Tray Efficiency Calculation Example

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. 

Tray efficiency is calculated as previously demonstrated and will not be repeated, except that normally stripping tray efficiencies run lower than rectification efficiencies. For ammonia-water stripping such as this example most over-all efficiencies run 50-60%. 

Example 8-42 Mass Transfer Efficiency Calculation for Baffle Tray Column (used by permission [211])... 

Distillation trays in a fractionator operate between 10 and 90 percent efficiency. It is the process person s job to make them operate as close to 90 percent efficiency as possible. Calculating tray efficiency is simple. Compare the vapor temperature leaving a tray to the liquid temperature leaving the trays. For example, the efficiency of the tray shown in Fig. 1.2 is 100 percent. The efficiency of the tray in Fig. 1.3 is 0 percent. 

Overall effect. A procedure for evaluating the overall effect (combining the direct and indirect effects on tray efficiency) was developed by Nelson, Olson, and Sandler (156). This method is based on the Fenske, Underwood, and Gilliland (Eduljee version) shortcut relationships (Secs. 3.2.1 to 3.2.5) and was shown to work well when comparing to a more rigorous procedure. An example (using an x-y diagram) in Sec. 7.3.6 demonstrates how differences between true and apparent volatility affect efficiencies calculated from test data. 

The Murphree tray efficiency is calculated from Equation 14.35, with Noc = 1-42 (Example 14.2) ... 

A value for the Mutphree vapor-phase efficiency Mv is then calculated for the overall iray by adjusting the point efficiency Eoc lo take into account the effects of liquid mixing and entrainment. A summary of the AlChE design proendure for hubhle-cap trays and an example of its application ate given by King.22... 

In our example we have assumed a reflux ratio of 1.4R ,in (= 1.19). The respective diagram needed to determine the number of theoretical stages is given in Figure 3.3.18, from which we obtain eleven theoretical stages. As a rule of thumb, we take a value of 0.6 for the stage (tray) efficiency and by Eq. (3.3.23) we would finally calculate a practical number of stages of 18. 

When chemical equilibrium is achieved quickly throughout the liquid phase, the problem becomes one of properly defining the physical and chemical equilibria for the system. It is sometimes possible to design a tray-type absorber by assuming chemical equilibrium relationships in conjunction with a stage efficiency factor, as is done in distillation calculations. Rivas and Prausnitz [AIChE 25, 975 (1979)] have presented an excellent discussion and example of the correct procedures to be followed for systems involving chemical equilibria. 

Example 2 Estimation of overall column efficiency. A continuous fractionation unit has been designed to operate on a liquid feed containing components, A, B, C, and D. Calculations have shown that 20 theoretical stages are necessary in the column, not including the reboiler. On the basis of the following data, estimate the overall column efficiency and the number of actual trays needed in the column by (a) Fig. 16-9, (b) Eq. (4), and (c) Eq. (6) ... 

Calculate the effect of the change in slope of the equilibrium line on the local efficiency in a sieve-tray distillation column. Use the benzene-toluene system as an example, and predict / for plates where the mixture is mostly toluene and for those where it is mostly benzene, starting with an estimated value of for the middle of the column. 

D15. The large-scale column in Example 16-4 has a feed that is a saturated liquid with a feed mole frac z = 0.5, and separation is essentially conplete (x 1 and 0). The Murphree vapor efficiency is often approximately constant in columns. Assume the value calculated in Example 16-4, E]y[Y = 0.97, is constant in the large-scale column (plug flow trays). Calculate Ep. and Kya in the stripping section at x = 0.10 and x = 0.30, and in the enriching section at x = 0.9. Repeat the enriching section calculation at x = 0.7 (shown in Example 16-41 as a check on your procedure. 

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