Distillation Column Operation McCabe Method

The operating line in the rectifying section is calculated by performing a mass balance to the upper part of the column from a tray n, just above the feed, including the condenser 

Similarly, we obtain the operating line for the stripping section by means of a mass balance from tray m, just below the feed, involving the reboiler as follows  

It is assumed that the mass transfer from the liquid phase to the vapor phase is small in each of the sections so that the liquid and vapor streams are constant through 

The feed can be in different aggregation states as compressed liquid, saturated liquid, a vapor-liquid mixture, saturated vapor, and superheated vapor. We define the liquid and vapor fraction as I l and respectively  

FIGURE 4.14 McCabe-Thiele method for binary distillations. 

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Annual cost for distillation column. The McCabe-Thiele simplifying assumptions apply for this case, and the number of theoretical plates can be determined by the standard graphical method shown in Fig. 11-8. The slope of the enriching operating line is 1.5 /(1.5 + 1) = 0.6. From Fig. 11-8, the total number of theoretical stages required for the given separation is 12.1. 

Recall that when we designed distillation columns with the graphical McCabe-Thiele method, we specified the relative flow rates of liquid and vapor to obtain the operating lines. What diameter of column is needed to accommodate the absolute flow rates If the column is too narrow le., the sieve plate area is too small), the liquid will pass over the sieve plate too quickly and not equilibrate with the vapor. If the colunm is too wide, the liquid will not cover the tray completely and the vapor will blow through without equilibrating. 

The graphical McCabe-Thiele methods studied in the previous sections for the design of distillation columns are also widely used to analyze the operation of an existing column. In this case the total number of trays in the column Nj-is fixed. The feed tray may also be fixed, or, if there are multiple feed points available on the column, it may be varied. These fixed-column problems are called rating problems, as opposed to the design problems, in which Nt is calculated. 

Figure 8.1.20. Vapor-liquid equilibrium curve, operating lines for enriching section and stripping section and construction of ideal stages and q Une for a feed consisting of vapor and liquid in a multistage distillation column having ideal equilibrium stages the McCabe-Thiele method.

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 a constant distillate composition is required, this can be achieved by increasing the reflux ratio as the system is depleted in the more volatile material. Calculations are again made with the McCabe-Thiele diagram as described by Bogart and illustrated by the following example. Other methods of operating batch columns are described by Ellerbe. ... 

The end of each sub-task is detected as the following violation takes place. At some point the reflux ratio used approaches the actual minimum value for the corresponding composition in the vessel. At this point a new reflux ratio has to be used. The limiting composition at the end of the sub-task is found using the simple graphical method of McCabe-Thiele. The distillate amount and the amount remaining in the vessel are calculated from simple mass balance equations. The operating time of the sub-task is found from the overall material balance around the top of the column. This procedure is repeated until the desired yield is achieved. 

To design such a process, the McCabe-Thiele method may be used to determine the number of theoretical separation stages, as examined in Sections 3.3.2-3.3.4 for distillation, absorption (gas scrubbing), and liquid-liquid-extraction. Thus, we obtain the number of theoretical extraction stages of a countercurrent extraction column based on the equilibrium curve (solubility of extract in the solvent for a given content in the solid) and the operating line. The latter depends on the extract content of the solid feed and residue, and on the in- and outlet extract concentration in the solvent The extract content of the feed is fixed, and the value of the residue is specified by the required degree of extraction. The inlet content of the extract in the solvent is also fixed, as either pure solvent is used or the value is specified by separation of the extract from the used solvent after the extraction. Therefore, the only parameter that is left is the outlet concentration of the extract in the solvent, which depends on the ratio of the solvent flow to the feed rate of the solid feedstock (mass balance). 

The operation of a binary distillation has two important limiting cases minimum and maximum stages for a given separation. Minimum stages occur when the column is operated with total reflux (i.e., no top product is withdrawn). This situation, when applied to the McCabe-Thiele method, uses the y = x line as the mass balance for both rectifying and stripping. The situation is depicted in Figure 12-11. 

Although simple distillation marks the first analysis of batch distillation process, the graphical analysis presented by [39] provided the basis for analyzing batch distillation operating modes. The difference between simple distillation and batch distillation operations is the relation between the distillate composition xd and the bottom composition xb due to the presence of reflux and column internals as shown in Figure 4.4. If one assumes constant molal overflow Lj = Lj-i =. . = Lo = L and Vj = Vj- =. . = Vi = V), then McCabe-Theile s method can be used. 

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