Minimum reflux distributed feed columns

Try this for yourself Reproduce Figure 6.10 using DODS-DiFe and the given parameters. Try and find other minimum reflux designs for a distributed feed column by changing parameters such as a, Rai f< < product compositions. 

The reader should be aware that the minimum reflux scenarios presented here are just one of three possible ways the minimum reflux limit can be obtained in distributed feed columns. The designs shown thus far all depicted minimum reflux when the vertex of the internal CS adjacent to the topmost rectifying section lies exactly on its profile, that is, a pinch occurs on the topmost rectifying CS. It is perfectly valid for the minimum reflux condition to be determined by the bottommost stripping profile, or indeed where the TTs of the internal CSs do not overlap one another. The latter case is shown in Figure 6.12 where the column reflux has been reduced and TTs cascade around one another, thereby limiting any further column reflux reduction. The general requirement for minimum reflux is however the same as for simple columns any reflux value below the minimum reflux value will lead to a discontinuous path of profiles, and minimum reflux is therefore the last reflux where a continuous path is still maintained. 

FIGURE 6.13 A distributed feed column at minimum column reflux for acetone/ benzene/ chloroform system with a feed distribution of [0.5,0.5]. Solid profiles indicate CPM profiles while circles indicate Aspen generated compositions. 

FIGURE 6.15 Distributed feed column at (a) minimum reflux and (b) below minimum reflux. 

It is blatant that both scenario 1 and 2 are feasible as both the TTs from the internal CSs overlap the product producing profiles. The vertices of both these TTs are located some way from the profiles therefore, a reduction in the reflux for both scenarios will have energetic advantages and still be feasible. However, it would seem that the second scenario may be more beneficial than the first, because its TFs vertex is located fiirth away from the profiles. We can proceed to determine what the minimum reflux conditions of the distributed feed columns are. We thus have to find the reflux values that will result in either of TTs vertices lying precisely on a profile. This is shown in Figure 6.17a and b for Scenario 1 and 2, respectively. 

Underwood s method (36). This method solves an equation which relates feed composition, thermal condition of the feed, and relative volatility at the average temperature of the column for a factor 6 which lies numerically between the relative volatilities of the keys. This factor is substituted in a second equation which relates minimum reflux to relative volatility and distillate composition. The method assumes constant relative volatility at the mean column temperature and constant molar overflow (Sec. 2.2.2). This method gives reasonable engineering accuracy for systems approaching ideality (28). The Underwood method has traditionally been the most popular for minimum reflux determination, When no distributed key components are present, the method is... 

For the case of minimum reflux, the distinction between distributed and undistributed components is clearer, since heavy nonkey components are generally absent from the distillate, and light nonkey components are not present in the bottoms. The concentrations of these species can go to zero because of an infinite number of plates in the column and conditions that lead to a progressive reduction in concentration for each plate beyond the feed plate. 

For the conditions of Problem 12.7, compute the minimum external reflux rate and the distribution of the nonkey components at minimum reflux by the Underwood equation if the feed is a bubble-point liquid at column pressure. 

Calculate the product distribution, the minimum theoretical stages, the minimum reflux, and the theoretical stages at l.S times minimum LID and locate the feed stage. The column is to have a partial condenser and a partial reboiler. 

In the mode of minimum reflux, i min at sharp distillation without distributed components traj ectory of the top (bottom) section goes from the product point xd xb) to the trajectory tear-off point Sj Sj) into the boundary element, containing one additional component referring to product components, that is the closest one by phase equilibrium coefficient, then it goes from point S (Sj) to the point of trajectory tear-off S (S ) inside concentration simplex, then it goes from point to point X/ I (xf) in the feed cross-section of the column. Along with that, material balance should be valid in the feed cross-section. 

We have a considerable limitation of sharp extractive distillation process in the column with two feeds the process is feasible if the top product components number is equal to one or two. This Umitation arises because, in the boundary element formed by the components of the top product and the entrainer, there is only one point, namely, point iV+, that belongs to the trajectory bundle of the intermediate section. If Eq. (6.11) is valid, then the joining of the trajectories of the intermediate and top sections takes place as at direct split in two-section columns in the mode of minimum reflux. If Eq. (6.12) is valid then joining goes on as at split with one distributed component. 

Thermodynamic losses caused by mixing of flows of different composition in the feed cross-section of the colunm (A2). These losses always arise at separation of multicomponent mixture at any split without distributed components. The losses are absent only at the preferable split when the compositions of the liquid and vapor parts of feeding coincide (in the mode of minimum reflux) or are close (at the reflux bigger than minimum) to the composition of the liquid flow from the top section of the column and to the composition of vapor flow from the bottom section of the column, respectively. 

Joining condition at minimum reflux for split with distributed component feed cross-section composition point for one column s section must belong to the sep-aratrix min-r ux region and the other to the separatrix sharp distillation region for given product points and reflux ratio and satisfy the material balance in feed cross-section x/ i e andxf e Reg or Xf.i and... 

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