Pressure dependent mechanism for H/O/C(1) chemistry

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1 Paper # P-22 Topic: Kinetics 5 th US ombustion Meeting rganized by the Western States Section of the ombustion Institute and osted by the University of alifornia at San Diego March 25-28, Pressure dependent mechanism for //(1) chemistry Joseph W. Bozzelli, Rubik Asatryan, hris J. Montgomery 2 and had Sheng 1 Department of hemistry and Environmental Science, New Jersey Institute of Technology, Newark, NJ 07102, USA 2 Reaction Engineering International, Salt Lake ity, UT 84101, USA A pressure dependent kinetic sub-mechanism for x x 1 species is developed based on literature data for reactions of the hydrogen-oxygen subset and paths involving abstraction of hydrogen atoms. Pressure and temperature dependent rate constants are determined for bimolecular, chemical activation (association and addition) and unimolecular (thermal) dissociation reactions using multi-frequency QRRK analysis for k(e) and master Equation analysis for fall-off. Pressure and temperature dependent rate constants are expressed in the form of 7x3 hebyshev polynomials over 0.01 to 100 atm and 300 to 3000K. The chemical activation systems include reactions of, 2,, 2 with the following carbon species:, =, 2 =, 2, 3, 3 plus selected 2 species, with dissociation analysis for stabilized adducts. Improved rate constants are used for 2 + reaction (near pressure independent) expressed as k 1a = 8.45 x10 8 xt 1.21 exp(17267cal/rt) and k 1b =7.14x10 7 xt 1.57 exp(17721cal/rt) cm 3 mol -1 s -1 (two alternative channels leading to the same 2 + products via different transition states) at BS-QB3 level calculations and QRRK/ME analysis. hemkin model results are compared with ignition time (delay) experiments in the / 2 / x system versus fuel equivalence ratio and pressure. The mechanism consists of ~35 species and 150 reactions, with over 40 being pressure dependent. 1. Introduction ydrocarbon combustion processes involve varieties of chemical activation (bimolecular association or addition) reactions through highly energized species that can undergo rapid transformations before collisional stabilization. Elementary reaction steps in such processes including also unimolecular dissociation of small molecules are pressure dependent and need to be characterized properly in detailed chemical kinetic models [1-3]. A methodology for implementation of the combined pressure and temperature dependences of these reactions based on the quantum RRK/Master Equation analysis has been developed and evaluated in a number of our studies [3-6]. In this study we present a mechanism that includes pressure dependence for some 30 chemical activation and the corresponding unimolecular dissociation reactions on adducts in these system. The reactions encompass the 2 / 2 reaction subset through two carbon atoms and oxygenated one and two carbon moieties, // 1 / 2. The model consists of 125 species and 650 elementary reactions, with over 295 of which being pressure dependent. Reactions of the hydrogen-oxygen subset and paths involving abstraction of hydrogen atoms from molecules are based on evaluated 1

2 literature data [7-11]. Pressure independent chemistry of 2 -chemistry is also based on evaluated literature data. The mechanism is applied to predict ignition delay times in 2 / and to a number of studies involving 1 / 2 oxidation where experimental data at different pressures is available. The objective of this project is to develop a fundamentally based, pressure dependent reaction mechanism for // 1 / 2 modeling in both low moderate (up to 1100K) and high temperature, near stoichiometric and fuel lean reaction systems. It is also intended that the mechanism be useful as a sub-mechanism for larger hydrocarbon and oxygenated hydrocarbon models. 2. Detailed hemical-kinetic Model The mechanism includes radical pool determining subsets and chemically activated reactions of, 2,, 2 with the following carbon species:, =, 2 =, 2, 3, 3 plus a significant fraction of 2 species reactions with 2,, 2. The mechanism also includes the corresponding dissociation reactions of important adducts that become stabilized. Pathways for formation and oxidation of higher molecular weight products such as 2 - hydrocarbons are also included. A listing of chemical activation reactions is in Table 1. The stabilized adducts formed by these addition and association reactions are also treated for pressure fall-off. Table 1: The Main hemical Activation Reactions included in the Master Mechanism NJ-REI-1 + 2, 2, adducts cis and trans rotamers of and Unimolecular dissociation of = = +,, 2, 2, and unimolecular dissociation of adducts 2 = unimolecular dissociation 3 +,, 2,,, 2, 3, 3 and unimolecular dissociation of adducts 2 + 2, 3, 2 and unimolecular dissociation 4, 2, 3, 3 unimolecular dissociation , 2,, 3 and isomerization to 2 (vinylidene) 2 3 +, 2,, == (ketenyl radical) + 2, ,, 2, 3 3 = +,, 2, adducts ( 3 (=) 2 +, 2, adducts () 2 3 (=) 2

3 3 2 +,,, 2, 2 adducts 3 2, dissociation, reaction with + 2, 2 - adduct dissociation dissociation, reaction with 2, 2 - adduct dissociation dissociation channels dissociation channels 3 2 dissociation ,, 2, 3 Pressure- and temperature dependent rate constants are calculated using multi frequency quantum Rice-Ramsperger - Kassel (QRRK) formalism for k(e). Two methods are employed to analyze the collision deactivation of the energized adducts (fall-off region): master equation analysis and the modified strong collision model). Reduced set of vibration frequencies is used to reproduce accurately ratios of density of states to partition coefficient [6, 12] implemented in the TERM computer package [13]. 3. Improvements in Kinetics Parameters of the + 2 Reaction ne example is the pressure dependence and ratio of reaction paths as functions of pressure and temperature in the elementary reaction system of carbon monoxide with hydroxyl and with hydroperoxy radicals (reactions 38 and 39; see Table 2 and the next section for details; the numbering of the mechanism) (38, 39) The potential energy surfaces are either calculated from high level (composite) computational chemistry methods or taken from literature data. QRRK analysis of the rates of the first reaction between 2 and is described in Ref. [11] and in this study. Ab initio and Density Functional Theory based computational chemistry is employed to evaluate the potential energy hypersurface of 2 + ( 3 ) system using BS-APN, BS-QB3 multilevel methods and SD(T)/6-311+G(d,p) single level calculations. Three pathways are found that result in the + 2 products, depending on the initial orientation of reagents. The two lowest energy pathways proceed either via -trans metastable intermediate (TS-t) or via only transition state with cis-oriented fragment (TSc). Rate parameters are presented in Table 2 for both reaction pathways denoted as reactions 38 and 39, correspondingly. Experimental thermochemistry of rxn (38) is accurately reproduced by the BS-QB3 multilevel method kcal mol -1 vs. calculated kcal mol -1. The rate determining step in reaction 38 is the barrier TS-t with enthalpy of 16.7 kcal/mol relative to reagents at BS-QB3 level. Transition state of reaction 39 is only 0.7 kcal mol -1 higher than TS-t. Isodesmic reaction analyses carried out for enthalpy of adduct leads to f o 298 = kcal/mol. Atomization analyses resulted in kcal mol -1. 3

4 QRRK/ME analysis has been performed for determination of rate parameters. Rigid-rotorharmonic-oscillator approximation was employed to determine vibration, translation and external rotation contributions to S (298K) and p(t) at 500 T/K 1500 (TVR). Scaled vibration frequencies and moments of inertia of the optimized structures calculated at B3LYP/6-31G(d,p) are used as an inputs in SMPS computer program [15] employing standard statistical thermodynamic methods. The torsion frequencies calculated for the internal rotors are excluded from TVR calculations. Instead, contributions from hindered rotations are calculated additionally using VIBIR code [16]. orrections to unpaired electrons are also included in calculations of S (298K) and p(t). The fitted rate equation for forward reaction of 2 + formation (reaction 38 via TS-t) corresponds to k 38 = 8.45x10 8 x T 1.21 exp(17267cal/rt) cm 3 mol -1 s -1 at K at BS-QB3 level calculations and QRRK/ME analysis. Alternative bimolecular reaction 39 via TS-c obeys k 39 = 7.14 x 10 7 x T 1.57 exp (17721 cal /RT) cm 3 mol -1 s -1 equation (Table 2) Enthalpy ( K) Kcal/mol TS TS TS1-t TS1-c TS cis TS Z- (=) TS8 TS7 25 TS TS11 38 E- (=) TS TS Figure1: Enthalpy diagram for 3 system calculated by omposite BS-QB3 Method. Reaction (38) via trans- intermediate is highlighted in green, Reaction (39) via cis-orientation of TS (wavy bonded pathway) in red. xygenation of radical is in blue (right hand). Energies are in kcal mol -1 relative to 2 + reagents. The effect of these reactions in predicting τ =f (Rco, T) was analyzed and deemed significant. 4

5 4. Ignition Delay in / 2 / 2 system To test and validate our pressure dependent mechanism we use it to evaluate the global combustion properties and the autoignition of 2 / fuel mixtures with 2 /N 2 /Ar oxidizing mixtures as studied by Mittal et al. [17] The experimental conditions are 15 to 50 bar (in a rapid compression machine) and to 1044 K and varied 2 / ratios (see below) P=15bar T= P=14.3 atm Ignition Time, ms Rco vs NJ-REI-IA Rco vs NJ-REI-IB Rco vs NJ-REI-I Rco vs W-05 Rco vs W-99 Rco vs Expt Ignition Delay (mcs) K/T vs Detailed 1000K/T vs Skeletal 1000K/T vs Expt Rco Figure 2: (a) Ignition delay times as a function of mole fraction, Rco, at 14.8atm, K Molar composition: (2+)/ 2 /N 2 /Ar/ = 12.5/ 6.25/ / [17]. 2/2 submechanism from [9] is used (1A includes rxns 26 and 38,1B-only 26 and 1-only 38); (b) Temperature dependence for molar composition 2 / 2 //N 2 = 0.017/ 0.175/ 0.156/ at 14.3 atm (experiment [18]). 1000K/T Model predictions the full detailed mechanism show the very good agreement with the experimental ignition delays versus pressure, temperature and ratio of / 2 experimental data of Mittal et al. [17], Fig 2a. In full accordance with the experimental data [17], the replacement of even small amounts of 2 with (increase of Rco) leads to the permanent inhibition of autoignition. The model presented here is predicts the more pronounced inhibition trends at higher pressures. Agreement with the experimental data was improved when the new calculated parameters for reaction 38 and pressure dependent block 26 (vide infra) were added. Table 1: Reduced kinetic model relevant to / 2 / 2 combustion. Rate coefficients of elementary reactions are expressed in moles, cubic cm, sec, kcal mol -1 and Kelvin. Number Reaction A N E a Source = E [11] = E [11] = E [11] 4 + = E [7] 6 + +M= 2 + M 2.200E [11] M = 2 + M 2.800E [11] M= M 7.400E [11] = E [10] = E [10] = E [7] 5

6 = E [8] = E [7] = E [7] = E [7] = E [7] = E [7] = E [11] = E [11] M = 2 + M 6.020E [11] = E [11] 26* + = atm 14.3atm 6.780E E This work 38** + 2 = E This work 39** + 2 = E This work 51 + = E [11] 52 + M = + +M 1.870E [11] 55* + 2 = atm 14.3atm 1.900E E *- Pressure dependent reactions; rate parameters derived at P=1.1 and 14.3 atm partial cases for illustration (Fig1b). **- See, section 5. ** two pathways See Fig. 1. This work 5. Reduced (Skeletal) Mechanism for ombustion of 2 / 2 / Mixtures Modified sensitivity analysis is performed to reduce the detailed sub-mechanism for computational fluid dynamic modeling able to represent experimental ignition data of 2 / 2 / mixture. Unlike to the popular hemkin (Senkin) sensitivity analysis that uses the partial derivatives of the reaction rates to the species source terms at a given time step, the method used in this study for selection of relevant reactions gives the sense an integral, of the sensitivities, up to the time of ignition. We determine the effect of a single reaction on a derived quantity, in this case the ignition delay. A skeletal or shortened reaction set was derived by sequentially removing each reaction from the set and calculating the relative error in the ignition delay compared to the full mechanism results. This was performed for constant-volume, adiabatic auto-ignition calculations with an initial temperature of 1050 K, initial pressures 14.3 and 1.1 atm. with initial composition as specified in the experiments of [18]. The skeletal mechanism for the 2 - system is a superset of all reactions whose removal resulted in a relative ignition delay error greater than This gives a mechanism with 13 species and 31 reactions. Table 1 shows a reduced set of the elementary reactions determined by sensitivity analysis as the major contributors to the rates of the - 2 system. The reaction rate coefficients k of the elementary reactions are expressed in modified Arrhenius form: k = AT n exp ( E a /RT). As it expected, for the (- 2 ) system, the model shows most of the hydrocarbon reactions as being unimportant. The sensitive to ignition of / 2 / 2 mixture set includes our calculated parameters for near pressure independent reaction 38 as well as a pressure dependent reaction between and. 6

7 We recalculated τ(t) dependence of ignition delay times in comparison with the experimental data under the same conditions (Fig. 2b represents only data at the case of P=14.3 atm and molar ratio of mixture 2 / 2 //N 2 equal to 0.017/0.175/0.156/0.652). The reduced mechanism presented in Table 1 accurately reproduces the ignition delay data of detailed kinetic model as a function of temperature, as is illustrated in Fig.1b and 2 ydrocarbon oxygen reaction systems 1 to 4 illustrate potential energy surfaces for a 4 of the oxygenated hydrocarbon, chemical activation, reaction systems included in our mechanism:.= + 2, 3 +, 3 = + 2, respectively Figure 3: Potential energy diagram of -.= + 2 activation system (Mebel et al. 1993). Figure 4: Potential energy diagram of 3. + activation system Bozzelli and Dean (1993) Figure 5: Lowest energy pathways for 3.= + 2 activation system calculated at BS-Q level. 7

8 Figure 6: Potential energy diagram of activation system, BS-QB3 Level. Figures 7 to 12 illustrate model fits to 1 hydrocarbon oxidation experiments at varied fuel equivalence, temperature and pressure conditions. Figure 7: omparison of model and experimental data for methanol pyrolysis at 1073 K, 1 atm and initial methanol mole fraction of 3.95%. Figure 8: omparison of model and experimental data for methanol oxidation at 873 K, 5 atm, Φ = 1.0 and initial methanol mole fraction of 0.78%. 8

9 Figure 9: omparison of model and experimental data for methane/methanol mixture oxidation at 873 K, 5 atm, Φ = 1.0 and X 0 ( 4 ) = 0.39%, X 0 ( 3 ) = 0.39%. Figure 10: omparison of model and experimental data from eld/dryer [19] at 1043 K, 2.1 atm, Φ = 0.86 and X 0 ( 3 ) = Figure 11: omparison of model and experimental data from eld/dryer [19] at 1043 K, 2.1 atm, Φ = 0.86 and X 0 ( 3 ) = Time scales do not match, but model fits change in species concentration with bimodal shape. Figure 12: omparison of model and experimental data from eld/dryer [19] at 781 K, 15.0 atm, Φ = 2.59 and X 0 ( 3 ) =

10 7. oncluding Remarks An elementary, pressure dependent, kinetic mechanism for 1 and 2 hydrocarbon oxidation and combustion is developed. The mechanism includes chemical activation reaction analysis and dissociation of stabilized adducts using QRRK/ME analysis for pressure dependence. Analysis shows that the mechanism is relevant for complex mixtures and accurately predicts ignition delay times for different model systems. It also predicts 1 and 2 hydrocarbon oxidation as a function of temperature and pressure. New kinetic parameters for the reaction of 2 + reaction were determined and shown to improve the modeling ignition delay times. A reduced mechanism for the 2 / reaction system was developed based on the sensitivity analysis of reaction sets to be able to characterize τ(t) dependence for carbon monoxide combustion process. The sensitivity analysis also illustrates an importance of the 39 reactions for these conditions. Numerical calculations using reduced (skeletal) chemistry show excellent agreement with the experimental data, thereby confirming the prediction of detailed kinetic scheme calculations. Acknowledgments This work is supported by WPAFB - STTR ontract with Reaction Engineering International. References [1] K.A. olbrook, M.J. Pilling, S.. Robertson, Unimolecular Reactions, John Wiley & Sons, 1996 [2] A.M. Dean J. Phys. hem. 89 (1985) [3] A.Y. hang, J.W. Bozzelli, A.M. Dean, Zeitschrift für Physikalische hemie 214 (2000)1533 [4] A.M. Dean, J.W. Bozzelli, EMAT: A computer code to estimate rate constants for chemically activated reactions, ombust Sci. Tech., 80 (1991) [5] W.-. Ing,.Y. Sheng, J.W. Bozzelli, Fuel Processing Technology 83 (2003) [6]. Sheng, A.Y. hang, A.M. Dean, J.W. Bozzelli, J. Phys. hem. A 106(2002) [7]. Wang, A. Laskin and.k. Law, A Detailed Kinetic Model of 2 - And 3 - Fuel ombustion, June 1999 [8] G. P. Smith, D.M. Golden, M. Frenklach, N.W. Moriarty, B. Eiteneer, M. Goldenberg,. Thomas Bowman, R.K. anson, S. Song, W.. Gardiner, Jr., V.V. Lissianski, and Z. Qin [9] M. onnaire,. J. urran, J.M. Simmie, W.J. Pitz,.K. Westbrook, Int. J. hem. Kinetics 36 (2004) 603. [10] M. Frenklach,. Wang,.-L. Yu, M. Goldenberg,.T. Bowman, R.K. anson, D.F. Davidson, E.J. hang, G.P. Smith, D.M. Golden, W.. Gardiner and V. Lissianski, [11] M.A. Mueller, R.A. Yetter, F.L. Dryer, Int. J. hem. Kinet. 31(1999)113 [12] A. Y. hang, Joseph W. Bozzelli, E. Ritter, A. M. Dean Density of State Determination from eat apacity Data: Microscopic Properties from Macroscopic, Internat J. hem. Kinetics 29, p (1997). [13] E. Ritter, J.W. Bozzelli, Int. J. hem. Kinetics, 23 (1991) 767 [14] R. Asatryan, L. Rutz,. Bockhorn, J. Bozzelli, omputational Thermochemistry and kinetics for the 2 + Reaction, Int l Workshop on Gas Kinetics, 2006, Karlsruhe, Germany (full paper to be submitted). [15]. Sheng, PhD dissertation, NJIT, 2001 [16] T.. Lay, PhD dissertation, NJIT, 1994 [17] G. Mittal,.-J. Sung, R.A. Yetter, Int. Journal hemical Kinetic 38(2005)516 [18] Y. Dong, X. You, D.A. Sheen,. Wang, R. Kinslow, M. all, A.T olley, M.G. Andac, F.N. Egolfopoulos, Proceedings of the ombustion Institute 31 (2007) In press. [19 T.J. eld, F.L. Dryer, Int. J. hem. kinetics, 30 (1998)

Pathway and Kinetic Analysis on the Propyl Radical + O2 Reaction System

URL-J-126375 Rev. 1 PREPRINT Pathway and Kinetic Analysis on the Propyl Radical + 2 Reaction System J.W. Bozzelli W.J. Pitz This paper was prepared for submittal to the Fourth International onference on