Models fundamental process

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 ... 

The last example is particularly noteworthy because it represents the current state of the art in utilizing fundamental process models in RTO. 

Quantitative models for predicting quality can be classified into two categories (1) fundamental process models, which are based on physical and chemical events that occur in the autoclave, and (2) regression-type models, which are based on a statistical fit of the observed product quality to the input raw material properties and the process conditions used. 

When available, fundamental process models are preferred. For many complex processes such as composite manufacturing in general and autoclave curing in particular, however, these models are often not available. This lack of availability is due to an inadequate understanding of the complex events that take place during the process. A fundamental process model is occasionally available, but it is still unsuitable for on-line model predictive control application due to the extensive computing time required to solve the model s equations. This lack of... 

In contrast, plant-wide optimization involves a large number of variables throughout a slowly responding plant. For this situation, a model-based method is required to approach the best conditions within reasonable times. A fundamental process model provides information on the effects of optimization variables on the profit and potential inequality constraints over a wide range of conditions. A model-based approach is required for the following situations. 

Kilian, A (1999), Control of an Acid Sulpite Batch Pulp Digester Based on a Fundamental Process Model, Master s Dissertation, University of Pretoria... 

This concept extends nicely to the model reduction problem, as illustrated in Fig. 4. There, Mo represents a fundamental process model, to be reduced ultimately to a simple model Mn... 

Holland, C. D., "Fundamentals and Modeling of Separation Processes," Prentice-Hall, Englewood Cliffs, N.J. (1975). 

The next part of the procedure involves risk assessment. This includes a deterrnination of the accident probabiUty and the consequence of the accident and is done for each of the scenarios identified in the previous step. The probabiUty is deterrnined using a number of statistical models generally used to represent failures. The consequence is deterrnined using mostiy fundamentally based models, called source models, to describe how material is ejected from process equipment. These source models are coupled with a suitable dispersion model and/or an explosion model to estimate the area affected and predict the damage. The consequence is thus determined. 

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... 

A key feature of MFC is that future process behavior is predicted using a dynamic model and available measurements. The controller outputs are calculated so as to minimize the difference between the predicted process response and the desired response. At each sampling instant, the control calculations are repeated and the predictions updated based on current measurements. In typical industrial applications, the set point and target values for the MFC calculations are updated using on-hne optimization based on a steady-state model of the process. Constraints on the controlled and manipulated variables can be routinely included in both the MFC and optimization calculations. The extensive MFC literature includes survey articles (Garcia, Frett, and Morari, Automatica, 25, 335, 1989 Richalet, Automatica, 29, 1251, 1993) and books (Frett and Garcia, Fundamental Process Control, Butterworths, Stoneham, Massachusetts, 1988 Soeterboek, Predictive Control—A Unified Approach, Frentice Hall, Englewood Cliffs, New Jersey, 1991). 

In concentrated wstems the change in gas aud liquid flow rates within the tower and the heat effects accompanying the absorption of all the components must be considered. A trial-aud-error calculation from one theoretical stage to the next usually is required if accurate results are to be obtained, aud in such cases calculation procedures similar to those described in Sec. 13 normally are employed. A computer procedure for multicomponent adiabatic absorber design has been described by Feiutnch aud Treybal [Jnd. Eng. Chem. Process Des. Dev., 17, 505 (1978)]. Also see Holland, Fundamentals and Modeling of Separation Processes, Prentice Hall, Englewood Cliffs, N.J., 1975. 

Ideally, a mathematical model would link yields and/or product properties with process variables in terms of fundamental process phenomena only. All model parameters would be taken from existing theories and there would be no need for adjusting parameters. Such models would be the most powerful at extrapolating results from small scale to a full process scale. The models with which we deal in practice do never reflect all the microscopic details of all phenomena composing the process. Therefore, experimental correlations for model parameters are used and/or parameters are evaluated by fitting the calculated process performance to that observed. 

Boundary membranes play a key role in the cells of all contemporary organisms, and simple models of membrane function are therefore of considerable interest. The interface of two immiscible liquids has been widely used for this purpose. For example, the fundamental processes of photosynthesis, biocatalysis, membrane fusion and interactions of cells, ion pumping, and electron transport have all been investigated in such interfacial systems. 

As for normal liquids, modeling of droplet processes of melts provides tremendous opportunities to improve the understanding of the fundamental phenomena and underlying physics in the processes. It also provides basic guidelines for optimization and on-line control of the processes. This section is devoted to a comprehensive review of process models, computational methods, and numerical modeling results of the droplet processes of melts. The emphasis of this section will be placed on the droplet processes in spray atomization for metal powder production, and spray forming for near-net shape materials synthesis and manufacturing. Details of these processes have been described in Ref. 3. 

The fundamental issues to be addressed in the process modeling include spray enthalpy, gas consumption, spray mass distribution, microstructure of solidified droplets, and droplet-substrate interactions. The effects of atomization gas chemistry, alloy composition and operation conditions on the resultant droplet properties are also to be investigated in the process modeling. 

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