Degradation of Organic Carbon in Pharmaceutical Wastewater: a Kinetic Approach

Abstract

This study aimed to investigate the degradation kinetics of the total organic carbon (TOC) in real pharmaceutical wastewater. Because of the complexity of real wastewaters and the lack of knowledge on all reactions involved in their chemical degradation, the use of a kinetic approach becomes difficult. To overcome this difficulty, we adopted a kinetic model based on chemical equations validated for mechanisms of free radical generation. Photo-Fenton reactions were performed in a 1-L tubular reactor. The developed model satisfactorily described the degradation kinetics of TOC in wastewater, with an R² of 0.9997. The TOC degradation rate constant (k_d) was estimated at 1 × 10¹¹ L² mol² s⁻¹, in agreement with literature values for the degradation kinetics of organic compounds. UV radiation had a positive effect on degradation, contributing to HO^• formation. The adopted mathematical approach was highly sensitive to the formation rate constant of HO^• from H₂O₂ (k₄). By assuming the reaction to follow variable order kinetics (β = 1 and β = 2), it was possible to improve the goodness of fit of the model. Our results suggest, albeit in an incipient way, that the approach used in this study can be extended to the kinetic understanding of other complex wastewaters.

Appendix

Molar balance equations used in the model

$$ \frac{d\left[ TOC\right]}{dt}=-{k}_d\left[ TOC\right]\left[{HO}^{\bullet}\right]\left[{H}^{+}\right] $$

(A1)

$$ {TOC}_{\mathrm{red}}=\frac{TOC_i-{TOC}_f}{TOC_i}\times 100 $$

(A2)

$$ {Fe}^{2+}+{H}_2{O}_2\ {\displaystyle \begin{array}{c}{k}_1\\ {}\to \end{array}}\ {Fe}^{3+}+{HO}^{\bullet }+{OH}^{-} $$

(A3)

$$ \frac{d\left[{Fe OH}^{2+}\right]}{dt}=-{k}_{2f}\left[{Fe}^{3+}\right]-{k}_{2r}\left[{Fe OH}^{2+}\right]\left[{H}^{+}\right]-{k}_3\left[{Fe OH}^{2+}\right] $$

(A4)

$$ \frac{d\left[{Fe}^{3+}\right]}{dt}={k}_1\left[{Fe}^{2+}\right]\left[{H}_2{O}_2\right]-{k}_{2f}\left[{Fe}^{3+}\right]+{k}_{2r}\left[{Fe OH}^{2+}\right]\left[{H}^{+}\right]-{k}_{6f}\left[{Fe}^{3+}\right]+{k}_{6r}\left[ Fe{(OH)}_2^{+}\right]\left[{H}^{+}\right]+{k}_7\left[{Fe OH}^{+}\right]\left[{H}_2{O}_2\right]+{k}_8\left[{Fe}^{2+}\right]\left[{HO}^{\bullet}\right] $$

(A5)

$$ {r}_1={k}_1\left[{Fe}^{2+}\right]\left[{H}_2{O}_2\right] $$

(A6)

$$ {Fe}^{3+}+{H}_2O{\displaystyle \begin{array}{c}{k}_{2r}\\ {}\leftrightharpoons \\ {}{k}_{2f}\end{array}}{ Fe OH}^{2+}+{H}^{+} $$

(A7)

$$ \frac{d\left[{HO}^{\bullet}\right]}{dt}={k}_1\left[{Fe}^{2+}\right]\left[{H}_2{O}_2\right]+{k}_3\left[{Fe OH}^{2+}\right]+{k}_7\left[{Fe OH}^{+}\right]\left[{H}_2{O}_2\right]-{k}_8\left[{Fe}^{2+}\right]\left[{HO}^{\bullet}\right]+2{k}_4{\left[{H}_2{O}_2\right]}^{\beta }-\alpha {k}_d\left[ TOC\right]\left[{HO}^{\bullet}\right]\left[{H}^{+}\right] $$

(A8)

$$ {r}_2={k}_{2f}\left[{Fe}^{3+}\right]-{k}_{2f}\left[{Fe OH}^{2+}\right]\left[{H}^{+}\right] $$

(A9)

$$ \frac{d\left[{H}^{+}\right]}{dt}=0 $$

(A10)