1. Introducción a la Optimización de procesos químicos. Curso 2005/2006 PROBLEM SOLVING FOR OPTIMIZATION Decisions: 1. Purchase feed type A 2. Process feed to max. utilization of machinery Max Profit s.t. Max Rate Fi The results from the mathematical analysis must satisfy the needs in the real world! RealityModelResults interpretation Implementation

2. Introducción a la Optimización de procesos químicos. Curso 2005/2006 Before we begin this process, we will be confident that The problem involves optimization - Some degrees of freedom remain after safety, etc. A model-based approach is appropriate - Not an empirical approach The likely benefit is worth the effort - Answer is not obvious - Changes will likely yield substantial improvement PROBLEM SOLVING FOR OPTIMIZATION

3. Introducción a la Optimización de procesos químicos. Curso 2005/2006 PROB. SOLV. FOR OPTIMIZATION USING THE SIX-STEP PROBLEM SOLVING METHOD Its circular, not linear We look back after each step. 1 2 3 4 5 6 1 2 34 5 6 If step is complex, can apply all six steps inside one major step

4. Introducción a la Optimización de procesos químicos. Curso 2005/2006 PROB. SOLV. FOR OPTIMIZATION 1. Engage 2. Define a. Current, desired,deviation b. Define obj, constr., variables c. Define the scenarios 3. Explore a. Mental model b. Model variables c. Prior experience d. Qualitative aspects/bounds 4. Plan Solution a. Model-based, b. Model complexity 5. Do it a. Solution method b. Debug c. Evaluate scenarios d. Sensitivity analysis 6. Evaluate: Look back a. Meets goals? b. Extra benefits/problems? c. Develop heuristics d. Communicate & document

5. Introducción a la Optimización de procesos químicos. Curso 2005/2006 1. ENGAGE - Be confident and calm a.Read and listen to information from all stakeholders b.Do not be concerned about proposing silly solutions I want to and I can! PROB. SOLV. FOR OPTIMIZATION Manage your time; Apply your problem-solving skills, and Be confident!

6. Introducción a la Optimización de procesos químicos. Curso 2005/2006 2. DEFINE - Concentrate on the objective of the optimization study Do not force the problem definition to be suitable for a specific solution method at this step PROB. SOLV. FOR OPTIMIZATION I only know linear programming, so this must be an LP problem!

7. Introducción a la Optimización de procesos químicos. Curso 2005/2006 2. DEFINE - Concentrate on the objective of the optimization study (contd) a.Sketch the problem and label variables Observe the real system, if possible b.Confirm/establish goals with priorities. We must understand all goals more important than the objective function so that we will satisfy these: for example, - Safety - Product quality PROB. SOLV. FOR OPTIMIZATION

8. Introducción a la Optimización de procesos químicos. Curso 2005/2006 2. DEFINE - Concentrate on the objective of the optimization study (contd) c. Specify the following aspects of the problem: - objective function - variables to be predicted - number of degrees of freedom for optimization - inequality constraints You should be able to state these is words and explain them, as well as specify mathematical relationships d. Look for/eliminate inconsistencies PROB. SOLV. FOR OPTIMIZATION

9. Introducción a la Optimización de procesos químicos. Curso 2005/2006 2. DEFINE - Concentrate on the objective of the optimization study (contd) e.Define range of conditions to be investigated: production rates, product qualities, feed materials, economics, likely model errors (parametric and structural), solution variables (e.g., types of equipment, temperatures) steady-state or dynamic PROB. SOLV. FOR OPTIMIZATION

10. Introducción a la Optimización de procesos químicos. Curso 2005/2006 2. DEFINE - Concentrate on the objective of the optimization study (contd) f. Be sure that hard constraints are true. We can often violate normal policies or investment limits for a good reason. g. Define the desired solution in words h. Establish facts from opinions. Collect initial evidence. PROB. SOLV. FOR OPTIMIZATION

11. Introducción a la Optimización de procesos químicos. Curso 2005/2006 3. EXPLORE - Form a rich mental image of the problem a. See if you can determine qualitative aspects of the problem - define the system and likely balances - shape of the feasible region (operating window) - contours of the objective function - likely location of the optimum (interior or boundary) PROB. SOLV. FOR OPTIMIZATION In this step, use simple models to establish bounds on the possible solutions.

12. Introducción a la Optimización de procesos químicos. Curso 2005/2006 3. EXPLORE - Form a rich mental image of the problem (contd) b. Determine all of the variables needed to solve the optimization problem with sufficient accuracy, e.g., - Intermediate variables (concentration along a PFR) - Feed properties (which concentrations, enthalpy, etc.) - Environmental variables (cooling water) - physical properties (what accuracy?) Why? This will help when we formulate a model. PROB. SOLV. FOR OPTIMIZATION

13. Introducción a la Optimización de procesos químicos. Curso 2005/2006 3. EXPLORE - Form a rich mental image of the problem (contd) c. Challenge the assumption that optimization is needed. Try your best to find the solution using simple principles and models. - Why cant you solve the problem without the model? - What must the model tell you and with what accuracy? - Is there an obvious (sub-) optimal solution? - Can you determine the best values of a subset of the variables? d. Find relevant prior experience - Literature- Colleagues- Prior solutions PROB. SOLV. FOR OPTIMIZATION

14. Introducción a la Optimización de procesos químicos. Curso 2005/2006 PROB. SOLV. FOR OPTIMIZATION 4. PLAN - Formulate the optimization model Now, we make a major decision - the model formulation that determines the model accuracy! How accurate is good enough? We might have to formulate and solve the model perform a sensitivity analysis to determine whether the accuracy is good enough for the decisions if accuracy not acceptable, iterate with other model

15. Introducción a la Optimización de procesos químicos. Curso 2005/2006 PROB. SOLV. FOR OPTIMIZATION 4. PLAN - Formulate the optimization model 1. First, we need to decide the basic approach Does information for a model exist? Model-based optimization Empirical optimization N F T process must exist! experiments are costly more delay for modelling possible w/o model slow but presistent and accurate Lots of applications of both! New process can be investigated experiments are not needed model required fast if model exists depends on model accuracy Y

16. Introducción a la Optimización de procesos químicos. Curso 2005/2006 PROB. SOLV. FOR OPTIMIZATION 4. PLAN - Formulate the optimization model 2. Model complexity Model-based variables needed? Only input / output for each process Detailed, fundamental models Typically, models are greatly simplified models of complex processes Typically, models are based on fundamental balances, phys. prop., rate expressions, etc. These can be quite complex This is more accurate, but requires more time and $. Is it (1) possible and (2) required? Many intermediate variables

17. Introducción a la Optimización de procesos químicos. Curso 2005/2006 PROB. SOLV. FOR OPTIMIZATION 4. PLAN - Formulate the optimization model Input/output models LinearNon-linear Inputs = manipulated and disturbance variables Outputs = key dependent variables (flows, quality, energy consumption, etc.) This will yield a LP problem that can be solved reliably for large problems This will yield a non- linear optimization problem. Typically, the problem that can be solved reliably for large problems. (No promises for NL models!)

18. Introducción a la Optimización de procesos químicos. Curso 2005/2006 PROB. SOLV. FOR OPTIMIZATION 4. PLAN - Formulate the optimization model Linear I/O Models FD = 0.50F FB = F - FD Qrb = ( *2.2)F Qc = F(2.2) FD FDmax Represents standard operating conditions. Constraint models are approximate. These models can be determined from plant data or simplifications of fundamental models.

19. Introducción a la Optimización de procesos químicos. Curso 2005/2006 PROB. SOLV. FOR OPTIMIZATION 4. PLAN - Formulate the optimization model Non-linear I/O Models F = FD + FB F(XF) = FD(XD) + FB(XB) V = (RR+1) FD Qc = V Rm = [XD/XF- (1-XD)/(1-XF)]/(1- ) FD FDmax Model obeys fundamental balances and uses correlations for complex aspects of the process. Key non-linearities are represented, but model is not necessarily highly accurate. See EHL pg 453

20. Introducción a la Optimización de procesos químicos. Curso 2005/2006 PROB. SOLV. FOR OPTIMIZATION 4. PLAN - Formulate the optimization model Detailed, fundamental models Lumped Parameter Distributed Parameter Part. Diff. Equations ODE or PDE Ord. Diff. equations Algebraic equations s-s dynamic s-s PF Reactor CSTR

21. Introducción a la Optimización de procesos químicos. Curso 2005/2006 PROB. SOLV. FOR OPTIMIZATION 4. PLAN - Formulate the optimization model Mat. Balance on trays Component Mat. balance on trays Energy balance on trays Physical properties Heat exchangers Tray hydraulics (flooding) Can determine the best operation with high accuracy. Flooding constraints on individual trays can be modelled. The interaction between distillation and heat exchange can be optimized. Detailed, fundamental models

22. Introducción a la Optimización de procesos químicos. Curso 2005/2006 PROB. SOLV. FOR OPTIMIZATION 4. PLAN - Formulate the optimization model Before proceeding, we must check our formulation. 1.Does the model address the issues in Step 2, DEFINE? 2.Does the model contain the qualitative behaviors that you have predicted in Step 3, EXPLORE? 3.Is this solvable? Here is where we might have to compromise! Iterate between Steps 2 + 4 Iterate between Steps 3 + 4 Carefully evaluate the formulation to find reasonable simplifications.

23. Introducción a la Optimización de procesos químicos. Curso 2005/2006 PROB. SOLV. FOR OPTIMIZATION 5. DO IT - Solve the optimization problem a.Select a solution method. The chart below shows some criteria and selections for problems with continuous variables. Linear equations Non-linear with small problem, black-box model Non-linear with large problem, open equation model Linear Program Non-linear program using analytical derivatives Non-linear program using numerical derivatives

24. Introducción a la Optimización de procesos químicos. Curso 2005/2006 PROB. SOLV. FOR OPTIMIZATION 5. DO IT - Solve the optimization problem b.Select a software package. The chart below shows some criteria and selections for problems with continuous variables. Linear equations Non-linear with small problem, black-box model Non-linear with large problem, open equation model Linear Program Small - Excel Large - GAMS Non-linear program GAMS Non-linear program Using existing program: optimizer from library using the same language. e.g., MATLAB

25. Introducción a la Optimización de procesos químicos. Curso 2005/2006 PROB. SOLV. FOR OPTIMIZATION 5. DO IT - Solve the optimization problem c.Check your formulation and solution method: DEBUG. 1.Cross check solutions with previously published, other methods, qualitative understanding (from EXPLORE), changing convergence tolerances, etc. 2.Change the sign of the objective function - does the solution change? 3.Try other initial conditions (for NLP) 4.Check balances independently 5.Solve smaller parts of problem; then, combine.

26. Introducción a la Optimización de procesos químicos. Curso 2005/2006 PROB. SOLV. FOR OPTIMIZATION 5. DO IT - Solve the optimization problem d.Solve all scenarios specified in Step 2, DEFINE 1.Check solver diagnostics for lack of convergence, alternative solutions - anything not indicating unique optimum. 2.Collect results in side-by-side tables, so that you can see how variables and constraint activities change in scenarios. 3.Provide an explanation for every scenario - NEVER report the numbers alone! 4.Summarize the conclusions and likely benefits, if any, for implementing results

27. Introducción a la Optimización de procesos químicos. Curso 2005/2006 PROB. SOLV. FOR OPTIMIZATION 5. DO IT - Solve the optimization problem e.Build confidence in your results - concentrate on the decision variables 1.Assumptions - Does the solution obey all key assumptions, or have variables moved too far? 2.Sensitivity - Evaluate the sensitivity of the decisions and objective to changes in key parameters that are uncertain. 3. Relative importance - Evaluate the importance of each decision variable. Could you gain the benefits with a subset of opt. variables?

28. Introducción a la Optimización de procesos químicos. Curso 2005/2006 PROB. SOLV. FOR OPTIMIZATION 5. DO IT - Solve the optimization problem f.If you have the opportunity, implement the results 1.Potential Problem Analysis - Evaluate how these decisions influence other issues, including safety. How can problems be eliminated or mitigated? 2.Schedule - Develop a sequence for implementation. 3.Maintenance - Establish how the decisions will be maintained; in a plant, is control required? 4.Monitoring - Closely monitor the behavior to ensure that it follows the predictions of the analysis.

29. Introducción a la Optimización de procesos químicos. Curso 2005/2006 PROB. SOLV. FOR OPTIMIZATION 6. EVALUATE - Look back and learn a.Have you solved the problem? 1.Done? - Was the model and optimization approach appropriate? If not, must iterate with a different approach. - If the limit was accuracy, try more accurate model - If the limit was computing, try simpler model 2.Simple solution? - Now that you have optimization results, can you find a heuristic that would give similar results in the future without (or with limited) mathematical analysis?

30. Introducción a la Optimización de procesos químicos. Curso 2005/2006 PROB. SOLV. FOR OPTIMIZATION 6. EVALUATE - Look back and learn b.Check results of this problem 1.Consistency - Is the implementation consistent with all prior parts of the PS method? 2.Objective - Has the goal been achieved? If not, what factors have limited us? How can we improve further? 3.Engineering - What uncertainty in model structure or values has limited the achievements? 4.Unexpected factors - Have you encountered unexpected safety, legal, ethical issues?

31. Introducción a la Optimización de procesos químicos. Curso 2005/2006 PROB. SOLV. FOR OPTIMIZATION 6. EVALUATE - Look back and learn c.Guidelines (experience factors) for the future 1.Problem Insights - What have you learned about this problem that could be used in the future? - Model accuracy- Parameter uncertainty - Variables changed- Useful objective function 2.General Insights - What can be used in many problems? - Performance of optimization method - Performance of software - Sensitivity analysis

32. Introducción a la Optimización de procesos químicos. Curso 2005/2006 PROB. SOLV. FOR OPTIMIZATION 6. EVALUATE - Look back and learn d.Spreading the word 1.Engineering - How can you teach others about the use of optimization through this example? 2.Maintenance - How can we monitor, evaluate, decide when to optimize again? - Personnel training- Additional sensors - real-time calculations 3.Communication - How will you communicate these complex calculations to the people running the plant? What about management?