Моделирование и численное исследование физико-химических закономерностей 1,4-цис-полиизопрена, полученного в присутствии модифицированных каталитических систем

Abstract

Построена математическая модель, описывающая процесс получения полиизопрена в присутствии микрогетерогенных титансодержащих каталитических систем с учетом динамики активных центров. Построение модели носило поэтапный характер, при котором модель, описывающая периодический процесс, была дополнена рекуррентными соотношениями с целью описания процесса в каскаде реакторов идеального перемешивания. Численное решение прямой задачи позволило провести анализ молекулярно-массового распределения получаемого продукта в зависимости от исходной загрузки. The aim of this work is building a mathematical model that describes the process of producing polyisoprene in the presence of microheterogeneous titanium-containing catalytic systems, taking into account the dynamics of active centers and numerical calculation of the main physicochemical properties of the resulting product. The main methodology for compiling the mathematical model is the application of the kinetic approach, which consists of compiling and numerically solving the kinetic equations for all types of particles involved in the process. Previously, the distribution of active centers of the applied catalytic system was studied. The confirmed polycentricity of the used catalyst, represented by two types of active centers, is reflected in the nature of the description of the mathematical model. To reduce the system of differential equations to the final form, the method of moments was applied, which allows evaluating the complex properties of the obtained product by its averaged molecular characteristics. A model that permits describing the scale of batch reactors was modified by a macrokinetic module that takes into account possible energy and hydrodynamic laws of the process. For this, recurrence relations were introduced that are valid for the description of continuous mixing reactors. The software package developed by the authors of the work allows carring out a computational experiment for various technological conditions for conducting a continuous process. Based on the results of its launch, the dependences of conversion and averaged molecular characteristics on time in the context of each polymerizer were obtained. Thus, the numerical solution of the direct problem is capable analyzing the molecular weight distribution of the obtained product depending on various parameters of the initial load, for both the batch and continuous modes of the process. The dependences obtained by calculation showed satisfactory agreement with experimental data