Ahmed_2025_Sci.Rep_15_5573

This study examines the semi-analytical expression of a hollow cylindrical fiber membrane bioreactor catalyzed by an immobilized enzyme (lipase), focusing on the dynamic kinetic resolution (DKR) of racemic (R)- and (S)-ibuprofen ester through the homotopy perturbation method (HPM). This method effectively solves the coupled non-linear system of second-order ordinary differential equations (ODEs), incorporating the mass transfer associated with the DKR reaction rate. The DKR rate equations are computed utilizing both enantiomers, which represent the enzymatic hydrolysis of the substrate within the barrier's support matrix, where the racemization term is negligible. Additionally, the corresponding racemization of the unreacted substrate outside the membrane is considered, where the enzymatic hydrolysis term is negligible. The dimensionless steady-state solution for the dynamics of the mean integrated effectiveness factor (MIEF) related to convective hydrolysis-racemization phenomena quantifies the local effectiveness factor, which impacts the Thiele modulus and the bulk initial concentrations of a substance within the membrane layer. The Bodenstein number is a critical parameter that optimizes reaction conditions, enhances mixing efficiency, and mitigates mass transfer limitations. The normalized values from the sensitivity analysis are analyzed to identify the key parameters of the present system. The conversion efficiency and limitations of the proposed model utilizing HPM are presented. Our proposed solution compares the semi-analytical expression with the simulated numerical results of BVP-4c using the built-in solver in MATLAB R2023b software, demonstrating good agreement across all values of the reaction parameters. The agreement between semi-analytical and numerical computations demonstrates the validity of these approximation methods. The findings provide significant insights for enhancing membrane reactor design and improving the efficiency of industrial processes for racemic ibuprofen ester production.