Multicomponent distillation Fenske equation

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. 

Minimum stages for total reflux. Just as in binary distillation, the minimum number of theoretical stages or steps, can be determined for multicomponent distillation for total reflux. The Fenske equation (11.4-23) also applies to any two components in a multicomponent system. When applied to the heavy key H and the light key L, it... 

Truly multicomponent solutions based on continuous distillation shortcut methods have been proposed for batch distillation. The Fenske, Underwood, and Gilliland equations or correlations are commonly used in conjunction with each other to solve continuous distillation problems as described in Section 12.3. Diwekar and Madhavan (1991) describe how these techniques may be modified for the design of batch distillation columns for variable and constant reflux cases. 

Owing to the availability of high-speed computers, short cut methods for designing distillation processes (e.g. McCabe-Thiele and Ponchon-Savarit for binary systems or the equations of Fenske, Underwood and Gilliland for multicomponent mixtures, see Gmehling and Brehm, 1996 and Satder, 2001 for details) are no longer required. 

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