Process Modeling Fundamentals

As indicated in the previous chapter, models are used for a variety of applications, such as study of the dynamic behavior, process design, model-based control, optimization, controllability study, operator training and prediction. These models are usually based on physical fundamentals, conservation balances and additional equations. In this chapter the conservation balances for mass, momentum, energy and components are introduced. 

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Because RtR controllers generally are model-based controllers, the availability of a process model (fundamental or empirical) is of great utility. However, if a dynamic model is not easily obtained due to the complexity of the process, run-to-run control can still be carried out. The majority of models used in RtR control for semiconductor applications are steady-state models (Moyne et al., 2001). These pure gain models assume that the process drift is slow. The RtR controller is typically an integral controller plus a bias term. When the output measurement is noisy, it is useful to employ an observer or filter to estimate the actual process output. In this case, controllers can be designed using the techniques presented in Sections 17.5 and 17.6. 

Documentation of experimental method so that work can be reproduced at a later time Appropriate data handling statistical methods conclusions based on fact, supportable by data Define and execute critical experiments to prove or disprove hypothesis Mechanistic or fundamental interpretation of data preferred Communication of Conclusions to Incorporate Technical Learning in Organization Experimental W rk Done in Support of New or Existing Processes Should be Captured in Process Models... 

FIG. 26-54 Horizontal dispersion coefficient for Pasquill-Gifford plume model, Reprinted ffomD. A. Ct owl and J. F. Louvar, Chemical Process Safety, Fundamentals with Applications, Z.9.90, p. 138. Used hy permission of Ft entice Hall)... 

Hessel, V., Hardt, S., and Lowe, H. (2004) Chemical Micro Process Engineering Fundamentals, Modeling, and Reactions, Wiley-VCH Verlag GmbH. 

V. Hessel, S. Hardt and H. Lowe Chemical Micro Process Engineering - Fundamentals, Modelling and Reactions, Wiley-VCH, Weinheim (2004). 

Chemical Micro Process Engineering Fundamentals, Modelling and Reaaions Volker Hessel, Steffen Hardt, Holger Lowe... 

Pais L. S., Rodrigues A. E. (1998) Separation of Enantiomers by SMB Chromatography Strategies of Modeling and Process Performance, Fundamentals of Adsorption 6 Proceedings of the Sixth International Conference of Fundamentals of Adsorption, F Meunier (ed.), Elsevier, Paris, p. 371-376. 

Finally, an important characteristic identified in chemical production processes are time-consuming and costly setup operations. Thus, the representation of time is a critical issue in the modeling of chemical production processes. Three fundamental deficiencies of the representation result if continuous processes are modeled by standard bucket-oriented lot-sizing models. These are the carry-over of setup states... 

Model equations. Fundamental process models are very useful in optimizing the design and operation of LPCVD systems. A fundamental model of an LPCVD reactor similar to Figure El4.5a was presented by Jensen and Graves (1983) and included the following simplifying assumptions ... 

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