Obtaining Tray Efficiency

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(l) 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. 

Vital et al. (131) present an extensive tabulation of tray efficiency data collected from the published literature, Data interpolation is one of the more reliable methods for obtaining tray efficiency, provided the data are good and the rules recommended for data scale-up (Secs. 7.3,6 and 7.3.7) are followed. 

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. 

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],... 

A notable feature of high-pressure distillation is the high efficiency that is usually obtained on trays. Figures close to 100% are not uncommon. However, the efficiency of trayed columns has been shown to increase only from atmospheric pressure up to a pressure of 11.5 bar. At higher operating pressures, the efficiency of the trays decreases with increasing pressure. There is an entrainment of vapour in the liquid phase which is carried back down the column. For example, for a C4-hydrocarbon separation the tray efficiency will be reduced by 16% as the pressure is raised from 11.5 bar to 27.6 bar. 

Most efficiency data reported in the literature are obtained at total reflux, and there are no indirect VLE effects. For measurements at finite reflux ratios, the indirect effects below compound the direct effect of Fig. 14-42. Consider a case where apparent < OW and test data at a finite reflux are analyzed to calculate tray efficiency. Due to the volatility difference Rmin.apparent > hmin,tme- Since the test was conducted at a fixed reflux flow rate, (R/Rmia)appaieot < (R/RmiIJtme- A calculation based on the apparent R/Rmin will give more theoretical stages than a calculation based on the true R/Rmin. This means a higher apparent efficiency than the true value. 

The indirect effects add to those of Fig. 14-42, widening the gap between true and apparent efficiency. The indirect effects exponentially escalate as minimum reflux is approached. Small errors in VLE or reflux ratio measurement (this includes column material balance as well as reflux rate) alter R/Rmin. Near minimum reflux, even small R/Rmin errors induce huge errors in the number of stages, and therefore in tray efficiency. Efficiency data obtained near minimum reflux are therefore meaningless and potentially misleading. 

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. 

St is calculated by any of the methods in Chaps. 2 to 6- Once the tray efficiency is known, the number of actual trays can be obtained from... 

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. 

Using the slopes of the equilibrium curve obtained in (4) above, and the appropriate mixing model, convert point to Murphree tray efficiencies. 

High tray efficiency is achieved when all the contactor units are delivering gas uniformly into liquid that is evenly distributed over the entire tray surface. The beneficial effects of a liquid concentration gradient are obtained if liquid crossflow is used, where the liquid enters on one side of the tray and makes one pass across the tray. For tower diameters larger than 4 ft, better liquid distribution and less change in liquid head can often be achieved by using split flow, radial flow, or cascade flow, as illustrated in Fig. 16-5. 

Light-component analysis and the TBP and API gravity for the feed are given in Table 13-29. Representation of this feed by pseudocomponents is given in Table 13-30 based on 16.7°C (30°F) cuts from 82 to 366°C (180 to 690°F), followed by A1.1°C (TS T) and then 55.6°C (100°F) cuts. Actual tray numbers are shown in Fig. 13-114. Corresponding theoretical-stage numbers, which were determined by trial and error to obtain a reasonable match of computed- and measured-product TBP distillation curves, are shown in parentheses. Overall tray efficiency appears to be approximately 70 percent for the tower and 25 to 50 percent for the sidecut strippers. 

The actual number of stages is equal to the number of equihbrimn stages divided by the fractionator efficiency(overall column efficiency). Although the tray efficiency will vary, we will use the fractionator efficiency. The fiactionator efficiency is obtained from the O Coimel correlation given in Figure 6.17. Vital et al. [46] have reviewed and tabulated fractionator and absorber efficiencies for many systems. These data may help to arrive at a reasonable fractionator efficiency. 

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). 

The units for pressure might not show up as atm. If not, you can change the units for entering any quantities hitting the function key F5. After setting the pressure, choose Return which moves the cursor to Heaters/cooiers. No heat is to be added or removed except for the condenser and reboiler, so we move the cursor on down to Efficiencies. Here we enter the Murphree tray efficiency. We enter 1 as the default to obtain ideal trays throughout the column. 

Lewis (1936) was the first to provide a model for relating the point efficiency to the tray efficiency for the special case in which the liquid flows across the tray in plug flow (e.g., with no horizontal mixing). In the so-called Lewis Case I, the vapor entering the tray is assumed to be well mixed and we obtain (see, e.g., Lockett, 1986) ... 

In this section we show how the matrix generalization of the binary tray efficiency equation (Eq. 13.2.3) may be obtained. 

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