制取苯酐模型的S系统解析

Solution of a model of producing phthalic anhydride use the S-system method

高精度的数值法被用于求解邻二甲苯制取苯酐模型中。此方法是将基本的微分方程改写为S系统(synergisticandsaturablesystem)的标准形式,结合变阶变步长的泰勒级数法进行求解,得到了不同进料温度和不同压强下的苯酐和二氧化碳收率分布以及反应器床层的轴向温度分布曲线,并与龙格库塔法的计算结果做了对比。分析得出热点温度和苯酐及二氧化碳收率随着进料温度增大而增大,同时苯酐及二氧化碳收率也随着操作压强的增大而增大。当进料温度为638K时热点温度变的非常高,而且进料温度相差1度时热点温度会相差几十度。精确求解不同进料温度和操作压强下的热点温度对工程实际操作中催化剂的保护和设备维护有着十分重要的指导意义。

A highly accurate numerical method for solving a model of producing phthalic anhydride is presented. In this method, one first recasts fundamental equations into S-system （synergistic and saturable system） canonical form and then solves the resulting set of simultaneous first-order different equations by a variable-order, variable-step Taylor series method. The yield of phthalic anhydride and carbon dioxide and the axial temperature distribution is found at different feeding temperatures and pressures, and it is compared with the result which is computed by the Runge-Kutta method. The hot spot temperature and the yield of the phthalic anhydride and CO2 increase with the increase of the feeding temperature. Meanwhile, the yield of the phthalic anhydride and CO2 also increase with the increase of the operating pressure. The hot spot temperature becomes so high when the feeding temperature at 638 K, and it will change dozens of degrees Celsius when the feeding temperature changes one. Obtaining the exact hotspot temperature under different feed temperatures and operating pressures has a very important instructional significance for protecting the catalyst and equipment maintenance in engineering practice.