Simulating Zn, Cd and Ni Transport in Disturbed and Undisturbed Soil Columns: Comparison of Alternative Models

  • Samira Morsali
  • Hossein BabazadehEmail author
  • Shahram Shahmohammadi-Kalalagh
  • Hossein Sedghi
Research paper


This study compared four solute transport models for three heavy metals, i.e. Zn, Cd and Ni, in two disturbed and undisturbed loamy soil columns. The models include convection–dispersion equation (CDE), mobile–immobile model (MIM), fractional advection–dispersion equation (FADE) and the continuous time random walk model (CTRW). The experiments were carried out for each metal at three initial concentrations (C0 = 50, 100 and 150 mg L−1) and three replications in both soil columns. The results indicated that CDE, MIM, FADE and CTRW, with r2 > 0.98 and RMSE < 0.06, were capable of describing the BTCs of these heavy metals adequately. Compared to FADE and CTRW, CDE and MIM had better BTC fits with higher r2 values and lower RMSE values in both soil columns. The models in the disturbed soil had a better fit than the undisturbed soil. As C0 was increased, the retardation factor (R) of Zn, Cd and Ni decreased. Regardless of the type of soil column, R reveals the trend: Zn > Ni > Cd. The hydrodynamic dispersion coefficient (D) in the undisturbed soil was higher than the disturbed soil. The spreading parameter (β) of CTRW and the fractional differentiation orders (α) in FADE were approximately 1.0 and 1.7, respectively. Consequently, the heavy metal transport within both soil columns were anomalous or non-Fickian transport. However, CDE and MIM, which are based on Fickian diffusion law, were more appropriate for simulating heavy metal transport through two soil columns in comparison with CTRW and FADE.

Article Highlights

  • Simulation of solute transport for three heavy metals, i.e. Zn, Cd and Ni.

  • Comparison of solute behavior in disturbed and undisturbed loamy soil columns.

  • Apply convection–dispersion equation (CDE), mobile–immobile model (MIM), fractional advection–dispersion equation (FADE) and the continuous time random walk model (CTRW).

  • Apply models in different initial concentration.

  • Sensitivity analysis of the most influential factors on the model output.


Fractional differentiation orders Heavy metals Hydrodynamic dispersion Retardation factor Spreading parameter introduction 


Compliance with Ethical Standards

Conflict of interest

On behalf of all authors, the corresponding author states that there is no conflict of interest.


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Copyright information

© University of Tehran 2019

Authors and Affiliations

  1. 1.Department of Water Sciences and EngineeringScience and Research Branch, Islamic Azad UniversityTehranIran
  2. 2.Department of Water Sciences and EngineeringTabriz Branch, Islamic Azad UniversityTabrizIran

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