A distillation column at \(1.0 \mathrm{~atm}\) with a total condenser and a total reboiler is separating ethanol from water. Reflux is returned as a saturated liquid, and boilup is returned as a saturated vapor. Assume CMO is valid and stages are equilibrium stages. \(1000 \mathrm{kmol} / \mathrm{h}\) of a saturated liquid feed that is \(32.0 \mathrm{~mol} \%\) ethanol is fed to the column on the optimum feed stage. Distillate is \(80.0 \mathrm{~mol} \%\) ethanol, and bottoms is \(2.0 \mathrm{~mol} \%\) ethanol. A liquid side stream is removed on the eighth stage from the top of the column at a flow rate of \(S=457.3 \mathrm{kmol} / \mathrm{h}\). This liquid is sent to an intermediate reboiler and vaporized to a saturated vapor, which is returned to the column at its optimum feed location. External reflux ratio is \(\mathrm{L}_{0} / \mathrm{D}=1.86\). Find the optimum feed locations of the feed and of the vapor from the intermediate reboiler. Find the total number of equilibrium stages required. VLE data are in Table 2-1. Be very neat!

Table 2-1

Transcribed Image Text:

TABLE 2-1. Vapor-liquid equilibrium data for ethanol and water at 1 atm y and x in mole fractions XEtoh Xw YEtoh Yw T, C 0 1.0 0 1.0 100 0.019 0.981 0.170 0.830 95.5 0.0721 0.9279 0.3891 0.6109 89.0 0.0966 0.9034 0.4375 0.5625 86.7 0.1238 0.8762 0.4704 0.5296 85.3 0.1661 0.8339 0.5089 0.4911 84.1 0.2337 0.7663 0.5445 0.4555 82.7 0.2608 0.7392 0.5580 0.4420 82.3 0.3273 0.6727 0.5826 0.4174 81.5 0.3965 0.6035 0.6122 0.3878 80.7 0.5079 0.4921 0.6564 0.3436 79.8 0.5198 0.4802 0.6599 0.3401 79.7 0.5732 0.4268 0.6841 0.3159 79.3 0.6763 0.3237 0.7385 0.2615 78.74 0.7472 0.2528 0.7815 0.2185 78.41 0.8943 0.1057 0.8943 0.1057 78.15 1.00 0 1.00 0 78.30