WORKSHOP Saint Denis La Plaine, November Mechanism Reduction: Methodologies and Examples

Transcription

1 SAFe and Efficient hydrocarbon oxidation processes by KINetics and Explosion expertise and development of computational process engineering tools Project No. EVG1-CT WORKSHOP Saint Denis La Plaine, November 2006 Mechanism Reduction: Methodologies and Examples M. Fairweather, J.F. Griffiths,, R. Porter, A.S. Tomlin University of Leeds 1

2 Mechanism Reduction Mechanism Reduction The Process by which a comprehensive chemical reaction mechanism is reduced in size. Can be taken to a wide range of levels by various techniques. Redundant species Identification and removal. Redundant reaction Identification and removal. These lead to reduced schemes that are still ordinary chemical reaction mechanisms, i.e. sets of elementary chemical reactions that constitute a minimal set required to reproduce the behaviour of the full scheme. 2

3 Mechanism Reduction Background and Issues Sensitivity Analysis - The mathematical basis by which redundant species and reactions may be identified has a long history. The main problem we face is how to apply them in a systematic and efficient manner to the chemical system we are interested in here a fuel/oxidiser composition evolving in time with heat generation and subsequent temperature increase. CHEMKIN TM : Reaction Design, KINALC: 3

4 Mechanism Reduction Automation Why? Manual reductions involve many laborious steps. Running full kinetic models with multiple initial conditions Interpreting results of local sensitivity analysis methods at each condition. Producing and testing the reduced mechanisms. Many man hours potentially to be saved. Less prone to Human error. Ultimately leads to better mechanisms. 4

5 Mechanism Reduction 1200 Temperature/time profile, butane autoignition T / K The numbers at the red symbols indicate the numbers of necessary species identified as being important at that point. t / s 5

6 Mechanism Reduction Automation procedure Automate the process of selecting relevant points at which to perform Sensitivity Analysis. Integrate the mathematical procedures of Sensitivity analysis within the numerical integration code. Encapsulate everything within Unix shell scripts to automate the repetitive aspects and perform all aspects of data and mechanism manipulations. 6

7 Mechanism Reduction Lumping Techniques Designed to further reduce reaction mechanisms by lumping species and/or reactions. Advantage of reducing yet further the mechanism size, and reducing computational effort. Disadvantage that the scheme that is so produced is losing it s connection to physical reality as manifested by a set of identifiable individual elementary chemical reactions, ultimately it may end up as a purely abstract set of mathematical equations. Will illustrate with respect to Reaction lumping as performed by application of the Quasi-Steady State Approximation (QSSA). These start to show the difficulties, it s application is not amenable to automation, and the resulting mechanisms are less flexible in their use. 7

8 Mechanism Reduction Compounds Investigated Alkanes (propane, butane, heptane) Cycloalkanes (cyclohexane) Alkenes (hexene) Aromatics (o,m,p-xylene) 8

9 n-heptane An Ignition diagram generated from the full scheme (358 species, 2411 reactions) 2.0 Ignition Boundary Cool Flame Boundary Mechanism Reduction Initial Conditions Ignition P/atm 1.0 Cool flames 0.5 Slow reaction

10 Temperature-time time profiles At the 3 designated points in the previous diagram, from the full scheme (358 species, 2411 reactions) Point Point 2 Point

11 Temperature-time time profiles After redundant species removed (257 species,1256 reactions) Point Point 2 Point

12 Temperature-time time profiles After redundant species & reactions removed (236 species, 810 reactions) The Skeleton mechanism Point Point 2 Point

13 Ignition diagram comparisons 2.0 Full Scheme (358 species, 2411 reactions) Skeleton Scheme (236 species, 810 reactions) Mechanism Reduction Initial Conditions P/atm

14 Skeleton structure H 16 8 radical abstractions 6 product channels other isomers (4 isomers) alkene + R + +H OOH + H 16 (4 isomers) 31 product channels OOH other isomers (25 isomers) + OOH (25 isomers) OH + product 14

15 Skeleton structure reduction Aim to remove most R, QOOH, QOOH and R radicals How? By the systematic application of the quasi steady state approximation (QSSA) 15

16 QSSA Candidate species? formal mathematical techniques allow their identification most, if not all, radicals. Incorporated into our automated reduction procedures. k 2 A B k -1 d[b] dt k 1 C = 0, hence k 1 [A]=[B](k -1 + k 2 ), hence [B]=[A] k 1 k -1 + k 2 k A C k where k = k k -1 + k 2 16

17 QSSA Complex schemes R34 OO 2 product channels Q 1 OOH 2 product channels Q 4 OOH Q 2 OOH Q 3 OOH 4 product channels 4 product channels Q 1 OOH Q 4 OOH Q 2 OOH Q 3 OOH OH + H 14 O 3 decomposition products 17

18 QSSA Complex schemes The simultaneous equations obtained from such a complex set of interactions are too intractable to be solved manually Therefore do it computationally with MAPLE Gives solutions of the form: [Q 1 OOH] = [R34 ] f 1 (k) [Q 2 OOH] = [R34 ] f 2 (k) etc. Hence, replace the QSSA species and associated reactions with: k 1 R34 (+ ) product channel 1 k 13 product channel 13 18

19 H 16 8 radical abstractions 6 product channels other isomers (4 isomers) alkene + R + +H OOH + H 16 (4 isomers) 31 product channels OOH other isomers (25 isomers) + OOH (25 isomers) OH + product 19

20 H 16 8 radical abstractions 6 product channels other isomers (4 isomers) alkene + R + +H OOH + H 16 (4 isomers) 31 product channels OOH other isomers (25 isomers) + OOH (25 isomers) OH + product 20

21 H 16 8 radical abstractions alkene + H + 6 product channels other isomers (4 isomers) alkene + R + OOH + +H H 16 (4 isomers) 31 product channels OOH other isomers (25 isomers) + OOH (25 isomers) OH + product 21

22 6 product channels alkene + H alkene + R H 16 8 radical abstractions + other isomers (4 isomers) + OOH + +H H 16 (4 isomers) 31 product channels OOH other isomers (25 isomers) + OOH (25 isomers) OH + product 22

23 H 16 8 radical abstractions alkene + H + 6 product channels other isomers alkene + R + (4 isomers) 33 product channels Each product channel of + has a unique effective rate coefficient in terms of all of the other rate coefficients that were removed by applying the QSSA. Create a customised numerical integration code for this new mechanism that contains these complex expressions as derived from MAPLE. 23

24 full (358 species, 2411 reactions). species removed (257 species, 1256 reactions). species & reactions removed (236 species, 810 reactions). QSSA reduction (122 species, 515 reactions). QSSA reduction with (118 species, 507 reactions) Point Point 2 Point

25 H 16 (4 isomers) 8 radical abstractions 6 product channels alkene + H alkene + R 33 product channels Remove all the heptyl isomers. Keep the heptylperoxy isomers. Remove all subsequent C7 radicals produced from heptylperoxy. 25

26 full (358 species, 2411 reactions). species & reactions removed (236 species, 810 reactions). QSSA reduction of the reduced scheme (118 species, 530 reactions). Point 1 Point 2 Point

27 Further reduction Go back to the original methods of identifying redundant species and reactions, apply these to the QSSA reduced scheme. Identify product only species, amalgamate them into single dummy species. 27

28 full (358 species, 2411 reactions), 140s species & reactions removed (236 species, 810 reactions), 58s QSSA reduction of the reduced scheme (118 species, 530 reactions), 19s further normal reduction of the QSSA scheme (110 species, 452 reactions), <9s replacement of product only species with a dummy species (83 species, 452 reactions) Point 1 Point 2 Point

29 Even the most extreme reduction does a good job Full mechanism (358 species 2411 reactions) Skeleton mechanism (236 species 810 reactions) QSSA reduced mechanism (83 species 452 reactions) Ignition P/torr Cool flames Slow reaction

30 Reduction Example - Cyclohexane Cyclohexane in air, Stoichiometric proportions 499 species, 1298 irreversible reversible reactions 2.5 p / atm stage ignition Slow Reaction Cool flame 2 cf Slow Reaction T a / K 30

31 Reduction Example - Cyclohexane Full scheme, 499 species, 2323 reactions Stage - 1, Species reduced, 104 species, 541 reactions Stage - 2, Reaction reduced, 100 species and 238 reactions 2.5 P / atm stage 1.0 Ignition Slow 0.5 Cool flames Reaction Slow 0.0 Reaction T a / K 31

32 Reduction Example - Cyclohexane By concentrating in a particular area, a better reduction can be achieved for that area of interest, eg. In this case for minimum ignition temperatures. Scope for further reduction via QSSA Pressure / atm Full scheme Reduction conditions 60 species, 290 mixed reactions T a / K 32

33 Conclusions Conclusions Methods of applying sensitivity analysis have been automated. Allows mechanisms to be reduced in an efficient manor with minimal user intervention. These methods allow redundant species and reactions to be identified and removed. Lumping methods, in particular reaction lumping as implemented by applying the QSSA have shown that significant further reductions can be made without loss of accuracy. Demonstrated in this presentation with respect to n-heptane and cyclohexane. 33