Colburn relationship

Colburn relationship found that the optimum number of trays varies from 2 to 3 times the number at total reflux. Gilliland [Ind. Eng. Chem, . 32, 1220 (1940)] from the establishment of an empirical relationship between reflux ratio and theoretical trays based on a study of existing columns indicated that... 

Overall Column Efficiency Calculated values of E, , must be corrected for entrainment, if any, by the Colburn equation [Eq. (14-101)]. The resiJting corrected efficiency is then converted to column efficiency by the relationship of Lewis [Ind. Eng. Chem., 28, 399 (1936)] ... 

The theoretical and mathematical treatment of azeotropic data has been covered by several authors, including Benedict and coworkers (1), and Scheibel and Friedland (50). Licht and Denzler (37) have discussed the thermodynamic conditions necessary and sufficient for azeotropism. Colburn (8) has reviewed the calculations associated with azeotropic and extractive distillation, and Hodgson (24) stresses the relationship between azeotropic distillation, extractive distillation, and liquid-liquid extraction. 

A.P. Colburn 8c R.L. Pigford, General Theory of Diffusional Operations , includes sections on equilibrium relationships, rate of mass transfer, countercurrent apparatus, and... 

Earlier it,was noted that a definite relationship exists between the heat transfer coefficient and the mass transfer coefficient. Chilton and Colburn [10] developed Equation 3.31, which will be restated here ... 

Colburn WA (1981) Simultaneous pharmacokinetic and pharmacodynamic modeling. J Pharmacokin Biopharm 9 367 Dingemanse J, Van Bree JB, Danhof M (1989) Pharmacokinetic modeling of anticonvulsant reponse of Phenobarbital in rats. J Pharmacol Exp Ther 249 601-608 Hoffman A, Goldberg A (1994) The relationship between receptor-effector unit heterogeneity and the shape of the concentration-effect profile pharmacodynamic implications. J Pharmacokinet Biopharm 22 449-468... 

Another concept sometimes used as a basis for comparison and correlation of mass transfer data in columns is the Chilton-Colburn analogy (35). This semi-empirical relationship was developed for correlating mass- and heat-transfer data in pipes and is based on the turbulent boundary layer model... 

If both tubes are heated, the function is the sum of the above two functions divided by 1 4- Dp/Da [Stephan, Chem. Ing. Tech., 34, 207 (1962)]. The Colburn form of relationship may be employed for the individual walls of the annulus by using the individual friction factor for each wall [see Knudsen, Am. Inst. Chem. Eng. J., 8,566 (1962)] ... 

Most mass transfer correlations in the literature are reported in terms of the Colburn J factor as a function of the Reynolds number. The relationship between and the numbers we have been discussing is... 

Mass-Transfer Units The mass-transfer unit concept follows directly from mass-transfer coefficients. The choice of one or the other as a basis for analyzing a given application often is one of preference. Colburn [Ind. Eng. Chem., 33(4), pp. 450-467 (1941)] provides an early review of the relationship between the height of a transfer unit and volumetric mass-transfer coefficients (k a). From a differential material balance and application of the flux equations, the required contacting height of an extraction column is related to the height of a transfer unit and the number of transfer units... 

Below, we present some model relationships between observed concentration and effect size, as examples from a considerable volume of literature. The reader is referred to key texts for comprehensive coverage of this topic (e.g. Smolen, 1971 Gibaldi and Perrier, 1982, Dayneka et al., 1993 Levy, 1993 Lesko and Williams, 1994 Colburn, 1995 Derendorf and Hochhaus, 1995 Gabrielsson and Weiner, 1997 Sharma and Jusko, 1997). 

Each of the modified Re3molds analogy relations (5.237) and (5.238) includes an additional Sc and Pr dependency, respectively. These relationships are often referred to as the Chilton-Colburn analogies [20, 60] (p 364). 

One of the most extensively ured and successful analogies—the j factor of Chilton and Colburn 10—was proposed as an empirical relationship based on available expurimantal data al that time ... 

The equation is simple to use but requires a computation of the exit liquid composition and y at both ends of the column. This can be avoided by use of an equation developed by Colburn which incorporates the equilibrium relationship y mx and the material balance expression Li i - x) = Gu(y - y,) to eliminate the need for y. This equation is for absorption ... 

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