Question 5 in the morning session of the 2011 case
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5. In a packed tower operated in countercurrent mode, a pure solvent is used to absorb the harmful components in a gas mixture. The equilibrium relationship is known to be Y=2X, the liquid-to-gas ratio in the operation is L/V=2, the concentration of the gas phase entering the tower is 0.008 (mole fraction), and the concentration of the liquid phase leaving the tower is 0.0035 (mole fraction). If a plate tower is used instead, what will be the required number of theoretical plates? (A) 6 (B) 5 (C) 8 (D) 7 How do you solve this question? Is the number of theoretical plates equal to the number of mass transfer units? m=L/V; S = 1, and it’s impossible to determine the number of mass transfer units when using this formula! Need some advice! Thank you.
When S = 1, the number of theoretical plates is numerically equal to the number of mass transfer units.
This problem is really easy to solve! Look up the page on absorption in the Chemical Process Design Manual (Volume 1); there’s a formula there that can be used to handle this situation.!lol
This post was last edited by zwp997 on 2015-6-19 22:47. Nt＝Nog=(Y1-Y2)/(Y1-Y*)=(0.008-0.001)/(0.008-2*0.0035)=7
Yb=0.008, Xa=0, Xb=0.0035. Based on the material balance equation V(Yb–Ya) = L(Xb–Xa), it follows that Ya=0.001. Using the formula for the absorption factor (with S=1 to find the limit), Nog = (Yb–mXa)/(Ya–mXa) – 1 = 7; when S=1, Nt = Nog = 7. Therefore, D is chosen
This post was last edited by yaojin911 on 2015-6-21 at 00:36. From the given information: ① Y1 = 0.008 ÷ (1 – 0.008) = 0.008065; ② X1 = 0.0035 ÷ (1 – 0.0035) = 0.003512; ③ X2 = 0 (pure solvent); ④ A = L / (mV) = 1 = 1/S. Also, since L/V = (Y1 – Y2) / (X1 – X2), it follows that Y2 = 0.001041. Therefore, 1 – A = 1 – S = 0, which means that Nt, Nog, and Nol cannot be calculated. Hence, the step-by-step calculation method must be used. According to the problem, the slope of the operating line, L/V, is equal to the slope of the equilibrium line, m; that is, L/V = m = 2. Thus, the two lines are parallel. Based on the ladder diagram, each “step” has the same height. Since Y = 2X, the equilibrium line passes through the origin. Therefore, the height of the last step is equal to the intercept of the operating line. The height of one step is (Y1 – L/V · X1) = 0.001041. Consequently, the total number of theoretical plates is (Y1 – Y2) / 0.001041 = 6.747. I’m not very skilled, and I didn’t find any statement indicating that Nog = Nt; that’s why I could only calculate it in this way. Feel free to share your thoughts