Chapter 11 Problems
These are excellent problems to practice distillation calculations for non-ideal solutions. Actually, most distillations involve non-ideal liquid phases. Only those chemicals with similar chemical structures are ideal enough to use Raoult’s law. If you happen to have VLE graphs, the McCabe-Thiele method is identical, only you can’t separate beyond the azeotrope if one exists. For the Lewis method, you can use a polynomial fit of the VLE graphs as you did for some of the problems in Chapter 6. However, those polynomial equations are only good for a specific pressure. A more flexible option is to use an activity coefficient model like the Wilson equation used for the ethanol-water mixture.
See my tutorial YouTube “Distillation of Non-Ideal Mixtures”. I will warn you that the activity coefficient depends on the liquid phase composition so it is difficult to avoid circular references in Excel. I solved this problem by working the problem “upside down”, starting at the bottom of the column. I explain this in the book and tutorial. If you have a cleverer way of solving this problem, by all means, let me know!
11.1 A saturated liquid consisting of 20 mol% ethanol and 80 mol% water is fed to the bottom tray of a seven-tray distillation column equipped with a total condenser and partial reboiler and operating at 1 atm. The reflux ratio is 2.0 and the bottoms flow rate is 80 mol/s. Calculate all unknown flowrates, compositions, and temperatures using the Lewis method with Wilson activity coefficients LEW = 0.2002 and LWE = 0.8156. Assume equilibrium trays and EMO.
11.2 Follow the tutorial "Fitting Non-Ideal VLE Data" to find the Wilson coefficients for Acetone-Isopropanol. Use the VLE values in the VLE spreadsheet (vary last pages). Since there is no azeotrope use values at x = 0.3, 0.5, and 0.7. So the activity γ = yP/xP*. Note that the Wilson coefficients vary with concentration but they all generate VLE data that fit as well as the NRTL equation.
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 using the Wilson activity coefficients instead of a polynomial fit like you did in problem 6.10.