Ahmed L Niyaz, Thomas Praveen
Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore, 632014, Tamilnadu, India.
Sci Rep. 2025 Feb 15;15(1):5573. doi: 10.1038/s41598-025-89583-z.
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.
本研究考察了固定化酶（脂肪酶）催化的中空圆柱形纤维膜生物反应器的半解析表达式，重点是通过同伦摄动法（HPM）对消旋（R）-和（S）-布洛芬酯进行动态动力学拆分（DKR）。该方法有效地求解了二阶常微分方程（ODEs）的耦合非线性系统，纳入了与DKR反应速率相关的传质过程。利用两种对映体计算DKR速率方程，这两种对映体代表了底物在屏障支撑基质内的酶促水解，其中消旋化项可忽略不计。此外，还考虑了膜外未反应底物的相应消旋化，其中酶促水解项可忽略不计。与对流水解-消旋化现象相关的平均积分有效因子（MIEF）动力学的无量纲稳态解量化了局部有效因子，其影响膜层内物质的西勒模数和本体初始浓度。 Bodenstein数是优化反应条件、提高混合效率和减轻传质限制的关键参数。分析灵敏度分析的归一化值以确定本系统的关键参数。给出了利用HPM提出的模型的转化效率和局限性。我们提出的解决方案将半解析表达式与使用MATLAB R2023b软件中的内置求解器得到的BVP-4c模拟数值结果进行了比较，结果表明在所有反应参数值上都具有良好的一致性。半解析计算与数值计算之间的一致性证明了这些近似方法的有效性。这些发现为改进膜反应器设计和提高外消旋布洛芬酯生产的工业过程效率提供了重要见解。
