1. Mid Term Review Terry A. Ring CH EN 5253 Design II

2. WeekDayLecture TopicAssignments Due Date 112-JanCourse Overview LectureReview Chapters 7,8,9 14-JanReview of Project Economics Generation of Economics Spread Sheet HW 1 16-JanReview of Project EconomicsAttainable Rection - HW 2 219-JanMLK Holiday 21-Jan Review of Reactors - Selectivity & Heat EffectsSeparation Trains, HW 2 AssignedHW 1 23-JanAttainable Region 326-JanSeparations 28-JanDistillation TrainsHW-3 AssignedHW 2 30-JanSeparations and Reactors 42-FebReactor, Separation and Recycle 4-FebReactor, Separation and RecycleHW-4 AssignedHW 3 6-FebReactor, Separation and Recycle 59-FebHeat and Power Integration 11-FebHeat and Power IntegrationHW-5 AssignedHW 4 13-FebHeat and Power Integration 616-FebPresident's Day Holiday 18-FebOptimization on Process FlowsheetsHW-6 AssignedHW 5 20-FebEffects of Impurities on Reactors - HX 723-Feb Effects of Impurites on Separators, Recycle 25-FebPlantwide ControlHW-7 AssignedHW 6 27-FebPlantwide Control 82-MarReview for Exam 4-MarSequential Batch ProcessingHW 7 6-MarMid Term ExamExam

3. Reactor Heat Effects S,S&L Chapter 7

4. Managing Heat Effects Reaction Run Away –Exothermic Reaction Dies –Endothermic Preventing Explosions Preventing Stalling

5. Temperature Effects Thermodynamics/Equilibrium Kinetics

6. Unfavorable Equilibrium Increasing Temperature Increases the Rate Equilibrium Limits Conversion

7. Reactor with Heating or Cooling Q = UA ΔT

8. Best Temperature Path

9. Optimum Inlet Temperature Exothermic Rxn

10. Inter-stage Cooler Exothermic Equilibria Lowers Temp.

11. Inter-stage Cold Feed Exothermic Equilibria Lowers Temp Lowers Conversion

12. Reaction Selectivity Parallel Reactions –A+B  R (desired) –A  S Series Reactions –A  B  C(desired)  D Independent Reactions –A  B (desired) –C  D+E Series Parallel Reactions –A+B  C+D –A+C  E(desired) Mixing, Temperature and Pressure Effects

13. Rate Selectivity Parallel Reactions –A+B  R (desired) –A+B  S Rate Selectivity (α D - α U ) >1 make C A as large as possible (β D –β U )>1 make C B as large as possible (k D /k U )= (k oD /k oU )exp[-(E A-D -E A-U )/(RT)] –E A-D > E A-U T  –E A-D < E A-U T 

14. Reactor Design to Maximize Desired Product

15. Maximize Desired Product Series Reactions –A  B(desired)  C  D Plug Flow Reactor Optimum Time in Reactor

16. Real Reaction Systems More complicated than either –Series Reactions –Parallel Reactions Effects of equilibrium must be considered Confounding heat effects All have Reactor Design Implications

17. Engineering Tricks Reactor types –Multiple Reactors Mixtures of Reactors –Bypass –Recycle after Separation Split Feed Points/ Multiple Feed Points Diluents Temperature Management Sorted Out with Attainable Region Analysis

18. Attainable Region S,S&L Chapt. 7

19. Attainable Region Graphical method that is used to determine the entire space feasible concentrations Useful for identifying reactor configurations that will yield the optimal products

20. Procedure Step 1: Construct a trajectory for a PFR from the feed point, continuing to complete conversion or chemical equilibrium Step 2: When the PFR bounds a convex region, this constitutes a candidate AR. The procedure terminates if the rate vectors outside the candidate AR do not point back into it. Step 3: The PFR trajectory is expanded by linear arcs, representing mixing between the PFR effluent and the feed stream, extending the candidate AR. Step 4: Construct a CSTR trajectory to see if the AR can be extended. Place linear arcs, which represent mixing, on the CSTR trajectory to ensure the trajectory remains convex. Step 5: A PFR trajectory is drawn from the position where the mixing line meets the CSTR trajectory. If the PFR trajectory is convex, it extends the previous AR to form a expanded AR. Then return to step 2. Otherwise, repeat the procedure from Step 3.

21. Example Reactions Rate Equations

22. Step 1 Begin by constructing a trajectory for a PFR from the feed point, continuing to the complete conversion of A or chemical equilibrium Solve the PFR design equations numerically –Use the feed conditions as initial conditions to the o.d.e. –Adjust integration range,  (residence time), until complete conversion or to equilibrium

23. PFR Design Equations

24. Solve Numerically Runge-Kutta

25. Solve Numerically

26. Step 2 Plot the PFR trajectory from the previous results. Check to see if rate vectors outside AR point back into it (e.g. Look for non- convex regions on the curve. Tangent line passing (1,0)) Desired

27. Step 3 Expand the AR as much as possible with straight arcs that represent mixing of reactor effluent and feed stream PFR  (1-  )

28. Interpreting points on mixing line Larger Attainable Region PFR C A =0. 2187 C B =0.00011 C A =0.72 C B =0.00004 C A =1 C B =0  (1-  ) PFR C A =1 C B =0 (1-  )

29. Mixing of Streams Reactant Bypass Vector Equation, i component is C A, j component is C B α =fraction of mixture of stream 1in the mixed stream Feed mixing fraction:  = 0. 64

30. Step 4 If a mixing arc extends the attainable region on a PFR trajectory, check to see if a CSTR trajectory can extend the attainable region For CSTR trajectories that extend the attainable region, add mixing arcs to concave regions to ensure the attainable region remains convex Solve CSTR multiple NLE numerically –Vary  until all feed is consumed or equilibrium is reached

31. CSTR Design Equations

32. Solve numerically at various  until complete conversion or equilibrium is achieved

33. CSTR Extends Attainable Region CSTR

34. Plot extends attainable region i.c. for step 5 CSTR C A =1 C B =0  (1-  ) Enlarges Attainable Region

35. Possible Configuration at this point CSTR C A =1 C B =0  β PFR  β = 0  β = 0 1-α-β 0.38 β = 1 α = 0

36. Profit ($) = 15000*C B -15*C A 2 Optimal point not at highest selectivity PFR CSTR

37. Conclusions Need to know feed conditions AR graphical method is 2-D and limited to 2 independent species Systems with rate expressions involving more than 2 species need to be reduced –Atom balances are used to reduce independent species –Independent species = #molecular species - #atomic species If independent species < 2, AR can be used by Principle of Reaction Invariants

38. Separation Trains S, S&L Chapt. 8

39. Separation Methods Absorption Stripping Distillation Membrane Separations Crystallization etc

40. Use of Separation Units

41. Column Sequences No. of Columns –N c =P-1 P= No. of Products No. of Possible Column Sequences –N s =[2(P-1)]!/[P!(P-1)!] P= No. of Products –P=3, N c =2, N s =2 –P=4, N c =3, N s =5 –P=5, N c =4, N s =14 –P=6, N c =5, N s =42 –P=7, N c =6, N s =132 No. of Possible Column Sequences Blows up!

42. How do I evaluate which is best sequence?

43. Marginal Vapor Rate Marginal Annualized Cost~ Marginal Vapor Rate Marginal Annualized Cost proportional to –Reboiler Duty (Operating Cost) –Reboiler Area (Capital Cost) –Condenser Duty (Operating Cost) –Condenser Area (Capital Cost) –Diameter of Column (Capital Cost) Vapor Rate is proportional to all of the above

44. Selecting Multiple Column Separation Trains Minimum Cost for Separation Train will occur when you have a –Minimum of Total Vapor Flow Rate for all columns –R= 1.2 R min –V=D (R+1) V= Vapor Flow Rate D= Distillate Flow Rate R=Recycle Ratio

45. Azeotrope Conditions Conditions on the Activity Coefficient Minimum Boiling, γ j L > 1 Maximum Boiling, γ j L < 1 x j =y j, j=,1,2,…C

46. Raoult’s Law

47. Importance of Physical Property Data Set In all cases –Need sophisticated liquid phase model to accurately predict the activity coefficient for the liquid. For High Pressure Cases Only –Also need sophisticated (non-ideal) gas phase fugacity model

48. Multi-component Azeotropes Residue Curve Map –dx j /dť = dx j /d ln(L) = x j – y j Integrate from various starting points

49. Defining Conditions for Multi- component Azeotrope t goes from 0 to 1, ideal to non-ideal to find Azeotrope

50. Distillation X B, X F and Y D form a line for a Distillation Column Line can not cross Azeotrope line

51. Ethanol/Water Distillation with Benzene To Break Azeotrope

52. Pressure Swing to Break Azeotrope Temp. of Azeotrope vs. Pressure Mole Fraction of Azeotrope

53. Reactor-Separation Train- Recycle Chapt. 7&8

54. Trade-off between Reactor and Separator Factors –Reactor Conversion of limiting reactant Effects cost and size of Separation Train –Reactor Temperature and mode of operation (adiabatic, isothermal, etc.) Effect utility costs for separation and reaction Effect impurities from side reactions –High Reactor Pressure for Le Chatlier cases (less moles of product) Higher cost for recycle compression

55. Trade-off between Reactor and Separator Factors, cont. –Use of excess of one or more reactant to increase equilibrium conversion and/or reaction rate Increases cost of separation train –Use of diluents in adiabatic reactor to control temperature in reactor Increases cost of separations train –Use of purge to avoid difficult separation. Decreases the cost of separations Loss of reactants – increase cost of reactants May increased cost of reactor, depending on the purge-to- recycle ratio

56. Factors that effect recycle/purge Factor –Excess reactants Increases recycle flow Increases separation costs –Concentration of impurities to be purged Effects the recycle-to-purge ratio –Reactor outlet temperature and pressure Increase cost of utilities in separation Increase cost to recycle - compressor

57. Compare Recycle Concepts Costs Benefits

58. Feedback effects of Recycle Loop Small disturbance on feed Large effect on recycle flow rate/composition Snowball effect on reactor/separator

59. Heat Integration Chapter 9 Terry Ring University of Utah

60. Costs Heat Exchanger Purchase Cost – C P =K(Area) 0.6 Annual Cost –C A =i m [ΣC p,i + ΣC P,A,j ]+sF s +(cw)F cw i m =return on investment F s = Annual Flow of Steam, –$5.5/ston to $12.1/ston = s F cw =Annual Flow of Cold Water –$0.013/ston = cw

61. Lost Work = Lost Money Transfer Heat from T 1 to T 2 ΔT approach Temp. for Heat Exchanger T o = Temperature of Environment Use 1 st and 2 nd laws of Thermodynamics LW=QT o ΔT/(T 1 T 2 ) –ΔT=T 1 -T 2 –T o = Environment Temperature Q= UAΔT lm T1T1 T2T2 Q

62. Heat Integration Make list of HX Instead of using utilities can you use another stream to heat/cool any streams? How much of this can you do without causing operational problems? Can you use air to cool? –Air is a low cost coolant. Less utilities = smaller cost of operations

63. Terms HEN=Heat Exchanger Network MER=Maximum Energy Recovery Minimum Number of Heat Exchangers Threshold Approach Temperature Optimum Approach Temperature

64. Process

65. Minimize Utilities For 4 Streams

66. Adjust Hot Stream Temperatures to Give ΔT min

67. Enthalpy Differences for Temperature Intervals

68. Pinch Analysis Minimum Utilities

69. Pinch Analysis ΔT app MER values

70. How to combine hot with cold? At Pinch (temp touching pinch) –Above Pinch Connect C c ≥C h –Below Pinch Connect C h ≥C c Not touching Pinch temp. –No requirement for C c or C h

71. 4 Heat Exchanger HEN for Min. Utilities C c ≥C h C h ≥C c MER Values

72. Stream Splitting Two streams created from one one heat exchanger on each piece of split stream with couplings 1 1a 1b 1a 1

73. Optimization of HEN How does approach delta T (ΔT min ) effect the total cost of HEN? Q= UA ΔT LW=QT o ΔT/(T 1 T 2 ) –More Utility cost

74. Costs Heat Exchanger Purchase Cost – C P =K(Area) 0.6 Annual Cost –C A =i m [ΣC p,i + ΣC P,A,j ]+sF s +(cw)F cw i m =return on investment F s = Annual Flow of Steam, –$5.5/ston to $12.1/ston F cw =Annual Flow of Cold Water –$0.013/ston

76. Change ΔT min C P =K(Area) 0.6 Area=Q/(UF ΔT min ) More Lost Work LW=QToΔT/(T1T2)

77. Optimization of Process Flowsheets Chapter 24 Terry A. Ring CHEN 5353

78. Degrees of Freedom Over Specified Problem –Fitting Data –N variables >>N equations Equally Specified Problem –Units in Flow sheet –N variables =N equations Under Specified Problem –Optimization –N variables <<N equations

79. Optimization Number of Decision Variables –N D =N variables -N equations Objective Function is optimized with respect to N D Variables –Minimize Cost –Maximize Investor Rate of Return Subject To Constraints –Equality Constraints Mole fractions add to 1 –Inequality Constraints Reflux ratio is larger than R min –Upper and Lower Bounds Mole fraction is larger than zero and smaller than 1

80. PRACTICAL ASPECTS Design variables, need to be identified and kept free for manipulation by optimizer –e.g., in a distillation column, reflux ratio specification and distillate flow specification are degrees of freedom, rather than their actual values themselves Design variables should be selected AFTER ensuring that the objective function is sensitive to their values –e.g., the capital cost of a given column may be insensitive to the column feed temperature Do not use discrete-valued variables in gradient-based optimization as they lead to discontinuities in f(d)

81. Optimization Feasible Region –Unconstrained Optimization No constraints –Uni-modal –Multi-modal –Constrained Optimization Constraints –Slack –Binding

82. LINEAR PROGRAMING (LP) equality constraints inequality constraints objective function w.r.t. design variables The N D design variables, d, are adjusted to minimize f{x} while satisfying the constraints

83. EXAMPLE LP – GRAPHICAL SOLUTION A refinery uses two crude oils, with yields as below. Volumetric YieldsMax. Production Crude #1Crude #2(bbl/day) Gasoline70316,000 Kerosene692,400 Fuel Oil246012,000 The profit on processing each crude is: $2/bbl for Crude #1 and $1.4/bbl for Crude #2. a)What is the optimum daily processing rate for each grade? b)What is the optimum if 6,000 bbl/day of gasoline is needed?

84. EXAMPLE LP –SOLUTION (Cont’d) Step 1. Identify the variables. Let x 1 and x 2 be the daily production rates of Crude #1 and Crude #2. maximize Step 2. Select objective function. We need to maximize profit: Step 3. Develop models for process and constraints. Only constraints on the three products are given: Step 4. Simplification of model and objective function. Equality constraints are used to reduce the number of independent variables (N D = N V – N E ). Here N E = 0.

85. EXAMPLE LP –SOLUTION (Cont’d) Step 5. Compute optimum. a)Inequality constraints define feasible space. Feasible Space

86. EXAMPLE LP –SOLUTION (Cont’d) Step 5. Compute optimum. b)Constant J contours are positioned to find optimum. J = 10,000 J = 20,000 J = 27,097 x 1 = 0, x 2 = 19,355 bbl/day

87. EXAMPLE LP – GRAPHICAL SOLUTION A refinery uses two crude oils, with yields as below. Volumetric YieldsMax. Production Crude #1Crude #2(bbl/day) Gasoline70316,000 Kerosene692,400 Fuel Oil246012,000 The profit on processing each crude is: $2/bbl for Crude #1 and $1.4/bbl for Crude #2. a)What is the optimum daily processing rate for each grade? b)What is the optimum if 6,000 bbl/day of gasoline is needed?

88. Dealing with Impurities in Processes and Process Simulators ChEN 5253 Design II Terry A. Ring There is not chapter in the book on this subject

89. Impurity Effects Heat Exchange Reactors Separation Systems Recycle Loops

90. Impurities in Heat Exchange Impurities effect heat capacity –Lower C p Various options –Raise C p Increase H 2 Impurities effect the enthalpy of stream –Total heat of condensation is less due to impurity –Total heat of vaporization is less due to impurity

91. Impurities in Separation Trains Non-condensable Impurities –Build up in Distillation column – Big Trouble!! Condensable Impurities –Cause some products to be less pure May not meet product specifications Can not sell this product – Big Trouble!! –Rework cost –Waste it –Sell for lower price

92. Processes are tested for Impurity Tolerance Add light and heavy impurities to feed –Low concentration All impurities add to 0.1 % of feed (may need to increase Tolerance in Simulation) –Medium concentration All impurities add to 1% of feed –High concentration All impurities add to 10% of feed Find out where impurities end up in process Find out if process falls apart due to impurities –What purges are required to return process to function.

93. Impurities in Separation Trains It is important to know where the impurites will accumulate in the train Which products will be polluted by which impurities –Is that acceptable for sale of product?

94. Purging Impurities Find the point in the process where the impurities have the highest concentration –Put Purge here Put a purge in almost all recycle loops

95. Plant-Wide Controllability Control Architecture –DoF analysis Dynamic Analysis No. of valves –DoF analysis Steady State Analysis No. of valves – No. of liquid level loops Product Flow Control or Feed Flow Control Types of control –Single loop PID –Gain Scheduling –Ratio control –Cascade Control –Multi-variable control –Model Based control (MPC) –Override control

96. Distillation Control Types of Control –LV control –DV –LB –DB –(L/D)(V/B) –(L/F)(V/F)

97. The End