Mathematical modeling and kinetics of batch and continuous electro-catalytic oxidation of pharmaceutical-contaminated...

An accurate yet simple model is the key to the design and control of intricate electro-catalytic oxidation of pharmaceutical contaminated wastewater. For both batch and unsteady-state continuous flow stirred tank reactors (CSTR), batch reactor models have been used earlier. Further, these models do not correlate rate to the operating conditions, and consider pseudo-first/second-order kinetics. Here, first-principles models are proposed by formulating unsteady-state mass balances, modifying them to attain realistic final conditions, and incorporating fractional variable-order kinetics. Following integral analysis, analytical solutions are obtained. These are independently applicable to design, unlike a numerical solution. Nonlinear regression is performed to estimate the model parameters from the transient experimental data. The simulations yield markedly accurate model parameters together with a better fit to the experimental data of Ti/RuO₂-mediated amoxicillin-trihydrate electro-oxidation, for CSTR and batch reactors. For the batch reactor, the operating conditions are varied one at a time. Their effects on the model parameters are elucidated based on the oxidant and transformation species formed. The computed optimum model parameters are: rate constant 3.318 × 10^-3 mg^-0.092 m^1.276 min^-1, order 1.092, initial rate 4.032 × 10² mg m^-2 min^-1, and final conversion 90.6% in 180 min. The corresponding operating conditions are: pH 2.0, feed 50 mg L^-1, electrolyte 2 g L^-1, and current 1 A. A simple generalized power-law correlation, associating rate to the operating conditions, is then estimated. Statistical analysis of these models using central composite design delivers R² 0.99, predicted R² 0.96, and optimum set close to the above. The corresponding sensitivity analysis and generalized correlation, both show applied current to be the most significant operating condition. The dynamic modeling approaches proposed here can be extended to model, control, and scale-up complex reaction systems.