1. Tier 3:
Open-Ended Problem

2. Open-Ended Problem: Styrene Production from Ethylbenzene:
A Data Reconciliation Problem with Model Uncertainties and Multiple Solutions
*Flowsheet taken from Felder & Rousseau “Elementary Principles of Chemical Processes”, page 487.

3. Liquid-Liquid Extractor
Open-Ended Problem
Reactor
Condenser
Distillation Column
Liquid-Liquid Extractor
F10 (S)
F9 (EB,S)
F7 (H)
F8 (EB,W,S)
F6 (EB,W,S,H)
F4 (EB,W)
F5 (W)
F3 (EB)
F2 (EB)
F1 (EB)
A simplified flowsheet for the production of styrene from ethylbenzene is shown here. In order to prevent undesirable side reactions and to clean carbon deposits from the catalyst, steam is mixed with the ethylbenzene prior to the reactor. In the reactor, ethyelbenzene is reacted to form styrene and hydrogen, with a conversion rate of approximately 35%. Hydrogen is removed from the mixture with a condenser, and the water is removed with an extractor. The styrene is separated from the ethylbenzene with a distillation column, and removed as a final product, while the ethylbenzene is recycled.
EB – Ethylbenzene (C8H10) W – Water (H2O)
S – Styrene (C8H8) H – Hydrogen (H2)

4. Open-Ended Problem Variable Measurement (kg/h) Variance (kg/h) F1 1775 F2
365 7 F3
535 F4
4145 75 F5
3641 F6
4147 F7
4.1
0.2 F8
4135 F9
542
F10
178
The raw measurements for the flow rates and their respective variance are shown in Table 1.
Table 1: Raw Measurements and Variance for Flow Rates

5. Open-Ended Problem Variable Measurement Variance x4,EB 0.122 0.009
x4,W
0.877
x6,EB
0.081
x6,W
0.881
x6,S
0.046
x6,H
0.001
x8,EB
0.080
x8,W
0.779
x8,S
0.045
x9,EB
0.656
x9,S
0.346
And the raw measurements for the mass fractions and their respective variance are shown in Table 2.
Table 2: Raw Measurements and Variance for Mass Fractions

6. Open-Ended Problem The Problem: RECONCILE FLOWS AND MASS FRACTIONS
Flow measurement devices are very old.
Many gross errors suspected!!
RECONCILE FLOWS AND MASS FRACTIONS
The problem with this process is that the mass balances are not matching the data. As the flow measurement instrumentation is all very old, it is suspected that many of them contain gross errors. To save time and money, instead of replacing all the measurement devices, it is desired to use data reconciliation to determine which devices should be replaced.

7. Open-Ended Problem Possibly Useful Information:
(Cp)EB(vapor) = T J/molºC
(Cp)W(vapor) = T J/molºC
(T in ºC)
Stream #
Temperature in ºC (before heat exchanger)
Temperature in ºC (after heat exchanger) 3 25
500 4
600 5
700 6
560
Included here is some information that may or may not be useful in reconciling the data.
Table 3: Temperatures for Various Streams

8. Open-Ended Problem Models with Uncertainty: F7 = F6x6,H F5 = F8x8,W
F8x8,EB = F6x6,EB
F8x8,S = F6x6,S
F8x8,W = F6x6,W
F9x9,EB = F8x8,EB
F9x9,S = F8x8,S
F10 = F9x9,S
F2 = F9x9,EB
Mass balances performed around the condenser, extractor, and the distillation column are assumed to have uncertainty, as the separation processes are not perfect. For these balances, the Monte Carlo simulation method will be sufficient.

9. Calculate the variance of % conversion and the 3 reactor balances!
Open-Ended Problem
Trial #
% Conversion 1 36 2 3 33 4 35 5 6 34 7 37 8 9 10
Models with Uncertainty:
F6x6,EB = (1 - %C)(F4x4,EB)
F6x6,S = (%C)(0.98)(F4x4,EB)
F6x6,H = (%C)(0.02)(F4x4,EB)
(C8H10 C8H8 + H2)
Also, the mass balances around the reactor are assumed to have additional uncertainty as a result of varying reactor conversions. Monte Carlo simulation can again be used here to determine model uncertainty, if the conversion percentage is considered as a measurement with its own variance as well. All other balance equations (which are not shown here) can be assumed to be exact.
Calculate the variance of % conversion and the 3 reactor balances!
Table 4: Conversion Percentages of Reactor

10. Open-Ended Problem Solution #1 Solution #2 Stream # Flow Rate (kg/hr)
175 2
365
325 3
540
500 4
4466
4135 5
3926
3635 6 7
3.8
3.5 8
4462.2
4131.5 9
536.2
496.5 10
185.2
171.5
Presented in Table 5 are two different solutions that satisfy the mass and energy balances.
Table 5: Two Possibly Correct Solutions

11. Open-Ended Problem Which, if either, solution is more probable?
Gross errors present in measurements for F4, F5, F6, F8, and F10.
Gross errors present in measurements for F2, F3, F7, F9, and F10.
It can be seen that the assumption of either solution being valid results in the conclusion that there are five measurement devices containing gross error. So, which solution is more valid? Is there a better solution?
Which, if either, solution is more probable?

12. Open-Ended Problem GOOD LUCK! Hints: Only 1 heat balance required.
“Tune” model uncertainties and examine results.
Try both nonlinear and bilinear approaches.
Always strive for the lowest possible objective function!!!
GOOD LUCK!