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Fuels oxidation chemistry

Fuels oxidation chemistry. Module B , Section 3 This course was developed by: Edward S. Blurock (Lund University) Gladys Moréac (Lund University). E ngines. CO. An EC funded NoE on Energy Conversion in Engines. Outline. Mechanism Generation Reactive Center and Reaction Generation

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Fuels oxidation chemistry

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  1. Fuels oxidation chemistry • Module B, Section 3 • This course was developed by: • Edward S. Blurock (Lund University) • Gladys Moréac (Lund University) Engines CO An EC funded NoE on Energy Conversion in Engines

  2. Outline • Mechanism Generation • Reactive Center and Reaction Generation • Complete Mechanism Generation • Optimization • Mechanism Reduction • Lumping • Skeletal • Phase Optimized Mechanisms • QSSA Reduced Mechanisms • Tabulation Methods • Mechanism Optimization • Automatic Reaction Coefficient Optimization

  3. Mechanism Generation • Single Reaction Generation • Generic Reaction Classes • Definition of Reactive Center and Environment • Application of Reaction Class to Species • Recognition of reactive center • Application of bond/valence changes • Reaction Pathways • Sub-Mechanisms • Complete Mechanism Generation • Exhaustive Application of Reaction Classes • Filtering of unwanted reactions • Controlled Generation • Generate only a fixed path of reactions

  4. Mechanism Generation • Why automatic generation? • Detailed mechanisms of large hydrocarbons too large and too complex now to do by hand • Hundreds to thousands of species and reactions • Automation is another level of thinking • Not thinking of individual species and reactions • Rather classes of species and reactions • Classes: • Groups of reactions and species with similar properties

  5. Single Reaction Generation • Key Concept • Reaction Center • The set of bonds and atom valences that change in the course of a reaction Generic Loss of Radical to Form Olefin Generic Group Replaced by an Oxygen

  6. Single Reaction Generation • Reaction Pattern • Supplemented with the Environment around Center • (Functional Groups which can effect reaction rate) Peroxyl Group Influence on bonding Include Bonding of Carbon

  7. Single Reaction Generation • Correspondence Between Reactants and Products • Determines how the bonding and atom valences are changed in the course of the reaction • The Reactive Center Changes • The surrounding functional Groups are unchanged

  8. Single Reaction Generation • Reaction Formation • Match Reactant of Reaction Pattern with Reactant Correspondence to Pattern Rest of Reactant

  9. Single Reaction Generation • Reaction Formation • Change as Specified in the Reactive Center • The changes specified by the Pattern • Are Performed on the Reactant CH3CH2CH2CHCH2OOH CH3CH2CHCH2 + OOH

  10. Mechanism Generation • Single Reaction Generation • Generic Reaction Classes • Definition of Reactive Center and Environment • Application of Reaction Class to Species • Recognition of reactive center • Application of bond/valence changes • Reaction Pathways • Sub-Mechanisms • Complete Mechanism Generation • Exhaustive Application of Reaction Classes • Filtering of unwanted reactions • Controlled Generation • Generate only a fixed path of reactions

  11. Reaction Pathway R + O = R. +OH CH3CH2CH2CH3 + O = .CH2CH2CH2CH3 R. + O2 = ROO. CH2CH2CH2CH3 + O2 = OOCH2CH2CH2CH3 ROO. = .QOOH .OOCH2CH2CH2CH3 = HOOCH2CHCH2CH3 .QOOH + O2 = OOQOOH HOOCH2CHCH2CH3 = HOOCH2CH(OO)CH2CH3 OOQOOH = OQOOH HOOCH2CH(OO)CH2CH3 = CHOC(OOH)CH2CH3 + OH OQOOH = products + OH CHOC(OOH)CH2CH3 = OH + products

  12. Reaction Pathway A Sequence generates a sub-mechanism tree of reactions

  13. Mechanism Generation • Single Reaction Generation • Generic Reaction Classes • Definition of Reactive Center and Environment • Application of Reaction Class to Species • Recognition of reactive center • Application of bond/valence changes • Reaction Pathways • Sub-Mechanisms • Complete Mechanism Generation • Exhaustive Application of Reaction Classes • Filtering of unwanted reactions • Controlled Generation • Generate only a fixed path of reactions

  14. Generation of Mechanism • The Problem of the Combinatorial Explosion • In principle • everything can react with everything • in a multitude of ways • A large part of detailed mechanism production • Is deciding what is important and what is not • The decision of how large the mechanism can be depends on how it is going to be used.

  15. Generation of Mechanism • Multiple Applications of Reaction Classes on Species • Question: • On which species do you apply the reaction classes? • Exhaustive with Filtering: • Apply the reaction classes to all species. Filter out unreasonable reactions. • Repeat on the all products. • Controlled: • Define a set of sequences of reaction classes. • Apply the seed molecule to the first reaction class. • For the rest, only apply the previous products to the next reaction class in the sequence.

  16. Exhaustive with Filtering • For all reaction classes For all species currently present • Generate a Single Reaction • Determine whether reaction is reasonable • Yes: Add products to next list of species and add reaction to list of reactions • No: Add Nothing • In a sense, this is the way ‘nature’ does it.

  17. Exhaustive with Filtering The key to the success of this is the filtering out of unreasonable reactions. This is closer to what nature does (nature’s filter is, of course, perfect). Can create very large mechanisms (depending on filter/accuracy) These are biased by the modeler only in the description of the reaction classes. Complete chemistry is described. Could enhance prediction and new pathways

  18. Exhaustive with Filtering • Example: NETGEN • Rate-Based Generation Criterion • Rchar : Characteristic rate (maximum rate of formation of all species) • Rmin = eRchar : Minimum rate allowed (e determines range) • Species kept in mechanism if rate of formation greater than Rmin • Examples: • De Witt, M.J., Dooling, D.J., Broadbelt, L.J, Ind. Eng. Chem. Res., 39, 2228-2237 (2000) • Tetradecane pyrolysis: large extensive mechanisms • Grenda J.M., Androulaktis, I.P., Dean, A.M., Green Jr., W.H., Ind. Eng. Chem. Res,42, 1000-1010 (2003) • Pressure dependent reactions through cycloalkyl intermediates • Use of Quantum Rice-Ramsperger-Kassel (QRRK) for pressure dependence

  19. Controlled Generation • Define a set of reaction pathways to make up the mechanism • Establish the set of seed molecules • For each seed and each pathway : • Apply the seed species to the first step of pathway • Apply the products of the last step to the next step in the pathway • Repeat 2 until no more steps in the pathway • The set of species and reactions make up this sub-mechanism • Combine the set of sub-mechanisms together to form the final generated mechanism • Check for species and reaction correspondences between submechanisms • Include only the unique set of species and reactions • Combine the final generated mechanism with Base mechanism • Check for species and reaction correspondences between submechanisms • Include only the unique set of species and reactions

  20. Controlled Generation • Each Pathway Represents a Submechanism

  21. Controlled Generation • A • seed molecule • applied to a specific • Pathway • Is a • Sub-Mechanism • All the sub-mechanisms are combined into one • Generated mechanism

  22. Controlled Generation • Efficient and Compact Mechanisms: • Controlled Generation allows complex chemistry to be introduced with relatively small mechanisms for large hydrocarbons • Interactive Artificial Intelligence Approach • It basically mimics how a modeler would generate a mechanism by hand • The processes are automated • The details are left to the automation process • Higher Level of Thinking • Modeler thinking in terms of classes of species and reactions • The mechanism is organized in pathways and submechanism • The individual reactions are transparent to the modeler

  23. Outline • Mechanism Generation • Reactive Center and Reaction Generation • Complete Mechanism Generation • Optimization • Mechanism Reduction • Lumping • Skeletal • Phase Optimized Mechanisms • QSSA Reduced Mechanisms • Tabulation Methods • Mechanism Optimization • Automatic Reaction Coefficient Optimization

  24. Mechanism Reduction • There is a trade-off between complexity and detail of model and computational time. • Often mechanisms are used to calculate the chemical source terms within larger more complex computations • (Computational Fluid Dynamics) • Goal: • Transform to computationally simpler form

  25. Mechanism Reduction • Goal: To reproduce the details of the complex mechanism in an equivalent small mechanism. • Techniques: • Condense: Condense the information to a computationally compact form (Lumping) • Limit Conditions: Under a limited set of conditions, eliminate unused portions of the mechanism are eliminated (Skeletal,POSM) • Tabulation: In local regions of source term space, approximations are tabulated (PRISM, ISAT, Flamelets) • Reformulate: Reformulation of the source term equations to computationally simpler form (QSSA, CSP) • Progress Variables: Use of a reduced number of coordinates to access source term state information • Combinations: Hybrids of the above

  26. Outline • Mechanism Generation • Reactive Center and Reaction Generation • Complete Mechanism Generation • Optimization • Mechanism Reduction • Lumping • Skeletal • Phase Optimized Mechanisms • QSSA Reduced Mechanisms • Tabulation Methods • Mechanism Optimization • Automatic Reaction Coefficient Optimization

  27. Mechanism Reduction: Lumping • For the most part, the calculation of the differential equations associated with source terms goes with the cube of the number of species involved. • Reduce the number of species by combining • equivalent species together • The definition of equivalent • depends on the level of modeling

  28. Lumped species in n-heptane Mechanism Schematic representation for the lumping of four different 5-ring alkylperoxy radicals 5r-C7H14OOH

  29. Lumped species in n-heptane Mechanism Concentration of Species Lumped Together Add to Single Lumped Species 6r-QOOH Species RO2 Species p = 40bar,  = 1.0, T = 800K

  30. Lumped Mechanism : n-heptane Detailed n-C7H16 1624 reactions 203 species L-C7H15 Detailed 1624 reactions 203 species L-C7H15O2 A-5r A-6r A-7r A-8r B-5r B-6r B-7r B-8r C-5r C-6r C-7r C-8r A = C7H14OOH, B = HOO-C7H14O2, C = O-C7H13OOH and D = Carbonyl + OH L = Lumped species, 5r, 6r, 7r and 8r represent the size of the ring D-5r D-6r D-7r D-8r 1-2 = 1 position of OOH and 2 is radical site 1362 reactions 142 species

  31. Lumped Mechanism – Same As Detailed Laminar flame speed for n-heptane/air mixture at p=1 bar and Ti=298K Davis and Law Experimental data (symbols) Detailed mechanism (solid line) Lumped mechanism (dashed line)

  32. Outline • Mechanism Generation • Reactive Center and Reaction Generation • Complete Mechanism Generation • Optimization • Mechanism Reduction • Lumping • Skeletal • Phase Optimized Mechanisms • QSSA Reduced Mechanisms • Tabulation Methods • Mechanism Optimization • Automatic Reaction Coefficient Optimization

  33. Mechanism Reduction: Skeletal Validity under Limit Conditions Under a limited set of conditions (which can be quite extensive), unused species of the mechanism are eliminated Unused Criteria Through post-processing of detailed mechanism determine the species which, if eliminated will not effect the final results

  34. Skeletal Mechanisms: Criteria Necessity Analysis: A single parameter indicating the extend a species is used within a mechanism Based on: If a species is determined to be ‘not necessary’ for entire range of validity, then it is eliminated from the mechanism • Reaction flow analysis • Gives the atomic mass flow through the given reactions. • Sensitivity Analysis • Finds important (sensitive) species for the wanted results.

  35. Skeleton Mechanism : n-heptane Detailed n-C7H16 n-C7H16 L-C7H15 L-C7H15 1362 reactions 142 species Lumped 1624 reactions 203 species Lumped L-C7H15O2 L-C7H15O2 n n n n - - - - C C C C H H H H 7 7 7 7 16 16 16 16 1362 reactions 1362 reactions L L L L - - - - C C C C H H H H 142 species 142 species 7 7 7 7 15 15 15 15 A-5r A-6r A-7r A-8r A-5r A-6r A-7r L L L L - - - - C C C C H H H H O O O O 7 7 7 7 15 15 15 15 2 2 2 2 A A A A - - - - 5r 5r 5r 5r A A A A - - - - 6r 6r 6r 6r A A A A - - - - 7r 7r 7r 7r A A A A - - - - 8r 8r 8r 8r B-5r B-5r B-6r B-6r B-7r B-7r B-8r B B B B - - - - 5r 5r 5r 5r B B B B - - - - 6r 6r 6r 6r B B B B - - - - 7r 7r 7r 7r B B B B - - - - 8r 8r 8r 8r C C C C - - - - 5r 5r 5r 5r C C C C - - - - 6r 6r 6r 6r C C C C - - - - 7r 7r 7r 7r C C C C - - - - 8r 8r 8r 8r C-5r C-6r C-7r C-5r C-6r C-7r C-8r D D D D - - - - 5r 5r 5r 5r D D D D - - - - 6r 6r 6r 6r D D D D - - - - 7r 7r 7r 7r D D D D - - - - 8r 8r 8r 8r L = Lumped species, 5r, 6r, 7r and 8r represent L = Lumped species, 5r, 6r, 7r and 8r represent L = Lumped species, 5r, 6r, 7r and 8r represent L = Lumped species, 5r, 6r, 7r and 8r represent the size of the ring D-5r D-5r D-6r D-6r D-7r D-7r D-8r the size of the ring the size of the ring the size of the ring 470 reactions 64 species

  36. Outline • Mechanism Generation • Reactive Center and Reaction Generation • Complete Mechanism Generation • Optimization • Mechanism Reduction • Lumping • Skeletal • Phase Optimized Mechanisms • QSSA Reduced Mechanisms • Tabulation Methods • Mechanism Optimization • Automatic Reaction Coefficient Optimization

  37. Mechanism Reduction: POSM • Phase Optimized Skeletal Mechanism • Recognition that a combustion process goes through phases and in each phase an even more reduced skeletal mechanism used • Phases determined automatically through machine learning clustering techniques with necessity parameter as base • Simple recognition function to determine in which phase the process is in is determined by a decision tree machine learning technique • Results translated to FORTRAN routines

  38. Phase Optimized Skeletal Mechanism • Heptane-Toluene Mechanism • Original Full Skeleton Mechanism 126 Species • Five Combustion Phases Determined • Initial Phase: 76 Species • Pre-Ignition: 85 Species • Ignition Phase Before: 90 Species • Ignition Phase After: 100 Species • Post Ignition Phase: 51 Species • Speed up factor of 3 to 10 • Tunèr, M., Blurock, E. S. and Mauss, F., Accepted for publication in conference, Power Train and Fluid Systems, SAE 2005.

  39. Mechanism Reduction: Tabulation • Divide up source term space into very local regions and use a local approximation for each region • Build up set of local regions dynamically during calculation • If a new point, set up a local approximation • If an existing point, use approximation • Dynamically set up a tree search structure to address local regions • Given a point, the tree search structure allows efficient access to appropriate local approximation

  40. Outline • Mechanism Generation • Reactive Center and Reaction Generation • Complete Mechanism Generation • Optimization • Mechanism Reduction • Lumping • Skeletal • Phase Optimized Mechanisms • QSSA Reduced Mechanisms • Tabulation Methods • Mechanism Optimization • Automatic Reaction Coefficient Optimization

  41. Quasi-Steady State Assumption • Class of Methods: Time Scale Decomposition • Separation of fast and slow processes • Fast processes of full phase space fall into (slow) lower dimensional manifold • Decoupling (two sets of equations) of system into fast and slow modes • Quasi-Steady State Assumption: • Some Species are in equilibrium (dC/dt=0) • Formation and Consumption are relatively fast reactions • Their solution can be calculated algebraically instead of solving the differential equations

  42. Outline • Mechanism Generation • Reactive Center and Reaction Generation • Complete Mechanism Generation • Optimization • Mechanism Reduction • Lumping • Skeletal • Phase Optimized Mechanisms • QSSA Reduced Mechanisms • Tabulation Methods • Mechanism Optimization • Automatic Reaction Coefficient Optimization

  43. Mechanism Reduction: Tabulation • ISAT: First Order Polynomial Approximation • Pope, S., Combust. Theory Modelling 1:41-63 (1997) • PRISM: Second Order Polynomial Approximation • Frenklach, M., Wang, H. and Rabinowitz, M., Energy Combust. Sci 18:47-73 (1992) • Blurock, E. S., Lehtiniemi, H., Mauss, F. and Gogan, A., • Berichte der Energie und Varfahrenstechnik (2005) • Combination: First and Second Order Combined • Ebenezer, N., Blurock, E. S. and Mauss, F., • 4th Mediterranean Combustion Symposium (2005)

  44. Outline • Mechanism Generation • Reactive Center and Reaction Generation • Complete Mechanism Generation • Optimization • Mechanism Reduction • Lumping • Skeletal • Phase Optimized Mechanisms • QSSA Reduced Mechanisms • Tabulation Methods • Mechanism Optimization • Automatic Reaction Coefficient Optimization

  45. Temperature Exponent Frequency Factor Activation Energy Optimization of Rate Coefficients

  46. y Optimization of Rate Coefficients Frenklach, M., Wang H. and Rabinovitz, M. J., "Optimization and Analysis of Large Chemical Kinetic Mechanism using the Solution Mapping Method - Combustion of Ethane". Prog. Energy Combustion Sci., 1992. 18: p. 47-73. Function to Optimize Model – Experimental Data Response Surface

  47. Reduction-Optimization Cycle

  48. Reduction-Optimization Cycle Experiment (line), Original (black dots), Optimized (red triangles), Over-Reduced (white dots) Re-Optimized (purple x) target values.

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