Guillaume Dayma

Zeynep Serinyel

Maxime Carbonnier

Junfeng Bai

Yuxiang Zhu

Chong-Wen Zhou

Alan Kéromnès

Benoîte Lefort

Luis Le Moyne

Philippe Dagaut

Luis Lemoyne

Oxidation of pentan-2-ol -Part II: Experimental and modeling study

Keywords: pentan-2-ol, kinetics, jet-stirred reactor, shock tube, detailed mechanism, biofuels

à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

Alcohols are presented as an important family of potential biofuels that can be synthesized from renewable feedstocks. Due to their higher energy density than ethanol and their better solubility in gasoline, larger alcohols have recently been the focus of many studies. So far, alcohols up to C 4 have been extensively studied, however fewer studies were performed for larger (C ≥ 5) alcohols. As far as pentanol isomers are concerned, pentan-1-ol, pentan-3-ol, 3-methyl,butan-1-ol, and 2-methyl,butan-1-ol have already been investigated experimentally in the literature in terms of speciation [START_REF] Togbé | Experimental and detailed kinetic modeling study of 1-pentanol oxidation in a JSR and combustion in a bomb[END_REF][START_REF] Dayma | Experimental and Detailed Kinetic Modeling Study of Isoamyl Alcohol (Isopentanol) Oxidation in a Jet-Stirred Reactor at Elevated Pressure[END_REF][3][START_REF] Wang | Experimental and kinetic modeling study of n-pentanol pyrolysis and combustion[END_REF][START_REF] Van De Vijver | Decomposition and isomerization of 1-pentanol radicals and the pyrolysis of 1-pentanol[END_REF], laminar burning velocities [START_REF] Li | Laminar Flame Speeds and Kinetic Modeling of n-Pentanol and Its Isomers[END_REF][START_REF] Nativel | Laminar flame speeds of pentanol isomers: An experimental and modeling study[END_REF][START_REF] Park | A comprehensive experimental and modeling study of 2-methylbutanol combustion[END_REF] and ignition delay times [START_REF] Park | A comprehensive experimental and modeling study of 2-methylbutanol combustion[END_REF][START_REF] Heufer | A comparison of longer alkane and alcohol ignition including new experimental results for n-pentanol and n-hexanol[END_REF][START_REF] Sarathy | A comprehensive experimental and modeling study of iso-pentanol combustion[END_REF][START_REF] Tang | High temperature ignition delay times of C5 primary alcohols[END_REF]. These isomers have different oxidation behaviors depending on their chemical structure. Large secondary C 5 alcohols such as pentan-2-ol are much less studied. Köhler et al. [START_REF] Köhler | 1-, 2-and 3-Pentanol combustion in laminar hydrogen flames -A comparative experimental and modeling study[END_REF] investigated hydrogen flat flames doped with linear pentanols using molecular-beam mass spectrometry. Li et al. [START_REF] Li | Laminar Flame Speeds and Flame Instabilities of Pentanol Isomer-Air Mixtures at Elevated Temperatures and Pressures[END_REF] measured laminar flame speeds of pentan-1-, -2-, and -3-ol as well as 2-methyl, butan-1-ol [START_REF] Li | Measurements of laminar flame speeds and flame instability analysis of 2-methyl-1-butanol-air mixtures[END_REF]. Carbonnier et al. [START_REF] Carbonnier | An experimental and modeling study of the oxidation of 3-pentanol at high pressure[END_REF] studied the oxidation of pentan-3-ol in a JSR and measured ignition delay times. The aim of this study is to provide new kinetic data through a detailed product analysis of pentan-2-ol in a jet-stirred reactor (JSR) and by measuring ignition delay times behind reflected shock waves, for the first time. A chemical kinetic mechanism was developed and used to reproduce the present data and analyze the reaction pathways.

Experimental

Jet-stirred reactor (Orléans)

Experiments were performed in a fused silica jet-stirred reactor (JSR) already described in details [START_REF] Dagaut | A jet-stirred reactor for kinetic studies of homogeneous gas-phase reactions at pressures up to ten atmospheres (≈1 MPa)[END_REF] and used in previous studies [START_REF] Dayma | Experimental and Detailed Kinetic Modeling Study of Ethyl Pentanoate (Ethyl Valerate) Oxidation in a Jet Stirred Reactor and Laminar Burning Velocities in a Spherical Combustion Chamber[END_REF][START_REF] Veloo | Experimental and modeling study of the oxidation of n-and iso-butanal[END_REF][START_REF] Veloo | Jet-stirred reactor and flame studies of propanal oxidation[END_REF]. The reactor itself is surrounded by a regulated electrical oven and can be heated up to 1250 K. It is located inside a pressure-resistant jacket, allowing the pressure to rise up to 10 atm. As in previous studies [START_REF] Zhang | Experimental and kinetic modeling study of trans-methyl-3-hexenoate oxidation in JSR and the role of C=C double bond[END_REF][START_REF] Bugler | An experimental and modelling study of n-pentane oxidation in two jet-stirred reactors: The importance of pressure-dependent kinetics and new reaction pathways[END_REF], the liquid fuel (CAS 6032-29-7, 98 % purity from Merck) was atomized by a nitrogen flow and vaporized in a heated chamber. The fuel + N 2 mixture is carried to the reactor by a heated quartz capillary. The oxidizing stream (O 2 + N 2 ) flowed separately to avoid oxidation before reaching the 4 injectors providing stirring. Gaseous flowrates are regulated by thermal mass flow controllers (Brooks 5850E) whereas the liquid fuel is injected by an HPLC pump (Shimadzu LC10 AD VP) with an online degasser (Shimadzu DGU-20 A3). A low-pressure sonic probe was used to freeze the reactions and take samples for online and off-line analyses. Samples were analyzed online by FTIR or stored at low-pressure for offline GC analysis. Traces of pent-1-ene, trans-pent-2-ene and cis-pent-2-ene (2 ppm of each) as well as water (200 ppm) were detected in the fuel and accounted for in the simulations. The carbon balance was checked after each experiment and was found to be within ±15 %. Uncertainties on the species mole fractions are due to several factors described in [START_REF] Serinyel | Kinetics of oxidation of cyclohexanone in a jet-stirred reactor: Experimental and modeling[END_REF] and are estimated to be around ±15 %. Identified and quantified intermediate species include pentan-2-one, formaldehyde, acetaldehyde, ethylene, methane, propene, pent-1-ene, pent-2-ene (cis and trans isomers). Methylvinylketone, buta-1,3-diene, and acrolein were quantified as well but to a lesser extent, and some other species were present in trace amounts (penta-1,3-diene). All experiments were performed at 10 atm between 700 and 1180 K after checking that no low-temperature reactivity was observed between 500 and 700 K for the mixture ϕ = 0.5.

High pressure shock tube (Nevers)

The ignition of mixtures of pentan-2-ol (1 %) + O 2 diluted in argon were experimentally studied in a high-pressure shock tube (HPST) in DRIVE. The experimental conditions cover a temperature range of 1070-1460 K at 20 and 40 bar for equivalence ratios of 0.5, 1 and 2. A stoichiometric pentan-2-ol/air mixture was also tested at 20 bar. The HPST was previously described in details by El-Merhubi et al. [START_REF] Merhubi | A high pressure experimental and numerical study of methane ignition[END_REF]. It consists in a stainless-steel tube (diameter 50 mm) divided into two sections (driven section 5 m and driver section 4 m) by a double diaphragm. Two stainless-steel tanks, connected to the tube through a manifold, are used to prepare the tested mixture from high purity gases (> 99.995 %) and pentan-2-ol (> 98 %). To avoid any contamination, the vacuum system pumps down the tube between each test and prior to mixture preparation below 5 Pa. A heating system keeps the complete system at 80 °C to prevent fuel condensation by maintaining its partial pressure at least three times lower than its vapor pressure. The position of the shock wave is detected thanks to four piezoelectric pressure transducers (PCB 113B22) located in the last part of the driven sections. At the endwall, an additional piezoelectric pressure transducer (Kister 603B1) records post-shock pressure, P 5 , which is used to calculate the ignition delay time between the impact of the shock wave and the ignition event, defined by the maximum slope of the pressure signal. The shock velocity, calculated from the recorded pressure signals, and the initial conditions are used to calculated post-shock temperature, T 5 , thanks to the equilibrium software Gaseq [START_REF] Morley | Gaseq version 0.79[END_REF]. Temperature T 5 is determined with an accuracy of ± 1 % which corresponds to ±10-15 K over the temperature range. A vertical error bar of 25 % was applied to these results, accounting for uncertainties on shock velocity determination and mixture preparation.

Kinetic modeling

The kinetic model used in the simulations was developed by introducing a sub-mechanism of pentan-2-ol into an in-house C 0 -C 4 base (635 species in 3842 reactions). The thermochemical parameters of the fuel and its radicals were evaluated as described in an accompanying paper (Oxidation of pentan-2-ol -Part I: Theoretical investigation on the decomposition and isomerization reactions of pentan-2-ol radicals). For all other new species, Thergas [START_REF] Muller | Thergas -A computer program for the evaluation of thermochemical data of molecules and free radicals in the gas phase[END_REF], based on Benson's group additivity, was used. All kinetic simulations were performed using Chemkin-PRO [26] using the Perfectly Stirred Reactor and Constant Volume modules for the JSR and shock tube simulations, respectively. Fuel reactions include water elimination, unimolecular initiations by C-C, C-O, and C-H bond breaking, bimolecular initiations with O 2 , and H-abstractions by small radicals. Through these last reactions, the fuel can yield six distinct primary radicals which are named pent2oh-1 (CCCC(OH)C*), pent2oh-2 (CCCC*(OH)C), pent2oh-3 (CCC*C(OH)C), pent2oh-4 (CC*CC(OH)C), pent2oh-5 (C*CCC(OH)C), and pent2o (CCCC(O*)C). Rate constants for H-abstraction reactions were carefully selected in order to reproduce either the global reactivity as well as the product distribution:

 Rate constants for pentan-2-ol + H were taken from Sivaramakrishnan et al. [START_REF] Sivaramakrishnan | Rate Constants for the Thermal Decomposition of Ethanol and Its Bimolecular Reactions with OH and D: Reflected Shock Tube and Theoretical Studies[END_REF] for pent2oh-1, pent2oh-2, and pent2o, from Sarathy et al. [START_REF] Sarathy | A comprehensive chemical kinetic combustion model for the four butanol isomers[END_REF] for pent2oh-3, and from Sivaramakrishnan et al. [START_REF] Sivaramakrishnan | High-temperature rate constants for H/D + C2H6 and C3H8[END_REF] for pent2oh-4 and pent2oh-5.

 Rate constants for pentan-2-ol + OH were taken from Hashemi et al. [START_REF] Hashemi | High-pressure pyrolysis and oxidation of ethanol[END_REF] for pent2oh-1 and pent2o, from Zheng et al. [START_REF] Zheng | Kinetics of the Hydrogen Abstraction Reaction From 2-Butanol by OH Radical[END_REF] for pent2oh-2 and pent2oh-3, and from Sivaramakrishnan and Michael [START_REF] Sivaramakrishnan | Rate constants for OH with selected large alkanes: Shock-tube measurements and an improved group scheme[END_REF] for pent2oh-4 and pent2oh-5.  Rate constants for pentan-2-ol + HO 2 were taken from Mendes et al. [START_REF] Mendes | Rate Constant Calculations of H-Atom Abstraction Reactions from Ethers by HȮ2 Radicals[END_REF] for all radicals except pent2o for which the rate constant was taken from Sarathy et al. [START_REF] Sarathy | A comprehensive chemical kinetic combustion model for the four butanol isomers[END_REF].  Finally, rate constants for pentan-2-ol + CH 3 were taken from Carstensen and Dean [START_REF] Carstensen | Development of Detailed Kinetic Models for the Thermal Conversion of Biomass via First Principle Methods and Rate Estimation Rules, Computational Modeling in Lignocellulosic Biofuel Production[END_REF] for pent2oh-1, pent2oh-2, and pent2oh-3, from Dayma et al. [START_REF] Dayma | Experimental and Detailed Kinetic Modeling Study of Isoamyl Alcohol (Isopentanol) Oxidation in a Jet-Stirred Reactor at Elevated Pressure[END_REF] for pent2oh-4 and pent2oh-5, and from Sarathy et al. [START_REF] Sarathy | A comprehensive chemical kinetic combustion model for the four butanol isomers[END_REF] for pent2o.

As far as pent2oh-5 and pent2oh-4 radicals are concerned, rate constants were estimated as for primary and secondary C-H, respectively as in alkanes. Unimolecular fuel initiations are an important class of reactions for ignition delay times but not so important under JSR conditions. Their rate constants were taken from butan-2-ol [START_REF] Sarathy | A comprehensive chemical kinetic combustion model for the four butanol isomers[END_REF]. Pressure-dependent rate constants for -scission and isomerization reactions were calculated as described in the Part 1 of this paper. One of the main oxygenated intermediate species observed in pentan-2-ol oxidation is pentan-2-one, which is produced either by -scission or oxidation of the -hydroxyalkyl radical (pent2oh-2). Therefore sub-mechanisms involving reactions of pentan-2-one and methyl vinyl ketone were also considered, partly in analogy with our previous studies on butanone and pentan-3-ol oxidation [START_REF] Carbonnier | An experimental and modeling study of the oxidation of 3-pentanol at high pressure[END_REF][START_REF] Thion | An experimental study in a jet-stirred reactor and a comprehensive kinetic mechanism for the oxidation of methyl ethyl ketone[END_REF]. Both the mechanism and thermochemistry files are provided as supplementary material.

Results and discussion

JSR experiments

Figure 1 represents fuel mole fraction at different equivalence ratios investigated and compared with pentan-1-ol and pentan-3-ol under the same conditions. Reactivity starts being observed around 760 K for all mixtures, pentan-2-ol being slightly less reactive than pentan-3-ol, itself less reactive than pentan-1-ol (note that no data were available for pentan-1-ol at = 4). While almost all the fuel is consumed by 880 K for the lean mixtures, conversion for the = 4 mixture, at this temperature is around 70%. It is to be noted that some additional experiments were performed between 500-700 K for the = 0.5 mixture, and no low-temperature reactivity was observed. The conversion of these three linear pentanols was also compared to that of n-pentane under stoichiometric conditions (P = 10 atm, = 0.7 s and an initial mole fraction of 1000 ppm) in Figure S1 in the Supplementary Material. This figure shows that, although n-pentane exhibits a low-temperature reactivity under these conditions, its main reactivity is shifted by 25-30 K towards higher temperatures as compared to pentan-2-ol. Focus of the present study being the oxidation of pentan-2-ol, the difference of reactivity between the three isomers and n-pentane is beyond the scope of this study, and will be addressed in a future work. In Figure 2, the mole fraction evolutions of pentan-2-ol were plotted for the five different equivalence ratios. From this figure, it can be seen that the consumption of the fuel is equivalence ratio dependent and that a higher reactivity is observed as the mixtures get leaner at a given temperature. Conversion starts ca. 770 K at all equivalence ratios, then pentan-2-ol mole fraction goes down below the detection limit at 970 K when  = 0.35 whereas at  = 4, pentan-2-ol was still detected at 1090K. Moreover, a second slope appears and increases at higher temperature while the equivalence ratio increases too: this phenomenon was already reported during the oxidation isopentanol and pentan-3-ol [START_REF] Dayma | Experimental and Detailed Kinetic Modeling Study of Isoamyl Alcohol (Isopentanol) Oxidation in a Jet-Stirred Reactor at Elevated Pressure[END_REF][START_REF] Carbonnier | An experimental and modeling study of the oxidation of 3-pentanol at high pressure[END_REF].

Figure 3 represents mole fractions of the major species quantified for mixtures = 0.5, 1, and 2 ( = 0.35 and 4 are provided as Figure S2 in the Supplementary Material). The major hydrocarbon products quantified are C 2 H 4 , CH 4 , C 3 H 6 , trans-2-C 5 H 10 , cis-2-C 5 H 10 , and 1-C 5 H 10 . The major oxygenated intermediates include formaldehyde, acetaldehyde, pentan-2-one, the latter ketone being a specific product of the fuel. Its molar fraction is well predicted by the model regardless of the equivalence ratio. Although not detected under these conditions, the formation of enols by oxidation or -scission was considered. Enols can then react by tautomerism yielding ketones or aldehydes when the double bond and OH are neighbors, or by H-abstraction reactions. A unique unsaturated ketone, methyl vinyl ketone (but-1-en-3-one), was observed, the mole fraction of which decreases when the equivalence ratio increases. Other major intermediates directly related to fuel radical decomposition are pent-2-ene isomers and pent-1-ene, quantified around 25 ppm (trans-2-C 5 H 10 ), 15 ppm (cis-2-C 5 H 10 ), and 10 ppm (1-C 5 H 10 ) at = 4, the mole fractions of which decrease with the equivalence ratio. Figure 4 shows the primary decomposition pathways of pentan-2-ol for the stoichiometric mixture at 830 K in JSR. Fuel is mainly consumed by H-abstraction reactions by OH radicals (81 % of the flow rate). HO 2 and CH 3 radicals, to a lesser extent, contribute to increase the formation of pent2oh-2, the most abundant of the primary radicals. Considering C-H bond dissociation energies, the bond on the carbon bearing the alcohol function is the weakest (94.7 kcal mol -1 ) of pentan-2-ol whereas the bond on the secondary carbon adjacent to it is slightly strengthened (99.7 kcal.mol -1 ) by the presence of the neighboring OH group. Thus, 42 % of pentan- 2-ol produces pent2oh-2 and only 14 % yields pent2oh-3, a similar flow rate (16 %) of pentan-2-ol leads to pent2oh-4, whereas pent2oh-5, pent2oh-1, and pent2o are much less produced by H-abstraction reactions, 9 %, 6 %, and 5 % respectively. Pentan-2-one appears as a major intermediate during the oxidation of pentan-2-ol. Its peak mole fraction reaches 133 ppm at  = 0.35 and only 82 ppm at  = 4, demonstrating its formation depends on the equivalence ratio: indeed, under the conditions of Figure 4, pentan-2-one is almost exclusively (99.1 %) produced by pent2oh-2 + O 2 ⇌ nC 3 H 7 COCH 3 +HO 2 . By H-abstraction reactions, pentan-2-one yields four different radicals, CCCC(=O)C*, CCC*C(=O)C, CC*CC(=O)C, and C*CCC(=O)C. Among these, CC*CC(=O)C is the most abundant one (40 %), followed by CCC*C(=O)C (29 %). CC*CC(=O)C yields 20 % of the propene formed while CCC*C(=O)C is responsible for more than 75 % of the formation of methylvinylketone. Pent-1-ene is only produced from pent2oh-1, its mole fraction remaining relatively equivalence ratio independent. Pent-2-ene (both trans-and cis-isomers) are exclusively produced from pent2oh-3 and their mole fractions increase with the equivalence ratio.

Shock tube experiments

Mixtures of 1% pentan-2-ol in O 2 /Ar were tested in a high-pressure shock tube at 20 and 40 bar and equivalence ratios of 0.5, 1 and 2 between 1070 and 1460 K. In addition, a stoichiometric mixture of pentan-2ol in air was also tested at 20 bar. For the longest ignition delay times, a pressure rise was recorded after the reflected shock wave prior to the main ignition event, due to facility effects. This pressure rise was estimated to be ca. 7.0 %/ms and was modeled as a heat gain of 40 cal/s at 20 bar in Ar and 80 cal/s at 20 bar in air and at 40 bar in Ar. The experimental ignition delay time was defined as the time at which the pressure increased by 25 % from the initial P 5 value as detailed in Figure 5. All experimental pressure traces are provided as supplementary material. Numerical and experimental data comparisons are presented in Figure 6. The influence of the experimental conditions (temperature, pressure and equivalence ratio) on ignition delay times is in agreement with what is commonly observed for hydrocarbons at high temperatures: ignition delay times decrease with increasing pressure and temperature for a given mixture and mixtures ignite faster when the equivalence ratio goes from 2 to 0.5. The effect of equivalence ratio appears more clearly at 20 bar than at 40 bar. In addition, ignition delay times are shorter when the fuel concentration increases, i.e. the dilution decreases. Overall, the kinetic mechanism agrees very well with the data for all mixtures and pressures even though, at the lowest temperatures in air, the mechanism tends to overestimate the IDT. A sensitivity analysis was also performed on the temperature at the ignition point for a 1% pentan-2ol/O 2 /Ar mixture at 19.39 bar, 1213 K, and = 1. The ten most sensitive reactions are represented in Figure 7. Among these reactions, most of them involve small species belonging to the C 0 -C 3 basis, but two unimolecular initiation steps also appear as significantly sensitive. These reactions occur through the rupture of the first and third weakest C-C bonds. Their rate constants are pressure-dependent and are coming from butan-2-ol [START_REF] Sarathy | A comprehensive chemical kinetic combustion model for the four butanol isomers[END_REF]. Unexpectedly, the rupture of the second weakest C-C bond yielding the formation of CH 3 and a radical of butan-1-ol is less sensitive. These pressure-dependent rate constants would certainly benefit from a reevaluation to improve our model prediction.

Finally, a comparison was done between experimental ignition delay times of pentan-2-ol and pentan-3-ol under same conditions (1 % fuel,  = 1, and P 5 = 40 bar) and is presented in Figure 8. From this figure, it can be noticed that, as it was observed in jet-stirred reactor, pentan-3-ol is slightly more reactive than pentan-2-ol. Although beyond the scope of this study, a reason for pentan-3-ol being more reactive than pentan-2-ol could come from the production of ketone. Indeed, Carbonnier et al. [START_REF] Carbonnier | An experimental and modeling study of the oxidation of 3-pentanol at high pressure[END_REF] observed smaller mole fractions of pentan-3-one during the oxidation of pentan-3-ol than pentan-2-one mole fractions in this study, for a same Temperature A-factor sensitivity mixture. Furthermore, as detailed in the reaction pathway analysis, pentan-2-one partly yields propene while pentan-3-one produces ethylene. This different behavior between these two isomers clearly needs further investigations.

Conclusion

High pressure oxidation of pentan-2-ol was investigated experimentally in a JSR and in a shock tube, for the first time. Mole fraction profiles of the reactants, final products, and stable intermediates were identified and quantified by gas chromatography analyses, mass spectrometry, and Fourier transform infrared spectrometry after sonic probe sampling at five different equivalence ratios. Ignition delay times were measured for 1% fuel in O 2 /Ar mixtures at 20 and 40 bar for 3 equivalence ratios and for a stoichiometric mixture in air at 20 bar. Under the investigated conditions, pentan-2-ol did not show any cool flame behavior and was found to produce various pentan-2-one as well as pent-1-ene, and cis-and trans-pent-2-ene as C 5 intermediates. A submechanism for pentan-2-ol was developed in order to represent the data with good performance, both in JSR and in shock tube. Thermochemistry of pentan-2-ol and its radicals, together with rate constants for β-scission and isomerization reactions were calculated and presented in an accompanying paper. Thermochemistry was found to be very sensitive towards the products distribution through isomerization. In addition, selecting the right set of rate constants for H-abstractions among the various rate constants recently published for alcohols has been tricky, which suggest further work in that direction. Experimental fuel mole fraction was compared with previous oxidation studies of pentan-1-ol and pentan-3-ol under the same conditions and the global reactivity of pentan-2-ol was found to be lower than both of the other linear isomers. More data would certainly be useful, such as detailed speciation at lower pressure or pyrolysis in order to unravel more about pentan-2-ol kinetics and further refine the kinetic mechanism.

Figure 1 . 4 Figure 2 .

 142 Figure 1. Pentan-2-ol (black symbols) mole fraction at all equivalence ratios investigated (P = 10 atm, and = 0.7 s) compared to pentan-1-ol (grey symbols) and pentan-3-ol (open symbols) (lines are drawn to guide the eye).

Figure 3 .

 3 Figure 3. Species mole fractions as a function of temperature for three equivalence ratios = 0.5, = 1, and = 2 at P = 10 atm, and = 0.7 s. Symbols are experimental data and lines are simulations.

Figure 4 .

 4 Figure 4. Major fuel decomposition pathways for pentan-2-ol oxidation at T = 830 K, = 1, P = 10 atm, and τ = 0.7 s.

Figure 5 .

 5 Figure 5. Experimental and numerical pressure traces at P 5 = 38.53 bar, T 5 = 1117 K, and = 1.

Figure 6 .

 6 Figure 6. Ignition delay times of 1% pentan-2-ol/O 2 /Ar mixtures at (left) 20 bar and (right) 40 bar. Symbols are experimental data and lines are simulations.

Figure 7 .

 7 Figure 7. Temperature A-factor sensitivity analysis at ignition point for a 1% pentan-2-ol/O 2 /Ar mixture at 19.39 bar, 1213 K, and = 1.

Figure 8 .

 8 Figure 8. Comparison of ignition delay times of stoichiometric mixtures of 1% pentan-2-ol/O 2 /Ar mixtures and 1% pentan-3-ol/O 2 /Ar mixtures at 40 bar.

Acknowledgements

Authors gratefully acknowledge funding received from Bourgogne council under the PARI2 program (No 2016-9201AAO048S01891) and Labex Caprysses (convention ANR-11-LABX-0006-01) and National Science and Technology Major Project in China (2017-III0004-0028).


Zeynep Serinyel

Guillaume Dayma

Valentin Glasziou

Maxence Lailliau

Philippe Dagaut

A pyrolysis study on C4-C8 symmetric ethers

Keywords: ethers, kinetics, jet-stirred reactor, pyrolysis

à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

In the search for biofuels ethers have attracted attention recently. Symmetric ethers such as diethyl ether and dibutyl ether have been studied in various experimental set-ups in oxidative conditions, although fewer studies are available in pyrolysis. Among the symmetric ethers pyrolysis of diethyl ether was recently studied in a jet-stirred reactor [START_REF] Vin | Diethyl ether pyrolysis study in a jet-stirred reactor[END_REF] and shock tubes [START_REF] Yasunaga | A Multiple Shock Tube and Chemical Kinetic Modeling Study of Diethyl Ether Pyrolysis and Oxidation[END_REF][START_REF] Sela | High-Temperature Unimolecular Decomposition of Diethyl Ether: Shock-Tube and Theory Studies[END_REF]. All three studies reported species profiles as a function of temperature and were performed at rather lower pressures (between 1 and 3 atm). Our team has been working on the oxidation of ethers as these molecules present interesting low-temperature chemistry [START_REF] Thion | A chemical kinetic study of the oxidation of dibutyl-ether in a jet-stirred reactor[END_REF][START_REF] Serinyel | A high pressure oxidation study of di-n-propyl ether, Fuel, accepted[END_REF], while on the other hand, chemistry at very rich conditions and pyrolysis is not well known. These parts of the kinetic mechanism therefore remain uncertain and unvalidated. This study, hence is an attempt to widen our condition range and understand how these fuels decompose in pyrolytic conditions, highlighting some specific channels. To the best of our knowledge no such data exist for di-n-propyl, di-iso-propyl and dibutyl ethers.

The aim of this study is to provide new kinetic data through a detailed product analysis of the pyrolysis of 4 symmetric ethers; namely, diethyl (DEE), di-n-propyl (DPE), di-iso-propyl (DIPE) and di-n-butyl (DBE) ethers in a jet-stirred reactor at 10 atm, for the first time. A chemical kinetic mechanism is developed based on our previous studies [START_REF] Thion | A chemical kinetic study of the oxidation of dibutyl-ether in a jet-stirred reactor[END_REF][START_REF] Serinyel | A high pressure oxidation study of di-n-propyl ether, Fuel, accepted[END_REF][START_REF] Serinyel | An experimental chemical kinetic study of the oxidation of diethyl ether in a jet-stirred reactor and comprehensive modeling[END_REF] and used to represent the present data.

Experimental

The jet-stirred reactor (JSR) used in this work has been described previously [START_REF] Dagaut | A jet-stirred reactor for kinetic studies of homogeneous gas-phase reactions at pressures up to ten atmospheres (≈1 MPa)[END_REF]. It consists in a fused silica jet-stirred reactor located inside a regulated electrical resistance oven of ≈3kW surrounded by insulating ceramic wool and a stainless-steel pressure-resistant jacket. The liquid fuel is brought by an HPLC pump to the entrance of a vaporization system where it is atomized by a nitrogen flow (50L/h) and then vaporized in a heated chamber. The fuel+N 2 mixture is carried to the reactor by a quartz capillary, while the N 2 stream is conveyed independently to the reactor. All gaseous flowrates are regulated by thermal mass flow controllers (Brooks 5850E). The two flows merged right ahead of the reactor, in which they are injected by four nozzles that ensure stirring. The sampling system, which consists in a thermocouple attached to a low-pressure sonic probe, can be moved along a vertical axis to check the temperature and the composition homogeneity inside the reactor. Residence time distribution studies have shown that under the conditions of the present study the reactor is operating under macro-mixing conditions [START_REF] Dagaut | A jet-stirred reactor for kinetic studies of homogeneous gas-phase reactions at pressures up to ten atmospheres (≈1 MPa)[END_REF]. Samples are analyzed online by means of FTIR and stored at low pressure for offline GC analysis. The fuels (> 99.5 % purity) were supplied by Sigma Aldrich (DEE, DBE) and TCI Chemicals (DPE, DIPE), and high purity N 2 (Air Liquide) was used. Uncertainties on the species mole fractions is due to several factors described in [START_REF] Serinyel | Kinetics of oxidation of cyclohexanone in a jet-stirred reactor: Experimental and modeling[END_REF] and are very difficult to evaluate precisely. These are estimated to be around ±15 %. All experiments were performed at 10 atm operating pressure and between 750 and 1140 K with an initial fuel mole fraction of 0.1 % and a residence time of 0.7 s.

Kinetic modeling

The kinetic model used in the simulations is obtained by introducing a sub-mechanism representing DIPE pyrolysis into our current mechanism on ethers. The thermochemical parameters of the fuel (DIPE) and related species were evaluated using Thergas [START_REF] Muller | Thergas -A computer program for the evaluation of thermochemical data of molecules and free radicals in the gas phase[END_REF], which uses the group additivity methods proposed by Benson [START_REF] Benson | Thermochemical Kinetics[END_REF]. Other species (related to DEE, DPE, DBE) are already present in the mechanism and in the thermochemistry file. Kinetic simulations were performed using the PSR module from Chemkin-II [START_REF] Glarborg | PSR: A Fortran Program for Modeling Well-Stirred Reactors[END_REF]. Structures of the ethers are presented in Figure 1. The pyrolysis sub-mechanism of DIPE was constructed similarly to other ethers, and includes unimolecular pathways and H-abstraction reactions, consistent with the other ether sub-mechanisms as well as an iso-propanol sub-mechanism. For the moment no oxidation mechanism is included but this will be the scope of a future study and hence this sub-mechanism will be detailed then. The kinetic model gathering all ethers and the references therein are provided as supplementary material as well as the thermochemistry.

Results and discussion

Figure 1 illustrates the experimental reactivity of the ethers in order to compare easily. In pyrolytic conditions the order of reactivity is different than that in oxidation. DIPE and DPE show higher (and similar) reactivity at lower temperatures, while DBE shows the lowest reactivity at higher temperatures. At lower temperatures, reactivity is quite similar as the experimental points are within their uncertainty, the difference can be seen at higher temperatures where propyl ethers are more reactive then the rest. The simulation results are provided in supplementary material showing similar reactivities for dipropyl and dibutyl ethers while DEE appears to be the least reactive due to its smaller chain, at a given temperature > 950 K. Figure 1 shows also the evolution of the specific alcohols from the molecular reaction of the ether, which follows the same tendency. For example, iso-propanol formed via DIPE ⇌ C 3 H 6 + iso-C 3 H 7 OH, appears at lower temperatures and reaches a higher peak than ethanol (DEE ⇌ C 2 H 4 + C 2 H 5 OH), n-propanol (DPE ⇌ C 3 H 6 + n-C 3 H 7 OH) and n-butanol (DBE ⇌ 1-C 4 H 8 + n-C 4 H 9 OH). Evolution of the pyrolysis intermediates are shown separately for each ether in Figures 2345. One can observe that all ethers have common pyrolysis intermediates such as CO, C 2 H 4 , H 2 and CH 4 , which means H-abstraction reactions by H and CH 3 and -scission reactions of primary radicals are dominating. Reaction path analyses are performed at 1000 K for all ethers (Figs. [START_REF] Serinyel | An experimental chemical kinetic study of the oxidation of diethyl ether in a jet-stirred reactor and comprehensive modeling[END_REF][START_REF] Dagaut | A jet-stirred reactor for kinetic studies of homogeneous gas-phase reactions at pressures up to ten atmospheres (≈1 MPa)[END_REF][START_REF] Serinyel | Kinetics of oxidation of cyclohexanone in a jet-stirred reactor: Experimental and modeling[END_REF][START_REF] Muller | Thergas -A computer program for the evaluation of thermochemical data of molecules and free radicals in the gas phase[END_REF]. Note that at this temperature the fuels do not all have the same conversion.

Figure 6. Reaction path analysis for DEE pyrolysis at 1000 K According to in Fig. 6, at 1000 K, the fuel is mainly consumed by hydrogen abstraction reactions by H atoms (71 %) and CH 3 radicals (17 %) to yield the two primary radicals. The C 2 H 5 OC 2 H 5 s radical is formed in preference given the lower bond energy of the C-H bond adjacent to the ether oxygen [START_REF] Serinyel | An experimental chemical kinetic study of the oxidation of diethyl ether in a jet-stirred reactor and comprehensive modeling[END_REF]. A small part of the flux forms ethanol and ethylene via molecular reaction. This is the only formation route of ethanol (40 ppm peak at 1050 K) and corresponds to 10% of ethylene formation. Ethylene is one of the major pyrolysis species of DEE and 80 % of its formation is via C-H scission of ethyl radicals, which are formed via -scission of the primary fuel radical C 2 H 5 OC 2 H 5 s, also forming acetaldehyde. Other major products are CO, methane and H 2 .

All major and minor species are well-predicted by the model except ethane, which is under-predicted by a factor of 2. This species owes half of its formation to the recombination of methyl radicals and the other half to Habstraction reactions by ethyl radicals, from formaldehyde and acetaldehyde mainly. Although not shown in Fig. 3, some H 2 O formation is observed and predicted at T > 1000 K, via dehydration of ethanol. Figure 8. Reaction path analysis for DIPE pyrolysis at 1000 K Fig. 8 illustrates the main decomposition pathways of DIPE and subsequent major intermediates. DIPE can yield two primary fuel radicals, namely dipe1 and dipe2. DIPE is the most reactive of all ethers investigated in this study (Fig. 2), its major pyrolysis products include C 3 H 6 , C 2 H 4 , H 2 , CH 4 and iso-propanol. This latter alcohol peaks at a higher mole fraction, around 450 ppm (Fig. 2). To the best of our knowledge there is no direct measurement or a theoretical investigation of the rate constant of this molecular reaction, which we estimated in analogy with methyl tertiary butyl ether by Choo et al. [START_REF] Choo | Very low-pressure pyrolysis (VLPP) of t-butylmethyl ether[END_REF], which is a study conducted at very low pressures. This resulted in a rate constant higher than those assumed for the molecular reactions of DEE, DPE and DBE, which are estimated as fits from NIST values, also note that there are more H-atoms available in DIPE. There are only two equivalent tertiary H-atoms available for abstraction while 12 primary C-H sites (slightly stronger than primary C-H in alkanes) are present for the molecular reaction, which is probably why this fuel decomposes mainly this way and the H-abstraction reaction appear less important. One could expect, hence this fuel to be less reactive than other ethers in oxidative conditions, but this will be the scope of a further study. An important flux of the fuel hence forms iso-propanol and propene. This is the only formation route of isopropanol, while it is responsible for 68 % of propene formation. The rest of the propene formation is due to the dehydration of iso-propanol (14 %), -scission of n-propyl radicals (10 %) and of dipe2 radicals (5 %). Ethylene, another major intermediate, is mainly formed by the ipso-addition of H to propene (40 %) andscission reactions of n-propyl (41 %) and ethyl radicals (14 %), to a lesser extent. Formation of the n-propyl radicals is the result of both H addition to propene and isomerization of iso-propyl radicals, which are abundantly produced from the -scission of dipe1 radical. Acetone can be counted among the minor pyrolysis intermediates, its formation is mostly via -scission of the dipe1 radical (80 % at 1000 K, and this goes down to 60 % at 1100 K) as well as the C-H -scission of the iso-propanol tertiary radical. The main consumption pathway of acetone is by C-C scission yielding CH 3 CO and CH 3 radicals. The discrepancy with acetone mole fraction and the model is within 15 % between 900 and 1050 K and 30 % when T > 1050 K. Note that in DIPE sub-mechanism, like in DPE, we did not consider any isomerization of the fuel radical, for the same reason explained above. Figure 9. Reaction path analysis for DBE pyrolysis at 1000 K Pyrolysis of DBE follows similar pathways as the other ethers (Fig. 9). Given its longer chain, 4 primary fuel radicals can be formed by H-abstraction by H atoms (64 %) and CH 3 radicals (11 %). Among these, the most abundant is the a-radical, which forms butanal (92 % of butanal formation) and butyl radicals. The formation of butyl radicals proceeds to 68 % via this pathway, the rest is the result of the -scission of the C 4 H 9 OCH 2 radicals. They decompose exclusively to ethylene and ethyl radicals by -scission, which represents 38 % of ethylene formation at 1000 K. Because the fuel reactivity is over-estimated above 990 K, one can see in Fig. 6 that the mole fractions of major intermediates are overestimated as well, such as H 2 and CH 4 . About half of CH 4 formation is due to H-abstraction from DBE and butanal, as this aldehyde is very reactive in this temperature range. Butanal is therefore an important intermediate both in oxidation [START_REF] Thion | A chemical kinetic study of the oxidation of dibutyl-ether in a jet-stirred reactor[END_REF] and pyrolysis, and in these conditions its decomposition takes place mostly by H-abstraction reactions by H and CH 3 (as opposed to OH in oxidation) as well as unimolecular reactions to a lesser extent.

It is to be noted that some benzene formation is observed at temperatures higher than 1000-1050 K with mole fractions around 90 ppm for DPE, DPE and DBE, and around 20 ppm for DEE at 1140 K. The formation pathways of benzene are the same for all ethers and mainly go through via reactions allene/propyne and propargyl radicals: C 3 H 4 + C 3 H 3 ⇌ C 6 H 6 + H and also via the reaction between 1-buten-3-yne (vinyl acetylene) and acetylene: C 4 H 4 + C 2 H 2 ⇌ C 6 H 6 according to the mechanism. Vinyl acetylene is formed by C-H scission of butadienyl radicals and acetylene via vinyl radicals produced from ethylene, a common abundant high temperature reaction intermediate for all ethers investigated.

Conclusion and Perspectives

Pyrolysis of 4 symmetric ethers were performed in a JSR at 10 atm. In these high-pressure conditions bimolecular reactions such as H-abstraction reactions by H atoms and CH 3 radicals are found to be dominant in fuel decomposition as well as the in the decomposition of the intermediate species. Although these reactions are always considered in oxidation mechanisms, they are hardly ever the dominating ones except at very rich conditions. As oxidation studies are more common, emphasis is always given to the H-abstraction reactions by OH and HO 2 radicals. This study shows that an attempt in evaluating the rate constants of these reactions for ethers could be useful for a complete understanding of ether oxidation. Moreover, at lower pressures isomerization of ether radicals can become important, implying a better assessment of thermochemistry and rate constants of these reactions. As a perspective, pyrolysis at 1 atm can reveal more importance in the unimolecular decomposition pathways both for ethers themselves and their intermediates. In this study, the molecular reaction yielding the alcohol was found to be more important among the unimolecular pathways as ethanol, n-and isopropanol and butan-1-ol were quantified and are only formed by this reaction, the rate constant of which is only estimated. This study, along with the previous oxidation studies, represents another step in our understanding of ether chemistry and brings up the need of a systematic approach in determining site specific rate constants of important fuel related reactions of ethers.

Figure 1 .

 1 Figure 1. Experimental reactivity of the ethers and evolution of the specific alcohols

Figure 2 .

 2 Figure 2. Mole fractions of intermediate species from DEE pyrolysis

  Figure 7. Reaction path analysis for DPE pyrolysis at 1000 K Fig.7illustrates the main decomposition pathways of DPE and subsequent intermediates. A small part of the fuel (9%) forms propanol and propene via molecular reaction, similarly to DEE. Also, formation of ethyl radicals and C 2 H 5 OCH 2 is possible to a small extent. The decomposition of DPE most takes place through Habstraction reactions by H atoms (62 %) and CH 3 radicals (14 %) forming three primary radicals, with dpe1 favored. Formation of propanal is almost exclusively (97%) due to the -scission of dpe1. Acyl radicals that can easily be formed from propanal decompose into CO and ethyl radicals by -scission, representing 28 % of • C 2 H 5 formation at 1000 K. The remaining part of the formation of • C 2 H 5 radicals is the -scission of propoxy radicals ⇌ nC 3 H 7 O + C 3 H 6 ) and unimolecular decomposition of the fuel, to 46 % and 19 %, respectively. Formation of ethylene, a major intermediate, is due to • C 2 H 5 radicals (37 %), nC 3 H 7 radicals (52 %) and to dpe3 radicals to smaller extent (8 %), and is well predicted by the model. The biggest discrepancy is observed with a minor product, formaldehyde, over-predicted by about a factor of 2.5. Formaldehyde is produced by thescission of C 3 H 7 OCH 2 and nC 3 H 7 O radicals, and is consumed by H-abstraction by H and CH 3 . Note that possible isomerization reactions among DPE radicals are not considered as any analogy would have been probably very uncertain. In the case of DEE, we have included the rate constant calculated by Sakai for DEE radicals because it was calculated specifically for DEE, and the impact on overall predictions is very small.

	O	10 % 75 %	O OH C 2 H 5 OC 2 H 5 s 13 % + CH 3 + H	O C 2 H 5 OC 2 H 5 p + 13 %	+ -H + C 2 H 5 O -H 87 %	O C 2 H 3 -H + H (38 %) + C 2 H 5 (12 %) + CH 3 (47 %) 50 % -CH 2 O CH 3 +CH 3 (+M) C 2 H 6 C 2 H 2 H 2 12 % 38 % + CH 3 + H	CH 4	+ HCO	H + CO

Acknowledgements

The authors would like to acknowledge the funding received from Labex Caprysses (convention ANR-11-LABX-0006-01)