Uncertainty Quantification in Chemical Modeling

Authors

  • A. Mirzayeva German Aerospace Center (DLR), Institute of Combustion Technology, 70569, Stuttgart, Germany
  • N. A. Slavinskaya German Aerospace Center (DLR), Institute of Combustion Technology, 70569, Stuttgart, Germany
  • M. Abbasi German Aerospace Center (DLR), Institute of Combustion Technology, 70569, Stuttgart, Germany
  • J. H. Starcke German Aerospace Center (DLR), Institute of Combustion Technology, 70569, Stuttgart, Germany
  • W. Li Mechanical Engineering, University of California at Berkeley, Berkeley, CA 94563, USA
  • M. Frenklach Mechanical Engineering, University of California at Berkeley, Berkeley, CA 94563, USA

DOI:

https://doi.org/10.18321/ectj706

Abstract

A module of PrIMe automated data-centric infrastructure, Bound-to-Bound Data Collaboration (B2BDC), was used for the analysis of systematic uncertainty and data consistency of the H2/CO reaction model (73/17). In order to achieve this purpose, a dataset of 167 experimental targets (ignition delay time and laminar flame speed) and 55 active model parameters (pre-exponent factors in the Arrhenius form of the reaction rate coefficients) was constructed. Consistency analysis of experimental data from the composed dataset revealed disagreement between models and data.
Two consistency measures were applied to identify the quality of experimental targets (Quantities of Interest, QoI): scalar consistency measure, which quantifies the tightening index of the constraints while still ensuring the existence of a set of the model parameter values whose associated modeling output predicts the experimental QoIs within the uncertainty bounds; and a newly-developed method of computing the vector consistency measure (VCM), which determines the minimal bound changes for QoIs initially identified as inconsistent, each bound by its own extent, while still ensuring the existence of a set of the model parameter values whose associated
modeling output predicts the experimental QoIs within the uncertainty bounds. The consistency analysis suggested that elimination of 45 experimental targets, 8 of which were self- inconsistent, would lead to a consistent dataset. After that the feasible parameter set was constructed through decrease uncertainty parameters for several reaction rate coefficients. This dataset was subjected for the B2BDC framework model optimization and analysis on. Forth methods of parameter optimization were applied, including those unique in the B2BDC framework. The optimized models
showed improved agreement with experimental values, as compared to the initiallyassembled
model. Moreover, predictions for experiments not included in the initial dataset were investigated. The results demonstrate benefits of applying the B2BDC methodology for development of predictive kinetic models.

References

(1). M. Frenklach, “PrIMe,” URL: http://primekinetics.org.

(2). R. Feeley, P. Seiler, A. Packard, and M. Frenklach, J. Phys. Chem. A 108 (44) (2004) 9573–9583. Crossref DOI: https://doi.org/10.1021/jp047524w

(3). M. Frenklach, A. Packard, P. Seiler, and R. Feeley, Int. J. Chem. Kinet. 36 (1) (2004) 57–66. Crossref DOI: https://doi.org/10.1002/kin.10172

(4). T. Russi, A. Packard, R. Feeley, and M. Frenklach, J. Phys. Chem. A 112 (12) (2008) 2579–2588. DOI: https://doi.org/10.1021/jp076861c

(5). T. Russi, A. Packard, and M. Frenklach, Chem. Phys. Lett. 499 (1-3) (2010) 1–8. Crossref DOI: https://doi.org/10.1016/j.cplett.2010.09.009

(6). M. Frenklach, A. Packard, and R. Feeley, "Optimization of Reaction Models with Solution Mapping," Modeling of Chemical Reactions, edited by R.W. Carr, 1st ed., Elsevier, Amsterdam, 2007, pp. 243–293. Crossref DOI: https://doi.org/10.1016/S0069-8040(07)42006-4

(7). P. Seiler, M. Frenklach, A. Packard, and R. Feeley, Optim. Eng. 7 (4) (2006) 459–478. Crossref DOI: https://doi.org/10.1007/s11081-006-0350-4

(8). M. Frenklach, P. Combust. Inst. 31 (1) (2017) 125–140. Crossref DOI: https://doi.org/10.1016/j.proci.2006.08.121

(9). N.A. Slavinskaya, U. Riedel, S.B. Dworkin, and M.J. Thomson, Combust. Flame 159 (3) (2012) 979–995. Crossref DOI: https://doi.org/10.1016/j.combustflame.2011.10.005

(10). Hedge, W. Li, J. Oreluk, Packard, A.M. Frenklach, Consistency analysis for massively inconsistent datasets in Bound-to-Bound Data Collaboration. In preparation.

(11). R. Atkinson, D.L. Baulch, R.A. Cox, J.N. Crowley, R.F. Hampson, R.G. Hynes, M.E. Jenkin, M.J. Rossi, and J. Troe, Atmospheric Chemistry and Physics 4 (2004) 1461–1738. Crossref DOI: https://doi.org/10.5194/acp-4-1461-2004

(12). H. Wang, X. You, A.V. Joshi, S.G. Davis, A. Laskin, F. Egolfopoulos, and C.K. Law, “USC Mech Version II. High-Temperature Combustion Reaction Model of H2/CO/C1-C4 Compounds,” URL: http://ignis.usc.edu/USC_Mech_II.htm.

(13). J.A. Miller, and C.F. Melius, Combust. Flame 91 (1) (1992) 21–39. Crossref DOI: https://doi.org/10.1016/0010-2180(92)90124-8

(14). T. Kathrotia, M. Fikri, M. Bozkurt, M. Hartmann, U. Riedel, and C. Schulz, Combust. Flame 157 (7) (2010) 1261–1273. DOI: https://doi.org/10.1016/j.combustflame.2010.04.003

(15). D.L. Baulch, C.T. Bowman, C.J. Cobos, R.A. Cox, Th. Just, J.A. Kerr, M.J. Pilling, D. Stocker, J. Troe, W. Tsang, R.W. Walker, J. Warnatz, J. Phys. Chem. Ref. Data 34 (3) (2005) 757. Crossref DOI: https://doi.org/10.1063/1.1748524

(16). J. Troe, P. Combust. Inst. 28 (2000) 1463–1469. Crossref DOI: https://doi.org/10.1016/S0082-0784(00)80542-1

(17). N. Cohen and K.R. Westberg, J. Phys. Chem. Ref. Data 12 (1983) 531. Crossref DOI: https://doi.org/10.1063/1.555692

(18). I.G. Zsély, J. Zádor, T. Turányi, P. Combust. Inst. 30 (2005) 1273–1281. Crossref DOI: https://doi.org/10.1016/j.proci.2004.08.172

(19). H. Sun, S.I. Yang, G. Jomaas, and C.K. Law, P. Combust. Inst. 31 (1) (2007) 439–446. Crossref DOI: https://doi.org/10.1016/j.proci.2006.07.193

(20). J.J. Troe, J. Phys. Chem. 83 (1979) 114–126. Crossref DOI: https://doi.org/10.1021/j100464a019

(21). J. Li, Z. Zhao, A. Kazakov, M. Chaos, F.L. Dryer, and J.J. Scire, Int. J. Chem. Kinet. 39 (2007) 109–136. Crossref DOI: https://doi.org/10.1002/kin.20218

(22). D.F. Davidson, and R.K. Hanson, "Interpreting Shock Tube Ignition Data," WSSCI Fall 2003 Meeting, University of California at Los Angeles, 2003. Crossref DOI: https://doi.org/10.21236/ADA422646

(23). E.L. Petersen, and R.K. Hanson, Shock Waves 10 (2001) 405–420. Crossref DOI: https://doi.org/10.1007/PL00004051

(24). E.L. Petersen, M.J.A. Rickard, M.W. Crofton, E.D. Abbey, M.J. Traum, and D.M. Kalitan, Meas. Sci. Technol. 16 (2005) 1716–1729. Crossref DOI: https://doi.org/10.1088/0957-0233/16/9/003

(25). E.L. Petersen, and R.K. Hanson, Shock Waves 15 (2006) 333–340. Crossref DOI: https://doi.org/10.1007/s00193-006-0032-3

(26). F.L. Dryer, and M. Chaos, Combust. Flame 152 (1-2) (2008) 293–299. Crossref DOI: https://doi.org/10.1016/j.combustflame.2007.08.005

(27). D.F. Davidson, and R.K. Hanson, Shock Waves 19 (2009) 271–283. Crossref DOI: https://doi.org/10.1007/s00193-009-0203-0

(28). M. Ihme, Combust. Flame 159 (2012) 1592–1604. Crossref DOI: https://doi.org/10.1016/j.combustflame.2011.11.022

(29). J. Urzay, N. Kseib, D.F. Davidson, G. Iaccarino, and R.K. Hanson, Combust. Flame 161 (2014) 1–15. Crossref DOI: https://doi.org/10.1016/j.combustflame.2013.08.012

(30). A.B. Mansfield, and M.S. Wooldridge, Combust. Flame 161 (2014) 2242–2251. Crossref

(31). K.P. Grogan, and M. Ihme, P. Combust. Inst. 35 (2015) 2181–2189. Crossref DOI: https://doi.org/10.1016/j.proci.2014.07.074

(32). D.M. Kalitan, J.D. Mertens, M.W. Crofton, and E.L. Petersen, J. Propul. Power 23 (2007) 1291– 1301. Crossref DOI: https://doi.org/10.2514/1.28123

(33). E.L. Petersen, D.M. Kalitan, A.B. Barrett, S.C. Reehal, J.D. Mertens, D.J. Beerer, R.L. Hack, and V.G. McDonell, Combust. Flame 149 (1-2) (2007) 244–247. DOI: https://doi.org/10.1016/j.combustflame.2006.12.007

(34). J.D. Mertens, D.M. Kalitan, A.B. Barrett, and E.L. Petersen, P. Combust. Inst. 32 (2009) 295– 303. Crossref DOI: https://doi.org/10.1016/j.proci.2008.06.163

(35). J. Herzler and C. Naumann, Combust. Sci. Technol. 180 (2008) 2015–2028. Crossref DOI: https://doi.org/10.1080/00102200802269715

(36). M.C. Krejci, O. Mathieu, A.J. Vissotski, S. Ravi, T.G. Sikes, E.L. Petersen, A. Kérmonès, W. Metcalfe, H.J. Curran, J. Eng. Gas Turbines Power 135 (2) (2013) 021503. Crossref DOI: https://doi.org/10.1115/1.4007737

(37). A.B. Mansfield, M.S. Wooldridge, Combust. Flame 161 (9) (2014) 2242–2251. Crossref DOI: https://doi.org/10.1016/j.combustflame.2014.03.001

(38). O. Mathieu, M.M. Kopp, E.L. Petersen, P. Combust. Inst. 2013, 34, (2) 3211–3218. Crossref DOI: https://doi.org/10.1016/j.proci.2012.05.008

(39). S.S. Vasu, D.F. Davidson, R.K. Hanson, Energy Fuels 25 (3) (2011) 990–997. Crossref DOI: https://doi.org/10.1021/ef1015928

(40). M. Goswami, S.C. Derks, K. Coumans, W.J. Slikker, M.H. de Andrade Oliveira, R.J. Bastiaans, C.C. Luijten, L.P. H. de Goey, and A.A. Konnov, Combust. Flame 160 (9) (2013) 1627–1635. Crossref DOI: https://doi.org/10.1016/j.combustflame.2013.03.032

(41). F.N. Egolfopoulos, N. Hansen, Y. Ju, K. Kohse- Höinghaus, C.K. Law, and F. Qi, Prog. Energ. Combust. 43 (2014) 36–67. Crossref DOI: https://doi.org/10.1016/j.pecs.2014.04.004

(42). J. Natarajan, T. Lieuwen, and J. Seitzman, Combust. Flame 151 (1-2) (2007) 104–119. Crossref DOI: https://doi.org/10.1016/j.combustflame.2007.05.003

(43). M.I. Hassan, K.T. Aung, and G.M. Faeth, J. Propul. Power 13 (2) (1997) 239–245. Crossref DOI: https://doi.org/10.2514/2.5154

(44). J. Natarajan, Y. Kochar, T. Lieuwen, and J. Seitzman, P. Combust. Inst. 32 (2009) 1261– 1268. Crossref DOI: https://doi.org/10.1016/j.proci.2008.06.110

(45). S. Sun, S. Meng, Y. Zhao, H. Xu, Y. Guo, Y. Qin, Int. J. Hydrogen Energy 41 (4) (2016) 3272– 3283. Crossref DOI: https://doi.org/10.1016/j.ijhydene.2015.11.120

(46). D. Lapalme, P. Seers, Int. J. Hydrogen Energy 39 (7) (2014) 3477–3486. Crossref DOI: https://doi.org/10.1016/j.ijhydene.2013.12.109

(47). Y. Xie, J. Wang, N. Xu, S. Yu, Z. Huang, Int. J. Hydrogen Energy 39 (7) (2014) 3450–3458. Crossref DOI: https://doi.org/10.1016/j.ijhydene.2013.12.037

(48). W.B. Weng, Z.H. Wang, Y. He, R. Whiddon, Y.J. Zhou, Z.S. Li, K.F. Cen, Int. J. Hydrogen Energy 40 (2) (2015) 1203–1211. Crossref DOI: https://doi.org/10.1016/j.ijhydene.2014.11.056

(49). Y. Zhang, W. Shen, M. Fan, H. Zhang, S. Li, Combust. Flame 161 (10) (2014) 2492–2495. Crossref DOI: https://doi.org/10.1016/j.combustflame.2014.03.016

(50). Y. Xie, J. Wang, N. Xu, S. Yu, M. Zhang, Z. Huang, Energy Fuels 28 (5) (2014) 3391–3398. Crossref DOI: https://doi.org/10.1021/ef4020586

(51). R.J. Kee, F.M. Rupley, and J.A. Miller, “CHEMKIN-II: A FORTRAN chemical kinetics package for the analysis of gas- phase chemical kinetics," SAND89-8009B, UC-706; Sandia National Laboratories: Albuquerque, NM, 1993.

(52). Kintech Lab Ltd., “Chemical Workbench®,” Software Package, URL: http://www.kintechlab.com/.

(53). X. You, T. Russi, A. Packard, and M. Frenklach, P. Combust. Inst. 33 (1) (2011) 509–516. Crossref DOI: https://doi.org/10.1016/j.proci.2010.05.016

(54). T. Varga, C. Olm, T. Nagy, I.G. Zsély, É. Valkó, R. Pálvölgyi, H.J. Curran, T. Turányi, Int. J. Chem. Kinet. 48 (8) (2016) 407–422. Crossref DOI: https://doi.org/10.1002/kin.21006

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Published

24-01-2018

How to Cite

Mirzayeva, A., Slavinskaya, N. A., Abbasi, M., Starcke, J. H., Li, W., & Frenklach, M. (2018). Uncertainty Quantification in Chemical Modeling. Eurasian Chemico-Technological Journal, 20(1), 33–43. https://doi.org/10.18321/ectj706

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