Rate expression model from thermodynamics application and optimal kinetic parameters determination for urea synthesis and production process

Urea, an essential organic fertilizer, enhances soil fertility by providing 0.466 nitrogen for maximum crop yield. In this study, urea is synthesized from NH₃ and CO₂ in an equilibrium reaction process adhering to Le Chatelier's principle, maintained under process conditions: flow rate of 63.5 kg/s, temperature of 184 °C, and pressure of 160 kg/cm². A new rate expression model, formulated in terms of extent of reaction and mole fraction, was developed based on mass action relations and thermodynamic models. Two industrial reactors were considered: a plug flow reactor (PFR) at Notore and a continuous stirred tank reactor (CSTR) at Indorama plants. Transient reactor models, based on material and energy balance conservation principles, were numerically resolved using MATLAB version 2020 with specified input conditions. A non-linear regression statistical optimization model was employed to refine kinetic parameter values, ensuring optimal and high-quality urea yield. Model validations were conducted using literature data, revealing higher urea yields of 0.726 and 0.7032 for the CSTR and PFR, respectively. Deviations (0.134, 0.10 to 1.135 and 0.635, 0.326 to 0.850) and root mean square errors (RMSE) (0.043, 0.033 to 0.193 and 0.137, 0.087 to 0.162) were observed when validated against plant and literature values for the CSTR and PFR respectively. The refined kinetic parameters (activation energies, Arrhenius constants, and rate constants) exhibited negligible deviations (0.0004–0.0466 and 0.0004 to 0.0491) and RMSE (0.0228, 0.0055, and 0.0256 and 0.0241, 0.0096, and 0.0269) when validated against plant data, significantly enhancing urea yield in CSTR and PFR reactors respectively.