Chemical engineering modelling

Chemical Engineering Dynamics An Introduction to Modelling and Computer Simulation, Third Edition J. Ingham, I.J. Dunn, E Heinzle, J.E. Prenosil, J.B. Snape 

Copyright 2007 WILEY-VCH Verlag GmbH Co. KGaA, Weinheim ISBN 978-3-527-31678-6 

Kapur (1988) has listed thirty-six characteristics or principles of mathematical modelling. Mostly a matter of common sense, it is very important to have them restated, as it is often very easy to lose sight of the principles during the active involvement of modelling. They can be summarised as follows  

The mathematical model can only be an approximation of real-life processes, which are often extremely complex and often only partially understood. Thus models are themselves neither good nor bad but should satisfy a previously well defined aim. 

Modelling is a process of continuous development, in which it is generally advisable to start off with the simplest conceptual representation of the process and to build in more and more complexities, as the model develops. Starting off with the process in its most complex form often leads to confusion. 

The mathematical model can only be an approximation of real-life processes, which are often extremely complex and often only partially understood. Thus models are themselves neither good nor bad but, as pointed out by Kapur, will either give a good fit or a bad fit to actual process behaviour. Similarly, it is possible to develop several different models for the same process, and these will all differ in some respect in the nature of their predictions. Indeed it is often desirable to try to approach the solution of a given problem from as many different directions as possible, in order to obtain an overall improved description. The purpose of the model also needs to be very clearly defined, since different models of a process, each of which has been developed with a particular purpose in mind, may not satisfy a different aim for which the model was not specifically constructed. 

Of course, whilst the aim of the modelling exercise is always to obtain as realistic a description of the process phenomena as possible, additional realism often involves additional numerical complexity and will demand additional data, which may be difficult or impossible to obtain. A marginal additional degree of realism can thus become rapidly outweighed by the large amount of extra time and effort needed. 

Often it is possible to consider the process or plant, as a system of independent sub-sets or modules, which are then modelled individually and combined to form a description of the complete system. This technique is also used in the large scale commercial simulation software, in which various library sub-routines or modules for the differing plant elements, are combined into a composite simulation program. 

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As the flow of a reacting fluid through a reactor is a very complex process, idealized chemical engineering models are useful in simplifying the interaction of the flow pattern with the chemical reaction. These interactions take place on different scales, ranging from the macroscopic scale (macromixing) to the microscopic scale (micromixing). 

Developing chemical engineering models for fundamental biological interactions. 

PLATE 7 Chemical engineers develop models to understand the formation, transport, and environmental fate of airhorne pollutants such as ozone. This photograph shows a graphic display of a chemical engineering model for ozone concentrations in the Los Angeles hasin. Courtesy, John Seinfeld, California Institute of Technology. 

The combinatorial term Pcomb(X,S) in Eq. (11) denotes a usually small correction for size and somewhat also for shape dilferences of the solutes and solvents, which is reasonably well understood from chemical engineering models. It is an empirical function, depending only on the surface areas and volumes of solute and solvent molecules, which are reasonably known from the COSMO cavities. The error arising from the approximations made in the combinatorial term can be expected to be much less than IkJ mol, or 0.17 log units, and hence can be safely neglected in the context of drug solubiUty estimation. 

L.S. Pedersen, P. Glarborg, K. Dam-Johansen, P.W. Hepburn, and G. Hesselmann. A Chemical Engineering Model for Predicting NO Emissions from Pulverised Coal Flames. Combust. Sci. Techn., 132 251-314,1998. 

As mentioned earlier, I was not aware of the details of the chemical engineering models and Guggenheim s QUAC approximation, when I developed the COSMO-RS model. From a brief glance at that part of the literature I had got the impression that all these models are basically lattice theories, while I wanted to... 

Some important chemical engineering modelling and simulation fields as well as related activities are briefly presented here. First, we can see that the traditional modelling procedures or computer-aided process engineering cover a much narrower range of modelling tools than those mentioned here. A broader spectrum of... 

The first approaches to compare stochastic models and chemical engineering were made in 1950, with the Higbie [4.1] and Dankwerts transfer models [4.2]. Until today, the development of stochastic modelling in chemical engineering has been remarkable. If we made an inventory of the chemical engineering modelling studies we could see that a stochastic solution exists or complements all the cases [4.3-4.8]. 

Computational chemical engineering modeling applied to energy and reactor design... 

In chap 1 a survey of the elements of transport phenomena for single phase multicomponent mixtures is given. This theory serves as basis for the development of most chemical engineering models as well as the multiphase flow concepts to be presented in the following chapters. The first part of the chapter considers laminar single phase flows for multicomponent mixtures. In the second part of the chapter the governing equations are applied to turbulent flows. 

Fig. 3.64. UML model of a design process in chemical engineering (modeling environment)...

Chemical Network Problems Solved on NASA/Goddard s Massively Parallel Processor (MPP) Computer Symbolic Computation and Chemical Engineering Model Development An Overall Strategy for the Systematic Synthesis and Optimization of Large-Scale Chemical Processing Systems Synthesis of Solids Processing (Heuristics Selection)... 

The first group of models that is used to describe adsorption onto activated carbon filters are the so-called chemical engineering models. These consider the filter as a chemical reactor, usii the conventional equations for mass and heat transfer to describe the transport processes... 

The occurrence of a rate process and a thermodynamic equilibrium state is common in chemical engineering models. Thus, certain parts of a whole system may respond so quickly that, for practical purposes, local equilibrium may be... 

However, chemical engineering models comprise usually a large number of algebraic constraints highly nonlinear in composition. The projection of eq. (1.3) gives rise to the following quantities ... 

Using methods from graph theory, it is explained which part of the kinetic description is influenced by the complexity of the detailed reaction mechanism and which part is not. This is an important step in the so-called gray-box approach, which is widely applied in chemical engineering modeling. 

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