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Kinetic modeling of the photocatalytic degradation of clofibric acid in a slurry reactor

  • Advanced Oxidation Technologies: Advances and Challenges in IberoAmerican Countries
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Abstract

A kinetic study of the photocatalytic degradation of the pharmaceutical clofibric acid is presented. Experiments were carried out under UV radiation employing titanium dioxide in water suspension. The main reaction intermediates were identified and quantified. Intrinsic expressions to represent the kinetics of clofibric acid and the main intermediates were derived. The modeling of the radiation field in the reactor was carried out by Monte Carlo simulation. Experimental runs were performed by varying the catalyst concentration and the incident radiation. Kinetic parameters were estimated from the experiments by applying a non-linear regression procedure. Good agreement was obtained between model predictions and experimental data, with an error of 5.9 % in the estimations of the primary pollutant concentration.

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Abbreviations

a v :

Catalytic surface area per unit suspension volume (cm−1)

C :

Molar concentration (mol cm−3)

BQ:

Benzoquinone

CA:

Clofibric acid

4-CP:

4-Chlorophenol

C m :

Catalyst mass concentration (g cm−3)

ea :

Local volumetric rate of photon absorption (Einstein cm−3 s−1)

e x :

Direction cosine (dimensionless)

g :

Asymmetry factor (dimensionless)

l :

length of flight (cm)

MC:

Monte Carlo

p :

Scattering phase function

q w :

Incident radiation flux (Einstein s−1 cm−2)

R i :

Random number

RMSE:

Root mean square error (%)

r :

Reaction rate (mol cm−3 s−1)

r gs :

Superficial rate of electron-hole generation (mol cm−2 s−1)

Sg:

Specific surface area (cm2 g−1)

t :

Time (s)

V :

Volume (cm3)

x :

Axial coordinate (cm)

x:

Position vector (cm)

α i , α ′ i :

Kinetic parameter

β :

Volumetric extinction coefficient (cm−1)

ε :

Hold-up (dimensionless)

η ph :

number of photons

ν:

Stoichiometric coefficient

\( \overline{\phi} \) :

Wavelength averaged primary quantum yield (mol Einstein−1)

σ :

Volumetric scattering coefficient (cm−1)

θ :

Spherical coordinate (rad)

ω :

Albedo (dimensionless)

abs:

Absorbed

AR :

Catalytic reaction area

BQ:

Benzoquinone

CA:

Clofibric acid

4-CP:

4-Chlorophenol

λ :

Dependence on wavelength

HG:

Henyey and Greenstein

R:

Reactor

T:

Total

Tk:

Tank

0:

Initial condition

< >:

Denotes average value over a given space

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Acknowledgments

The authors are grateful to Universidad Nacional del Litoral (UNL), Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), and Agencia Nacional de Promoción Científica y Tecnológica (ANPCyT) for financial support. We also thank Antonio C. Negro for his valuable help during the experimental work.

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Authors and Affiliations

  1. Instituto de Desarrollo Tecnológico para la Industria Química, Universidad Nacional del Litoral and Consejo Nacional de Investigaciones Científicas y Técnicas, Güemes 3450, Santa Fe, 3000, Argentina

    Agustina Manassero, María Lucila Satuf & Orlando Mario Alfano

Authors
  1. Agustina Manassero
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  2. María Lucila Satuf
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  3. Orlando Mario Alfano
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Corresponding author

Correspondence to Orlando Mario Alfano.

Additional information

Responsible editor: Angeles Blanco

Appendix

Appendix

Considering the competitive adsorption mechanism between CA and their principal intermediates, we can write the following equations:

$$ \left[C{A}_{\mathrm{ads}}\right]={K}_{\mathrm{CA}}\left[{\mathrm{site}}_{\mathrm{CA}}\right]{C}_{\mathrm{CA}} $$
(18)
$$ \left[4\hbox{-} {\mathrm{CP}}_{\mathrm{ads}}\right]={K}_{4\hbox{-} \mathrm{CP}}\left[{\mathrm{site}}_{\mathrm{CA}}\right]{C}_{4\hbox{-} \mathrm{CP}} $$
(19)
$$ \left[{\mathrm{BQ}}_{\mathrm{ads}}\right]={K}_{\mathrm{BQ}}\left[{\mathrm{site}}_{\mathrm{CA}}\right]{C}_{\mathrm{BQ}} $$
(20)
$$ \left[{O}_{2,\mathrm{ads}}\right]={K}_{{\mathrm{O}}_2}\left[{\mathrm{site}}_{{\mathrm{O}}_2}\right]{C}_{{\mathrm{O}}_2} $$
(21)

where [j ads] represents the concentration of the specie j adsorbed on the catalyst surface, K j is the equilibrium adsorption constant, [site j ] represents the superficial concentration of vacant adsorption sites, and C j is the concentration of j in the suspension bulk.

Making a balance of sites we can relate the concentration of vacant sites to the total concentration of sites, [site j,T ]. Balance of absorption sites for O2:

$$ \left[{\mathrm{site}}_{{\mathrm{O}}_2,T}\right]=\left[{\mathrm{site}}_{{\mathrm{O}}_2,\mathrm{oc}}\right]+\left[{\mathrm{site}}_{{\mathrm{O}}_2}\right] $$
(22)

where \( \left[{\mathrm{site}}_{{\mathrm{O}}_2,\mathrm{oc}}\right] \) represent the superficial concentration of occupied sites by O2. Introducing Eq. (21) into Eq. (22):

$$ \left[{\mathrm{site}}_{{\mathrm{O}}_2}\right]=\frac{\left[{\mathrm{site}}_{{\mathrm{O}}_2,T}\right]}{K_{{\mathrm{O}}_2}{C}_{{\mathrm{O}}_2}+1} $$
(23)

Balance of absorption sites for the main organic compounds:

$$ \left[{\mathrm{site}}_{\mathrm{CA},\mathrm{T}}\right]=\left[{\mathrm{site}}_{\mathrm{CA},\mathrm{oc}}\right]+\left[{\mathrm{site}}_{\mathrm{CA}}\right] $$
(24)
$$ \left[{\mathrm{site}}_{\mathrm{CA},\mathrm{T}}\right]=\left[{\mathrm{CA}}_{\mathrm{ads}}\right]+\left[4\hbox{-} {\mathrm{CP}}_{\mathrm{ads}}\right]+\left[{\mathrm{BQ}}_{\mathrm{ads}}\right]+\left[{\mathrm{site}}_{\mathrm{CA}}\right] $$
(25)

Introducing Eq. (18)–(20) in Eq. (25):

$$ \left[{\mathrm{site}}_{\mathrm{CA}}\right]=\frac{\left[{\mathrm{site}}_{\mathrm{CA},T}\right]}{\left({K}_{\mathrm{CA}}{C}_{\mathrm{CA}}+{K}_{4\hbox{-} \mathrm{CP}}{C}_{4\hbox{-} \mathrm{CP}}+{K}_{\mathrm{BQ}}{C}_{\mathrm{BQ}}+1\right)} $$
(26)

Taking to account the assumption (v) made in the Kinetic model, the superficial degradation rate of i specie can be represented by:

$$ {r}_i={k}_i\left[\cdot \mathrm{OH}\right]\left[{i}_{\mathrm{ads}}\right] $$
(27)

where k i is the kinetic constant of the reaction between the organic compound and hydroxyl radicals, [⋅OH] is the concentration of hydroxyl radicals on the surface of the TiO2 particles, and [i ads] represents the superficial concentration of i. Therefore, considering Eq. (27), the degradation pathway depicted in Fig. 3, and the reaction scheme presented in Table 3, the final degradation rate expressions for CA, 4-CP, and BQ are:

$$ {r}_{\mathrm{CA}}={k}_5\left[\cdot \mathrm{OH}\right]\left[{\mathrm{CA}}_{\mathrm{ads}}\right]+{k}_6\left[\cdot \mathrm{OH}\right]\left[{\mathrm{CA}}_{\mathrm{ads}}\right]=\left({k}_5+{k}_6\right)\left[\cdot \mathrm{OH}\right]\left[{\mathrm{CA}}_{\mathrm{ads}}\right] $$
(28)
$$ {r}_{4\hbox{-} \mathrm{CP}}={k}_7\left[\cdot \mathrm{OH}\right]\left[4\hbox{-} {\mathrm{CP}}_{\mathrm{ads}}\right]+{k}_8\left[\cdot \mathrm{OH}\right]\left[4\hbox{-} {\mathrm{CP}}_{\mathrm{ads}}\right]=\left({k}_7+{k}_8\right)\left[\cdot \mathrm{OH}\right]\left[4\hbox{-} {\mathrm{CP}}_{\mathrm{ads}}\right] $$
(29)
$$ {r}_{\mathrm{BQ}}={k}_9\left[\cdot \mathrm{OH}\right]\left[{\mathrm{BQ}}_{\mathrm{ads}}\right] $$
(30)

Considering the superficial rate of appearance and disappearance of electrons, holes, and hydroxyl radicals shown in Table 3 and applying the kinetic micro-steady state approximation for the concentration of these species, the following expressions are obtained:

$$ {r}_{{\mathrm{e}}^{-}}={r}_{\mathrm{gs}}-{k}_2\left[{e}^{-}\right]\left[{h}^{+}\right]-{k}_3\left[{e}^{-}\right]\left[{O}_{2,\mathrm{ads}}\right]\approx 0 $$
(31)
$$ {r}_{{\mathrm{h}}^{+}}={r}_{\mathrm{gs}}-{k}_4\left[{h}^{+}\right]\left[{\mathrm{H}}_2{\mathrm{O}}_{\mathrm{ads}}\right]-{k}_2\left[{e}^{-}\right]\left[{h}^{+}\right]\approx 0 $$
(32)
$$ {r}_{\cdot \mathrm{OH}}={k}_4\left[{h}^{+}\right]\left[{\mathrm{H}}_2{\mathrm{O}}_{\mathrm{ads}}\right]-\left({k}_5+{k}_6\right)\left[{\mathrm{CA}}_{\mathrm{ads}}\right]\left[\cdot \mathrm{OH}\right]-\left({k}_7+{k}_8\right)\left[4\hbox{-} {\mathrm{CP}}_{\mathrm{ads}}\right]\left[\cdot \mathrm{OH}\right]-{k}_9\left[{\mathrm{BQ}}_{\mathrm{ads}}\right]\left[\cdot \mathrm{OH}\right]-{\displaystyle \sum_l}{k}_l^{\prime \prime}\left[\cdot OH\right]\left[{Y}_{l,\mathrm{ads}}\right]\approx 0 $$
(33)

where \( {r}_{{\mathrm{e}}^{-}},{r}_{{\mathrm{h}}^{+}}\mathrm{and}\ {r}_{\cdot \mathrm{OH}} \) correspond to the reaction rate of electrons, holes and hydroxyl radicals, respectively.

Operating with Eqs. (31–33) we obtain the expression for [⋅OH]:

$$ \left[\cdot \mathrm{OH}\right]=\frac{k_3{k}_4\left[{\mathrm{H}}_2{\mathrm{O}}_{\mathrm{ads}}\right]\left[{O}_{2,\mathrm{ads}}\right]\left\{-1+\sqrt{\frac{1+4{r}_{\mathrm{gs}}{k}_2}{k_3{k}_4\left[{\mathrm{H}}_2{\mathrm{O}}_{\mathrm{ads}}\right]\left[{\mathrm{O}}_{2,\mathrm{ads}}\right]}}\right\}}{2{k}_2\left\{\left({k}_5+{k}_6\right)\left[{\mathrm{CA}}_{\mathrm{ads}}\right]+\left({k}_7+{k}_8\right)\left[4\hbox{-} {\mathrm{CP}}_{\mathrm{ads}}\right]+{k}_9\left[{\mathrm{BQ}}_{\mathrm{ads}}\right]+{\displaystyle {\sum}_l}{k}_l^{\prime \prime}\left[{Y}_{l,\mathrm{ads}}\right]\right\}} $$
(34)

Considering assumptions (vi), (vii) and (viii) of the kinetic model and introducing Eq. (34) into Eq. (28) we obtain:

$$ {r}_{CA}=\frac{\left({\delta}_{2,1}+{\delta}_{2,2}\right)\left[{\mathrm{CA}}_{\mathrm{ads}}\right]\left\{-1+\sqrt{1+{\delta}_1{r}_{gs}}\right\}}{\delta_3\left\{\left({k}_5+{k}_6\right)\left[{\mathrm{CA}}_{\mathrm{ads}}\right]\left({k}_7+{k}_8\right)\left[4\hbox{-} {\mathrm{CP}}_{\mathrm{ads}}\right]+{k}_9\left[{\mathrm{BQ}}_{\mathrm{ads}}\right]\right\}+1} $$
(35)

where

$$ \begin{array}{cc}\hfill {\delta}_{2,1}=\frac{k_3{k}_4{k}_5\left[{\mathrm{H}}_2{\mathrm{O}}_{\mathrm{ads}}\right]\left[{\mathrm{O}}_{2,\mathrm{ads}}\right]}{2{k}_2{\displaystyle {\sum}_l}{k}_l^{\prime \prime}\left[{Y}_{l,\mathrm{ads}}\right]}\hfill & \hfill {\delta}_{2,2}=\frac{k_3{k}_4{k}_6\left[{\mathrm{H}}_2{\mathrm{O}}_{\mathrm{ads}}\right]\left[{O}_{2,\mathrm{ads}}\right]}{2{k}_2{\displaystyle {\sum}_l}{k}_l^{\prime \prime}\left[{Y}_{l,\mathrm{ads}}\right]}\hfill \\ {}\hfill {\delta}_1=\frac{4{k}_2}{k_3{k}_4\left[{\mathrm{H}}_2{\mathrm{O}}_{\mathrm{ads}}\right]\left[{O}_{2,\mathrm{ads}}\right]}\hfill & \hfill {\delta}_3=\frac{1}{{\displaystyle {\sum}_l}{k}_l^{\prime \prime}\left[{Y}_{l,\mathrm{ads}}\right]}\hfill \end{array} $$

Introducing Eq. (18–20) and Eq. (26) in Eq. (35):

$$ {r}_{\mathrm{CA}}=\frac{\left({\delta}_{2,1}+{\delta}_{2,2}\right){K}_{\mathrm{CA}}{C}_{\mathrm{CA}}\left[{\mathrm{site}}_{\mathrm{CA},T}\right]\left\{-1+\sqrt{1+{\delta}_1{r}_{\mathrm{gs}}}\right\}}{1+\left\{\left[{\mathrm{site}}_{\mathrm{CA},T}\right]{\delta}_3\left({k}_5+{k}_6\right){K}_{\mathrm{CA}}+{K}_{\mathrm{CA}}\right\}{C}_{\mathrm{CA}}+\left\{\left[{\mathrm{site}}_{\mathrm{CA},T}\right]{\delta}_3\left({k}_7+{k}_8\right){K}_{4\hbox{-} \mathrm{CP}}+{K}_{4\hbox{-} \mathrm{CP}}\right\}{C}_{4- CP}+\left\{\left[{\mathrm{site}}_{\mathrm{CA},T}\right]{\delta}_3{k}_9{K}_{\mathrm{BQ}}+{K}_{\mathrm{BQ}}\right\}{C}_{\mathrm{BQ}}} $$

Taking into account assumptions (ix) and (x) we obtain the kinetic expression that describes the rate of degradation of CA:

$$ {r}_{\mathrm{CA}}\left(\boldsymbol{x},t\right)=\frac{\left({\alpha}_{2,1}+{\alpha}_{2,2}\right){C}_{\mathrm{CA}}\left(\boldsymbol{x},t\right)}{1+{\alpha}_3{C}_{\mathrm{CA}}\left(\boldsymbol{x},t\right)+{\alpha}_1^{\prime }{C}_{4\hbox{-} \mathrm{CP}}\left(\boldsymbol{x},t\right)+{\alpha}_2^{\prime }{C}_{\mathrm{BQ}}\left(\boldsymbol{x},t\right)}\left(-1+\sqrt{1+\frac{\alpha_1}{a_v}{e}^a\left(\boldsymbol{x},t\right)}\right) $$

Where

$$ \begin{array}{cc}\hfill {\alpha}_1={\delta}_1\overline{\phi}\hfill & \hfill {\alpha}_{2,1}={\delta}_{2,1}{K}_{\mathrm{CA}}\left[{\mathrm{site}}_{\mathrm{CA},T}\right]\hfill \\ {}\hfill {\alpha}_{2,1}={\delta}_{2,1}{K}_{CA}\left[{\mathrm{site}}_{\mathrm{CA},T}\right]\hfill & \hfill {\alpha}_3={\delta}_3\left({k}_5+{k}_6\right){K}_{\mathrm{CA}}\left[{\mathrm{site}}_{\mathrm{CA},T}\right]+{K}_{\mathrm{CA}}\hfill \\ {}\hfill {\alpha}_1^{\prime }={\delta}_3\left({k}_7+{k}_8\right){K}_{4- CP}\left[{\mathrm{site}}_{\mathrm{CA},T}\right]+{K}_{4\hbox{-} \mathrm{CP}}\hfill & \hfill {\alpha}_2^{\prime }={\delta}_3{k}_9{K}_{\mathrm{BQ}}\left[{\mathrm{site}}_{\mathrm{AC}\ \mathrm{totals}}\right]+{K}_{\mathrm{BQ}}\hfill \end{array} $$

Following the same procedure for 4-CP and BQ, reaction rates expressions were obtained for each of them:

$$ \begin{array}{c}\hfill {r}_{4\hbox{-} \mathrm{CP}}\left(\boldsymbol{x},t\right)=\frac{\left({\alpha}_{4,1}+{\alpha}_{4,2}\right){C}_{4\hbox{-} \mathrm{CP}}\left(\boldsymbol{x},t\right)}{1+{\alpha}_3{C}_{\mathrm{CA}}\left(\boldsymbol{x},t\right)+{\alpha}_1^{\prime }{C}_{4\hbox{-} \mathrm{CP}}\left(\boldsymbol{x},t\right)+{\alpha}_2^{\prime }{C}_{\mathrm{BQ}}\left(\boldsymbol{x},t\right)}\times \left(-1+\sqrt{1+\frac{\alpha_1}{a_v}{e}^a\left(\boldsymbol{x},t\right)}\right)\hfill \\ {}\hfill {r}_{\mathrm{BQ}}\left(\boldsymbol{x},t\right)=\frac{\alpha_5{C}_{\mathrm{BQ}}\left(\boldsymbol{x},t\right)}{1+{\alpha}_3{C}_{\mathrm{CA}}\left(\boldsymbol{x},t\right)+{\alpha}_1^{\prime }{C}_{4\hbox{-} \mathrm{CP}}\left(\boldsymbol{x},t\right)+{\alpha}_2^{\prime }{C}_{\mathrm{BQ}}\left(\boldsymbol{x},t\right)}\times \left(-1+\sqrt{1+\frac{\alpha_1}{a_v}{e}^a\left(\boldsymbol{x},t\right)}\right)\hfill \end{array} $$

Where

$$ \begin{array}{cc}\hfill {\alpha}_{4,1}=\frac{k_7{K}_{4- CP}{k}_3{k}_4\left[{\mathrm{H}}_2{\mathrm{O}}_{\mathrm{ads}}\right]\left[{O}_{2,\mathrm{ads}}\right]\left[{\mathrm{site}}_{\mathrm{CA},T}\right]}{2{k}_2{\displaystyle {\sum}_l{k}_l\left[{Y}_l\right]}}\hfill & \hfill {\alpha}_{4,2}=\frac{k_8{K}_{4- CP}{k}_3{k}_4\left[{\mathrm{H}}_2{\mathrm{O}}_{\mathrm{ads}}\right]\left[{\mathrm{O}}_{2,\mathrm{ads}}\right]\left[{\mathrm{site}}_{\mathrm{CA},T}\right]}{2{k}_2{\displaystyle {\sum}_l{k}_l\left[{Y}_l\right]}}\hfill \\ {}\hfill {\alpha}_5=\frac{k_9{K}_{4- CP}{k}_3{k}_4\left[{\mathrm{H}}_2{\mathrm{O}}_{\mathrm{ads}}\right]\left[{\mathrm{O}}_{2,\mathrm{ads}}\right]\left[{\mathrm{site}}_{CA,T}\right]}{2{k}_2{\displaystyle {\sum}_l{k}_l\left[{Y}_l\right]}}\hfill & \hfill \hfill \end{array} $$

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Manassero, A., Satuf, M.L. & Alfano, O.M. Kinetic modeling of the photocatalytic degradation of clofibric acid in a slurry reactor. Environ Sci Pollut Res 22, 926–937 (2015). https://doi.org/10.1007/s11356-014-2682-5

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