Comments about Model Assumptions

FIGURE 9.11 Nickel and vanadium concentration profiles in (—) liquid bulk and (—) surface of catalyst as functions of reactor length at400°C and LHSV =1.5 h . (Lines) Simulated, (symbols) experimental. 

It seems that using equations based on judicious criteria for estimating thermodynamic and transport properties in a heterogeneous reactor model, some insights 

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At this time a few comments about the model of Parilis et al. is appropriate. Their theory predicts that no kinetic emission can occur up to a certain threshold energy the yield then increases linearly with energy until at higher energy the slope again changes and the yield finally becomes linear with velocity. The majority of experimental results appear to confirm these trends suggesting that there is some truth in the basic assumptions. 

Brunauer (see Refs. 136-138) defended these defects as deliberate approximations needed to obtain a practical two-constant equation. The assumption of a constant heat of adsorption in the first layer represents a balance between the effects of surface heterogeneity and of lateral interaction, and the assumption of a constant instead of a decreasing heat of adsorption for the succeeding layers balances the overestimate of the entropy of adsorption. These comments do help to explain why the model works as well as it does. However, since these approximations are inherent in the treatment, one can see why the BET model does not lend itself readily to any detailed insight into the real physical nature of multilayers. In summary, the BET equation will undoubtedly maintain its usefulness in surface area determinations, and it does provide some physical information about the nature of the adsorbed film, but only at the level of approximation inherent in the model. Mainly, the c value provides an estimate of the first layer heat of adsorption, averaged over the region of fit. 

Some comments are needed to explain the choice of assumptions made in the HOSE model. It is also useful to take into account experience gathered after about of 15 years of its application. 

Equations fl6-86bl and tl6-921 are not identical because they are based on different models. Both models assume that the continuous phase is well mixed, but their assumptions about the dispersed phase are different. These differences emphasize the comments in Chapter 15 that analysis of mass transfer remains a topic for research and discussion. With identical values of KQ.E a, Eq. fl6-921 always predicts a higher value for E than does Eq. n6-86bl. This is illustrated in Example 16.5. Another way of looking at this is that with the same E, a larger KQ.E a value will be back-calculated from Eq. (16-... 

We make a primary distinction with respect to methodological approach. There is a vast amount of descriptive research about channel structure and conflict that performs analysis of empirical data or discusses evidence obtained anecdotally or by case study. We comment on this in Section 2.1. This chapter is primarily interested in analytical model-based research, which is introduced in Section 2.2. This literature will subsequently be partitioned with respect to assumptions concerning control structure and channel type. 

MIRSKY I want to comment on Dr. Heintzen s remark. About ten years ago I developed a model which I thought was the worst model I ever developed, yet I came up with the same stress distribution as Dr. Streeter got with different assumptions. So we have to be careful. We may end up with the same results with different assumptions. 

A further comment seems to be necessary concerning the phrase that the purpose of models is "to describe or to explain" an experimental phenomenon. Clearly, the most satisfactory descriptions of an experiment are the experimental curves themselves. The first step towards a model would be to reduce this usually very large amount of information by equivalently representing or simulating it in terms of as few and as simple relationships as possible, perhaps in the form of a mathematical formula. Such a reduction of information is stated by saying that a model describes an experiment. If we succeed, however, in establishing the description on the basis of the knowledge or at least of some intuitive assumptions about the specific molecular structure of the real system, we would call the model an explanation. 

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