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Chemical Kinetics
               Module B, Section 3
               This course was developed by:
               • Edward ...
Motivation
                   Chemical kinetics:
                   –Description of chemical oxidation behavior of
       ...
Purpose of Presentation
          An outline of the state of the art in modeling complex
            chemistry.
          ...
Why Model fuels ?
   Real fuel:
   - Diesel, Gasoline, Biofuels
   or Kerosene Fuels
   - Too complex to model
   using al...
Examples of model components
   Gasoline:
     - PRF (Primary Reference Fuels): iso-octane, n-heptane
     - mono-aromatic...
Examples of chemical model
  Global: One or very few reactions.
    “Shell Model” (5 species, 8 reactions).
       Halstea...
Mechanism structure
   Whether produced by hand or generated automatically,
   the structure of the mechanism is the same
...
Reaction Pathway
                       Classic low temperature alkane pathway
         Generic:                          ...
Sub-Mechanism
             A pathway generates a sub-mechanism tree of reactions




Engi  CO
       nes                  ...
Outline
       Detailed Mechanism Generation
              – Reactive Center and Reaction Generation
              – Compl...
Detailed Mechanism Generation
   Single Reaction Generation
      – Generic Reaction Classes
          Definition of React...
Why Detailed Mechanism Generation?
   Detailed mechanisms of large hydrocarbons:
          Too large and too complex now t...
Single Reaction Generation
                               Reaction Center
             The set of bonds and atom valences ...
Single Reaction Generation
                           Reaction Pattern
       Supplemented with the Environment around Rea...
Single Reaction Generation
                                                         Ra       Rc         The Reactive
     ...
Single Reaction Generation
                               Reaction Formation
                  Match Reactant of Reaction ...
Single Reaction Generation
  Reaction pattern:
                                                                           ...
Mechanism Generation
   Single Reaction Generation
      – Generic Reaction Classes
         Definition of Reactive Center...
Reaction Pathway
                       Classic low temperature alkane pathway
         Generic:                          ...
Reaction Pathway
             A pathway generates a sub-mechanism tree of reactions




Engi  CO
       nes               ...
Detailed Mechanism Generation
   Single Reaction Generation
      – Generic Reaction Classes
         Definition of Reacti...
Combinatorial Explosion
              The number of combinations of applications of reaction
                  classes can...
Combinatorial Explosion
   Everything can react with everything in a multitude of ways !

                     A large par...
Exhaustive with Filtering

                                                                                  Seed molecule...
Controlled Generation

                       Only products of last step are used in next step


                         ...
Outline
       Detailed Mechanism Generation
              – Reactive Center and Reaction Generation
              – Compl...
Mechanism Reduction
  • Reduce the effective number of species and reactions in the
    differential equations to solve fo...
Mechanism Reduction
          Goal: To reproduce the details of the complex mechanism in an
            equivalent small m...
Outline
       Detailed Mechanism Generation
              – Reactive Center and Reaction Generation
              – Compl...
Species Lumping

     Mechanism is reduced through combination of species to a
       smaller number of lumped species

  ...
Example of Chemical Lumping
                 Schematic representation for the lumping of four different
                  ...
Lumped species in n-heptane Mechanism
                                                Concentration of Species Lumped Toge...
Lumped Mechanism :
                                                                                                       ...
Lumped Mechanism – Same As Detailed
                  Laminar flame speed for n-heptane/air mixture
                      ...
Outline
       Detailed Mechanism Generation
              – Reactive Center and Reaction Generation
              – Compl...
Mechanism Reduction: Skeletal

          Reduction through elimination of Reactions and
                              Spec...
Skeletal Mechanisms: Criteria
   Local Sensitivity (Expensive to calculate):
      How does a small perturbation of an
   ...
Finding skeletal mechanisms
        Examples of semi-automated methods that use knowledge
                       gained by...
Finding skeletal mechanisms
                           Fully automated optimization methods:

  Binary Optimization (inclu...
Skeleton Mechanism : n-heptane
                                                                                           ...
Outline
       Detailed Mechanism Generation
              – Reactive Center and Reaction Generation
              – Compl...
Time Scale Analysis
Separation of fast and slow processes
Fast processes of full phase space fall into
(slow) lower dimens...
Time Scale Analysis
   Separation of solution in terms of fast and slow time scales

   Quasi-Steady State Approximation:
...
Outline
       Detailed Mechanism Generation
              – Reactive Center and Reaction Generation
              – Compl...
Adaptive Chemistry
     Principle:
         – A combustion process is composed of several regions
     Method:
         – ...
Example: Polynomial Based
   Principle:
          – The phase is represented by a polynomial
          – Phases are accumu...
Example: Library

    Probability Density Function (PDF)
           A stochastic method that uses distribution functions t...
Skeletal Mechanism Based
  Principle:
      – Small number of phases
      – each is a skeletal mechanism

  A Priori Opti...
Example of Adaptive Chemistry
                                Two-zone zero-dimensional stochastic reactor
               ...
Outline
       Detailed Mechanism Generation
              – Reactive Center and Reaction Generation
              – Compl...
Optimization of Rate Coefficients
                        N
                   rk   ci Ak T n exp   Ek RT 
          ...
Optimization of Rate Coefficients


         Function to Optimize
       Model – Experimental Data

                      ...
Reduction-Optimization Cycle

                                        4.5                                                 ...
Needs for future
     – Fundamental experimental data needed:
            Shock tube
            RCM                      ...
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EcoEngines Chemical Kinetics

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Single Lecture about combustion kinetics given at the EcoEngines summer school in September 2006

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Transcript of "EcoEngines Chemical Kinetics"

  1. 1. Chemical Kinetics Module B, Section 3 This course was developed by: • Edward S. Blurock (Lund University) • Gladys Moréac (Lund University) Engi CO Engi COnes nes 1 © An EC funded NoE on Energy Conversion in Engines 2006 Edward S. Blurock, Gladys Moréac, Lund University - All rights reserved. Confidential
  2. 2. Motivation Chemical kinetics: –Description of chemical oxidation behavior of commercial fuels. –Detail is needed to describe: - fuel oxidation - pollutant formation - CO emission - NOx formation - chemistry behind knock,etc. Engi CO nes 2 © 2006 Edward S. Blurock, Gladys Moréac, Lund University - All rights reserved. Confidential
  3. 3. Purpose of Presentation An outline of the state of the art in modeling complex chemistry. – Many techniques will be presented – Too little time to present details What you should get out of the presentation – That the methods presented exist – What the methods accomplish, their purpose – For more detail follow the key references given Engi CO nes 3 © 2006 Edward S. Blurock, Gladys Moréac, Lund University - All rights reserved. Confidential
  4. 4. Why Model fuels ? Real fuel: - Diesel, Gasoline, Biofuels or Kerosene Fuels - Too complex to model using all the components Model Fuel: Reproduce the oxidation characteristics of a real fuel (Diesel, Gasoline, Kerosene Fuels…) Example of composition of a commercial Engi CO diesel fuel, from Dagaut,P., PCCP, 4, 2079-2094 (2002). nes 4 © 2006 Edward S. Blurock, Gladys Moréac, Lund University - All rights reserved. Confidential
  5. 5. Examples of model components Gasoline: - PRF (Primary Reference Fuels): iso-octane, n-heptane - mono-aromatic: toluene, benzene, propylbenzene... Diesel: - PRF and/or linear alkanes - Poly-aromatic: α-methylnaphthalene... Kerosene: - PRF and/or linear alkanes - Poly-aromatic - Naphtenes: propyl-cyclohexane... Biofuels: Conventional fuels + additives (ETBE, MTBE, methanol...) Engi CO nes 5 © 2006 Edward S. Blurock, Gladys Moréac, Lund University - All rights reserved. Confidential
  6. 6. Examples of chemical model Global: One or very few reactions. “Shell Model” (5 species, 8 reactions). Halstead, M. P.; Kirsch, L. J.; Prothero, A.; Quinn, C. P., Proc. Roy. Soc. London, A346, 515-538 (1975). Reduced/Lumped: Valid under a limited set of conditions (T, P..) - n-heptane oxidation and pyrolysis mechanism (41 species, 266 reactions) Held, T. J.; Marchese, A. J.; Dryer, F. L., Combust. Sci. Technol., 123, 107-146 (1997). - n-decane oxidation mechanism (98-273 species and 644-1282 reactions) Glaude, P. A.; Battin-Leclerc, F.; Fournet, R.; Warth, V.; Côme, G. M.; Scacchi, G., Combust. Flame, 122, 451-462 (2000) Detailed: Valid under a wide range of conditions. - n-heptane oxidation mechanism (550 species and 2450 reactions) Curran, H. J.; Gaffuri, P.; Pitz, W. J.; Westbrook, C. K. Combust.Flame, 114, 149-177 (1998). - n-decane oxidation mechanism (506 species and 3684 reactions) Moréac, G., Blurock, E. S., Mauss, F.; to be published in Combust. Sci. Technol. (2006) Engi CO nes 6 © 2006 Edward S. Blurock, Gladys Moréac, Lund University - All rights reserved. Confidential
  7. 7. Mechanism structure Whether produced by hand or generated automatically, the structure of the mechanism is the same Species: Hydrocarbon Fuel, oxidizer, intermediates, products... Reactions: How the species react with each other Pathways: Succesive set of reactions Sub-mechanisms: Blocks of related reactions from a pathway Detailed mechanism: Combined set of sub-mechanisms Engi CO nes 7 © 2006 Edward S. Blurock, Gladys Moréac, Lund University - All rights reserved. Confidential
  8. 8. Reaction Pathway Classic low temperature alkane pathway Generic: Example: R + O2 = ●R +O2H CH3CH2CH2CH3 + O2 = ●CH2CH2CH2CH3 + O2H R + O2 = ●ROO CH2CH2CH2CH3 + O2 = ●OOCH2CH2CH2CH3 ● ● OOCH2CH2CH2CH3 = HOOCH2●CHCH2CH3 ROO = ●QOOH ● ● QOOH + O2 = ●OOQOOH HOOCH2●CHCH2CH3 + O2= HOOCH2CH(OO)CH2CH3 ● HOOCH2CH(OO)CH2CH3 = HCOCH(OOH)CH2CH3 + OH OOQOOH = ●OQOOH + OH ● HCOCH(OOH)CH2CH3 = products + OH OQOOH = products + OH ● Engi CO nes 8 © 2006 Edward S. Blurock, Gladys Moréac, Lund University - All rights reserved. Confidential
  9. 9. Sub-Mechanism A pathway generates a sub-mechanism tree of reactions Engi CO nes 9 © 2006 Edward S. Blurock, Gladys Moréac, Lund University - All rights reserved. Confidential
  10. 10. Outline Detailed Mechanism Generation – Reactive Center and Reaction Generation – Complete Mechanism Generation – Optimization Mechanism Reduction – Skeletal – Time Scale Analysis – Lumping – Adaptive Chemistry Rate coefficient Optimization – Automatic Reaction Coefficient Optimization Engi CO nes 10 © 2006 Edward S. Blurock, Gladys Moréac, Lund University - All rights reserved. Confidential
  11. 11. Detailed 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 Engi CO nes 11 © 2006 Edward S. Blurock, Gladys Moréac, Lund University - All rights reserved. Confidential
  12. 12. Why Detailed Mechanism 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 Chemical classes: Groups of reactions and species with similar properties Engi CO nes 12 © 2006 Edward S. Blurock, Gladys Moréac, Lund University - All rights reserved. Confidential
  13. 13. Single Reaction Generation Reaction Center The set of bonds and atom valences that change in the course of a reaction Examples: A C C C C ● ● ● A Generic Loss of Radical to Form Olefin O C C C C ● ● ● O Generic Group Replaced by an Oxygen Engi CO nes 13 © 2006 Edward S. Blurock, Gladys Moréac, Lund University - All rights reserved. Confidential
  14. 14. Single Reaction Generation Reaction Pattern Supplemented with the Environment around Reactive Center (Functional Groups which can effect reaction rate) Ra Rc O H O H C O C O C C ● ● Rb Rd Include Bonding C+ C O H O of Carbon ● Ra Rc Peroxyl Group Influence on bonding C+ O H O C ● Engi CO Rb Rd nes 14 © 2006 Edward S. Blurock, Gladys Moréac, Lund University - All rights reserved. Confidential
  15. 15. Single Reaction Generation Ra Rc The Reactive Center Changes O H C O C ● Rb Rd Correspondence Between Reactants and Products Ra Rc O H C O C ● The surrounding functional Rb Rd Groups are unchanged Determines how the bonding and atom valences are changed in the course of the reaction Engi CO nes 15 © 2006 Edward S. Blurock, Gladys Moréac, Lund University - All rights reserved. Confidential
  16. 16. Single Reaction Generation Reaction Formation Match Reactant of Reaction Pattern with Reactant Ra Rc O H C O Reaction Pattern C ● Rb Rd H H H H Reactant O H C C O C C ● H H H H Engi CO nes 16 © 2006 Edward S. Blurock, Gladys Moréac, Lund University - All rights reserved. Confidential
  17. 17. Single Reaction Generation Reaction pattern: Ra Rc Ra Rc + ●O C C O H C O O H C ● Rb Rd Rb Rd Application to form a specific reaction: H H H H H H H H + ●O H H C C O H C C C C O O H C C ● H H H H H H Chemical formula in the mechanism: CH3CH2●CHCH2OOH CH3CH2CHCH2 + OOH ● Engi CO nes 17 © 2006 Edward S. Blurock, Gladys Moréac, Lund University - All rights reserved. Confidential
  18. 18. 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 Engi CO nes 18 © 2006 Edward S. Blurock, Gladys Moréac, Lund University - All rights reserved. Confidential
  19. 19. Reaction Pathway Classic low temperature alkane pathway Generic: Example: R + O2 = ●R +O2H CH3CH2CH2CH3 + O2 = ●CH2CH2CH2CH3 + O2H R + O2 = ●ROO CH2CH2CH2CH3 + O2 = ●OOCH2CH2CH2CH3 ● ● OOCH2CH2CH2CH3 = HOOCH2●CHCH2CH3 ROO = ●QOOH ● ● QOOH + O2 = ●OOQOOH HOOCH2●CHCH2CH3 + O2= HOOCH2CH(OO)CH2CH3 ● HOOCH2CH(OO)CH2CH3 = HCOCH(OOH)CH2CH3 + OH OOQOOH = ●OQOOH + OH ● HCOCH(OOH)CH2CH3 = products + OH OQOOH = products + OH ● Engi CO nes 19 © 2006 Edward S. Blurock, Gladys Moréac, Lund University - All rights reserved. Confidential
  20. 20. Reaction Pathway A pathway generates a sub-mechanism tree of reactions Engi CO nes 20 © 2006 Edward S. Blurock, Gladys Moréac, Lund University - All rights reserved. Confidential
  21. 21. Detailed 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 Engi CO nes 21 © 2006 Edward S. Blurock, Gladys Moréac, Lund University - All rights reserved. Confidential
  22. 22. Combinatorial Explosion The number of combinations of applications of reaction classes can increase rapidly with species size n-butane n-hexane n-decane Engi CO nes 22 © 2006 Edward S. Blurock, Gladys Moréac, Lund University - All rights reserved. Confidential
  23. 23. Combinatorial Explosion 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 How to avoid the combinatorial explosion? – Filtering of unreasonable reactions – Controlled generation of only the wanted reactions Engi CO nes 23 © 2006 Edward S. Blurock, Gladys Moréac, Lund University - All rights reserved. Confidential
  24. 24. Exhaustive with Filtering Seed molecule Filter out Generate next reaction End if no products Product pool 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 Engi CO nes 24 © 2006 Edward S. Blurock, Gladys Moréac, Lund University - All rights reserved. Confidential
  25. 25. Controlled Generation Only products of last step are used in next step Generate Generate ... Seed molecule first step Second step Product pool Examples: Moréac, G., Blurock, E. S.;Automatic generation of a detailed mechanism for the oxidation of n-decane, to be published in Comb. Sci. Technol. (2006) Blurock, E. S., Detailed Mechanism Generation 1: Generalized Reactive Properties as Reaction Class Substructures. J. Chem. Inf. Comp. Sci., 44, 1336-1347 (2004) Engi CO nes 25 © 2006 Edward S. Blurock, Gladys Moréac, Lund University - All rights reserved. Confidential
  26. 26. Outline Detailed Mechanism Generation – Reactive Center and Reaction Generation – Complete Mechanism Generation – Optimization Mechanism Reduction – Skeletal – Time Scale Analysis – Lumping – Adaptive Chemistry Rate coefficient Optimization – Automatic Reaction Coefficient Optimization Engi CO nes 26 © 2006 Edward S. Blurock, Gladys Moréac, Lund University - All rights reserved. Confidential
  27. 27. Mechanism Reduction • Reduce the effective number of species and reactions in the differential equations to solve for source terms • Computational Cost in a mechanism is – Number of Species: squared increase (building Jacobian) – Number of Reactions: linear increase (evaluating exponential) • Used to calculate the chemical source terms within larger more complex computations (Computational Fluid Dynamics) Key reference: Tomlin, A.S.; Turanyi, T.; Pilling, M.J. “Mathematical tools for the construction, investigation and reduction of combustion mechanisms” in “Low temperature combustion and auto-ignition; Comprehensive Chemical Kinetics”, 35, Pilling, M.J. Ed.; Elsevier: Amsterdam, 293-437 (1997). Engi CO nes 27 © 2006 Edward S. Blurock, Gladys Moréac, Lund University - All rights reserved. Confidential
  28. 28. 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 Engi CO nes 28 © 2006 Edward S. Blurock, Gladys Moréac, Lund University - All rights reserved. Confidential
  29. 29. Outline Detailed Mechanism Generation – Reactive Center and Reaction Generation – Complete Mechanism Generation – Optimization Mechanism Reduction – Lumping – Skeleton – Time Scale Analysis – Adaptive Chemistry Rate coefficient Optimization – Automatic Reaction Coefficient Optimization Engi CO nes 29 © 2006 Edward S. Blurock, Gladys Moréac, Lund University - All rights reserved. Confidential
  30. 30. Species Lumping Mechanism is reduced through combination of species to a smaller number of lumped species Chemical Lumping: – Based on species structure and/or reactivity Formal Lumping: – Mathematical transformation between lumped and unlumped (for example, linear combination of species concentrations) Li, G.; Rabitz, H. Chem. Eng. Sci., 44, 1413-1430, 1989. Engi CO nes 30 © 2006 Edward S. Blurock, Gladys Moréac, Lund University - All rights reserved. Confidential
  31. 31. Example of Chemical Lumping Schematic representation for the lumping of four different 5-ring alkylperoxy radicals OOH H2 H2 CH C C H3 C C C CH3 H H2 HOO H2 H2 CH C C H3C C C CH3 H H2 5r-C7H14OOH OOH H2 H2 CH C C H3C C C CH3 H H2 HOO H2 H2 CH C C H3 C C C CH3 H H2 Engi CO nes 31 © 2006 Edward S. Blurock, Gladys Moréac, Lund University - All rights reserved. Confidential
  32. 32. Lumped species in n-heptane Mechanism Concentration of Species Lumped Together Add to Single Lumped Species 6r-QOOH Species RO2 Species -4 2 10 1-C H O Concentration [mole/cm ] Concentration [mole/cm ] C H OOH1-3 -6 3 3 2 10 7 15 2 7 14 2-C H O C H OOH2-4 7 15 2 7 14 3-C H O C H OOH3-1 -6 1 10 -4 7 15 2 7 14 1 10 4-C H O C H OOH3-5 7 15 2 7 14 Added Species C H OOH4-2 -7 8 10 L-C H O 7 14 Added Species 7 15 2 -5 6r-C H OOH 5 10 -7 4 10 7 14 0 0 0.27 0.29 0.31 0.33 0.35 0.27 0.29 0.31 0.33 0.35 t [msec] t [msec] Engi CO p = 40bar,  = 1.0, T = 800K nes 32 © 2006 Edward S. Blurock, Gladys Moréac, Lund University - All rights reserved. Confidential
  33. 33. Lumped Mechanism : n-heptane 1624 reactions n-C7H16 203 species Detailed 3-C7H15 1-C7H15 2-C7H15 4-C7H15 1362 reactions 1-C7H15O2 2- C7H15O2 n-C7H16 3- C7H15O2 4- C7H15O2 A1-2 A1-3 A1-4 A1-5 A2-1 A2-3 A2-4 A2-5 A2-6 A3-1 A3-2 A3-4 A3-5 A3-6 A3-7 A4-1 A4-2 A4-3 142 species B1-3 B1-4 B1-5 B1-2 B2-3 B2-4 B2-5 B2-6 B1-3 B2-3 B3-4 B3-5 B2-5 B1-5 B1-4 B2-4 B3-4 B1-2 L-C7H15 C1-2 C1-3 C1-4 C1-5 C2-1 C2-3 C2-4 C2-5 C2-6 C3-1 C3-2 C3-4 C3-5 C3-6 C3-7 C4-1 C4-2 C4-3 D1-2 D1-3 D1-4 D1-5 D2-1 D2-3 D2-4 D2-5 D2-6 D3-1 D3-2 D3-4 D3-5 D3-6 D3-7 D4-1 D4-2 D4-3 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 D-5r D-6r D-7r D-8r L = Lumped species, 5r, 6r, 7r and 8r represent Engi the size of the ring CO nes 33 © 2006 Edward S. Blurock, Gladys Moréac, Lund University - All rights reserved. Confidential
  34. 34. Lumped Mechanism – Same As Detailed Laminar flame speed for n-heptane/air mixture at p=1 bar and Ti=298 K Davis and Law Experimental data (symbols) Detailed mechanism (solid line) Lumped mechanism (dashed line) 50 40 n-heptane-air S [cm/sec] 30 L 20 10 Engi CO 0.6 0.8 1.0 1.2 1.4 1.6 1.8  nes 34 © 2006 Edward S. Blurock, Gladys Moréac, Lund University - All rights reserved. Confidential
  35. 35. Outline Detailed Mechanism Generation – Reactive Center and Reaction Generation – Complete Mechanism Generation – Optimization Mechanism Reduction – Lumping – Skeletal – Time Scale Analysis – Adaptive Chemistry Rate coefficient Optimization – Automatic Reaction Coefficient Optimization Engi CO nes 35 © 2006 Edward S. Blurock, Gladys Moréac, Lund University - All rights reserved. Confidential
  36. 36. Mechanism Reduction: Skeletal Reduction through elimination of Reactions and Species Under a limited set of conditions (which can be quite extensive), unused species and reactions of the mechanism are eliminated if they are considered inert under those conditions Engi CO nes 36 © 2006 Edward S. Blurock, Gladys Moréac, Lund University - All rights reserved. Confidential
  37. 37. Skeletal Mechanisms: Criteria Local Sensitivity (Expensive to calculate): How does a small perturbation of an input parameter affect an output parameter Example: How does a rate constant affect the temperature k/T Reaction Flow Analysis: The flux through a given reaction or molecule (related to reaction rates) Heat Release: When combined with reaction rates, a non-computationally expensive indicators of necessity of reactions Engi CO nes 37 © 2006 Edward S. Blurock, Gladys Moréac, Lund University - All rights reserved. Confidential
  38. 38. Finding skeletal mechanisms Examples of semi-automated methods that use knowledge gained by derived criteria: Necessity Parameter: Combination of sensitivity and flows Soyhan, H.S.; Mauss, F.; Sorusbay, C., Combust. Flame, 125, 906-919 (2001). Directed Relation Graph: Uses of flow analysis Lu, T; Law, C. K., Combust. Flame, 144, 24-36 (2006). Heat Release/Rates: Criteria for elimination of reactions Wang, H.; Frenklach, M., Combust. Flame, 87, 365-370 (1991). Principle Component Analysis: Linear combination of species Vajda, S.; Valko, P.; Turányi, T., Int. J. Chem. Kinet., 17, 55-81 (1985). Engi CO nes 38 © 2006 Edward S. Blurock, Gladys Moréac, Lund University - All rights reserved. Confidential
  39. 39. Finding skeletal mechanisms Fully automated optimization methods: Binary Optimization (inclusion or exclusion of reaction/species): – Integer Programming Androulakis, I.P., AICHE, 46, 361-371 (2000). – Genetic Algorithms Edwards, K.; Edgar, T.F.; Manousiouthakis, V.I. Computers Chem Engng., 22, 239- 246 (1998). Direct Simulation: Motivated by Stochastic Modeling Mosbach, S.; Su, H. Kraft, M., Proc. Combust. Institute, 30, 1301-1308 (2005). Engi CO nes 39 © 2006 Edward S. Blurock, Gladys Moréac, Lund University - All rights reserved. Confidential
  40. 40. Skeleton Mechanism : n-heptane 1624 reactions Detailed n-C7H16 203 species 3-C7H15 1-C7H15 2-C7H15 4-C7H15 N- 1-C7H15O2 2- C7H15O2 3- C7H15O2 4- C7H15O2 C7H16 A1-2 A1-3 A1-4 A1-5 A2-1 A2-3 A2-4 A2-5 A2-6 A3-1 A3-2 A3-4 A3-5 A3-6 A3-7 A4-1 A4-2 A4-3 B1-3 B1-4 B1-5 B1-2 B2-3 B2-4 B2-5 B2-6 B1-3 B2-3 B3-4 B3-5 B2-5 B1-5 B1-4 B2-4 B3-4 B1-2 C1-2 C1-3 C1-4 C1-5 C2-1 C2-3 C2-4 C2-5 C2-6 C3-1 C3-2 C3-4 C3-5 C3-6 C3-7 C4-1 C4-2 C4-3 L-C7H15 470 reactions D1-2 D1-3 D1-4 D1-5 D2-1 D2-3 D2-4 D2-5 D2-6 D3-1 D3-2 D3-4 D3-5 D3-6 D3-7 D4-1 D4-2 D4-3 64 species n-C7H16 L-C7H15O2 1362 reactions Lumped L-C7H15 142 species L-C7H15O2 A-5r A-6r A-7r A-5r A-6r A-7r A-8r B-5r B-6r B-7r B-8r B-5r B-6r B-7r C-5r C-6r C-7r C-8r D-5r D-6r D-7r D-8r C-5r C-6r C-7r L = Lumped species, 5r, 6r, 7r and 8r represent the size of the ring D-5r D-6r D-7r Engi CO nes 40 © 2006 Edward S. Blurock, Gladys Moréac, Lund University - All rights reserved. Confidential
  41. 41. Outline Detailed Mechanism Generation – Reactive Center and Reaction Generation – Complete Mechanism Generation – Optimization Mechanism Reduction – Lumping – Skeletal – Time Scale Analysis – Adaptive Chemistry Rate coefficient Optimization – Automatic Reaction Coefficient Optimization Engi CO nes 41 © 2006 Edward S. Blurock, Gladys Moréac, Lund University - All rights reserved. Confidential
  42. 42. Time Scale Analysis 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 (QSSA): – Some Species fall into (close to) equilibrium (dC/dt=0) within time scale considered – Close to Equilibrium, they move along the same path in composition space (reduced dimension). – Their solution can be calculated algebraically instead of solving the differential equations Engi CO nes 42 © 2006 Edward S. Blurock, Gladys Moréac, Lund University - All rights reserved. Confidential
  43. 43. Time Scale Analysis Separation of solution in terms of fast and slow time scales Quasi-Steady State Approximation: Solving algebraically QSSA species Atkins, P., Physical Chemistry. Academic Press, New York, 927–935 (1994). Identification of QSSA species through ‘Importance’ Lovas, T.; Nilsson, D.; Mauss, F., Proc. of Combustion Symposium, 28, 1809-1816 (2002). Eigenvalues of Jacobian Matrix: Eigenvalues determine fast and slow reacting species – Intrinsic Low Dimensional Manifold (IDLM): Mass, U.; Pope, S.B., Combust. Flame, 88, 903-914 (1992). – Computational Singular Perturbation (CSP): Lam, S.H.;Goussis, D.A., Int. J. Chem. Kinet., 26, 461-486 (1994). Engi CO nes 43 © 2006 Edward S. Blurock, Gladys Moréac, Lund University - All rights reserved. Confidential
  44. 44. Outline Detailed Mechanism Generation – Reactive Center and Reaction Generation – Complete Mechanism Generation – Optimization Mechanism Reduction – Lumping – Skeletal – Time Scale Analysis – Adaptive Chemistry Rate coefficient Optimization – Automatic Reaction Coefficient Optimization Engi CO nes 44 © 2006 Edward S. Blurock, Gladys Moréac, Lund University - All rights reserved. Confidential
  45. 45. Adaptive Chemistry Principle: – A combustion process is composed of several regions Method: – Each region has its own representation of the chemistry – At each time step the phase chemistry is used The methods differentiate by: – Representation of the chemical phases – Determination of the phases – Optimization of the phase chemistry – Recognition of which phase should be used Engi CO nes 45 © 2006 Edward S. Blurock, Gladys Moréac, Lund University - All rights reserved. Confidential
  46. 46. Example: Polynomial Based Principle: – The phase is represented by a polynomial – Phases are accumulated dynamically building up a library – Search of phase through a tree structure ISAT: 1st degree polynomial approximation established through Jacobian matrix. Phase size based on curvature. Pope, S., Combust. Theory Modelling, 1, 41-63 (1997). PRISM: 2nd degree polynomial established through factorial design. Phase size is fixed in coordinate space. Tonse, S.; Moriarty, N.; Brown, N.; Frenklach, M., Israel J. of Chem., 39, 97-106 (1999). APTAB: PRISM approximation based on accumulated ISAT points (no factorial design). Ngozi, N.; Blurock, E.S.; Mauss, F., Proc. Symp. (Med.) Combust., 4 (2005). Engi CO nes 46 © 2006 Edward S. Blurock, Gladys Moréac, Lund University - All rights reserved. Confidential
  47. 47. Example: Library Probability Density Function (PDF) A stochastic method that uses distribution functions to describe the fluctuating scalars in a turbulent field. Pope, S. B. PDF methods for turbulent reactive flows. Prog. Energy Combust. Sci. 11,119-92 (1985). Flamelets “Thin diffusion layers embedded in a turbulent non- reactive flow field.” Peters, N., Turbulent combustion, Cambridge University Press, Cambridge, (2000). Engi CO nes 47 © 2006 Edward S. Blurock, Gladys Moréac, Lund University - All rights reserved. Confidential
  48. 48. Skeletal Mechanism Based Principle: – Small number of phases – each is a skeletal mechanism A Priori Optimized: – Each region/phase is set up before the calculation – Each phase is optimized (global optimization) Bhattacharjee, B.; Schwer, D.A.; Barton, P.I.; Green, W.H., Combust. Flame, 135, 191-208 (2003). Machine Learning Based: – Each phase is determined by a cluster of species importance – Each phase is minimized with respect to species importance – Phase recognition by a machine learning deduced decision tree Tunér, M.; Blurock, E.S.; Mauss, F., SAE 2005-01-3813 (2005). Engi CO nes 48 © 2006 Edward S. Blurock, Gladys Moréac, Lund University - All rights reserved. Confidential
  49. 49. Example of Adaptive Chemistry Two-zone zero-dimensional stochastic reactor model (SRM) for SI-Engine calculations. Each particle in the PDF (Probability Density Function) calls a different phase at each time-step during the calculation. The basic idea behind the SRM is to divide the mass within the cylinder into an arbitrary Engi CO number of particles, and to use a Stochastic Monte Carlo process with an operator splitting algorithm. nes 49 © 2006 Edward S. Blurock, Gladys Moréac, Lund University - All rights reserved. Confidential
  50. 50. Outline Detailed Mechanism Generation – Reactive Center and Reaction Generation – Complete Mechanism Generation – Optimization Mechanism Reduction – Lumping – Skeletal – Time Scale Analysis – Adaptive Chemistry Rate coefficient Optimization – Automatic Reaction Coefficient Optimization Engi CO nes 50 © 2006 Edward S. Blurock, Gladys Moréac, Lund University - All rights reserved. Confidential
  51. 51. Optimization of Rate Coefficients N rk   ci Ak T n exp   Ek RT  S  i ,k k i Temperature Frequency Factor Activation Energy Exponent Engi CO nes 51 © 2006 Edward S. Blurock, Gladys Moréac, Lund University - All rights reserved. Confidential
  52. 52. Optimization of Rate Coefficients Function to Optimize Model – Experimental Data   N Ψ θ     r y  y r  θ 2 obs r r 1 Response Surface NR NR NR NR φ   0    i X i    i X i    ij X i X j y 2 i j i i i Frenklach, M.; Wang H.; Rabinovitz, M. J., Prog. Energy Combustion Sci., 18, 47-73 (1992). Engi CO nes 52 © 2006 Edward S. Blurock, Gladys Moréac, Lund University - All rights reserved. Confidential
  53. 53. Reduction-Optimization Cycle 4.5 6 4 CPU Time 5 3.5 Optimization 3 Time [sec] 4 Error [CAD] Optimization 2.5 3 2 1.5 2 1 Reduction 0.5 1 25 30 35 40 45 50 55 60 # Species Engi CO nes 53 © 2006 Edward S. Blurock, Gladys Moréac, Lund University - All rights reserved. Confidential
  54. 54. Needs for future – Fundamental experimental data needed: Shock tube RCM auto-ignition engines JSR, PFR species concentrations Flames species concentrations and velocities – New mechanism for the oxidation of future fuels (biofuels...) – Computer technology will enable more detailed chemical models Engi CO nes 54 © 2006 Edward S. Blurock, Gladys Moréac, Lund University - All rights reserved. Confidential
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