Estimating Tray Efficiency

Some of the available methods for estimating tray efficiencies will be described. A useful summary of the AIChE bubble-cap tray method is in the book of King (1980, pp. 621-626). Some of the literature that has found fault with this method is cited by Vital et al. (1984). 

Example 12 Estimating Tray Efficiency For the column in Example 9, estimate the tray efficiency, given that at the relative volatility near the feed point is 1.3 and the viscosity is 0.25 cP. 

The design of absorbers (and strippers) typically involves a computer-assisted, Iray-by-tray. heat- and material-balance calculation to determine the required number of equilibrium stages, which arc then related to the required number of actual trays by an estimated tray efficiency. More recently, a non-equilibrium stage model has been developed for computer application which considers actual trays (or sections of packing) and performs a heat and material balance for each phase on each actual tray, based on mass and heat transfer rates on that tray. 

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. 

Design data for separation of the particular or similar mixture in a packea column are not available. Design procedures are better estabhshed for tray-type columns than for packed columns. This is particularly so with respect to separation efficiency since tray efficiency can be estimated more accurately than packed height equivalent to a theoretical stage (HETP). 

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. 

Analysts must recognize the above sensitivity when identifying which measurements are required. For example, atypical use of plant data is to estimate the tray efficiency or HTU of a distillation tower. Certain tray compositions are more important than others in providing an estimate of the efficiency. Unfortunately, sensor placement or sample port location are usually not optimal and, consequently, available measurements are, all too often, of less than optimal use. Uncertainty in the resultant model is not minimized. 

After actual theoretical trays are determined (see Actual reflux and theoretical stages) one needs to estimate the actual physical number of trays required in the distillation column. This is usually done by dividing the actual theoretical trays by the overall average fractional tray efficiency. Then a few extra trays are normally added for offload conditions, such as a change in feed composition. 

Example 8-13 Estimating Distillation Tray Efficiency by Equations 8-7OA and 8-7OB (used by permission of McFarland et al. [86])... 

Unfortimately, the efficiencies for tray and overall column operation are incomplete and nullify to a certain extent some very high quality theoretical performance design. Tray efficiencies may be estimated by Figure 8-29 or Table 8-11. 

Figure 8-137 is used for estimating the entrainment-flood point. Liquid particle entrainment is generally considered as reducing tray efficiency (performance). 

As with distillation, the correlation for overall tray efficiency for absorbers, given in Equation 10.7, should only be used to derive a first estimate of the actual number of trays. More elaborate and reliable methods are available, but these require much more information on tray type and geometry and physical properties. If the column is to be packed, then the height of the packing is determined from Equation 9.64. As with distillation, the height equivalent of a theoretical plate (HETP) can vary... 

One last contribution to HETP in this chapter is to establish tray efficiency by simply running one of the tray programs and inputting T for the tray method selection. The program will give you the well-proven tray efficiency two-film method [1]. Then refer to Table 3.10 and estimate your HETP minimum required. I always recommend adding at least 6 in to the HETP for a reasonable, safe design. 

The number of trays is determined by dividing the theoretical number of stages, which is obtained from the relationships in Section III, by the appropriate tray efficiency. It is best to use experimental efficiency data for the system when available, but caution is required when extending such data to column design, because tray efficiency depends on tray geometry, liquid and gas loads, and physical properties, and these may vary from one contactor to another. In the absence of data, absorption efficiency can be estimated using O Connell s empirical correlation. This correlation should not be used outside its intended range of application. 

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. 

If good VLE data are not available, vary reflux ratio and find by test the combination of reflux and stages that will give the desired separation. Assume that a commercial column with the same number of trays and operating at the Bame reflux ratio will give the same separation as the Oldershaw column. The number of plates thus calculated can sometimes be reduced by estimating the efficiency enhancement from point to column efficiency. 

The Murphree (and Hausen) efficiencies of both components in a binary mixture are equal although they cannot be less than 0, they may be greater than 1. A table of typical values of Murphree tray efficiency can be found in Sec. 14. Also described in Sec. 14 are methods for estimating Murphree efficiencies when they are not known. 

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