Constant relative volatility systems

It is important to point out that, although only two differential equations have to be solved for the ternary case (Equation 2.2), phase equilibrium data for all three components need to be known since the Xi relationship, for instance, is a function 

FK URE 23 A residue curve map for (a) a constant relative volali Iky system widi a = [5, 1 ] and (b) die nonideal acetone/benzene/chlorofonn system using the NRTL model atP= atm. 

It is also customary to show the positive direction of movement of the residue curves on the maps [3]. This direction corresponds to the way the tr ectory would be generated during batch boiling, and is therefore related to forward integration towards positive infinity. Thus, the profiles move from the low-boiling component to the high-boiling component, as indicated. 

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Furthermore, other residue curves can be produced in the same manner by simply altering the initial charge composition, and integrating Equation 2.8. The entire MET can then be populated with residue curves. However, it is logical to only show a few curves, as is done in Figure 2.5a. Such a collection of residue curves is known as a residue curve map. Figure 2.5a shows a three component RCM for a constant relative volatility system, as indicated... 

Geometrically, Equation 2.24 represents a straight line in Xi X2 space and is only a function of the volatilities of the system. An example of the discontinuity for a constant relative volatility system is shown in Figure 2.17a through a dashed line on the outside of the MET. 

FIGURE 3 A CPM for a constant relative volatility system with a = [5, 1, 2] using arbitrarily specified conditions Xa = [0.2,0.3] and = 5. The MBT is shown as solid black lines. The discontinuity is indicated by the dashed line. 

Figure 3.21 shows a very different behavior in the pinch point loci from those given for the constant relative volatility system. However, the same properties still exist at infinite reflux the nodes are at their RCM positions, and at R = 1 the only... 

To further demonstrate the insight that may be gained from CPMs, sharp splits present an interesting mathematical study because they are cases where at least one element of is zero. It should be clear that even though an element of Xa has a value of zero, it does not necessarily mean that the component is not present it merely implies that its net flow is zero, that is, equal molar flowrates of that component in the vapor and liquid streams. This restriction forces a pinch point (mathematically) to lie on the same axis where X is fixed. In other words, when X is restricted to lie on a single axis (or extended axis) of the MET, at least one pinch point is restricted to lie on this axis too. This gives us a unique opportunity to manipulate profiles in a desired direction on that specific axis where one entry of Xa is zero. This is easily seen in a constant relative volatility system, where the TT lies on the Xi =0 axis, in Figure 3.28a. 

As an example, consider the plot shown in Figure 6.5 for a constant relative volatility system. Here, we have chosen to spht the feed into two equal parts, thereby creating only one internal CS. The total feed stream has a composition p= [0.3,0.4] and flowrate 1 mol/s. The product specifications are x = [0.990, 0.001] and Xg= [0.001, 0.573], and the reflux ratio in the uppermost CS is / ai =4. 

Figure 7.4 shows that the Amplified DPE with the difference vector behaves in much the same way as the original DPE where profiles have been altered and nodes have been shifted even outside the positive composition space. As before, with constant relative volatility systems, we are able to connect the (shifted) nodes with straight lines to form a transformed triangle (TT). 

Specify Constant Relative Volatilities. In the DiFe package, only constant relative volatility systems are allowed. Here, the user should specify volatilities in the form [L, H, I] for the Low, High, and Intermediate boiling components, respectively. 

We discussed using the Fenske equation to find the minimum number of trays in Chapter 2 for constant relative volatility systems. We found the minimum number of trays more rigorously in Chapter 3 by using the simulator to find the number of stages where the... 

G3. Write a computer, spreadsheet, or calculator program to find the number of equilibrium stages and the optimum feed plate location for a binary distillation with a constant relative volatility. System will have CMO, saturated liquid reflux, total condenser, and a partial reboiler. The given variables will be F, Zp, q Xg, Xp, a, and Lq/D. Test your program by solving the following... 

Figure 8-7. Distillation curves at total reflux for constant relative volatility system A = benzene, B = toluene, C = cumene = 2.4, a gg =1.0, a eg = 0.21 stages are shown as x.

Alternation of these two equations results in values for x, Xg, and x on every stage. These values (see Example 8-31 are then plotted in Figures 8-7 and 8=S. The starting mole fracs are chosen so that the distillation curves fill the entire space of the diagrams. If the relative volatility is constant, then the vapor mole fracs can be easily calculated fromEq. (5=30). Substituting Eq. (5=30) into Eq. (8=25a) and solving for Xy+i, we obtain the recursion relationship for the distillation curve for constant relative volatility systems. 

Another issue is that the effect of pressure on the design is not explored here because we are assuming constant relative volatility systems. The column pressure is fixed at 8 bar in this work. Pressure is very important in reactive distillation because of the effect of temperature on both vapor-liquid equilibrium and reaction kinetics. For exothermic reactions, the optimum column pressure is affected by the competing effects of temperature on the specific reaction rates and the chemical equilibrium constant. 

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