Mathematical modeling of the dynamics of homogeneous reactions in the cascade of perfect mixing reactors

Present study tackles theoretical analysis and mathematical modeling of the process of homogeneous first-order reaction in the cascade of perfect mixing reactors of continuous action (PMR-C). The modeling of chemical reactors is based on the thermal and material balances in combination with chemical kinetics. The mathematical model of the dynamics of the process of homogeneous first-order reaction in the PMR-C cascade is represented in the form of equations of change in the molar fraction of substance over time and a change in the inner energy of the ideal flow of substance. In the present work, we calculated, by the mathematical model, the process of acetic anhydride hydrolysis in 5 sequentially connected PMR-C. Calculation by the model is performed by the Runge-Kutta method of third order. We obtained temperature profiles for the dynamics of the process of acetic anhydride hydrolysis for a cascade of PMR-C. The temperature gradient in reactor grows over time; consequently, it takes on a constant value. We analyzed the impact of the volume of reaction mixture on the depth of the course of the process both for the separate perfect mixing reactors and for the cascade of perfect mixing reactors. With an increase in the volume of mixture, the reaction rate increases, while the speed of reaching the necessary degree of conversion decreases. The speed of reaching the maximum degree of conversion for the cascade of reactors compared with one perfect mixing reactor of the same volume is considerably higher. Recommendations regarding the course of the process are formulated. We calculated the value of cost for conducting the process of acetic anhydride hydrolysis depending on the change in temperature. Minimum cost is attained at temperature 341 K and amounts to UAH 1.70 million per year.
Математическая модель динамики процесса гомогенной реакции первого порядка в каскаде реакторов идеального смешения построена уравнением изменения мольной доли вещества со временем и изменением внутренней энергии идеального потока вещества. Расчет по модели осуществлено методом Рунге-Кута третьего порядка для реакции гидролиза уксусного ангидрида. Получены профили температур динамики процесса, рассчитан стоимостной показатель
Математична модель динаміки процесу гомогенної реакції першого порядку в каскаді реакторів ідеального змішування побудована рівнянням зміни мольної частки речовини з часом і зміною внутрішньої енергії ідеального потоку речовини. Розрахунок по моделі здійснено за методом Рунге-Кута третього порядку для реакції гідролізу оцтового ангідриду. Отримано профілі температур динаміки процесу, розраховано вартісний показник