Chan and Fair method

Plug flow tends to maximize the ratio of Murphree to point efficiency. As stated earlier, point efficiencies predicted by the Chan and Fair method tend to be high (12). Combining the two, one would expect this correlation to give optimistic efficiency estimates for large-diameter columns. 

Chan and Fair Method. Chan and Fair (1984a) retained the AIChE (1985) procedure for calculation of the but developed an alternative correlation for the number of transfer units in the vapor phase Nj/ as follows ... 

AIChE method Chan and Fair method Zuiderweg method... 

The AIChE and Chan and Fair methods have given quite different estimates of the point efficiency for this system Zuiderweg s method falls in between. In fact, this example is based on experiments carried out by Plaka et al. (1989) and the column dimensions are for their column. The point efficiency determined by Plaka et al. in a number of experiments is around 75-80%. In this case we see that the method of Chan and Fair has given an acceptable estimate of the experimentally determined value, whereas the AIChE method severely underpredicts the point efficiency. The latter result is in accord with the findings of Plaka et al. ... 

Use the Chan and Fair method to estimate the numbers of transfer units and, hence,... 

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. 

Theoretical Efficiency Prediction Theoretical tray efficiency prediction is based on the two-film theory and the sequence of steps in Fig. 14-41. Almost all methods evolved from the AIChE model (AIChE Research Committee, Bubble Tray Design Manual, New York, 1958). This model was developed over 5 years in the late 1950s in three universities. Since then, several aspects of the AIChE model have been criticized, corrected, and modified. Reviews are given by Lockett (Distillation Tray Fundamentals, Cambridge University Press, Cambridge, England, 1986) and Chan and Fair [Ind. Eng. Chem. Proc. 

The AIChE Bubble Tray Design Manual (AIChE, 1958 Gerster et al., 1958) presented the first comprehensive estimation procedure for numbers of transfer units. For many years this remained the only such procedure available in the open literature the work of organizations like Fractionation Research Incorporated (FRI) was available only to member companies. However, during the last 15 years or so there has been a revival of distillation research and other comprehensive estimation procedures have been published (e.g., Zuiderweg, 1982 Chan and Fair, 1984a). We summarize these methods below. The text by Lockett (1986) provides an excellent summary of what is available in the open literature on distillation tray design for those interested in further study. 

Chan and Fair (1984b) carried out a case study involving a six component de-ethanizer. The full matrix method presented above was compared to pseudobinary methods of estimating the component efficiencies. They found insignificant differences between the matrix and pseudobinary efficiency methods. However, considering the nature of their system, this should not come as a great surprise. 

The results of the many investigations to indeed confirm that individual component efficiencies are likely to be different. It is less clear that the matrix methods provide uniformly better predictions of component efficiencies than simpler effective diffusivity type approaches as shown in, for example, the data of Chan and Fair (1984b) and Ognisty and Sakata (1987). 

Based on these ideas, develop multicomponent forms of the AIChE, Chan and Fair, and Zuiderweg methods of computing numbers of transfer units. 

A better estimate of overall plate efficiency can be made with the Lockett and Leggett version of the empirical O Connell correlation, as shown in Figure 14.3. In this plot, the overall plate efficiency depends on the product of the average liquid-phase viscosity in cP and a dimensionless volatility factor. For distillation, the volatility factor is the average relative volatility between the light and heavy key components, aLK,HK- For absorbers and strippers, the volatility factor is 10 times the average AT-value of the key component. If an even better estimate of the plate efficiency is desired, and in particular one that depends on plate location and component, a semitheoretical method developed by Chan and Fair (1984a), based on the... 

Example 13.17 shows a comparison between efficiencies calculated by the O Connell and Chan/Fair methods. 

Tray Efficiency for the Separation of Acetone and Benzene, by (a) O Connell Method (b) Chan/Fair Method. 

With a more mechanistic model for predicting tray point efficiency, Garcia and Fair showed a better fit to a large database than did the older Chan-Fair model. A parity plot for the Garcia-Fair work is given in Figure 12.64. The newer method is more complex, however, and requires a fairly elaborate computer program. 

It is worthy of note that in addition to triolborates and trifluoroborates [279], boronic esters and the triphenylboroxine have also been used in place of arylboronic acids. The performances of the systems, first described by Chan and Lam, were however not overwhelming and the copper was used in stoichiometric amount [285]. A catalytic version was recently introduced by Yu et al. who presented a very simple method allowing in absence of the additive, the base and the ligand, the coupling of several arylboroxines with a large panel of N-nucleophiles, in fair to excellent yields (Scheme 29) [286]. 

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. 

Problem 12.6 deals with the dimensioning of a large ethylbenzene/styrene tray-type fractionator. The overall column efficiency for the sieve trays is to be estimated, based on the same conditions given for Problem 12.6. Two methods will be used (a) the O Connell (Figure 12.60) approximate method and (b) the Chan/Fair more basic method [Equation (12.84)], corrected for entrainment and liquid crossflow effects. 

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