Tray efficiency, Murphree

Aa Active area, same as bubbling area m2 ft2 Erriv. Em z Murphree tray efficiency, gas -/- -/-... 

Ea Murphree tray efficiency, -/- -/- Hol Height of an overall transfer m ft... 

Overall column efficiency can be calculated from the Murphree tray efficiency by using the relationship developed by Lewis [Ind. Eng. Chem. 28, 399 (1936)]. 

Murphree Tray Efficiency [Ind. Eng. Chem. 17, 747 (1925)] This is the same as point efficiency, except that it applies to the entire tray instead of to a single point (Fig. 14-40b) ... 

If both liquid and vapor are perfectly mixed, liquid and vapor compositions on the tray are uniform, and the Murphree tray efficiency will coincide with the point efficiency at any point on the tray. In practice, a concentration gradient exists in the liquid, and x at the tray outlet is lower than x on the tray (see Fig. 14-40b). This frequently lowers y relative to t/ , thus enhancing tray efficiency [Eq. (14-134)] compared with point efficiency. The value of y may even drop below yn. In this case, Emv exceeds 100 percent [Eq. (14-134)]. 

The dry Murphree efficiency calculated thus far takes into account the vapor and liquid resistances and the vapor-liquid contact patterns, but is uncorrected for the effects of entrainment and weeping. This correction converts the dry efficiency to a "wet or actual Murphree tray efficiency. Colburn [Eq. (14-98), under "Entrainment ] incorporated the effect of entrainment on efficiency, assuming perfect mixing of liquid on the tray. 

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...

A detailed model of the pilot-plant MVC was derived and validated against experimental data in a previous study (Barolo et al., 1998 and also see Chapter 4). The model consists of material and energy balances, vapour liquid equilibrium on trays (with Murphree tray efficiency to account for tray nonideal behaviour), liquid hydraulics based on the real tray geometry, reflux subcooling, heat losses, and control-law calculations based on volumetric flows. The model provides a very accurate representation of the real process behaviour, but is computationally expensive for direct use within an optimisation routine. Greaves et al. (2003) used this model as a substitute of the process. 

For tray columns, an alternative approach uses Murphree tray efficiencies (Sec, 7,1.1). This efficiency is easy to incorporate into an x-y diagram, and the diagram construction can he performed using actual rather than ideal stages. The Murphree tray efficiency is defined as... 

Figure 7.3 shows the sequence of steps converting phase resistances into a tray efficiency. Gas and liquid film resistances are added to give the point efficiency (Sec. 7.1,2), Had both vapor and liquid on the tray been perfectly mixed, the Murphree tray efficiency would have equaled the point efficiency (see Sec. 7,1.1). Since the phases are not perfectly mixed, a model of the vapor- and liquid-mixing patterns is... 

In order to convert point efficiencies to Murphree tray efficiencies, the Chan and Fair correlation uses the same general mixing model as the AIChE model (125). This model uses Lewis case 1 (Sec. 7.1.3), i.e., mixed vapor and plug flow of liquid. In addition, some liquid back-mixing is assumed and correlated via an eddy diffusion coefficient. The model gives... 

The effective slope of the equilibrium curve, m, and therefore A. [Eq. (7.5)1 differs for each component. Therefore, each component has a different ratio of gas-phase resistance to liquid-phase resistance [Eq. (7.13)] and a different ratio of overall column efficiency to Murphree tray efficiency [Eq. (7.4)]. 

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

Figure 7.11 shows the same Murphree tray efficiency for the binary pair of key components separated. In the upper part of the column, separation is between the LK and the HK. These behave like a hi-... 

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. 

Example 8 Calculation of Rate-Based Distillation The separation of 655 Ib 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 carried 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 will 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 will be set at 167 Ib moPh 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 will be used. Plug flow of vapor and complete mixing of liquid will 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-calculate from the computed tray compositions, the component vapor-phase Murphree-tray efficiencies. 

The rate-based model gave a distillate with 0.023 mol % ethylbenzene and 0.0003 mol % styrene, and a bottoms product with essentially no methanol and 0.008 mol % toluene. Murphree tray efficiencies for toluene, styrene, and ethylbenzene varied somewhat from tray to tray, but were confined mainly between 86 and 93 percent. Methanol tray efficiencies varied widely, mainly from 19 to 105 percent, with high values in the rectifying section and low values in the stripping section. Temperature differences between vapor and liquid phases leaving a tray were not larger than 5°F. 

Conversion to Murphree Tray Efficiency. For complete liquid mixing on the tray, as found in small columns (e.g., Oldershaws) and in some vacuum columns where the volumetric flow of vapor is much higher than that of the liquid, Eog = Emv- For the opposite case of plug flow of liquid across the tray. 

The next step in predicting tray efficiency for design would be to take into account the effects of 1) tray and tower configuration and 2) hydraulic conditions on the tray. For the effects of the former, one can refer to a comprehensive treatise by W. K. Lewis, In this somewhat idealized study, the advantage of plug flow of liquid across the tray and its flow direction for the liquid on each tray is shown. Such an arrangement can produce Murphree tray efficiencies as high as 150% from a point efficiency of 80%. 

Two efficiency definitions are in common use for engineering design overall tray efficiency and Mur-phree tray efficiency. Murphree tray efficiency basis can be set on either the vapor phase or the liquid phase. Most literature reports data on a vapor phase... 

Murphree tray efficiency is defined as the approach to equilibrium on an individual tray by ... 

Efficiency in multiple component systems is far more complex. Every component may have a different efficiency at each stage. Components may interact and composition profiles may even reverse. The equilibrium slope for each component depends on many coupling and interaction effects. Therefore, overall efficiency cannot be easily derived from Murphree tray efficiencies. Most designs for both binary and multiple component systems use overall efficiency values based on operating data or test systems. 

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. 

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