McCabe-Thiele Vapor Feed

Operating Lines The McCabe-Thiele method is based upon representation of the material-balance equations as operating lines on the y-x diagram. The lines are made straight (and the need for the energy balance obviated) by the assumption of constant molar overflow. The liqmd-phase flow rate is assumed to be constant from tray to tray in each sec tiou of the column between addition (feed) and withdrawal (produc t) points. If the liquid rate is constant, the vapor rate must also be constant. 

The reason for this simple relationship is that the concept of minimum reflux implies an infinite number of stages and thus no change in composition from stage to stage for an infinite number of stages each way from the pinch point (the point where the McCabe-Thiele operating lines intersect at the vapor curve for a well-behaved system, this is the feed zone). The liquid refluxed to the feed tray from the tray above is thus the same composition as the flash liquid. 

Consider a propane concentration of 88 percent in the feed. The McCabe-Thiele diagram, based on the Fig. 7.12a interpretation of the test data, predicts a pinch just below the feed (Fig. 7.12e). Due to the pinch, the concentration of propane in the tower bottom will be 17 percent, i.e,. much higher than the 2 percent propane in the test data. In practice, this pinch will probably be eliminated by increasing the boilup ratio (i.e., reducing the slope of the operating line). However, increasing the boilup ratio means more liquid and vapor traffic, a greater heat load on the reboiler, and possibly, a premature capacity bottleneck. 

The McCabe-Thiele method can be used for the design of columns with side streams and multiple feeds. The liquid and vapor flows in the sections between the feed and takeoff points are calculated, and operating lines are drawn for each section. 

The liquid-phase composition profiles are shown in Figure 14.8, the temperature profiles in Figure 14.9. In this example, the liquid and vapor temperatures are almost equal. The pressure profile is not shown since it was more or less a straight line between the specified top tray pressure and the computed bottom pressure reported in Table 14.3. The pseudo McCabe-Thiele diagram and efficiency profiles are shown in Figures 14.10 and 14.11. In this case we see that the efficiencies of acetone and methanol are essentially equal over most of the column with the efficiency of water somewhat higher. Interestingly, the efficiencies decrease in the lower portion of the column below the acetone-methanol feed. 

The McCabe-Thiele method will be used. The side draw is more concentrated in acetone than either feed and should therefore be located above the feeds. Calculate the internal liquid and vapor flow rates and the slope of the operating line between the condenser and the side draw ... 

The feed, at a flow rate of 100 kmol/h, is sent as saturated vapor to the distillation column. The column is equipped with a partial condenser with a vapor product, and a reboiler. For a solvent rate of 500 kmol/h, it is required to determine the required number of equilibrium stages and the optimum feed location for a reflux ratio of 1.5 times the minimum. The McCabe-Thiele method may be used on a solvent-free basis. 

Total reflux is similar to minimum reflux in that it is not usually a real condition. In total reflux, all of the overhead vapor is returned to the column as reflux, and all of the liquid is returned as boilup, so that there are no distillate and bottom flows out of the column. At steady-state, this means that the feed stream flowrate is also zero. Total reflux is used in actual columns during start up and also to test their efficiency. Total reflux is useful in a McCabe-Thiele analysis in order to find the minimum number of stages required for a given separation. 

The lower part of the column is covered by stepping off stages in a fashion similar to that in the upper part of the column, and the final conni of theoretical stages is then determined. The Ponchon-Savarit method may be used for many situations more complex lhan the simple one just described mixed vapor-liquid distillate product, side draw streams, multiple feeds, and so on. Standard unit operations textbooks should be consulted for more dentils on this methnd. As mentioned, it suffers from a need for enthalpy-concentration data, but even a crude approximation based on linear variation of enthalpy with concentration can be better than the McCabe-Thiele approach if there is a very large difference in the latent heats of vaporization of the iwo components being distillnd. 

If the equilibrium data are given in analytical form, a McCabe-Thiele computer program can be used. Appendix F is an example of a Mathcad programs to implement the McCabe-Thiele method (Hwalek, 2001). It generates the required VLE data from the Antoine equation for vapor pressure and the NRTL equation for liquid-phase activity coefficients. Appendix F-l is for column feed as saturated liquid Appendix F-2 is for column feed as saturated vapor. 

This linear relationship between the total pressure, P, and the mole fraction, x, of the most volatile species is a characteristic of Raoult s law, as shown in Figure 7.18a for the benzene-toluene mixture at 90°C. Note that the bubble-point curve (P-x) is linear between the vapor pressures of the pure species (at x, = 0, 1), and the dew-point curve (P-yJ lies below it. When the (x, yi) points are graphed at different pressures, the familiar vapor-liquid equilibrium curve is obtained, as shown in Figure 7.18b. Using McCabe-Thiele analysis, it is shown readily that for any feed composition, there are no limitations to the values of the mole fractions of the distillate and bottoms products from a distillation tower. 

Consider stream L2, which was generated by flashing part of the feed stream and then condensing part of the resulting vapor. Since the material in L2 has been vaporized once and condensed once, it probably has a concentration close to that of the original feed stream (To check this, you can do the appropriate flash calculation on a McCabe-Thiele diagram) Thus, it is appropriate to use L2 as an additional feed stream to... 

This problem was also run on the Aspen Plus process simulator (see Problem 4.G1 and chapter appendix). Aspen Plus does not assume CMO and with an appropriate vapor-liquid equilibrium (VLE) correlation (the nonrandom two-liquid model was used) should be more accurate than the McCabe-Thiele diagram, which assumes CMO. With 5 equilibrium stages and feed on stage 4 (the optimum location), = 0.9335 and Xg = 0.08365, which doesn t meet the specifications. With 6 equilibrium stages and feed on stage 5 (the optimum), Xq = 0.9646 and Xg = 0.0768, which is slightly better than the specifications. The differences in the McCabe-Thiele and process simulation results are due to the error involved in assuming CMO and, to a lesser extent, differences in equilibrium. 

Since the column shown in Figure 4-23A has four sections, there will be four operating lines. This is illustrated in the McCabe-Thiele diagram of Figure 4-23B. One would specify that the liquid be withdrawn at flow rate S at either a specified concentration Xg or a given stage locatiom The saturated vapor is at concentration yg = Xg. Thus there is a horizontal feed line at yg. If the optimum location for... 

D26. A distillation column with a partial condenser and a total reboiler is separating acetone and ethanol. There are two feeds. One feed is 50.0 mol% acetone, flows at 100.0 mol/min, and is a superheated vapor where approximately 1 mole of liquid will vaporize on the feed stage for each 20 moles of feed. The other feed is a saturated liquid, flows at 150.0 mol/min and is 35.0 mol% acetone. We desire a distillate product that is = 0.85 mole fraction acetone and a bottoms product that is Xg = 0.10 mole fraction acetone. The column has a partial condenser and a total reboiler. Boilup is returned as a saturated vapor. Column operates at a pressure of 1.0 atin. Assume CMO and use a McCabe-Thiele diagram. VLE data are given in Problem 4.D7. 

C5. Using a McCabe-Thiele diagram for a binary system, show why increasing N may not be sufficient to keep constant purity compared to the base case if the diameter balancing method in Figure 10-18A (base case is saturated vapor feed) or 1Q-19A (base case is saturated liquid feed) is used to reduce the column volume. Although this demonstration is for a binary system, the logic is true for multicomponent systems also. 

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