Many industrially important liquid systems are difficult or impossible to separate by simple continuous distillation because the phase behavior contains an azeotrope, a tangent pinch, or an overall low relative volatility. One solution is to combine distillation with one or more complementary separation technologies to form a hybrid. An example of such a combination is the dehydration of ethanol using a distillation-membrane hybrid, as shown in Figure 6.28.

The membrane performance is specified by defining a membrane separation factor, \(\alpha_{m}\), and membrane cut, \(\theta\) :

In a given application, \(100 \mathrm{~mol} / \mathrm{s}\) of a saturated liquid containing \(37 \mathrm{~mol} \%\) ethanol and \(63 \mathrm{~mol} \%\) water must be separated to yield a product which is \(99 \mathrm{~mol} \%\) ethanol, and a residue containing \(99 \mathrm{~mol} \%\) water. The solution will be fed to a

distillation column operating at atmospheric pressure, with a partial reboiler and a total condenser. The reflux ratio will be 1.5 the minimum. The distillate will enter a membrane with parameters \(\alpha_{m}=70\) and \(\theta=0.6\). The membrane boosts the concentration so that the permeate stream is the ethanol-rich product \(\left(x_{P}=0.99\right)\). The retentate stream is returned as a saturated liquid to the column to the tray at the nearest liquid concentration. Calculate

(a) The molar flow rate of the product and of the residue.

(b) The molar flow rate and composition of the distillate coming out of the column.

(c) The molar flow rate and composition of the retentate returned to the column.

(d) The number of ideal stages required, and the optimal location of the two feeds(the original feed and the retentate recycle) to the distillation column.

Transcribed Image Text:

am xp (1-xR) XR (1-xp) (6-113) P D (6-114)