Kinetic Analysis and Particle Swarm Optimization Simulation Algorithm-Based Error Minimization in the Epoxidation of Castor Oil Via the Prilezhaev Reaction
摘要
This study investigates the kinetic modeling of castor oil epoxidation via the Prilezhaev reaction using in situ generated peracetic acid, with a focus on optimizing the process through Particle Swarm Optimization (PSO). Experimental procedures involved the use of ZSM-5/H₂SO₄, with reactions monitored by titration, FTIR, NMR, and GPC analysis. FTIR confirmed successful epoxidation through the appearance of characteristic oxirane peaks at 852 cm⁻¹ and the disappearance of alkene bands. NMR spectra showed reduction of olefinic (5.2–5.4 ppm) and allylic protons (1.8–2.0 ppm), and emergence of epoxide ring signals (3.6–3.8 ppm). GPC revealed a drop in weight-average molecular weight (Mw) from 9732 to 1013 g/mol and polydispersity index (PDI) from 7.66 to 1.51, confirming chain scission during epoxidation. The reaction was modeled through a system of second-order differential equations representing peracid formation, epoxide synthesis, and degradation. Two models were compared—one spanning 0–60 min (including reversible reactions) and another from 30 to 60 min (unidirectional). PSO achieved an R² of 0.52 for the full model and R² of 0.98 for the 30–60 min range. The unidirectional model demonstrated superior predictive accuracy, suggesting that inclusion of reversibility introduced noise, especially during early reaction stages. This highlights PSO’s limitations in handling reversible systems and supports the use of simplified forward-reaction kinetics, focusing on epoxide formation and ring-opening steps while excluding the reverse formation of peroxy acid. This approach improves model performance in epoxidation processes while still benefiting from the fast convergence of the PSO algorithm compared to other algorithms.