Minimum reflux simple columns

Try this for yourself using DODS-SiCo and the TT design option, design minimum reflux simple columns, trying various a values, and product qrecifications. 

Porter and Momoh have suggested an approximate but simple method of calculating the total vapor rate for a sequence of simple columns. Start by rewriting Eq. (5.3) with the reflux ratio R defined as a proportion relative to the minimum reflux ratio iimin (typically R/ min = 1-D- Defining Rp to be the ratio Eq. (5.3) becomes... 

In Chapter 9, it was shown how the Underwood Equations can be used to calculate the minimum reflux ratio. A simple mass balance around the top of the column for constant molar overflow, as shown in Figure 11.3, at minimum reflux gives ... 

Equations, determine sequences of simple and complex columns that minimize the overall vapor load. The recoveries will be assumed to be 100%. Assume the actual to minimum reflux ratio to be 1.1 and all the columns, with the exception of thermal coupling and prefractionator links, are fed with saturated liquid. Neglect pressure drop through columns. Relative volatilities can be calculated from the Peng-Robinson Equation of State with interaction parameters set to zero. Pressures are allowed to vary through the sequence with relative volatilities recalculated on the basis of the feed composition for each column. Pressures of each column are allowed to vary to a minimum such that the bubble point of the overhead product is 10°C above the cooling water return temperature of 35°C (i.e. 45°C) or a minimum of atmospheric pressure. 

To redistribute the stages in the remaining sections, a shortcut simulation is used to find out the required number of trays, the feed tray location and the minimum reflux ratio for each column in the sequence. To make use of the existing column with the same number of trays (24 trays) iterations are required to adjust the sum of the rectifying sections in each column equal to 24 (number of trays in the main column). Finally, the sequence of the simple columns is merged into a complex column. The main column is not changed, but the side strippers and pump arounds need to be relocated or adjusted. 

It is also worth mentioning that in the case of simple columns, there are in fact three cases where minimum reflux can occur. Recall that minimum reflux is obtained where one composition profile pinches, or terminates, on the other. The three cases are therefore as follows ... 

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 14 Feasible sharp split simple column designs at (a) minimum reflux and (b) above minimum reflux. 

Scenario 2 is able to achieve minimum reflux value of 1.37, considerably lower than both the simple column with a minimum reflux of 2.02 or Scenario 1 with a minimum reflux of 1.83. This constitutes a considerable energy saving. It should... 

Since the CSs above and below the feed stream merely reduce to a pseudo simple column, it follows that we should be able to find the minimum reflux for it, just as we would do for a conventional simple column. The reflux in the CS below the feed (a stripping CS) can, exactly like simple columns (refer to Section 5.3.2), also be related to the reflux in a CS above the feed through ... 

Chapter 5, we can find the minimum reflux for this pseudo simple column uang the parameters in Table 6.1. For the simplified sharp split, constant relative volatility problem this means that the TTs of both CSs have to just touch one another, effectively an algebraic colinearity condition. This is shown in figure 6.34 for arbitrary product specifications using the TT technique. 

We have now demonstrated quick and relatively simple algebraic method to design thermally coupled columns at minimum reflux conditions. All relative... 

In the following sections, simple methods for choosing column pressure, for calculating the minimum reflux and the minimum number of stages, and for sizing columns will be introduced. 

Figure 6.14 shows trajectories of the intermediate section for separation 1 1, 2 3 at different modes. Pseudoproduct points ( > — Dj+D) is located at side 1-2, and joining of the intermediate and bottom sections in the mode of minimum reflux goes on in the same way as for the simple column at indirect split. Trajectory of the intermediate section r tears off from side 1-2 in point Sn, and point of side product xd can coincide with point Sn (Fig. 6.14a) or lie at segment 1 - Sri (Fig. 6.14b). The first of these two modes is optimal because the best separation between top and side products (the mode of the best separation) is achieved at this mode. Zones of constant concentrations in the top and intermediate sections arise in point Sri = AC2- Therefore, in the mode of minimum reflux in the intermediate section, there are two zones of constant concentrations. At the reflux bigger than minimum, point 5 1 moves to vertex 2 and at i = oo this point reaches it (i.e., at i = 00, pure component 2 can be obtained in the infinite column as a side product). Therefore, for the colunuis with side withdrawals of the products, the mode of the best separation under minimum reflux corresponds to joining of sections in points 5 1 and of the trajectory bundle of the intermediate section (at sharp separation) or in its vicinity (at quasisharp separation). The trajectory of the column with a side product at minimum reflux at best separation may be described as follows ...

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). 

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. 

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. 

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