Journal of Flow Chemistry

, Volume 9, Issue 1, pp 59–71

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

• Abril Cruz-López
• Mario E. Cordero
• Luis G. Zárate
• Martín R. Cruz-Díaz
• Gianpaolo Fontana
• Ever Peralta-Reyes
Full Paper

## 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.

## Keywords

BDD electrodes Electrochemical flow reactor 2-chlorophenol degradation Mathematical modeling

## 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

ACross = Wch × (Sch − Se)

Area of cross section, m2

PWet = 2Wch + 2(Sch − Se)

Wet perimeter, m

Wch

Channel width, m

Sch

Channel thickness, m

Se

Electrode thickness, m

VT

Tank volume, L

Q

Liquid flow rate, L min−1

j

Current density, A cm2

C2 −  CPh

Concentration of 2-chlorophenol, mol m−3

C2 −  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

pKa

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

-ri

Reaction rate model, mol m−3 h−1

C0

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

t

Time, h

Di

Diffusion coefficient, m2 s−1

P

Pressure, Pa

Pinit

Initial pressure, Pa

Phydro

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

Ni

Molar flux, mol h−1 m−2

R2

Correlation coefficient

## Greek

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

## Dimensionless groups

$$\operatorname{Re}=\frac{u{D}_H}{\nu }$$

Reynolds number, dimensionless

## Acronyms

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

## Notes

### 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.

## Supplementary material

41981_2018_27_Fig10_ESM.png (17 kb)
ESM 1

(PNG 16 kb)

41981_2018_27_MOESM1_ESM.tif (40 kb)
High Resolution (TIF 40 kb)

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## Authors and Affiliations

• 1
• Abril Cruz-López
• 1
• 1
• Mario E. Cordero
• 2
• Luis G. Zárate
• 2
• Martín R. Cruz-Díaz
• 3
• Gianpaolo Fontana
• 1
• Ever Peralta-Reyes
• 1
Email author
1. 1.Campus Puerto ÁngelUniversidad del MarOaxacaMexico