Abstract
A new solution for advective-dispersive solute transport of sequentially decaying species is developed for a three-dimensional aquifer of finite thickness, finite width, semi-infinite extent along the direction of flow, dual porosity, equilibrium linear sorption, and first-order decay of both the sorbed and dissolved mass with coefficients that may differ in the mobile and immobile domains, and an arbitrary time-dependent source expressed as a first- or third-type boundary condition over a rectangular patch perpendicular to groundwater flow. The system of equations is solved in closed form in the Laplace domain. The model is benchmarked against a single-species analytical model, MT3DMS, and RT3D. The intended use of the model is to guide the selection of transport parameters for and check the accuracy of more complex numerical solute transport models.
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This work does not contain observations from experiments or field studies. The model for the benchmark simulations described in Sect. 3 can be reproduced using the presented analytical solution and public domain numerical transport models MT3DMS and RT3D.
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Acknowledgements
The author wishes to thank Christopher Neville of S.S. Papadopulos & Associates, Inc., for providing documentation for the benchmark model (Neville 2004); Junqi Huang, Stephen Kraemer, and Matthew Small of the EPA Office of Research and Development for their review of and helpful comments on a draft report documenting this model; and the Associate Editor and two anonymous reviewers whose constructive comments helped improve the manuscript.
Funding
The coding of the analytical solution and the preparation of the benchmark simulations was funded by the U.S. Environmental Protection Agency (EPA) under contract EP-S9-13-02. This manuscript was prepared outside of work funded by and does not represent the views of the EPA.
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The code will be published in an upcoming EPA report.
Plain Language Summary
A semi-analytical solution is developed for the solute transport of chain-decaying species in a three-dimensional aquifer of finite thickness and dual porosity. Sorption and decay coefficients may differ in the mobile and immobile domains. The source is given by first- or third-type boundary condition with arbitrary time dependency for specified concentration. Benchmark simulations compare the model results against MT3DMS and RT3D.
Appendix
Appendix
The following symbols, with units shown in brackets, are used to represent aquifer and chemical properties and transport parameters. Units are shown as length, mass, and time (L, M, T). Additional symbols for combined variables are defined in the text.
\(a_{x}\), \(a_{y}\), \(a_{z}\) | Dispersivity in the principal directions [L] |
b | Aquifer thickness [L] |
\(C \left( x ,y ,z ,t\right) \) | Concentration [M/L\(^{3}\)] |
\(D_{m}\) | Molecular diffusion coefficient in water [L\(^{2}\)/T] |
\(D_{x} ,D_{y} ,D_{z}\) | Dispersion coefficients in principal directions [L\(^{2}\)/T] |
f | Mass fraction of sorbent in contact with mobile dissolved mass [-] |
K | Distribution coefficient [L\(^{3}\)/M] |
m and i | Subscripts for mobile and immobile regions, respectively; |
Variables without index apply to both regions | |
i | Superscript for i-th species |
q | Darcy flux in the x-direction [L/T] |
w | Aquifer width [L] |
\(\alpha \) | Transfer coefficient for mass exchange between mobile |
and immobile domains [T\(^{ -1}\)] | |
\(\phi \) | Proportion of mobile porosity [-] |
\(\lambda \) | First-order decay coefficient [T\(^{ -1}\)] |
\(\rho \) | Dry bulk density of soil [M/L\(^{3}\)] |
\(\theta \) | Water content (porosity for fully saturated soil) [-] |
\(\theta _{m} =\phi \theta \) | Mobile porosity [-] |
\(\theta _{i} =\left( 1 -\phi \right) \theta \) | Immobile porosity [-] |
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Perina, T. Semi-Analytical Three-Dimensional Solute Transport of Sequentially Decaying Species with Mobile-Immobile Regions, Sorption, Decay, and Arbitrary Transient Source. Math Geosci 54, 745–762 (2022). https://doi.org/10.1007/s11004-021-09975-5
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DOI: https://doi.org/10.1007/s11004-021-09975-5