Efficiency point

Hence the point efficiency Hqq may be computed if both and in the bubbling area are known. These paiameteis are determined by the prevailing... 

The first of these gives E directly. The second gives a point efficiency [Eq. (18-30)]. The third involves the prediction of individual phase efficiencies. 

Direct Scale-Up of Laboratory Distillation Ljficiency Measurements It has been found by Fair, Null, and Bolles [Ind. Eng. Chem. Process Des. Dev., 22, 53 (1983)] that efficiency measurements in 25- and 50-mm (1- and 2-in-) diameter laboratory Oldersbaw columns closely approach tbe point efficiencies [Eq. (14-129)] measured in large sieve-plate columns. A representative comparison of scales of operation is shown in Fig. 14-37. Note that in order to achieve agreement between efficiencies it is necessaiy to ensure that (1) tbe systems being distilled are tbe same, (2) comparison is made at tbe same relative approach to tbe flood point, (3) operation is at total reflux, and (4) a standard Oldersbaw device (a small perforated-plate column with downcomers) is used in tbe laboratoiy experimentation. Fair et al. made careful comparisons for several systems, utibzing as large-scale information tbe published efficiency studies of Fractionation Research, Inc. 

Theoretical Predictive Methods Tbe approach to equilibrium on a plate may be defined as tbe ratio of tbe aclual change in gas composition as it passes through tbe plate to tbe change that would have occurred if tbe gas bad reached a state of equibbrium with tbe liqmd. If a point on plate n is considered, this definition leads to tbe point efficiency ... 

FIG. 14-37 Overall column efficiency of 25-mm Oldersbaw column compared with point efficiency of 1,22-m-diameter-sieve sieve-plate column of Fractionation Research, Inc, System = cyclohexane-n-heptane, [(Fair, Null, and Bolles, Ind, Eng, Chem, Process Des, Dev, 22, 53 (i.982),]... 

Tbe best-established theoretical method for predicting E is that of tbe AlCbE [Buhhle-Tray Design Manual, American Institute of Chemical Engineers, New York, 1958). It is based on tbe sequential prediction of point efficiency, Murpbree efficiency, and overall column efficiency ... 

On tbe basis of tbe two-film model for mass transfer, and relating all efficiencies to gas-pbase concentrations (for convenience only a similar development can be made on tbe basis of bquid concentrations), point efficiency can be expressed in terms of transfer units ... 

Transfer units are dimensionless and are defined further in Sec. 5. According to Eq. (14-133), tbe evaluation of point efficiencies reduces... 

In summary, the point efficiency E g is computed from Eq. (14-132) using N g ffom Eq. (14-113), Ng from Eq. (14-134) and m based on the relative voatility of the system. For a binary mixture and a zone of constant relative volatihty,... 

The method for estimating point efficiency, outhned here, is not the only approach available for sieve plates, and more mechanistic methods are under development. For example, Prado and Fair [Ind. Eng. Chem. Re.s., 29, 1031 (1990)] have proposed a method whereby bubbling and jetting are taken into account however the method has not been vahdated tor nonaqueous systems. Chen and Chuang [Ind. Eng. Chem. Re.s., 32, 701 (1993)] have proposed a more mechanistic model for predicting point efficiency, but it needs evaluation against a commercial scale distillation data bank. One can expect more development in this area of plate efficiency prediction. 

Example 12 Estimation of Plate Efficiency For the conditions of Examples 9 and 11, estimate the point efficiency of the tray. Additional property data ... 

Ejfects of Gas and Liquid Mixing As noted previously, it is necessary in most instances to convert point efficiency E g to Murphree plate efficiency E, ,. This is true because of incomplete mixing only in small laboratoiy or pilot-plant columns, under special conditions, is the assumption E g = E, , likely to be valid. For a crossflow plate with no hquid mixing there is plug flow of hquid. For this condition of liquid flow, Lewis [Ind. Eng. Chem., 28, 399 (1936)] analyzed effects of gas mixing on efficiency. He considered three cases ... 

Types of columns and packings. A slow distillation rate is necessary to ensure that equilibrium conditions operate and also that the vapour does not become superheated so that the temperature rises above the boiling point. Efficiency is improved if the column is heat insulated (either by vacuum jacketing or by lagging) and, if necessary, heated to Just below the boiling point of the most volatile component. Efficiency of separation also improves with increase in the heat of vaporisation of the liquids concerned (because fractionation depends on heat equilibration at multiple liquid-gas boundaries). Water and alcohols are more easily purified by distillation for this reason. 

The plate/txay efficiency is the integrated effect of all the point efficiencies. 

Biddulph [90] emphasizes the importance of using point efficiencies rather than tray efficiencies or overall column efficiencies, due to the wide fluctuations that often exist. 

Sakata [180] evaluates the degree of mixing of the liquid as it flows across a tray and its effect on the tray efficiency, Figure 8-30. For plug flow the liquid flows across the tray with no mixing, while for partial or spot mixing as it flow s over the tray, an improved tray efficiency can be expected. For a completely mixed tray liquid, the point efficiency for a small element of the tray, Eog> tray efficiency, E V, are equal. 

Mols of distillate or overhead product, lb mols/hr or batch distillation, mols Mols component, i, in distillate Vaporization efficiency of steam distillation Overall column efficiency Overall tray efficiency Eqg = Murphree point efficiency, fraction Murphree plate/tray efficiency, = E ... 

Point efficiency (Murphree point efficiency). If the vapour and liquid compositions are taken at a point on the plate, equation 11.64 gives the local or point efficiency, Emv. 

The approach taken is semi-empirical. Point efficiencies are estimated making use of the two-film theory , and the Murphree efficiency estimated allowing for the degree of mixing likely to be obtained on real plates. 

Chan and Fair (1984a) have published an alternative method for point efficiencies on sieve plates which they demonstrate gives closer predictions than the AIChE method. 

The mass transfer resistances in the vapour and liquid phases are expressed in terms of the number of transfer units, No and NL. The point efficiency is related to the number of transfer units by the equation ... 

Figure 11.15. Relationship between point efficiency and number of liquid and vapour transfer units...

The Murphree efficiency EmV is only equal to the point efficiency Emv if the liquid on the plate is perfectly mixed. On a real plate this will not be so, and to estimate the plate efficiency from the point efficiency some means of estimating the degree of mixing is needed. The dimensionless Peclet number characterises the degree of mixing in a system. For a plate the Peclet number is given by ... 

The relation between the plate efficiency and point efficiency with the Peclet number as a parameter is shown in Figure 11.16a and b. The application of the AIChE method is illustrated in Example 11.12. 

Figure 11.16. Relationship between plate and point efficiency...

Chan, H. and Fair, J. R. (1984a) Ind. Eng. Chem. Proc. Des. Dev. 23, 814. Prediction of point efficiencies on sieve trays. 1. Binary systems. 

This analysis refers to a small area for vertical flow, and Emv is therefore the point or local Murphree efficiency. The relation between this point efficiency and the tray efficiency depends on the nature of the liquid mixing on the tray. If there is complete mixing of the liquid, x = xn for the liquid, and ye and y will also be constant over a horizontal plane. The tray efficiency EMv = Emv. With no mixing of the liquid, the liquid may be considered to be in plug flow. If ye = mx + b and Emv is taken as constant over tray, it may be shown" 91 that ... 

Equation 11.138 gives the point efficiency for cases where all the resistance occurs in the gas phase. In these equations ... 

Figures 1 and 2 indicate that the insecticidal efficiency of oils of paraflSnic composition against adult female California red scale is better than that of oils of naphthenic composition. The curves show that the toxicity to red scale of the lighter portions of the two oils tested is low, and that there is an increase to a peak of maximum efficiency with increase in molecular size. These findings agree in general with field experience in California in ths application of spray oils for the control of California red scale. However, the correlations shown in Figures 1 and 2 indicate that an optimum is reached, and that beyond this point efficiency against the scale decreases with further increase in molecular size.

---