Kinetic parameter estimation and numerical implementation comparison for resin-catalyzed esterification

Abstract

The esterification reaction is essential for producing esters widely used in chemical, pharmaceutical, and biofuel applications. This study develops and evaluates a computational methodology for modeling heterogeneous esterification kinetics in an isothermal batch reactor, implemented independently in Scilab, Python, and R. The kinetic formulation was based on a simplified Eley–Rideal-type approach, considering a reversible reaction and water inhibition through an adsorption term. The resulting system of ordinary differential equations was used to estimate the apparent kinetic coefficient ( k _d ), water adsorption constant ( K _W ), and equilibrium constant ( K _eq ) from 20 experimental reaction profiles obtained from independent literature studies. Parameter estimation was performed using nonlinear estimation procedures, while the ODE systems were solved using LSODA in R and Scilab and adaptive RK45 in Python. The calculated profiles reproduced the experimental data with average coefficients of determination of 0.9908 ± 0.00399 for Scilab, 0.9905 ± 0.00399 for Python, and 0.9851 ± 0.00960 for R, indicating high consistency among the three computational approaches. Differences in estimated parameters were mainly attributed to the distinct parameter-estimation and numerical-integration procedures adopted in each implementation. Independently calculated equilibrium constants agreed well with the values incorporated into the kinetic formulation, supporting the proposed simplification. Temperature dependence was consistent with the Arrhenius relationship, while confidence ellipse analysis indicated correlation between the forward and reverse reaction parameters. Overall, the proposed methodology provides a reproducible framework for kinetic parameter estimation and simulation of heterogeneous esterification systems across different computational environments.