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Tier 3: Open-Ended Problem

Tier 3: Open-Ended Problem. 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. F2 (EB). F7 (H). Reactor.

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Tier 3: Open-Ended Problem

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  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. F2 (EB) F7 (H) Reactor F6 (EB,W,S,H) Distillation Column F8 (EB,W,S) Condenser Liquid-Liquid Extractor F9 (EB,S) F4 (EB,W) F10 (S) F1 (EB) F5 (W) F3 (EB) Open-Ended Problem EB – Ethylbenzene (C8H10) W – Water (H2O) S – Styrene (C8H8) H – Hydrogen (H2)

  4. Open-Ended Problem Table 1: Raw Measurements and Variance for Flow Rates

  5. Open-Ended Problem Table 2: Raw Measurements and Variance for Mass Fractions

  6. Flow measurement devices are very old. Many gross errors suspected!! Open-Ended Problem The Problem: RECONCILE FLOWS AND MASS FRACTIONS

  7. Open-Ended Problem Possibly Useful Information: (Cp)EB(vapor) = 118 + 0.3T J/molºC (Cp)W(vapor) = 33.46 + 0.0069T J/molºC (T in ºC) Table 3: Temperatures for Various Streams

  8. 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 Open-Ended Problem Models with Uncertainty:

  9. (C8H10 C8H8 + H2) Open-Ended Problem Models with Uncertainty: • F6x6,EB = (1 - %C)(F4x4,EB) • F6x6,S = (%C)(0.98)(F4x4,EB) • F6x6,H = (%C)(0.02)(F4x4,EB) Calculate the variance of % conversion and the 3 reactor balances! Table 4: Conversion Percentages of Reactor

  10. Open-Ended Problem Table 5: Two Possibly Correct Solutions

  11. Solution #1 Gross errors present in measurements for F4, F5, F6, F8, and F10. Gross errors present in measurements for F2, F3, F7, F9, and F10. Solution #2 Open-Ended Problem Which, if either, solution is more probable?

  12. 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!

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