Calculation of Distillation at Minimum Reflux for Ideal Mixtures

The approximate method of calculation of the minimum reflux mode for three-component mixtures at the absence of tangential pinch was suggested in the work (Stichlmair, Offers, Potthofk 1993). 

The previously enumerated methods of calculation of the minimum reflux mode for nonideal zeotropic and azeotropic mixtures have considerable defects (1) they presuppose preliminary setting of possible separation product compositions, which is a comphcated independent task for azeotropic mixtures (2) they embrace only three- and four-component mixtures or only special splits and (3) they do not take into consideration the leap of concentrations in feed cross-section. 

In practice, the enumerated calculation methods are hardly used when designing distillation units because of these defects. Calculation of the minimum reflux mode is not conducted at aU, and the working reflux number and number of plates in the sections are chosen, as a rule, arbitrarily, based on the designer s intuition and experience, which can lead to considerable overstating of separation costs. 

To overcome these defects, it was necessary to apply the conception of sharp separation and to develop the theory of distillation trajectory tear-off from the boundary elements of concentration simplex at sharp separation (Petlyuk, Vinogradova, Serafimov, 1984 Petl50ik, 1998) and also to develop the geometric theory of section trajectories joining in feed cross-section in the mode of minimum reflux that does not contain simplifications and embraces mixtures with any number of components and any splits (Petlyuk Danilov, 1998 Petlyuk Danilov, 1999b Petlyuk Danilov, 2001a Petlyuk Danilov, 2001b). 

The significance of the methods, based on the geometric distillation theory, consists in their universality, rigor, and reliability. To obtain the result, it is not necessary to set any estimation parameters and possible separation product compositions minimum reflux number for these compositions and distillation trajectory at this reflux number are defined in the process of this calculation. 

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Calculation of Distillation at Minimum Reflux for Ideal Mixtures... 

Availability of these conditions allowed Underwood (1948) to obtain general solution, connecting separation product compositions at minimum reflux with the mode parameters (e.g., with Vr and U ). Even before (Hausen, 1934,1935), distillation trajectories of the ideal mixtures in the one-section columns (Fig. 5.1a) were investigated by means of calculation, and it was shown that the part of distillation trajectory located inside the concentration triangle is rectilinear for the ideal mixture (Fig. 5.1b). Later, linearity of distillation trajectories of three-component ideal mixtures at sharp separation was rigorously proved (Levy et al, 1985). 

A distillation column is separating 100 mol/s of a 30 mol% acetone, 70 mol% methanol mixture at atmospheric pressure. The feed enters as a saturated liquid. The column has a total condenser and a partial reboiler. We desire a distillate with an acetone content of 72 mol%, and a bottoms product with 99.9 mol% methanol. A reflux ratio of 1.25 the minimum will be used. Calculate the number of ideal stages required and the optimum feed location. VLE for this system is described by the modified Raoult s law, with the NRTL equation for calculation of liquid-phase activity coefficients, and the Antoine equation for estimation of the vapor pressures. 

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