Multicomponent distillation minimum reflux ratio

Simple analytical methods are available for determining minimum stages and minimum reflux ratio. Although developed for binary mixtures, they can often be applied to multicomponent mixtures if the two key components are used. These are the components between which the specification separation must be made frequendy the heavy key is the component with a maximum allowable composition in the distillate and the light key is the component with a maximum allowable specification in the bottoms. On this basis, minimum stages may be calculated by means of the Fenske relationship (34) ... 

Unequal Molal Flow, 63 Ponchon-Savarit Method, 63 Example 8-21 Ponchon Unequal Molal Overflow, 65 Multicomponent Distillation, 68 Minimum Reflux Ratio — Infinite Plates, 68 Example 8-22 Multicomponent Distillation by Yaw s Method, 70 Algebraic Plate-to-Plate Method,... 

The two most frequently used empirical methods for estimating the stage requirements for multicomponent distillations are the correlations published by Gilliland (1940) and by Erbar and Maddox (1961). These relate the number of ideal stages required for a given separation, at a given reflux ratio, to the number at total reflux (minimum possible) and the minimum reflux ratio (infinite number of stages). 

Colburn (1941) and Underwood (1948) have derived equations for estimating the minimum reflux ratio for multicomponent distillations. These equations are discussed in Volume 2, Chapter 11. As the Underwood equation is more widely used it is presented in this section. The equation can be stated in the form ... 

Colburn, A. P. (1941) Trans. Am. Inst. Chem. Eng. 37, 805. The calculation of minimum reflux ratio in the distillation of multicomponent mixtures. 

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. 

While Eq, (2) has been found satisfactory to employ for many cases of multicomponent distillation, use this equation with caution, as it may produce high values of the minimum reflux ratio when the composition of the light key in the distillate is not predominant. 

Z. Colburn, A. P., The Calculation of Minimum Reflux Ratio in the Distillation of Multicomponent. Mixtures, Tra7is. AIChE, Vol. 37, p. 805, 1941. 

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

MINIMUM REFLUX RATIO. The minimum reflux ratio for a multicomponent distillation has the same significance as for binary distillation at this reflux ratio, the desired separation is just barely possible, but an infinite number of plates is required. The minimum reflux ratio is a guide in choosing a reasonable reflux ratio for an operating column and in estimating the number of plates needed for a given separation at certain values of the reflux ratio. 

NUMBER OF IDEAL PLATES AT OPERATING REFLUX. Although the precise calculation of the number of plates in multicomponent distillation is best accomplished by computer, a simple empirical method due to Gilliland is much used for preliminary estimates. The correlation requires knowledge only of the minimum number of plates at total reflux and the minimum reflux ratio. The correlation is given in Fig. 19,5 and is self-explanatory. An alternate method devised by Erbar and Maddox is especially useful when the feed temperature is between the bubble point and dew point. 

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

An exact method for calculating the minimum number of separating stages has been developed by Harbert [182], who refers the volatilities of the individual components to the vapour pressure of the most volatile constituent. An excellent article bj Bruijn [183] deals with the theory of multicomponent distillation at a minimum reflux ratio. The thermodynamic foundation of multicomponent rectifications has been treated systematically by Wagner in a series of publications [183a]. Starting from the physical properties of mixtures the various steps in distillation practice are described in an exemplary manner. The description is supplemented by a great number of references. 

In multicomponent distillation, it may be necessary to estimate the minimum reflux ratio using classical methods [1,2]. This estimate usually requires the solution of a polynomial in of degree n, such as the equation... 

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. 

Sugie, H., Benjamin, C. Y. L. (1970). On the Determination of Minimum Reflux Ratio for a Multicomponent Distillation Column with Any Number of Side-Cut Streams. Chem. Eng. Set., 25,1837-46. 

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... 

Example 8-25 Scheibel-Montross Minimum Reflux, 80 Minimum Number of Trays Total Reflux — Constant Volatility, 80 Chou and Yaws Method, 81 Example 8-26 Distillation with Two Sidestream Feeds, 82 Theoretical Trays at Operating Reflux, 83 Example 8-27 Operating Reflux Ratio, 84 Estimating Multicomponent Recoveries,... 

If one or more unit operations have been given infeasible specifications, then the flowsheet will never converge. This problem also occurs with multicomponent distillation columns, particularly when purity specifications or flow rate specifications are used, or when nonadjacent key components are chosen. A quick manual mass balance around the column can usually determine whether the specifications are feasible. Remember that all the components in the feed must exit the column somewhere. The use of recovery specifications is usually more robust, but care is still needed to make sure that the reflux ratio and number of trays are greater than the minimum required. A similar problem is encountered in recycle loops if a component accumulates because of the separation specifications that have been set. Adding a purge stream usually solves this problem. 

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. 

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