Practical Relevance of the Ideal Model

Band Profiles of Two Components with the Meal Model 

Appendix - The Five Different Cases of Separations of Binary Mixtures 

This section summarizes the analytical solutions of the ideal model with a Langmuir competitive isotherm in the different cases identified . 

End Time of the Concentration Plateau and Begirming of the Rear Continuous Profile, Eq. 8.29  

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The lack of data is obvious and surprising at a time when the Ruhrchemie/ Rhone-Poulenc process has been in operation for more than 20 years. A rigid reaction rate model, established under idealized conditions, becomes complex and complicated when it is transferred to the hydroformylation of lower olefins under conditions relevant to the industrial practice, as the mass transfer phenomena involved in a triphasic system (gas-liquid-liquid) in large reactors have to be taken... 

Information concerning the relevant adsorption equilibria is generally an essential requirement for the analysis and design of an adsorption separation process. In Chapter 3 we considered adsorption equilibrium from the thermodynamic perspective and developed a number of simple idealized expressions for the equilibrium isotherm based on various assumptions concerning the nature of the adsorbed phase. The extent to which these models can provide a useful representation of the behavior of real systems was considered only superficially and is reviewed in this chapter. Since many practical adsorption systems involve the simultaneous adsorption of more than one component, the problems of correlating and predicting multicomponent equilibria from singlecomponent data are of particular importance and are therefore considered in some detail. 

In a lot of tests in the literature for the characterization of RP-phases, retention factors of often ideal analytes are used to rank the phases according their hydrophobic character. Irrespective of the analytes used, one should consider the principle question as to whether retention factors are a suitable criterion for comparison at all. The retention behavior (i.e., a measure of the hydrophobicity) is, from the practical point of view, only of secondary interest. In the case of comparison tests, the aim is to identify columns that separate any compotmds similarly well, and a measure of the separability is the selectivity. Besides the retention factor, also the third parameter, the plate number, seems to be less suitable. It depends on so many factors that one needs a very large-scale standardization procedure to relate detected differences in plate numbers exclusively to differences in the quality of the packing procedure of several columns. One should only consider the simple case that the next column is better/worse packed. It is quite labor-intensive to obtain statistically relevant results in this context. Also in the case of the declaration of asymmetry factors, a correlation is generally assumed between asymmetry and silanophilicity. This undoubtedly exists, but not exclusively. Also, if a comparison of columns is made correctly, of what use is the information that two columns are similarly well-packed and have similar silanophilic character in relation to two standard bases as model compounds ... 

More generally, the presence or absence of good clinical data imposes limits on the economic evaluations that can be conducted. It is usually easier to undertake economic evaluations of drug therapies, where there are usually some reasonable clinical data, as compared with medical devices or procedures. However, even for drugs, the data from standard Phase 3 clinical trials are far from ideal. These trials are usually conducted under conditions that are atypical of normal practice. In addition, they are often of short duration and often fail to compare the most relevant alternatives for economic evaluation. This means that decision-analytic modeling is usually required as a supplement to, or alternative to, economic analysis alongside trials. 

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