Applying Bayesian statistics and MCMC to ozone reaction kinetics: Implications for water treatment models

Ozonation is an advanced oxidation process widely used for water and wastewater treatment. The pseudo-first-order kinetic model is frequently applied for designing and scaling this treatment, offering insights into oxidation pathways through ozone reaction rate constants (k_O3,P and k_OH,P) and the exposure ratio term (R_t). This work evaluates the kinetic constants for ozonation reactions involving three pharmaceuticals, caffeine (CAF), atenolol (ATL), and propranolol (PRO), classified as emerging contaminants (ECs), with the aim of guiding future research and industrial applications for various pollutants. Two estimation methods were compared: the conventional indirect linearization method and a novel direct Bayesian approach employing the Monte Carlo Markov Chain (MCMC) method with the Metropolis-Hastings (MH) algorithm. Additionally, measurement uncertainties (σ_med - 1, 2 and 5%) were incorporated into the direct method, enabled by Bayesian inference, to assess the impact of noise on the estimation of kinetic constants. This consideration is critical for ensuring safety, efficiency, and reproducibility in industrial applications. Results indicated that the direct Bayesian method was both accurate and promising. It effectively estimated the pollutant concentration curves despite the presence of noise, providing improved parameter adjustments compared to the indirect method. While, σ_med influenced the parameter estimation, the Bayesian approach maintained a superior fit to the curves even with measurement noises, showing applicability of the proposed method. The obtained Markov chains exhibited good convergence, particularly for the direct oxidation parameter (k_O3,P), suggesting the method's effectiveness and sensitivity to the molecular structure of each compound. Furthermore, the use of direct residual ozone measurement (sensors) in this study was found to influence parameter prediction, leading to variations in rate constants compared to values reported in the literature. Therefore, this study recommends using the direct Bayesian method with the exposure ratio term for more reliable industrial-scale ozonation applications, offering a significant advancement over traditional approaches.