1. 1 Chapter 1 USES OF OPTIMIZATION FORMULATION OF OPTIMIZATION PROBLEMS OVERVIEW OF COURSE

2. 2 Chapter 1 OPTIMIZATION OF CHEMICAL PROCESSES T.F. EDGAR, D.M. HIMMELBLAU, and L.S. LASDON UNIVERSITY OF TEXAS MCGRAW-HILL – 2001 (2 nd ed.) PART I – PROBLEM FORMULATION II – OPTIMIZATION THEORY AND METHODS III – APPLICATIONS OF OPTIMIZATION APPENDICES (MATRIX OPERATIONS)

3. 3 Chapter 1 PHILOSOPHY OF BOOK Most undergraduates learn by seeing how a method is applied Practicing professionals need to be able to recognize when optimization should be applied (Problem formulation) Optimization algorithms for reasonably-sized problems are now fairly mature Focus on a few good techniques rather than encyclopedic coverage of algorithms

4. 4 Chapter 1 The Nature and Organization of Optimization Problems Chapter 1

5. 5 WHY OPTIMIZE? 1.Improved yields, reduced pollutants 2.Reduced energy consumption 3.Higher processing rates 4.Reduced maintenance, fewer shutdowns 5.Better understanding of process (simulation) But there are always positive and negative factors to be weighed

6. 6 Chapter 1

7. 7

8. 8 OPTIMIZATION Interdisciplinary Field Max Profit Min Cost Max Efficiency Requires 1.Critical analysis of process 2.Definition of performance objective 3.Prior experience (engr. judgment)

9. 9 Chapter 1

10. 10 Chapter 1

11. 11 Chapter 1

12. 12 Chapter 1 Figure E1.4-3 Optimal Reflux for Different Fuel Costs Flooding constraint Min reflux to achieve separation

13. 13 Chapter 1

14. 14 Chapter 1

15. 15 Chapter 1

16. 16 Chapter 1

17. 17 Chapter 1 Material Balance Reconciliation

18. 18 Chapter 1 Least squares solution: opt. m A is the “average” value any constraints on m A ?

19. 19 Chapter 1

20. 20 Chapter 1 THREE INGREDIENTS IN OPTIMIZATION PROBLEM

21. 21 Chapter 1

22. 22 Chapter 1 TABLE 1 THE SIX STEPS USED TO SOLVE OPTIMIZATION PROBLEMS 1.Analyze the process itself so that the process variables and specific characteristics of interest are defined, i.e., make a list of all of the variables. 2. Determine the criterion for optimization and specify the objective function in terms of the above variables together with coefficients. This step provides the performance model (sometimes called the economic model when appropriate).

23. 23 Chapter 1 3. Develop via mathematical expressions a valid process or equipment model that relates the input-output variables of the process and associated coefficients. Include both equality and inequality constraints. Use well-known physical principles (mass balances, energy balances), empirical relations, implicit concepts, and external restrictions. Identify the independent and dependent variables (number of degrees of freedom).

24. 24 Chapter 1 4. If the problem formulation is too large in scope: (A)Break it up into manageable parts and/or (B)Simplify the objective function 5. Apply a suitable optimization technique to the mathematical statement of the problem. 6. Check the answers and examine the sensitivity of the result to changes in the coefficients in the problem and the assumptions.

25. 25 Chapter 1 EXAMPLES – SIX STEPS OF OPTIMIZATION specialty chemical 100,000 bbl/yr. how many bbl produced per run? Step 1 define variables Q = total # bbl produced/yr (100,000) D = # bbl produced per run n = # runs/yr

26. 26 Chapter 1 Step 2 develop objective function inventory, storage cost = k 1 D production cost= k 2 + k 3 D per run (set up operating cost)cost per unit (could be nonlinear)

27. 27 Chapter 1 Step 3 evaluate constraints D>0 Step 4 simplification – none necessary

28. 28 Chapter 1 Step 5 computation of the optimum analytical vs. numerical solution

29. 29 Chapter 1

30. 30 Chapter 1 Step 6 Sensitivity of the optimum subst D opt into C

31. 31 Chapter 1

32. 32 Chapter 1 RELATIVE SENSITIVITY (Percentage change)

33. 33 Chapter 1 PIPELINE PROBLEM

34. 34 Chapter 1 Equality Constraints

35. 35 Chapter 1

36. 36 Chapter 1 min (C oper + C inv. ) subject to equality constraints need analytical formula for f substituting for ∆p,

37. 37 Chapter 1 (constraint eliminated by substitution)

38. 38 Chapter 1 optimum velocity non-viscous liquids3 to 6 ft/sec. gases (effect of ρ)30 to 60 ft/sec. at higher pressure, need to use different constraint (isothermal) for large L, ln ( ) can be neglected exceptions: elevation changes, slurries (settling), extremely viscous oils (laminar flow, f different)

39. 39 Chapter 1 Heat Exchanger Variables 1.heat transfer area 2.heat duty 3.flow rates (shell, tube) 4.no. passes (shell, tube) 5.baffle spacing 6.length 7.diam. of shell, tubes 8.approach temperature 9.fluid A (shell or tube, co-current or countercurrent) 10.tube pitch, no. tubes 11.velocity (shell, tube) 12.∆p (shell, tube) 13.heat transfer coeffs (shell, tube) 14.exchanger type (fins?) 15.material of construction (given flow rate of one fluid, inlet temperatures, one outlet temp., phys. props.)