Column distillation McCabe-Thiele method

McCabe-Thiele diagrams for adsorption, 320 for binary distillation, 326, 329, 330, 332, 334 for countercurrent multistage separator, 309 for extraction, 317 for ion exchange, 322 for rectifying column, 314 McCabe-Thiele method for distillation, 310-315, 322-340... 

A fractionating column is required to distill a liquid containing 25 per cent benzene and 75 per cent toluene by mass, to give a product of 90 per cent benzene. A reflux ratio of 3.5 is to be used, and the feed will enter at its boiling point. If the plates used are 100 per cent efficient, calculate by the Lewis-Sorel method the composition of liquid on the third plate, and estimate the number of plates required using the McCabe-Thiele method. 

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. 

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. 

Equimolar counterdiffusion can be assumed in this case (as will be shown in a later chapter, this is the basis of the McCabe-Thiele method of analysis of distillation columns). Methanol diffuses from the interface towards the bulk of the gas phase therefore, yM = 0.707 and yA1 = 0.656. Since they are not limited to dilute solutions,... 

An alternative approximate solution to this problem can be obtained through the use of k -type coefficients. As mentioned in Example 2.3, the McCabe-Thiele method of analysis of distillation columns assumes equimolar counterdiffusion, which would justify the use of k-type coefficients regardless of the concentration levels. This would be exactly so only if the molar latent heats of vaporization of both components were equal. Although in this case there is a significant difference between the two heats of vaporization, we will show that the approximate solution is fairly close to the rigorous solution obtained above. It is easily shown that in this case, assuming steady-state equimolar counterdiffusion,... 

We now have all the material available for the graphical calculation of distillation conditions by the McCabe-Thiele method. This is one of the most used and simplest methods for the calculation of batch and continuous distillations of binary mixtures. It involves the simplifying assumptions that the molar heats of evaporation of the components and their mixtures are identical, and there are no heat losses from the column the consequence ist that the vapour and liquid flow rates, in moles per unit time, are constant throughout any section of the column, provided there is no addition or withdrawal of material. 

Figure 2.1 McCabe—Thiele method distillation column.

This problem-solving algorithm should be used as a guide, not as a conputer code to be followed exactly. The wide variety of possible configurations for distillation columns will allow a lot of practice in using the McCabe-Thiele method for solving problems. 

Lee J.W., Hauan S., Lien K.M. and Westerberg A. (2000c). A graphical method for designing reactive distillation columns II. The McCabe-Thiele method. Proceedings of the Royal Society of London Series A Mathematical Physical and Engineering Sciences 456, 1965-1978. 3.2.7, 3.2.7, 3.4... 

Figure 11.4-3. Distillation column showing material-balance sections for McCabe-Thiele method.

Based on the same equations for the distillation columns design presented in Section 4.3.2, we formulate the problem to determine the number of trays as function of the L/D ratio. We use McCabe-Thiele method to compute the number of theoretical trays, where the equilibrium composition is given by the following equation ... 

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. 

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. 

The elegance and simplicity of the McCabe-Thiele method make it tempting for the beginning student to view it as the centerpiece of binary distillation column design. There are, in fact, a number of key questions that need to be addressed before proceeding with plate calculations, setting reflux rations, and the like. 

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 design of a distillation column is based on information derived from the VLE diagram describing the mixtures to be separated. The vapor-liquid equilibrium characteristics are indicated by the characteristic shapes of the equilibrium curves. This is what determines the number of stages, and hence the number of trays needed for a separation. Although column designs are often proprietary, the classical method of McCabe-Thiele for binary columns is instructive on the principles of design. 

Design a distillation column to separate benzene, toluene, and xylene, using (1) the McCabe-Thiele xy diagram and (2) the Fenske-Underwood-Gilliland (FUG) method. Compare the results with each other. Assume that the system is ideal. 

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. ... 

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