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Plenary Lecture, ESCAPE 19, Krakow, Poland, 14 – 17 June 2009

The Development of an Advanced Systems Synthesis Environment: Integration of MI(NL)P Methods and Tools for Sustainable Applications. Zdravko Kravanja University of Maribor, Faculty of Chemistry and Chemical Engineering, Smetanova 17, 2000 Maribor, Slovenia.

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Plenary Lecture, ESCAPE 19, Krakow, Poland, 14 – 17 June 2009

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  1. The Development of an Advanced Systems Synthesis Environment: Integration of MI(NL)P Methods and Tools for Sustainable Applications Zdravko Kravanja University of Maribor, Faculty of Chemistry and Chemical Engineering, Smetanova 17, 2000 Maribor, Slovenia Plenary Lecture, ESCAPE 19, Krakow, Poland, 14 – 17 June 2009

  2. Slovenia in pictures Area: 20,273 km2Population: 2.0 million Capital city: LjubljanaLanguage: Slovenian; also Italian and Hungarian in nationally mixed areasCurrency: EURO, €Member of EU - 1 May 2004 EU Presidency for 2008

  3. Environmental Performance Index (EPI) http://epi.yale.edu/CountryScores Slovenia has rank 15 Plenary Lecture, ESCAPE 19, Krakow, Poland, 14 – 17 June 2009

  4. Outline • Introduction • Process Synthesis and Sustainability, Challenges • Capabilities of an EO Modular MINLP Process Synthesizer MIPSYN • Aplications • Conclusion Plenary Lecture, ESCAPE 19, Krakow, Poland, 14 – 17 June 2009

  5. But thecreative principle resides in mathematics. In a certain sense, therefore, I hold true that pure thought can grasp reality, as the ancients dreamed. Albert Einstein Plenary Lecture, ESCAPE 19, Krakow, Poland, 14 – 17 June 2009

  6. Key idea for today and tomorrow In (bio)chemical supplay chain the traditional use of optimization techniques and tools is not sufficient unless its efficiency and applicationsare consistently upgraded with sustainable principles Plenary Lecture, ESCAPE 19, Krakow, Poland, 14 – 17 June 2009

  7. Creative Principles ofMathematical Programming Optimality Competitive advantage Feasibility Constraints satisfied IntegralitySimultaneous considerations Creative principles of MP enables: • Creation of new knowledge and • New innovative solutions Study of solutions enables one to get new insights,e.g. simultaneous HI also reduces raw material usage (Lang, Biegler, Grossmann, 1988). Plenary Lecture, ESCAPE 19, Krakow, Poland, 14 – 17 June 2009

  8. Introduction • Incentives for sustainabledevelopment • Main problems that have to be circumvented: • Population growth • Limited resources • Environmental and society destruction • How prevent the worming for 2oC in the next 2 decades?! • Answer: Sustainable development • New role of PSE: Sustainable PSE of paramount importance Plenary Lecture, ESCAPE 19, Krakow, Poland, 14 – 17 June 2009

  9. 3 X 3 Sustainability Matrix (M. F. Jischa, Chem. Eng. Technol. 21, 1998) 27 8 1 Figure 1: Diagonal asa measureof sustainability Plenary Lecture, ESCAPE 19, Krakow, Poland, 14 – 17 June 2009

  10. Environmental Aspects (Voss, 1994) Environmental constraints Opt. Criteria Material brought into the environment Carrying capacity of the ecosystem min emission of pollutant < -> Consummation rates of renewables Their regeneration rates max renewables < -> Non-renewable resources only if future generation would not be compromised min non-renewables -> In addition: Multiobjective approach Environmentally friendly innovation -> Plenary Lecture, ESCAPE 19, Krakow, Poland, 14 – 17 June 2009

  11. MINLP Model Formulation for Different Levels of Innovations: } • a) Objective function as a real-world economic function (cost benefit approach): • Max Profit = Production income - Raw material cost - Utility cost • - Investment cost – Environmental loss b) Equality constraints: mass and energy balances, design equations c) and d) Inequality constraints: product specifications, operational, environmental and feasibility constraints, logical disjunctive constraints for selection of sustainable alternatives Plenary Lecture, ESCAPE 19, Krakow, Poland, 14 – 17 June 2009

  12. Sustainable and Integrated (Bio)chemical Supply Chain Synthesis r 27 Sustainability 8 1 (Marquardt Wolfgang, Lars Von Wedel, and Birget Bayer.AspenWorld 2000, Orlando, FL, 2000) Fig.?? Figure 2: Diagonal asa measureof sustainability Plenary Lecture, ESCAPE 19, Krakow, Poland, 14 – 17 June 2009

  13. Sustainable Product-Process Synthesis “Synthesis is the automatic generation of design alternativesand the selection of the better ones based on incomplete information” A. W. Westerberg (1991) Extension: Sustainable product-process synthesisis theautomatic generation of design candidates and the multiobjective selection of the better ones based on the creative postulation of sustainable alternatives integraly accross the whole chemical supply chain. Plenary Lecture, ESCAPE 19, Krakow, Poland, 14 – 17 June 2009

  14. Many complex interactions Simultaneous Discrete and continuous decisionsMINLP Uncertainty Flexibility Dynamic systemsMIDNLP, multiperiod Rule-based decisions Logic-based Multicriterial Multiobjective Challenges Related to the Manifolds Nature of the Synthesis Problems Features Approach Plenary Lecture, ESCAPE 19, Krakow, Poland, 14 – 17 June 2009

  15. Simultaneous Synthesis and Heat Integration- Methanol Example Problem Figure 3: Methanol process and HEN superstructure Figure 4: Optimal process scheme with HI HEN • Process synthesis and: • sequential HEN synthesis: - 1,192,000 $/yr (loss!) • simultaneous HI by Duran-Grossmann’s model: - 292,000$ $/yr (loss!) • simultaneous HEN synthesis by Yee’s model: • Yee, Grossmann, Kravanja (1990)1,845,000 $/yr (profit!). • Kravanja and Grossmann (1994) 2,613,000 $/yr (profit!) Plenary Lecture, ESCAPE 19, Krakow, Poland, 14 – 17 June 2009

  16. Different Modeling Complexities Table 1: Types of optimization problems and models Kravanja Z., 2003, Chem. Biochem. Eng. Q. 17 (1), 1-3. Plenary Lecture, ESCAPE 19, Krakow, Poland, 14 – 17 June 2009

  17. Incentives for the development of MP-based tools for process synthesis: • Several general MINLP solvers www.gamsworld.org/minlp/solvers.html • Logic-based solver LOGMIP (Vecchietti and Grossmann, 1997) • Global MINLP Optimizer BARON (Sahinidis, 2000) • Almost no tool specialized in MINLP synthesis Plenary Lecture, ESCAPE 19, Krakow, Poland, 14 – 17 June 2009

  18. Capabilities of Mixed-Integer Process SYNthesizer MIPSYN Extension of PROSYN-MINLP Kravanja, Z. and I.E. Grossmann, Computers chem. Engng.,1990Kravanja, Z. and I.E. Grossmann, 1994 • Robustnes: • Interactive vs.Automated mode of execution • NLP initialization by a simple flowsheet simulation • Different NLP and MILP optimizers • Efficient handling of process superstructures • M/D strategy with alternative decomposition schemes of the superstructure • Multilevel MINLP strategies • Efficient handling of models: • Data- and topology independent modeling • Convex-hull and alternative convex-hull modeling formulation • Model generation from modules of process units and interconnection nodes • Simultaneous heat integration • Algorithmic power: • Different extensions of the OA algorithm • Different convexifications to prevent poor local solutions • Integer-infeasible path optimization • Higher-level capabilities: • Multiobjective synthesis • Multiperiod synthesis • Flexible synthesis in the presence of uncertain parameters Plenary Lecture, ESCAPE 19, Krakow, Poland, 14 – 17 June 2009

  19. MIPSYN and Logic Based OA Or when NLP is not imroving Plenary Lecture, ESCAPE 19, Krakow, Poland, 14 – 17 June 2009

  20. MIPSYN flowchart Topology P_STRUCT.DAT Components P_ COMPON.DAT Data P_DATA.DAT User’s modules MY_MODEL.DAT Model generator MIPSYN Libraries: AP/OA/ER - Process modules M/D - Components properties NLP initializer Simple simulator GAMS NLP solvers: CONOPT, MINOS, SQP MILP solver: CPLEX, OSL, Solution P_OPTIMUM.RES Procedure overview P_B.RES Plenary Lecture, ESCAPE 19, Krakow, Poland, 14 – 17 June 2009

  21. Chemical Engineering (MIPSYN) NLP optimization Process sybsystems Flowsheets MINLP synthesis: Reactor networks Separator networks Heat exchanger networks Overall HI process flowsheets Applications Different levels of problem abstraction and application • More general MINLP solver • Process synthesizer • Synthesizer shell for different domains Mechanical Engineering (TOP) NLP optimization • Timbes trases • Composite floor systems MINLP synthesis of mechanical structures: • Gates for hydropower dams • Steel frames • Steel buildings Plenary Lecture, ESCAPE 19, Krakow, Poland, 14 – 17 June 2009

  22. PROSYN-MINLP verion Plenary Lecture, ESCAPE 19, Krakow, Poland, 14 – 17 June 2009

  23. MipSyn β Version Plenary Lecture, ESCAPE 19, Krakow, Poland, 14 – 17 June 2009

  24. Multilevel-hierarchical MINLP Synthesis Combination of the hierarchical strategy and MINLP superstrucutre approach (Kravanja and Grossmann;1997) • MINLP 1: RCT network: • Detailed RCT network model • Simple SEP model • Simultaneous heat integration Tagret HI Identify SEP tastks Tagret HI • MINLP 2: SEP/RCT network: • Detailed RCT models • Detailed SEP models • Targeted heat integration Loop Identify process streams Profit UB STOP if UP≈LB HI • MINLP 3: HEN synthesis • Fixed RCT/SEP structure • Detailed RCT and SEP modules • Staged HEN synthesis model LB Identify SEP tastks Plenary Lecture, ESCAPE 19, Krakow, Poland, 14 – 17 June 2009

  25. MINLP 1: Initial Reactor Network and Simplified Separation Superstructure Plenary Lecture, ESCAPE 19, Krakow, Poland, 14 – 17 June 2009 HDA example

  26. MINLP 1 – Optimal Solution Identified separations Targeted HI Upper Bound 6.505 M$/yr Plenary Lecture, ESCAPE 19, Krakow, Poland, 14 – 17 June 2009

  27. MINLP 2: Detailed RCT and Identified SEP Plenary Lecture, ESCAPE 19, Krakow, Poland, 14 – 17 June 2009

  28. MINLP2: Optimal Solution Identified hot andcoldstreams Targeted HI Upper Bound 5.892 M$/yr Plenary Lecture, ESCAPE 19, Krakow, Poland, 14 – 17 June 2009

  29. MINLP 3: HEN Synthesis within Fixed Flowsheet Lower Bound 5.201 M$/yr Plenary Lecture, ESCAPE 19, Krakow, Poland, 14 – 17 June 2009

  30. MINLP 2 Resolved MINLP II resolved: UB = 5.240 M$/yr MINLP III: LB = 5.201 M$/yr STOP OPTIMAL SOLUTION: → Since UP≈LB Plenary Lecture, ESCAPE 19, Krakow, Poland, 14 – 17 June 2009

  31. Multilevel Synthesis of Mechanical Structure SYNTHESIS OF ROLLER HYDRAULIC STEEL GATE Hydroelectric Project Blanda, Iceland (S. Kravanja, A. Soršak, Z. Kravanja; 2003) MINLP1: topology optimization • relaxed standard dimensions • OAs accumulated for MINLP2 MINLP2: simultaneous topology and standard dimension optimization • discrete standard dimension • OAs accumulated for MINLP3 MINLP3: simultaneous topology, standard and rounded dimension • optimization and pre-screening • 10 discrete dimensions on each side from the optimal solution of MINLP2 LINKED MULTILEVEL HIERARCHICAL STRATEGY (LMHS) • Superstructure : • 2 main gate element • 4 to 6 horizontal girders • 5 to 9 vertical girders Plenary Lecture, ESCAPE 19, Krakow, Poland, 14 – 17 June 2009

  32. Optimal Structures Optimal solution: 8804 € Self-manufacturing costs of the erected gate: 13498 € 35% net profit 19622y! Plenary Lecture, ESCAPE 19, Krakow, Poland, 14 – 17 June 2009

  33. Optimal Synthesis Under Uncertainty • Statement: Engineering problems have in the practice much larger numbers of uncertain parameters than we can handle rigorously • Consequences: • Flexible but suboptimal (safety factors) • Optimal at nominal conditions but may be inoperable • Motivation: The synthesis and design of flexible and optimal engineering structure • Goal: An automated and robust strategy for problems with up to 100 ofuncertain parameters. Plenary Lecture, ESCAPE 19, Krakow, Poland, 14 – 17 June 2009

  34. MINLP Synthesis Under Uncertainty • Integration over space of Θ – stochastic optimization: EC or EP • 2NP feasibility constraints + 5NP Gaussian quadrature points Total:2NP+ 5NP Answer: Simplified approach Plenary Lecture, ESCAPE 19, Krakow, Poland, 14 – 17 June 2009

  35. Minimal Set of Feasibility Constraints Definition: Critical points are those the worst combinations of uncertain parameters that determine optimal oversizing of design variables needed to achieve desired flexibility • Extreme vertex points when the problem is convex No 2NP • A priory determination of Critical Points (Novak Pintarič and Kravnja, 2008) • Sequential scanning of all vertex points • Without sequential scanning of all vertex points • KKT based method (rigorous) • Iterative method • Approximate non-iterative method No= ND • Combination of Critical Points by using set covering problem No≤ ND (less than ND/5) Plenary Lecture, ESCAPE 19, Krakow, Poland, 14 – 17 June 2009

  36. Apriory Identification of Critical Pointsand Minimal Set of Feasibility Constraints Maximization of di NLPi • Drawback: approximative • Advantages: • Model size depend on the number of design variables • Robust • Can be applied to complex large-size process models • No ≤ ND (less than ND/5) Plenary Lecture, ESCAPE 19, Krakow, Poland, 14 – 17 June 2009

  37. Approximate Stochastic Optimization Approximate expected objective function in CBP Assure flexibility of design in min No CP Enforce approximate trade-offs Plenary Lecture, ESCAPE 19, Krakow, Poland, 14 – 17 June 2009

  38. Three-level MINLP Strategy for Flexible MINLP Synthesis MINLP level 1: Deterministic non-flexible synthesis at the nominal conditions MINLP levels 2 and 3: Flexible stochastic MINLP synthesis Significant reduction of problem's size! Flexibility analysis ot the final optimal solution Level2 Level3 Plenary Lecture, ESCAPE 19, Krakow, Poland, 14 – 17 June 2009

  39. Synthesis of Flexible Heat Integrated Methanol Process From Kravanja, Z., Grossmann, I. E. (1990). Updated prices • Structurealternatives: • Two feeds • One- ordouble stage compression of the feed • Two reactors • One- ordouble stage compression of the recycle stream • 8 y • HEN: • One-stage MINLP model • 4 hot and 2 cold process streams partitioned into several segments • 38 y for the selection of the matches Plenary Lecture, ESCAPE 19, Krakow, Poland, 14 – 17 June 2009

  40. Level 1: Deterministic Non-flexible Synthesis at the Nominal Conditions MINLP I HEN: 2 HEs and 2 coolers • Profit of 37.37 MUSD/yr • Not feasible if small deviations in the uncertain parameters from the nominal values Plenary Lecture, ESCAPE 19, Krakow, Poland, 14 – 17 June 2009

  41. Flexible MINLP Synthesis 27 uncertain parameters: Gauss distribution, 6 σ interval • Product demand (1) • Heat transfer coefficients (9) • Price for methanol (1) • Composition of the feeds for H2 • and CO (4) • Utility prices (3) • Raw material prices (2) • Temperature of the feeds (2) • Pressure of the feeds (2) • Conversion parameters for • reactors (2) • Compression efficiency (1) MINLP Level 2: Flexible MINLP synthesis at nominal condition • Only 4 critical vertices !!! • Profit reduced from 37.37 to 33.04 MUSD/a • The same optimal structure as deterministic one MINLP Level 3: Flexible MINLP synthesis at CBP • Profit reduced from 33.04 to 32.72MUSD/a • The same optimal structure Flexibility analysis:Flexibility index 1.000 Plenary Lecture, ESCAPE 19, Krakow, Poland, 14 – 17 June 2009

  42. Comparison Plenary Lecture, ESCAPE 19, Krakow, Poland, 14 – 17 June 2009

  43. Multiobjective Sustainable Process Synthesis Novak Pintarič and Kravanja, 2005 Two-step superstructural MINLP approach • 1steconomic-basedMINLP step for basic process superstructure that comprises technological end economical alternatives Base case solution • 2ndmultiobjective MINLP step for sustainable superstructure, augmented by additional environmental and other alternatives Sustainable solution • Strength: • Simultaneous approach • Numerous interactions exploited • Drawback: • Richness of the solution depends on • the abundance of alternatives Plenary Lecture, ESCAPE 19, Krakow, Poland, 14 – 17 June 2009

  44. Solution of the Multiobjective Multilevel MINLP Problem a) Weighted sum method: b)  -constraint method where: Relative economic index: Relative environmental index: Plenary Lecture, ESCAPE 19, Krakow, Poland, 14 – 17 June 2009

  45. Solution of the Multiobjective MINLPHDA Case Study 1st economic-basedMINLP step Fig. 8: Basic process superstructure Plenary Lecture, ESCAPE 19, Krakow, Poland, 14 – 17 June 2009

  46. HDA Case Study 1stEconomic-basedMINLP Step Fig. 2: Economically optimal process flowsheet – base case Plenary Lecture, ESCAPE 19, Krakow, Poland, 14 – 17 June 2009

  47. HDA Case Study 2stMultiobjective SustainableMINLP Step Recycling of diphenyle Heat integration Fig. 9: Superstructure, enlarged by sustainable alternatives Plenary Lecture, ESCAPE 19, Krakow, Poland, 14 – 17 June 2009

  48. HDA Case Study (Cont.) 2stMultiobjective SustainableMINLP Step Scalar parametric optimization: Relative profit Very good solutions ! Size of NLPs: 1400 variables 1300 constraints Size of MILPs: 55 binary, 2004 c. variables up to 2040 constraints 1/4h CPU on 1.8 GHz Intel Pentium M processor 1G RAM Relative environmental index Fig. 10: “Pareto curve” obtained by scalar parametric optimization Plenary Lecture, ESCAPE 19, Krakow, Poland, 14 – 17 June 2009

  49. Multiobjective Sustainable Process Synthesis • Alternatives withsynergistic effects on economic and environmental criteria. • More profitable and less environmentally harmful solution can be obtained • Most of alternatives do not show clear trends in their impacts on economic and environmental indicators. • Interactions can be very complex and unpredictable. • Importance of the simultaneous approach to the sustainable synthesis of process schemes. Plenary Lecture, ESCAPE 19, Krakow, Poland, 14 – 17 June 2009

  50. y=0,1 xLO xUP xa,UP= xUP Xa,LO=xLO 0 y=0 y=1 xLO xUP xS,LO=0 xS,UP= xUP Efficient MINLP model formulations Translation of variables (Ropotar and Kravanja; 2008, 2009) y = 0 → xa = xf xLO∙y ≤ xs ≤ xUP∙y: Declared: 0 ≤ xs ≤ xUP y=1 → xa = xs xs = xa – xf(1 – y) xf + (xLO – xf)y ≤ xa ≤ xf + (xUP – xf)y Declared:xLO ≤ xa ≤ xUP Fig1.a: In conventional discrete/continuous formulation Fig.1b: In alternative discrete/continuous formulation Plenary Lecture, ESCAPE 19, Krakow, Poland, 14 – 17 June 2009

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