H A Gueniche

J Biet

P A Glaude

R Fournet

F Battin-Leclerc
email: frederique.battin-leclerc@ensic.inpl-nancy.fr

A COMPARATIVE STUDY OF THE FORMATION OF AROMATICS IN RICH METHANE FLAMES DOPED BY UNSATURATED COMPOUNDS

Keywords: Laminar premixed flame, benzene, toluene, unsaturated soot precursors

For a better modeling of the importance of the different channels leading to the first aromatic ring, we have compared the structures of laminar rich premixed methane flames doped with several unsaturated hydrocarbons: allene and propyne, because they are precursors of propargyl radicals which are well known as having an important role in forming benzene, 1,3-butadiene to put in evidence a possible production of benzene due to reactions of C 4 compounds, and, finally, cyclopentene which is a source of cyclopentadienylmethylene radicals which in turn are expected to easily isomerizes to give benzene. These flames have been stabilized on a burner at a pressure of 6.7 kPa (50 Torr) using argon as dilutant, for equivalence ratios (φ) from 1.55 to 1.79. A unique mechanism, including the formation and decomposition of benzene and toluene, has been used to model the oxidation of allene, propyne, 1,3-butadiene and cyclopentene. The main reaction pathways of aromatics formation have been derived from reaction rate and sensitivity analyses and have been compared for the three types of additives. These combined analyses and comparisons can only been performed when a unique mechanism is available for all the studied additives.

INTRODUCTION

While the formation of PAHs and soot has represented an important area of interest for kineticists for two decades, questions still remain concerning even the formation and the oxidation of the first aromatic compounds. In previous studies, the formation of benzene is mostly related to the reactions of C 2 (acetylene), C 3 or C 4 unsaturated species [START_REF] Cole | Formation mechanisms of aromatic compounds in aliphatic flames[END_REF][START_REF] Westmoreland | Forming benzene in flames by chemically activated isomerization[END_REF][START_REF] Miller | Kinetic and thermodynamic issues in the formation of aromatic compounds in flames of aliphatic fuels[END_REF][START_REF] Marinov | Modelling of aromatic and polycyclic aromatic hydrocarbon formation in premixed methane and ethane flames[END_REF][START_REF] Wang | A detailed kinetic modeling study of aromatics formation in laminar premixed acetylene and ethylene flames[END_REF][START_REF] Mcenally | Studies of aromatic hydrocarbon formation mechanisms in flames: Progress towards closing the fuel gap[END_REF][START_REF] Law | Benzene precursors and formation routes in a stoichiometric cyclohexane flame[END_REF]. Nevertheless, some papers suggest a link between C 6 and C 5 cyclic species [START_REF] Ritter | Kinetic study on thermal decomposition of chlorobenzene diluted in hydrogen[END_REF][START_REF] Lamprecht | Fuel-rich flame chemistry in low pressure cyclopentene flames[END_REF][START_REF] Lifshitz | Decomposition and ring expansion in methylcyclopentadiene: single-pulse shock tube and modeling study[END_REF][START_REF] Hansen | Identification of C 5 H x Isomers in fuel-rich flames by photoionization mass spectrometry and electronic structure calculations[END_REF]. In a recent paper [START_REF] Gueniche | Rich methane premixed laminar flames doped with light unsaturated hydrocarbons: I. Allene and propyne[END_REF], we have investigated the reactions, in a rich methane flame, of allene and propyne because they are precursors of propargyl radicals which have an important role in forming benzene. In a second part [START_REF] Gueniche | Rich methane premixed laminar flames doped with light unsaturated hydrocarbons: II. 1,3-butadiene[END_REF], we have analyzed the reactions of 1,3-butadiene under similar conditions and put in evidence an important route to the production of benzene due to reactions of C 4 compounds. To finish this work, we have studied the reactions of cyclopentene which is a source of C 5 radicals [START_REF] Gueniche | Rich methane premixed laminar flames doped with light unsaturated hydrocarbons: III. Cyclopentene[END_REF]. The purpose of the present paper is to compare the results obtained in these three studies for the formation of benzene and toluene and the routes to their formation. The use of methane as the background gas makes these flames more representative of the combustion of a real fuel compared to a flame containing an unsaturated soot precursor as the only reactant.

EXPERIMENTAL PROCEDURE AND MAIN RESULTS

The experiments were performed using a horizontal laminar premixed flat flame burner housed in a water-cooled vacuum chamber evacuated by two primary pumps and maintained at 6.7 kPa (50 Torr) by a regulation valve [START_REF] Gueniche | Rich methane premixed laminar flames doped with light unsaturated hydrocarbons: I. Allene and propyne[END_REF]. This chamber was equipped with a silica microprobe for sampling and a thermocouple for temperature measurements. The position of the burner could be vertically adjusted, while the housing and its equipments were kept fixed.

Gas flow rates were controlled by mass flow regulators. The flow rate of liquid cyclopentene was controlled using a liquid mass flow controller, mixed with the carrier gas and then evaporated by passing through a single pass heat exchanger [START_REF] Gueniche | Rich methane premixed laminar flames doped with light unsaturated hydrocarbons: III. Cyclopentene[END_REF]. Temperature profiles were obtained using a PtRh (6%)-PtRh (30%) type B thermocouple (diameter 100 µm) coated with an inert layer to prevent catalytic effects. Radiative heat losses were corrected using the electric compensation method.

Figure 1 presents the experimental temperature profiles for methane flames doped with allene, 1,3-butadiene and cyclopentene. The profiles measured with propyne is very close to that with allene. In the studied flames, the temperature ranged from 600 K near the burner up to 2150 K.

FIGURE 1

Gas samples were directly obtained by connecting through a heated line (temperature between 393 and 423 K) the quartz probe to a volume which was previously evacuated. The pressure drop between the flame at a pressure of 6.7 kPa (50 Torr) and the inlet of the probe at a pressure always below 1.3 kPa (10 Torr) ensured that reactions were frozen. Stable species profiles were determined by gas chromatography. Chromatographs at atmospheric pressure with a Carbosphere packed column and helium or argon as carrier gas were used to analyse O 2 , H 2 , CO and CO 2 by thermal conductivity detection and CH 4 , C 2 H 2 , C 2 H 4 , C 2 H 6 by flame ionisation detection (FID). Heavier hydrocarbons from C 3 to C 7 were analysed on a Haysep packed column by FID and nitrogen as carrier gas. The identification was performed using GC/MS and by comparison of retention times.

The experimental conditions used for the four flames are summarized in Table 1; φ was equal to 1.55 in the flames seeded with allene and propyne and to 1.79 in the two others. Due to problems of stability and in order to get a wider reaction zone above the burner, a slightly higher dilution yield has been used in the flame of cyclopentene compared to the 3 other flames. This higher dilution explains the lower temperature profile obtained with cyclopentene compared to 1,3-butadiene, as shown in fig. 1.

In the pure methane flame (containing 20.9% (molar) of methane and 33.4 % of oxygen corresponding to an equivalent ratio of 1.25 [START_REF] Gueniche | Rich methane premixed laminar flames doped with light unsaturated hydrocarbons: I. Allene and propyne[END_REF]) and in all the doped ones, quantified products included carbon monoxide and dioxide, hydrogen, ethane, ethylene, acetylene, propyne (p-C 3 H 4 ), allene (a-C 3 H 4 ), propene (C 3 H 6 ) and propane (C 3 H 8 ). Several C 3+ products which cannot be detected in the pure methane flame have also been analysed:

• in the case of C 3 additives, butadienes, 1-butene, iso-butene, 1-butyne, vinylacetylene and benzene (toluene could be quantified for flames of richer mixtures, but was not detected in the flames studied here) [START_REF] Gueniche | Rich methane premixed laminar flames doped with light unsaturated hydrocarbons: I. Allene and propyne[END_REF],

• in the case of 1,3-butadiene, 1,2-butadiene, butynes, vinylacetylene, diacetylene, 1,3-pentadiene, 2-methyl-1,3-butadiene (isoprene), 1-pentene, 3-methyl-1-butene, benzene and toluene [START_REF] Gueniche | Rich methane premixed laminar flames doped with light unsaturated hydrocarbons: II. 1,3-butadiene[END_REF],

• in the case of cyclopentene, butadienes, vinylacetylene, diacetylene, cyclopentadiene, 1,3-pentadiene, benzene and toluene [START_REF] Gueniche | Rich methane premixed laminar flames doped with light unsaturated hydrocarbons: III. Cyclopentene[END_REF].

In the four flames, the carbon balance calculated from the initial reactant mole fractions, the measured product mole fraction and the simulated argon mole fraction is better than + 10% whatever the position in the flame.

DESCRIPTION OF THE DETAILED KINETIC MODEL

The mechanism proposed to model the oxidation of allene, propyne, 1-3-butadiene and cyclopentene (see supplementary file in the website of the journal) includes a mechanism built to model the oxidation of C 3 -C 4 unsaturated hydrocarbons [START_REF] Gueniche | Rich methane premixed laminar flames doped with light unsaturated hydrocarbons: I. Allene and propyne[END_REF][START_REF] Gueniche | Rich methane premixed laminar flames doped with light unsaturated hydrocarbons: II. 1,3-butadiene[END_REF], our previous mechanisms for the oxidation of benzene [START_REF] Costa | Experimental and modeling study of the oxidation of benzene[END_REF], toluene [START_REF] Bounaceur | Experimental and modeling study of the oxidation of toluene[END_REF] and cyclopentene [START_REF] Gueniche | Rich methane premixed laminar flames doped with light unsaturated hydrocarbons: III. Cyclopentene[END_REF]. Thermochemical data were estimated using software THERGAS [START_REF] Muller | A computer program for the evaluation of thermochemical data of molecules and free radicals in the gas phase[END_REF], which is based on the additivity methods proposed by Benson [START_REF] Benson | Thermochemical kinetics[END_REF].

Reaction base for the oxidation of C 3 -C 4 unsaturated hydrocarbons [START_REF] Gueniche | Rich methane premixed laminar flames doped with light unsaturated hydrocarbons: I. Allene and propyne[END_REF][START_REF] Gueniche | Rich methane premixed laminar flames doped with light unsaturated hydrocarbons: II. 1,3-butadiene[END_REF] This C 3 -C 4 reaction base [START_REF] Gueniche | Rich methane premixed laminar flames doped with light unsaturated hydrocarbons: I. Allene and propyne[END_REF][START_REF] Gueniche | Rich methane premixed laminar flames doped with light unsaturated hydrocarbons: II. 1,3-butadiene[END_REF] (6 isomers), as well as some reactions for linear and branched C 5 compounds and the formation of benzene. In this reaction base, pressure-dependent rate constants follow the formalism proposed by Troe [START_REF] Troe | Fall-off curves of unimolecular reaction[END_REF] and efficiency coefficients have been included.

Mechanisms for the oxidation of benzene and toluene

Our mechanism for the oxidation of benzene contains 135 reactions and includes the reactions of benzene, cyclohexadienyl, phenyl, phenylperoxy, phenoxy, hydroxyphenoxy, cyclopentadienyl, cyclopentadienoxy and hydroxycyclopentadienyl free radicals, as well as the reactions of orthobenzoquinone, phenol, cyclopentadiene, cyclopentadienone and vinylketene which are the primary products yielded [START_REF] Costa | Experimental and modeling study of the oxidation of benzene[END_REF].

The mechanism for the oxidation of toluene contains 193 reactions and includes the reactions of toluene, benzyl, tolyl, peroxybenzyl (methylphenyl), alcoxybenzyl and cresoxy free radicals, as well as the reactions of benzaldehyde, benzyl hydroperoxyde, cresol, benzylalcohol, ethylbenzene, styrene and bibenzyl [START_REF] Bounaceur | Experimental and modeling study of the oxidation of toluene[END_REF]. To avoid an overprediction of toluene in the C 3 and C 4 flames, the rate constant of the decomposition of this molecule to give phenyl and methyl radicals, which is not well known, has been taken equal to the value proposed by Colket and Seery [START_REF] Colket | Reaction mechanisms for toluene pyrolysis[END_REF].

Mechanism proposed for the oxidation of cyclopentene [START_REF] Gueniche | Rich methane premixed laminar flames doped with light unsaturated hydrocarbons: III. Cyclopentene[END_REF] We have considered the unimolecular reactions of cyclopentene, the additions of H-atoms and OH radicals to the double bonds and the H-abstractions by oxygen molecules and small radicals. radicals were also written, while those by breaking of a C-H bond are not considered. The reactions of cyclopentadiene are part of the mechanism for the oxidation of benzene, but reactions for the consumption of methylcyclopentene and methylcyclopentadiene, obtained by recombination of cyclopentadienyl and methyl radicals had to be added. [START_REF] Gueniche | Rich methane premixed laminar flames doped with light unsaturated hydrocarbons: I. Allene and propyne[END_REF][START_REF] Gueniche | Rich methane premixed laminar flames doped with light unsaturated hydrocarbons: II. 1,3-butadiene[END_REF][START_REF] Gueniche | Rich methane premixed laminar flames doped with light unsaturated hydrocarbons: III. Cyclopentene[END_REF] In order to investigate the relative importance of the different channels, the formation of aromatic compounds was considered through the C 3 , the C 4 and the C 5 pathways:

Ways of formation of aromatic compounds

• For the C 3 pathway, we have used a value of 1x10 12 cm 3 .mol -1 s -1 for the recombination of two propargyl radicals to give phenyl radicals and H-atoms, which is in good agreement with that recently proposed by Miller and Klippenstein [START_REF] Miller | The Recombination of Propargyl Radicals and Other Reactions on a C 6 H 6 Potential[END_REF] and Rasmussen et al. [START_REF] Rasmussen | Propargyl recombination: estimation of the high temperature, low pressure rate constant from flame measurements[END_REF]. Note that because of the low pressure of our study, we have considered the formation of phenyl radicals and Hatoms to be the dominant channel from the recombination of propargyl radicals. Due to addition of the toluene mechanism including the ipso-addition of toluene with H-atoms leading to benzene and methyl radicals and to avoid an overprediction of benzene in the case of the flame doped with allene, we have removed from our previous mechanism [START_REF] Gueniche | Rich methane premixed laminar flames doped with light unsaturated hydrocarbons: I. Allene and propyne[END_REF] the addition of propargyl radicals to allene leading to benzene and H-atoms and the recombination between allene and propargyl radicals to produce phenyl radicals and two H-atoms. These reactions were not considered by Rasmussen et al. [START_REF] Rasmussen | Propargyl recombination: estimation of the high temperature, low pressure rate constant from flame measurements[END_REF].

• For the C 4 pathway, all the reactions between C 2 species and n-C 4 H 3 , n-C 4 H 5 radicals or 1,3-butadiene molecules and leading to aromatic and linear C 6 species have been considered as proposed by Westmoreland et al. [START_REF] Westmoreland | Forming benzene in flames by chemically activated isomerization[END_REF]. We have written the main reactions of 1,4-cyclohexadiene: its dehydrogenation to give benzene with a rate constant proposed by Ellis and Freys [START_REF] Ellis | The thermal unimolecular isomerisation of bicyclo[3,1,0]hex-2-ene and decomposition of cyclohexa-1[END_REF] and the H-abstractions by H-atoms and OH radicals to give C 6 H 7 radicals with rate constants proposed by Dayma et al. [START_REF] Dayma | Experimental and modeling study of the oxidation of cyclohexene[END_REF].

• For the C 5 pathway, we have considered the isomerization between both radicals deriving from methylcyclopentadiene by H-abstractions (cyclopentadienylmethylene and methylcyclopentadienyl) and the formation of cyclohexadienyl radicals from cyclopentadienyl methylene radicals as proposed by Lifshitz et al. [START_REF] Lifshitz | Decomposition and ring expansion in methylcyclopentadiene: single-pulse shock tube and modeling study[END_REF]. As it was not considered by Lifshitz et al.

[10], we have not written the formation of cyclohexadienyl radicals from methyl cyclopentadienyl radicals as proposed by Marinov et al. [START_REF] Marinov | Modelling of aromatic and polycyclic aromatic hydrocarbon formation in premixed methane and ethane flames[END_REF], but the recombination with H-atoms of these resonance stabilized radicals was also added. In order to reproduce the important formation of toluene experimentally observed in the flame doped with cyclopentene, we have considered the formation of benzyl radicals from the addition of acetylene to cyclopentadienyl radicals with a rate constant about 3 times larger than that usually considered for such an addition [START_REF] Heyberger | Oxidation of small alkenes at high temperature[END_REF]. While the decomposition of benzyl radicals to form acetylene and cyclopentadienyl radicals, which was considered in our mechanism for the oxidation of toluene, has been studied by several authors [START_REF] Braun-Unkhoff | A shock tube study on the thermal decomposition of toluene and of the phenyl radical at high temperature[END_REF][START_REF] Jones | Decomposition of the benzyl radical: quantum chemical and experimental (shock tube) investigations of reaction pathways[END_REF] and has been shown to occur through a several-step mechanism, the reverse addition has never been directly investigated.

COMPARISON OF THE FORMATION OF BENZENE AND TOLUENE IN THE FOUR

FLAMES

All the simulations have been performed using PREMIX of CHEMKIN II [START_REF] Kee | Chemkin II. A fortran chemical kinetics package for the analysis of a gas-phase chemical kinetics[END_REF] with estimated transport coefficients, the same kinetic mechanism and using the experimental temperature profile as an input. To compensate the perturbations induced by the quartz probe and the thermocouple, the temperature profile used in calculations is an average between the experimental profiles measured with and without the quartz probe, with a slight shift away from the burner surface, as shown in figure 1.

Comparisons between experimental results and simulations are displayed for benzene in fig. 2 and for toluene in fig. 3: the unique model reproduces correctly the experimental formation of these two aromatic compounds in the four flames. Compared to our previous simulation with less complete mechanisms [START_REF] Gueniche | Rich methane premixed laminar flames doped with light unsaturated hydrocarbons: I. Allene and propyne[END_REF][START_REF] Gueniche | Rich methane premixed laminar flames doped with light unsaturated hydrocarbons: II. 1,3-butadiene[END_REF], the simulated maximum mole fractions of benzene have been increased by a factor 1.08, 1.10 and 1.48, for the flame of allene, propyne and 1,3-butadiene, respectively. A detectable concentration of toluene is predicted, but not observed experimentally for the flames containing C 3 additives and the production of toluene is underestimated by a factor 3 for the flame doped with cyclopentene.

FIGURES 2 AND 3

The experimental results show important changes in the formation of aromatic compounds depending on the additives. The production of aromatic compounds occurs the closest to the burner in the flames doped by C 3 compounds and the furthest in the flame seeded by cyclopentene. As the concentration of obtained aromatic species depends strongly on equivalence ratio, Table 1 presents the maximum mole fractions of benzene and toluene simulated for all the flames under the same conditions as in the flame of cyclopentene. Note however that the fact to use the same temperature profile for all the flames as for the flame of cyclopentene involves a slight overestimation of temperature. The flame showing the largest formation of benzene is the one doped with cyclopentene. Under the same conditions, the simulated maximum of the peak of benzene is 3.8 times smaller in the flame doped with 1,3-butadiene, 5.5 times in the flame doped by allene and 6.6 times in that doped by propyne. The difference between the flames doped by allene and propyne is connected to differences in the rates of formation and consumption of propargyl radicals between both flames [START_REF] Gueniche | Rich methane premixed laminar flames doped with light unsaturated hydrocarbons: I. Allene and propyne[END_REF]. The flame doped with 1,3-butadiene exhibits the lowest production of toluene.

The simulated peak of toluene would be around 4 times larger in the flames doped with C 3 compounds and almost 25 times in that doped with cyclopentene.

DISCUSSION

Figure 4 presents a reaction rate analysis for the production and consumption of aromatic compounds for the flames doped with allene (a similar picture is obtained for propyne), 1,3-butadiene and cyclopentene. Figure 5 presents a sensitivity analysis for the reactions for which a variation of the rate constant has an important effect on the formation of benzene and toluene.

These figures show well that the ways of formation of aromatic compounds are very different depending on the additive.

FIGURES 4 AND 5

In the allene flame, phenyl radicals are mainly obtained by self-combination of propargyl radicals.

Combinations of phenyl radicals with H-atoms and methyl radicals lead to benzene and toluene, respectively. As they derive directly from propargyl and phenyl radicals, benzene and toluene are primary products. That explains why their formation occurs early in the flame, as propargyl radicals are directly obtained from allene and propyne by H-abstractions. The production of benzene is relatively weak because the self-combination of propargyl radicals, at the low pressure studied here, leads mainly to phenyl radicals which react rapidly with oxygen molecules. As shown in figure 4, the rate of the reaction of phenyl radicals with oxygen molecules to give phenoxy radicals is equal to six times that of the formation of benzene. It is worth noting that our simulation using a value of the rate constant for the self-combination of propargyl radicals close to that given in the literature leads to a good agreement for the formation of benzene. This rate constant has the most important sensitivity coefficient for the formation of benzene. Many similarities exist between allene and propyne flames in both reactivity and product formation. Nevertheless, the pool of small radicals is slightly larger in the propyne flame, which leads to a faster consumption of propargyl radicals and a lower formation of benzene than in the flame seeded by allene [START_REF] Gueniche | Rich methane premixed laminar flames doped with light unsaturated hydrocarbons: I. Allene and propyne[END_REF]. In this flame, the C 5 pathway accounts for 5% of the formation of benzene, since the decomposition of phenoxy radicals leads to cyclopentadienyl radicals. The contribution of the C 4 pathway is negligible. The reactions which have the largest influence on the formation of toluene are the combination of propargyl radicals and that of methyl and phenyl radicals (see fig. 5). This last reaction has also a promoting effect on the formation of benzene as 10% of this aromatic compound is obtained through the ipso-addition of Hatoms to toluene with elimination of methyl radicals.

Of particular interest in the flames doped by 1,3-butadiene and cyclopentene is that the production of benzene is mainly due to other reactions rather than to the C 3 pathway as it is often the case in the flames described in the literature [START_REF] Rasmussen | Propargyl recombination: estimation of the high temperature, low pressure rate constant from flame measurements[END_REF]. Note however that the relative importance of the C 4 and C 5 pathway compared to the C 3 one considerably depends of the products assumed for the recombination of two propargyl radicals.

In the 1,3-butadiene flame, benzene is mainly formed from the addition/cyclization of vinyl radicals to produce cyclohexadiene which reacts either by dehydrogenation or by methatheses with H-atoms and OH radicals, followed by the decomposition of the obtained cyclic C 6 H 7 radicals. While the rate constant having the most important sensitivity coefficient for the formation of benzene in the flame including the C 4 additive is that of the reaction between 1,3-butadiene and vinyl radicals, figure 4 points out also an important contribution of the C 5 pathway to the formation of cyclohexadienyl radicals (about 40%). This is explained by a production of cyclopentadiene deriving, via methylcyclopentenyl radicals, from a reaction between acetylene and the resonance stabilized 1-buten-3-yl radicals which are obtained by H-addition to 1,3-butadiene. These reactions which are included in the present mechanism explain the important increase of the formation of benzene compared to our previous mechanism [START_REF] Gueniche | Rich methane premixed laminar flames doped with light unsaturated hydrocarbons: II. 1,3-butadiene[END_REF]. Only 1% of the formation of benzene is due to the C 3 pathway, since allene and propyne are minor products of the oxidation of 1,3-butadiene.

In the cyclopentene flame, the major source of benzene is the isomerization of cyclopentadienyl methylene radicals which are obtained either directly by H-abstractions by H-atoms or OH radicals from methylcyclopentadiene or by isomerisation from the resonance stabilized methyl cyclopentadienyl radicals. In this flame, the most important reaction for the formation of methylcyclopentadienyl radicals is the unimolecular decomposition of methylcyclopentadiene by breaking of a C-H bond. This decomposition has the most important sensitivity coefficient for the formation of benzene. The H-abstractions by H-atoms and OH radicals are only minor channels.

Methylcyclopentadiene is obtained from the recombination of methyl and cyclopentadienyl radicals, these last radicals deriving from cyclopentadiene are a major product of the oxidation of cyclopentene. While the contribution of the C 4 pathway is negligible, that of the C 3 pathways is 7% of the total production of benzene. Propargyl radicals are produced by beta-scission from 1-pentyn-5yl radicals, which are obtained by ring opening from vinylic cyclopentenyl radicals.

In the 1,3-butadiene and cyclopentene flames, the most important way to give toluene is the addition of resonance stabilized cyclopentadienyl radicals to acetylene. Consequently, the reactions which have the largest influence on the formation of toluene are the addition of cyclopentadienyl radicals to acetylene giving benzyl radicals and the combination of these last radicals with H-atoms.

In the 1,3-butadiene flame, as the flow of formation of toluene is around 10 times lower than that of benzene (see figure 4), the combination of methyl and phenyl radicals is also of some importance.

Whatever the type of flames, cyclopentadienyl radicals are rapidly obtained from the decomposition of phenoxy radicals, which are produced by the reaction of phenyl radicals with oxygen molecules.

Due to their resonance stabilization, they are present with an important concentration in every system containing phenyl radicals and benzene. The formation of toluene by addition of cyclopentadienyl radicals to acetylene could then be of importance in many combustion systems rich in acetylene.

Other aromatic molecules, which are predicted by simulation but could not be detected experimentally due to the chromatographic column used, are phenol, benzaldehyde and ethylbenzene. Phenol is obtained by combination of H-atoms and phenoxy radicals. Benzaldehyde and ethylbenzene derived from benzyl radicals by reaction with O-atoms and methyl radicals, respectively, and their degradation reactions produce phenyl radicals and benzene, respectively. In the cyclopentene flame, 5% of benzene is formed via ethylbenzene.

CONCLUSION

This paper compares the formation of benzene and toluene in a rich (Φ=1.8) methane flame consecutively seeded with allene, propyne, 1,3-butadiene, and cyclopentene and shows that the amount of aromatic compounds formed are very different depending on the additive. This effect is due to differences in the pathways of formation of these aromatic species depending on the dopant.

evolving versions of the mechanism from our first paper [START_REF] Gueniche | Rich methane premixed laminar flames doped with light unsaturated hydrocarbons: I. Allene and propyne[END_REF] up until the one presented here clearly demonstrates the need to use the most detailed models so that no important reaction is omitted and the degree of coupling between the reactions involved in the different pathways leading to aromatic compounds. The reaction rates and sensitivity analyses presented in this paper allow these reaction links to be better identified. 1.21x10 -5 3.33x10 -5 1.27x10 -4 X(toluene) max 8.78x10 -5 7.51x10 -6 2.00x10 -6 5.00x10 -5 Benzene

  Unimolecular reactions include dehydrogenation to give cyclopentadiene, decompositions by breaking of a C-H bond and isomerization to give 1,2-pentadiene. The reactions of cyclopentenyl radicals involve isomerizations, decompositions by breaking a C-C bond to form linear C 5 radicals including two double bonds or a triple bond and the formation of cyclopentadiene by breaking of a C-H bond or by oxidation with oxygen molecules and terminations steps. Termination steps are written only for resonance stabilized cyclopentenyl radicals: disproportionations with H-atoms and OH radicals yield cyclopentadiene, combinations with HO 2 radicals lead to ethylene and CH 2 CHCO and OH radicals (after decomposition of the obtained hydroperoxide) and combinations with CH 3 radicals form methylcyclopentene. The decomposition by breaking a C-H bond of cyclopentyl radicals lead to the formation of 1-penten-5-yl radicals. The isomerizations (for the radical stabilized isomer) and the decompositions by breaking of a C-C bond of the linear C 5

Figure 1 :

 1 Figure 1: Experimental (symbols) temperature profiles measured without the probe and

Figure 2 :

 2 Figure 2: Experimental (symbols) and simulated (lines) profiles of benzene in a methane flame

Figure 3 :

 3 Figure 3: Experimental (symbols) and simulated (lines) profiles of toluene in a methane flame

Figure 4 :

 4 Figure 4: Reaction rates analysis for the formation and consumption of benzene and toluene for a

Figure 5 :

 5 Figure 5: Variation of the normalized (compared to the value obtained with the initial

  Figure 1

Figure 5

 5 Figure 5

Table 1 :

 1 Experimental flame characteristics: initial flow velocities at 333 K (in cm/s), equivalence ratios (φ), initial reactant mole fractions (X(Ar) 0 , X(O 2)0 , X(CH 4)0, X(additive) 0 ) and C/H and C/O ratios, and maximum mole fractions of benzene and toluene (X(benzene) max and X(toluene) max )

	simulated under the same conditions (φ, dilution yield, initial additive mole fraction and
	temperature profile) as in the flame seeded by cyclopentene.
	Additive	allene	propyne	1,3-butadiene cyclopentene
	Initial flow velocity	36	36	36	36
	φ	1.55	1.55	1.79	1.79
	X(Ar) 0	0.432	0.432	0.423	0.556
	X(O 2)0	0.334	0.334	0.331	0.267
	X(CH 4)0	0.209	0.209	0.207	0.153
	X(additive) 0	0.025	0.025	0.033	0.024
	C/H	0.303	0.303	0.330	0.340
	C/O	0.425	0.425	0.512	0.511
	X(benzene) max 1.56x10 -5

LIST OF SUPPLEMENTAL MATERIAL :

1 supplemental file: mechanism-gueniche et al.-2007

CAPTION FOR SUPPLEMENTAL MATERIAL :

Mechanism (in CHEMKIN format) for the oxidation of allene, propyne, 1,3-butadiene and cyclopentene in low pressure flames.


Valeriy V Dvoeglazov

Weyl

Weyl and Majorana for Neutral Particles

come

Weyl and Majorana for Neutral Particles

1. Weyl Formalism.

The Weyl formalism is just a massless limit of the Dirac equation:

[iγ µ ∂ µ ]Ψ(x) = 0 . (1)
Of course, it can be re-written in the 2-component forms:

[p 0 + σ • p]χ(x) = 0 , [p 0 -σ • p]φ(x) = 0 . (2)
However, if we apply the Noether theorem to the Lagrangian

L = i 2 [ Ψγ µ ∂ µ Ψ -∂ µ Ψγ µ Ψ] (3)
we obtain the current operator

J µ = Ψγ µ Ψ , (4)
as in the massive case. So, it is doubtful that we can use the massless limit of the Dirac equation for neutral particles. In Refs. [2]- [START_REF] Dvoeglazov | [END_REF] we considered the procedure of construction of the field operators ab initio (including for neutral particles). The Bogoliubov-Shirkov method has been used.

In the present article we investigate the spin-1/2 and spin-1 cases in different bases. The Majorana theory of the neutral particles is well known [7]. We look for relations of the Dirac-like field operator to the Majorana-like field operator. It seems that the calculations in the helicity basis give mathematically and physically reasonable results. Usually, everybody uses the following definition of the field operator [START_REF] Itzykson | Quantum Field Theory[END_REF] in the pseudo-Euclidean metrics:

Ψ(x) = 1 (2π) 3 h d 3 p 2E p [u h (p)a h (p)e -ip µ •x µ + v h (p)b † h (p)e +ip µ •x µ ] , (5)
as given ab initio. The momentum-space 4-spinors ( u-and v-) satisfy the equations: (p-m)u h (p) = 0 and (p+m)v h (p) = 0, respectively; the h is the polarization index. It is easy to prove from the characteristic equations Det(p ∓ m) = (p 2 0 -p 2 -m 2 ) 2 = 0 that the solutions should satisfy the energy-momentum relations p 0 = ±E p = ± √ p 2 + m 2 for both u-and vsolutions.

The general scheme of construction of the field operator has been given in [START_REF] Bogoliubov | Introduction to the Theory of Quantized Fields[END_REF]. In the case of the (1/2, 0) ⊕ (0, 1/2) representation we have:

Ψ(x) = 1 (2π) 3 dp e ip•x Ψ(p) . (6)
We know the condition of the mass shell: (p 2 -m 2 ) Ψ(p) = 0. Thus, Ψ(p) = δ(p 2 -m 2 )Ψ(p). After simple transformations we obtain

Ψ(x) = 1 (2π) 3 h d 3 p 2E p θ(p 0 ) u h (p)a h (p)| p 0 =E p e -i(E p t-p•x) + + u h (-p)a h (-p)| p 0 =E p e +i(E p t-p•x)
During the calculations we had to represent 1 = θ(p 0 ) + θ(-p 0 ) above in order to get positive-and negative-frequency parts. We did not yet assumed, which equation does this field operator (namely, the u-spinor) satisfy, with negative-or positive-mass and/or p 0 = ±E p . We should transform u h (-p) to the v h (p) 4-spinor. The procedure is the following one [1,2].

In the Dirac case we should assume the following relation in the field operator:

h=±1/2 v h (p)b † h (p) = h=±1/2 u h (-p)a h (-p) , (7)
which is compatible with the "hole" theory and the Feynman-Stueckelberg interpretation. We need Λ µλ (p) = vµ (p)u λ (-p). By direct calculations, we find

-mb † µ (p) = λ Λ µλ (p)a λ (-p) . (8)
Hence, Λ µλ = -im(σ • n) µλ , n = p/|p|, and

b † µ (p) = +i λ (σ • n) µλ a λ (-p) . (9)
Multiplying ( 7) by ūµ (-p) we obtain

a µ (-p) = -i λ (σ • n) µλ b † λ (p) . (10)
The equations are self-consistent. The details of the helicity basis are given in Refs. [START_REF] Rück | [END_REF]11]. However, in this helicity case we have:

Λ hh (p) = vh (p)u h (-p) = iσ y hh . (11)
So, someone may argue that we should introduce the creation operators by hand in every basis. It is well known that "particle=antiparticle" in the Majorana theory [7]. So, in the language of the quantum field theory we should have:

b µ (E p , p) = e iϕ a µ (E p , p) . (12)
Usually, different authors use ϕ = 0, ±π/2 depending on the metrics and on the forms of the 4-spinors and commutation relations. So, on using [START_REF] Bogoliubov | Introduction to the Theory of Quantized Fields[END_REF] and the above-mentioned postulate we come to:

a † µ (p) = +ie iϕ (σ • n) µλ a λ (-p) . (13)
On the other hand, on using [START_REF] Rück | [END_REF] we make the substitutions

E p → -E p , p → -p to obtain a µ (p) = +i(σ • n) µλ b † λ (-p) . (14)
The totally reflected ( 12)

is b µ (-E p , -p) = e iϕ a µ (-E p , -p). Thus, b † µ (-p) = e -iϕ a † µ (-p) . (15)
Combining with (14), we come to

a µ (p) = +ie -iϕ (σ • n) µλ a † λ (-p) , (16)
and

a † µ (p) = -ie iϕ (σ * • n) µλ a λ (-p) . (17)
This contradicts with the above equation unless we have the preferred axis in every inertial system. Next, we can use another Majorana anzatz Ψ = ±e iα Ψ c with usual definitions

C = e iϑ c 0 iΘ -iΘ 0 K , Θ = 0 -1 1 0 . ( 18
)
Thus, on using Cu * ↑ (p) = iv ↓ (p), Cu * ↓ (p) = -iv ↑ (p) we come to other relations between creation/annihilation operators

a † ↑ (p) = ∓ie -iα b † ↓ (p) , (19)
a † ↓ (p) = ±ie -iα b † ↑ (p) , (20)
which may be used instead of (12). Due to the possible signs ± the number of the corresponding states is the same as in the Dirac case that permits us to have the complete system of the Fock states over the (1/2, 0) ⊕ (0, 1/2) representation space in the mathematical sense. 1 However, in this case we deal with the self/anti-self charge conjugate quantum field operator instead of the self/anti-self charge conjugate quantum states. Please remember that it is the latter that answers for the neutral particles.

We conclude that something is missed in the foundations of both the original Majorana theory and its generalizations in the (1/2, 0) ⊕ (0, 1/2) representation.

We define the self/anti-self charge-conjugate 4-spinors in the momentum space [12]:

Cλ S,A (p) = ±λ S,A (p) , ( 21
) Cρ S,A (p) = ±ρ S,A (p) . ( 22
)
Such definitions of 4-spinors differ, of course, from the original Majorana definition in x-representation:

ν(x) = 1 √ 2 (Ψ D (x) + Ψ c D (x)) , (23)
Cν(x) = ν(x) that represents the positive real C-parity field operator. However, the momentum-space Majorana-like spinors open various possibilities for description of neutral particles (with experimental consequences, see [13]). For instance, "for imaginary C parities, the neutrino mass can drop out from the single β decay trace and reappear in 0νββ, a curious and in principle experimentally testable signature for a non-trivial impact of Majorana framework in experiments with polarized sources." Thus, in the accustomed basis the explicit forms of the 4-spinors of the second kind λ S,A ↑↓ (p) and ρ S,A ↑↓ (p) are:

λ S ↑ (p) = 1 2 E p + m        ip l i(p -+ m) p -+ m -p r        , λ S ↓ (p) = 1 2 E p + m        -i(p + + m) -ip r -p l (p + + m)        (24) λ A ↑ (p) = 1 2 E p + m        -ip l -i(p -+ m) (p -+ m) -p r        , λ A ↓ (p) = 1 2 E p + m        i(p + + m) ip r -p l (p + + m)       
In this basis one has

ρ S ↑ (p) = -iλ A ↓ (p) , ρ S ↓ (p) = +iλ A ↑ (p) , (25)
ρ A ↑ (p) = +iλ S ↓ (p) , ρ A ↓ (p) = -iλ S ↑ (p) . (26)
The λ-and ρ-spinors are connected with the u-and v-spinors by the following formula:

       λ S ↑ (p) λ S ↓ (p) λ A ↑ (p) λ A ↓ (p)        = 1 2        1 i -1 i -i 1 -i -1 1 -i -1 -i i 1 i -1               u +1/2 (p) u -1/2 (p) v +1/2 (p) v -1/2 (p)        , (27)
provided that the 4-spinors have the same physical dimension.

We construct the field operators on using the procedure above with λ S η (p). Thus, the difference is that 1) instead of u h (±p) we have λ S η (±p); 2) possible change of the annihilation operators, a h → c η . Apart, one can make corresponding changes due to normalization factors. Thus, we should have

η=±1/2 λ A η (p)d † η (p) = η=±1/2 λ S η (-p)c η (-p) . ( 28
)
We find surprisingly:

d † η (p) = - ip y p σ y ητ c τ (-p) , c η (-p) = - ip y p σ y ητ d † τ (p) . ( 29
)
The bi-orthogonal anticommutation relations are given in Ref. [12]. See other details in Ref. [14,15]. Concerning with the P ,C and T properties of the corresponding states see Ref. [15] in this model. The above-mentioned contradictions may be related to the possibility of the conjugation which is different from that of Dirac. Both in the Diraclike case and the Majorana-like case (c η (p) = e -iϕ d η (p)) we have difficulties in the construction of field operators.

The Spin-1.

We use the results of Refs. [START_REF] Yu | Introduction to Elementary Particle Physics[END_REF][START_REF] Weinberg | The Quantum Theory of Fields[END_REF][START_REF] Dvoeglazov | Photon: Old Problems in Light of New Ideas[END_REF] in this Section. The polarization vectors of the standard basis are defined [START_REF] Varshalovich | Quantum Theory of Angular Momentum[END_REF]:

µ (0, +1) = - 1 √ 2        0 1 i 0        , µ (0, -1) = + 1 √ 2        0 1 -i 0        , ( 30
) µ (0, 0) =        0 0 0 1        , µ (0, 0 t ) =        1 0 0 0        . (31)
The Lorentz transformations are ( p i = p i /|p|):

µ (p, σ) = L µ ν (p) ν (0, σ) , (32)
L 0 0 (p) = γ , L i 0 (p) = L 0 i (p) = p i γ 2 -1 , L i k (p) = δ ik + (γ -1) p i p k . (33)
Hence, for the particles of the mass m we have:

u µ (p, +1) = - N √ 2m          -p r m + p 1 p r E p +m im + p 2 p r E p +m p 3 p r E p +m          , u µ (p, -1) = N √ 2m          -p l m + p 1 p l E p +m -im + p 2 p l E p +m p 3 p l E p +m          , (34)
u µ (p, 0) = N m          -p 3 p 1 p 3 E p +m p 2 p 3 E p +m m + (p 3 ) 2 E p +m          , u µ (p, 0 t ) = N m        E p -p 1 -p 2 -p 3        . (35)
N is the normalization constant for u µ (p, σ). They are the eigenvectors of the parity operator (γ 00 = diag(1 -1 -1 -1)):

P u µ (-p, σ) = -u µ (p, σ) , P u µ (-p, 0 t ) = +u µ (p, 0 t ) . (36)
It is assumed that they form the complete orthonormalized system of the (1/2, 1/2) represntation, * µ (p, 0 t ) µ (p, 0 t ) = 1, * µ (p, σ ) µ (p, σ) = -δ σ σ . The helicity operator should act as:

(S • p) p µ ±1 = ± µ ±1 , (S • p) p µ 0,0 t = 0 . (37)
The eigenvectors are in the helicity basis:

µ +1 = 1 √ 2 e iα p           0 -p 1 p 3 +ip 2 p √ (p 1 ) 2 +(p 2 ) 2 -p 2 p 3 -ip 1 p √ (p 1 ) 2 +(p 2 ) 2 (p 1 ) 2 + (p 2 ) 2           , µ -1 = 1 √ 2 e iβ p           0 p 1 p 3 +ip 2 p √ (p 1 ) 2 +(p 2 ) 2 p 2 p 3 -ip 1 p √ (p 1 ) 2 +(p 2 ) 2 -(p 1 ) 2 + (p 2 ) 2           (38) µ 0 = 1 m         p E p p 1 E p p 2 E p p 3         , µ 0 t = 1 m        E p p 1 p 2 p 3        . ( 39
)
The normalization is the same as in the standard basis. The eigenvectors µ ±1 are not the eigenvectors of the parity operator (γ 00 R) of this representation. However, the µ 1,0 , µ 0,0 t are. Various-type field operators are possible in this representation. Let us remind the procedure to get them.

A µ (x) = 1 (2π) 3 d 4 p δ(p 2 -m 2 )e -ip•x A µ (p) = = 1 (2π) 3 λ d 3 p 2E p [ µ (p, λ)a λ (p)e -ip•x + µ (-p, λ)a λ (-p)e +ip•x ] . ( 40
)
We should transform the second part to * µ (p, λ)b † λ (p) as usual. In such a way we obtain the states which are considered to be the charge-conjugate states. In this Lorentz group representation the charge conjugation operator is just the complex conjugation operator for 4-vectors. We postulate

λ µ (-p, λ)a λ (-p) = λ * µ (p, λ)b † λ (p) . (41)
Then we multiply both parts by µ (p, σ), and use the normalization conditions for polarization vectors.

In the ( 1 2 , 1 2 ) representation we can also expand (apart of the equation ( 41)) in a different way. For example,

λ µ (-p, λ)c λ (-p) = λ µ (p, λ)d † λ (p) . (42)
From the first definition we obtain:

       b † 0 t (p) -b † +1 (p) -b † 0 (p) -b † -1 (p)
Possibly, we should think about modifications of the Fock space in this case. Alternatively, one can think to introduce several field operators for the ( 1 2 , 1 2 ) representation. The Majorana-like anzatz is compatible for the 0 t time-like polarization state only in this basis of this representation. However, the corresponding matrices Λ 2 in the helicity basis are different. Here they are:

2 .

 2 The Spin-1/2.

  σ) µ (-p, λ)a λ (-p) =

  σ) µ (-p, λ)a λ (-p) =

Please note that the phase factors may have physical significance in quantum field theories as opposed to the textbook nonrelativistic quantum mechanics, as was discussed recently by several authors.

Acknowledgements. I acknowledge discussions with colleagues at recent conferences.

 (45)This is compatible with the Majorana-like anzatzen. Of course, the same procedure can be applied in the construction of the quantum field operator for F µν .

The solutions of the Weinberg-like equation

are found in Refs. [START_REF] Yu | Introduction to Elementary Particle Physics[END_REF][START_REF] Sankaranarayanan | [END_REF]21,22]. Here they are:

where D S is the matrix of the (S, 0) representation of the spinor group SL(2, c). In the (1, 0) ⊕ (0, 1) representation the procedure of derivation of the creation operators leads to somewhat different situation:

However, if we return to the original Weinberg equations [

) = 0 with the field operators:

The applications of u µ (-p)u λ (-p) = δ µλ and u µ (-p)u λ (p) = [1-2(S•n) 2 ] µλ prove that the equations are self-consistent. This situation signifies that in order to construct the Sankaranarayanan-Good field operator (which was used by Ahluwalia, Johnson and Goldman [21]) we need additional postulates. One can try to construct the left-and the right-hand side of the field operator separately each other. In this case the commutation relations may also be more complicated.

Repeating the above procedures, on using (52) and the Majorana postulate, we come to:

On the other hand, on using the inverse relation, namely, that for a µ (-p), we make the substitutions E p → -E p , p → -p to obtain

The totally reflected Majorana anzatz is b µ (-E p , -p) = e iϕ a µ (-E p , -p).

Combining with (55), we come to

In the basis where S z is diagonal the matrix S y is imaginary [START_REF] Varshalovich | Quantum Theory of Angular Momentum[END_REF]. So, (S * • n) = S x n x -S y n y + S z n z , and (S * • n) 2 = (S • n) 2 in the case of S = 1. So, we conclude that there is the same problem in this point, in the aplication of the Majorana-like anzatz, as in the case of spin-1/2. Similarly, one can proceed with (53). Meanwhile, the attempts of constructing the self/anti-self charge conjugate states failed in Ref. [12]. Instead, the Γ 5 S c

[1] -self/anti-self conjugate states have been constructed therein.

Conclusions.

We conclude that something is missed in the foundations of both the Weyl theory, the original Majorana theory and its generalizations. Similar problems exist in the theories of higher spins.


domain: spi sde

text:
BENCHMARK OF CIRCULARITY INDICATORS AND LINKS WITH LCA SCORE LCA Study n° 2020-03 -Summary Centrale Supelec &

SCORE LCA is an association that has been created to financially support collaborative research on LCA and related topics. It aims to promote and

Introduction

Motivation and stake of moving toward a circular economy for industry

The concept of circular economy (CE) calls for a more sustainable and reasoned management of resources throughout the life cycle of products and systems. Such an economic paradigm is characterized, on the technosphere side, by looping flows and by promoting maintenance, reconditioning and recycling operations, while being accompanied by service and take-back offers that make these practices operational. Circularity aims to maintain the high value and usefulness of products, materials and resources at all times, thus minimizing waste generation and environmental impact. In this line, a growing number of companies and local authorities is committed to engage in the transition of their business models towards "circular" models. On both sides, a need is emerging for medium-and long-term management of investments and material and energy flows at the level of territories and industrial organizations. Therefore, it became necessary to develop methodologies and tools based on relevant investment and flow management indicators for the variety of stakeholders concerned.

At the same time, many tools, methods, and indicators are currently available and can be activated to diagnose the environmental performance of a company's products, services, projects, and activities. In front of this multitude of tools, it is not straightforward for industrialists to identify the most relevant ones with regard to the objective and the timeframe of the project. Similarly, if we favour an analysis based on the principle of the circular economy, many indicators are available but are often limited to a diagnosis. As such, in order to promote projects that are favorable to the ecological transition and that create value for the company, it is necessary to mobilize indicators that will be used to monitor activities towards greater circularity and environmental preservation.

Emerging demand on circular economy assessment

As mentioned in the text of the SCORELCA call for projects NB 2020-03, more and more organizations want to achieve circular economy objectives and are taking steps in this direction. In order not only to monitor their progress but also to communicate their progress, these organisations need circularity indicators, as key performance indicators (KPIs), that enable them to achieve their objectives. The use of indicators seems a fortiori relevant for such a complex concept -multi-scale, multi-actor, advocating life cycle consideration and systemic thinking -as the circular economy. Indicators have the capacity to synthesize the complexity of our changing environments into a more easily understandable, manageable, and exploitable amount of information. More generally, such circularity indicators can be used for informational (e.g., benchmarking, decision support), improvement (identifying points of progress), managerial (leading change), communicative, formative, or educational purposes.

A common vision -shared by academics, industry, and political bodies (Ellen MacArthur Foundation, 2015; [START_REF] Geissdoerfer | The Circular Economy-A new sustainability paradigm?[END_REF][START_REF] Saidani | How to assess product performance in the circular economy? Proposed requirements for the design of a circularity measurement framework[END_REF] -has emerged on the need to measure the progress and impacts of this transition. Thus, many circularity indicators have been developed in recent years as tools and catalysts towards more circular practices, under the sine qua non condition that the actors involved in this transition can have access to and properly employ the indicators that are most appropriate for them, as illustrated in Figure 1. However, the progressive implementation, outside of any normative context, of these indicators has led to an heterogeneity of approaches to measure circularity (Saidani et al., 2019a). Although the notion of circular economy is increasingly discussed and recognized as contributing to the achievement of the Sustainable Development Goals, there is still no consensus on a stabilized definition of circular economy: 114 definitions of circular economy, transcribed into 17 categories, were notably identified by [START_REF] Kirchherr | Conceptualizing the circular economy: An analysis of 114 definitions[END_REF]. This can be seen as one of the reasons for the vagueness and wide variety of indicators developed in relation to the circular economy, whether in terms of their scope of action, their primary objectives, or their preferred uses.

The aim of this project is both to provide clarity on this multitude of available indicators, as well as to help select a set of circularity indicators that are the most relevant, specific, and operational for an organization. In practice, although a wide variety of indicators have been developed in recent years, it remains to be seen how widely they have been adopted and how mature they are in their use by industrial players, particularly in an integrated way with the design and development process. On the one hand, it seems that these circularity indicators -which can be considered as high-level heuristics or KPIs -and their associated tools are more rapidly deployable and easier to understand than certain environmental assessment methods and indicators such as life cycle assessment (LCA). On the other hand, to support sustainable decision-making, it remains to provide tangible proof that these indicators are correlated with an economic, environmental and/or societal "better". It is thus necessary to be able to validate whether this shift to more circular practices brings about a "better" outcome to the three pillars of sustainable development, for example, by comparing these intrinsic circularity indicators with certain indicators designed to gauge economic, environmental and/or social performance, thus assessing the consequential circularity of existing circularity loops and verifying (or not) the compatibility of the circular economy equation with the one of sustainable development.

SCORE

Objectifs and content of the study

The main objective of this study is to provide SCORELCA members with operational, complete, and harmonized indicators to measure the circularity of their activity. The secondary objective of this study is to make the link with other methods, in particular LCA, in order to integrate these indicators into existing environmental assessment tools if possible. The study is structured in three parts: state of the art, detailed analysis, and recommendations (see Figure 2).

Part 1: Literature review

The objective of this first part is to establish a robust state of the art concerning circularity indicators, of which there are a plethora. This state of the art is based on an exhaustive inventory of literature sources, and on an in-depth examination of a smaller number of indicators, in order to enable a selection and synthesis of 10 notable indicators.

Inventory and selection criteria

The literature review was based on the work carried out by Michaël Saidani in 2018 [START_REF] Saidani | Monitoring and advancing the circular economy transition -Circularity indicators and tools applied to the heavy vehicle industry[END_REF]Saidani et al., 2019a), which identified 55 indicators of circularity. This work led to the creation of an online tool, the Circularity Indicators Advisor (CIA) (http://circulareconomyindicators.com/). The survey carried out as part of this study consisted of completing this work with the new publications published in the period 2019-2020. The bibliographical search thus carried out, which was completed at the end of 2020, made it possible to identify a total of 105 references corresponding to as many sets of circularity indicators. All these sources were referenced in an Excel spreadsheet, provided as one of the main deliverables of this study.

Academic papers dealing with c-indicators include, for example, the taxonomy of 55 sets of circularity indicators (Saidani et al., 2019a) or the critical review of 74 approaches, methods, and tools for assessing circularity performance at a micro scale (Roos Lindgreen et al., 2020). Other sources, nonacademic but developed by business consulting groups (e.g., the Circular Transition Indicators) and environmental or institutional organizations (e.g., the 10 key indicators to drive the circular economy in France) were also considered.

Analysis and classification of circularity indicators

Intermediate conclusion on the state of the art and reflection

Following this update of the circularity indicators census and statistical study, we can see the following trends: continuous growth since 2010, relatively homogeneous distribution on the three micro/meso/macro scales, indicators mainly developed by academics/university researchers (what about their applicability and practicability questioned in the following parts), cross-cutting indicators for the most part but a recent trend towards specification (e.g., the evolution of the Ellen MacArthur Foundation's Material Circularity Indicator for the building sector), recycling is the most considered/quantified circular economy loop, links between inherent circularity and circularity are more important than others. e.g. evolution of the Ellen MacArthur Foundation's Material Circularity Indicator for the building sector), recycling is the most considered/quantified circular economy loop, links between inherent (or intrinsic) circularity and environmental/economic/social consequence are not systematic.

Other aspects to be explored, some of which were mentioned and questioned during the SCORELCA 2021 annual feedback seminar, include: the distribution of indicators and their ability to cover both the technosphere and the biosphere so as to reflect the issues of each sphere; circularity indicators that can substitute for LCA (validation study through correlation); indicators for companies without expertise in eco-design or circular economy, i.e. indicators that do not require large internal resources, but that allow for progress in the right direction; circularity indicators more specifically for the services sector (to Circularity Performance highlight potentially hidden material flows). i.e., indicators that do not require a significant amount of internal resources, but that allow progress to be made in the right direction; circularity indicators more specifically for the service sector (to highlight potentially hidden material flows). Several of these unexplored aspects in an advanced or synthetic way, such as the link between circularity and life cycle analysis, are discussed and deepened in the following sections.

Part 2: In-depth analysis of 10+ c-indicators

Following the state of the art that enabled the inventory of published methods and indicators, and which showed the great diversity and heterogeneity of approaches, this second part consists of carrying out an in-depth analysis of about ten ad hoc and complementary indicators from among all those identified. To do this, the following tasks must be carried out sequentially:

 Develop a method for selecting these ten or so c-indicators and make the selection;  Design a factsheet according to the main criteria to be analyzed;  Complete the analysis according to each of the key criteria.

Selection process

We adopted an empirical and pragmatic method for the selection of the ten or so c-indicators on which to conduct a detailed analysis.

The first sorting criterion adopted is the type of method: among the 105 "sets of indicators", some methods are prescriptive (i.e., they give recommendations or guidelines, for the design of products or for the conduct of a company's circular economy strategy), others are indicators (i.e., calculation methods for measurement). For this study, only the measurement indicators are retained. The second sorting criterion is the transparency (i.e. formula for calculating the available indicator) of the method (or indicator), which is similar to the criterion of operationality. Once these initial sorting operations had been carried out, we sorted them into categories:  On the one hand, the expectations (needs) of the industrial members of SCORELCA: The final choice of an indicator from the corresponding set (for example, which recycling indicator to choose from among all the recycling indicators), judged to be the "best" indicator, is ultimately based on Michaël Saidani's expertise, and confronted with a discussion and validation with the industrialists and SCORELCA partners who have followed this project. Finally, the last criterion, allowing the selection of indicators to be "completed", is that of the completeness of the set of indicators with regard to the various issues of the circular economy. The synopsis illustrating the selection method is shown in Figure 9.


SCORE

List of the c-indicators selected

Following the process described in the previous subsection (selection method), a shortlist of indicators ranked according to the stated criteria is proposed below.

Two global evaluation indicators at the company level: Circulytics and CTI

 Circulytics (Ellen MacArthur Foundation tool): A new tool that reveals the extent to which a company has achieved circularity across its entire operations using a comprehensive set of indicators. It measures circularity in two main ways: enablers (what companies do for circular economy) and outcomes (Impact of the circularity action on inputs, used materials, energy, product reparability)

 Circular Transition Indicators (CTI):

The CTI is the first self-assessment framework and online tool to measure circular business performance. This module calculates to what extent the organization is capable of guaranteeing material flows that loop back into the value chain after a product's technical lifetime. It defines an organization's circularity performance as the average between % circular inflow and % circular outflow.

Two indicators for assessing circularity at material and product levels: MCI and PCI

 Material Circularity Indicator (MCI): The MCI, developed by the Ellen MacArthur Foundation, combines aspects of lifetime and intensity of use with the proportion of recycled material and the share of materials in a product that can be recycled in a single indicator, applicable at the product or company level. It considers material rates of recycling and reuse, measures how restorative flows are maximized and linear flows are minimized, and also the length and intensity of the product's use.

 Product Circularity Indicator (PCI):

The PCI is a new aggregated indicator at a product level, developed as an augmented version of the MCI.

One product design indicator (potential circularity): CCET (and two alternatives: CEIP, CPI)

 Concept Circularity Evaluation Tool (CCET): The CCET aims to support the evaluation of alternative product concepts in terms of their circularity potential in the early stages of product design and development. The CCET was iteratively developed based on an extensive literature review of the success criteria for tool development, guidelines, and existing tools for circular product design and development and strong collaboration with manufacturing companies.

 Circular Economy Indicator Prototype (CEIP): Using a points-based questionnaire (15 questions), the CEIP is initially intended to be used by manufacturing and/or retail companies of tangible goods with access to bills of materials. They would use the CEIP to measure and evaluate the performance of their products.

 Through a guided questionnaire of twenty attributes (ATT#) desired for a circular economy, that are based on and grouped within the four building blocks (BB#) of circular economy defined by Ellen MacArthur Foundation, the Circularity Potential Indicator (CPI) aims at evaluating the circularity potential of industrial products (during design, re-design or benchmarking phases) as well as providing keys for improvement and monitoring the circularity of products and businesses practices.

Two indicators of reuse/recycling and extension of the lifespan of products from a resource circularity perspective: RPI and CLI

 The Reuse Potential Indicator (RPI) indicates how much one material is "resource-like" rather than "waste-like" according to the currently available technologies. The proposed reuse potential indicator quantifies technical reusability. The tool specifies a continuum of how resource-like or waste-like materials are.

 Circularity & Longevity Indicators (CLI) combine two approaches -frequency (circularity) and duration of use (longevity) of products -to determine resource efficiency.

One set of 3 MFA-type material flow indicators: End-of-Life Recycling Rates (EoL-RRs)

 End-of-Life Recycling Rate (EoL-RR): performance of functional recyling, considering just pure materials  Recycled Content (RC): fraction of secondary inputs in the total input of material production  Old Scrap Ratio (OSR): fraction of old scrap in the recycling flow

One c-indicator of energy flow: CI

 Circularity Index (CI) formula :

 Circularity Index (CI) = αβ, maximum value = 1  α = recovered end-of-life (EOL) material / total material demand  β = 1energy required to recover material / energy required for primary production One set of indicators for circularity at the scale of a territory: RMFCE  Regional Material Flow tools for the Circular Economy (RMFCE)

Newly designed factsheet for the selected c-indicators

The selected indicators are transposed into self-supporting indicator sheets. Inspired by existing sheets published in the literature, the new sheets have been developed (completed and illustrated) with a view to teaching. These original factsheets are based on the classification criteria set out in Part 1.

Hereafter is the new factsheet model illustrated through the MCI, which is currently one of the most used circularity indicators, although it has some limitations. The other factsheets are available in the full report, and in the native format (PPT) for SCORELCA members, or on-demand.

Partie 3: Links with Life Cycle Assessment (LCA)

In this third part, it is appropriate to illustrate the different possible synergies and/or conflicts (trade-offs) between LCA and circularity indicators in a practical way (with concrete examples) for SCORELCA members, as schematically illustrated in the two-dimensional graph in Figure 11. While we adopt the assumption that the circular economy remains (or should remain) a means to achieve the environmental, societal, and economic objectives of sustainable development, it would be of particular interest to see when circularity does and does not work towards sustainable development, and which parameters (in the loops) are critical. We can imagine three possible avenues to explore the links between LCA and circularity indicators: iii.

LCA is used to verify the appropriateness of a set of circularity indicators (to be validated on known products, to save time compared to performing an LCA).

General remarks

On the one hand, CE focuses on maintaining (preserving and increasing) resource values for the economy. In doing that, CE considers also different levels of application: at the macro level, it focuses on material exchanges between the economy and the environment, and also internationally; at the structural or meso level, the emphasis is on material flows in industrial systems, distinguishing not only categories of materials but also sectors and industrial branches; at the micro or business level, it focuses on firms and their products. CE strategies often assume that it is always good to keep individual resources within the economy, either in use for as long as possible, or through cycling loops in technical or biological cycles [START_REF] Pena | Using life cycle assessment to achieve a circular economy[END_REF].

On the other hand, LCA focuses mainly on product level and on all the impacts associated to the product life cycle, i.e. not only on the impacts related to the use of materials and resources but on all those impacts that can be relevant for a product category. LCA does not advocate for any specific strategy but simply provides an assessment framework to understand the environmental, social, and economic implications of different options to deliver a function or service. In this way, LCA and its related approaches may serve as the science-based methodology to assess the benefits or otherwise of specific CE strategies, and also the occasions where keeping the resources within the economy for longer may actually be counter-productive (e.g., due to the costs of removing toxic substances contaminating such resources) [START_REF] Pena | Using life cycle assessment to achieve a circular economy[END_REF].

In all, the advantages of combining circular economy indicators with life cycle assessment include: identifying environmental trade-offs of circularity choices, broaden environmental analysis with LCA. However, in some cases, circular economy principles (or the application of circular economy strategies) and life cycle assessment results can have opposing views. Circular economy encourages recycling (no questions asked), while according to life cycle assessment, energy recovery is sometimes more beneficial. Additionally, does not yet have all the answers when dealing with circular economy projects. For example, addressing the dissipative losses of raw materials are hardly taken into account by standard resource depletion indicators. Also, downcycling and upcycling are not straightforward to evaluate (Quantis, 2017). Finally, current research gaps include joint representation methods and how results are affected by methodological differences and limitations (e.g., the end-of-life allocation approach (cut-off, system expansion, hybrid approach), consequential vs. attributional approach (rebound effects on other actors and parts of the system), or the evaluation of secondary material quality loss).

In broad terms, it can be highlighted that [START_REF] Pena | Using life cycle assessment to achieve a circular economy[END_REF]:  CE prioritizes the continued use of resources. This implies maintaining the highest level of utility of materials through recycling, either within the economy, typically through a network of industrial sectors, or in natural ecosystem processes, and may involve extending the lifetime of products to minimize the need for wasteful recycling activities.  Methodologies and frameworks for the CE and the circularity assessment indicators are in development and aim mainly at augmenting the perceived value by increasing the utility value of resources within the economy.  LCA can be used to measure and assess the environmental and social performance of a defined system in a circular economy, to ensure optimal decision-making.  LCA is a well-established and standardized methodology adopted by industry worldwide, which allows characterizing the environmental performance of product systems, not only in relation to the impact associated to resource use, but to the whole range of impact categories relevant through the life cycle of the product.

In this line, the Life Cycle Initiative encourages LCA professionals to address the technical and scientific shortcomings involved in the assessment of CE projects, notably [START_REF] Pena | Using life cycle assessment to achieve a circular economy[END_REF]:  Consistent accounting for changes in stocks of resources that respect mass balance principles;  Consistent modelling of open recycling loops;  The inclusion of all relevant resources and impacts, i.e., a full environmental, social and economy-wide (LCSA) perspective;  Transparency of assumptions, reliability of data, and critical interpretation of results and tradeoffs between a globally agreed number of impact categories.

In particular, it is important to recall here that seeking to maximize the performance or score/rate of circularity is not always the best option in terms of the costs and energy to be deployed (e.g., related to reverse logistics to collect all products, processing of certain materials). Indeed, achieving 100% circularity is often incompatible with the current industrial economic reality, end-of-life channels, and available technologies. In this sense, circularity performance should be used and optimized (as a cursor to be adjusted) as a lever to guarantee economic and environmental benefits. In practice, these tradeoffs between economic, environmental, and circularity performance should be considered and optimized simultaneously. For example, a mathematical optimization model [START_REF] Saidani | Framing Product Circularity Performance for Optimized Green Profit[END_REF] has been proposed to find the circularity performance(s), maximizing the profile and minimizing the carbon footprint (see the Pareto frontier of 'circular green profit' in Figure 12). To bring new insights on the question "Do circulatory indicators and LCA provide the same results in the assessment of circular strategies?", the CIRAIG (Polytechnique Montreal) compared circularity and life cycle assessment indicators for circular economy strategies on two industrial case studies: (i) increasing circularity for a plastic product company (case study #1), (ii) end-of-life strategies for used tires (case study #2). A third case study [START_REF] Saidani | Comparing life cycle impact assessment, circularity and sustainability indicators for sustainable design: results from a hands-on project with 87 engineering students[END_REF] is available in the full report.

The objective for case study #1 is to assess the environmental relevance of initiatives and strategies to improve the circularity of a plastic product company: proposal of circularity strategies and scenarios to improve the score of circularity (MCI and CTI), organizational life cycle assessment and circularity assessment to better understand the link between maximizing circularity and minimizing life cycle impacts. For case study #2, Lonca et al. (2018) LCA and MCI to assess the potential of used tire management strategies to (i) avoid burden shifting and (ii) improve material circularity. The results of both case studies provide a good insight for tire manufacturers on how to manage used tires to better contribute to the CE objective. The study reveals that MCI is relevant to support circular design to preserve the specific materials that make up the product. But LCA provides a complementary perspective on a broader scope in terms of system boundaries and complementary indicators needed to measure the pressure on pollution-thus helping to avoid burden shifting, as illustrated in Figures 16 and17.

Conclusion and perspectives

Identifying, selecting, and deploying the most appropriate circularity indicators is essential to both assess and improve the performance of products, companies, and regions in a circular and sustainable economy perspective. The various contributions, analyses, and recommendations -for example, the database of more than a hundred circularity indicators -can serve as a solid basis for recombining indicators based on their complementarity, as well as for enriching them with their respective specificities to build new indicators that respond to the issues of industrialists who value life cycle analysis more highly. In practice, the methodology for selecting circularity indicators, coupled with the two-dimensional graph of circularity performance and environmental impacts, can be used as a model for developing a set of indicators, coupled with a dashboard, to report on the direct and indirect environmental impact (link with LCA) of a project, the circularity potential of projects in the upstream phase, and to steer the project in the execution phase. The results of this project can also be used as a contribution to standardization in ISO/TC 323 (see Figure 18), and a presentation of these results in the mirror group "WG Metrics" of the AFNOR X30M Commission is also a prospect. In order to help the user in the selection of appropriate indicators, a query tool has been developed (Saidani et al., 2019a) with the aim of making this taxonomy more easily exploitable and operational for, for example, organizations working on development projects and strategies related to the circular economy and being in search of steering indicators. This tool is intended for both industrial practitioners (product designers, engineers in design offices) and decision-makers (project managers, financial managers). For ease of use and distribution, the tool is developed on Microsoft Excel with the use of macros. The selection tool is flexible and will be updated with new c-indicators. A web-based version of this tool is also available:

The C-indicators Advisor (CIA) platform (http://www.circulareconomyindicators.com/) is an online platform with an international scope developed by CentraleSupélec to both select and implement the right circular economy indicator(s) and unlock and track the circularity performance of products (see Figure 19). It is a free platform but requires voluntary registration.

of 21 Figure 1 -

 211 Figure 1 -Circularity indicators : current challenges and opportunitiesTowards a sustainable circular economy: positioning and promising perspectivesComplementary to the SCORELCA project (2019) on "Material loops, product loops and LCA" (Study No. 2018-02), which resulted in recommendations for the assessment of the environmental performance of loops, this project aims to dive further into circularity assessment, and produce recommendations for circularity indicators that integrate the environmental aspect. These analyses and recommendations will be based on a structured analysis of existing indicators and may serve as a contribution to standardization at ISO/TC 323. In addition to producing measurements, these circularity indicators must also lead to useful and justified actions on the part of industrial players, through, e.g., transition management, improvement, or mitigation plans. Although circularity indicators seem to be a good help to accompany and guide these practitioners in taking into account the components of the circular economy, there is a notable gap between the (theoretical) indicators developed by academics and their (practical) use in industrial reality. The co-construction of these indicators is a way forward. In this spirit, the inventory and classification of circularity indicators can serve as a basis not only for testing and validating (or not) their proper understanding by designers, engineers, manufacturers, or project managers, but also for identifying the shortcomings of current indicators in order to consider their consolidation, combination and/or the construction of new indicators[START_REF] Saidani | Des indicateurs catalyseurs de l'économie circulaire[END_REF].

Figure 2 -

 2 Figure 2 -Stepwise approach of the study 1. Performing a systemic state of the art: identification and analysis of indicators  Specify the objectives that organizations wish to achieve with circularity indicators;  Develop specifications for the circularity indicators to appropriately address the organisations' objectives.. 2. In-depth analysis of 10 circularity indicators  Propose a methodology for selecting the 10 indicators to be detailed;  To develop a template for these indicators;  To highlight the links between circularity indices, material flows, criticality indices, and LCA 3. Links with LCA and recommendations  Produce recommendations on the use of appropriate, credible and operational circularity indicators;  To provide recommendations on the implementation of the most relevant indicators in different contexts for their internal and external communication and to make them evolve in order to better meet the organizations' objectives.

  Figure 3 below shows the set of classification criteria used. This figure shows an increase in the categories of the circularity indicator taxonomy compared to (Saidani et al., 2019a), based on a review of existing literature, brainstorming, and feedback from SCORELCA members.

Figure 3 -

 3 Figure 3 -Set of classification criteria used for the analysis of the identified sets of indicators(illustrated, the ten initial criteria in blue(Saidani et al., 2019a), the five new criteria in gold)

of 21 Figure 4 -Figure 5 -

 2145 Figure 4 -Distribution of academic/consultant/government sources

Figure 6 -

 6 Figure 6 -Breakdown by circularity perspective (potential or actual circularity) N.B.: Potential circularity indicators are particularly developed at a micro level, to be deployed when designing new products to assess their circularity potential.

Figure 7 -

 7 Figure 7 -Breakdown (number of c-indicators) by circular economy loops: recycling, repair, reuse, etc.

Figure 8 -

 8 Figure 8 -Breakdown by type of performance: intrinsic (flow) vs. consequential (impact) N.B.: Indicator sets covering both intrinsic and consequential circularity are mainly found at a macro scale (region, country).

  Need for sectoral indicators (specific to the industrial sector);  Need for micro indicators (at product or project level) and meso indicators (for reporting and steering at company level)  On the other hand, the objective characteristics distinguishing the indicators, such as:  Indicators of recycling/material recovery ;  Indicators of product reuse;  Indicators on the circularity of materials/resources on a territorial scale;  Indicators on energy ;  Economic indicators ;  Social indicators ;  Design indicators (for circularity) ;  Aggregate indicator(s) ("score" of circularity).

Figure 9 -

 9 Figure 9 -Overview of the method for selecting the 10 indicators

Figure 10 -

 10 Figure 10 -10 factsheets associated with the selected circularity indicators

  i. LCA output data (flows/midpoints/endpoints) are used as input data for the calculation of circularity indicators; ii. Circularity indicator(s) are integrated into the LCA output as a flow/midpoint/endpoint indicator (Saidani et al., 2019c);

Figure 11 -

 11 Figure 11 -Potential trade-offs between circularity and LCA. Source : Saunier, 2019, Webinar ACLCA

SCOREFigure 12 -

 12 Figure 12 -Illustrations of the relationships and trade-offs between circularity, economic andenvironmental performance to be optimised[START_REF] Saidani | Framing Product Circularity Performance for Optimized Green Profit[END_REF]

Figure 13 -Figure 14 -Figure 15 -

 131415 Figure 13 -System boundaries for case study #1. Source : Saunier, 2019, Webinar ACLCA

Figure 16 -Figure 17 -

 1617 Figure 16 -Description of case study #2. Sources : Saunier, 19, Webinar ACLCA ; Lonca et al., 18.

Figure 18 -

 18 Figure 18 -Current working groups for a series of ISO standards on circularity. AFNOR.

Figure 19 -

 19 Figure 19 -Web-platform "The C-indicators Advisor (CIA)", http://www.circulareconomyindicators.com

Two environmental impact indicators (in link with LCA): RBR and RCBR

  In order to keep the maximum number of 10 factsheets, the selected circularity indicators are grouped by "category" (i.e., related indicators are summarised within the same sheet, see Figure10):

	Categories	Indicators	Acronyms	Tools
	Factsheet 1: Circualrity	Circulytics	Circulytics	Web-based
	performance at the
	company level (corporate	Circular Transition Indicators	CTI	Web-based
	reporting)
	Factsheet 2: Circularity at	Material Circularity Indicator	MCI	Excel
	the material level
	Factsheet 3: Circularity at	Product Circularity Indicator	PCI	Excel
	the product level
	Factsheet 4: Circularity	Concept Circularity Evaluation Tool CCET	Excel
	performance of design
	alternatives
	Factsheet 5: Reuse and	Reuse Potential Indicator	RPI	Formulas
	life extension	Circularity and Longevity Indicators	CLI
	Factsheet 6: Material flow	End-of-Life Recycling Rate	EoL-RR	Formulas
	(MFA-like)	Recycled Content	RC
		Old Scrap Ratio	OSR
	Factsheet 7: Energy flow	Circularity Index	CI	Formulas
		Circularity of Material Quality	Qc	Formulas
	Factsheet 8: Circularity at	Regional Material Flow tools for the	RMFCE	Formulas
	a territorial level	Circular Economy		Excel template
	Factsheet 9:	Recycle Benefit Rate	RBR	Formulas
	Environmental impact of	Recycled Content Benefit Rate	RCBR
	circularity
	Factsheet 10: Socio-	Socio-economic Indicator for EoL	SEI-EoL	Formulas
	economic impact	Strategies for Bio-based Products	TCR
		Total Circular Revenue	TCO
		Total Cost of Ownership
	 Recycle Benefit Rate (RBR) and Recycled Content Benefit Rate (RCBR): Recyclability Benefit
	Rate and the Recycled Content Benefit Rate indicators express the potential environmental
	benefits from recycling compared to disposal (e.g., incineration), taking into account life cycle
	thinking.
	Socio-economic impact indicator(s) (in link with LCC and SLCA): SEI-EoL, TCR and TCO

 Socio-economic Indicator for EoL Strategies for Bio-based Products (SEI-EoL): The socioeconomic aspects of EoL alternatives associated with bio-based products have been neglected. This paper contributes to filling this gap by proposing a new socio-economic indicator for EoL (SEI-EoL), calculating the values of the 25 socio-economic criteria including: 5 criteria (each) related to workers, consumers, general society, local community, value chain actors.  Total Circular Revenue (TCR), Total Cost of Ownership (TCO). SCORE LCA Study n° 2020-03 -Summary Centrale Supelec & Evea -August 2021 Page 12 of 21

organize cooperation between companies, institutional and scientists in order to support the evolution of LCA methods and its practical implementation at European and international level.

 This work has been supported by ADEME (Agence de l'Environnement et de la Maîtrise de l'Energie) www.ademe.fr


C Barthe-Dejean

F Lutton

M Michel

Ganil-Spiral2 Caen

France M Dubuisson

SEISMIC ANALYSIS FOR SAFETY REQUIREMENTS OF SPIRAL2 ACCELERATOR

The SPIRAL2 Accelerator at GANIL is a superconducting ions continuous wave LINAC with two associated experimental areas. Mechanical engineers have been highly involved in the design of SPIRAL2 equipment since the beginning of the project in 2004. During the development phase, Computer Aided Design and calculation codes have been used throughout the complete process: from the ion sources, the LINAC, the beam transport lines and the experimental halls equipped with detectors. SPIRAL2 has to meet different safety requirements, among which seismic hazard. This involves justifying that the integrity of the radiologic containment barrier is always maintained in case of earthquake. This paper reports the improvement in design and calculation methods performed by GANIL engineers to meet the seismic safety requirements, specifically the non-missility feature of the equipment. The modalspectral simulations, used to demonstrate the mechanical strength of equipment in case of earthquakes, was an important part of this design activity in the past 10 years. New methods have been used to calculate welds, fasteners and the ground anchor of the structural supports of the heaviest equipment.

INTRODUCTION

The non-missility criteria consists in preventing equipment weighing more than 500 kg at height 1.5 m to be projected on ground floor or walls of the building, which is used as containment barrier. The mechanical supports and frames have to withstand dynamic load corresponding to earthquake S.M.S (Security Maximum Seism) [START_REF] Cingal | Rapport de Sureté de l'INB n°113[END_REF]. Also, fasteners and anchors to ground have to be analysed to prove that they withstand such loads. For example, LINAC supporting frame had to be reinforced for seismic load after first installation (Fig. 1).

Figure 1: Additional supporting features LINAC A. All calculation have been performed with the Finite Element Analysis Code ANSYS 2020 R1. The spectral load in three directions X, Y and Z is provided by Civil Engineering (Fig. 2) and implemented in the Finite Element Model and combined to gravity. First, a modal analysis is performed to identify the Eigen modes of the structure.

Then two load cases will be compared to identify the most severe: gravity + seism or gravity -seism. The X, Y and Z direction loads are also combined to each others: either by quadratic combination, or by Newmark combination. In this example, only the structural frame and the feet of the vacuum chamber has to be calculated in order to prove that the FALSTAFF detector will not be projected under seismic load. We will focus on the fasteners and anchorage analysis even if welds and stresses are also post-treated.

Figure 3 shows how the equipment is clamped to the frame with metal plates and to the ground. The bonded anchors that have been calculated and selected according to the method described in [START_REF]Design of Bonded Anchors[END_REF].

Fasteners Analysis

All the fasteners are represented in the F.E. model as beam elements (Fig. 4). A program -code lines-has been developed to extract shear and tension load on each fasteners. The analysis is then made using the combined load criteria described in Eurocode 3 [START_REF] Maitre | Formulaire de la Construction Mécanique selon l'Eurocode[END_REF] and in Eq. ( 1) below.

….

, , , < 1 (1)
In Eq. ( 1) Ft is tension load in bolt, Fs is shear load in bolt, Ft,Rd is tension strength of stainless steel bolt, Fv,Rd is shear strength of the bolts. The tension strength of the stainless steel fasteners are previously determined. The results show that the fasteners M8 in stainless steel A4-70 fulfils the combined load criteria.

Bonded Anchors

The force and moment are extracted from the model and the most loaded feet using an online code developed by anchors supplier HILTI (Fig. 5).

EXAMPLE 2: WATER RETENTION S3

The cooling circuit of the beam-dump of the experimental area S3 is a closed circuit. The heat exchanger (Fig. 6) of the cooling circuit is located in the S3 experimental area, which is 9.5 meters underground in the SPIRAL2 accelerator building. The water retention tray of the exchanger has to be waterproof and maintain its structural integrity in case of seismic event . The tray and the structure holding the exchanger components (valve, tubes, tanks..) are made of stainless steel 316L.The tray has to contain the entire volume of water of the closed circuit in case of leakage because the water is potentially contaminated. The aim of the calculation is to prove that no crack or damage will appear on the tray and that the structure will hold the different exchanger equipment under seismic load.

Mechanical Stresses

The results are post-treated in terms of Von Mises Stresses for all mechanical parts (Fig. 7). (2)

Welds Analysis

The strength of welding joint are calculated with the method described in Eurocode 3 -Part 1-8 [START_REF] Maitre | Formulaire de la Construction Mécanique selon l'Eurocode[END_REF]. The safety coefficient for stainless steel structure is ϒ M2 =1.25 and applied in order to compensate the dispersion of the thresholds of materials. The mechanical strength criteria described in [START_REF] Maitre | Formulaire de la Construction Mécanique selon l'Eurocode[END_REF] are normally adapted to static load. The fact that a modal-spectral calculation is performed leads to a non-dynamic type of analysis and therefore allows to use static mechanical strength law. Figure 8 shows a sketch with stresses needed to calculated weld criteria

Figure 2 :

 2 Figure 2: Spectral load based on S.M.S.in S3.

EXAMPLE 1 :

 1 NFS DETECTORNFS (Neutron for Science) is the first experimental area linked to SPIRAL2 accelerator. NFS is composed of a time-of-flight baseline and irradiation stations. A new detection system named FALSTAFF has been installed in the Time-of-flight NFS area as shown. This detector fully equipped weighs 592 kg, and hence is subject to non-missility requirements, has been clamped to ground as shown in Fig.3.

Figure 3 :

 3 Figure 3: FALSTAFF detection assembly drawing.In this example, only the structural frame and the feet of the vacuum chamber has to be calculated in order to prove that the FALSTAFF detector will not be projected under seismic load. We will focus on the fasteners and anchorage analysis even if welds and stresses are also post-treated.Figure3shows how the equipment is clamped to the frame with metal plates and to the ground. The bonded anchors that have been calculated and selected according to the method described in[START_REF]Design of Bonded Anchors[END_REF].

  31st Int. Linear Accel. Conf. LINAC2022, Liverpool, UK JACoW Publishing ISBN: 978-3-95450-215-8 ISSN: 2226-0366 doi:10.18429/JACoW-LINAC2022-MOPORI11 MOPORI11 Content from this work may be used under the terms of the CC BY 4.0 licence (© 2021). Any distribution of this work must maintain attribution to the author(s), title of the work, publisher, and DOI 252 Technology Industrial developments

Figure 4 :

 4 Figure 4: F.E. model frame and beam for fasteners.A program -code lines-has been developed to extract shear and tension load on each fasteners. The analysis is then made using the combined load criteria described in Eurocode 3[START_REF] Maitre | Formulaire de la Construction Mécanique selon l'Eurocode[END_REF] and in Eq. (1) below.….

Figure 5 :

 5 Figure 5: Forces and moment at most loaded feet. The wedge anchor selected for this equipment is HILTI HL-M12 with an embedment in concrete of 80 mm. The FALSTAFF Detection holding structure fulfil seismic requirements as shown in [4].

Figure 6 :

 6 Figure 6: Exchanger structure and retention tray.The water retention tray of the exchanger has to be waterproof and maintain its structural integrity in case of seismic event . The tray and the structure holding the exchanger components (valve, tubes, tanks..) are made of stainless steel 316L.The tray has to contain the entire volume of water of the closed circuit in case of leakage because the water is potentially contaminated. The aim of the calculation is to prove that no crack or damage will appear on the tray and that the structure will hold the different exchanger equipment under seismic load.

Figure 7 :

 7 Figure 7: Max stress in the supporting beam. Von Mises Stresses are compared to Yield Strength as shown in Eq. (2) of the stainless steel with a safety factor of λ=1,1..

Content from this work may be used under the terms of the CC BY 4.0 licence (© 2021). Any distribution of this work must maintain attribution to the author(s), title of the work, publisher, and DOI The main criteria to meet is based on equivalent stress as described in Eq. ( 3) and ( 4):

The main difficulty was to find a way to extract the loads and shell stress at the junction element from Finite Element simulation. The transferred load will allow to calculate analytically the shear and tensile stress on the weld area (Fig. 9). To achieve this, a specific computer program has been developed by an external specialised company and code lines inserted in the Finite Element model. [START_REF] Barthe-Dejean | Tenue aux séismes du bac de rétention du refroidissement de l'Arrêt faisceau S3[END_REF], and consequently there is no risk of damage or leakage on the tray and on the structure in case of earthquake.

CONCLUSION

The calculations and analysis described here shows the difficulty to match theoretical Eurocode 3 criteria with global F. E. Simulation. The code lines used to extract relevant values from model was one of the key to solve that problem. The computer program was sub-contracted to an external expert and is now adapted for each new calculation. Each SPIRAL2 heavy equipment is now in line with seismic requirements. A method has been summarized for all seismic calculation at GANIL-SPIRAL2 [START_REF] Barthe-Dejean | Guide méthodologique pour Calculs de Tenue aux Séismes des équipements mécaniques[END_REF] and [START_REF] Barthe-Dejean | Mechanical Engineering Design and Simulation for Spiral2 Accelerator at GANIL[END_REF].

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