Time and space nonlocalities underlying fractional-derivative models: Distinction and literature review of field applications

Y Zhang, DA Benson, DM Reeves - Advances in Water Resources, 2009 - Elsevier
We investigate the spatiotemporal nonlocality underlying fractional-derivative models as a
possible explanation for regional-scale anomalous dispersion with heavy tails. Properties of …

Contaminant transport in heterogeneous aquifers: A critical review of mechanisms and numerical methods of non-Fickian dispersion

Z Guo, R Ma, Y Zhang, C Zheng - Science China Earth Sciences, 2021 - Springer
Natural aquifers usually exhibit complex physical and chemical heterogeneities, which are
key factors complicating kinetic processes, such as contaminant transport and …

Tempered anomalous diffusion in heterogeneous systems

MM Meerschaert, Y Zhang… - Geophysical Research …, 2008 - Wiley Online Library
Passive tracers in heterogeneous media experience preasymptotic transport with scale‐
dependent anomalous diffusion, before eventually converging to the asymptotic diffusion …

A simple and efficient random walk solution of multi-rate mobile/immobile mass transport equations

DA Benson, MM Meerschaert - Advances in Water Resources, 2009 - Elsevier
We extend the particle-tracking method to simulate general multi-rate mass transfer (MRMT)
equations. Previous methods for single-rate equations used two-state Markov chains and …

Transport upscaling in heterogeneous aquifers: What physical parameters control memory functions?

M Willmann, J Carrera… - Water Resources …, 2008 - Wiley Online Library
Power law tailing is often observed in the breakthrough curves (BTCs) of tracer tests. Tailing
is attributed to heterogeneity of aquifer properties and cannot be properly modeled by …

Upscaling solute transport in rough single-fractured media with matrix diffusion using a time fractional advection-dispersion equation

D Lei, HG Sun, Y Zhang, T Blaszczyk, Z Yu - Journal of Hydrology, 2023 - Elsevier
Complex structures in fractures and the rock matrix, which are difficult to map exhaustively at
the local scale, can dominate contaminant transport in fractured aquifers. An upscaled …

Influence of eddies on conservative solute transport through a 2D single self-affine fracture

Z Dou, Z Chen, Z Zhou, J Wang, Y Huang - International Journal of Heat …, 2018 - Elsevier
The solute transport regime is highly dependent upon the heterogeneity of the flow field. In
this study, the influence of eddies on conservative solute transport through a two …

Geological entropy and solute transport in heterogeneous porous media

M Bianchi, D Pedretti - Water Resources Research, 2017 - Wiley Online Library
We propose a novel approach to link solute transport behavior to the physical heterogeneity
of the aquifer, which we fully characterize with two measurable parameters: the variance of …

A distributed-order time fractional derivative model for simulating bimodal sub-diffusion in heterogeneous media

M Yin, R Ma, Y Zhang, S Wei, GR Tick, J Wang… - Journal of …, 2020 - Elsevier
Bimodal transport due to dual-mobile advection or mass exchange between mobile and
immobile zones has been widely observed for pollutants moving in heterogeneous media …

Coupling of mass transfer and reactive transport for nonlinear reactions in heterogeneous media

M Willmann, J Carrera, X Sanchez‐Vila… - Water resources …, 2010 - Wiley Online Library
Fast chemical reactions are driven by mixing‐induced chemical disequilibrium. Mixing is
poorly represented by the advection‐dispersion equation. Instead, effective dynamics …