Chapter 6: Mathematical Analysis of Distillation Columns

These problems ask you to calculate temperatures, flow rates, and compositions of all streams in distillation columns with 10 trays, a total condenser, and a partial reboiler. Assume EMO (equimolal overflow) and that the trays are equilibrium stages, including the partial reboiler.

The “brute force” method is not as convenient since we have so many stages. Instead you can make stage-by-stage calculations using the Lewis method. Typically, a solution can be found if the feed is completely specified (including feed stage) and two more process specifications are made. For example, the reflux ratio and the distillate flow rate could be specified. The unknowns for the total condenser are x_{D} (all compositions are identical for a total condenser), V_{1}, D, L_{0}, and T_{C}. The relationships and specifications are D, R, one mole balance, and one equilibrium relationship. That still leaves one DOF. So another variable must be guessed – usually x_{D}. The resulting value for x_{B} after working down the column is then compared to that calculated with an overall mole balance. The guess is then refined and the calculations are repeated.

I have a YouTube tutorial on the Lewis method using the non-ideal ethanol-water mixture. Since we haven't used non-ideal activity coefficients yet, I'll demonstrate using a polynomial fits of the VLE data. You will also need to do this in some of the problems below.

6.1 50 mol/s of an equimolar mixture of benzene and toluene is fed to the fifth tray of a 10-tray distillation column operating at 1 atm. The feed is a saturated liquid at 1 atm such that it all contributes to the liquid flowing down the column. The distillate flow rate is 25 mol/s and the reflux ratio is 1. Determine all unknown flow rates, compositions, and temperatures.

6.2 100 mol/h of a liquid at containing 10.0 mol% ethanol and 95.0 mol% water is fed to the ninth tray of a 10-tray distillation column operating at 1 atm. The feed is a saturated liquid at 1 atm such that it all contributes to the liquid flowing down the column. The distillate is 80.0 mol% ethanol and the reflux ratio is 3.0. Determine all unknown flow rates, compositions, and temperatures.

6.3 1,000 kmol/h of a vapor containing 70 mol% water and 30 mol% isopropanol is fed to the fifth tray of a 10-tray distillation column operating at 1 atm. The feed is a saturated liquid at 1 atm such that it all contributes to the liquid flowing down the column. 80 mol% of the water fed to the process is in the liquid product and the reflux ratio is 3.0. Determine all unknown flow rates, compositions, and temperatures.

6.4 200 mol/s of an equimolar mixture of n-hexane and n-octane is fed to the fifth tray of a 10-tray distillation column operating at 1000 mm Hg. The feed is a saturated liquid such that it all contributes to the liquid flowing down the column. The distillate flow rate is 50 mol/s and the reflux ratio is 2.0. Determine all unknown flow rates, compositions, and temperatures.

6.5 100 mol/s of an equimolar mixture of styrene and ethylbenzene is fed to the fifth tray of a 10-tray distillation column operating under vacuum at 100 mm Hg. The feed is slightly subcooled such that the liquid flow rate below the feed tray is 125 mol/s greater than the liquid flow rate above the feed tray. The flow rates of distillate and bottoms are equal. The reflux ratio is 2.0. Determine all unknown flow rates, compositions, and temperatures.

6.6 100 mol/s of a mixture containing water (60 mol%) and methanol (40 mol%) is fed to the ninth tray of a 10-tray distillation column operating at 1 atm. The feed is a saturated liquid at 1 atm such that it all contributes to the liquid flowing down the column. The bottoms is 90.0 mol% water and the reflux ratio is 1.25. Determine all unknown flow rates, compositions, and temperatures.

6.7 10 gal/h of a 20-proof ethanol in water mixture is to be concentrated to 90-proof in a 10-tray distillation column operating at 1 atm. The feed to Tray 8 is a slightly subcooled liquid so that the liquid flowing down from the feed stage is 5.0 mol% greater than expected because the feed condenses some of the vapor flowing up into the feed stage. The reflux ratio is 2.0. Determine all unknown flow rates, compositions, and temperatures.

6.8 1.0 m^{3} (STP)/s of 40 mol% n-butane and balance n-hexane is fed to the sixth tray of a 10-tray distillation column operating at 2 bar (absolute). The feed is a saturated vapor at 2 bar such that it all contributes to the vapor flowing up the column. The bottoms flow rate is 20.0 mol/s and 80% of the n-butane fed to the process is in the distillate. Determine all unknown flow rates, compositions, and temperatures.

6.9 100 mol/s of a vapor containing equimolar amounts of benzene and chlorobenzene is fed to the fifth tray of a 10-tray distillation column operating at 1 atm. The feed is a saturated vapor at 1 atm such that it all contributes to the vapor flowing up the column. The distillate flow rate is 50 mol/s and the reflux ratio is 2.0. Determine all unknown flow rates, compositions, and temperatures.

6.10 1000 kmol/day of an equimolar mixture of acetone and isopropanol is fed to the 8th tray of a 10-tray distillation column operating at atmospheric pressure. The thermodynamic state of the feed is such that it all enters the liquid flowing down the column. 90 mol% of the acetone fed to the column is captured in the distillate and its flow rate is 500 kmol/day. Determine all unknown flow rates, compositions, and temperatures.