Uncertainty-Quantified Kinetic Model Discrimination for Photocatalytic Reactor Design: A Bootstrap Based Framework

Abstract

Translating laboratory-scale photocatalytic batch data into continuous reactor design remains a critical challenge in reaction engineering, particularly when kinetic model selection is based solely on the coefficient of determination (R2) and parameter uncertainty is ignored. In this study, a data-driven framework is developed that integrates nonlinear kinetic model discrimination, bootstrap-based uncertainty quantification, and uncertainty propagation into plug-flow reactor (PFR) sizing. Time–concentration data from methylene blue degradation over a WO3/BiVO4 photocatalyst (C0 = 10 mg L-1) were fitted to six nonlinear kinetic models using Particle Swarm Optimization (PSO). Model discrimination was performed using the bias-corrected Akaike Information Criterion (AICc) and Akaike weights, decisively selecting the Elovich model (ΔAICc > 30 vs. pseudo-first-order; Akaike weight > 0.99). Parameter uncertainty was quantified via nonparametric bootstrap resampling (2000 replicates), yielding well-constrained 95% confidence intervals (α: 2.02-2.28 mg g-1 min-1; β: 0.34-0.42 g mg-1). The identified kinetics were embedded into a steady-state PFR model, and bootstrap parameter distributions were propagated to generate a reactor length design envelope for 90% pollutant removal. The nominal reactor length was 1.25 m, with a 95% confidence interval of 1.18-1.35 m (±7%). This narrow design envelope demonstrates robust parameter identifiability and provides a statistically defensible basis for reactor sizing, moving beyond single-point deterministic estimates. The proposed methodology offers a transferable framework for integrating nonlinear kinetic discrimination and uncertainty quantification into photocatalytic reactor engineering.