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Numerical Modeling of Phenol Adsorption on Granular Activated Carbon Fixed Bed: Comparison of Two Numerical Methods to Solve the Advection-dispersion Equation

Mounira Kolli ORCID logo, Safia Semra, Fatiha Benmahdi, Mohamed Bouhelassa and Michel Sardin


This paper presents a comparison between some numerical methods and techniques for solving the nonlinear advection-dispersion equation, which may be used to describe the adsorption of phenol into a granular activated carbon fixed bed under local equilibrium conditions. The adsorption is described by the Langmuir isotherm, which makes the advection-dispersion equation nonlinear. This equation is solved successively by using the approximation and linearization techniques. For each technique, two types of numerical algorithms are used. Concerning the first one, the Implicit and the Runge Kutta schemes are used. As for the second one, the Modified Picard iteration and the Newton Raphson scheme are applied. Simulation results have been compared to each other and to the experimental data as well. Both of the Implicit and the Runge Kutta algorithms have led to superimposed simulated breakthrough curves. Both of the modified Picard and Newton Raphson schemes have given identical results too. However, comparing to the experimental data, the obtained solution, using the approximation technique, has underestimated the retardation of solute and failed in fitting the experimental breakthrough. The Obtained solution, using the linearization technique, has correctly fitted the experimental results under all the conditions of: feed flow rate, activated carbon bed height and the inlet phenol concentration.


Symbols used

ULinear flow velocity(m/s)
CSolute concentration into liquid phase(mg/m3)
CpSolute concentration into stationary phase(mg/m3)
C0Initial concentration of source fluid(mg/m3)
DLHydrodynamic dispersion coefficient(m2/s)
KlLangmuir constant(m3/mg)
LLength of column(m)
sSolid phase solute concentration(mg/g)
SmaxTotal concentration of available sorption sites(mg/g)
MAdsorbent mass(mg)
VSolution volume(m3)
xSpace variable(m)

Greek letters

ρbulk density(mg/m3)
εvolumetric water contentdimensionless


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Received: 2019-11-23
Revised: 2020-03-04
Accepted: 2020-03-05
Published Online: 2020-06-03

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