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Mathematical modeling of the anodic oxidation of organic pollutants: a review

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Abstract

Anodic oxidation is a promising method for removing organic pollutants from water due to its high nonselectivity and effectiveness. Nevertheless, its widespread application is limited due to its low current efficiency, high energy consumption and low treatment rates. These problems may be overcome by the optimization of the process parameters, reactor design and electrode geometry, by coupling the experimental investigations with mathematical modeling. Here we review the modeling of anodic oxidation with focus on basics of this process, the competition phenomenon in real wastewater, flow cells and batch cells, historical aspects, general modeling equations, modeling with plate electrodes, modeling with porous 3-dimension electrodes and the density functional theory. Mathematical modeling can provide current, voltage and concentration distributions in the system. Mathematical modeling can also determine the effects on the performance of parameters such as diffusion layer thickness, flow velocity, applied current density, solution treatment time, initial concentration and diffusion coefficients of organic pollutants, electrode surface area, and oxidation reaction rate constant. Mathematical models allow to determine whether the limiting factor of the process is kinetics or diffusion, and to study the impact of competition of phenomena. The density functional theory provides information on probable reaction pathways and by-products.

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Abbreviations

Blue-TiO2 :

Blue-titanium dioxide

C6H6 :

Benzene

CH3COCH3 :

Acetone

(C2H5)3N :

Triethylamine

CH3OH :

Methanol

Cl− :

Chloride ions

ClCH꞊CCl2 :

Trichloroethylene

ClO3 − :

Chlorate

CO2 :

Carbon dioxide

H2 :

Hydrogen

H2CO3 :

Carbonic acid

H2O :

Water

IrO2-Ta2O5 :

Iridium dioxide-tantalum pentoxide electrode

NaClO4 :

Sodium perchlorate

NO2 :

Nitrogen dioxide

O3 :

Ozone

O3/H2O2 :

Ozone/hydrogen peroxide

PO4 3− :

Phosphate

RuO2-TiO2 :

Ruthenium oxide-titania electrode

S2O8 2− :

Peroxodisulfate

Ti4O7 :

Sub-stoichiometric titanium oxide

Ti/Pt:

Titanium covered by platinum electrode

B:

Boron

Carbon/Graphite:

Carbon-coated graphite electrode

CH3CH3 :

Ethane

CH3COOH:

Acetic acid

C6H5NH2 :

Aniline

C6H5OH:

Phenol

Cl2 :

Chlorine

ClO− :

Hypochlorite

ClO4 − :

Perchlorate

C2O6 2− :

Peroxodicarbonate

HCO3 − :

Hydrogen carbonate

HClO:

Hypochlorous acid

HCOOH:

Formic acid

NaCl:

Sodium chloride

Na2SO4 :

Sodium sulfate

O2 :

Oxygen

OCH3 :

Methoxy groups

·OH:

Hydroxyl radicals ()

P2O8 4− :

Peroxodiphosphate

SO4 2− :

Sulfate

TinO2 n −1 :

Magnéli phases of sub-stoichiometric titanium oxides

Ti/PbO2 :

Titanium-coated lead dioxide electrode

Ti/SnO2 :

Titanium-coated tin dioxide electrode

A :

Electrode area (m2)

c :

Concentration (mol m−3)

c s :

Concentration at the electrode surface (mol m−3)

C R :

Concentration of anodic reactants (mol m−3)

c tp :

Tracer particles concentration (mol m−3)

COD :

Chemical oxygen demand (mol O2 m−3)

D :

Diffusion coefficient of the compound (m2 s−1)

d reac :

Reaction zone thickness (m)

\(\overline{f}\) :

Body force (N kg−1)

\(\overline{i}\) :

Current density (A cm−2)

i lim :

Limiting current density (A m−2)

i lim,ne − :

Limiting current density of DET(A m−2)

i 0 :

Exchange current density(A cm−2)

\(\overline{j}\) :

Flux density (mol m−2 s−1)

k · O H :

·OH recombination rate constant (m3 mol−1 s−1)

P :

Given loading (mol COD s−1)

Pe :

Peclet number

R :

Reactive term (mol m−3 s−1)

R c :

Electrolyte ohmic resistance (Ω)

r i :

Oxidation rate of each compound in the reaction zone (mol m−2 s−1)

Sh :

Sherwood number

t :

Time (s)

t s :

Special time (s)

\(\overline{u}\) :

Linear fluid velocity (m s−1)

V R :

Reservoir volume (m3)

ΔV work :

Cell potential (V)

X :

COD conversion (%)

X cr :

Critical conversion

Α :

Electron transfer coefficient

A req :

Required electrode area (m2)

c b :

Bulk concentration (mol m−3)

C 0 :

Concentration of cathodic reactants (mol m−3)

C :

Dimensionless tracer particles concentration

c tp 0 :

Initial tracer particles concentration (mol m−3)

COD0 :

Initial chemical oxygen demand (mol O2 m−3)

E sp :

Specific energy consumption (kW h kg COD−1)

F :

Faraday’s constant(C mol−1)

i :

Current intensity (A)

i appl :

Applied current density (A m−2)

i lim 0 :

Initial limiting current density (A m−2)

i · OH :

Initial limiting current density, corresponding to the total mineralization of organic compounds (A m−2)

J :

Flux (mol s−1)

k m :

Mass transfer coefficient (m s−1)

L x :

Axial length (m)

p :

Applied pressure (Pa)

Q cr :

Critical specific charge (Ah m−3)

\(\overline{R}\) :

Universal gas constant (J mol−1 K −1)

Re :

Reynolds number

Sc :

Smidt number

T :

Temperature (K)

t cr :

Critical time (s)

u int :

Interstitial liquid velocity (m s−1)

V :

Volume of electrolyte (dm3)

ΔV i :

Oxidation potential of each process (V)

X l :

Dimensionless axial length (m)

x :

Axis coordinate along the distance (m)

z :

Charge

δ [delta] :

Diffusion layer thickness (m)

ε [epsilon] :

Effectiveness factor

ε Cl − [epsilon Cl] :

Faradic yield as a function of chloride (Cl−) concentration

η a [eta a] :

Overpotential of anodic reaction (V)

θ [theta] :

Dimensionless time

μ [mu] :

Dynamic viscosity (Pa s)

τ [tau] :

Electrolysis time (s)

φ [phi, small letter] :

Electric potential (V)

α i [alpha i] :

Proportion of electrons involved in a particular electrochemical process corresponds to each process i

α ·OH [alpha OH] :

Term accounts for the fraction of current directed toward ·OH production

δ(exp) [delta exp] :

Diffusion layer thickness obtained experimentally (m)

ε i [epsilon i] :

Faradaic yield

η c [eta c] :

Overpotential of cathodic reaction (V)

θ i [theta i] :

Parameter represents the oxidation efficiency

ρ[rho] :

Liquid density (kg m−3)

ϕ [phi] :

Dimensionless parameter expressing the ratio between the chemical reaction rate and the mass transfer coefficient

φ [phi, small bold letter] :

Normalized current efficiency

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Funding

This research was funded by Russian Science Foundation, project No. 22-79-10177.

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Authors and Affiliations

  1. Department of Civil, Chemical and Environmental Engineering, University of Genoa, Via All’Opera Pia, 15, 16145, Genoa, Italy

    Ekaterina Skolotneva, Davide Clematis & Marco Panizza

  2. Physical Chemistry Department, Kuban State University, 149 Stavropolskaya Str., Krasnodar, Russia, 350040

    Andrey Kislyi, Anastasiia Klevtsova & Semyon Mareev

Authors
  1. Ekaterina Skolotneva
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  2. Andrey Kislyi
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  3. Anastasiia Klevtsova
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  4. Davide Clematis
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  5. Semyon Mareev
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  6. Marco Panizza
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Contributions

ES, DC, MP and SM contributed to conceptualization and writing—review and editing; ES and SM contributed to methodology; ES, AK and AK contributed to software, project administration, funding, visualization and investigation; SM contributed to resources; ES, AK, AK and SM contributed to writing—original draft preparation; and SM, DC and MP supervised the study. All authors have read and agreed to the published version of the manuscript.

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Correspondence to Ekaterina Skolotneva or Semyon Mareev.

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Skolotneva, E., Kislyi, A., Klevtsova, A. et al. Mathematical modeling of the anodic oxidation of organic pollutants: a review. Environ Chem Lett 22, 1521–1561 (2024). https://doi.org/10.1007/s10311-023-01693-0

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  • DOI: https://doi.org/10.1007/s10311-023-01693-0

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