Question from the 2016 professional exam regarding calculating the minimum amount of steam required for upward flow in a tower reactor
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3. The plant operates a continuous distillation column to separate a formaldehyde mixture. The feed formaldehyde concentration is 0.55 (mole fraction, the same hereafter), with a flow rate of 315 kmol/h; the feed is at the bubble point, a total condenser is used at the column top, and reflux occurs at the dew point. The formaldehyde concentration in the distillate is 0.96, while that in the bottom stream is 0.1. If the average relative volatility of formaldehyde under these operating conditions is 2.0, what is the minimum vapor flow rate from the column bottom (in kmol/h)? A.444 B.333 C.122 D.245 Why did I get **108 kmol/h** as my answer? General approach to solving the problem: First, perform material balance: F = D + W. 0.55F = 0.96D + 0.1W; given that F = 315, then D = 164.8 kmol/h. The feed has a dew point, so q = 0. yq = yF, a = 2, and yF = 0.7097 ； Rmin=1.567 V=L+D, V=V’+F. V’=(1+1.567)D-F=2.567×164.8-315=108 kmol/h. Why **is there no correct one? May I ask where I made the mistake?
Hey, you must be mistaken; it should be Yq=Xf, when q=0
I was really screwed by the textbooks. This is my university textbook. I’ve been keeping it for over 10 years. Principles of Chemical Engineering (2nd Edition), edited by Wang Zhikui, 2nd edition published in 1998
Dew point feed is saturated steam feed, equation 6-44 – where did this book let you down?
This post was last edited by biturbo on 2017-3-6 at 10:42. ① Apply formula 6-44 directly; Rmin = 2.4. The rest of the process is the same as yours, so choose D. ②If you do the calculations by yourself, there is an issue with your values for this step: “a=2, yF=0.7097, Rmin=1.567”. The value of yF=0.7097 that you calculated actually results from substituting x=0.55 into the equilibrium equation, which corresponds to the case where the feed rate q is 1. . . ③For the feed with dew point, q=0, yq=yF=0.55; using the gas-liquid equilibrium equation, xq is found to be 0.379. Substituting this value into the formula Rmin= (xD-yq)/(yq-xq) gives Rmin=(0.96-0.55)/(0.55-0.379)=2.4. It’s the same in all cases
Oh, I see; I was misled by the person upstairs. It is fine to have a saturated steam feed of yq=yF. I misunderstood it myself. The feed composition given in the problem is 0.55; this is not xF, but rather the gas-phase composition, which should be yF. Simply substitute this value into the formula to carry out the calculation. I mistook this 0.55 for xF. Then substitute it into the equilibrium equation to calculate yF. It’s naturally wrong. Minor mistakes can be deadly
I’m not misleading you! Xf is 0.55; the textbook I studied states that when q=0, Yq=Xf, and when q=1, X=Xf. What’s the problem here?
Q-line equation: Yq = (q/q-1)X – (1/q-1)Xf
I’m sorry; I wasn’t precise enough. I carefully studied the replies from those two enthusiastic sea enthusiasts as well as the textbook. The problem lies in one aspect: the understanding of these feed compositions, xF, yF, as well as xq, yq. I have already posted the image of my textbook above; yq=yF. Here, he uses yF to represent the molar fraction of the volatile components in the composition of the feed gas phase. The textbook is a bit confusing when using xq, yq, xf, xW, and xD. In xq and yq, x and y represent the phases, indicating two-phase equilibrium. In xF, xW, and xD, x denotes only the volatile components. These two meanings are different. Therefore, different interpretations appear in various textbooks. From this perspective, it is problematic in my textbook to use yF to represent the gas-phase volatile components in the feed. Because relative to xF, yF should represent the molar fraction of the poorly volatile component. Regardless of whether the feed is in liquid phase, a vapor-liquid mixture, saturated steam, superheated steam, etc., the volatile components in the feed should be denoted by xF. It can be seen from the derivation of the q-line equation that y and x are related to the phase state, whereas xF, xW, and xD are independent of the phase state. Even if the overhead distillate D or the bottom difficult-to-vaporize components W contain two phases, they are still represented by xW and xD, rather than yD and yW. The shapes of the q-line on the y-x graph are also shown in various editions of the textbooks, for q=0, >0,