Figure 11.39. Vapour-liquid equilibrium data for hydrocarbons
With a binary system, if the feed composition xf and the top product composition xd are known for one component, then the composition of the bottoms xw may have any desired value, and a material balance will determine the amounts of the top and bottom products D and W. This freedom of selecting the compositions does not apply for mixtures with three or more components. Gilliland and Reed(37) have determined the number of degrees of freedom for the continuous distillation of a multicomponent mixture. For the common case in which the feed composition, nature of the feed, and operating pressure are given, there remain only four variables that may be selected. If the reflux ratio R is fixed and the number of plates above and below the feed plate are chosen to give the best use of the plates, then only two variables remain. The complete composition of neither the top nor bottom product can then be fixed at will. This means that some degree of trial and error is unavoidable in calculating the number of plates required for any desired separation. Thus, if a trial composition is taken, and it is found that for the given bottom composition the desired top composition is not obtained with the selected reflux ratio, then an adjustment must be made in the bottom composition. An exact fit in a calculation of this kind is not essential since the equilibrium data and the plate efficiency are known with only limited accuracy. This problem is frequently simplified if a sharp cut is to be made between the components, so that all of the more volatile components appear in the top and all of the less volatile in the bottom product.
In the fractionation of multicomponent mixtures, the essential requirement is often the separation of two components. Such components are called the key components and by concentrating attention on these it is possible to simplify the handling of complex mixtures. If a four-component mixture A - B - C -D, in which A is the most volatile and D the least volatile, is to be separated as shown in Table 11.3, then B is the lightest component appearing in the bottoms and is termed the light key component. C is the
Table 11.3. Separation of multicomponent mixture
Feed Top product Bottoms
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