Comparison and Validation of Detailed Kinetic Models for the

Article Cite This: Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

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Comparison and Validation of Detailed Kinetic Models for the Oxidation of Light Alkenes Gianmaria Pio,† Vincenzo Palma,‡ and Ernesto Salzano*,† †

Dipartimento di Ingegneria Civile, Chimica, Ambientale e dei Materiali, Università di Bologna, via Terracini 28, 40131 Bologna, Italy Dipartimento di Ingegneria Industriale, Università di Salerno, via Giovanni Paolo II 132, 84084 Fisciano, Salerno, Italy

‡

ABSTRACT: The increasing interest in light alkenes oxidation for the development of detailed kinetic model is mainly due to their relevance in the combustion chemistry of most common fuels and their formation in the oxidation of higher alkanes. This study analyses the detailed kinetic mechanisms for the oxidation of linear lighter alkenes, ethylene, propylene and 1-butene, through the comparison of several combustion kinetic models retrieved from current literature with respect to the experimental data for the laminar burning velocity in air, and for the ignition delay time, by varying either reactant concentration or initial temperature. The mechanisms by University of California, San Diego (UCSD), Konnov group (KOM), University of Southern California (USC), Saudi Aramco 2.0 (SAM), Lawrence Livermore National Laboratory (LLNL), and Politecnico of Milano (CRECK) have been evaluated through a unified statistical analysis. A sensitivity analysis for the laminar burning velocity was also performed to assess and compare the reactions described in the studied models and sort by relevance. Best fits are produced by the LLNL and the UCSD model even if the optimal results can depend on the specific hydrocarbon. We then produced a new mechanism by adding the UCSD for C3 and LLNL for C4 or more, which resulted to work better.

1. INTRODUCTION Light alkenes are increasing in their relevance in industrial chemistry and combustion because of their utilization as raw material for several industrial processes and the production as intermediate compounds during the oxidation of heavier hydrocarbons.1 Nevertheless, only ethylene (ethene) has been widely studied, whereas propylene (propene) and 1-butylene (butene), despite their potential industrial relevance, have yet to be studied in greater detail. This study presents a comparison and validation of the currently available kinetic models for the oxidation of ethene, propene and butene in air, through their validation with experimental data retrieved from literature. The kinetic models include the mechanism by the University of California, San Diego (UCSD),2 Konnov group (KOM),3 University of Southern California (USC),4 Saudi Aramco Mechanism 2.0 (SAM),5 Lawrence Livermore National Laboratory (LLNL),6 Politecnico of Milan (CRECK),7 and GRI-Mech 3.0,8 which however does not include C3 and C4 compounds. For the aims of this work, the laminar burning velocity (SU) and the ignition delay time (IDT) have been analyzed. Their values are key parameters in kinetics modeling because they contain fundamental information regarding reactivity, exothermicity, flame shape, and diffusivity.9 The results have been validated with experimental data retrieved from the current literature by detailed statistical analysis. A sensitivity analysis for SU was performed to evaluate the main differences between the analyzed models. © XXXX American Chemical Society

2. METHODOLOGY The analysis was first performed by SU simulations, carried out assuming 1D flame, in perfectly adiabatic conditions, by using the Newton iteration technique to solve the mass and thermal balances by means of the Cantera suite.10 The grid parameters were: slope = 0.07; curve = 0.14. The total grid points number was 230. The relative error (RTol) and absolute error (ATol) criteria were 1.0 × 10−9 and 1.0−14 for the steady-state problem and 1.0 × 10−5 and 1.0 × 10−14 for the time-stepping problem (used by the code as a first attempt solution). The results were compared with experimental data obtained by different techniques (counter-flow flames, heat flux burner, spherical bomb), and methodologies for the flame stretch evaluation (linear, nonlinear). More specifically, data of Egolfopoulos et al.,11 Hirasawa et al.,12 and Kumar et al.,13 were obtained by using a counter-flow flame apparatus, data collected by Hassan et al.14 and Jomaas et al.15 adopted a spherical flame technique, for ethylene SU. Besides, Burke et al.16 have collected SU data from several authors for propylene SU. In this work, the heat flux method results obtained by Lund University (Lund), CNRS-Nancy, Universitè de Lorraine (LRPG), and Vrije Universiteit Brussel (VUG) and the data obtained by using counter-flow flames17 Received: Revised: Accepted: Published: A

March 29, 2018 May 3, 2018 May 8, 2018 May 8, 2018 DOI: 10.1021/acs.iecr.8b01377 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

Article

Industrial & Engineering Chemistry Research and spherical propagating flames15 have been considered. For 1-butene, several authors have reported SU data by using counter-flow flame and spherical bomb.18−22 Regarding the IDT, the experimental data for stoichiometric ethylene23,24 propylene16 and butylene25 as obtained by using the shock tube equipment have been considered. Additional data reported by Li et al.,23 obtained by the rapid compression machine (RCM) have been used. In this respect, the increase in pressure was adopted as a monitoring parameter for the model validation.23 The models have been validated by using different statistical parameters: the quadratic sum (QS) of the difference between N model (VMod) and experimental values (VExp), R2 coefficient, the fractional bias (FB), the normalized mean square error (NMSE), and fraction of predictions (FAC-2) satisfying eqs 1−5 (the subscript av indicates the average value):

affected by changes in its rate constant, compared to reactions with a low sensitivity.

3. RESULTS 3.1. Ethene. Figure 1 reports the calculated and experimental values for the SU of ethylene in air at ambient T

N

QS =

∑ (Vmod,i − Vexp,i)2

(1)

i

N

R2 =

FB =

∑i ((Vmod, i − Vmod,av)(Vexp, i − Vexp,av))2 N

(2) Figure 1. Calculated and experimental SU of ethene at 298 K and 1 bar, as a function of φ.

∑i (Vexp, i − Vmod, i) 0.5· ∑i (Vexp, i + Vmod, i)

NMSE =

0.5 ≤

N

∑i (Vmod, i − Vmod,av)2 ∑i (Vexp, i − Vexp,av)2

(3)

and P (298 K, 1 bar) with respect to φ (calculated with respect to air) in the range 0.4−1.9. Since the R2 coefficient cannot be used as a stand-alone parameter in the model evaluation, FAC-2, FB, and NMSE were calculated. The detailed FB and NMSE results are not reported for the sake of brevity. It is however worth noting that the GRI model does not respect any one of the previously defined acceptance criteria (|FB| < 0.3). Hence, this model has not been considered in further analyses. The USCD, SAM, USC, KOM, and LLNL models are in good agreement with experimental data, with the exception of Egolfopoulos et al.11 In addition, UCSD model overpredicts the experimental SU at 298 K, although slightly. Figure 2 shows the SU obtained at 360, 400, and 470 K and the comparison with the experiments of Kumar et al.13 The trends are also confirmed for different initial temperature of the unburned gases. The UCSD, SAM, USC, KOM, and LLNL mechanisms respect all the acceptance criteria given above. FAC-2 approaches 1 in all the studied conditions. Figure 3 shows the quality of fitting for all the models, through the FB and NMSE values. Clearly, the UCSD, SAM, USC, KOM, and LLNL models result above the 95% confidence limits curve for FB. The SAM, USC, KOM, and LLNL models underpredict the experimental results, whereas UCSD is close to the vertical axis, i.e., the model shows the best performance in predicting the experimental data. It is however worth noting that at the single temperature of 298 K the LLNL and SAM performs slightly better than UCSD. Overall, UCSD, LLNL, and SAM are quite similar if the SU of ethene is considered. By using the same kinetic models, the dependency of the IDT with the initial temperature was calculated and compared with the aforementioned experimental data (Figure 4). The USC shows however the best fitting with the experimental data for IDT even if all models show discrepancy at low temperature.

( QSN ) Vmod,av ·Vexp,av

Vmod, i Vexp, i

(4)

≤ 2.0 (5)

The ideal model has NMSE = 0, FB = 0, and FAC-2 = 1. In this work, the models have been considered acceptable if FAC-2 > 0.8, |FB| < 0.3, and the random scatter of data, evaluated through NMSE, is smaller than 0.5.26 Among the accepted models, the closest to axis origin has been suggested as the role mechanism. The FB and NMSE values are not suitable for exponential trend rating; for this reason in the present work, IDT goodness of fitting has been evaluated considering the QS, R2, and FAC-2 parameters. The sensitivity analysis investigates the effect of parameter change on the solution of the mathematical models, i.e., the kinetic model. For the simulated SU, the parameters depend on the operative conditions, the equivalence ratio φ, and reaction kinetic parameters (R1 for the generic reaction (i) as described by the general equation: SU = SU(T, P, φ, R1, ...,R1, ..., Rn). The sensitivity analyses were then carried out by setting appropriate perturbations in SU on a stoichiometric mixture at ambient T and P, in order to isolate the kinetic path effects and increase the knowledge of the relationships between the input and output uncertainties. The reactions were sorted by relevance in the SU determination, considering the absolute value of the normalized sensitivity coefficients (NSC) for each reaction i, defined as follows: NSCi =

ki ∂SU SU ∂ki

(6)

where ki represents the reaction rate coefficient. A reaction with a high sensitivity factor indicates that the SU will be strongly B

DOI: 10.1021/acs.iecr.8b01377 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

Article

Industrial & Engineering Chemistry Research

Figure 2. Experimental and numerical SU of ethene at 360 K (left), 400 K (center), and 470 K (right).

Figure 5 shows only the normalized sensitivity coefficients (SN) of the most important reactions for the studied models. The

Figure 3. Overall FB and NMSE for SU of ethene oxidation in air.

Figure 5. Normalized sensitivity coefficients for the S U of stoichiometric ethene−air mixtures at 298 K and 1 bar.

reaction list reported is composed of 15 reactions, divide into 3 sectors: 1−5 involving C 0 compounds, 6−10 for C 1 compounds, and 11−15 for the C2−C3 compounds. As expected, the reaction H + O2 ⇄ O + OH is dominant for all the studied models. This reaction is considered responsible for the typical belt-shape curve of the SU for most hydrocarbons: At higher φ, a lower oxygen concentration inhibits this reaction, which leads to lower values of the SU. In addition, the reaction CO + OH ⇄ CO2 + H is dominant for lean mixtures, with it being the most important step in heat and H production.1 The reaction H + O2 + M ⇄ O + OH is relevant in the UCSD models. Finally, it is worth noting that the best models assessed above give a strong relevance to the reaction CH2CO + O ⇄ CH2 + CO2. 3.2. Propene. Figure 6 reports the numerical and experimental data for the SU of propene at 298 K (Figure 6, left), 358 K (Figure 6, center), and 398 K (Figure 6, right). The models considered predict lean and rich conditions quite well. In all cases, the USC and UCSD models underestimate the experimental data especially at nearly stoichiometric conditions, whereas the LLNL overestimates the SU. However, all the studied models respect the statistical acceptance criteria. Figure 7 gives an overall representation of the quality of the models. The SAM model shows the best fit with the experimental data.

Figure 4. Calculated and experimental IDT values of stoichiometric ethene-air mixture vs temperature.

Of note is that the effect of pressure on ethylene IDT was neglected in this work, being the studied ranges of temperature and pressure 1100−1400 K and 10−15 bar, where data are unaffected by these parameters for all the compositions of the ethylene−air mixtures.27 Starting from the calculated data, the apparent activation energy (Ea) can be also calculated. All the considered models underestimate the value but the UCSD model, which predicts the activation energy relatively well: a model value of Ea/R = 22 017 K (where R is the gas constant) is obtained to be compared with the experimental value Ea/R = 25 364 K.23 Finally, a sensitivity analysis for SU at stoichiometric concentration and ambient T and P. For the sake of simplicity, C


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Figure 6. Calculated and experimental SU of propene at 298 K (left), 358 K (center), and 398 K (right).

14 569 K) show the best agreement with the experimental value of Ea/R = 15489 K.16 Figure 9 shows the sensitivity analysis for

Figure 7. Overall fractional bias and normalized mean square error for propene SU.

For the sake of brevity, the IDT measurements reported by Burke et al.16 obtained by different tools for stoichiometric propene−air mixtures at a starting pressure equal to 10 bar and initial temperature in the range 1100−1400 K were analyzed. Figure 8 shows experimental and simulations results carried out in the same conditions and considering an increase in pressure as ignition criteria. Both SAM and UCSD are able to predict well all the experimental IDT. The apparent activation energy (Ea) obtained by SAM (Ea/R = 14 569 K) and UCSD (Ea/R =

Figure 9. Normalized sensitivity coefficients SN for the SU of stoichiometric propene−air mixtures at ambient T and P.

the SU at stoichiometric concentration and ambient T and P, in terms of SN values. The reactions were divided into three categories (C0, C1, and Cn ≥ C2). The sensitivity analysis underlines that the reactions H + O2 ⇄ O + OH and CO + OH ⇄ CO2 + H are dominant, as for ethene. However, their relevance is increased by the number of carbon atoms. Furthermore, it is worth noting that HCO + M ⇄ CO + H + M and C2H3 + O2 ⇄ CH2CHO + O relevance is strongly modified with respect to ethene, despite the abundance of C2 compounds. Also, the analysis indicates a C3H5 formation as the main step in propene decomposition, with C3H6 + H ⇄ H2 + C3H5 and C3H6 + OH ⇄ H2O + C3H5 being the most relevant C3 reactions for all the studied models. 3.3. 1-Butene. It is worth mentioning that the UCSD model has not been included because this mechanism is focused on C0−C3.Figure 10 reports the obtained numerical results and the comparison with experimental data. Apparent inconsistencies in experimental results can be attributed to the differences in SU determination methods and tools. Indeed, it is worth noting how the LLNL curve approaches to the results obtained by premixed spherical bomb by Fenard et al.18 and premixed counter-flow configuration and linear extrapolation for the unstretched flame by Davis and Law19 for all the studied mixture, whereas SAM and USC predict well the nonlinear extrapolated data by the nonpremixed counter-flow twin flame configuration reported by Zhao et al.20 Additional data for the

Figure 8. Calculated and experimental IDT for stoichiometric propene−air mixtures at 10 bar. D


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Table 1. Models QS for the Calculated IDT Values for 1Butene at Different Pressures P (bar) 10 30 50 average

USC 3.34 4.78 3.28 1.11

× × × ×

SAM −1

10 10−5 10−8 10−1

LLNL −3

5.10 × 10 8.84 9.48 × 10−6 2.95

2.83 3.14 1.32 1.14

× × × ×

Creck −2

10 10−1 10−6 10−1

1.86 2.84 4.95 7.14

× × × ×

10−1 10−2 10−8 10−2

Figure 10. 1-Butene SU at 300 K, 1 bar, and different equivalence ratio φ.

maximum laminar burning velocity, calculated at equivalence ratio equal to 1.1, were considered as reported by Walker et al.21 and NFPA.22 Eventually, an overall evaluation of the quality of fitness is not consistent for this substance. Figure 11 reports the validation of the obtained IDT with experimental data, at different pressures. The experimental results refer to the work of Li et al.25 and were obtained by rapid compression machine (RCM) and high-pressure shock tube (HPST) at stoichiometric conditions and pressures of 10, 30, and 50 bar. Fitting quality was evaluated for all the investigated pressure individually and on the entire range by computing the QS average. This overall analysis is strongly affected by the maximum QS value of each model since they spread largely by change in pressure (Table 1). Figure 12 reports the normalized sensitivity coefficients, where the reactions were sorted by the SN, considering the main C4 reactions and 10 reactions with the highest relevance among the C0−C3 list. No large discrepancies among the models are reported except for the C4 reactions. The two reactions C4H8-1 + H ⇄ C3H6 + CH3 and C4H8-1 + H ⇄ C2H4 + C2H5 are particularly relevant in the USC and SAM mechanisms and negligible for LLNL. This could be related to the observation that the two reactions are in series in the LLNL model, where C4H7-1 is formed as an intermediate product. Hence, the following decomposition reactions have low relevance.

Figure 12. Normalized sensitivity coefficients for SU of stoichiometric 1-butene−air mixtures at 300 K and 1 bar.

In this work, a new (unified) model has been also built. The new model includes the C4 kinetic equations from LLNL into the UCSD model, which shows high quality in reproducing SU and IDT data for Cn < C4. Figure 13 shows the global statistical analysis, including this new model. Results show that the overall quality of the SU and IDT predictions are clearly improved.

4. CONCLUSION Laminar burning velocity and ignition delay time have been calculated by using different kinetic models. The analysis confirms the ability of UCSD to reproduce experimental data for ethene and propene oxidation in air. However, this model does not include C4 kinetics. Besides, the LLNL mechanism shows high quality in predicting the 1-butene data and allows further extension to higher alkenes and alkanes. A unified model (UCSD + LLNL for C4 kinetic) has been built and positively improves the overall quality of simulations.

Figure 11. Experimental and calculated ignition delay time (IDT) for 1-butene at stoichiometric concentration in air vs temperature, and initial pressure of 10 bar (left), 30 bar (center), and 50 bar (right). E


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with preheat and ignition delays at high pressures. Combust. Flame 2008, 153, 343. (14) Hassan, M. I.; Aung, K. T.; Kwon, O. C.; Faeth, G. M. Properties of Laminar Premixed Hydrocarbon/Air Flames at Various Pressures. J. Propul. Power 1998, 14, 479. (15) Jomaas, G.; Zheng, X. L.; Zhu, D. L.; Law, C. K. Experimental determination of counterflow ignition temperatures and laminar flame speeds of C2-C3 hydrocarbons at atmospheric and elevated pressures, 30th. Proc. Combust. Inst. 2005, 30, 193. (16) Burke, S. M.; Burke, U.; McDonagh, R.; Mathieu, O.; Osorio, I.; Keesee, C.; Morones, A.; Petersen, E. L.; Wang, W.; DeVerter, T. A. An experimental and modeling study of propene oxidation. Part 2: Ignition delay time and flame speed measurements. Combust. Flame 2015, 162, 296. (17) Davis, S. G.; Law, C. K.; Wang, H. Propene pyrolysis and oxidation kinetics in a flow reactor and laminar flames. Combust. Flame 1999, 119, 375. (18) Fenard, Y.; Dayma, G.; Halter, F.; Foucher, F.; Serinyel, Z.; Dagaut, P. Experimental and modeling study of the oxidation of 1butene and cis-2-butene in a jet-stirred reactor and a combustion vessel. Energy Fuels 2015, 29, 1107. (19) Davis, S. G.; Law, C. K. Determination of and Fuel Structure Effects on Laminar Flame Speeds of C1 to C8 Hydrocarbons. Combust. Sci. Technol. 1998, 140, 427. (20) Zhao, P.; Yuan, W.; Sun, H.; Li, Y.; Kelley, A. P.; Zheng, X.; Law, C. K. Laminar flame speeds, counterflow ignition, and kinetic modeling of the butene isomers. Proc. Combust. Inst. 2015, 35, 309. (21) Walker, P. L.; Wright, C. C. Hydrocarbon Burning Velocities Predicted by Thermal Versus Diffusional Mechanisms. J. Am. Chem. Soc. 1952, 74, 3769. (22) NFPA 68: Standard on Explosion Protection by Deflagration Venting; National Fire Protection Association: Quincy, MA, 2007. (23) Penyazkov, O. G.; Sevrouk, K. L.; Tangirala, V.; Joshi, N. Highpressure ethylene oxidation behind reflected shock waves. Proc. Combust. Inst. 2009, 32, 2421. (24) Kopp, M. M.; Petersen, E. L.; Metcalfe, W. K.; Burke, S. M.; Curran, H. J. Oxidation of Ethylene–Air Mixtures at Elevated Pressures, Part 2: Chemical Kinetics. J. Propul. Power 2014, 30, 799. (25) Li, Y.; Zhou, C. W.; Curran, H. J. An extensive experimental and modeling study of 1-butene oxidation. Combust. Flame 2017, 181, 198. (26) Patel, V. C.; Kumar, A. Evaluation of three air dispersion models: ISCST2, ISCLT2, and SCREEN2 for mercury emissions in an urban area. Environ. Monit Assess 1998, 53, 259. (27) Kopp, M. M.; Donato, N. S.; Petersen, E. L.; Metcalfe, W. K.; Burke, S. M.; Curran, H. J. Oxidation of ethylene−air mixtures at elevated pressures, part 1: experimental results. J. Propul. Power 2014, 30, 790.

Figure 13. Overall analysis for ethene, propene and 1-butene, including the unified model defined in this work (UCSD + LLNL model for the C4 kinetic).

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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REFERENCES

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Comparison and Validation of Detailed Kinetic Models for the

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