Distillation underwood multicomponent

Underwood, A. J. V., Fractional Distillation of Multicomponent Mixtures, Chemical Engineering Progress, 44, 603 (1948). 

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. (1948) Fractional distillation of multicomponent mixtures. Chemical Engineering and Processing, 44, 603-614. 

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. 

Figure 8-47. Short-cut solution of Fenske-Underwood-Gilliland theoretical trays for multicomponent distillation. Used by permission, Frank, O., Chem. Eng. Mar. 14 (1977), p. 109.

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 ... 

In the years from 1940 through the 1960s, several notable shortcut fractionation methods were published. Of these, one method that included several of these earlier methods has stood out and is today more accepted. Fenske, Underwood, and Gilliland [9-12] are the core of this proposed method. Yet one more entry is added, the Hengstebeck [13] proposed method to apply multicomponent distillation. As these earlier methods pointed out only two component separations (called binary systems), the Hengstebeck added contribution is most important for multicomponent applications. 

For single separation duty, Diwekar et al. (1989) considered the multiperiod optimisation problem and for each individual mixture selected the column size (number of plates) and the optimal amounts of each fraction by maximising a profit function, with a predefined conventional reflux policy. For multicomponent mixtures, both single and multiple product options were considered. The authors used a simple model with the assumptions of equimolal overflow, constant relative volatility and negligible column holdup, then applied an extended shortcut method commonly used for continuous distillation and based on the assumption that the batch distillation column can be considered as a continuous column with changing feed (see Type II model in Chapter 4). In other words, the bottom product of one time step forms the feed of the next time step. The pseudo-continuous distillation model thus obtained was then solved using a modified Fenske-Underwood-Gilliland method (see Type II model in Chapter 4) with no plate-to-plate calculations. The... 

Data for the two examples are given in Table I. The i , values, as determined by Eq. (2), appear in Table II. This table shows that the values of R , calculated by Eq. (2) are closest to those of the Underwood method, which is more often the approximation preferred in preliminary multicomponent distillation design. Although it yields slightly lower values, Eq, (2) offers the advantage of being simple and taking less computational time. Further, it does not involve trial and error. 

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. 

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

Shortcut methods for handling multicomponent batch distillation have been developed for the two cases of constant reflux and constant distillate composition (Diwekar and Mandhaven, 1991 Sundaram and Evans, 1993). Both methods avoid tedious stage-by-stage calculations of vapor and liquid compositions by employing the Fenske-Underwood-Gilliland (FUG) shortcut procedure for continuous distillation, described in Section 6.8, at succesive time steps. In essence, they treat batch distillation as a sequence of continuous, steady-state rectifications. As in the FUG method, no estimations of compositions or temperatures are made for intermediate stages. 

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