Minimum reflux mode calculation

For nonideal zeotropic and azeotropic mixtures, the solution of the task of minimum reflux mode calculation in such a statement run across the insurmountable calculating difficulties in the majority of cases. 

The development of distillation traj ectory bundles theory at finite reflux showed that the task of minimum reflux mode calculation for nonideal zeotropic and azeotropic mixtures can be solved in another statement at set composition xf and thermal state q of feeding, it is necessary to determine minimum reflux number i min for the set product compositions xd and xb of sharp separation and set permissible concentrations of admixtures in the products. 

For intermediate sections of columns with side products, with side sections, and of Petlyuk columns location of the stationary points of separatrix trajectory bundles (regions Reg jjfj) is the same as for simple columns, product compositions of which coincide with pseudoproduct compositions of these intermediate sections (possible product regions Rego and Reg of simple columns and possible pseudoproduct regions Regn and Reg of intermediate sections coincide). This extends the use of methods of minimum reflux mode calculation worked out for the simple columns to the previously mentioned complex columns and complexes. 

The analysis of the minimum reflux mode is used at the stage of sequence selection, as well as at the stage of determination of optimum reflux ratios and the quantity of column trays. The geometric theory of distillation makes it possible to develop the general methods of calculation of minimum and more reflux mode. 

Unfortunately, the method of Underwood cannot be applied to nonideal mixtures and even to ideal ones, relative volatilities of the components that depend on the temperature. Therefore, tray by tray method was used for the calculation of minimum reflux mode for such ideal mixtures (Shiras, Hanson, Gibson, 1950 Erbar Maddox, 1962 McDonough Holland, 1962 Holland, 1963 Lee, 1974 Chien, 1978 Tavana Hanson, 1979) and others. 

However, numerous questions remained unsolved in these works (1) the methods of prediction of possible product compositions for a given feed composition were absent, which does not allow to calculate minimum reflux mode (2) the methods of calculation were good only for two special splits direct and indirect ones, but these methods were not good for the intermediate splits (3) the peculiarities arising in the case of availability of a-lines, surfaces, and hypersurfaces that are characteristic of nonideal and azeotropic mixtures were not taken into consideration and (4) the sudden change of concentrations in the feed cross-section was not taken into consideration. 

The approximate calculation method of minimum reflux mode (Koehler, Aguirre, Blass, 1991) - the method of the smallest angle, which holds good for mixtures with any component numbers and for any sphts, including frequently found at azeotropic mixtures separation cases of tangential pinch, is based on the calculation of reversible distillation trajectories for the given product compositions. 

The approach to calculation of the minimum reflux mode, based on eigenvalue theory, was introduced in the work (Poellmann, Glanz, Blass, 1994). In contrast to the above-mentioned works of Doherty and his collaborators this method calculates the mode of minimum reflux not only for direct and indirect, but also for intermediate split of four-component 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. 

The algorithm of calculation of minimum reflux mode at tangential pinch has some peculiarities. At tangential pinch in top section (L/y) = =... 

Figure 5.35 is carried out according to the results of calculation of (L/y) " for equimolar mixture pentane(l)-hexane(2)-heptane(3)-octane(4) were made at separation of it with distributed component at spht 1,2 23,4 at different distribution coefficients of component 2 between products. This figure shows the location of rectifying plane S - S - and of bottom section trajectory in minimum reflux mode at several characteristic values of distribution coefficient of component 2 (1) at joining at the type of direct spht (1 2,3,4) (Fig. 5.35b X02 = 0.1, x/ = Aj+, zone of constant concentrations is located in feed cross-section in bottom...

As far as the second assumption is concerned, as was mentioned in Section 5.5, it does not influence the compositions in the stationary points. Therefore, it does not influence the first two stages of the described algorithms of calculation of minimumreflux mode. This assumption could have some influence only at the third stage of the algorithms, when curvature of separatrix trajectory bundles should be taken into consideration. Therefore, the assumption about equilibrium plates at calculation of minimum reflux mode is even more justified than at calculation of finite columns. 

Therefore, the stated algorithm of calculation of minimum reflux mode, based on the geometry of the trajectory bundles in concentration space, are potentially as one likes precise and most general, because they embrace any spUts on mixtures with any components number and any degree of nonideahty. 

Determine other possible sharp splits for this mixtures, calculate the minimum reflux mode for each. 

Therefore, the conceptual calculation of infinite column with intermediate input and/or output of heat consists in two stages (1) calculation of minimum reflux mode for adiabatic column, and (2) determination of opt 7, opt opt 7, and opt < 5, ( pinch method ). 

Columns with several inputs of feed have one or several intermediate sections, located between these inputs of feed. To calculate minimum reflux mode... 

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). 

In Chapter 5, to develop a general algorithm of calculation of minimum reflux mode for columns with one feed, we had to understand the location of reversible distillation trajectories and the structure of top and bottom section trajectory bundles. 

General Algorithm of Calculation of Minimum Reflux Mode... 

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... 

The general algorithm of calculation of the minimum reflux mode for columns of extractive distillation with two feeds requires the check-up of the conditions of trajectories joining for the cases of bottom and top control feed and requires the determination of the values of (E/E) bigger of these two... 

In particular, for the most widespread spht with one-component entrainer and one-component top product nim = 2, wzr = 1), the joining of intermediate section trajectories with the trajectories of the top and the bottom sections goes on the way it is at direct split in two-section colunms. This uses the simplest modification of the algorithm of calculation of the minimum reflux mode. 

We now discuss the general algorithm of calculation of minimum reflux mode for the column with several side withdrawals located above and below feed cross-section at sharp separation in each section and at the best separation between products. 

Minimum reflux mode is determined by the conditions of joining of trajectories of two sections adjacent to the feed cross-section. Therefore, the interconnected parameters (L/V) " and (V/L) " are determined initially for these two sections. Compositions in points x and x g are calculated preliminarily for these sections at set requirements to compositions of all the products at the conditions of sharp or quasisharp separation in each section. Minimum reflux mode is calculated in the same way as for the simple column that separates initial raw materials into products of compositions x jy and x g. Liquid and vapor flow rates for the other sections are calculated at the obtained values of (L/V) " and (L/L)f" with the help of material balance equations (strictly speaking, with the help of equations of material and thermal balance). 

We now turn to the columns with side strippings (for the colunms with side rectifiers, the calculation of minimum reflux mode is carried out the same way). 

Figure 6.15 shows the simple example of separation of a four-component mixture into four pure components in a column with side strippings. As for the columns with side withdrawals of the products, the calculation of minimum reflux mode should be started with determination of the conditions of joining of trajectories of two sections adjacent to feed cross-section. For section ri, the pseudoproduct equals the sum of top and two side products. The minimum reflux mode for the first two-section column is calculated the same way it is done for the corresponding simple column with split 1,2,3 4 (indirect split). In a more general case, when the bottom product contains more than one product component, the intermediate split will be in this column. 

In contrast to distillation of homogeneous mixtures, it is not expedient for the heteroazeotropic complex to carry out calculation of minimum reflux mode before calculation of the necessary number of trays. It is offered in Chapter 7 to carry out at the beginning calculation of the necessary number of trays at reflux with one phase and then, only if this reflux is not sufficient, to determine necessary flow rate of reflux with both phases. 

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[... 

The first group of heuristic rules can be substantiated if some assumptions about the mixture under separation are accepted. Such substantiation was made in the works (Modi Westerberg, 1992) and (Westerberg Wahnschafft, 1996) using the Underwood method for calculation of summary vapor flow in the sequence of column in the minimum reflux mode. 

For estimation of the expenditures, it was proposed in many works to use the summary vapor flow V in all columns of the sequence under consideration, calculated according to the Underwood method for the minimum reflux mode. Such approach presupposes that the mixture is a close-to-ideal one and that expensive... 

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