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Mathematical modeling of the electrochemical degradation of 2-chlorophenol using an electrochemical flow reactor equipped with BDD electrodes

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Abstract

The objective of this work was to develop a mathematical model of an electrochemical flow reactor for the degradation of 2-chlorophenol. The reactor operates in batch recirculation and undivided mode under mass transport control and under galvanostatic conditions. The mathematical model proposed here was simulated on COMSOL Multiphysic® 5.3 software (involving the continuity and Navier-Stokes equation in a laminar regime, and the diffusion-convection equation with reaction term) interacting with the MATLAB® version R 2017a software (continuous stirred tank). The electrolysis process was carried out at a current density of 0.14 A m−2, a liquid flow rate of 1 L min−1 and pH = 7.3. The main results show that the mathematical model proposed here is in a very good agreement with the experimental study (correlation coefficient of 0.9917 and a reduced root-mean-square error of 0.4041). The final concentration of 2-chlorophenol estimated by the mathematical model was 0.0013 mol m−3, while the experimental concentration reached was 0.0001 mol m−3, confirming the predictive capacity of the mathematical model, as well as the efficiency of the electrochemical process implemented.

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Abbreviations

u :

Liquid flow velocity, m s−1

\( {D}_H=\frac{4{A}_{Cross}}{P_{Wet}} \) :

Equivalent hydraulic diameter of the rectangular flow channel, m

A Cross = W ch × (S ch − S e):

Area of cross section, m2

P Wet = 2W ch + 2(S ch − S e):

Wet perimeter, m

W ch :

Channel width, m

S ch :

Channel thickness, m

S e :

Electrode thickness, m

V T :

Tank volume, L

Q :

Liquid flow rate, L min−1

j :

Current density, A cm2

C 2 −  CPh :

Concentration of 2-chlorophenol, mol m−3

C 2 −  CPh, 0 :

Initial concentration of 2-chlorophenol, mol m−3

\( {C}_{2- CPh}^{\mathrm{exp}} \) :

2-CPh concentrations of experiment, mol m−3

\( {C}_{2- CPh}^{theor} \) :

2-CPh concentrations of theoretical model, mol m−3

pH:

Logarithmic scale of acidity or basicity, dimensionless

•OH:

Hydroxyl radical

pK a :

Negative base-10 logarithm of the acid dissociation constant

\( {K}_{ow}^a \) :

Octanol–water partition coefficient, dimensionless

k :

Apparent first-order reaction rate constant, h−1

-r i :

Reaction rate model, mol m−3 h−1

C 0 :

Outlet concentration of the 2-CPh from tank that feeds the reactor, mol m−3

t :

Time, h

D i :

Diffusion coefficient, m2 s−1

P :

Pressure, Pa

P init :

Initial pressure, Pa

P hydro :

Hydrodynamic pressure, Pa

Ι :

Unit momentum vector, dimensionless

F :

Volume force, N m−3

\( \tilde{n} \) :

Unit normal vector, dimensionless

g :

Gravity acceleration constant, m s−2

n :

Number of data points

N i :

Molar flux, mol h−1 m−2

R 2 :

Correlation coefficient

ν :

Kinematic viscosity of the fluid, m2 s−1

ρ :

Density of the fluid, kg L−1

μ :

Dynamic viscosity of the fluid, kg m−1 s−1

∇ :

Gradient

\( \operatorname{Re}=\frac{u{D}_H}{\nu } \) :

Reynolds number, dimensionless

UHPLC :

Ultrahigh-performance liquid chromatography

BDD:

Boron-doped diamond

2-CPh :

2-chlorophenol

DSA:

Dimensionally stable anode

RTD:

Residence time distribution

CST:

Continuous stirred tank

RMSE:

Reduced root-mean-square error

CFD:

Computational fluid dynamics

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Acknowledgements

The authors are thankful for the support of the Programa para el Desarrollo Profesional Docente (PRODEP), [Project DSA/103.5/16/10242 with CUP: 2II1605, 2016]. We also wish to thank Ph.D. Aitor Aizpuru for checking the text.

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Authors and Affiliations

  1. Campus Puerto Ángel, Universidad del Mar, Ciudad Universitaria S/N, 70902 Puerto Ángel, San Pedro Pochutla, Oaxaca, Mexico

    Alejandro Regalado-Méndez, Abril Cruz-López, Juan Mentado-Morales, Gianpaolo Fontana & Ever Peralta-Reyes

  2. Escuela de Ingeniería Química, Universidad Popular Autónoma del Estado de Puebla, Sur 21, 72410 Barrio de Santiago, Puebla, Mexico

    Mario E. Cordero & Luis G. Zárate

  3. Departamento de Ingeniería y Tecnología, Facultad de Estudios Superiores Cuautitlán, Universidad Nacional Autónoma de México, Av. 1° de Mayo, 54740, Cuautitlán Izcalli, Estado de México, Mexico

    Martín R. Cruz-Díaz

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  1. Alejandro Regalado-Méndez
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Correspondence to Alejandro Regalado-Méndez or Ever Peralta-Reyes.

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Regalado-Méndez, A., Cruz-López, A., Mentado-Morales, J. et al. Mathematical modeling of the electrochemical degradation of 2-chlorophenol using an electrochemical flow reactor equipped with BDD electrodes. J Flow Chem 9, 59–71 (2019). https://doi.org/10.1007/s41981-018-00027-4

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