Mathematical Modeling and Sensitivity Analysis on Cadmium Transport in Kaolinite under Direct Current Electric Field

Milad Rezaee, Mostafa Nasrollahi Gisel, Saman Saffari


Soil pollution is a challenging concern for environmentalists. Different remediation methods have been proposed to remediate polluted soils. Most of the existing methods cannot purify low permeable soils. Electrokinetic remediation (EKR) is an effective method which can remediate fine-grained soils. Understanding the physicochemical phenomena of the EKR is necessary to achieve efficient experimental framework. Therefore, the present study aims to introduce a theoretical and mathematical model for the EKR process. In the present model, different transport phenomena including ion migration, electroosmotic flow, and diffusion were considered. In addition, Chemical reactions such as adsorption/desorption, precipitation/dissolution, water autoionization reaction, and electrolysis reaction were considered. For modeling purpose, a set of partial differential and algebraic equations were used to model the remediation process. The implicit finite difference numerical model showed a good capability of simulating the EKR process. The sensitivity analysis on the retardation and tortuosity factors represented that the retardation factor had a considerable effect on the pH and cadmium concentration profiles. Although tortuosity factor did not have a significant impact on the pH profile, it had a non-negligible effect on the cadmium concentration profile.


Numerical Model; Finite Difference; Chemical Reaction; Electrokinetic; Cadmium; Sensitivity Analysis.


Virkutyte, J. Sillanpää, M. and Latostenmaa, P. Electrokinetic soil remediation - Critical overview, Sci. Total Environ., 289 (2002): 97–121. doi: 10.1016/s0048-9697(01)01027-0.

Acar, Y.B. and Alshawabkeh, A.N. Electrokinetic remediation. II: Theoretical Study, J. Geotech. Eng., 122 (1996): 173–185. doi: 10.1061/(asce)0733-9410(1996)122:3(173).

Kim, S.O. Kim, W.S. and Kim, K.W. Evaluation of electrokinetic remediation of arsenic-contaminated soils, Environ. Geochem. Health, 27 (2005): 443–453. doi:10.1007/s10653-005-2673-z.

Al-Shahrani, S.S. and Roberts, E.P.L. Electrokinetic removal of caesium from kaolin, J. Hazard. Mater., 122 (2005): 91–101. doi:10.1016/j.jhazmat.2005.03.018.

Saeedi, A. Li, L.Y. and Gharehtapeh, A. Effect of alternative electrolytes on enhanced electrokinetic remediation of hexavalent chromium in clayey soil. Int. J. Environ. Res. 7(2013): 39-50.doi:10.22059/IJER.2012.584.

Reddy, K.R. Maturi, K. and Cameselle, C. Sequential Electrokinetic Remediation of Mixed Contaminants in Low Permeability Soils. Journal of environmental engineering. 135 (2009): 989–999.doi:10.1061/(asce)ee.1943-7870.0000077.

Vereda-Alonso, C. Rodríguez-Maroto, J. M. García-Delgado, R. A. Gómez-Lahoz, C. and García-Herruzo, F. Two-dimensional model for soil electrokinetic remediation of heavy metals: Application to a copper spiked kaolin, Chemosphere, 54(2004): 895–903.doi: 10.1016/j.electacta.2006.01.087.

Reddy, K.R. and Cameselle, C. Electrochemical Remediation Technologies for polluted soils, sediments and groundwater, Wily, 2009. doi: 10.1002/9780470523650.

Acar Y. B. and Alshawabkeh, A. N. Principles of electrokinetic remediation, Environ. Sci. Technol., 27(1993): 2638–2674.doi: 10.1021/es00049a002 .

Chang, C. M. Wang, M. K. Chang, T. W. Lin, C. and Chen, Y. R. Transport modeling of copper and cadmium with linear and nonlinear retardation factors, Chemosphere, 43(2001): 1133–1139. doi: 10.1016/s0045-6535(00)00176-4.

Kim, S. Kim, J. Kim, K. and Yun, S. Models and Experiments on Electrokinetic Removal of Pb(II) from Kaolinite Clay, Separation Science and Technology, 39 (2004): 1927–1951. doi: 10.1081/ss-120030775 .

Kim, S.O. Kim, J. J. Yun, S. T. and Kim, K. W. Numerical and experimental studies on Cadmium(II) transport in kaolinite clay under electrical fields, Water, Air Soil Pollut. 150 (2003): 135–162. doi: 10.1023/A:102618180

Park, J. S. Kim, S. O. Kim, K. W. Kim, B. R. and Moon, S. H. Numerical analysis for electrokinetic soil processing enhanced by chemical conditioning of the electrode reservoirs, J. Hazard. Mater., 99 (2003): 71–88. doi: 10.1016/s0304-3894(03)00038-4.

Amrate S. and Akretche, D. E. Modeling EDTA enhanced electrokinetic remediation of lead contaminated soils, Chemosphere, 60 (2005): 1376–1383.doi: 10.1016/j.chemosphere.2005.02.021.

Mascia, M. Palmas, S. Polcaro, A. M. Vacca, A. and Muntoni, A. Experimental study and mathematical model on remediation of Cd spiked kaolinite by electrokinetics, Electrochim. Acta, 52(2007): 3360–3365. doi: 10.1016/j.electacta.2006.04.066 .

Al-Hamdan A. Z. and Reddy, K. R. Electrokinetic Remediation Modeling Incorporating Geochemical Effects, J. Geotech. Geoenvironmental Eng., 134 (2008): 91–105. doi: 10.1061/(asce)1090-0241(2008)134:1(91)

Paz-García, J. M. Johannesson, B. Ottosen, L. M. Ribeiro, A. B. and Rodríguez-Maroto, J. M. Modeling of electrokinetic processes by finite element integration of the Nernst-Planck-Poisson system of equations, Sep. Purif. Technol. 79(2011): 183–192. doi: 10.1016/j.seppur.2011.02.023.

Miao T. and Pan, T. A Multiphysics Model for Evaluating Electrokinetic Remediation of Nuclear Waste-Contaminated Soils, Water, Air, Soil Pollut. 226(2015): 77. doi: 10.1007/s11270-014-2292-3.

Asadollahfardi, G. Rezaee, M. and Tavakoli Mehrjardi, G. Simulation of Unenhanced Electrokinetic Process for Lead Removal from Kaolinite Clay, Int. J. Civ. Eng., 14 (2016): 263-270. doi: 10.1007/s40999-016-0049-7.

Rezaee, M. Kargar, P. and Mohammad Hosseini, A. Electrokinetic Remediation of Zinc and Copper Contaminated Soil : A Simulation-based Study. Civil Engineering Journal. 3(2017): 690–700. doi: 10.21859/cej-03096.

Kim, S. O. Moon, S. H. and Kim, K. W. Removal of Heavy Metals from Soils using Enhanced Electrokinetic Soil Processing, Water. Air. Soil Pollut. 125(2001): 259–272.doi: 10.1023/A:1005283001877.

Mitchell, J. K. Fundamentals of Soil Behavior. Wiley, 1993.

Alshawabkeh, A.N. Theoretical and Experimental Modeling of Removing Contaminants from Soils by an Electric Field, PhD thesis, The Louisiana State University, 1994.

Probstein, R.F.Physicochemical Hydrodynamics – An Introduction. Wiley 1994.

Holmes, P. Electrochemistry of Semiconductors. Academic Press, 1962.

Sposito, G. The Chemistry of Soils, Oxford University Press, 1989.

Hizal, J. and Apak, R. Modeling of cadmium(II) adsorption on kaolinite-based clays in the absence and presence of humic acid, Appl. Clay Sci., 32 (2006): 232–244.doi: 10.1016/j.clay.2006.02.002.

Srivastava, P. Singh, B. and Angove, M. Competitive adsorption behavior of heavy metals on kaolinite, J. Colloid Interface Sci., 290 (2005), 28–38. doi: 10.1016/j.jcis.2005.04.036 .

Ikhsan, J. Johnson, B. and Wells, J. A Comparative Study of the Adsorption of Transition Metals on Kaolinite., J. Colloid Interface Sci., 217 (1999): 403–410.doi: 10.1006/jcis.1999.6377 .

Lide, D. R.CRC Handbook of Chemistry and Physics. CRC Press 2009. doi: 10.1021/ja906434c

Rezaee, M. Numerical Modeling of Electrokinetic Remediation of Heavy Metal Contaminated Kaolinite Soil. MS.c. Thesis, Kharazmi University, 2014.

Rezaee, M. Asadollahfardi, G. and Gisel, M. Finite Difference Modeling of Electro-kinetic Process to Remove Lead from Kaolinite, First National Conference on Soil Mechanics and Foundation Engineering, 2014.

Asadollahfardi, G. Nasrollahi Gisel, M. and Rezaee, M. Electrochemical Remediation Technology : Fundamentals , Benefits and Challenges Third international symposium on environmental and water resource engineering, 2015.

Full Text: PDF

DOI: 10.28991/cej-030940


  • There are currently no refbacks.

Copyright (c) 2017 Milad Rezaee, Mostafa Nasrollahi Gisel, Saman Saffari

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.