Using automated techniques to generate reduced mechanisms Louise Whitehouse University of Leeds Department of Chemistry

Introduction Why reduce mechanisms? Techniques used in mechanism reduction –Sensitivity analysis –Quasi-steady-state analysis –Species lumping Reduction of the Master Chemical Mechanism (MCM) v2.0 Development and improvement of automatic reduction methods. Reduction of the isoprene subset of MCM. Reduction of the isoprene subset of the Common Reactive Intermediates (CRI) mechanism.

Reasons for mechanism reduction Large mechanisms such as the full MCM contain large numbers of reactions and species. Running scenarios is very computationally expensive –5 day run can take several hours to simulate. By reducing the dimension of the system – it is possible to accurately represent species without having to deal with a large and expensive mechanism. –this will allow the investigation of a wider range of conditions in a shorter time period.

Automation of mechanism reduction Reasons for automation Large mechanisms make it unfeasible to carry out analysis by hand. Automation allows selection of tolerance parameter and automatic generation of reduced mechanism Techniques that can be used to do this: sensitivity analysis –removal of redundant species –removal of redundant reactions removal of quasi-steady-state species species lumping

Sensitivity analysis - removal of redundant species Important species –the ones we are interested in e.g. HOx, NOx, NO 3, PAN, O 3, H 2 O 2, RO2, HCHO, CH 3 CHO, MVK, MACR Necessary species –Must be included to produce accurate results for the important species. –Coupled to the important species via significant reactions. Redundant species –Not significantly coupled to the set of important and necessary species. –Can therefore be removed from the mechanism. Identification of redundant species –Effect of change in concentration of species i on the rate of production of an N-membered group of important species. –Given by the sum of squares of normalised Jacobian elements (1)

Sensitivity Analysis (2) - Removal of redundant reactions Rate sensitivity analysis effect of a perturbation of a rate parameter on the rate of production of a necessary or important species. The overall sensitivity measure F j is given by: Any reaction j for which F j < threshold can be removed from the mechanism. f i is the right-hand side of the i th rate equation k j is the rate of the j th reaction

Quasi-steady-state analysis This assumption will cause an error Δc i and this can be found for a species by calculating, If the QSSA error is small the species can be removed from the mechanism by applying the approximation (3). Sensitivity analysis tends to lead to the removal of slow time-scales. Large numbers of fast and intermediate time-scales still remain. Species associated with these fast time-scales can be identified using quasi-steady-state-analysis (QSSA). The QSSA involves assuming that for a species c i, (3) (4)

Species Lumping Formation of selected species. Lumped Reactions A common approach to removing species with intermediate timescales is species lumping. Lumped Species Lumped Products Products divided can be replaced by: This leads to reduction in the dimension of the system. A group of species can be represented in the mechanism by a single variable.

Reduction of the Master Chemical Mechanism Automation of these techniques required to reduce MCM v2. MCM contains ~11000 reactions and 3500 species –Impossible to conduct the analysis by hand. 90 trajectories were examined representing polluted UK conditions. Using PUMA data from Birmingham and Middlesbrough 0ppb < total NOx < 300 ppb 0.25 < VOC/NOx < 3 The scenarios were run with emissions and initial conditions designed to simulate the required range of conditions.

Reduction of the MCM (1) Sensitivity and quasi- steady-state analysis stages of reduction removed many species with fast and slow time- scales. Fast <10 -4 s Slow >10 5 s (~1 day)

Reduction of the MCM (2) Intermediate Total At stage 5 of the reductions the reduced mechanism contained 1969 species and 6168 reactions. These techniques leave a large block of species with intermediate time-scales which all contribute in some way to the formation routes of the important and necessary species chosen. The number of species with intermediate time-scales can be reduced by the application of species lumping.

Select new species S i Does S i have the same or similar lifetime to S 1 ? Does S i react in the same number of reactions as S 1 YES Selecting species lumping groups NO Do the reactions have rate coefficients within a given percentage of the same reaction rate for S 1 ? YES NO In reactions with the same rate coefficients does S i react with the same species as S 1 ? YES Add S i to species lump group YES NO

Peracid Example 115 peracids lifetime range 6.48 ×10 3 – 8.1 ×10 4 s 1.08 ×10 3 – 8.1 ×10 4 range of lifetimes (s) 9.35 ×10 3 – 1.31 × ×10 4 – 1.96 × ×10 4 – 5.29 × ×10 3 – 1.0 ×10 4 number of species range of reaction rate with OH (s) 4.52 × – 3.7 × × – 3.03 × × – 1.47 × × – 5.35 × × – 3.69 × J(41) J(24), J(41) J(15), J(41) J(22), J(41) J(18), J(19), J(41) Identical rates:

Formation of lumped equations The i species R j, were originally each formed in only one reaction as follows, with rate coefficient k j. If the group of species R j satisfy the lumping criteria and all react with NO at a rate k 1 then i equations, can be replaced by a single equation, where

Relative product concentrations New lumped species R lump will be formed through i production channels. The ratio between the rate at which the lumped species is formed through each channel can be used to calculate a variable coefficient for each product species in the lumped equation i.e. σ j σ j can be defined as,

Un-lumped Peracid example C 6 H 5 CO 3 H + H 2 O +O 2 + OH C 6 H 5 O 2 + OH + CO 2 C 6 H 5 CO 3 + H 2 O 2-CH 3 C 6 H 4 CO 3 2-CH 3 C 6 H 4 CO 3 H + H 2 O +O 2 + OH 2-CH 3 C 6 H 4 O 2 +OH +CO 2 2-CH 3 C 6 H 4 CO 3 H + H 2 O CH 3 CO 3 + H 2 O CH 3 CO 3 H 2 +O 2 CH 3 O 2 + OH + CO 2 CH 3 CO 3 + H 2 O + OH 6 Reactions All have a chemical lifetime of 8.1×10 4 s. Each species reacts with OH at a rate in the range × s Each species reacts with O 2 at rate represented by J(41). Each species is produced at the same rate, k.

Lumped Peracid Example Define a lump: LUMP1CO 3 H = CH 3 CO 3 H + C 6 H 5 CO 3 H + 2-CH 3 C 6 H 4 CO 3 H CH 3 CO 3 C 6 H 5 CO 3 H 2-CH 3 C 6 H 4 CO 3 + H 2 O LUMP1CO 3 H + H 2 O +O 2 + OH σ 1 CH 3 O 2 + σ 2 C 6 H 5 O 2 + σ 3 2-CH 3 C 6 H 4 O 2 OH + CO 2 σ 1 CH 3 CO 3 + σ 2 C 6 H 5 CO 3 + σ 3 2-CH 3 C 6 H 4 CO 3 H + H 2 O 2 Reactions θ 1 =k[ CH 3 CO 3 ] θ 2 =k[ C 6 H 5 CO 3 ] θ 3 =k[2- CH 3 C 6 H 4 CO 3 H]

Peracid Example continued 4 reactions and 2 species have been removed from the system. This lump was a part of a much larger lump. Creation of the full lump leads to the removal of –58 species –116 reactions. The reaction rate with OH varied over the whole group between 4.52× – 3.7× These techniques can be used on a total of 68 groups.

Comparison of results with full mechanism 802 species lumped into 68 groups. 734 species removed reactions removed. The final lumped mechanism contains 4391 reactions and 1235 species This was shown to be able to accurately reproduce species concentrations over a wide range of conditions.

Species remaining at each level of reduction Fast <10 -4 sIntermediate Slow >10 5 sTotal

Scenario 8 – High NOx

Scenario 63 – Low NOx

Conclusions to MCM reduction Final reduced mechanism –Number of species reduced by 64%. –Computational time reduced by 88%. Errors –< 5% for many of the trajectories studied and 10% for the majority. Lumping strategy could be significantly improved to increase optimality. –Current technique for identification of valid lumps still involves manual selection and implementation. It was decided to apply the same techniques to a subset of the MCM v3.2 to develop them and to compare the results with mechanisms reduced by hand. This would also allow the development of a more automated lumping strategy.

Isoprene mechanism An MCM derived isoprene mechanism was constructed and run over three different scenarios. These looked at the time series of the 13 most important compounds: –HOx, NOx, NO3, PAN, O3, H2O2 and RO2,HCHO, CH3CHO, MVK and MACR. Three scenarios were chosen with different [VOC]/[NOx]. Isoprene was kept constant along the five day run scenario COO3O3 SO 2 H2H2 H2O2H2O2 C5H8C5H8 NONO2 [VOC]/ [NOx] H I ,1 L All concentrations are ppb.

Reduction of the isoprene subset This mechanism had previously been reduced by removing redundant reactions and species and QSSA species by hand. These reduction techniques were repeated using the automated routines. In addition the techniques used for species lumping were developed to make the identification of potential lumps simpler. It should then be possible to compare the size and accuracy of the mechanisms using the two strategies.

Implementation of species lumping Many reactions in the MCM have the same rate coefficient. This method of species lumping exploits this by identifying the number of reactions each species reacts in and the rate coefficient of that reaction. This information is stored in a matrix and then sorted to automatically generate groups of species which react at the same rate with the same species. Each group can then be automatically replaced in the reaction and species source files by a single lumped species. Unfortunately it is not yet possible to tell which species or potential lumps will cause accuracy problems. This is currently under investigation.

Development of lumping techniques Reactions with the same reactants and fractional rates are combined to form a single reaction. –2.4× × 0.8 × RO2ISOPAO2→ISOPAO –2.4× × 0.1 × RO2 ISOPAO2→HC4ACHO –2.4× × 0.1 × RO2 ISOPAO2→ISOPAOH become a single equation of the form, –2.4× × RO2 ISOPAO2 → 0.8 ISOPAO HC4ACHO+ 0.1ISOPAOH This allows more reactions to be considered when automatically searching for potential lumps.

Species removed using lumping Number of species Example species Reactions + L17ISOPAO2HO 2 NONO 3 L210ISOPBOOHOH L42CH2OOCO L56CH3CO3HO 2 NONO 2 L72MACRO2HO 2 NO L82PRONO2AO2HO 2 ScenarioNumber lumps Species involvedremoved H I L e.g. Low

Results full reduced mechanisms HIL species reactions full reduced mechanisms HIL species reactions Automatic results after QSSA full reduced mechanisms HIL species reactions Automatic results after lumping Manual results after QSSA

Results After QSSA significantly more species and reactions have been removed by the manual method This suggests that the automatic method needs to be adjusted to allow greater levels of reduction. After lumping is applied species numbers are lower for all scenarios reactions numbers are lower for the I and L scenarios.

Lifetimes for Isoprene After automatic lumping many slow lifetimes still remain. Again this indicates that the automatic sensitivity analysis stage could be improved.

Lifetime range plots After automatic lumping many slow lifetimes still remain. Again this indicates that the automatic sensitivity analysis stage could be improved. Fast time-scales are almost entirely eliminated. FastSlow Time (s)<10 -4 >10 5 (1 day)

Results - High NOx Conditions

Results - Intermediate NOx Conditions

Results - Low NOx Conditions

Common Reactive Intermediates Mechanism 1 The CRI mechanism is a lumped reduced mechanism. –~570 reactions and ~250 species. Derived from the MCM therefore has potential for the application of species lumping. –Identification of large groups with potential for lumping should be possible. The isoprene subset examined contained 160 species and 439 reactions. Scenarios H, I and L are again used for the reduction. There are no emissions added. 1 Jenkin et al. Atm. Env 36 (2002)

Potential Lumps – CRI mechanism There are 6 main potential lump groups. Number of species Example Species Reactions + L142NRN15O2NO 3 HO 2 NO L220ETHGLY L33CARB17OH L411C2H5NO3OH L54RN10NO3OH L643C2H5OOHOH This could potentially lead to the removal of 117 species and 297 reactions.

Lumping In total 128 species and 345 reactions are removed –This is due to some species gaining infinite lifetimes when other species are lumped. –Other species have very short lifetimes and can also be removed. The mechanism can be reduced to –32 species and 94 reactions for high and intermediate NOx –45 species and 151 reactions for low NOx. Lumping of CRI mechanism allows a larger proportion of the remaining species to be lumped than in the ordinary isoprene mechanism.

Lifetimes for Crimech Isoprene reduction Large number of all lifetime ranges are removed.

Lifetime range plots FastSlow Time (s)<10 -4 >10 5 (1 day) Large number of all lifetime ranges are removed.

Crimech High NOx

Crimech Intermediate NOx

Crimech low NOx

Crimech pan plots low high

Future work Reduce full Crimech mechanism using species lumping. Improve application of automatic sensitivity analysis. Refine isoprene reductions to eliminate more slow species and eliminate further reactions. Carry out specific comparisons between reduced mechanisms produced via the two techniques.

Acknowledgements Thanks to Roberto and Mike Jenkin for providing me with various mechanisms.