392 Chapter Seven

This means both vapor and liquid loads are raised and lowered simul-

taneously. Increasing vapor rate reduces efficiency, while increasing liquid

rates raises efficiency. The two effects normally cancel each other, and

efficiency is practically independent of load changes (assuming no excessive

entrainment or weeping). Figure 7.106 shows a typical dependence of tray

efficiency on vapor and liquid loads for a commercial-scale distillation

column. Anderson et al. (97) show a similar dependence for several different

valve trays.

Reflux ratio, Reflux ratio was stated to have a small effect on efficiency (5).

Viscosity* Efficiency increases as liquid viscosity diminishes (5,149,

150,186). As discussed earlier (Sec. 7.2.2), lower liquid viscosity usually

implies higher liquid diffusivity, and therefore, lower resistance to mass

transfer in the liquid phase. It was also argued that bubbles formed in high-

viscosity liquids are larger and generate less interfa-cial area (186).

Relative volatility. Efficiency increases as relative volatility is lowered

(5,149,150). As discussed earlier (Sec. 7.2.2), lower volatility reduces the significance of the liquid phase resistance, and therefore, raises efficiency.

Surface tension* There is uncertainty regarding the effect of surface tension on tray efficiency. Often, it is difficult to divorce the surface tension effects from those of other physical properties. For this reason, it is difficult to tell

whether the effects described below are real or imaginative. Measurements by Fane and Sawistowski (116,11?) show little effect of

surface tension on efficiency in the froth regime, and a rise of tray efficiency with lower surface tension in the spray regime. The surface tension gradient

(Sec. 6.4,4) appears to have an effect. A positive gradient (surface tension increases down the column) enhances efficiency in the froth regime (108,116,117,146,189,190) while a negative gradient enhances efficiency in the spray regime (108,116,117). The magnitude of these enhancements is

uncertain. Surface tension effects have frequently been used to explain observed

composition effects (184,187,189) or discrepancies between theory and experiment (146), Zuiderweg (146) and Dribika and Biddulph (189) argue

that the Marangoni effect (Sec. 6.4.4) stabilizes the froth and therefore enhances efficiency. The enhancement is related to

M = (y* - x) ^ (7.37)

Tray Efficiency 393

The difference v* - x represents the mass transfer driving force, while dvldx represents the change in surface tension with concentration. Both Zuiderweg and Dribika and Biddulph show that with large values of Af (10 to 20 dynes/cm), point efficiency can be enhanced by as much as a factor of 1,5 to 2.0. However, these enhancement factors are the ratios of measured to predicted point efficiencies, and the predictions are based on the notoriously unreliable theoretical correlations (Sec. 7.2.1). Lockett (12J points out that the above enhancement factors remain high even at the froth-spray transition, and this is inconsistent with the argument. Further, experiment by Ellis and Legg i214) have demonstrated no significant effects of surface tension gradients on efficiency.

For low-viscosity absorption systems, one set of data (186) shows that in the froth regime tray efficiency increases as surface tension is reduced, while for high-viscosity absorption systems, surface tension had little effect on mass transfer (186).

Pressure. Tray efficiency slightly increases with pressure in the froth regime (17,105,119). The apparent pressure effect could be a reflection of the rise in efficiency with a reduction in liquid viscosity and in rel-ative volatility. (Note; As distillation pressure rises, so does the equi-librium temperature; this in turn leads to a decrease in liquid viscosity.)

At pressures higher than 150 to 300 psia, and especially at high liquid rates, vapor entrainment in the downcomer liquid becomes important, and may lead to a reduction in tray efficiency with further raises in pressure (105).

Liquid and vapor entrainment. Both represent a recycling of lower-purity material which contaminates the tray liquid or vapor, both counteract the mass transfer process and lower efficiency. Liquid and vapor entrainment are discussed in Sees. 6.2.11 and 6.4.5, respectively.

Weeping. This represents liquid short-circuiting the stage and con-taminating the tray below with more volatile material. Further dis-cussion is in Sec, 6.2.12.

Special considerations In multipass trays. In a multipass tray, vapor distribution between the passes is largely determined by the hole area, while liquid distribution is largely a function of the weir height and length. If the geometry of the passes is perfectly identical, the dis-tribution of vapor and liquid is the same for each pass, and tray effi-ciency is uniform. This is readily achievable in two-pass trays, where the design of each pass is identical to the other, but not so when a

394 Chapter Seven

larger number of passes is involved. For instance, in a four-pass tray, weir length of the center passes differs from that of the side passes. Unless allowed for in the design, the L/V ratio will vary from pass to pass, with a resulting reduction in tray efficiency, as demonstrated by Bolles (191).

Bolles (191) correlated the reduction in efficiency in terms of the distribution ratio, ie., the maximum-pass L/V ratio divided by the minimum-pass L/V ratio. The L and V for each pass are determined from the normal pressure balance and hydraulic relationships, applied to each pass. At high distribution ratios, a substantial drop in tray efficiency occurs. Bolles shows that if this distribution ratio is kept lower than 1.2, the loss in efficiency due to maldistribution is negligible. Bolles recommends designing multipass trays for such low distribution ratios, Detailed guidelines for achieving low distribution ratios (<1.2), thus minimizing the effects of pass maldistribution on efficiency, are contained in a companion book (1) and in Bolles's paper (191).

7.3.5 Tray efficiency In multlcomponent

separations

Component efficiencies. In binary mixtures, the efficiencies of each of the two components are identical- In multlcomponent separations, component efficiencies are all different because

1. Each component has a different diffusivity, both in the vapor and in the liquid.

2. In a multicomponent mixture, the diffusion rate of a component de-pends not only on its own concentration in the mixture, but also on the concentration of other components. This may lead to coupling and interaction of the mass transfer among various components. Some examples are (192) a. Reverse diffusion—Mass transfer opposite to the concentration

driving force. b. Diffusion barrier—No net mass transfer even though a concen

tration driving force exists, c. Osmotic diffusion—Mass transfer in the absence of a concentra

tion driving force. 3. The effective slope of the equilibrium curve, m, and therefore \ [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)].

Design practice. A computational case study by Toor and Burchard (192) demonstrates that accounting for the above factors can alter the

Tray Efficiency 395

stage requirement for a multicomponent separation by 30 to 40 percent. Several other authors (12,145,193,194) also warn against assuming equal component efficiencies in multicomponent distillation design. Nonetheless, individual component efficiencies are seldom used in design practice, due to the following reasons:

■ Multicomponent efficiency prediction methods are based on theoret-ical binary efficiency methods. As previously stated (Sec. 7,2.1), the reliability of those methods leaves a lot to be desired. This difficulty can be bypassed when reliable efficiency data Eire available for the binary pairs making up the multicomponent mixture. As demonstrated by Vogelpohl (193), binary efficiency data can be extended to multicomponent systems using a multicomponent computation method.

■ Few commercial simulations are geared to handle rigorous multi-component efficiency computations.

■ Rigorous methods for computing multicomponent efficiencies are complex, difficult to use for design, and often of unknown reliability. The ideal method, which is simple enough, yet reliable, is still being sought. The main bottleneck here is the availability of adequate commercial-scale data that will permit proper testing of the various methods.

Pseudo binary method. The most common and generally the simplest procedure used for multicomponent efficiencies, it proceeds in the fol-lowing steps (12):

1. From the column simulation in terms of theoretical stages, locate representative stages in each section of the column.

2. For each representative stage, select light key and heavy key com-ponents, and calculate the composition of the pseudo binary mixture as

y : ------ ̂ _ {7(38a)

XK + JHK

XliK = *"* (7.386)

*IK + #HK

Some judgment is required in selecting the pseudo keys, and the two components selected are often not the same for different parts of the column. The light- and heavy-key approach can be extended to allow for multi-pair efficiencies that may be different. The choice of binary pairs depends on feed and product compositions, volatility

396 Chapter Seven

differences, components of major interest for design, and the components which are

the majority fraction of the mixture.

3. Predict the binary diffusion coefficients of the keys in each phase at the mixture

temperature and pressure.

4. Calculate YLK and XLK on adjacent theoretical trays n and rt + 1, and determine the

slope of equilibrium curve m from

m v ------------- v— (7.39)

5. Use the binary correlations (Sec. 7.2.1) to predict E00 and E^jt possibly also E0. The

section efficient E0 is then used to determine the number of trays in each section of

column when used in conjunction with a theoretical-stage simulation.

6. There are three options for applying the efficiency:

a. Use the section efficiency E0 in conjunction with a theoretical-

stage simulation to determine the number of trays in each sec

tion. This is least accurate, but can be used with commercial

theoretical-stage simulations.

b. Assume the Murphree tray efficiency EMV calculated in item 5

above is the same for all components, then apply the Murphree

tray efficiency in a column simulation. This option is simple,

more accurate than the previous, but requires a simulation that

can use Murphree efficiencies. This option reliably predicted

composition profiles both for similar (195) and dissimilar <145)

components, but it is unknown whether it always works so

well. Chan and Fair (145) expect it to generally work well,

especially if the key components dominate the feed mixture

to the column.

c. Repeat the above steps, calculating Murphree efficiencies for

many binary pairs. This requires the solution to a linear set of

equations in order to obtain the component mole fractions in

the mixture. Ognisty and Sakata (195) show that for systems of

either similar or dissimilar components, this option predicts

composition profiles practically as accurately as the rigorous

diffusional interaction method below. This option, however, in

creases the complexity of the pseudo binary method, and also

makes it difficult to use with most commercial simulations.

With a large number of components, this option becomes as

complex as a rigorous diffusion method (195).

Individual component efficiency method. Another simple procedure, it

was recommended for the AIChE tray efficiency correlation (125). It yields individual

component efficiency but takes no account of diffusional interaction. It proceeds as

follows (12);