A distillation calculation problem
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This post was last edited by sclzlth on 2011-4-2 09:47. Which expert can solve this problem? Thank you! A distillation column with only one theoretical plate and a reboiler is used to separate a two-component mixture. The feed rate is 20 Kmol/h, with a composition of 0.5 (mole fraction, the same hereafter). The feed enters at the bottom of the column; q=1, the volatility a=3, and the reflux ratio R=3. The composition of the distillate is xD=0.8. What is the yield of the light component?
Using the retention section equation and substituting the relevant values – R=3, q=1, F=20, x1=xf=0.5, W=F-D, WXw=FXf-DXd – yields y2=0.575. Since the feed is at the bottom of the tower, y2 represents the gas phase composition in the reboiler. Applying the gas-liquid equilibrium equation and using a=3 as well as y2=0.575, we obtain X2=Xw=0.31. By combining the equations F=D+W and FXf=DXd+WXw, we find that D=7.76. Finally, the yield is DXd/FXf=62.1%
Reply to 2# kaminocmyhc: Based on the first theoretical plate and the vapor-liquid equilibrium equation, X1 is calculated to be 0.571. The equation for the distillation section is y = 0.75x + 0.2; using this to find y2. Then, via the vapor-liquid equation, x2 = xw = 0.36 is obtained. Substituting this value into the material balance equation gives D = 6.36. The final result is Dxd/Fxf = 50.9%. Everyone is welcome to continue the discussion in order to improve together
This post was last edited by kaminocmyhc on 2011-4-6 at 12:02. Reply 3# sclzlth: Your answer is correct. I misunderstood some of the basic concepts of distillation. But the second section is a reboiler, and it should be calculated using the equations for the stripping section, rather than the equations for the distillation section to determine y2, right?
Reply to 4# kaminocmyhc: First of all, thank you for paying attention to this post, for participating in the discussion, and for offering valuable suggestions. I hope everyone can improve through this. The original problem involves feeding at the bottom of the tower, with the reboiler considered as one theoretical plate; this operation has only a distillation section, no stripping section!
This post was last edited and replied to by baha on 2011-4-7 at 16:48. Reply 5# sclzlth: I also think that the equation for the retention section should be included; with feed at the bottom of the tower, the reboiler is equivalent to one tray.