E nginesCO © 2005 Edward S. Blurock, Gladys Moréac, Lund University - All rights reserved. 1 Confidential Fuels oxidation chemistry Module B, Section 3 This course was developed by: Edward S. Blurock (Lund University) Gladys Moréac (Lund University) An EC funded NoE on Energy Conversion in Engines E ngines CO

CO © 2005 Edward S. Blurock, Gladys Moréac, Lund University - All rights reserved. 2 Confidential 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

E nginesCO © 2005 Edward S. Blurock, Gladys Moréac, Lund University - All rights reserved. 3 Confidential 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

E nginesCO © 2005 Edward S. Blurock, Gladys Moréac, Lund University - All rights reserved. 4 Confidential 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

E nginesCO © 2005 Edward S. Blurock, Gladys Moréac, Lund University - All rights reserved. 5 Confidential 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

E nginesCO © 2005 Edward S. Blurock, Gladys Moréac, Lund University - All rights reserved. 6 Confidential 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

E nginesCO © 2005 Edward S. Blurock, Gladys Moréac, Lund University - All rights reserved. 7 Confidential 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

E nginesCO © 2005 Edward S. Blurock, Gladys Moréac, Lund University - All rights reserved. 8 Confidential Single Reaction Generation Reaction Formation Match Reactant of Reaction Pattern with Reactant Correspondence to Pattern Rest of Reactant

E nginesCO © 2005 Edward S. Blurock, Gladys Moréac, Lund University - All rights reserved. 9 Confidential Single Reaction Generation Reaction Formation Change as Specified in the Reactive Center The changes specified by the Pattern Are Performed on the Reactant CH3CH2CH2CHCH2OOHCH3CH2CHCH2OOH+

E nginesCO © 2005 Edward S. Blurock, Gladys Moréac, Lund University - All rights reserved. 10 Confidential 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

E nginesCO © 2005 Edward S. Blurock, Gladys Moréac, Lund University - All rights reserved. 11 Confidential Reaction Pathway R + O = R. +OH R. + O2 = ROO. ROO. =.QOOH.QOOH + O2 = OOQOOH OOQOOH = OQOOH OQOOH = products + OH CH3CH2CH2CH3 + O =.CH2CH2CH2CH3 CH2CH2CH2CH3 + O2 = OOCH2CH2CH2CH3.OOCH2CH2CH2CH3 = HOOCH2CHCH2CH3 HOOCH2CHCH2CH3 = HOOCH2CH(OO)CH2CH3 HOOCH2CH(OO)CH2CH3 = CHOC(OOH)CH2CH3 + OH CHOC(OOH)CH2CH3 = OH + products

E nginesCO © 2005 Edward S. Blurock, Gladys Moréac, Lund University - All rights reserved. 12 Confidential Reaction Pathway A Sequence generates a sub-mechanism tree of reactions

E nginesCO © 2005 Edward S. Blurock, Gladys Moréac, Lund University - All rights reserved. 13 Confidential 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

E nginesCO © 2005 Edward S. Blurock, Gladys Moréac, Lund University - All rights reserved. 14 Confidential 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.

E nginesCO © 2005 Edward S. Blurock, Gladys Moréac, Lund University - All rights reserved. 15 Confidential 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.

E nginesCO © 2005 Edward S. Blurock, Gladys Moréac, Lund University - All rights reserved. 16 Confidential 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.

E nginesCO © 2005 Edward S. Blurock, Gladys Moréac, Lund University - All rights reserved. 17 Confidential 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

E nginesCO © 2005 Edward S. Blurock, Gladys Moréac, Lund University - All rights reserved. 18 Confidential Exhaustive with Filtering Example: NETGEN Rate-Based Generation Criterion –R char : Characteristic rate (maximum rate of formation of all species) –R min =  R char : Minimum rate allowed (  determines range) –Species kept in mechanism if rate of formation greater than R min Examples: De Witt, M.J., Dooling, D.J., Broadbelt, L.J, Ind. Eng. Chem. Res., 39, (2000) –Tetradecane pyrolysis: large extensive mechanisms Grenda J.M., Androulaktis, I.P., Dean, A.M., Green Jr., W.H., Ind. Eng. Chem. Res,42, (2003) –Pressure dependent reactions through cycloalkyl intermediates –Use of Quantum Rice-Ramsperger-Kassel (QRRK) for pressure dependence

E nginesCO © 2005 Edward S. Blurock, Gladys Moréac, Lund University - All rights reserved. 19 Confidential Controlled Generation A.Define a set of reaction pathways to make up the mechanism B.Establish the set of seed molecules C.For each seed and each pathway : 1.Apply the seed species to the first step of pathway 2.Apply the products of the last step to the next step in the pathway 3.Repeat 2 until no more steps in the pathway 4.The set of species and reactions make up this sub-mechanism D.Combine the set of sub-mechanisms together to form the final generated mechanism 1.Check for species and reaction correspondences between submechanisms 2.Include only the unique set of species and reactions E.Combine the final generated mechanism with Base mechanism 1.Check for species and reaction correspondences between submechanisms 2.Include only the unique set of species and reactions

E nginesCO © 2005 Edward S. Blurock, Gladys Moréac, Lund University - All rights reserved. 20 Confidential Controlled Generation Each Pathway Represents a Submechanism

E nginesCO © 2005 Edward S. Blurock, Gladys Moréac, Lund University - All rights reserved. 21 Confidential Controlled Generation A seed molecule applied to a specific Pathway Is a Sub-Mechanism All the sub-mechanisms are combined into one Generated mechanism

E nginesCO © 2005 Edward S. Blurock, Gladys Moréac, Lund University - All rights reserved. 22 Confidential 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

E nginesCO © 2005 Edward S. Blurock, Gladys Moréac, Lund University - All rights reserved. 23 Confidential 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

E nginesCO © 2005 Edward S. Blurock, Gladys Moréac, Lund University - All rights reserved. 24 Confidential 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

E nginesCO © 2005 Edward S. Blurock, Gladys Moréac, Lund University - All rights reserved. 25 Confidential 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

E nginesCO © 2005 Edward S. Blurock, Gladys Moréac, Lund University - All rights reserved. 26 Confidential 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

E nginesCO © 2005 Edward S. Blurock, Gladys Moréac, Lund University - All rights reserved. 27 Confidential 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

E nginesCO © 2005 Edward S. Blurock, Gladys Moréac, Lund University - All rights reserved. 28 Confidential Lumped species in n-heptane Mechanism Schematic representation for the lumping of four different 5-ring alkylperoxy radicals 5r-C 7 H 14 OOH

E nginesCO © 2005 Edward S. Blurock, Gladys Moréac, Lund University - All rights reserved. 29 Confidential Lumped species in n-heptane Mechanism 6r-QOOH SpeciesRO 2 Species p = 40bar,  = 1.0, T = 800K Concentration of Species Lumped Together Add to Single Lumped Species

E nginesCO © 2005 Edward S. Blurock, Gladys Moréac, Lund University - All rights reserved. 30 Confidential 1362 reactions 142 species n-C 7 H 16 L-C 7 H 15 L-C 7 H 15 O 2 A-5r B-5r C-5r D-5r A-6r B-6r C-6r D-6r A-7r B-7r C-7r D-7r A-8r B-8r C-8r D-8r L = Lumped species, 5r, 6r, 7r and 8r represent the size of the ring Lumped Mechanism : n-heptane 1624 reactions 203 species Detailed 1-2 = 1 position of OOH and 2 is radical site A = C 7 H 14 OOH,B = HOO-C 7 H 14 O 2,C = O-C 7 H 13 OOH andD = Carbonyl + OH 1624 reactions 203 species Detailed

E nginesCO © 2005 Edward S. Blurock, Gladys Moréac, Lund University - All rights reserved. 31 Confidential Lumped Mechanism – Same As Detailed Davis and Law Laminar flame speed for n-heptane/air mixture at p=1 bar and T i =298 K Experimental data (symbols) Detailed mechanism (solid line) Lumped mechanism (dashed line)

E nginesCO © 2005 Edward S. Blurock, Gladys Moréac, Lund University - All rights reserved. 32 Confidential 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

E nginesCO © 2005 Edward S. Blurock, Gladys Moréac, Lund University - All rights reserved. 33 Confidential 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

E nginesCO © 2005 Edward S. Blurock, Gladys Moréac, Lund University - All rights reserved. 34 Confidential Skeletal Mechanisms: Criteria Reaction flow analysis Gives the atomic mass flow through the given reactions. Sensitivity Analysis Finds important (sensitive) species for the wanted results. 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

E nginesCO © 2005 Edward S. Blurock, Gladys Moréac, Lund University - All rights reserved. 35 Confidential 470 reactions 64 species n-C 7 H 16 L-C 7 H 15 L-C 7 H 15 O 2 A-5r B-5r C-5r D-5r A-6r B-6r C-6r D-6r A-7r B-7r C-7r D-7r Skeleton Mechanism : n-heptane 1624 reactions 203 species Detailed Lumped n-C 7 H 16 L-C 7 H 15 L-C 7 H O 2 A-5r B- C- D- A-6r B- C- D- A-7r B- C- D- A-8r B- C- D- L = Lumped species, 5r, 6r, 7r and 8r represent the size of the ring 1362 reactions 142 species n-C 7 H 16 L-C 7 H 15 L-C 7 H O 2 A-5r B- C- D- A-6r B- C- D- A-7r B- C- D- A-8r B- C- D- L = Lumped species, 5r, 6r, 7r and 8r represent the size of the ring n-C 7 H 16 L-C 7 H 15 L-C 7 H O 2 A-5r B- C- D- A-6r B- C- D- A-7r B- C- D- A-8r B- C- D- n-C 7 H 16 L-C 7 H 15 L-C 7 H O 2 A-5r B- C- D- A-6r B- C- D- A-7r B- C- D- A-8r B- C- D- L = Lumped species, 5r, 6r, 7r and 8r represent the size of the ring 1362 reactions 142 species n-C 7 H 16 L-C 7 H 15 L-C 7 H 15 O 2 A-5r B-5r C-5r D-5r A-6r B-6r C-6r D-6r A-7r B-7r C-7r D-7r A-8r B-8r C-8r D-8r L = Lumped species, 5r, 6r, 7r and 8r represent the size of the ring 1362 reactions 142 species Lumped

E nginesCO © 2005 Edward S. Blurock, Gladys Moréac, Lund University - All rights reserved. 36 Confidential 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

E nginesCO © 2005 Edward S. Blurock, Gladys Moréac, Lund University - All rights reserved. 37 Confidential 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

E nginesCO © 2005 Edward S. Blurock, Gladys Moréac, Lund University - All rights reserved. 38 Confidential 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.

E nginesCO © 2005 Edward S. Blurock, Gladys Moréac, Lund University - All rights reserved. 39 Confidential 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

E nginesCO © 2005 Edward S. Blurock, Gladys Moréac, Lund University - All rights reserved. 40 Confidential 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

E nginesCO © 2005 Edward S. Blurock, Gladys Moréac, Lund University - All rights reserved. 41 Confidential 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

E nginesCO © 2005 Edward S. Blurock, Gladys Moréac, Lund University - All rights reserved. 42 Confidential 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

E nginesCO © 2005 Edward S. Blurock, Gladys Moréac, Lund University - All rights reserved. 43 Confidential 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., 4 th Mediterranean Combustion Symposium (2005)

E nginesCO © 2005 Edward S. Blurock, Gladys Moréac, Lund University - All rights reserved. 44 Confidential 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

E nginesCO © 2005 Edward S. Blurock, Gladys Moréac, Lund University - All rights reserved. 45 Confidential Optimization of Rate Coefficients Frequency Factor Temperature Exponent Activation Energy

E nginesCO © 2005 Edward S. Blurock, Gladys Moréac, Lund University - All rights reserved. 46 Confidential Optimization of Rate Coefficients y 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., : p Function to Optimize Model – Experimental Data Response Surface

E nginesCO © 2005 Edward S. Blurock, Gladys Moréac, Lund University - All rights reserved. 47 Confidential Reduction-Optimization Cycle

E nginesCO © 2005 Edward S. Blurock, Gladys Moréac, Lund University - All rights reserved. 48 Confidential Reduction-Optimization Cycle Experiment (line), Original (black dots), Optimized (red triangles), Over-Reduced (white dots) Re-Optimized (purple x) target values.