From equation 11.103: ln(VS2) = 1.1 and (S /S2) = 3.0. Product obtained, Db = S — S2 = (100 — 100/3) = 66.7 kmol. Amount of ethanol in product = x1 S1 — x2 S2
Thus: average composition of product = (51.5/66.7) = 0.77 mole fraction ethanol.
The heat required to provide the reflux = (4000 x 2.1 x 66.7) = 560,380 kJ. Heat required to provide reflux per kmol of product = (560,380/66.7) = 8400 kJ.
Thus in Example 11.12 the total heat required per kmol of product is (5320 + 4000) = 9320 kJ and at constant reflux ratio (Example 11.13) it is (8400 + 4000) = 12,400 kJ, although the average quality of product is 0.77 for the second case and only 0.75 for the first.
11.6.4. Batch or continuous distillation
A discussion on the relative merits of batch and continuous distillation is given by Ellis(36), who shows that when a large number of plates is used and the reflux ratio approaches the minimum value, then continuous distillation has the lowest reflux requirement and hence operating costs. if a smaller number of plates is used and high purity product is not required, then batch distillation is probably more attractive.
11.7. MULTICOMPONENT MIXTURES 11.7.1. Equilibrium data
For a binary mixture under constant pressure conditions the vapour-liquid equilibrium curve for either component is unique so that, if the concentration of either component is known in the liquid phase, the compositions of the liquid and of the vapour are fixed. It is on the basis of this single equilibrium curve that the McCabe-Thiele method was developed for the rapid determination of the number of theoretical plates required for a given separation. With a ternary system the conditions of equilibrium are more complex, for at constant pressure the mole fraction of two of the components in the liquid phase must be given before the composition of the vapour in equilibrium can be determined, even for an ideal system. Thus, the mole fraction in the vapour depends not only on xA in the liquid, but also on the relative proportions of the other two components.
Determining the equilibrium relationships for a multicomponent mixture experimentally requires a considerable quantity of data, and one of two methods of simplification is usually adopted. For many systems, particularly those consisting of chemically similar substances, the relative volatilities of the components remain constant over a wide range of temperature and composition. This is illustrated in Table 11.2 for mixtures of phenol, ortho and meta-cresols, and xylenols, where the volatilities are shown relative to ortho-cresol.
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