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Part 4 Nonlinear Programming

Part 4 Nonlinear Programming. 4.8 Examples. Example 1: Chemical Equilibrium. From thermodynamics of chemical reaction equilibrium , the equilibrium state of a closed system at constant temperature and pressure is the state at which its total Gibbs free energy is at a minimum.

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Part 4 Nonlinear Programming

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  1. Part 4 Nonlinear Programming 4.8 Examples

  2. Example 1: Chemical Equilibrium From thermodynamics of chemical reaction equilibrium, the equilibrium state of a closed system at constant temperature and pressure is the state at which its total Gibbs free energy is at a minimum. This criterion can be used to obtain the equilibrium composition of a given mixture by minimizing its free energy w.r.t. its composition.

  3. Given Data • An ideal gas mixture of 10 chemical species is maintained at T=298K and P=750Hg. • The 10 species are made of 3 atomic elements (e.g., H, O and C), and they are denoted as A, B and C. • The species formulas are:

  4. Gibbs free energy per mole of species s

  5. Total Gibbs Free Energy

  6. Total Number of Moles of Each Element

  7. NLP Model

  8. Linearly Constrained NLP Problem

  9. Example 2 Data Reconciliation

  10. Data Reconciliation

  11. Linearly Constrained NLP

  12. Always unknown!

  13. Case 1: Flows of streams 1, 2, 5 and 6 are measured Case 1 is a redundant and observable system.

  14. Case 2: Flows of streams 1 and 2 are measured Case 2 gives rise to a non-redundant observable system!

  15. Case 3: Flows of streams 1 and 6 are measured Case 3 is a redundant unobservable system.

  16. Table 2.2: Flow reconciliation of partially measured process

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