11.6.1. The process
In the previous sections conditions have been considered in which there has been a continuous feed to the still and a continuous withdrawal of products from the top and bottom. In many instances processes are carried out in batches, and it is more convenient to distil each batch separately. In these cases the whole of a batch is run into the boiler of the still and, on heating, the vapour is passed into a fractionation column, as shown in Figure 11.33. As with continuous distillation, the composition of the top product depends on the still composition, the number of plates in the column and on the reflux ratio used. When the still is operating, since the top product will be relatively rich in the more volatile component, the liquid remaining in the still will become steadily weaker in this component. As a result, the purity of the top product will steadily fall. Thus, the still may be charged with S1 mols of a mixture containing a mole fraction xs1 of the more volatile component. Initially, with a reflux ratio R1, the top product has a composition
xd1. If after a certain interval of time the composition of the top product starts to fall, then, if the reflux ratio is increased to a new value R2, it will be possible to obtain the same composition at the top as before, although the composition in the still is weakened to xs2. This method of operating a batch still requires a continuous increase in the reflux ratio to maintain a constant quality of the top product.
An alternative method of operation is to work with a constant reflux ratio and allow the composition of the top product to fall. For example, if a product of composition 0.9 with respect to the more volatile component is required, the composition initially obtained may be 0.95, and distillation is allowed to continue until the composition has fallen to some value below 0.9, say 0.82. The total product obtained will then have the required composition, provided the amounts of a given purity are correctly chosen.
One of the added merits of batch distillation is that more than one product may be obtained. Thus, a binary mixture of alcohol and water may be distilled to obtain initially a high quality alcohol. As the composition in the still weakens with respect to alcohol, a second product may be removed from the top with a reduced concentration of alcohol. In this way it is possible to obtain not only two different quality products, but also to reduce the alcohol in the still to a minimum value. This method of operation is particularly useful for handling small quantities of multi-component organic mixtures, since it is possible to obtain the different components at reasonable degrees of purity, in turn. To obtain the maximum recovery of a valuable component, the charge remaining in the still after the first distillation may be added to the next batch.
The case of a column with four ideal plates used to separate a mixture of ethyl alcohol and water may be considered. Initially there are S1 moles of liquor of mole fraction xs1 with respect to the more volatile component, alcohol, in the still. The top product is to contain a mole fraction xd, and this necessitates a reflux ratio R1. If the distillation is to be continued until there are S2 moles in the still, of mole fraction xs2, then, for the same number of plates the reflux ratio will have been increased to R2. If the amount of product obtained is Dh moles, then a material balance gives:
Thus: S1 xs1 - (S1 - Dh)xS2 = Dhxd and: S1 xS1 - S^2 = Dhxd - Dhxs2
where a and h are as shown in Figure 11.34. If 0 is the intercept on the Y-axis for any operating line, equation 11.48, then:
These equations enable the final reflux ratio to be determined for any desired end concentration in the still, and they also give the total quantity of distillate obtained. What is important, in comparing the operation at constant reflux ratio with that at constant product composition, is the difference in the total amount of steam used in the distillation, for a given quantity of product, Db.
If the reflux ratio R is assumed to be adjusted continuously to keep the top product at constant quality, then at any moment the reflux ratio is given by R = dLb/dDb. During the course of the distillation, the total reflux liquor flowing down the column is given by:
J0 Jr=r1
R dDb
To provide the reflux dLb the removal of a quantity of heat equal to À dLb in the condenser is required, where À is the latent heat per mole. Thus, the heat to be supplied in the boiler to provide this reflux during the total distillation QR is given by:
j0 JR=Ri
R dD
This equation may be integrated graphically if the relation between R and Db is known. For any desired value of R, may be obtained by drawing the operating line, and marking off the steps corresponding to the given number of stages. The amount of product Db is then obtained from equation 11.88 and, if the corresponding values of R and Db are plotted, graphical integration will give the value of / R dDb.
The minimum reflux ratio Rm may be found for any given still concentration from equation 11.56.
If the same column is operated at a constant reflux ratio R, the concentration of the more volatile component in the top product will continuously fall. Over a small interval of time dt, the top-product composition with respect to the more volatile component will change from xd to xd + dxd, where dxd is negative for the more volatile component. If in this time the amount of product obtained is dDb, then a material balance on the more volatile component gives:
More volatile component removed in product = dDb xd + which, neglecting second-order terms, gives: = xd dDb dXd 2
and:
Thus:
S dxs — dS(xd — Xs) ^ S2 dS r Xs2 dXs r>2 dS _ rx°-
JSx S Jxsx
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