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A novel analytical model of solute transport in a layered aquifer system with mixing processes in the reservoirs

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Abstract

Analytical models of solute transport have been widely used to aid the understanding of the physical and chemical processes undergone by substances introduced in a layered aquifer system. However, in previous studies, the advection component of transport was assumed to be one dimensional, while also ignoring the mixing processes that occur in the inlet and the outlet reservoirs. In this study, new sets of models describing those mixing processes are presented. Beyond that, these models were integrated into already existing models and the result is a novel analytical model of solute transport in aquifer-aquitard systems. The novel analytical solution was derived by the Laplace transform method and the finite-cosine Fourier transform method under the mobile-immobile (MIM) framework. The calculations take into account: the longitudinal and vertical dispersion, the molecular diffusion and the horizonal and vertical advection components of solute transport, as well as first-order chemical reaction, in both the aquifer and the aquitard. A finite-difference solution of the model is tested against experimental data in order to critique its reliability. Results indicate that the numerical and analytical solutions of the new model match well with experimental data. This new model outperforms the previous models in terms of interpreting experimental data. The mixing old and new water in the reservoirs during solute transport in aquifer-aquitard systems is important. Global sensitivity analysis demonstrates that the output concentration of solute in the aquifer-aquitard system is most sensitive to the volume of water in the inlet reservoir. The contribution of the molecular diffusion effect to the total mass flux of the tracer cross the aquifer-aquitard interface is much smaller than the contribution of the dispersive and advective effects.

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Data availability

The datasets used and/or analyzed during the current study are available from the corresponding author on reasonable request.

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Acknowledgements

The authors would like to thank the Editor and anonymous reviewers for their constructive comments which help us greatly improve the quality of the manuscript.

Funding

This research was partially supported by three Programs of the Natural Science Foundation of China (No.41772252 and No. 41972250); National Key Research and Development Program of China (No. 2021YFA0715900); Innovative Research Groups of the National Nature Science Foundation of China (No. 41521001), the Fundamental Research Funds for Central Universities, China University of Geosciences (Wuhan) (No. CUGGC07); the Natural Science Foundation of Hubei Province (2021CFA089); the 111 Program (State Administration of Foreign Experts Affairs & the Ministry of Education of China, No. B18049); the Belt and Road Special Foundation of the State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering(No. 2020492011), and Natural Science Foundation of Chongqing (cstc2020jcyj-msxmX1072).

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Authors and Affiliations

  1. State Environmental Protection Key Laboratory of Source Apportionment and Control of Aquatic Pollution, Ministry of Ecology and Environment, 388 Lumo Road, Wuhan, 430074, China

    Wenguang Shi & Quanrong Wang

  2. Hubei Key Laboratory of Yangtze River Basin Environmental Aquatic Science, School of Environmental Studies, China University of Geosciences, Wuhan, Hubei, 430074, People’s Republic of China

    Wenguang Shi & Quanrong Wang

  3. School of Environmental Studies, China University of Geosciences, 388 Lumo Road, Wuhan, 430074, China

    Wenguang Shi, Quanrong Wang & Musa Salihu Danlami

  4. Department of Materials Science and Engineering, Kwara State University, PMB 1530, MaleteIlorin, Kwara State, Nigeria

    Musa Salihu Danlami

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  1. Wenguang Shi
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  2. Quanrong Wang
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  3. Musa Salihu Danlami
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Contributions

Conceptualization, writing-review and editing, and supervision: QW. Methodology, writing original draft, derivation, code, and formal analysis: WS. Vetting and technical support: MSD.

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Correspondence to Quanrong Wang.

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Highlights

• A novel analytical model of solute transport in a layered aquifer system is developed.

• Mixing processes in the inlet and outlet reservoirs are important for solute transport in aquifer-aquitard system.

• The performance of a new analytical model is tested by comparing modeled results with experimental data.

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Shi, W., Wang, Q. & Salihu Danlami, M. A novel analytical model of solute transport in a layered aquifer system with mixing processes in the reservoirs. Environ Sci Pollut Res 29, 67953–67968 (2022). https://doi.org/10.1007/s11356-022-20495-5

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