Skip to main content
SpringerLink
Log in

Investigation and Improvement of Reaction Mechanisms Using Sensitivity Analysis and Optimization

  • Chapter
  • First Online:
Cleaner Combustion

Part of the book series: Green Energy and Technology ((GREEN))

Abstract

The Chapter will describe a range of mathematical tools for model sensitivity and uncertainty analysis which may assist in the evaluation of large combustion mechanisms. The aim of such methods is to determine key model input parameters that drive the uncertainty in predicted model outputs. Approaches based on linear sensitivity, linear uncertainty and global uncertainty analysis will be described as well as examples of their application to chemical kinetic modelling in combustion. Improving the robustness of model predictions depends on reducing the extent of uncertainty within the input parameters. This can be achieved via a variety of methods including measurements and theoretical calculations. Optimization techniques which bring together wide sources of data can assist in further constraining the input parameters of a model and therefore reducing the overall model uncertainty. Such methods and their recent application to several combustion mechanisms will be described here.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  • Balakrishnan S, Georgopoulos P, Banerjee I et al (2002) Uncertainty consideration for describing complex reaction systems. AIChE J 48:2875–2889

    Article  Google Scholar 

  • Baulch DL, Cobos CJ, Cox RA et al (1992) Evaluated kinetic data for combustion modeling. J Phys Chem Ref Data 21:411

    Article  Google Scholar 

  • Baulch DL, Cobos CJ, Cox RA et al (1994) Summary table of evaluated kinetic data for combustion modeling—supplement-1. Combust Flame 98:59–79

    Article  Google Scholar 

  • Baulch DL, Bowman CT, Cobos CJ et al (2005) Evaluated kinetic data for combustion modeling: supplement II. J Phys Chem Ref Data 34(3):757–1397

    Article  Google Scholar 

  • Bischof C, Carle A, Khademi P et al (1996) The ADIFOR 2.0 system for the automatic differentiation of FORTRAN 77 programes. IEEE J Comput Sci Eng 3:18–32

    Article  Google Scholar 

  • Bischof CH, Roh L, Mauer-oats AJ (1997) ADIC:an extensible automatic differentiation tool for ANSI-C. Soft Pract Exp 27:1427–1456

    Article  Google Scholar 

  • Bischof CH, Bucker HM, Rasch A (2004) Sensitivity analysis of turbulence models using automatic differentiation. SIAM J Sci Comput 26(2):510–522

    Article  MathSciNet  MATH  Google Scholar 

  • Blatman G, Sudret B (2010) Efficient computation of global sensitivity indices using sparse polynomial chaos expansions. Reliab Eng Syst Saf 95(11):1216–1229

    Article  Google Scholar 

  • Bowman C, Hanson R, Davidson D et al (2013) GRI-Mech 2.11.Available from http://www.me.berkeley.edu/gri_mech/. Accessed 15 March 2013

  • Brown NJ, Revzan KL (2005) Comparative sensitivity analysis of transport properties and reaction rate coefficients. Int J Chem Kinet 37:538–553

    Article  Google Scholar 

  • Brown MJ, Smith DB, Taylor SC (1999) Influence of uncertainties in rate constants on computed burning velocities. Combust Flame 117:652–656

    Article  Google Scholar 

  • Burke MP, Klippenstein SJ, Harding LB (2013) A quantitative explanation for the apparent anomalous temperature dependence of OH + HO2− > H2O + O2 through multi-scale modeling. Proc Combust Inst 34:547–555

    Article  Google Scholar 

  • Cantera An open-source, object-oriented software suite for combustion. http://sourceforge.net/projects/cantera/, http://code.google.com/p/cantera/. Accessed 15 March 2013

  • Cheng HY, Sandu A (2009) Uncertainty quantification and apportionment in air quality models using the polynomial chaos method. Environ Model Soft 24(8):917–925

    Article  Google Scholar 

  • Cord M, Sirjean B, Fournet R et al (2012) Improvement of the modeling of the low-temperature oxidation of n-butane: study of the primary reactions. J Phys Chem A 116(24):6142–6158

    Article  Google Scholar 

  • Davis SG, Mhadeshwar AB, Vlachos DG et al (2004) A new approach to response surface development for detailed gas-phase and surface reaction kinetic model optimization. Int J Chem Kinet 36:94–106

    Article  Google Scholar 

  • Davis S, Joshi A, Wang H et al (2005) An optimized kinetic model of H2/CO combustion. Proc Combust Inst 30:1283–1292

    Article  Google Scholar 

  • Davis MJ, Skodje RT, Tomlin AS (2011) Global sensitivity analysis of chemical-kinetic reaction mechanisms: construction and deconstruction of the probability density function. J Phys Chem A 115(9):1556–1578

    Article  Google Scholar 

  • Dunker AM (1981) Efficient calculation of sensitivity coefficients for complex atmospheric models. Atmos Environ 15(7):1155–1161

    Article  Google Scholar 

  • Dunker AM (1984) The decoupled direct method for calculating sensitivity coefficients in chemical kinetics. J Chem Phys 81(5):2385–2393

    Article  Google Scholar 

  • Faure C (2005) An automatic differentiation platform:Odyssée. Fut Gen Comput Sys 21(8):1391–1400

    Article  Google Scholar 

  • Feeley R, Seiler P, Packard A et al (2004) Consistency of a reaction dataset. J Phys Chem A 108:9573–9583

    Article  Google Scholar 

  • Feeley R, Frenklach M, Onsum M et al (2006) Model discrimination using data collaboration. J Phys Chem A 110:6803–6813

    Article  Google Scholar 

  • Feng X-J, Hooshangi S, Chen D et al (2004) Optimizing genetic circuits by global sensitivity analysis. Biophys J 87:2195–2202

    Article  Google Scholar 

  • Frenklach M (1984) Systematic optimization of a detailed kinetic model using a methane ignition example. Combust Flame 58(1):69–72

    Article  Google Scholar 

  • Frenklach M (2007) Transforming data into knowledge—process informatics for combustion chemistry. Proc Combust Inst 31:125–140

    Article  Google Scholar 

  • Frenklach M PrIMe Database. Available from http://www.primekinetics.org/. Available 15 March 2013

  • Frenklach M, Wang H, Rabinowitz MJ (1992) Optimization and analysis of large chemical kinetic mechanisms using the solution mapping method—combustion of methane. Prog Energy Combust Sci 18:47–73

    Article  Google Scholar 

  • Frenklach M, Wang H, Yu C et al (1995) GRI-Mech 1.2. Available from http://www.me.berkeley.edu/gri_mech/. Accessed 15 March 2013

  • Frenklach M, Packard A, Seiler P (2002) Prediction uncertainty from models and data. In: Proceeding of the American control conference, Anchorage

    Google Scholar 

  • Frenklach M, Packard A, Seiler P et al (2004) Collaborative data processing in developing predictive models of complex reaction systems. Int J Chem Kinet 36:57–66

    Article  Google Scholar 

  • Frenklach M, Packard A, Feeley R (2007) Optimization of reaction models with solution mapping. modeling of chemical reactions. R. Carr, Elsevier Science

    Google Scholar 

  • Goldsmith CF, Tomlin AS, Klippenstein SJ (2013) Uncertainty propagation in the derivation of phenomenological rate coefficients from theory: a case study of n-propyl radical oxidation. Proc Combust Inst 34:177–185

    Article  Google Scholar 

  • Helton JC, Johnson JD, Sallaberry CJ et al (2006) Survey of sampling-based methods for uncertainty and sensitivity analysis. Reliab Eng Syst Saf 91(10–11):1175–1209

    Article  Google Scholar 

  • Hughes KJ, Turányi T, Clague AR et al (2001) Development and testing of a comprehensive chemical mechanism for the oxidation of methane. Int J Chem Kinet 33:513–538

    Article  Google Scholar 

  • Hughes KJ, Griffiths JF, Fairweather M et al (2006) Evaluation of models for the low temperature combustion of alkanes through interpretation of pressure-temperature ignition diagrams. Phys Chem Chem Phys 8(27):3197–3210

    Article  Google Scholar 

  • Kee RJ, Rupley FM, Miller JA (1989) CHEMKIN-II:A FORTRAN chemical kinetics package for the analysis of gas-phase chemical kinetics. Sandia National Laboratories, Albuquerque

    Google Scholar 

  • Klippenstein SJ, Harding LB, Davis MJ et al (2011) Uncertainty driven theoretical kinetics studies for CH(3)OH ignition: HO(2) + CH(3)OH and O(2) + CH(3)OH. Proc Combust Inst 33:351–357

    Article  Google Scholar 

  • Konnov AA (2008) Remaining uncertainties in the kinetic mechanism of hydrogen combustion. Combust Flame 152:507–528

    Article  Google Scholar 

  • Li G, Rosenthal C, Rabitz H (2001) High dimensional model representations. J Phys Chem A 105:7765–7777

    Article  Google Scholar 

  • Li G, Wang S-W, Rabitz H (2002a) Practical approaches to construct RS-HDMR component functions. J Phys Chem A 106:8721–8733

    Article  Google Scholar 

  • Li G, Wang S-W, Rabitz H et al (2002b) Global uncertainty assessments by high dimensional model representations (HDMR). Chem Eng Sci 57:4445–4460

    Article  Google Scholar 

  • Li J, Zhao ZW, Kazakov A et al (2007) A comprehensive kinetic mechanism for CO, CH2O, and CH3OH combustion. Int J Chem Kinet 39(3):109–136

    Article  Google Scholar 

  • Lu T, Law C (2009) Toward accommodating realistic fuel chemistry in large-scale computations. Prog Energy Combust Sci 35:192–215

    Article  Google Scholar 

  • Miller D, Frenklach M (1983) Sensitivity analysis and parameter estimation in dynamic modeling of chemical kinetics. Int J Chem Kinet 15:677–696

    Article  Google Scholar 

  • Miller JA, Pilling MJ, Troe J (2005) Unravelling combustion mechanisms through a quantitative understanding of elementary reactions. Proc Combust Inst 30:43–88

    Article  Google Scholar 

  • Nagy T, Turányi T (2011) Uncertainty of Arrhenius parameters. Int J Chem Kinet 43:359–378

    Google Scholar 

  • Nagy T, Turányi T (2012) Determination of the uncertainty domain of the Arrhenius parameters needed for the investigation of combustion kinetic models. Reliab Eng Syst Saf 107:29–34

    Article  Google Scholar 

  • Najm H, Debusschere BJ, Marzouk YM et al (2009) Uncertainty quantification in chemical systems. Int J Numer Meth Eng 80:789–814

    Article  MathSciNet  MATH  Google Scholar 

  • Ó Conaire M, Curran HJ, Simmie JM et al (2004) A comprehensive modeling study of hydrogen oxidation. Int J Chem Kinet 36(11):603–622

    Article  Google Scholar 

  • Oakley J, O’Hagan A (2002) Bayesian inference for the uncertainty distribution of computer model outputs. Biometrika 89(4):769–784

    Article  Google Scholar 

  • Pilling MJ (2009) From elementary reactions to evaluated chemical mechanisms for combustion models. Proc Combust Inst 32:27–44

    Article  Google Scholar 

  • Prager J, Najm HN, Zádor J (2013) Uncertainty quantification in the ab initio rate-coefficient calculation for the \( {\text{CH}}_{ 3} {\text{CH}}\left( {\text{OH}} \right){\text{CH}}_{ 3} + {\text{OH }} - > {\text{CH}}_{ 3} {\text{C}}.\left( {\text{OH}} \right){\text{CH}}_{ 3} + {\text{H}}_{ 2} {\text{O}} \) reaction. Proc Combust Inst 34(1):583–590

    Google Scholar 

  • Qin Z, Lissianski V, Yang H et al (2000) Combustion chemistry of propane: a case study of detailed reaction mechanism optimization. Proc Combust Inst 28:1663–1669

    Article  Google Scholar 

  • Rabitz H, Alis OF (2000) Managing the tyranny of parameters in mathematical modelling of physical systems. In: Saltelli A, Chan K, Scott E (eds) Sensitivity analysis. Wiley, New York, pp 199–224

    Google Scholar 

  • Rabitz H, Aliu ÖF, Shorter J et al (1999) Efficient input-output model representations. Comput Phys Commun 117:11–20

    Article  MATH  Google Scholar 

  • Reagan MT, Najm HN, Ghanem RG et al (2003) Uncertainty quantification in reacting-flow simulations through non-intrusive spectral projection. Combust Flame 132(3):545–555

    Article  Google Scholar 

  • Reagan MT, Najm HN, Debusschere BJ et al (2004) Spectral stochastic uncertainty quantification in chemical systems. Combust Theor Model 8:607–632

    Article  Google Scholar 

  • Ruscic B, Pinzon RE, Morton ML et al (2004) Introduction to active thermochemical tables: several key enthalpies of formation revisited. J Phys Chem A 108:9979–9997

    Article  Google Scholar 

  • Russi T, Packard A, Feeley R et al (2008) Sensitivity analysis of uncertainty in model prediction. J Phys Chem A 112:2579–2588

    Article  Google Scholar 

  • Saltelli A, Scott M, Chen K (eds) (2000) Sensitivity analysis. Wiley, Chichester

    MATH  Google Scholar 

  • Saltelli A, Tarantola S, Campolongo F et al (2004) Sensitivity analysis in practice. A guide to assessing scientific models. Wiley, Chichester

    MATH  Google Scholar 

  • Saltelli A, Ratto M, Tarantola S et al (2006) Sensitivity analysis practices: strategies for model-based inference. Reliab Eng Syst Saf 91(10–11):1109–1125

    Article  Google Scholar 

  • Saltelli A, Ratto M, Andres T et al (2008) Global sensitivity analysis: the Primer. Wiley, New York

    Google Scholar 

  • Seiler P, Frenklach M, Packard A et al (2006) Numerical approaches for collaborative data processing. Optim Eng 7:459–478

    Article  MathSciNet  MATH  Google Scholar 

  • Sheen DA, Wang H (2011) The method of uncertainty quantification and minimization using polynomial chaos expansions. Combust Flame 158(12):2358–2374

    Article  Google Scholar 

  • Sheen DA, You X, Wang H et al (2009) Spectral uncertainty quantification, propagation and optimization of a detailed kinetic model for ethylene combustion. Proc Combust Inst 32:535–542

    Article  Google Scholar 

  • Sheen DA, Rosado-Reyes CM, Tsang W (2013) Kinetics of H atom attack on unsaturated hydrocarbons using spectral uncertainty propagation and minimization techniques. Proc Combust Inst 34:527–536

    Article  Google Scholar 

  • Skodje RT, Tomlin AS, Klippenstein SJ et al (2010) Theoretical validation of chemical kinetic mechanisms: combustion of methanol. J Phys Chem A 114(32):8286–8301

    Article  Google Scholar 

  • Smith G, Golden D, Frenklach M et al (1999) GRI-Mech 3.0. Available from http://www.me.berkeley.edu/gri_mech/. Accessed 15 March 2013

  • Sobol IM (2001) Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates. Math Comput Sim 55(1–3):271–280

    Article  MathSciNet  MATH  Google Scholar 

  • Sobol’ IM (1967) On the distribution of points in a cube and the approximate evaluation of integrals. USSR Comput Math Math Phys 7(4):86–112

    Article  MathSciNet  Google Scholar 

  • Storlie CB, Helton JC (2008) Multiple predictor smoothing methods for sensitivity analysis: description of techniques. Reliab Eng Syst Saf 93(1):28–54

    Article  Google Scholar 

  • Tomlin AS (2006) The use of global uncertainty methods for the evaluation of combustion mechanisms. Reliab Eng Syst Saf 91(10–11):1219–1231

    Article  Google Scholar 

  • Tomlin AS (2013) The role of sensitivity and uncertainty analysis in combustion modelling. Proc Combust Inst 34:159–176

    Article  Google Scholar 

  • Tomlin AS, Ziehn T (2011) The use of global sensitivity methods for the analysis, evaluation and improvement of complex modelling systems. In: Gorban AN, Roose D (eds) Coping with complexity: model reduction and data analysis, vol 75. Springer, Heidelberg, pp 9–36

    Google Scholar 

  • Tsang W (1992) Chemical kinetic data base for propellant combustion. II. Reactions involving CN, NCO, and HNCO. J Phys Chem Ref Data 21:753–791

    Article  Google Scholar 

  • Tsang W, Hampson RF (1986) Chemical kinetic database for combustion chemistry.1. Methane and related compounds. J Phys Chem Ref Data 15(3):1087–1279

    Google Scholar 

  • Turanyi T, Nagy T, Zsely IG et al (2012) Determination of rate parameters based on both direct and indirect measurements. Int J Chem Kinet 44(5):284–302

    Article  Google Scholar 

  • Turányi T, Zalotai L, Dóbé S et al (2002) Effect of the uncertainty of kinetic and thermodynamic data on methane flame simulation results. Phys Chem Chem Phys 4:2568–2578

    Article  Google Scholar 

  • Varga T, Zsély IG, Turányi T et al (2012) Kinetic analysis of ethyl iodide pyrolysis based on shock tube measurements. COST action CM0901 3nd annual meeting. Sofia, Bulgaria

    Google Scholar 

  • Wang SW, Georgopoulos PG, Li G et al (2001) Computationally efficient atmospheric chemical kinetic modeling by means of high dimensional model representation (HDMR). Lect Note Comput Sci 2179:326–333

    Article  Google Scholar 

  • Wang SW, Georgopoulos PG, Li GY et al (2003) Random sampling-high dimensional model representation (RS-HDMR) with nonuniformly distributed variables: application to an integrated multimedia/multipathway exposure and dose model for trichloroethylene. J Phys Chem A 107(23):4707–4716

    Article  Google Scholar 

  • Wang H, You X, Joshi A et al (2007) USC Mech Version II. High-temperature combustion reaction model of H2/CO/C1-C4 compounds. Available from http://ignis.usc.edu/USC_Mech_II.htm

  • Warnatz J (1984) Rate coefficients in the C/H/O system. In: Gardiner WC (ed) Combustion chemistry. Springer, New York, pp 197–361

    Google Scholar 

  • Westbrook CK, Dryer FL (1981) Chemical kinetics and modeling of combustion processes. Proc Combust Inst 18:749–767

    Google Scholar 

  • Westbrook CK, Dryer FL (1984) Chemical kinetic modeling of hydrocarbon combustion. Prog Energy Combust Sci 10:1–57

    Article  Google Scholar 

  • You XQ, Russi T, Packard A et al (2011) Optimization of combustion kinetic models on a feasible set. Proc Combust Inst 33:509–516

    Article  Google Scholar 

  • You XQ, Packard A, Frenklach M (2012) Process informatics tools for predictive modeling: hydrogen combustion. Int J Chem Kinet 44(2):101–116

    Article  Google Scholar 

  • Zádor J, Zsély IG, Turányi T et al (2005) Local and global uncertainty analyses of a methane flame model. J Phys Chem A 109:9795–9807

    Article  Google Scholar 

  • Zádor J, Zsély IG, Turányi T (2006) Local and global uncertainty analysis of complex chemical kinetic systems. Reliab Eng Syst Saf 91(10–11):1232–1240

    Article  Google Scholar 

  • Ziehn T (2008) Development and application of global sensitivity analysis methods in environmental and safety engineering. Ph.D., University of Leeds

    Google Scholar 

  • Ziehn T, Tomlin AS (2008) A global sensitivity study of sulphur chemistry in a premixed methane flame model using HDMR. Int J Chem Kinet 40:742–753

    Article  Google Scholar 

  • Ziehn T, Tomlin AS (2009) GUI-HDMR—a software tool for global sensitivity analysis of complex models. Environ Model Soft 24(7):775–785

    Article  Google Scholar 

  • Ziehn T, Hughes KJ, Griffiths JF et al (2009) A global sensitivity study of cyclohexane oxidation under low temperature fuel-rich conditions using HDMR methods. Combust Theory Model 13:589–605

    Article  Google Scholar 

  • Zsely IG, Varga T, Nagy T et al (2012) Determination of rate parameters of cyclohexane and 1-hexene decomposition reactions. Energy 43(1):85–93

    Article  Google Scholar 

  • Zsély IG, Zádor J, Turányi T (2005) Uncertainty analysis backed development of combustion mechanisms. Proc Combust Inst 30:1273–1281

    Article  Google Scholar 

  • Zsély IG, Zádor J, Turányi T (2008) Uncertainty analysis of NO production during methane combustion. Int J Chem Kinet 40:754–768

    Article  Google Scholar 

  • Zsély IG, Nagy T, Varga T et al (2012) Optimization of a hydrogen combustion mechanism. COST action CM0901 3nd annual meeting. Sofia, Bulgaria

    Google Scholar 

Download references

Acknowledgments

TT acknowledges the financial support of OTKA grants K84054 and NN100523. AST acknowledges the financial support of EPSRC through grants GR/R76172/01(P) and GR/R39597/01.

Author information

Authors and Affiliations

  1. Energy Research Institute, University of Leeds, Leeds, LS29JT, UK

    Alison S. Tomlin

  2. Institute of Chemistry, Eötvös University (ELTE), Budapest, Hungary

    Tamás Turányi

Authors
  1. Alison S. Tomlin
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Tamás Turányi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Alison S. Tomlin .

Editor information

Editors and Affiliations

  1. Laboratoire Reactions et Genie des Proce, ENSIC, Nancy Cedex, France

    Frédérique Battin-Leclerc

  2. Combustion Chemistry Centre, National University of Ireland, Galway, Ireland

    John M. Simmie

  3. Department of Energy Sciences, Division, University of Lund, Lund, Sweden

    Edward Blurock

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer-Verlag London

About this chapter

Cite this chapter

Tomlin, A.S., Turányi, T. (2013). Investigation and Improvement of Reaction Mechanisms Using Sensitivity Analysis and Optimization. In: Battin-Leclerc, F., Simmie, J., Blurock, E. (eds) Cleaner Combustion. Green Energy and Technology. Springer, London. https://doi.org/10.1007/978-1-4471-5307-8_16

Download citation

  • DOI: https://doi.org/10.1007/978-1-4471-5307-8_16

  • Published:

  • Publisher Name: Springer, London

  • Print ISBN: 978-1-4471-5306-1

  • Online ISBN: 978-1-4471-5307-8

  • eBook Packages: EnergyEnergy (R0)

Publish with us

Policies and ethics

Search

Navigation