Abstract A mathematical model is developed and designed for the cumene reactor in cumene production process in Hindustan Organic Chemicals Limited (HOCL), Kochi with improved operating conditions. High purity cumene is produced by the alkylation of benzene with propylene in this catalytic condensation process where solid phosphoric acid (SPA) is used as the catalyst. The mathematical model has been derived from mass and energy balance equations considering the reactor as fixed packed bed reactor and two different numerical methods are presented here to solve the modelling equations. The explicit finite difference method (FDM) involves the approximation of derivatives into finite differences, and in the other one, orthogonal collocation (OC), Ordinary Diffeential Equations (ODEs) are formed at the collocation points and are solved using Runge–Kutta fourth order numerical scheme. Here the analysis shows that the predictions from the model are in good alignment with the plant data. The combined feed has the optimum value of 1:2:8 for propylene, propane and benzene and the profiles of temperature and concentration can be obtained along the reactor. The model has been implemented in COMSOL Multiphysics as a packed bed reactor using the same parameters collected from the plant of study. It has been found that the reaction occurs at a satisfactory level even with a low temperature than the reactor temperature at the plant by changing the catalytic particle size. The reaction performance is also analysed for the physical properties like porosity and catalyst size.

中文翻译：

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四层填充床反应器中异丙苯生产过程的建模与性能分析

摘要 针对高知印度斯坦有机化工有限公司（HOCL）的异丙苯生产过程中的异丙苯反应器开发和设计了数学模型，并改进了操作条件。在这种使用固体磷酸 (SPA) 作为催化剂的催化缩合工艺中，苯与丙烯的烷基化反应生产出高纯度异丙苯。将反应器视为固定填充床反应器，从质量和能量平衡方程推导出数学模型，这里提出了两种不同的数值方法来求解建模方程。显式有限差分法 (FDM) 涉及将导数逼近为有限差分，另一种方法是正交搭配 (OC)，常微分方程 (ODE) 在配置点处形成，并使用 Runge-Kutta 四阶数值方案求解。这里的分析表明，模型的预测与工厂数据非常吻合。混合进料对丙烯、丙烷和苯的最佳值为1:2:8，并且可以沿反应器获得温度和浓度分布。该模型已在 COMSOL Multiphysics 中作为填充床反应器实施，使用从研究工厂收集的相同参数。已经发现，通过改变催化粒度，即使在低于工厂反应器温度的温度下，反应也能以令人满意的水平发生。还分析了反应性能的物理性质，如孔隙率和催化剂尺寸。