## O Connell Correlation

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FIG. 14-45 Overall column efficiency of 25-mm Oldershaw 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 (1982).]

given system, higher Oldershaw column efficiencies were measured under cellular foam conditions than under froth conditions. For this reason, Gerster [Chem. Eng. Progr. 59(3), 35 (1963)] warned that when cellular foam can form, scale-up from an Oldershaw column may be dangerous. The conclusions presented by Fair et al. do not extend to Oldershaw columns operating in the cellular foam regime. Cellular foam can be identified by lower pilot column capacity compared to a standard mixture that is visualized not to form cellular foam.

Heat losses are a major issue in pilot and Oldershaw columns and can lead to optimistic scale-up. Special precautions are needed to keep these at a minimum. Vacuum jackets with viewing ports are commonly used.

Uses of Oldershaw columns to less conventional systems and applications were described by Fair, Reeves, and Seibert [Topical Conference on Distillation, AIChE Spring Meeting, New Orleans, p. 27 (March 10-14, 2002)]. The applications described include scale-up in the absence of good VLE, steam stripping efficiencies, individual component efficiencies in multicomponent distillation, determining component behavior in azeotropic separation, and foam testing.

Empirical Efficiency Prediction Two empirical correlations which have been the standard of the industry for distillation tray efficiency prediction are the Drickamer and Bradford, in Fig. 14-46 [Trans. Am. Inst. Chem. Eng. 39, 319 (1943)] and a modification of it by O'Connell [Trans. Am. Inst. Chem. Eng. 42, 741 (1946)], in Fig. 14-47. The Drickamer-Bradford plot correlates efficiency as a function of liquid viscosity only, which makes it useful for petroleum cuts. O'Connell added the relative volatility to the x axis.

Lockett (Distillation Tray Fundamentals, Cambridge University Press, Cambridge, England, 1986) noted some theoretical sense in O'Connell's correlation. Higher viscosity usually implies lower diffu-sivity, and therefore greater liquid-phase resistance and lower efficiency. Higher relative volatility increases the significance of the liquid-phase resistance, thus reducing efficiency. Lockett expresses the O'Connell plot in equation form:

(The viscosity is in cP and EOC is fractional.) The volatility and viscosity are evaluated at the average arithmetic temperature between the column top and bottom temperatures. The relative volatility is between the key components.

The O'Connell correlation was based on data for bubble-cap trays. For sieve and valve trays, its predictions are likely to be slightly conservative.

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.

Des. Dev. 23, 814 (1984)]. An improved version of the AIChE model, which alleviated several of its shortcomings and updated its hydraulic and mass-transfer relationships, was produced by Chan and Fair.

The Chan and Fair correlation generally gave good predictions when tested against a wide data bank, but its authors also observed some deviations. Its authors described it as "tentative until more data become available." The Chan and Fair correlation is considered the most reliable fundamental correlation for tray efficiency, but even this correlation has been unable to rectify several theoretical and practical limitations inherited from the AIChE correlation (see Kister, Distillation Design, McGraw-Hill, New York, 1992). Recently, Garcia and Fair (Ind. Eng. Chem. Res. 39, 1818, 2000) proposed a more fundamental and accurate model that is also more complicated to apply.

The prime issue that appears to plague fundamental tray efficiency methods is their tendency to predict efficiencies of 80 to 100 percent for distillation columns larger than 1.2 m (4 ft) in diameter. In the real world, most columns run closer to 60 percent efficiency. Cai and Chen (Distillation 2003: Topical Conference Proceedings, AIChE Spring National Meeting, New Orleans, La., March 30-April 3, 2003) show that published eddy diffusivity models, which are based on small-column work, severely underestimate liquid backmixing and overestimate plug flow in commercial-scale columns, leading to optimistic efficiency predictions. Which other limitations (if any) in the theoretical methods contribute to the mismatch, and to what degree, is unknown. For this reason, the author would not recommend any currently published theoretical tray efficiency correlation for obtaining design efficiencies.

Example 12: Estimating Tray Efficiency For the column in Example 9, estimate the tray efficiency, given that at the relative volatility near the feed point is 1.3 and the viscosity is 0.25 cP.

Solution Table 14-12 presents measurements by Billet (loc. cit.) for ethyl-benzene-styrene under similar pressure with sieve and valve trays. The column diameter and tray spacing in Billet's tests were close to those in Example 9. Since both have single-pass trays, the flow path lengths are similar. The fractional hole area (14 percent in Example 9) is close to that in Table 14-12 (12.3 percent for the tested sieve trays, 14 to 15 percent for standard valve trays). So the values in Table 14-12 should be directly applicable, that is, 70 to 85 percent. So a conservative estimate would be 70 percent. The actual efficiency should be about 5 to 10 percent higher.

Alternatively, using Eq. (14-138) or Fig. 14-47, eoc = 0.492(0.25 x 1.3)-0'245 = 0.65 or 65 percent. As stated, the O'Connell correlation tends to be slightly conservative. This confirms that the 70 percent above will be a good estimate.

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