Chemical engineering processes are combinations of basic processes (hydrodynamic, diffusion, thermal, chemical, etc) that occur simultaneously (or in sequence) under conditions imposed by the complex geometry of the industrial contactors. The ordered sequence of separate stages (elementary processes) is the mechanism of the chemical engineering process. From this point of view, the structure of the mathematical description of the process depends on the mathematical description of the process depends on the mathematical description of the elementary processes involved and the interrelations between them. Therefore, the creation of the mathematical description of the elementary process involved is the first step towards the modeling of the entire chemical engineering process. The analysis of the separate stages of the modeled process shows that the main step is the creation of the mathematical structures of the model utilizing sub models of elementary process and the interrelation mechanisms. Obviously, these structures depend in the knowledge available about the process mechanisms.
A very important stage of model development is parameter identification through inverse problem solutions. The main difficulties are related to the incorrectness of the inverse problem. The mathematical structures developed become models after the evaluation of both the parameter significance and the model adequacy. The model created can be used for a qualitative analysis of the relation between the process mechanism and the values of the model parameters. This allows some levels of a hierarchical modeling to be defined as well as the scale-up effects of the processes. All these steps facilitate the subsequent simulation and very often they are required preliminary steps. The modeling and simulation of both the processes and the systems are related to a lot of calculation problems. Moreover, there are various approaches of the optimal process design, process control, and plant renovation. Many of the calculation problems are related to the solution of differential equations. Different analytical and numerical methods have to be used. The calculation problems of the identification of the model parameters need the use of sets, metric spaces, functional, variational and iterative methods, as well as different methods for function minimization. The modeling and simulation of chemical plant systems deal with quite specific calculation problems that should be solved with the help of graphs, matrixes, nonlinear, integer, and heuristic programming, etc.
Theoretical chemical engineering uses physical approximations of the mechanics of continua. Simply, this implies the material point of the medium corresponds to a volume sufficiently small with respect to the entire volume under consideration but at the same time sufficiently large with respect to the intermolecular distances of the medium. Modeling in chemical engineering utilizes mathematical structures provided by the mechanics of the continua. The theoretical analyses employing similarity theory models demonstrate that if the mathematical methods are very simple, the formalistic use of the theory could result in wrong results. Physical ideas form the basis of the similarity theory and its mathematical methods.
A very important stage of model development is parameter identification through inverse problem solutions. The main difficulties are related to the incorrectness of the inverse problem. The mathematical structures developed become models after the evaluation of both the parameter significance and the model adequacy. The model created can be used for a qualitative analysis of the relation between the process mechanism and the values of the model parameters. This allows some levels of a hierarchical modeling to be defined as well as the scale-up effects of the processes. All these steps facilitate the subsequent simulation and very often they are required preliminary steps. The modeling and simulation of both the processes and the systems are related to a lot of calculation problems. Moreover, there are various approaches of the optimal process design, process control, and plant renovation. Many of the calculation problems are related to the solution of differential equations. Different analytical and numerical methods have to be used. The calculation problems of the identification of the model parameters need the use of sets, metric spaces, functional, variational and iterative methods, as well as different methods for function minimization. The modeling and simulation of chemical plant systems deal with quite specific calculation problems that should be solved with the help of graphs, matrixes, nonlinear, integer, and heuristic programming, etc.
Theoretical chemical engineering uses physical approximations of the mechanics of continua. Simply, this implies the material point of the medium corresponds to a volume sufficiently small with respect to the entire volume under consideration but at the same time sufficiently large with respect to the intermolecular distances of the medium. Modeling in chemical engineering utilizes mathematical structures provided by the mechanics of the continua. The theoretical analyses employing similarity theory models demonstrate that if the mathematical methods are very simple, the formalistic use of the theory could result in wrong results. Physical ideas form the basis of the similarity theory and its mathematical methods.
