Tray efficiency prediction

Rigorous testing of a plant column is generally the most reliable method of obtaining tray efficiency. Test procedures are outside the scope of this book and are addressed in a companion book (1) and elsewhere (130). Alternative methods of obtaining tray efficiency are calculation and scaleup (or scale-down). Calculation is addressed in this section scaleup in Sec. 7.3. 

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Empirical Efficiency Prediction Two empirical correlations which have been the standard of the industry for distillation tray efficiency prediction are the Drickamer and Bradford, in Fig. 14-46 [Trans. Am. Inst. Chem. Eng. 39, 319 (1943)] and a modification of it by O Connell [Trans. Am. Inst. Chem. Eng. 42, 741 (1946)], in Fig. 14-47. The Drickamer-Bradford plot correlates efficiency as a function of liquid viscosity only, which makes it useful for petroleum cuts. O Connell added the relative volatility to the x axis. 

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 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. 

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. 

Example 8 Calculation of Rate-Based Distillation The separation of 655 lb mol/h of a bubble-point mixture of 16 mol % toluene, 9.5 mol % methanol, 53.3 mol % styrene, and 21.2 mol % ethylbenzene is to be earned out in a 9.84-ft diameter sieve-tray column having 40 sieve trays with 2-inch high weirs and on 24-inch tray spacing. The column is equipped with a total condenser and a partial reboiler. The feed wiU enter the column on the 21st tray from the top, where the column pressure will be 93 kPa, The bottom-tray pressure is 101 kPa and the top-tray pressure is 86 kPa. The distillate rate wiU be set at 167 lb mol/h in an attempt to obtain a sharp separation between toluene-methanol, which will tend to accumulate in the distillate, and styrene and ethylbenzene. A reflux ratio of 4.8 wiU be used. Plug flow of vapor and complete mixing of liquid wiU be assumed on each tray. K values will be computed from the UNIFAC activity-coefficient method and the Chan-Fair correlation will be used to estimate mass-transfer coefficients. Predict, with a rate-based model, the separation that will be achieved and back-calciilate from the computed tray compositions, the component vapor-phase Miirphree-tray efficiencies. 

The second classification is the physical model. Examples are the rigorous modiiles found in chemical-process simulators. In sequential modular simulators, distillation and kinetic reactors are two important examples. Compared to relational models, physical models purport to represent the ac tual material, energy, equilibrium, and rate processes present in the unit. They rarely, however, include any equipment constraints as part of the model. Despite their complexity, adjustable parameters oearing some relation to theoiy (e.g., tray efficiency) are required such that the output is properly related to the input and specifications. These modds provide more accurate predictions of output based on input and specifications. However, the interactions between the model parameters and database parameters compromise the relationships between input and output. The nonlinearities of equipment performance are not included and, consequently, significant extrapolations result in large errors. Despite their greater complexity, they should be considered to be approximate as well. 

Tray efficiency 0 j is supposed to represent a measure of the deviation from equilibrium-stage mass transfer assuming backmixed trays. However, the estimate of tray efficiency requires accurate knowledge of the equihbrium vaporization constant. Any deviations between the actual equihbrium relation and that predicted by the database will be embodied in the tray efficiency estimate. It is a tender trap to accept tray efficiency as a true measure of the mass transfer hmitations when, in fact, it embodies the uncertainties in the database as well. 

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. 

Considerable work on methods for pre-predicting fractionator tray efficiency continues to the present. Shortcut methods from the past differed rather widely.The... 

This suggests that caution must be exercised when establishing a tray efficiency for any type contacting device by (1) using actual test data if available for some similar system or (2) comparing several methods of predicting efficiency, and (3) possible use of a more conservative efficiency than calculated to avoid the possibility of ending up with a complete column with too few actual trays—a disastrous situation if not discovered prior to start-up operations. 

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],... 

Since tray efficiencies vary from one section to another, it is best to apply Eq. (14-132) separately for the rectifying and stripping sections. In practice, efficiency data and prediction methods are often too crude to give a good breakdown between the efficiencies of different sections, and so Eq. (14-132) is applied over the entire column. 

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. 

Three parameters were identified and adjusted to validate the model against the experiments. The parameters are the heat losses, the nominal tray holdup and the Murphree tray efficiency (EM). Figure 4.16 shows how EM is adjusted to match the dynamic model prediction and experimental temperature profile measured on Plate 12. Figure 4.17 shows the comparison between the experimental and model prediction of ethanol composition in the reflux drum, middle vessel and in the bottom of the column. Figures 4.16-17 show a good match between the model prediction and experiments. 

Figure 4.16. Adjustment of Murphree Tray Efficiency. Dotted line Experiment. Full lines Model Predictions. [Barolo et al., 1998]a...

Figure 7.3 Sequence of steps Tor thseretical prediction of tray efficiency.

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 O Connell correlation was based on data for bubble-cap trays, and it was stated (131) to predict 90 percent of the efficiency data within 10 percent, both for distillation and absorption. For sieve and valve trays, its predictions are likely to be slightly conservative (151). Ludwig (4) warns that O Connell s absorber correlation (Fig. 7.55, sometimes predicts efficiencies that are too high He believes that it can be used for stripping of gases from rich oils and for absorbers provided care is exercised not to accept too high values. 

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). 

Tray Efficiency The overall efficiencies of sieve trays typically are between 10 and 30 percent. One of the earliest models for predicting the overall tray efficiency was an empirical one reported by Treybal [Liquid Extraction, 2d ed. (McGraw-Hill, 1963)]. Krishna, Murty, and) Rao [Ind. Eng. Chem. Process Des. Dev., 7(2),... 

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