Tray efficiencies theoretical 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. 

Tbe best-established theoretical method for predicting E is that of tbe AlCbE [Buhhle-Tray Design Manual, American Institute of Chemical Engineers, New York, 1958). It is based on tbe sequential prediction of point efficiency, Murpbree efficiency, and overall column efficiency ... 

FIG. 14-41 Sequence of steps for theoretical prediction of tray efficiency (From H. Z. Faster, Distillation Design, copyright 1992 by McGraw-Hill reprinted by permission.)... 

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 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 AlChE 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. 

The combination of reasonable accuracy, good reliability, and simplicity, together with the weakness of theoretical tray efficiency correlations, rendered the O Connell distillation correlation (Fig. 7.5ar the standard of the industry. It has been recommended by most literature sources (4,10,18,33,126,131,151,152) as one of the best empirical methods available for tray efficiency prediction. The author has hed extensive favorable experience with the distillation correlation (Fig. 7.5a), and heard the same from many others in the industry. Frank (10) and the author believe that the O Connell plot is the best computational method for estimating distillation tray efficiency others (4,12,33), however, prefer theoretical methods. 

We recommend the use of overall column efficiency factors. Overall column efficiency refers to the ratio of ideal (or theoretical) trays and actual physical trays. This is a single value that can range from 30-90%. If we consider the case of a distillation column having 20 physical trays and overall efficiency of 0.5, we would model it as a column with 10 ideal trays. With this approach, every tray remains in thermodynamic equUibrium and predictions away from the base operating scenario are reasonable. In the present work, we model the DA301, a reformate... 

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."... 

Use the binary correlations (Sec. 7.2.1) to predict 0o and possibly also 0, The section efficiency E is then used to determine the number of trays in each section of column when used in conjunction with a theoretical-stage simulation. 

Plate contactors such as valve trays are evaluated in terms of a plate efficiency, which is inversely proportional to how closely the composition of the streams leaving a stage approach the predicted compositions at thermodynamic equilibrium. To obtain the number of stages required for any given separation, it is necessary to divide the computed number of theoretical stages by an average empirical fractional plate efficiency. 

Methods for predicting efficiency also parallel those for tray columns comparison against a similar installation, use of empirical methods, direct scaleup from laboratory or pilot plant, and use of theoretically derived models. Approaches by vendors of packing usually center on comparisons with similar installations (the so-called vendor experience ) and empirical approximations. Direct scaleup from small column studies is difficult with packed columns because of the unknown effects of geometrical factors and the variations of liquid distribution that are required for practical reasons. Theoretical or semitheoretical models are difficult to validate because of the flow effects on interfacial area. It may be concluded that there is no veiy good way to predict packed column efficiency, at least for the random type packings. 

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