Tray Efficiency Fundamentals

Rate of Mass Transfer in Bubble Plates. The Murphree vapor efficiency, much like the height of a transfer unit in packed absorbers, characterizes the rate of mass transfer in the equipment. The value of the efficiency depends on a large number of parameters not normally known, and its prediction is therefore difficult and involved. Correlations have led to widely used empirical relationships, which can be used for rough estimates (109,110). The most fundamental approach for tray efficiency estimation, however, summarizing intensive research on this topic, may be found in reference 111. 

Aside from the fundamentals, the principal compromise to the accuracy of extrapolations and interpolations is the interaction of the model parameters with the database parameters (e.g., tray efficiency and phase eqiiilibria). Compromises in the model development due to the uncertainties in the data base will manifest themselves when the model is used to describe other operating conditions. A model with these interactions may describe the operating conditions upon which it is based but be of little value at operating conditions or equipment constraints different from the foundation. Therefore, it is good practice to test any model predictions against measurements at other operating conditions. 

As might be expected, the vapour phase may offer the controlling resistance to mass transfer in high pressure distillations. Values for tray efficiencies at elevated pressure are scarce [23, 24]. The prediction of tray efficiency may be approached in several ways. One way is to utilize field performance data taken for the same system in very similar equipment. Unfortunately such data are seldom available. When they are available, and can be judged as accurate and representative, they should be used as a basis for efficiency specification [25], Another way is to utilize laboratory-or pilot-plant efficiency data. For example a small laboratory-Oldershaw tray-column can be used with the same system. Of course, the results must be corrected for vapour-and liquid mixing effects to obtain overall tray efficiencies for large-scale design [26], Another approach is the use of empirical or fundamental mass-transfer models [27-30],... 

Factors Affecting Tray Efficiency Below is a summaiy based on the industry s experience. A detailed discussion of the fundamentals is found in Lockett s book (Distillation Tray Fundamentals, Cambridge University Press, Cambridge, England, 1986). A detailed discussion of the reported experience, and the basis of statements made in this section are in Kister s book (Distillation Design, McGraw-Hill, New York, 1992). 

Theoretical Efficiency Prediction Theoretical tray efficiency prediction is based on the two-film theory and the sequence of steps in Fig. 14-41. Almost all methods evolved from the AIChE model (AIChE Research Committee, Bubble Tray Design Manual, New York, 1958). This model was developed over 5 years in the late 1950s in three universities. Since then, several aspects of the AIChE model have been criticized, corrected, and modified. Reviews are given by Lockett (Distillation Tray Fundamentals, Cambridge University Press, Cambridge, England, 1986) and Chan and Fair [Ind. Eng. Chem. Proc. 

The Chan and Fair correlation generally gave good predictions when tested against a wide data bank, but its authors also observed some deviations. Its authors described it as "tentative until more data become available. The Chan and Fair correlation is considered the most reliable fundamental correlation for tray efficiency, but even this correlation has been unable to rectify several theoretical and practical limitations inherited from the AIChE correlation (see Kister, Disfiliation Design, McGraw-Hill, New York, 1992). Recently, Garcia and Fair (Ind. Eng. Chem. Res. 39, 1818, 2000) proposed a more fundamental and accurate model that is also more complicated to apply. 

Alternative definitions of tray efficiency are sometimes used. Lockett (12) reviewed the pros and cons of several efficiency definitions. He cited the industry s experience that the more rigorous and theoretically correct a definition is, the more difficult it is to use, For instance, the Standart efficiencies are often considered the soundest fundamentally, but apparently have never been used for a design. For the design and operation engineer, the overall column (or section) efficiency is by far the most important. 

The above derivation assumes that vapor flows upward in plug flow and that there is no horizontal vapor mixing, while liquid flows horizontally in plug flow and there is no vertical mixing. Lockett and Uddin (12,122) and Standart (123,124) showed that these liquid flow assumptions are poor, unnecessary, and lead to incorrect implications regarding tray efficiency. By modifying the definition of NL, Lockett derived a fundamentally superior equation analogous to Eq. (7.13). Most theoretical models, however, use Eq. (7.13). Equation (7.13) is also the equation used for packed columns, but for packed columns, it is based on sounder assumptions (12). 

The point efficiency is a fundamental criterion of mass transfer, whereas the overall tray efficiency is the value that can be measured, especially for larger distillation columns. Large-column... 

Garcia, J. A. 1999. Fundamental Model for the Prediction of Distillation Sieve Tray Efficiency Hydrocarbon and Aqueous Systems. Ph.D. dissertation, Univ. of Texas at Austin. 

A third type of tray efficiency, the Murphree point efficiency, is used sometimes in attempts to correlate efficiency with fundamental mechanisms occurring on the iray, The point efficiency . is defined as follows ... 

Overall tray efficiency. The overall tray or plate efficiency Eq concerns the entire tower and is simple to use but is the least fundamental. It is defined as the ratio of the number of theoretical or ideal trays needed in an entire tower to the number of actual trays used. 

Since conditions vaiy throughout the column, it is more fundamental to deal with a tray efficiency. 

This is the loced iciency or point efficiency, and because a liquid concentration gradient is not involved, it cannot have a value greater than 1.0. Thus, it is a more fundamental concqM, but it suffers in application since concentration profiles of operating trays are difficult to predict. As in the case of the Mur ree tray efficiency, it is possible to use a liquid-phase point efficiency. 

To answer this fundamental question, we should realize that reducing the tower pressure will also reduce both the tower-top temperature and the tower-bottom temperature. So the change in these temperatures, by themselves, is not particularly informative. But if we look at the difference between the bottom and top temperatures, this difference is an excellent indication of fractionation efficiency. The bigger this temperature difference, the better the split. For instance, if the tower-top and tower-bottom temperatures are the same for a 25-tray tower, what is the average tray efficiency (Answer 100 percent + 25 = 4 percent.)... 

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