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COMBINATORIAL FRAMEWORK FOR PROCESS DESIGN AND SYNTHESIS

COMBINATORIAL FRAMEWORK FOR PROCESS DESIGN AND SYNTHESIS. Haryo Tomo adopted from Process Synthesis Lecture by Univ. Panonia Veszprem, Hungary. OUTLINE. General Introduction Approaches to Solve Process Design and Operations Problems Component Problems of Process Design and Operations

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COMBINATORIAL FRAMEWORK FOR PROCESS DESIGN AND SYNTHESIS

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  1. COMBINATORIAL FRAMEWORK FOR PROCESS DESIGN AND SYNTHESIS HaryoTomo adopted from Process Synthesis Lecture by Univ. Panonia Veszprem, Hungary

  2. OUTLINE • General Introduction • Approaches to Solve Process Design and Operations Problems • Component Problems of Process Design and Operations • Process Design Problems • Combinatorial Tools for Process Design • P-graph representation • Axioms of Combinatorially Feasible Structures • Combinatorial Algorithms • MSG for Generating the Superstructure • Structural Mappings • SSG for Generating Combinatorially Feasible Structures • Decision Mapping

  3. General Philosophyin Solving Process Design and Operations Problems • Conventional Approach • Conventional Mathematical Programming • Algorithmic Process Synthesis • Superstructure Concept • Rigorous Superstructure

  4. Conventional Approach to Solve Process Design and Operations Problems • Formulation as a general mathematical programming problem (e.g., LP, MILP, MINLP, NLP) • Application of a general-purpose solver (e.g., GAMS)

  5. Conventional Mathematical Programming Mathematical programming problem (objective function, constraints) General purpose solver Optimal solution

  6. Difficulty Process synthesis problems are not specified as standard optimization problems

  7. Process Synthesis Problem • Given: • set of products, • set of raw materials, • mathematical models of the operating units • Generate: • optimal process or • n-best processes or • every feasible process • Optimality criteria: • cost, waste generation, controllability, risk, or • combinations of them

  8. Algorithmic Process Synthesis Cost function and constraints for the operating units, raw materials, and products Model generation: Synthesis (Generating LP, MILP, MINLP, or NLP model) Mathematical programming model Solution: Analysis(Mathematical programming method) Optimal solution

  9. Question How to generate and how to solve the mathematical programming model?

  10. Algorithmic Process Synthesis Cost function and constraints for the operating units, raw materials, and products Model generation Generation of the Superstructure Generation of the mathematical model based on the Superstructure Mathematical programming model Solution of the model Optimal solution

  11. Question How to generate the superstructure?

  12. Rigorous Superstructure • Suppose that systematic procedure is available so that a valid mathematical programming model can be generated for a network of the given operating units • A network of operating units is defined to be a rigorous super-structure if the optimality of the resultant solution cannot be improved for any instance of the class of problems by any other procedure for network and model generation

  13. Multiscale Optimization • Classes of Process Synthesis Problems • Macroscopic • Mezoscopic • Microscopic • Systematic Hierarchical Approach • Algorithmic Synthesis of Supply Chains • Production Planning and Scheduling

  14. Levels of Abstraction • Industrial problems because of their complexity are examined in multiple levels of abstraction: • Macroscopic level: Elementary step: operating units • Mesoscopic level: Elementary step: equipments (Multiple equipments forms an operating unit.) • Microscopiclevel: Elementary step: physical / chemical / biochemical transformation (Inside one equipment.) - +

  15. Levels of Abstraction: Component Problems • Macroscopic level: Conceptual design • Reaction-Network Synthesis • Total-Flowsheet Synthesis • Mesoscopic level: • Separation-Network Synthesis • Heat-Exchanger-Network Synthesis • Scheduling • Process Control • Microscopiclevel: • Azetropic Distillation • Reaction Pathway Identification - +

  16. Macroscopic Level: Operating Units • Component problem: Total-Flowsheet Synthesis • Building blocks: operating unitsExample: ethylene direct chlorinating unit ethylenedichloride + water oxygen hydrocloric acid separating unit water ethylenedichloride + water ethylenedichloride -

  17. Macroscopic Level: Network of Operating Units chlorine ethylene oxygen hydrocloric acid Example: direct chlorinating unit oxychlorinatingunit separatingunit water pyrolyzingunit separatingunit vinyl chloride -

  18. Mesoscopic level: Equipments • Component problem: Separation-Network Syntehsis • Building blocks: equipmentsExample: distillation column hydrocloric acid vinyl chloride +hydrocloric acid +ethylenedichloride vinyl chloride +ethylenedichloride

  19. Mesoscopic level: Network of Equipments Example: implementing separating unit by two distillation columns separating unit hydrocloric acid vinyl chloride +hydrocloric acid +ethylenedichloride vinyl chloride ethylenedichloride

  20. Microscopic Level: Physical Transformations • Component problem: Heat-Exchanger-Network Synthesis • Building blocks: physical transformations Example: cooling heating +

  21. Microscopic Level:Network of Physical Transformations Example: distillation column with three distillation steps distillation column +

  22. COMBINATORIAL TECHNIQUE IN PROCESS DESIGN AND SYNTHESIS

  23. INTRODUCTION MINLP min g(x,y) s.t. f(x, y)£0 xÎÂn, yÎ{0, 1}m • Most MINLP model can not represent a practical problem. • Additional information is embedded implicitly in the model of a practical problem. • Idea: this information can effectively control the procedure.

  24. F F A A E E C C 1 1 D D 2 2 3 3 C C A A B B F F F F C C G K K 4 4 5 D J 6 F 7 7 H H G G D D H L L E 3 F F C 1 A 4 G D ILLUSTRATIVE EXAMPLE PNS 1 Operating units: Product: A Raw materials: E, G, J, K, L J 6 F Feasible flowsheet

  25. EXAMPLE PNS 1 Product: A Raw materials: E, G, J, K, L Plausible operating units

  26. Number of operating units: 7 binary variables: 7 combinations: 127 (=27-1)

  27. SYNTHESIS OF AN INDUSTRIAL PROCESS (EXAMPLE PNS 2) Product: A61 Raw materials: A1, A2, A3, A4, A6, A7, A8, A11, A15, A17, A18, A19, A20, A23, A27, A28, A29, A30, A34, A43, A47, A49, A52, A54

  28. PLAUSIBLE OPERATING UNITS

  29. PLAUSIBLE OPERATING UNITS (Cont’d)

  30. PLAUSIBLE OPERATING UNITS (Cont’d)

  31. Number of operating unit: 35 binary variables: 35 combinations: 34 billion subproblems at a B&B (worst case): 130 million

  32. SOURCE OF COMPLEXITY Combinatorial nature of the problem

  33. COMBINATORIAL TOOLS Our rigorous technique is based on combinatorics, especially, on the following items. • P-graph New structure representation. • Axioms The fundamental properties of combinatorially feasible process structures (e.g., every operating unit has at least one path leading to a product). • Algorithms Effective and rigorous combinatorial algorithms for process synthesis.

  34. STRUCTURAL REPRESENTATION • Simple directed graphs are incapable of providing an unambiguous representation in process synthesis. • Process graphs or P-graphs are introduced for structural representation in process synthesis.

  35. AMBIGUOUSGRAPHICAL REPRESENTATION: Digraph Case (1.1). Two different materials are produced separately, one by operating unit 02 and the other by operating unit 03. Moreover, it is necessary to feed both of these materials to operating unit 01 to generate the final product.Case (1.2). One material is produced by both operating units 02 and 03. This material is subsequently fed to operating unit Ol to generate the final product.

  36. AMBIGUOUSGRAPHICAL REPRESENTATION: Signal-flow graph Case (2.1). Two separate operating units, one receiving material B as its input and the other receiving material C as its input, produce the same material which is subsequently fed to another operating unit where material A (product) is generated.Case (2.2). A single operating unit, receiving materials B and C as its inputs, produces a material which is subsequently fed to another operating unit where material A (product) is generated.

  37. CONVENTIONAL AND P-GRAPH REPRESENTATION reactor distillation column P-graph reactor distillation column Formal definition

  38. UNAMBIGUOUSGRAPHICAL REPRESENTATION: P-graph P-graphs uniquely representing cases (1.2) and (2.1), case (2.2), case (1.1).

  39. A6 A6 A6 A3 A3 A3 A4 A4 A4 A14 A14 A7 A7 A8 A8 A18 A18 4 4 4 3 3 3 5 5 7 7 6 6 A15 A15 A27 A27 A28 A28 A29 A29 A30 A30 A2 A2 A13 A13 A10 A10 A12 A12 A17 A17 A19 A19 A16 A16 A20 A20 2 2 2 9 9 9 10 10 10 11 11 12 12 19 19 13 13 A25 A25 A9 A9 A32 A32 A34 A41 A41 A33 A33 A24 A24 A24 A31 A31 A26 A26 A11 A11 21 21 25 25 17 17 8 8 8 16 16 16 22 22 A43 A45 A45 A43 A21 A21 A51 A51 A37 A37 A54 A54 A38 A38 A46 A46 A23 A23 A36 A36 A50 A50 A39 A39 A44 A44 A22 A22 15 15 15 24 24 31 31 23 23 23 26 26 27 27 A48 A48 A52 A52 A53 A53 A1 A1 A56 A56 A49 A49 A47 A47 A55 A55 1 1 29 29 32 32 28 28 33 33 A58 A58 A5 A5 A57 A57 A61 A61 P-GRAPH REPRESENTATION OF A SYNTHESIS PROBLEM PNS 2 Notation:  material operating unit

  40. AXIOMS OF COMBINATORIALY FEASIBLE PROCESS STRUCTURES For given process synthesis problem, a P-graph satisfying the following five axioms is a combinatorially feasible structure. (S1) Every final product is represented in the structure. (S2) A material represented in the structure is a raw material if and only if it is not an output of any operating unit represented in the structure. (S3) Every operating unit represented in the structure is defined in the synthesis problem. (S4) Any operating unit represented in the structure has at least one path leading to a product. (S5) If a material belongs to the structure, it must be an input to or output from at least one operating unit represented in the structure.

  41. REDUCTION OF THE SEARCH SPACE Search Space Combinatorially Feasible Structures Feasible Structures

  42. D C E F G F 1 2 4 3 F A A B C D C G K L H J 5 7 6 D H F ILLUSTRATIVE EXAMPLE FOR THE COMBINATORIALLY FEASIBLE STRUCTURES:EXAMPLE PNS 1 Operating units given: Available raw materials: E, G, J, K, L Product: A

  43. J J 6 6 6 E E F F E E F F G G F F G E E F F F 3 3 3 3 4 4 4 4 3 D C C C C C C C D D C C D D 1 1 1 1 1 1 1 A A A A A A A A Solution #1 Solution #2 Solution #3 Solution #4 Solution #5 J J J L L K K 6 6 6 6 7 7 6 6 7 7 G G G E E F F F F G H H F H 3 3 4 4 4 4 5 5 4 4 5 C C D D C C D D D D D C 1 1 2 2 2 2 2 2 A A A A B B A A B B A A B B Solution #6 Solution #7 Solution #8 Solution #9 COMBINATORIALLY FEASIBLE STRUCTURES OF EXAMPLE PNS 1

  44. J K L L K 6 6 7 7 7 7 7 G E E F F H H G E G H F F F 3 5 4 4 3 3 3 5 C C D D C C C D D D 1 1 2 2 1 1 2 2 1 1 1 2 2 2 A A B B A A B B A A A B B B Solution #10 Solution #10 Solution #11 Solution #11 Solution #12 Solution #12 J L K J K L 6 6 7 7 6 6 7 7 G F F G G E E F F F F H H G F F H H 4 4 3 3 4 4 4 4 5 5 4 4 5 5 C C D D C C D D C C D D C C D D 1 1 2 2 1 1 2 2 1 1 2 2 1 1 2 2 A A B B A A B B A A B B A A B B Solution #16 Solution #13 Solution #14 Solution #15 Solution #15 COMBINATORIALLY FEASIBLE STRUCTURES OF EXAMPLE PNS 1 (Cont’d)

  45. K L J K L J 6 6 7 7 7 7 6 6 G G G E E F F H H E E F F H H E E F F 3 3 4 4 4 3 5 3 3 4 4 5 5 C C D D C C D D C C D D 1 1 2 2 1 1 2 2 1 1 2 2 A A B B A A B B A A B B Solution #17 Solution #18 Solution #19 Solution #19 COMBINATORIALLY FEASIBLE STRUCTURES OF EXAMPLE PNS 1 (Cont’d)

  46. SYNTHESIS OF AN INDUSTRIAL PROCESS(EXAMPLE PNS 2) Product: A61 Raw materials: A1, A2, A3, A4, A6, A7, A8, A11, A15, A17, A18, A19, A20, A23, A27, A28, A29, A30, A34, A43, A47, A49, A52, A54

  47. PLAUSIBLE OPERATING UNITS

  48. PLAUSIBLE OPERATING UNITS (Cont’d)

  49. PLAUSIBLE OPERATING UNITS (Cont’d)

  50. The five axioms reduce the 34 billion combinations of the operating units to 3,465 combinatorially feasible structures. The optimal solution is included in the set of 3465 feasible structures.

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