Assuming the validity of the DePriester Charts, make the following VLE calculations for the methane(1) / ethylene(2) / ethane(3) system:
a.) Pbub, given x1 = 0.10, x2 = 0.50 and t = -60oF.
b.) Pdew, given y1 = 0.50, y2 = 0.25 and t = -60oF.
c.) Tbub, given x1 = 0.12, x2 = 0.40 and P = 250 psia.
d.) Tdew, given y1 = 0.43, y2 = 0.36 and P = 250 psia.
Hints:
Do parts b and c only.
Use the results from my solution to this problem in HW#2, based on the DePriester Charts, as a starting point for SRK.
Use the SRK equations for mixtures to answer this question. The equations are the 2 SRK eqns in terms of Zliq and Zvap and three equilibrium eqns. The unknowns are The two Z's, two of the three yi's and the total pressure.
You will need to run Solver several times, tweaking your guesstimates of the unknown variables each time, in order to get Excel to converge to the correct answer. The correct answer is the one that yields the lowest value of the Ī£error^2.
2 comments:
A student emailed me the following question:
"I have all my 5 equations set up and am trying to simultaneously solve for the unknowns. Solver doesn't want to work for me. I get num! I think this is because Zliq is below Bliq and the same for vapor. I set a constraint for solver that Z is greater than B, but it won't listen. any suggestions."
I replied:
OK, you have 5 eqns:
3 of the them are y{i} phi{i}vap = x{i} phi{i}liq
The remaining 2 eqns are SRK eqns: one for liquid and one for vapor.
So far, so good.
You should also have 5 unks: Zvap, Zliq, P, x1 and x2.
Right ?
I used %error^2 for each equilibrium eqn and f(Z)^2 for the SRK eqns. I minimized SQRT of the sum of these 5 error terms (divided by 5. This is something like the %RMS error for the 5 eqns.
The easiest way to get Solver to go where you want it is to add FOUR constraints. Constrain both Zs to be > 0.04 AND constrain BOTH f'(Z) functions to be > 0 (to make sure the two roots you find are the sat vap and sat liq roots and not the meaningless one).
That should get you very close to the right answer in one pass in Solver. I you want, you can go onto the options tab and change the Estimates, Derivatives and Search methods. You can also run solver on each eqn, one at a time and then go back and do all 5 together. This often further reduces the %RMS. I managed to get my %RMS down to 5.7e-6. But I only got to something like 4e-4 in one try. Either way is fine.
Is it possile that when calculate bubble point pressures for some mixtures happen the SRK equation in Z for Zliq has only one root?
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