Phenomena-Based Modeling of Processing Systems

However, the theory of water based modeling of the reactor cooling by the decay heat removid system lately developed in Japan, leads to certain problems related to the effect of some physical phenomena on the process of transition to the natural flow. The comprehensive analysis made at the SSC RF IPPE on the results gained in many countries on the modeling theory has shown as follows ... 

It is the model library for fixed-bed catalytic reaction, fluidised-bed and various polymer reactors and so on. Different tools are available in gPROMS software for simulation and modelling of various systems. Some of the following are (i) multi-scale modelling of complex processes and phenomena, (ii) State-of-the-art model validation tools allow estimation of multiple model parameters from steady-state and dynamic experimental data, and provide rigorous model-based data analysis, (iii) The maximum amount of parameter information from the minimum number of experiments, (iv) The gPROMS-CFD Hybrid Multitubular interface provides ultimate accuracy in the modelling of... 

A model can be defined as a set of relationships between the variables of interest in the system being investigated. A set of relationships may be in the form of equations the variables depend on the use to which the model is applied. Therefore, mathematical equations based on mass and energy balances, transport phenomena, essential metabolic pathway, and physiology of the culture are employed to describe the reaction processes taking place in a bioreactor. These equations form a model that enables reactor outputs to be related to geometrical aspects and operating conditions of the system. 

Since the early days of quantum mechanics, the wave function theory has proven to be very successful in describing many different quantum processes and phenomena. However, in many problems of quantum chemistry and solid-state physics, where the dimensionality of the systems studied is relatively high, ab initio calculations of the structure of atoms, molecules, clusters, and crystals, and their interactions are very often prohibitive. Hence, alternative formulations based on the direct use of the probability density, gathered under what is generally known as the density matrix theory [1], were also developed since the very beginning of the new mechanics. The independent electron approximation or Thomas-Fermi model, and the Hartree and Hartree-Fock approaches are former statistical models developed in that direction [2]. These models can be considered direct predecessors of the more recent density functional theory (DFT) [3], whose principles were established by Hohenberg,... 

In complex systems such as three-phase reactors, the methods of mathematical modeling cannot provide the required information for process design and scale-up since it is practically impossible to take into account all existing phenomena and safely predict the influence of hydrodynamics, heat and mass transfer, or kinetics on each other (Datsevich and Muhkortov, 2004). Thus, models are almost always approximate in nature. They are based on a number of assumptions that cannot be met during scale-up. So, it is not surprising that industrial unit designers do not completely trust the results obtained from mathematical modeling. Thus, several systems cannot be fully modeled mathematically and other methods for scale-up are followed. 

As it follows from the above-said, nowadays any study of the autowave processes in chemical systems could be done on the level of the basic models only. As a rule, they do not reproduce real systems, like the Belousov-Zhabotinsky reaction in an implicit way but their solutions allow to study experimentally observed general kinetic phenomena. A choice of models is defined practically uniquely by the mathematical formalism of standard chemical kinetics (Section 2.1), generally accepted and based on the law of mass action, i.e., reaction rates are proportional just to products of reactant concentrations. 

All the mathematical formulations presented in the following chapters are mathematical models of polymer processing subsystems and systems that generally consist of a series of intricate, mostly transport-based, physical phenomena occurring in complex geometrical configurations. 

The next two chapters are devoted to ultrafast radiationless transitions. In Chapter 5, the generalized linear response theory is used to treat the non-equilibrium dynamics of molecular systems. This method, based on the density matrix method, can also be used to calculate the transient spectroscopic signals that are often monitored experimentally. As an application of the method, the authors present the study of the interfadal photo-induced electron transfer in dye-sensitized solar cell as observed by transient absorption spectroscopy. Chapter 6 uses the density matrix method to discuss important processes that occur in the bacterial photosynthetic reaction center, which has congested electronic structure within 200-1500cm 1 and weak interactions between these electronic states. Therefore, this biological system is an ideal system to examine theoretical models (memory effect, coherence effect, vibrational relaxation, etc.) and techniques (generalized linear response theory, Forster-Dexter theory, Marcus theory, internal conversion theory, etc.) for treating ultrafast radiationless transition phenomena. 

In order to make design or operation decisions a process engineer uses a process model. A process model is a set of mathematical equations that allows one to predict the behavior of a chemical process system. Mathematical models can be fundamental, empirical, or (more often) a combination of the two. Fundamental models are based on known physical-chemical relationships, such as the conservation of mass and energy, as well as thermodynamic (phase equilibria, etc.) and transport phenomena and reaction kinetics. An empirical model is often a simple regression of dependent variables as a function of independent variables. In this section, we focus on the development of process models, while Section III focuses on their numerical solution. 

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