Modeling non‐Fickian transport in geological formations as a continuous time random walk

By Brian Berkowitz, A. Cortis, M. Dentz, Harvey Scher. 2006

1,093 citations recorded by the source corpus.

Subfields: Civil and Structural Engineering, Environmental Engineering, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/dcc59bb13b316ec06572e37cc8658fc290fe3e16

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In Civil and Structural Engineering

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Citations in the corpus

Time and space nonlocalities underlying fractional-derivative models: Distinction and literature review of field applications (2009, methodology): “These techniques are the Stochastic Averaging of the classical ADE (SA-ADE) method, the (single- and) multiple-rate mass transfer (MRMT) method (see the recent work [64,65,68,69], also see [25,26,30,60,67,109,134,138,149,154], among many others), the continuous time random walk (CTRW) method [18,47,”
Experimental investigation of the thermal dispersivity term and its significance in the heat transport equation for flow in sediments (2012, background): “This tailing effect can be attributed to non-Fickian or anomalous transport [Kennedy and Lennox, 2001] caused by local scale heterogeneities [Berkowitz et al., 2006].”
Weak Ergodicity Breaking of Receptor Motion in Living Cells Stemming from Random Diffusivity (2014, background): “Fundamental questions about the nature of anomalous and nonergodic diffusion in disordered media arise in many fields, such as life sciences [28], soft condensed matter [51,52], ultracold gases [53,54], geology [55], and ecology [56].”
Overview to mathematical analysis for fractional diffusion equations - new mathematical aspects motivated by industrial collaboration (2010, background): “Since [1], there are trials for better modelling and we can refer to Berkowitz, Scher and Silliman [6], Y. Hatano and N. Hatano [18].”
Fractional conservation of mass (2008, background): “The fractional advection dispersion equation is known to be a special case of a general transport equation with convolution flux [7] and a limit case of the continuous time random walk with power-law particle jumps [4,10].”
Comparison of alternative models for simulating anomalous solute transport in a large heterogeneous soil column (2009, methodology): “The CTRW visualizes solute transport in a variable velocity field as a series of particle jumps or transitions via different paths with spatially changing velocities, and it allows waiting between jumps (Berkowitz et al., 2006).”
Perspective on theories of non-Fickian transport in heterogeneous media (2009, background): “A detailed review of the approach, on which we rely below, can be found in [8].”
Parameter estimation for fractional transport: A particle‐tracking approach (2009, background): “The mathematical equivalence between the time-fractional ADE and the CTRW scaling limit is well known [Meerschaert et al., 2002; Berkowitz et al., 2006].”
Pore‐scale intermittent velocity structure underpinning anomalous transport through 3‐D porous media (2014, methodology): “…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,…”
An inverse problem for a one-dimensional time-fractional diffusion problem (2012, background): “, viscoelastic materials, amorphous semiconductor and porous media [1].”
Transport upscaling in heterogeneous aquifers: What physical parameters control memory functions? (2008, background): “The memory function derived from such tracer test should be scaled (i.e., t2 increased in the same proportion than travel time [Berkowitz et al., 2006]) if caused by slow advection, but not if caused by diffusion.”
A finite element solution for the fractional advection–dispersion equation (2008, background): “Heterogeneities are regarded as the primary causes of non-Fickian migration of solute in porous media [5].”