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Optimization in Chemical Processes: Formulation, Theory, and Applications

This chapter provides an overview of the uses of optimization, formulation of optimization problems, and an introduction to the course. It covers the nature and organization of optimization problems, the reasons to optimize, and the interdisciplinary field of optimization.

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Optimization in Chemical Processes: Formulation, Theory, and Applications

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

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

  3. 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 Chapter 1

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

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

  6. Chapter 1

  7. Chapter 1

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

  9. Chapter 1

  10. Chapter 1

  11. Chapter 1

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

  13. Chapter 1

  14. Chapter 1

  15. Chapter 1

  16. Chapter 1

  17. Material Balance Reconciliation Chapter 1

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

  19. Chapter 1

  20. THREE INGREDIENTS IN OPTIMIZATION PROBLEM Chapter 1

  21. Chapter 1

  22. TABLE 1 THE SIX STEPS USED TO SOLVE OPTIMIZATION PROBLEMS • 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). Chapter 1

  23. 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). Chapter 1

  24. 4. If the problem formulation is too large in scope: • Break it up into manageable parts and/or • 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. Chapter 1

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

  26. Step 2 develop objective function inventory, storage cost = k1D production cost = k2 + k3 D per run (set up operating cost) cost per unit (could be nonlinear) Chapter 1

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

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

  29. Chapter 1

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

  31. Chapter 1

  32. RELATIVE SENSITIVITY (Percentage change) Chapter 1

  33. PIPELINE PROBLEM Chapter 1

  34. Equality Constraints Chapter 1

  35. Chapter 1

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

  37. (constraint eliminated by substitution) Chapter 1

  38. optimum velocity non-viscous liquids 3 to 6 ft/sec. gases (effect of ρ) 30 to 60 ft/sec. at higher pressure, need to use different constraint (isothermal) Chapter 1 for large L, ln ( ) can be neglected exceptions: elevation changes, slurries (settling), extremely viscous oils (laminar flow, f different)

  39. Heat Exchanger Variables (given flow rate of one fluid, inlet temperatures, one outlet temp., phys. props.) • heat transfer area • heat duty • flow rates (shell, tube) • no. passes (shell, tube) • baffle spacing • length • diam. of shell, tubes • approach temperature • fluid A (shell or tube, co-current or countercurrent) • tube pitch, no. tubes • velocity (shell, tube) • ∆p (shell, tube) • heat transfer coeffs (shell, tube) • exchanger type (fins?) • material of construction Chapter 1

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