Arij Ben

Skander Kaoubi

Laurie Starck

Towards an optimal formulation of alternative jet fuels: Enhanced Oxidation and Thermal Stability by the addition of cyclic molecules

Keywords: Jet fuel, Synthetic Paraffinic KeroseneHydroprocessed Esters and Fatty Acids, SPK, HEFA, oxidation, thermal, stability, PetroOxy, JFTOT, deposit, decalin, tetralin, toluene, xylene, 1-methylnaphthalene, npropylbenzene, trimethylbenzene, n-decane

Oxidation and thermal stability (OTS) are key concerns for the development of alternative jet fuels, as they imply complex physical and chemical phenomena such as autoxidation, pyrolysis, cooxidation reactions and transfer-limitation. The OTSof an alternative aviation fuel was characterized using PetroOxy test from 120-160°C and JFTOT test at 325°C. The alternative jet fuel is a Synthetic Paraffinic Keroseneproduced from Hydroprocessed Esters and Fatty Acids (HEFA-SPK). Results showed a high thermal stability of HEFA-SPK. However, a low oxidation stability was also observed. The oxidation stability of8model cyclicmolecules was evaluated. Results allowed to estimate the influence of the molecular structure of cyclic molecules on liquid phase reactivity involving the number and the hydrogenation of the aromatic rings and the number and chain-length of the aromatic alkyl groups.The addition of several alkylbenzenes increased almost linearly the induction period of HEFA-SPK. Tetralin and decalin acted as inhibitors of the radical chain mechanism at low concentration, although having inherently low oxidation stability. Besides offering a better oxidation stability, the addition of specific low fractions of several alkylbenzenes, tetralin and decalin to HEFA-SPK allowed to achieve a good thermal stability as well. These molecules represent good candidates to improve OTS of HEFA-SPK. This work opens the way for the development of future fit-for-purpose formulations of alternative jet fuels with an increased fraction of renewables.

BACKGROUND

Alternative jet fuels are receiving considerable attention for their potential to diversify energy sources and to reduce the impact of air transport on environment [START_REF] Lee | Transport impacts on atmosphere and climate: Aviation[END_REF] [START_REF] Stratton | Quantifying Variability in Life Cycle Greenhouse Gas Inventories of Alternative Middle Distillate Transportation Fuels[END_REF]. National and international Organizations have launched initiatives to increase their use in the coming years. The Biofuels Flight path project of the European Union aims to produce two million tons per year of aviation biofuels by 2020, corresponding to 3-4% of total jet fuel use in Europe. In Germany, AIREG targets 10% of alternative aviation fuels by 2025. The International Air Transport Association (IATA) estimates a realistic target of sustainable second generation bio jet to be near 3% by 2020.

The present study focuses on the oxidation and thermal stability (OTS) of a Synthetic Paraffinic Kerosene produced from Hydroprocessed Esters and Fatty Acids (HEFA-SPK) approved as synthetic blending component for alternative jet fuels. The current legislation allows its incorporation up to 50%vol in alternative jet fuels and a minimum aromatic content of 8%wt in the final blend (ASTM D7566) to ensure material compatibility. However, this level is conservative and does not take into account the influence of the molecular structure of aromatics on both material compatibility and OTS.For example, alkylnaphthalenes impact more significantly O-Nitrile rubber seal swell than alkylbenzenes [START_REF] Dewitt | Effects of Aromatic Type and Concentration in Fischer Tropsch Fuel on Emissions Production and Material Compatibility[END_REF]. Aromatics may produce an oxidation promoting or retarding effect [START_REF] Zuidema | Oxidation of lubricating oils[END_REF]. They also influence the thermal stability (or deposit formation at high temperature), which is a function of the molecular structure and the concentration of reactantsas well as of thetemperature regime [START_REF] Taylor | Deposit Formation from Deoxygenated Hydrocarbons. I. General Features[END_REF].

In this study, we investigated the OTS of HEFA-SPKand evaluated the influence on OTS of the addition of several pure cyclic compoundsnaturally present in conventional jet fuels. In the course of the work, oxidation stability and thermal stability measurements were carried-out using PetroOxy from 120-160°C and JFTOT test at 325°C, respectively. Results were analyzed and compared with previous literature work in order to improve the understanding of the oxidation and cooxidation kinetics of cyclic molecules and to definethe best candidate molecules to improve OTS of paraffinic fuels.

MATERIALS AND METHODS

PetroOxy test

The PetroOxy test is a widely used measurement for the oxidation stability of diesel and biodiesel [START_REF] Bacha | Oxidation Stability of Diesel/Biodiesel Fuels Measured by a PetroOxy Device and Characterization of Oxidation Products[END_REF]. Recently, it has been successfully employed for jet fuel oxidation stability studies [START_REF] Starck | Potential of alternative Fuels for aircraft : focus on thermal and oxidation stability[END_REF] [START_REF] Sicard | Oxidation stability of jet fuel model molecules evaluated by rapid small scale oxidation tests[END_REF]. The oxidation status is monitored through oxygen uptake by the fuel. A small sample (5ml) of a fuel is introduced in a closed and heated test cell under 7 bar of oxygen pressure. The decrease of oxygen pressure, measured continuously in the test cell, reflects oxygen consumption by the oxidation process. The induction period (IP) is defined by the time necessary to reach 10% of the pressure drop as illustrated in Figure 1. At the IP, oxygen remains sufficiently in excess within the test cell [START_REF] Sicard | Oxidation stability of jet fuel model molecules evaluated by rapid small scale oxidation tests[END_REF] permitting the use of the obtained data for global kinetics assessment. The repeatability error, calculated from 25 different samples tested at different temperatures repeated 2-3 times each, is related to IP according to: 𝝉 𝑰𝑷 = 𝟎. 𝟎𝟏𝟒 𝑰𝑷 + 𝟏. 𝟐𝟐𝟗 , indicating a relative error ofabout 2%. This value is in agreement with the level indicated in PetroOxy standard for middle distillate fuels (ASTM D 7545) as well as previously published results by Araujoet al. [START_REF] Araujo | FTIR assessment of the oxidation process of castor oil FAME submitted to PetroOXY and Rancimat methods[END_REF].Tests were conducted from 120 to 160°C for individual reagents, at 140 and 160°C, for HEFA-SPK/cyclic molecules mixtures, and at 140°C for n-decane/cyclic molecules mixtures.

Jet Fuel Thermal Oxidation Tester -ASTM D3241

The Jet Fuel Thermal Oxidation Tester (JFTOT) is a standard test procedure used to assess the thermal stability of conventional and alternative aviation fuels. The details of this method are provided elsewhere [START_REF]ASTM D3241-14be1, Standard Test Method for Thermal Oxidation Stability of Aviation Turbine Fuels[END_REF]. JFTOT rates jet fuels stability utilizing two metrics: filterable liquid particulates are monitored by pressure drop through a filter (dP filter), and surface deposits on the test tubes are assessed by visual rating after the test. Tests were carried on at 325°C meeting the specification of HEFA-SPK(ASTM D 7566 -11 a).

Fuel matrix

The reagents tested in this study were a commercial fossil JetA-1, three alternative paraffinic Hydroprocessed Esters and Fatty Acids (HEFA-SPK) and their blends with Jet A-1 at 25% and 75%vol. Besides, several model cyclic molecules were evaluated individually and in mixture with HEFA-SPK and ndecane, to better assess the complex interaction of cyclic molecules present in fossil jet fuel with alternative fuels composed mainly of linear and branched alkanes.

Conventional Jet A-1: The conventional Jet A-1 is a hydrotreated ultra-low sulfur jet fuel supplied by Total. In accordance with the regulation for hydrotreated jet fuels, an antioxidant additive was added. The GC2D of Jet A- Synthetic Paraffinic Kerosene -Hydroprocessed Esters and Fatty Acids (HEFA-SPK): Three additive-free HEFA-SPK (HEFA-50, HEFA-30 and HEFA-20) were studied. They are composed mainly of linear and branched alkanes (>99.5%wt). HEFA-20 and HEFA-30 have around 90%wt of branched paraffins and HEFA-50 has a sensibly higher fraction (93%wt). Figure 2 illustrates theircomposition according to carbon number. The distribution of branched alkanes has a bimodal shape centered on C12 and C16-C17. The distribution of linear alkanes presents a bimodal curve centered on C10-C11 and C17 for HEFA-20 and HEFA-30 and a C11-centered unimodal distribution for HEFA-50. Carbon number for branched alkane ( -)

Figure 2 : Distribution of normal and branched alkanes for HEFA-SPK -20, HEFA-SPK-30 and HEFA-SPK-50

Pure reagents: To evaluate the impact of molecule structure on stability, several pure molecules were evaluated. Five alkylaromatics presenting different branching configurations and number of benzene cycles, namely, toluene, xylene, n-propylbenzene (n-PB) and 1,2,4-trimethylbenzene (TMB) and 1methylnaphtalene (1-MN). Tetralin, n-propylcyclohexane and decalin are tested to evaluate the impact of the partial or total hydrogenation of aromatics. Purity of the chemical products is above 96% for all reagents. N-decane and n-dodecane are commonly used as model surrogates for middle-distillate transport fuels [11][12]. In this work, we selected n-decane as more representative of the kerosene cut. The list of reagents purity and additional information are summarized in Table 2. Blends: Mixtures of the abovementioned pure reagents with HEFA were carried out at three blending rates: 5, 10 and 25%vol. The first twoare situated on both sides of the current specification for minimum aromatics content for alternative jet fuels (8%wt), whereas, the last value corresponds to the aromatic content of the conventional Jet A-1 used in the present study. Only HEFA-SPK-30 was used for the mixtures as the three HEFA-SPK presentedvery similar oxidation behaviors (section 3.1.1). Mixtures of reagents with n-decane were also studied at 5, 10, 25 and 50%vol.

RESULTS AND DISCUSSION

Evaluation of the oxidation stability of HEFA-SPK, Jet A-1 and their blends

Figure 3.a presents the induction period (IP) as a function of the inverse of temperature (1000/T). The logarithm of IP is a linear function of the inverse of temperature indicating a typical Arrhenius trend of the global reactivity. The IPs of the three HEFA were similar in the temperature range investigated. This may result from either similar reactivity of the paraffins composing HEFA (although there are small changes in the fraction of normal and branched alkanes and chain length distribution), or compensating variances. The IP of HEFA is 2-3 times lower than that of jet fuel. This may be explained by the difference in chemical composition, mainly; cyclic compounds (aromatics/naphthenes) present at 55%wt in Jet A-1 that have different reactivity compared to paraffins. Besides, Jet A-1 contains antioxidant additives and, possibly, other naturally occurring antioxidants, heteroatoms or contaminants that can influence its reactivity as well [START_REF] Zabarnick | Chemical kinetic modeling of jet fuel autoxidation and antioxidant chemistry[END_REF][14]. Figure 3.b illustrates the effect of adding Jet A-1 on HEFA oxidation stability. We observe a non-linear and non-monotonous variation of the IP due to the addition of Jet A-1. First, IP increases to reach a maximum at intermediate concentration (25-75%vol). We note that the oxidation stability of HEFA/Jet A-1 mixtures is higher than that of Jet A-1 for an added fraction above 25%vol of Jet A-1.

In the next part of the study, we focus on the impact of cyclic molecules on OTS of HEFA, in an attempt to assess the non-linear, oxidation-inhibiting behavior observed with HEFA/Jet A-1 blends.

Evaluation of the oxidation stability of cyclic molecules

The oxidation stability of several cyclic pure compounds was evaluated from 120to 160°C. Figure 4 illustrates the induction period as a function of the inverse of temperature (1000/T) and Figure 5 illustrates the influence of molecule structure on IP at 140°C.

Oxidation stability of alkylaromatics

1-MN has almost twice as high induction period as toluene (Figure 5.a) in spite of the weaker  C-H Bond Dissociation Energy (BDE) of alkylnaphthalenes compared to structurally-related alkylbenzenes (2-3 kcal/mol) [START_REF] Igarashi | Autoxidation of alkylnaphthalenes. 1. Self-inhibition during the autoxidation of 1-and 2-methylnaphthalenes puts a limit on the maximum possible kinetic chain length[END_REF]. This trend can be associated to two phenomena:

(1) an autoretarding effect:among 1-MN oxidation products, some have an oxidation inhibiting effect [START_REF] Larsen | Oxidation Characteristics of Pure Hydrocarbons[END_REF]. For example, methylnaphthoquinones were identified by Igarashi et al. [START_REF] Igarashi | Autoxidation of alkylnaphthalenes. 1. Self-inhibition during the autoxidation of 1-and 2-methylnaphthalenes puts a limit on the maximum possible kinetic chain length[END_REF] as the most likely autoxidation retarders formed during methylnaphthalene oxidation, which can trap alkyl radicals R° more effectively than peroxyl radicals ROO°

(2) a self-inhibiting effect: the decomposition methylnaphthoxyl radical can be responsible of first order chain termination. This radical is produced mainly by the decomposition of an intermediate radical formed by the addition of1-MN peroxide to the naphthalene ring. This trend is amplified at higher temperature [START_REF] Igarashi | Autoxidation of alkylnaphthalenes. 1. Self-inhibition during the autoxidation of 1-and 2-methylnaphthalenes puts a limit on the maximum possible kinetic chain length[END_REF].

The IP of n-propylbenzene (n-PB) is 50% lower than that of toluene (Figure 5.c). It is mostly accepted that increasing the normal chain-length reduces the oxidation stability of alkylaromatics; the global reactivity of n-PB was found to be 3 times higher compared to that of toluene at 60°C [START_REF] Sajus | Kinetic Data on the Radical Oxidation of Petrochemical Compounds[END_REF]. Similarly, IP of alkylbenzenes having C5 to C18 side chain-length measured by Zuidema [START_REF] Zuidema | Oxidation of lubricating oils[END_REF] presented a quasi linear dependency of IP with the side chain-length. This can be associated partly with the higher ratio of secondary-to-primary carbon atoms, the former having a lower C-H BDE favoring H-abstraction reactions.Similar behavior is known for linear alkanes with increased reactivity along with the chain length. The rate of consumption measured by Gernigon [START_REF] Gernigon | Study of liquid-phase oxydation stability of hydrocarbon fuels : Influence of antioxidants[END_REF]increased with chain length for C10 to C14 nalkanes.

IP data of toluene, xylene and TMB (Figure 4.a) indicate a small influence of the number of methyl groups on the benzene ring. IP of xylene and toluene are sensibly close from 120-160°C. IP of TMB was 40% different from that of toluene from 120-160°C. Figure 5.b compares the three reagents along with benzene measured elsewhere [START_REF] Skolniak | Analysis of Changes in the Properties of Selected Chemical Compounds and Motor Fuels Taking Place During Oxidation Processes -Chapter 8[END_REF] at 140°C showing a small influence on IP of the number of methyl groups. Note however that Opeida [START_REF] Opeida | Cooxidation of Alkylaromatic Hydrocarbons in the Liquid Phase[END_REF] observed an increase of the global reactivity with the number of methyl groups on the benzene ring at a lower temperature range (60°C).

Oxidation stability of cyclic alkanes and tetralin

Figure 4.b presents the IP of cyclic alkanes, namely, decalin and n-propylcyclohexane (n-PC) as well as tetralin from 120-160°C. In comparison with n-PB, n-PC presents a lower IP especially at high temperature (4 times at 140°C).The IP of decalin was roughly similar to n-PC except at low temperature. Previous works comparing aromatics versus their hydrogenated derivatives. e.g. cyclohexane / benzene [START_REF] Skolniak | Analysis of Changes in the Properties of Selected Chemical Compounds and Motor Fuels Taking Place During Oxidation Processes -Chapter 8[END_REF], decalin or tetralin/naphthalene [START_REF] Zuidema | Oxidation of lubricating oils[END_REF]noted a higher stability of aromatics.

Summary

The oxidation stability of the tested cyclic compounds showed a significant influence of the molecular structure. They can be ranked as follows according to induction period (IP) criterion, alkylaromatics >> n-decane> cyclic alkanes >HEFA-SPK> tetralin at 140°C. However, temperature can have a strong influence on oxidation stability for paraffins, cyclic alkanes and tetralin in comparison with alkylaromatics.For example, n-decane has an oxidation stability close to several alkylaromatics, namely, toluene, xylene and n-PB at low temperature (120°C), however it decreases significantly with temperature.

Study of the Cooxidation of HEFA-SPK with cyclic compounds

In this section, the oxidation stability of binary mixtures of HEFA-SPK with cyclic compounds is evaluated.

A parallel is drawn with mixtures of n-decane with the same cyclic compounds tested at 140°C. Results are presented in Figure 6.

Cooxidation of HEFA-SPK with alkylaromatics

A non-linear logarithmic trend was observed with the addition of 1-MN. For example, the addition of 10%vol to HEFA-SPK significantly increased the induction period (27 times) approaching the IP of 1-MN itself, in agreement with previous measurements [5][21]. This trend is particularly interesting given that the addition of low fraction (5-10%vol) of 1-MN allows to improve significantly the oxidation stability of HEFA-SPK. A comprehensive investigation by Igarashi et al. [START_REF] Igarashi | Autoxidation of alkylnaphthalenes. 2. Inhibition of the autoxidation of n-hexadecane at 160. degree. C[END_REF] on the influence of added 8-22%vol fraction of naphthalene, 1-MN and 2-MN to n-hexadecane at 160°C demonstrated a retarding effect of similar amplitude for the three components. This allowed to favor the chemistry of naphthalene nucleus instead of that of methyl group chemistry [START_REF] Booser | Liquid Phase Hydrocarbon Oxidation[END_REF]. The oxidation retarding effect was associated to an increase of the termination rate constant (k t ) through two competing pathways:

(1) a second-order termination:through the addition of two peroxyl radicals (Reactions 3-4). This pathway is increasingly important with (methyl) naphthalene concentration

(2) a first order chain termination: through (methyl)naphthoxyl radical formation (Reactions 2-5).

Scheme 1 illustrates both pathways for 1-MN. At advanced oxidation progress methylnaphthalene can additionally produce oxidation inhibitors as abovementioned.

Scheme 1: Termination major pathways in 1-methylnaphthalene / n-alkane cooxidation [START_REF] Igarashi | Autoxidation of alkylnaphthalenes. 2. Inhibition of the autoxidation of n-hexadecane at 160. degree. C[END_REF], R designates all the peroxyl radicals present, n-decane (poly)peroxide, 1-MN peroxide and hydrogen peroxide.

In the case of alkylbenzenes, namely, xylene, n-PB, TMB and toluene, the induction period increased almost linearly with their volume fraction in HEFA-SPK (Figure 6.a) which suggests a different oxidation mechanism from that involved in 1-MN/paraffins mixture. The IP with 10%vol. of alkylbenzenes is about twice as high as HEFA-SPK.

Cooxidation of HEFA-SPK with decalin and tetralin

The IP of decalin/HEFA-SPK blends goes through a peak (twice as high as HEFA-SPK) at around 10%vol. of decalin (Figure 6.a). This result suggests an interesting inhibiting effect of decalin on the oxidation of paraffins at low concentration [23][24]. In a similar manner, the addition of tetralin to HEFA-SPK presents a pronounced retarding effect for a concentration below 10%vol. Although the intrinsic IP of tetralin is roughly equal to that of HEFA-SPK, the IP of their mixture at 10%vol is 4.6 folds higher than HEFA-SPK. The antioxidant activity of tetralin at low concentration was previously evidenced in mixtures with cumene [START_REF] Russell | The Competitive Oxidation of Cumene and Tetralin1,2[END_REF]; the addition of 3% mol of tetralin reducing cumene reactivity by two third. This trend was associated to the difference in propagation and cross termination rate constants. Besides, tetralin comprises four benzylic hydrogen atoms allowing to inhibit the cooxidation reactions involving peroxy radicals in autoxidation regime [START_REF] Ingold | 7th Preprints World Petroleum Congress[END_REF]. In addition, tetralin oxidation can lead to the formation of several oxygen-substituted hydrogen donors, including α-tetralone and α-tetralol (phenolic compounds), that contribute to refrain oxidation progress as well [START_REF] Robertson | 317. Studies of the autoxidation of tetralin. Part I. Investigation of autoxidation products[END_REF]. Compared to decalin, tetralin is known to be a better hydrogen donor, which may explain higher oxidation retardation observed here. However, at higher concentration, the oxidation kinetics of tetralin becomes leading so the IP of Tetralin/HEFA mixture tends to that of tetralin. Previous work of Gernigon [START_REF] Gernigon | Study of liquid-phase oxydation stability of hydrocarbon fuels : Influence of antioxidants[END_REF] support this hypothesis; the consumption rate of reactants during the oxidation of a blend of 40%wt tetralin with alkanes and aromatics showed a higher rate for tetralin consumption compared with the other constituents of the blend. Results present very similar trends to those observed for HEFA-SPK. First, we observe an oxidation inhibiting effect with the addition of all alkylaromatics. IP increases almost linearly with added alkylbenzenes, namely, xylene, n-PB and toluene, and with a logarithmic trendline with the addition of 1-MN. The IPs of mixtures of n-decane/decalin and n-decane/tetralin go through maximumsrespectively 1.6 and 4.5 times higher than that of HEFA-SPK. Similar trends observed in HEFA-SPK and n-decane suggest similar driving cooxidation kinetics of some paraffins with the cyclic molecules evaluated here. This initial finding broadens the application of the present study results, and would require deeper investigation.

Summary

The addition of cyclic molecules influences the oxidation stability of HEFA-SPK differently function of their structure. Alkylaromatics, namely, 1-MN, toluene, xylene and TMB improve the oxidation stability of HEFA-SPK. Tetralin and decalin improve HEFA stability at concentration below 25%vol. only.

Impact of molecule structures on deposit formation

Thermal stability measurements were carried out at 325°C using the test procedure described in section 1.2. Deposit rating of the tubes and the variation of filter pressure gradient (dP filter) are illustrated in Figure 7.a and b, respectively. JFTOT results indicatea very good thermal stability of HEFA-SPK. Tube rating and dP filter indicate 1 and 0, respectively. These levels are far below the specification of HEFA-SPK (3 and 25mm Hg, respectively).

Deposit formation from alkylaromatics/HEFA-SPK blends

The addition of 5%vol.toluene or xylene induced low tube ratingsand filter dPs indicative of low deposition tendency. Increasing the volume fraction to 15%vol.had no influence for toluene while it increased the quantity of tube deposit for xylene. Using 25%vol. resulted in significant amounts of deposits with tube ratingsthat exceeded the accepted level (Figure 7.a) for both reagents. In the studied conditions, the addition of both toluene and xylene at 5%vol. does not degrade the thermal stability of HEFA.

The addition of 5% and 25%vol. of 1-MN to HEFA-SPK produced a high amount of deposits at 325°C. Tube ratings indicate 4 and >4, respectively. A mixture of 25%vol. 1-MN and HEFA-SPK generated a large volume of insolubles inducing significant increases of filter dPs. 1-MN drastically reduces the thermal stability of HEFA-SPK at 325°C even at low concentration, although having a significant oxidation retarding effectas described in section 2.3 (Figure 7.a).

Deposits formation from tetralin and decalin/HEFA-SPK blends

JFTOT test with HEFA-SPK/5%vol. tetralin indicate a better thermal stability. The tube rating level was below HEFA-SPKwith no change in the filter dP as illustrated in Figure 7. Higher concentrations (15% or 25%vol.), led however to significant amounts of deposits whiletube ratings indicate levels above 3.

Tube ratings of the blends of 5, 15 and 25%vol. decalin/HEFA-SPK indicate a very low deposition rate with levels as low as that ofHEFA-SPK. Filter dP remain very low. In previous studies, decalin was found more thermally stable and produced fewer deposits than alkanes both at pyrolytic regime 450°C [START_REF] Song | Pyrolytic degradation studies of a coalderived and a petroleum-derived aviation jet fuel[END_REF] and autoxidation regime from 93-162°C [START_REF] Taylor | Deposit Formation from Deoxygenated Hydrocarbons. I. General Features[END_REF]. Song and Lai [START_REF] Song | Hydrogen-Transferring Pyrolysis of Cyclic and Straight-Chain Hydrocarbons[END_REF]have underlined the influence of steric confirmation with higher thermal stability of trans-decalin compared with cis-decalin at 450°C. This aspect was not considered in the present work as a commercial decalin (purity >98%) composed of a mixture of ci and trans isomers was used. Decalin, as a hydrogen donor effective in a wide temperature range, allows to stabilize the radicals generated from HEFA-SPK molecules cracking.

Summary

These results lead to an original finding regarding the influence of cyclic molecules on deposits formation. In fact, previous works examined the influence of mixtures of aromatics on thermal stability [START_REF] Klettlinger | Thermal stability testing of Fischer-Tropsch fuel and various blends with Jet A, as well as aromatic blend additives[END_REF][31]and evidenced in generala higher deposition tendency exacerbated by the presence of diaromatics. In a complementary perspective, the use of pure molecules in the present work allowed toemphasize molecular structure impact. The addition of specific cyclic molecules to HEFA-SPK, namely, xylene, toluene, tetralin (up to 5%) and decalin(up to 25%) allowedto improve or conserve a good thermal stability of HEFA-SPK. Considering the oxidation stability resultspresented in section 2.3, these molecules acted as oxidation inhibitors as well. Thus, representing good candidates to improvesimultaneously oxidation and thermal stability.

SUMMARY AND CONCLUSIONS

In this study, the oxidation and thermal stabilityof three HEFA-SPKwere measured with PetroOxy and JFTOT tests. HEFA-SPK was 2-3 times less stable than conventional Jet A-1. This was associated with the differences in chemical composition partly, the presence of cyclic compounds in jet A-1. Thus, we evaluated the influence of pure cyclic molecules on OTS of HEFA-SPK.The addition of cyclic molecules to HEFA-SPK induces different behaviors. Alkylbenzenes increased almost linearly the induction period of HEFA-SPK. 1-MN, induced a non-linear logarithmic increase of IP. Tetralin and decalin acted as oxidation inhibitors at low concentration although having inherently a low stability. This study led to an original finding regarding the influence of the molecule structure of several cyclic molecules on deposits formation. Besides improving the oxidation stability, the addition of low fraction of tetralin and decalin and several methylbenzenes such as xylene and toluene to HEFA-SPK allowed to improve or maintain good thermal stability according to JFTOT results. These molecules, naturally present in conventional fuels,may represent good candidates to improve oxidation and thermal stability of HEFA-SPK. By acting on the formulation itself, they bring a complementary perspective to additive packages widely used for aviation fuels.These results encourage further developments towards fit-for-purpose formulations of future alternative jet fuels. Further investigationswould allow to evaluate their potential on different jet fuel feedstocksand operating conditions.

Figure 1 :

 1 Figure 1 : Illustration of pressure variation during the oxidation of n-decane at 140°C, Induction Period (IP) equals 3.05 hours

Figure 3 :

 3 Figure 3: Induction period of a. HEFA-SPK and Jet fuel from 120-150°C, b. blends of HEFA-SPK/Jet A1 at 140°C

Figure 4 :Figure 5 :

 45 Figure 4 : Induction period of pure reagents, HEFA-SPK and n-decane function of inverse temperature from 120-160°C. a)alkylaromatics, b) naphthenes and tetralin. Symbols: full diamonds  : 1-MN,full circles  : xylene, star *: toluene (almost identical to xylene), blank diamonds : n-PB, full squares  : tetralin, full triangles : decalin, cross +: n-PC, bold solid line: n-decane andbold broken line: HEFA-SPK-30.

Figure 6 : 2 . 3 . 3 Figure 6 .

 62336 Figure 6 : Impact of the addition of cyclic compounds on the oxidation stability of: a) Cyclic compounds in HEFA-SPK at 140°C, b) Cyclic compounds in n-decane at 140°C. Symbols: full diamonds  : 1methylnaphthalene, full circles  : xylene, star *: toluene, blank squares: 1,2,4, trimethylbenzene, blank diamonds : n-PB, full squares  : tetralin, full triangles : decalin.

Figure 7 :

 7 Figure 7 : Evaluation of thermal stability by JFTOT tests at 325°C (ASTM D3204) of HEFA-SPK, HEFA-SPK/cyclic molecules blends at 5-25%vol. a)Tube deposit rating after JFTOT test. b) Filter clogging measurement by pressure gradient variation after JFTOT test.

Pressure (kPa) Time (h) Induction Period ΔP 10%Table 1 :

 1 Chemical composition of Jet A-1 and HEFA-SPK

			1200
	Characteristics	Unit	1050	JET-A1	HEFA-20		HEFA-30	HEFA-50
	Carbon content	%m/m	900	86.43		84.77		84.76	84.71
	Hydrogen content	%m/m	750	13.57		15.23		15.24	15.29
	Molar weight	g/mol	600	140.8		201.69		198.53	188.41
	N-paraffins	%m/m	0	1 17.03	2	8.93	3	4 9.52	6.73
	I-paraffins	%m/m		27.25		90.65		90.41	93.25
	Naphthenes	%m/m		29.39		0.02		0.07	0.02
	Mono-aromatics	%m/m		25.65		0		0	0
	Di-aromatics	%m/m		0.69		0		0	0
	Unknowns	%m/m		0		0.41		0	0
	Total	%m/m		100		100		100	100
		1 indicatesa carbon chain-length distribution ranging from C8 to C16 and centered on
	C10. It contained 17%wt normal alkanes, 27%wt branched alkanes, 30%wt cyclic alkanes and 25%wt
	aromatics as summarized in Table 1. Aromatics are composed of C8-C11 mono-aromatics, namely, xylene
	(and/or ethylbenzene) at 3.9%wt, propyl-, butyl-and pentyl-benzene at 8.3%wt, 4.1%wt and 2.2%wt,
	respectively. Derivatives of indane and tetralin may also be present at 4.3% wt. Naphthenes, distributed
	from C9-C13, are composed of monocyclic and bicyclic molecules at 22% and 7%wt, respectively.

Table 2 :

 2 List of the pure reagents tested

	Chemical family	Molecule designation	Abbreviation	Purity	Molecular weight	Molecular Formula	Skeletal formula
				%	g/mol	CxHy
	Linear alkane	n-decane	n-C10	99	212.4	C10H22
	Cyclic alkane	n-propyl-cyclohexane	n-PCH	99	126.2	C9H18
	Cyclic alkane	decalin	decalin	98	138.3	C10H20
	Aromatic	toluene	toluene	97	92.1	C7H8
	Aromatic	xylene	xylene	97	106.2	C8H10
	Aromatic	1,2,4 trimethyl-benzene	TMB	98	120.2	C9H12

ACKNOWLEDGMENTS

This work was carriedoutwithina French national research program entitled "Alternative Fuels for Aeronautics-CAER" supported by French Directorate-General for Civil Aviation (DGAC). Authors would like to thank Clara Horlaville and Benjamin Veyrat for conducting PetroOxy experiments and AD Systems for deposits characterization after JFTOT tests.


Géraud Granger Steria

Edouard Belin

Cyril Allignol

Nicolas Durand

MANAGEMENT RESEARCH AND DEVELOPMENT SEMINAR (ATM2011) 1 The Influence of Uncertainties on Traffic Control using Speed Adjustments

Keywords: speed adjustment, traffic complexity, conflict resolution

The RTA (Required Time Arrival) capabilities of aircraft FMS (Flight Management Systems) offer new opportunities to solve mid-term horizon conflicts (20 minutes in advance) with small speed adjustments. The ERASMUS project has shown promising results of up to 80% conflict resolution using small speed adjustments in the [-6%; +3%] range with 20 minutes advance notice. The hypotheses were based on very accurate trajectory predictions (TPs). In this article we show how the quality of these results decreases as the uncertainties on the trajectory prediction increase. Therefore we used the CATS (Complete Air Traffic Simulator) developed in the late 90s at CENA (Centre d'Etudes de la Navigation Aérienne) and constrained the solver to use only speed maneuvers for leveled or descending aircraft with different hypotheses on speed ranges and speed uncertainties. Results show that Traffic Control using Speed Adjustments (TCSA) can solve most of the conflicts even when we consider uncertainty on the TP. However, the number of maneuvers that need to be given to aircraft is highly influenced by the uncertainties used in the TP.

INTRODUCTION

Traffic Control using Speed Adjustments (TCSA) has been recently studied through the ERASMUS project. Several experiments were carried out in the Aix-en-Provence control center to test the ability of controllers to detect speed changes, check the compatibility of an automatic ground based speed adjustment tool with the controllers and pilots' working methods, and measure the potential benefit of the concept [START_REF] Bonini | How erasmus can support an increase in capacity in[END_REF], [GGG + 07], [START_REF] Cruck | Subliminal air traffic control: Human friendly control of a multi-agent system[END_REF], [START_REF] Ehrmanntraut | The potential of speed control[END_REF].

From a theoretical point of view, conflict resolution using speed adjustments has been studied by Pallotino, Feron and Bicci [START_REF] Pallottino | Conflict resolution problems for air traffic management systems solved with mixed integer programming[END_REF] and later by Vela, Solak, Singhose and Clarke [START_REF] Vela | A mixed integer program for flight-level assignment and speed control for conflict resolution[END_REF] using mixed integer linear programming in a simplified context where aircraft are leveled and can all change their speeds at the same time. It as also been studied by Durand and Alliot in the mid 90s with a stochastic optimization approach [START_REF] Durand | Automatic aircraft conflict resolution using genetic algorithms[END_REF]. This approach was used in the ERCOS (En Route Conflict Optimized Solver) [START_REF] Granger | Optimal resolution of en route conflicts[END_REF] that is integrated in the CATS (Complete Air Traffic Simulator) fast time simulator.

The current Air Traffic Management system can be conceptually divided into four layers or filters, each with a decreasing time horizon relative to the moment of departure: 1) Strategic (several months), ASM (Air Space Management): design of routes, sectors and procedures 2) (Pre-)Tactical (a few days to a few hours), ATFM (Air Traffic Flow Management): control centers opening schedules define hourly capacities of each open sectors (or groups of sectors). To respect these capacity constraints, the CFMU (Central Flow Management Unit) computes and updates flow regulations and reroutings according to the posted flight plans and resulting workload excess. 3) Real time (5/10 minutes), tactical control: surveillance, coordination with adjacent centers, conflict resolution by various simple maneuvers (heading, flight level, speed) transmitted to the pilots. 4) Emergency (less than 5 min), safety nets: groundbased (Short Term Conflict Alert, Minimum Safety Altitude Warning) and airborne (Traffic Alert and Collision Avoidance System, Ground Proximity Warning System).

The power of TCSA discribed by [START_REF] Bonini | How erasmus can support an increase in capacity in[END_REF] is that it has the potential to be added between layer 2 and layer 3 without affecting them. Consequently, it could increase the safety of the whole system by adding a layer and also increase the capacity if the number of conflicts solved is high enough. The purpose of this paper is to evaluate the potential number of conflicts that could be solved using fast time simulations on real data, and measure the effect of uncertainties on the results obtained.

Airlines and aircraft manufacturers will agree to pay for new onboard systems if it can be proven that the money invested provides some benefit in terms of efficiency (for example reducing delays) and/or safety. Slightly modifying the speeds of aircraft to increase their separation without interfering with the existing control system could add a safety layer, but the question is to measure the efficiency of the concept for different scenarios of uncertainties.

In this paper we propose to analyse the influence of speed uncertainty on the efficiency of mid-term speed adjustments.

Therefore we test different scenarios of speed adjustments using a [-5%,+5%] speed range, an anticipation time of 20 minutes corresponding to a mid-term time horizon, and two different update time steps (3 and 5) minutes. These scenarios are tested on real 2010 traffic data in the French airspace with different ground speed uncertainties (2%, 5% or 10%) and different vertical speed uncertainties (10% or 30%).

In the first part, we describe CATS, the simulator used. The second part details the maneuver modeling and the solver algorithm used. The third part describes the solver algorithm. In the last part, numerical results are presented.

I. THE COMPLETE AIR TRAFFIC SIMULATOR (CATS) A. General framework

Results presented in this paper rely on real data traffic simulation. The CAT Simulator takes as input flight plans given by airlines or pilots with or without regulation. In the application, the traffic used is the French real traffic of July 17 th 2010. The simulator uses the BADA tabulated model for modeling aircraft performances. For a given aircraft type, it gives a vertical speed and a ground speed which depends on the aircraft attitude (whether it is climbing, leveled or descending). For example, a B747 leveled at FL-300 has a GS of 490 kts. If it is climbing, its GS will be 480 kts and its VS 1000 ft/min. At FL-150, values would be respectively 430, 420 and 1800. Aircraft performances are in tabulated form describing ground speed, vertical speed, and fuel burn as a function of altitude, aircraft type and flight segment (cruise, climb or descent). The main dataset for aircraft flight performance used is the base of aircraft data (BADA) performance summary tables derived from the total energy model of EUROCONTROL.

Aircraft speeds can be modified by a random value to take into account different factors of uncertainty (aircraft load, winds, etc. . . ). These values can be either computed once at aircraft activation and remain the same for all the flight, or can be modified anytime during the flight. Uncertainty modeling for conflict detection and resolution is introduced in the next section.

Aircraft follow classical routes (from way-point to waypoint). The flight model is simple. An aircraft first climbs up to its RFL (Requested Flight Level), then remains leveled until its top of descent, then descends to its destination.

Aircraft flight is calculated per time step. The time step is always chosen in order to guarantee that two aircraft face to face flying at 500 kts could not cross without being closer than one standard separation at at least one time step. For all our simulations, we use a 15s time step.

B. General architecture of the system

We sketch here the architecture of the simulator. Each part will be detailed in the following sections. The system architecture is presented in figure 1 and 2. The system relies on three main processes P1, P2, and P3:

• P1 is the traffic simulator. P1 sends current aircraft positions and flight plans to process P2. Process P2 builds trajectory forecasts for T w minutes, does conflict detection by pairs and transforms 1-to-1 conflicts in n-aircraft conflicts. Then, process P3 (the problem solver) solves in parallel each cluster, as aircraft in each cluster are independent from aircraft in the other clusters. The problem solver sends to P2 new orders and P2 builds new trajectory forecasts based on these orders. Then P2 once again runs a conflict detection process to check that modified aircraft trajectories do not interfere with aircraft in another cluster, or with new aircraft. If no interference is found, new flight orders are sent to P1. If there are interferences, interfering clusters are joined and the solver is used again on that (these) cluster(s). The process is iterated until no interference between clusters remains, or no new aircraft is concerned by modified trajectories. The new orders are sent back to the traffic simulator.

The above process is iterated and all trajectories are optimized each δ minutes (3 or 5 minutes in the experiments). However, during the computation time, aircraft are flying and need to know if they must change their route or not. δ should be large enough to compute a solution, send it to the pilot and leave him enough time to begin the maneuver. Consequently, for each aircraft, at the beginning of the current optimization, trajectories are determined by the previous run of the problem solver and cannot be changed for the next δ minutes.

C. Conflict detection and clustering

1) Trajectory forecast and 1-to-1 conflict detection: As described above, the P2 process does trajectory prediction for T w minutes. This trajectory prediction is done again by a simulation on a slightly modified version of the Air Traffic simulator. But, as stated above, we assume that there is an error about the aircraft's future location because of ground speed prediction uncertainties 1 . Climbing and descending rate uncertainties are larger than ground speed uncertainties. Because the conflict free trajectory must be robust regarding these and many other uncertainties, an aircraft is represented by a point at the initial time. The point becomes a line segment in the direction of uncertainty (the speed direction here, see figure 3). The first point of the line "flies" at the maximum possible speed, and the last point at the minimum possible speed.

When changing direction on a beacon, the heading of the line segment's "fastest point" changes as described on figure 3.

To check the standard separation at time t, we compute the distance between the two line segments modeling the aircraft positions and compare it to the standard separation at each time step of the simulation.

In the vertical plane, we use a cylindrical modeling (figure 3). Each aircraft has a mean altitude, a maximal altitude and a minimal altitude. To check if two aircraft are in conflict, the minimal altitude of the higher aircraft is compared to the maximal altitude of the lower aircraft. Let us take an example. A B747 is leaving its departing airport (altitude 0) at t = 0. Its climb rate is 1800 ft/min and its ground speed is 175 kts. If we suppose that ground speed uncertainty is 5% and vertical speed uncertainty 20%, maximal and minimal climb rate are 1800 × 1.2 = 2160ft and 1800 × 0.8 = 1440 ft/min and ground speeds are respectively 184 and 166 kts. This means that 15s later, the fastest and highest point has traveled 0.76 Nm and 540 ft while the slowest and lowest has only traveled 0.69 Nm and 360 ft. This time however, 1 Ground track uncertainties will not be considered, as they do not increase with time and will be included in the standard separation when computing maximal and minimal speeds, the difference of altitude of both points must be taken into account. At 540 ft, the tabulated model gives a standard ground speed of 197 kts, so max ground speed is 197 × 1.2 = 237 kts. At 360 ft, standard ground speed is 189 kts, with a minimal ground speed of 151 kts. Thus, the height of the segment grows much faster than the 20% factor for some aircraft.

Duration T w can be changed, but must be at least equal to 2 × δ. A good evaluation of T w is difficult. With a perfect trajectory prediction, the largest T w should be chosen. However, this is not true as soon as uncertainties are included in the model. A large value of T w induces a large number of 1-to-1 conflicts, as the size of segments (modeling aircraft positions) grows quickly with time. Therefore, the conflict solver can become saturated.

2) Clustering: After pair detection, P2 clusters conflicting aircraft. Each equivalence class for the relation "is in conflict with" becomes a cluster.

For example, if aircraft A and B are in conflict in the T w window, and if B is also in conflict with C in the same time window, then A, B, C is the same cluster and will be solved globally by the conflict solver.

The conflict solver sends back to P2 maneuver orders for solving conflicts. Then P2 computes new trajectories for all aircraft and checks if new interferences appear. For example, if the new trajectory given to aircraft B to solve the conflict with A and C interferes with cluster D, E and with aircraft F , then A, B, C, D, E, F will be sent back to the problem solver as one conflict to solve.

The process will always converge. In the worst case, P3 will have to solve a very large cluster including all aircraft present in the next T w minutes. However, this technique is usually efficient because a very large number of clusters can be solved very quickly in parallel.

II. SOLVER MODELING

A. Maneuver modeling

In the CATS simulator, the conflict solver offers different maneuver options including heading changes (10, 20 or 30 degrees right or left), vertical maneuvers (flight level change, climbing interruption, descent anticipation, depending on if the aircraft is leveled, climbing or descending), or speed maneuvers. A maneuver starts at time t 1 and ends at time t 2 . In this paper, we will limit the maneuvers to speed modifications when the aircraft is leveled or descending. We do not allow speed modifications during the climbing phase because many aircraft cannot change their speeds during this phase without changing the climbing rates. Different ranges ([-15%, +15%], [-10%, +10%], [-5%, +5%]) of speed changes have been tested in the experiments in order to measure the influence of the this parameter.

A maneuver is determined by:

• t 0 : the beginning of the speed change.

• α: the speed change • t 1 : the end of the speed change.

For a conflict involving n aircraft, the dimension of the search space is 3 n.

B. Maneuver decision time

Because of uncertainties, some conflicts that are detected too early would not actually occur in the end. Consequently, deciding to move aircraft in such cases would be useless and could even generate other conflicts that would not occur if no maneuver had been decided. This explains why controllers do not solve conflicts too early. When there is no uncertainty, the earlier the maneuver is started, the lower the delay. However, if speed is not strictly maintained, the earlier the conflict is detected, the lower the probability it will actually happen. Thus, a compromise must be reached between the delay generated and the risk of conflict.

Because of uncertainties, maneuvers should be started as late as possible with respect to the aircraft constraints. First, it prevents the system from deciding unnecessary maneuvers. Second, an aircraft that is already maneuvering (i.e. changing speed) cannot do another maneuver before resuming its initial speed. The solver was modeled this way to keep the maneuvers simple to understand and execute. Starting maneuvers as late as possible increases the number of maneuverable aircraft.

C. A sliding forecast time window model

In order to limit the size of the problem and to be reactive to uncertainties, only the next T w minutes of the flights are considered. T w represents the lookahead time also called forecast time window. The situtation is reconsidered every δ minutes with δ << T w . δ is the time step used in the model to make the T w time window slide. This approach ensures that the problem can be updated every δ minutes : current aircraft positions are updated which reduces uncertainties.

In figure 4, at t = 0, the aircraft trajectory cannot be modified before t = δ because any maneuver requires advance notice. Any maneuver that would occur between t = δ and t = 2δ would be kept as a constraint for the next optimization run (in the example, no maneuver is decided). In figure 4, the maneuver described on the first line resulting from an optimization at t = 0 is reconsidered at time t = δ and then kept at time t = 2δ. The end of the maneuver can be recalculated until the optimization starting at t = 3δ.

Pilots should only be given maneuver orders that will not be modified; if no conflict occurs, no order will be given. In the example, the pilot will be notified of the beginning of the speed change at time δ and the end at time 3δ.

The size of the forecast time window is an important parameter. If it is too big, the size of the problem will include a very large number of variables and the resolution might be more difficult. If it is too small, the solutions found might be worse and the total delay induced over the day much higher. In order to solve conflicts with small speed adjustments, T w needs to be large enough. Based on the ERASMUS experiments, we decided to set T w = 20min for this analysis.

III. SOLVER ALGORITHM

Classical Evolutionary Computation (CEC) principles such as described in the literature [START_REF] Goldberg | Genetic Algorithms in Search, Optimization and Machine Learning[END_REF], [START_REF] Michalewicz | Genetic algorithms + Data Structures = Evolution Programs[END_REF] is used in the solver.

A. Fitness function

The cost function used in this part is simply the sum of the delays over the aircraft population.

Solutions respecting the separation constraints cannot be built easily. Consequently, we need to include the separation constraint in the fitness function.

The fitness function chosen is:

F = n - n i=1 ( δi δmax ) 1 + n rc
where n is the number of aircraft and n rc is the number of remaining conflicts.

The fitness function increases when the number of remaining conflicts and the delays decrease. It takes its values in [0, n].

B. Crossover operator

The conflict resolution problem is partially separable as defined in [START_REF] Durand | Genetic crossover operator for partially separable functions[END_REF], [START_REF] Durand | Automatic aircraft conflict resolution using genetic algorithms[END_REF]. In order to increase the probability of producing children with a better fitness than their parents, principles applied in [START_REF] Durand | Genetic crossover operator for partially separable functions[END_REF] were used. For each aircraft i of a population element, a local fitness F i value is defined as follows:

F i = 1 -( δi δmax ) 1 + nrc i
where nrc i is the number of remaining conflicts involving aircraft i.

Figure 5 presents the crossover operator. First two population elements are randomly chosen. For each parent A and B, fitness A i and B i of aircraft i are compared. If A i < B i , the children will take aircraft i of parent A. If B i < A i , the children will take aircraft i of parent B. If A i = B i children randomly choose aircraft A i or B i or even a combination of A i and B i .

C. Mutation operator

For each candidate to mutation, the delay of an aircraft having one of the worst local fitnesses is modified. If every conflict is solved, an aircraft is randomly chosen and its parameters changed. In practice, a number m is randomly chosen in the interval [1, n 2 ] and we pick up m times an aircraft to find the most constrained aircraft among these m trials. The delay of this aircraft is then either locally optimized or randomly modified with a probability of 50%. We may be tempted to always locally optimize the delay of the worst aircraft, but this would make the algorithm become very deterministic and lead to a premature convergence of the algorithm.

The crossover and mutation operators are more deterministic during the first generations because there are many conflicts to solve. They focus on making feasible solutions. When the solutions without conflicts appear in the population, they become less deterministic.

Sharing: The problem is highly combinatorial and may have many local optima. In order to prevent the algorithm from premature convergence, the sharing process introduced by Yin and Germay [START_REF] Yin | A fast genetic algorithm with sharing scheme using cluster analysis methods in multimodal function optimization[END_REF] is used. The complexity of this sharing process has the great advantage to be in n log(n) (instead of n 2 for classical sharing) if n is the size of the population. The distance used to compare two population elements p and q is:

D = n i=1 |δ p i -δ q i | n D. Parameters
In the experiments, the following parameters were empirically chosen: the size of the population was set to 100, 20% of the population is crossed, 60% is muted, the selection uses the stochastic remainder without replacement. A sharing process is used. As time to solve a problem is limited, the number of generations is limited to 500.

IV. EXPERIMENTAL RESULTS

CATS was used on a busy day of traffic (July 17 th 2010) in the French airspace. We were only interested in the upper airspace (above FL195). The number of flights in this airspace is 8870 for that specific day. Without any control maneuver, 2305 conflicts are detected (26% of the aircraft population). The mean time of flights is 57 minutes and the mean travelled distance in the french airspace is 394 nautical miles. Different experiments were done using CATS with different hypotheses.

Tables I and II give the results of simulations for δ = 3min and δ = 5min for different values of horizontal uncertainty (0, 2, 5 or 10) and vertical uncertainty (10 or 30%). Columns 4 and 5 give the number and percentage of remaining conflicts. Column 4 also gives the number of remaining conflicts that involve two leveled aircraft. Columns 6 and 7 give the number of maneuvered aircraft and the percentage of aircraft maneuvered. Columns 7 and 8 give the number of maneuvers and mean number of maneuvers per aircraft.

A scenario with no uncertainty and a [-15%, +15%] speed range was also tested (first line of tables I and II) in order to show what "theoretical" gain can be achieved on this specific day. In this case 97% of the conflicts could be solved by changing the speed of less than 2000 aircraft (20% of the aircraft population) which is very low. When the speed range is reduced to [-5%, +5%] the number of remaining conflicts doubles with a number of aircraft maneuvered slightly above 2000. Those results show that with a perfect TP most of the conflicts could be solved 20 minutes in advance with a small speed adjustment. The lower lines of the tables show how the results worsen when the uncertainty on the TP increases. For example, with a 5% horizontal speed uncertainty and 10% vertical speed uncertainty the number of aircraft maneuvered to solve the conflicts is tripled and the number of remaining conflicts grows to 15% which is still good. Results show that vertical uncertainty increases the number of conflicts and maneuvers because many conflicts involve climbing or descending aircraft. In the worse case tested (10% of uncertainty on both horizontal and vertical speeds and a δ = 5min) the number of remaining conflicts reaches 50% and the number of necessary maneuvers increases dramatically.

5% of horizontal speed uncertainty corresponds to 20 knots. When comparing the results using δ = 3min to those using δ = 5min it appears that the number of aircraft maneuvered increases by 10% and the number of remaining conflicts by 50%. This means that the solver is sensitive to the frequence of the detection and resolution cycle updates.

Results also show that uncertainties have a big influence on the number of maneuvers needed to solve the conflicts. Controllers are used to saying that they often have to solve conflicts that might never happen because of uncertainties. It appears that an automatic TCSA tool would encounter the same issue.

The results obtained during the ERASMUS project were slightly different because the speed range used was [-6%, +3%] and the seperation standard was 8 nautical miles. V. CONCLUSION Controllers are aware of the fact that part of their task is to solve many conflicts that would never occur, because they have to deal with uncertainty. Improvements in Trajectory Prediction offer new opportunities to enhance the efficiency and the safety of Air Traffic Management. Traffic Control using Speed Adjustments is one of the means that could be used to reach this goal. However, the expected gain of efficiency depends on the quality of the TP that can be used by the new tools.

This paper shows that having an accurate Trajectory Prediction is necessary to define a TCSA tool. These results do not suggest that we need to constrain the flight path to meet some Required Time Arrivals with a long advance notice. Instead, we need to be able to predict the future positions 20 minutes in advance with accuracy. Pilot attitude uncertainties are difficult to predict and our research was built on the strong hypothesis that the pilot would execute the maneuvers proposed by the solver using the Aircraft Flight Management System. Adding maneuver execution time uncertainty would probably worsen the results presented in this paper. This extra uncertainty needs to be studied carrefully. Having both controllers and pilots interacting with a medium term dolver is challenging because the controller will probably solve conflicts that are handled by the solver. This is why the ERASMUS experiments used a bigger separation standard. Pilot controller interaction with the medium term solver also needs to be modeled carefully and studied in future simulations to be able to give a realistic measure the possible gain of using TCSA.

Fig. 3 .

 3 Fig. 3. Modeling of speed uncertainties.

Fig. 4 .

 4 Fig. 4. The model and real time optimization.

  Fig. 5. Crossover operator

TABLE I δ

 I = 3min :NUMBER OF REMAINING CONFLICTS,NUMBER OF MANEUVERED AIRCRAFT AND NUMBER OF MANEUVERS FOR DIFFERENT UNCERTAINTIES AND DIFFERENT SPEED MODIFICATION RANGES.

	horiz	vert	speed	remaining % of rem maneuvered	% of acft	nb of nb of man per
	uncert uncert	range conf(leveled)	conflicts	aircraft maneuvered maneuvers	aircraft
	0	0 [-15 15]	100 (84)	4%	2026	21%	2634	0.3
	0	0 [-10 10]	107 (89)	5%	2057	23%	2700	0.3
	0	0	[-5 5]	205 (166)	9%	2349	26%	3060	0.34
	2	10	[-5 5]	251 (204)	11%	4162	47%	6058	0.68
	2	30	[-5 5]	334 (232)	14%	5284	60%	8258	0.93
	5	10	[-5 5]	517 (359)	22%	5773	65%	9688	1.09
	5	30	[-5 5]	591 (386)	26%	6544	74%	11995	1.35
	10	10	[-5 5]	1150 (801)	50%	7133	80%	14428	1.62
	10	30	[-5 5]	1410 (935)	61%	7593	86%	16675	1.88

TABLE II δ

 II = 5min :NUMBER OF REMAINING CONFLICTS,NUMBER OF MANEUVERED AIRCRAFT AND NUMBER OF MANEUVERS FOR DIFFERENT UNCERTAINTIES AND DIFFERENT SPEED MODIFICATION RANGES.