Multicomponent distillation minimum reflux Underwood

Colburn (1941) and Underwood (1948) have derived equations for estimating the minimum reflux ratio for multicomponent distillations. As the Underwood equation is more widely used, it is presented in this section. The equation can be stated in the form... 

Underwood AJV (1946) Fractional Distillation of Multicomponent Mixtures - Calculation of Minimum Reflux Ratio, 7 Inst Petrol, 32 614. 

Underwood,E.R., Fractional Distillation of Multicomponent Distillation -Calculation of Minimum Reflux Ratio, J. Inst Petrol., 32,274, 614, 1946. Van Winkle, M.C., Todd, W., Optimum Fractionation Design by Simple Graphics Methods, Chem. Eng., 78, 21,136,1971. 

Underwood, A. J. V. Fractional Distillation of Multicomponent Mixtures—Calculation of Minimum Reflux Ratio, J. Inst. Petrol. 32, 614 (1946). 

Use the Underwood equations to determine the minimum reflux ratio for multicomponent distillation. 

For multicomponent mixtures, all components distribute to some extent between distillate and bottoms at total reflux conditions. However, at minimum reflux conditions none or only a few of the nonkey components distribute. Distribution ratios for these two limiting conditions are shown in Fig. 12.14 for the debutanizer example. For total reflux conditions, results from the Fenske equation in Example 12.3 plot as a straight line for the log-log coordinates. For minimum reflux, results from the Underwood equation in Example 12.5 are shown as a dashed line. 

Underwood, A. J. V. (1946b). Fractional Distillation of Multicomponent Mixtures (Calculation of Minimum Reflux Ratio). J. Inst. Petrol, 32,614-26. Underwood, A. J. V. (1948). Fractional Distillation of Multicomponent Mixtures. Chem. Eng. Prog., 44,603-14. 

The Underwood equations (Underwood, 1948) provide a shortcut method for determining the minimum reflux ratio, ilmin, in multicomponent distillation under the following assumptions constant relative volatilities and constant molal overflows in the stripping section as well as in the enriching section. The minimum reflux ratio, i min> is obtained from a solution of the following two equations for n components ... 

Underwood equation A shortcut method used to estimate the minimum reflux ratio in a multicomponent distillation process. It was proposed by A. J. V. Underwood in 1948. 

In the calculations for multicomponent separations, it is often necessary to estimate the minimum reflux ratio of a multistage distillation column. A method developed for this purpose by Underwood [ 1 ], and described in detail by Treybal [2], requires the solution of the equation... 

The basic assumption of the Fenske-Underwood relation is that the ratio of the equilibrium constants or the relative volatility, as defined by Eq. (6.19), in a binary mixture or the two key components present in a multicomponent mixture remain constant over the temperatures encountered in the distillation column. If this can be assumed without the introduction of excessive error, the minimum number of plates at total reflux can be determined from... 

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