(FPL)2 144De tL
A graphical form of the above equations is shown in Fig. 7.4. The eddy diffusivity DE is calculated from the correlation of Barker and Self (139).
The Chan and Fair correlation does not include a term that per se accounts for weeping and entrainment. In principle, however, the FF
Figure 7.4 Mixing curves. (From "Bubble Tray Design Manual," by AIChE Research Committee, Distillation Subcommittee, 1958. Reprinted courtesy of the American Institute of Chemical Engineers.)
term in Eq. (7.19) makes an empirical correction for weeping and entrainment.
Limitations. The Chan and Fair correlation generally gave good predictions when tested against a wide data bank, but its authors also observed some deviations. Chan and Fair (134,135) describe it as "tentative until more data becomes available." Lockett (12) notes that the Chan and Fair correlation inherited the tendency to predict high point efficiencies from the AIChE correlation. Lockett also points out that the presence of the FF term in Eq. (7.19) implies that efficiency depends on tray spacing for fixed vapor and liquid loads. This implication is supported neither by theoretical nor by experimental evidence, and is considered by Lockett as "hardly reasonable."
The Chan and Fair correlation inherited several theoretical limitations from the AIChE correlation. This includes the validity of assumptions in the model for adding mass transfer resistances (Sec. 7.1.2) and the validity of plug flow plus backmixing model (Sec. 7.3.3'-Chan and Fair used the Barker and Self (139) correlation for predict ing eddy diffusivity. Lockett (12) reviewed 11 eddy diffusivity correlations, and recommended only the Shore and Haselden (140) and Zuiderweg (17) correlations for systems other than air/water. Like the AIChE model, the Chan and Fair correlation only considers axial eddy diffusion, while transverse dispersion may also be important (141,142). Both models assume perfectly mixed vapor, an assumption valid only for small-diameter columns (12); however, Diener (143) showed that tray efficiency is insensitive to vapor-mixing pattern when efficiency is less than 80 percent.
The Chan and Fair correlation also inherited several practical limitations from the AIChE correlation. It is based on a froth regime model, and is unlikely to be valid in the spray regime. Prado and Fair (110,144) have recently proposed a fundamental model that properly accounts for the flow regime, but needs some more work before becoming simple enough to be usable for design. The rough and empirical term accounting for weeping (in terms of FF) is better than nothing (in the AIChE correlation), but is far from satisfactory. The correlation does not account for vapor entrainment, and this can be important at high pressures and high liquid flows (17,104,105). The Chan and Fair correlation is complex and requires the use of diffusivities, which are often a nightmare to obtain with reasonable accuracy.
Chan and Fair (145) extended their correlation to multicomponent systems. Unfortunately, the extension was tested only against few data points, all derived from laboratoiy-scale columns. However, this extension represents a large improvement over most alternative theoretical correlations.
Alternative correlations. Zuiderweg (17) presented a correlation derived from the same basic model as the AIChE model. Different equations were presented for different flow regimes. Many of the equations were derived from a small data base. In a later paper (146), Zuiderweg noted that the correlation severely underpredicts efficiencies for the methanol-water system, but claims that it should still work for hydrocarbon systems. In another paper (105) Zuiderweg states that this correlation is possibly not more reliable than alternative theoretical models, but argues that it is simpler. Additional review comments on this correlation were made by Lockett (12). Another theoretical prediction method was developed by Stichlmair (29). The basic model is also similar to that of the AIChE correlation. However, in the froth regime, it predicts a strong effect of surface tension on interfacial area, and therefore efficiency. This prediction is inconsistent with experimental work (116) that showed little effect of surface tension on efficiency in the froth regime. Additional review comments on this correlation were made by Lockett (12).
Reliability. An inspection of Eq. (7.26) indicates that for large-diameter columns the liquid is always plug flow. An inspection of Fig. 7.4 suggests therefore a significant enhancement of tray efficiency as diameter increases. This, however, is seldom observed in practice (147,148).
Plug flow tends to maximize the ratio of Murphree to point efficiency. As stated earlier, point efficiencies predicted by the Chan and Fair method tend to be high (12). Combining the two, one would expect this correlation to give optimistic efficiency estimates for large-diameter columns.
The above problem is not unique to the Chan and Fair correlation. In fact, the author feels that this is the most reliable published theoretical efficiency correlation currently available. The current correlation inherited these high efficiency predictions from the AIChE model, and the problem extends to all other theoretical tray efficiency correlations the author has experience with. When the column diameter exceeds 4 ft, one can almost count on a theoretical correlation to predict between 80 and 100 percent efficiency, regardless of the service. In the real world, most columns run closer to 60 percent efficiency. Which of the limitations listed above, and to what extent, generates the problem is unknown. The author would not trust any theoretical tray efficiency correlation for obtaining design efficiencies unless proven that it has actually overcome the above overestimating problem.
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