Mathematical Modelling and Kinetic Analysis of Glycerol Carbonate Synthesis Using BaCaO Mixed Oxide Catalysts

Abstract

The rapid expansion of the biodiesel industry has resulted in the large-scale generation 
of crude glycerol, necessitating its efficient catalytic valorisation into value-added 
chemicals such as glycerol carbonate (GC). Among the available conversion pathways, 
the transesterification of glycerol with dimethyl carbonate (DMC) over heterogeneous 
catalysts offers a sustainable and environmentally benign route; however, the reaction 
kinetics and catalyst deactivation mechanisms of low-cost mixed-oxide catalysts remain 
inadequately understood. This study presents a comprehensive chemico-mathematical 
investigation of GC synthesis using a synthesized Barium–Calcium mixed oxide (BaCaO, 
1:2:1) catalyst. Experimental kinetic data were obtained under varying reaction 
temperatures (55–75 °C), catalyst loadings (1–5 wt%), and DMC-to-glycerol molar 
ratios. A reduced Langmuir–Hinshelwood–Hougen–Watson (LHHW) kinetic model was 
formulated and fitted to concentration–time profiles through nonlinear regression 
analysis. The developed model exhibited excellent predictive capability with a 
coefficient of determination (R²) of 0.987 and a root mean square error (RMSE) of 
0.011, while Akaike Information Criterion (AIC) analysis statistically confirmed it as 
the most appropriate reaction mechanism. The apparent activation energy (Eₐ) was 
determined to be 58.4 kJ mol⁻¹, indicating that glycerol carbonate formation proceeds 
predominantly under an intrinsic surface-reaction-controlled regime. Furthermore, a 
novel first-order catalyst deactivation model was developed to quantitatively describe 
catalyst performance decay, accurately correlating the reduction in GC yield from 
88.0% to 60.0% after three reuse cycles with the experimentally measured leaching of 
active Ca²⁺ species from 22.54 wt% to 1.94 wt%. The integrated kinetic and 
deactivation framework provides a robust predictive platform for reactor optimisation, 
catalyst regeneration scheduling, and industrial-scale implementation of sustainable 
glycerol valorisation technologies.