Chapter 7 Problems

These exercises provide excellent practice for graphical (McCabe-Thiele) design of distillation columns. This method is particularly well-suited if you know how the column is supposed to perform but need to know how many equilibrium stages are required and which is the optimum feed tray.

For a fixed number of stages and the feed stage identified, only two specifications were required in addition to the feed, for instance, R and x_D. There is one additional unknown in this case; the number of stages. That means one more piece of information is needed in order to solve a problem. This could be a flow rate, composition, reflux ratio, or boilup.

You will need a starting and end point on the xy graph – x_D and x_B. These can usually be determined using the overall process total and species mole balances. Then the operating lines are drawn using a specified reflux or boilup ratio. Finally, it is just a matter of stepping off the stages. Remember that VLE graphs for all these mixtures can be printed from Excel “VLE”.

If you want to be awesome - and I know you do - compare your results to a process simulator like ChemCAD or Aspen. Make plots of the L, x, V, y, and T profiles. Vary parameters such as the reflux ratio and predict how it will change your results.

7.1 100 mol/s of an saturated liquid mixture of benzene (50 mol%) and toluene (50 mol%) is fed to the optimum tray of a distillation column operating at 1 atm. The distillate flow rate is 45 mol/s, the bottoms flow rate is 55 mol/s, and the reflux ratio is 2. That is three specifications, but ... make a convincing argument why this problem does not have a unique solution.

7.2 100 kmol/h of a saturated liquid mixture of benzene (60 mol%) and chlorobenzene (40 mol%) is fed to the optimum tray of a distillation column operating at 1 atm. The distillate has a flow rate of 50 kmol/s and a composition of 0.95 mol B/mol. The reflux ratio is twice the minimum. Determine the number of stages and identify the feed stage.

7.3 100 mol/s of a saturated liquid mixture of acetone (30 mol%) and isopropanol (70 mol%) is fed to the optimum tray of a distillation column operating at 1 atm. The bottoms composition is 0.1 mol A/mol, the distillate flow rate is 25 mol/s, and the reflux ratio is 2.0. Determine the number of stages and identify the feed stage.

7.4 100 mol/s of a saturated vapor mixture of ethylbenzene (60 mol%) and styrene (40 mol%) is fed to the optimum tray of a distillation column operating at 100 mm Hg. The distillate flow rate is 60 mol/s with composition 0.85 mol E/mol. The reflux ratio is 8. Determine the number of stages and identify the feed stage.

7.5 50 mol/s of a mixed feed (½ vapor – ½ liquid) with overall composition 40 mol% ethanol and 60 mol% water is fed to the optimum tray of a distillation column operating at 1 atm. The bottoms flow rate is 30 mol/s, the distillate composition is 0.8 mol E/mol, and the reflux ratio is twice the minimum. Determine the number of stages and identify the feed stage.

7.6 100 mol/s of a saturated liquid consisting of 40 mol% isopropanol and 60 mol% water is fed to the optimum tray of a distillation column operating at 1 atm. The distillate flow rate is 40 mol/s and its composition is 0.68 mol I/mol. The reflux ratio is 4.23. Determine the number of stages and identify the feed stage.

7.7 100 kmol/h of a saturated liquid containing 40 mol% hexane and 60 mol% octane is fed to the optimum tray of a distillation column operating at 1 atm. The distillate flow rate is 35 mol/s and its composition is 0.97 mol H/mol. The reflux ratio is twice the minimum. Determine the number of stages and identify the feed stage.

7.8 500 mol/h of a mixture with equal amounts of liquid and vapor is fed to the optimum tray of a distillation column operating at 1 atm. The overall composition of the feed is 50 mol% methanol and 50 mol% water. The bottoms flow rate is 300 mol/s, the reflux ratio is 1.0, and the distillate composition is 0.95. Determine the number of stages and identify the feed stage.

7.9 100 mol of a saturated vapor containing 60 mol% hexane and 40 mol% heptane is fed to the optimum tray of a distillation column operating at 2 atm. The bottoms flow rate is 40 mol/s, the reflux ratio is 1.0, and the distillate composition is 0.80 mol Hex/mol. Determine the number of stages and identify the feed stage.

7.10 100 mol of a saturated liquid containing 30 mol% butane and 70 mol% hexane is fed to the optimum tray of a distillation column operating at 1 atm. The bottoms composition is 0.05 mol B/mol, the reflux ratio is 1.0, and the distillate composition is 0.99 mol B/mol. Determine the number of stages and identify the feed stage.