AIChE tray-efficiency prediction

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. 

This expression corresponds essentially to the limit of Pet —> 00 shown in Figure 8.3.6. A comprehensive background on stage efficiency for a plate in a distillation column, its relation to point efficiency, as well as a brief description of the AIChE tray-efHciency prediction method" has been provided by King (1980, pp. 621-622). 

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. 

The calculated point efficiency must be converted to overall column efficiency, which will lower its value and make it closer to the O Connell prediction. The calculated value of Eog is slightly higher than obtained experimentally (Eog = 0.83-0.92) at the University of Delaware for bubblecap trays (Annual Progress Report of Research Committee, Tray Efficiencies in Distillation Columns, AIChE, New York, 1955). 

Considerable work on methods for pre-predicting fractionator tray efficiency continues to the present. Shortcut methods from the past differed rather widely. The AIChE 1958 calculation method is 90% accurate,but definitely cannot be termed shortcut. 

Lee and Dudukovic [18] described an NEQ model for homogeneous RD in tray columns. The Maxwell-Stefan equations are used to describe interphase transport, with the AIChE correlations used for the binary (Maxwell-Stefan) mass-transfer coefficients. Newton s method and homotopy continuation are used to solve the model equations. Close agreement between the predictions of EQ and NEQ models were found only when the tray efficiency could correctly be predicted for the EQ model. In a subsequent paper Lee and Dudukovic [19] presented a dynamic NEQ model of RD in tray columns. The DAE equations were solved by use of an implicit Euler method combined with homotopy continuation. Murphree efficiencies calculated from the results of an NEQ simulation of the production of ethyl acetate were not constant with time. 

The above problem is not unique to the Chan and Fair correlation. In fact, the author feels that this is the most reliable published theo-reticeil efficienQr correlation currently available. The current correlation inherited these hi efficiency predictions from the AIChE model, and the problem extends to all other theoretical tray efficiency correlations the author has experience with. When the coliunn 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. 

AIChE, Bubble tray design manual, Prediction of fractionation efficiency, AIChE, New-York (1958). 

In spite of all the effort that has been expended on this topic, the prediction of mass transfer efficiency still is not on a satisfactory basis. The relatively elaborate method of the AIChE Bubble-Tray Manual (AIChE, New York, 1958) is based on the two-film theory but has not had a distinguished career. A number of simpler correlations have been proposed and have some value as general guidance. That literature has been surveyed recently by Vital, Grossel, and Olsen [Hyd. Proc., 55-56 (Oct. 1984) 147-153 (Nov. 1984) 75-78 (Dec. 1984)]. 

Limitations. The Chan and Fair correlation generally gave good predictions when tested against a wide data bank, but ita authors also observed some deviations. Chan and Fair (184,135) 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 (be 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 best-established theoretical method for predicting is that of the AIChE (Bubble-Tray Design Manual, American Institute of Chemical Engineers, New York, 1958). It is based on the sequential prediction of point efficiency, Murphree efficiency, and overall column efficiency ... 

The AIChE efficiency modeP was the first to use a rational approach to mass transfer efficiency. Equations (12.74) through (12.83) are used to predict point efficiency. The values of k a, kja, tg, and ti are deduced from laboratory measurements with small test trays containing bubble caps. No attempt is made to evaluate interfacial area a/. The detailed procedure is in reference 71. 

Numerous attempts have been made to develop useful correlations for predicting fire efficiency of tray towers. The most comprehensive study was carried out under sponsorship of the American Insthute of Chemical Engineers (AIChE) and resulted in the publication of the AlChE bubble tray design manual. The AIChE prediction method, which is aimed primarily at bubble-cap trays, involves first estimating the number of gas-phase and liquid-phase transfer units, Nc and N, for the specific conditions on the tray, combining these to obtain the number of overall gas transfer units Nqc, and predicting the point efficiency by the relationship... 

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