HW 4 - p 5.29 - Degree of Freedom Analysis on an Equilibrium Stage - 4 pts
Verify ND for unit operations (e) and (f) in Table 5.4. How would ND change if a vapor side stream was pulled off some stage located between the feed stage and the bottom stage?
posted by Dr. B at 2:34 PM
4 Comments:
Adding the number of equations for T & P equilibrium (2N), energy balances (N), and mol fractions of streams not including the feed streams (2N), I came up with 5N. I got 6N variables from the number of streams not including the feed streams (2N) times the 3 extra variables per stream besides the C number of components. This only gives 1N degrees of freedom when there's supposed to be 2N. The other variable and equation terms like the 2CN and 2C worked out fine. Just the N term is not tallying up. What am I missing?
karen:
Which part of the problem are you talking about (e) or (f) ?
Did you include material balance eqns anywhere ?
Did you include equilibrium equations anywhere ?
I thought deg Free = 2N + 2C +6 in part (e).
I could help you better if you told me how many streams you had and how many variables were associated with each stream.
I think you counted the eqns correctly, but did not count the variables correctly.
Perhaps you forgot about Q at each stage ?
This is part e. I didn't have N variables for Q before. I thought there would only be one Q term for the reboiler. Is heat generally transferred through the materials themselves in each stage or is it added and taken out?
So I took out the one variable for Q and I'm now 1 variable short of ND.
The variables I got:
2N(C+3)
for the in and out stream of N stages
2(C+3)
for the 2 extra streams
N
for heat transfer in each stage
1
number of stages
Total: 7N+2NC+2C+7
For equations:
CN
chemical equilibrium
2N
T&P at equilibrium
2N
mol fraction
2
mol fraction of feed stream
CN
material balance
N
energy balance
Total = 5N+2CN+2
karen:
Yes, in principle there is a Q for each stage. It is difficult to make a column perfectly adiabatic.
I think your main problem is that there are N+1 stages, not just N. The partial reboiler counts as an additional equilibrium stage.
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