Distillation Murphree

Most distillation systems ia commercial columns have Murphree plate efficiencies of 70% or higher. Lower efficiencies are found under system conditions of a high slope of the equiHbrium curve (Fig. lb), of high Hquid viscosity, and of large molecules having characteristically low diffusion coefficients. FiaaHy, most experimental efficiencies have been for biaary systems where by definition the efficiency of one component is equal to that of the other component. For multicomponent systems it is possible for each component to have a different efficiency. Practice has been to use a pseudo-biaary approach involving the two key components. However, a theory for multicomponent efficiency prediction has been developed (66,67) and is amenable to computational analysis. 

Murphree [85] developed point and overall distillation tray efficiencies, which are examined in detail in Reference 2. The expressions are [59] ... 

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 ... 

A mixture of alcohol and water containing 0.45 mole fraction of alcohol is to be continuously distilled in a column to give a top product of 0.825 mole fraction alcohol and a liquor at the bottom containing 0.05 mole fraction alcohol. How many theoretical plates are required if the reflux ratio used is 3 Indicate on a diagram what is meant by the Murphree plate efficiency. 

FIG. 14-40 Point and Murphree efficiencies, (a) Point. (b) Murphree. (From H. Z. Kister, Distillation Design, copyright 1992 by McGraw-HiU reprinted by permission.)... 

The point and Murphree efficiency definitions above are expressed in terms of vapor concentrations. Analogous definitions can be made in terms of liquid concentrations. Further discussion is elsewhere (Lockett, Distillation Tray Fundamentals, Cambridge University, Press, Cambridge, England, 1986). 

Equation (3.48) is known as point efficiency, having been given in a number of publications, one notable one being Distillation Principles and Design Procedures [7]. Equation (3.48) is the two-film method of predicting the ETF tray one-point efficiency, and refers to a small element of a tray that must be converted to a Murphree efficiency (Eq. 3.47) [8],... 

The fact that component efficiencies in multicomponent systems are unbounded means that the arithmetic average of the component Murphree efficiencies is useless as a measure of the performance of a multicomponent distillation process. Taylor, Baur, and Krishna [AIChE J., 50, 3134 (2004)] proposed the following efficiency for multicomponent systems ... 

FIG. 13-58 Component Murphree efficiencies and TBK average efficiency [defined by Eq. (1 59)] for nonideal distillation. 

Murphree-stage efficiency Time for distillation Parameter in Underwood equations... 

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. 

Entrainment Corrections. Above about 80% of flood, the recirculation of liquid as entrainment between trays undermines the countercurrent action of the tray column, and efficiency therefore suffers. This is a particular problem in vacuum distillation where it may be optimum to allow a certain amount of liquid entrainment in initial design. Figure 13.41 shows an approximate method for entrainment correction to column efficiency or Murphree efficiency. The abscissa scale is the same parameter used for flooding prediction (Figure 13.32(b)). The ordinate value is used to correct from a dry to a wet efficiency (with entrainment) ... 

These interaction phenomena have been discussed above in the context of ternary gas diffusion but are typical of the general multicomponent case. The practical implications of these interaction phenomena include such interesting possibilities as negative Murphree point efficiencies in multicomponent distillation as we shall see later (Chapter 13). 

The Murphree vapor-phase tray efficiency is defined by (refer to Fig. 12.1, which pictures vapor-liquid contacting on a distillation tray)... 

Figure 14.23. Murphree efficiencies for experimental extractive distillation column.

Vogelpohl, A., Murphree Efficiencies in Multicomponent Systems, The Institution of Chemical Engineers Symposium Series, No. 56, Distillation 1979, 2.1/25 -2.1/31 (1979). 

B Bottoms stream designation or molar flow rate D Distillate or overhead designation or molar flow rate E Murphree tray efficiency... 

Investigations of Hiibner and Schliinder [103a] show that the Murphree efficiency can be calculated sufficiently exactly with the turbulent diffusion model if the material transfer and the intensity of turbulent mixing in the vapour and liquid phases are known. The efficiencies in the countercurrent distillation of ternary mixtures are discussed by Vogelpohl and Ceretto [103b]. 

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