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Approximation of transient redox boundary conditions: its application to numerical analysis of iron plume migration near landfills

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Abstract

An efficient scheme is presented that attempts to implement the moving boundary conditions in a two-dimensional finite difference analysis model that simulates reductive dissolution and subsequent precipitation of iron species in surficial aquifer exposed to time-dependent redox boundary conditions near landfills. A mathematical and numerical model for simulating the vertical flux of oxygen through the variably saturated vadose zone and resulting hydrochemical response of groundwater system is developed and subsequently used to study dissolved iron plume migration phenomena from substrates beneath landfills. The proposed modeling scheme of the boundary condition is then applied to the groundwater system near an in-service landfill site located in state of Florida to produce an approximate solution to highly nonlinear boundary-value problems in hydrochemical systems subjected to various site geometries and soil conditions. As a result of the 12 years of consecutive runs with annually updated boundary conditions, a steady-state distribution of iron concentration is obtained and well compared with historical in situ data of groundwater iron concentrations depending on the desired degrees of accuracy.

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Abbreviations

HFO:

Hydrous ferric oxides

SSF:

Source strength function

TEA:

Terminal electron acceptors

\(\alpha_{\text{L}}\) :

Longitudinal dispersivity (L)

\(C\) :

Concentration of species (M/L3)

\({\text{Co}}\) :

Courant number

D :

Macrodispersion coefficient (L2/T)

\(D_{\text{e}}\) :

Effective diffusion coefficient (L2/T)

\(h\) :

Matric potential in vadose zone (L)

\(h_{\text{well}}\) :

Hydraulic head at a well (L)

J :

Advective–dispersive flux (M/L2/T)

K :

Equilibrium constant

K H :

Henry’s constant (1.3 × 10−3 mol/L/atm at 298.15 K)

K sat :

Saturated hydraulic conductivity (L/T)

\(K_{\text{L}}\) :

Overall liquid-side mass transfer coefficient (L/T)

\(k_{{}}^{\text{eff}}\) :

Effective permeability (L2)

\(k_{\text{r}}\) :

Relative permeability (L2)

\(\eta\) :

Porosity

\(R_{\text{s}}\) :

Respiratory consumption rate of oxygen (M/L2/T)

\(s_{\text{w}}\) :

Degree of water saturation

\(s_{\text{r}}\) :

Residual saturation

\(\mu\) :

Dynamic viscosity of water (M/L/T)

\(v_{x}\) :

Average pore water velocity (L/T)

\(\Delta z_{\text{VZ}}\) :

Vadose zone thickness (L)

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Acknowledgements

This work was supported by the Korean Ministry of Environment as Eco-Innovation Program (no. 2014000150017), the Hinkley Center for Solid and Hazardous Waste Management, and the Computer Laboratory for Granular Physics Studies in University of Florida. The authors would like to express their sincere gratitude to Dr. Nicolas Spycher at the Lawrence Berkeley National Laboratory for his useful comments on the iron cycling model in lake sediments. The authors also thank anonymous reviewers and the associate editor for helpful comments and suggestions in improving the content of this paper.

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Authors and Affiliations

  1. Department of Environmental Engineering and Sciences, Engineering School of Sustainable Infrastructure and Environment, University of Florida, Gainesville, USA

    Jaeshik Chung & Timothy G. Townsend

  2. Computer Laboratory for Granular Physics Studies, University of Florida, 1949 Stadium Rd. Room 365, P.O. Box 116580, Gainesville, FL, 32611, USA

    Jaeshik Chung & Jae H. Chung

  3. Water Cycle Research Center, Korea Institute of Science and Technology, Seoul, South Korea

    Jaeshik Chung

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  1. Jaeshik Chung
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Correspondence to Jae H. Chung.

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Chung, J., Chung, J.H. & Townsend, T.G. Approximation of transient redox boundary conditions: its application to numerical analysis of iron plume migration near landfills. Environ Earth Sci 78, 711 (2019). https://doi.org/10.1007/s12665-019-8683-4

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