1. © Universidad de Guanajuato, Mexico © University of Ottawa, Canada, 2004 Tier 3: Open-Ended Problem

2. © Universidad de Guanajuato, Mexico © University of Ottawa, Canada, 2004 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. © Universidad de Guanajuato, Mexico © University of Ottawa, Canada, 2004 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) EB – Ethylbenzene (C 8 H 10 )W – Water (H 2 O) S – Styrene (C 8 H 8 )H – Hydrogen (H 2 ) Open-Ended Problem

4. © Universidad de Guanajuato, Mexico © University of Ottawa, Canada, 2004 VariableMeasurement (kg/h)Variance (kg/h) F1F1 1775 F2F2 3657 F3F3 5357 F4F4 414575 F5F5 364175 F6F6 414775 F7F7 4.10.2 F8F8 413575 F9F9 5427 F 10 1785 Open-Ended Problem Table 1: Raw Measurements and Variance for Flow Rates

5. © Universidad de Guanajuato, Mexico © University of Ottawa, Canada, 2004 VariableMeasurementVariance x 4,EB 0.1220.009 x 4,W 0.8770.009 x 6,EB 0.0810.009 x 6,W 0.8810.009 x 6,S 0.0460.009 x 6,H 0.001 x 8,EB 0.0800.009 x 8,W 0.7790.009 x 8,S 0.0450.009 x 9,EB 0.6560.009 x 9,S 0.3460.009 Open-Ended Problem Table 2: Raw Measurements and Variance for Mass Fractions

6. © Universidad de Guanajuato, Mexico © University of Ottawa, Canada, 2004 Open-Ended Problem The Problem: Flow measurement devices are very old. Many gross errors suspected!! RECONCILE FLOWS AND MASS FRACTIONS

7. © Universidad de Guanajuato, Mexico © University of Ottawa, Canada, 2004 Stream #Temperature in ºC (before heat exchanger) Temperature in ºC (after heat exchanger) 325500 4600 525700 6560 Open-Ended Problem Table 3: Temperatures for Various Streams Possibly Useful Information: (C p ) EB(vapor) = 118 + 0.3T J/molºC (C p ) W(vapor) = 33.46 + 0.0069T J/molºC (T in ºC)

8. © Universidad de Guanajuato, Mexico © University of Ottawa, Canada, 2004 Open-Ended Problem 1)F 7 = F 6 x 6,H 2)F 5 = F 8 x 8,W 3)F 8 x 8,EB = F 6 x 6,EB 4)F 8 x 8,S = F 6 x 6,S 5)F 8 x 8,W = F 6 x 6,W 6)F 9 x 9,EB = F 8 x 8,EB 7)F 9 x 9,S = F 8 x 8,S 8)F 10 = F 9 x 9,S 9)F 2 = F 9 x 9,EB Models with Uncertainty:

9. © Universidad de Guanajuato, Mexico © University of Ottawa, Canada, 2004 Trial #% Conversion 136 2 333 435 5 634 737 836 934 1034 1)F 6 x 6,EB = (1 - %C)(F 4 x 4,EB ) 2)F 6 x 6,S = (%C)(0.98)(F 4 x 4,EB ) 3)F 6 x 6,H = (%C)(0.02)(F 4 x 4,EB ) Open-Ended Problem Models with Uncertainty: (C 8 H 10 C 8 H 8 + H 2 ) Calculate the variance of % conversion and the 3 reactor balances! Table 4: Conversion Percentages of Reactor

10. © Universidad de Guanajuato, Mexico © University of Ottawa, Canada, 2004 Open-Ended Problem Solution #1Solution #2 Stream #Flow Rate (kg/hr) 1175 2365325 3540500 444664135 539263635 644664135 73.83.5 84462.24131.5 9536.2496.5 10185.2171.5 Table 5: Two Possibly Correct Solutions

11. © Universidad de Guanajuato, Mexico © University of Ottawa, Canada, 2004 Open-Ended Problem Solution #1 Solution #2 Gross errors present in measurements for F 4, F 5, F 6, F 8, and F 10. Gross errors present in measurements for F 2, F 3, F 7, F 9, and F 10. Which, if either, solution is more probable?

12. © Universidad de Guanajuato, Mexico © University of Ottawa, Canada, 2004 Open-Ended Problem 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!