory tracer tests (Berkowitz et al., 2000, 2008; Levy and Berkowitz, 2003; Bromly and Hinz, 2004; Cortis and Berkowitz, 2004; Cortis et al., 2006; Xiong et al., 2006; Berkowitz and Scher, 2008) and field tracer migration (Berkowitz and Scher, 1997, 1998;…”
Possible problems of scale dependency in applications of the three‐dimensional fractional advection‐dispersion equation to natural porous media (2002, methodology): “As shown in recent publications, the Levy theory may be derived within the more general framework of continuous time random walk (CTRW) processes [Berkowitz and Scher, 1995; Berkowitz et al., 2000, 2002].”
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].”
Pore‐scale modeling and continuous time random walk analysis of dispersion in porous media (2006, background): “If these conditions are not satisfied, solute undergoes spreading in a preasymptotic regime for which the dispersion coefficient increases with time and the average distance traveled [Han et al., 1985; Koch and Brady, 1987; Gelhar et al., 1992; Salles et al., 1993; Sahimi, 1995; Berkowitz et al., 20”
Transport behavior of a passive solute in continuous time random walks and multirate mass transfer (2003, methodology): “, 1998] and laboratory experiments [Silliman and Simpson, 1987] suggests that the solutions are valid over a wide time range [Berkowitz et al., 1998; Berkowitz et al., 2000; Kosakowski et al., 2000].”
Simultaneous inversion for the space-dependent diffusion coefficient and the fractional order in the time-fractional diffusion equation (2013, background): “The slow diffusion is characterized by the long-tailed profile in the spatial distribution of densities as the time passes, which has been investigated and studied in many fields of applied sciences; see [5, 12, 16, 49, 55] and references therein.”
Non‐Fickian transport in homogeneous unsaturated repacked sand (2004, background): “Continuous time random walk (CTRW) [Montroll and Weiss, 1965; Scher and Lax, 1973; Berkowitz et al., 2000, 2001; Berkowitz and Scher, 2001] also has the potential to model a range of transport behaviors.”
Physical pictures of transport in heterogeneous media: Advection‐dispersion, random‐walk, and fractional derivative formulations (2002, methodology): “We note that non-Fickian transport has been observed even in small-scale, relatively homogeneous, laboratory-scale models [Berkowitz et al., 2000].”