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Open AccessArticle

Comparison of Time Nonlocal Transport Models for Characterizing Non-Fickian Transport: From Mathematical Interpretation to Laboratory Application

Department of Geological Sciences, University of Alabama, Tuscaloosa, AL 35487, USA
Department of Engineering Mechanics, Hohai University, Nanjing 210098, Jiangsu, China
Guangdong Provincial Key Laboratory of Soil and Groundwater Pollution Control, School of Environmental Science & Engineering, Southern University of Science and Technology, Shenzhen 518055, Guangdong, China
U.S. Geological Survey, Menlo Park, CA 94025, USA
Department of Aerospace Engineering and Mechanics, University of Alabama, Tuscaloosa, AL 35487, USA
School of Resources and Environmental Engineering, Hefei University of Technology, Anhui 230009, Hefei, China
Author to whom correspondence should be addressed.
Water 2018, 10(6), 778;
Received: 8 May 2018 / Revised: 25 May 2018 / Accepted: 11 June 2018 / Published: 13 June 2018
(This article belongs to the Special Issue Groundwater Contamination and Remediation)
Non-Fickian diffusion has been increasingly documented in hydrology and modeled by promising time nonlocal transport models. While previous studies showed that most of the time nonlocal models are identical with correlated parameters, fundamental challenges remain in real-world applications regarding model selection and parameter definition. This study compared three popular time nonlocal transport models, including the multi-rate mass transfer (MRMT) model, the continuous time random walk (CTRW) framework, and the tempered time fractional advection–dispersion equation (tt-fADE), by focusing on their physical interpretation and feasibility in capturing non-Fickian transport. Mathematical comparison showed that these models have both related parameters defining the memory function and other basic-transport parameters (i.e., velocity v and dispersion coefficient D) with different hydrogeologic interpretations. Laboratory column transport experiments and field tracer tests were then conducted, providing data for model applicability evaluation. Laboratory and field experiments exhibited breakthrough curves with non-Fickian characteristics, which were better represented by the tt-fADE and CTRW models than the traditional advection–dispersion equation. The best-fit velocity and dispersion coefficient, however, differ significantly between the tt-fADE and CTRW. Fitting exercises further revealed that the observed late-time breakthrough curves were heavier than the MRMT solutions with no more than two mass-exchange rates and lighter than the MRMT solutions with power-law distributed mass-exchange rates. Therefore, the time nonlocal models, where some parameters are correlated and exchangeable and the others have different values, differ mainly in their quantification of pre-asymptotic transport dynamics. In all models tested above, the tt-fADE model is attractive, considering its small fitting error and the reasonable velocity close to the measured flow rate. View Full-Text
Keywords: time nonlocal transport model; Non-Fickian diffusion; breakthrough curve time nonlocal transport model; Non-Fickian diffusion; breakthrough curve
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Lu, B.; Zhang, Y.; Zheng, C.; Green, C.T.; O’Neill, C.; Sun, H.-G.; Qian, J. Comparison of Time Nonlocal Transport Models for Characterizing Non-Fickian Transport: From Mathematical Interpretation to Laboratory Application. Water 2018, 10, 778.

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