Three-component mixtures minimum reflux

Figure 2.8. A location ofzones of constant concentration (pinches) in columns for distillation of three-component mixtures under minimum reflux (a) R < (first class of fractionation), (b) < R <...

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). 

For nonideal three-component mixtures, the methods of calculation of minimum reflux mode was developed in the works (Glanz Stichhnair, 1997 Levy Doherty, 1986). The simplifled method that was offered before for the columns with one feed (Stichlmair, Offers, Potthof, 1993) was developed in the work (Glanz Stichlmair, 1997). 

We now examine the conditions of joining of sections trajectories at a set flow rate of entrainer (i.e., at set value of the parameter E/D) for a three-component mixture in the mode of minimum reflux. Each of two feeds can be the control one, and the intermediate section trajectory in the mode of minimum reflux in both cases should pass through the saddle point Sm because this trajectory passes through the node point not only in the mode of minimum reflux, but also at reflux bigger than minimum (point arises at the boundary element of the concentration simplex because the extractive distillation under consideration is sharp). 

We now examine the four-component mixture for = 2 (Fig. 6.9a). The conditions of joining of section trajectories at a set flow rate of the entrainer in the mode of minimum reflux in the cases of top or bottom control feed do not differ from the conditions for three-component mixtures discussed above. In the case of bottom... 

It is expedient to determine the value of optimal distribution coefficient D /B at the stage of calculation of minimum reflux mode (see Section 6.8). In particular, at separation of a three-component mixture, the optimal value of coefficient /B[... 

In the rectification tower, four equations are available from material balances (overall and component material balances) for the separation of the four components. If the feed or input amount and its composition are known, then one has two unknown streams H (head product) and B (bottom product) and three unknown concentrations in each stream. Thus, generally there are eight unknown values for a four component mixture. Only two of these unknown values are to be determined. Thus the material balance of the rectification tower can be evaluated to obtain the top and bottom product rates. The vapor stream in the stripping section can be determined as the vapor stream ascending from the tower bottom. This stream can be taken as constant throughout the stripping section of the tower. This vapor stream plus the fraction of feed that is vapor will yield both the head product stream as well as the reflux stream that will be returned to the tower. The reflux ratio can be determined based on the minimum reflux. There is a method for the evaluation of the minimum reflux. This method will be shown in a later section. 

Numerous works (Levy, Van Dongen, Doherty, 1985 Levy Doherty, 1986 Julka Doherty, 1990) in which distillation trajectory bundles of three-and four-component mixtures for two sections of distillation column were used at hxed product compositions and at different values of reflux (vapor) number, are of great importance. They defined the conditions of two section trajectories joining in the feed cross-sections of the column in the mode of minimum reflux, and they developed the methods of this mode calculation for some splits. 

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. 

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). 

This develops the general algorithm of calculation of minimum reflux mode for the columns with two feed inputs at distillation of nonideal zeotropic and azeotropic mixtures with any number of components. The same way as for the columns with one feed, the coordinates of stationary points of three-section trajectory bundles are defined at the beginning at different values of the parameter (L/V)r. Besides that, for the intermediate section proper values of the system of distillation differential equations are determined for both stationary points from the values of phase equihbrium coefficients. From these proper values, one finds which of the stationary points is the saddle one Sm, and states the direction of proper vectors for the saddle point. The directions of the proper vectors obtain linear equations describing linearized boundary elements of the working trajectory bundle of the intermediate section. We note that, for sharp separation in the top and bottom sections, there is no necessity to determine the proper vectors of stationary points in order to obtain linear equations describing boundary elements of their trajectory bundles, because to obtain these linear equations it is sufficient to have... 

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