The basic schemes for the transformation of the pentane-hexane fraction catalytic isomerization, which are probable from the point of view of thermodynamics, have been considered. Based on the literary analysis of possible transformation schemes, the mechanism of the process and on the basis of experimental data, a mathematical model of the reactor block of the process was constructed and the kinetic parameters were determined. The foundations were laid for the subsequent solution of the tasks of the multi-purpose optimization of the catalytic isomerization process of the pentane-hexane fraction.
This article is devoted to the problem of developing a kinetic model of a complex chemical reaction using a parallel optimization method. The design of the kinetic model consists of finding the kinetic parameters of the reaction, which cannot be calculated analytically, and since the chemical reaction involves many stages, the optimization problem is multiextremal. As a chemical reaction, the process of catalytic isomerization of the pentane-hexane fraction is considered, which is now important due to the switch of the oil refining industry to the production of gasoline corresponding to the Euro-5 standard. On the basis of known industrial data on the concentrations of reaction components and the temperature at the outlet of the third reactor, the activation energies and pre-exponential factors of each reaction stage were calculated. To solve the optimization problem, the authors developed a parallel global search algorithm and a program based on Lipschitz optimization. The kinetic parameters found made it possible to develop a mathematical model of the process, which is in good agreement with industrial data. The developed mathematical model in future works will make it possible to study the dynamics of the gas–liquid flow in the reactor unit, taking into account diffusion and heat exchange processes through the catalyst layer.
This paper provides a brief overview of the existing definitions of a stiff system of differential equations. Further, on the example of the accepted scheme of chemical transformations of the catalytic isomerization process of the pentane-hexane fraction, the stiffness of the system of differential equations was studied. In the course of the work, a method for studying the direct kinetic problem for stiffness is presented. In the Matlab software, the results of solving a system of differential equations by five methods (solvers) were compared. The given method can be tried for solving other problems of chemical kinetics.
В данной работе представлена модифицированная вероятная схема химических превращений процесса каталитической изомеризации пентан-гексановой фракции. Схема разработана на основе решения обратной задачи химической кинетики с использованием численных методов решения жестких систем обыкновенных нелинейных дифференциальных уравнений (СОНДУ) -математического описания изменения концентраций, участвующих в реакциях веществ (прямая задача). Представлен краткий обзор существующих определений жестких СОНДУ. В среде Matlab было произведено сравнение результатов решения СОНДУ пятью методами (решателями) и выбраны эффективные методы решения прямой задачи. Приведенная методика анализа и выбора быстрых численных методов решения прямых задач может быть опробована для решения других обратных задач химической кинетики при исследовании механизмов сложных химических реакций. Ключевые слова: каталитическая изомеризация пентан-гексановой фракции, реакторный блок, матрица Якоби, собственные значения, жесткая система дифференциальных уравнений.
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