Michael Field

Lau

Barents Sea Mon

The use of gliders in the Pol clever and inexpensive methods for large sca exploration. In August and September o EXPLORER glider successfully completed a 3 the central Barents Sea to monitor the physi features over a transect between 72° 30' N latitude and between 32° E and 33° E longitu European FP7 ACCESS project and in coo Institute of Marine Research, Norway. The paper discusses the performanc EXPLORER vehicle during the mission in A behavior of the magnetic compass in close magnetic north pole is described and its resul flight of the glider. The reliability and robust is evaluated for operations in these difficul successful and cost-effective mission now o future opportunities to conduct repeat autono in the Barents Sea. I.

INTRODUCTION

A. Gliders in Our Oceans

The use of underwater gliders in the wor established. They provide a long endura platform that requires significantly redu logistics for the amount of data collected. T important in the Polar Regions, where recovery opportunities can be very limite application of gliders at high latitudes is di challenging navigation conditions (sea conditions) and cold water effects o performance.

Gliders modified for the Arctic envir being used in places such as Fram Strait [START_REF] Lee | Autonomous platforms in Proceedings of Ocean Obs09[END_REF] Sea [START_REF] Lee | Marginal Ice Zone Experiment Plan[END_REF], deployed with supporting infras long-range acoustic beacons and moorin under-ice navigation. These successful gl have involved significant cost and effort fo deployment of the supporting acoustic platfo

Here we present and evaluate the use of SEA EXPLORER glider conducting mo Barents Sea without any additional supporti

B. The Barents Sea

During the last decade, which has been observed in the Arctic [START_REF] Stocker | Climate chan basis[END_REF], climate change in has been illustrated by an unprecedented d [START_REF] Comiso | Accelerated cover[END_REF]. The Barents Sea is one of the most pr nitoring with a SEA EXP Glider urent Beguery 2 , Laurent Oziel 1 , Jean Claude Gascard S/UPMC/MNHN/IRD, Université Pierre et Marie Curie, P 2 ALSEAMAR, Meyreuil, France eld@locean-ipsl.upmc.fr, lbeguery@alseamar-alcen.com, el@locean-ipsl.upmc.fr, jga@locean-ipsl. the warmest ever n the Barents Sea decline in sea ice roductive areas in the world for fisheries and extracti This is also a key area for observing North Atlantic Ocean and the Arctic

The Barents Sea is a challengi glider, with a shallow average depth sea mounts rising to less than 50 m strong ocean currents, in some velocity of more than 25 cm/s [START_REF] Loeng | Features of the physica the Barents Sea[END_REF].

C. Magnetic Conditions

In 2014 the north magnetic p approximate position of 85° 55.56 Approaching the magnetic nort declination varies greatly over s inclination of the magnetic field app result in an unstable glider-hea resolving the course over ground us Within the area of the Barents Sea, ranges between 0° and +35°, while ranges between +78° and +84° [START_REF] Maus | The US/UK wor 2015[END_REF]. Paris, France on of mineral resources. g exchanges between the c Ocean. ing operating area for a h of 230 m and banks and m depth [START_REF] Loeng | Features of the physica the Barents Sea[END_REF], in addition to cases with an average pole was located at the 6' N 148° 49.86' W [START_REF] Maus | The US/UK wor 2015[END_REF]. h pole, the magnetic short distances and the proaches +90°, which can ading component when sing a magnetic compass. the magnetic declination the magnetic inclination ing the Barents Sea mission.

D. The SEA EXPLORER Glider

The SEA EXPLORER, shown in Fig underwater vehicle with a wingless design speeds of up to 0.5 m/s. The SEA EXPLOR mission -'SEA004' -was equipped with a CTD with a SBE43 dissolved oxygen sen ECO puck fluorometer and backscatterin altimeter for sea floor detection.

Here we use a standard model of the S glider, equipped with a 3D digital magne combines 3-axis accelerometers with sensors, providing a tilt-compensated headin

II. OPERATIONS AND PERFORM

A. Tromsø Fjords 1) Magnetic Compass Calibration

The SEA EXPLORER glider was tested and calibrated on land and in fjor Norway, in preparation for the Barents Sea m Following functional tests of the gl magnetic compass was calibrated in a c suspending the SEA EXPLORER from Following each calibration, performance d by pitching the glider up and down w orientating the SEA EXPLORER in th directions (due north, east, south and west) example of the performance data gathe calibration using approximate (+/-10°) m directions, and Fig. 4 shows an example of data following a calibration using precise ca

In Tromsø, Norway, the magnetic f include a declination of +7.91° and an inclin [START_REF] Maus | The US/UK wor 2015[END_REF]. Using an approximate magnetic ca g. 2, is a proven that can travel at RER used for this SeaBird pumped nsor, a WETLabs meter, and an SEA EXPLORER etic compass that 3-axis magnetic ng, pitch and roll.

MANCE comprehensively rds near Tromsø, mission. lider, the glider clear area while m a tree branch. data was gathered while physically he four cardinal . Fig. 3 shows an ered following a magnetic cardinal f the performance ardinal directions. field components nation of +78.35° alibration, Fig. 3 shows that when the glider is phys pitching down, becoming more p field, the compass reliably reads a n when the glider is pitching up, the c unstable between +10° to +15 perpendicular to the magnetic field, beyond +20° pitch, crossing the poin to the magnetic field and resolv component in the opposite direction observed when the glider is physic the 180° shift in compass reading down beyond -20° pitch, again cro perpendicular to the magnetic field during the 180° shift for both no headings, the compass readings tend shift. When the glider is physically west, the compass reading shifts physical heading point, from 45° pitching down, to 45° towards the so each direction shifting towards alig inclined magnetic field.

The performance data in Fig. example of how to fly the glider compass calibration no longer prec magnetic field. For example, when be best to limit the surfacing pitch a glider compass reading shifting by south, which would result in the gli to the north when it is already head be seen when heading south, to lim to -10°. The easterly and wester consistent and could be taken into accoun deviations in heading that might not be ex currents.

For the mission in the Barents Sea, the was precisely calibrated to the magneti Tromsø, resulting in a much improved pe glider compass for a full range of heading as shown in Fig. 4. However, this perform to the Tromsø area and its local magn differing to those expected along the Barent track (+15° to +18° declination, +79° to [START_REF] Maus | The US/UK wor 2015[END_REF]), as the compass could not be re-calibra The results of this precise calibration show is able to compensate for the high incl Tromsø using information from the 3D a declination offset of +16° was included in compensate for the approximate expected the Barents Sea track.

2

) 24-hour Fjord Mission

To demonstrate the ability of the SEA navigate in challenging magnetic condit mission was successfully completed using calibration of Fig. 3 in the northern section fjord south of Tromsø. The mission area of north-south orientation and is between 2 k with a maximum depth of 120 m [START_REF][END_REF].

Piloting the glider from Tromsø, the pitc adjusted to reduce the instability of the m and evaluate its performance as the northward and southward along the fj EXPLORER was deployed at 0813UTC o recovered at 0855UTC on 16 August, comp track of repeating north-south transects in shown in Fig. 5.

This successful test mission proved EXPLORER could be safely piloted in chal compass conditions based on the informatio the testing on land, in preparation for th Barents Sea.

B. Barents Sea Monitoring 1) Operations Overview

The deployment of the SEA EXPLORE was made possible with the help of the In Research, Norway, providing the opportun in the 2014 Mareano 3 expedition, departi 18 During the north transect, with the glid and gradually compensating for local curre compass occasionally showed two types of b

The first, shown in Fig. 6, occurred wh and pitching up, placing the glider compass the magnetic field, resulting in an noi oscillated rapidly by up to 180°. This occu of the pitching up cycles during the north tr normally be rectified by the pitching do followed.

The second type of bad behavior, show occurred when heading north and pitching stable shift of 180° that the glider then tr rolling. This repeats several times, during and pitching down, as the glider attempts to heading by rolling either left or right. It heading readings tend to the west, as was o approximate calibration in Tromsø, regard the glider rolls left or right. This occurred o cycles during the north transect, and wo rectified within 2 cycles.

During the south transect, the ma readings improved significantly, exhibitin bad behavior on less than 1% of the tot Fig. 9 SEA004 temperature, salinit during the south der heading north ents, the magnetic bad behavior. hen heading north s perpendicular to isy reading that urred during 20% ransect and would own section that wn in Fig. 7, also up, resulting in a ried to correct by both pitching up o reach the correct is noted that the observed with the dless of whether on another 20% of ould normally be agnetic compass ng the described tal cycles. Fig. 8 shows an example of the magnetic cycles of the south transect.

3) Bathymetry

The altimeter was initially disa and was to be enabled once approac bank. On 4 September, the glider with an alarm triggered from maki floor at 143 m depth, 50 m bathymetry [START_REF] Jakobsson | The Interna Arctic Ocean (IBCAO) Version[END_REF] and nautical chart which show a narrow ridge in the a depth of ~200 m. The contact with confirmed by a temporary offset i oxygen readings, indicating sediment in t which dissipated over the cycles that foll surface contact is also confirmed by th parameters which show a stable heading during the event: the glider gently coming t position briefly, then a clean change in pitch surface in response to the alarm conditions.

4) Science Payload

The high quality temperature, sa chlorophyll and depth data was successfu sent in real-time during surfacing periods, s which are shown in Fig. 9.

The dissolved oxygen plot shows two sediment or other material entered the resulting in a temporary offset in measure event occurred following the contact with t the second event occurred during the sou salinity readings are briefly affected at the b event and quickly rectify. Following recov it was noted that a slight constriction in t near the inlet of the oxygen sensor, dow salinity sensor, may have caused some sedi build-up and resulting in the longer duration

The initial profiles closely agreed with casts taken near the deployment location, 10. The difference in the readings at 35-45 due to the variation of the depth of the fre layer, as well as thermal inertia and hy sensors. This successful mission in the excellent high-resolution data in th significantly reduced cost and ef provided, along with the testing in th information on how to operate th these challenging conditions, a opportunities for improvement, such of the largest power consumers (e 2015) and endurance testing of th water conditions.

Another area of active develop behavior and reliability of the glid the Polar regions. It is feasible t calibration while deployed at sea; im set of movements while recording m then be used for a re-calibration o This could be performed several tim account for the significant di conditions along the track, resultin and overall efficiency of the glider.

This mission has proven the ro EXPLORER glider in this environm to future opportunities to conduct au the Barents Sea and key Arctic shelf IV. ACKNOWLED USION e Barents Sea provided his remote location with ffort. The mission also he Tromsø fjord, detailed he SEA EXPLORER in s well as identifying h as economizing the use expected update in early he battery pack in cold pment is to improve the der magnetic compass in to conduct the compass mplementing a controlled magnetic values that can f the magnetic compass. mes during a mission and fferences in magnetic ng in improved behavior obust ability of the SEA ment, and opens the door utonomous monitoring in f seas.

Fig. 1

 1 Fig. 1 Track of the SEA EXPLORER duri

Fig. 2

 2 Fig. 2 The SEA EXPLORER glider, (top) in the M (bottom) in Balsfjorden, Tromsø.

  Mediterranean and.

Fig. 3

 3 Fig.3Glider compass readings for fixed hea using an approximate magne

  August 2014. The SEA004 glider was deployed for m September 2014 from the rescue boat of th at a position of 73° 42.92' N 32° 9.77' Barents Sea, as shown in Fig. 1. The glid north over five days (north trans compensating for a strong current pushing east, reaching a northernmost position of 7 45.85' E. The glider then travelled west for travelling south for the remaining elev transect), again gradually compensating pushing the glider to the east. The SEA recovered on 19 September 2014, with 40% nt to explain any xplained the glider to the 74° 29.03' N 32° r two days before ven days (south g for a current A004 glider was % available battery power remaining, in challenging co the R/V Johan Hjort at a position of E, successfully completing a track o 2) Magnetic Compass Performa The magnetic compass perfo throughout the mission in the Bar occasionally had difficulty at the n the track, furthest from the magneti and quickly improved when mov Norwegian coast. The pitching an adjusted throughout the mission, ba data gathered in Tromsø. As a res low pitch angles during the nort

Fig. 6

 6 Fig. 6 Magnetic heading rapid 180° osc

Fig. 8

 8 Fig. 8 Magnetic heading durin

Fig. 10

 10 Fig. 10 Comparison between ship and glider CTD r deployment (separation of 2.5 km and 2

  DGMENTDr. Anne Helene and the way, as well as the crews V Johan Hjort for their esearch leading to these CCESS (Arctic Climate with funding from the ement n° 265863 within e European Commission NCES n the arctic observing network." ned Ocean Observations and e (MIZ) Program: Science and 201. WASHINGTON UNIV 012. nge 2013: The physical science mate Change, Working Group I ment Report (AR5)(Cambridge d decline in the Arctic sea ice 5.1 (2008). al oceanographic conditions of 991): 5-18. rld magnetic model for 2010rtverket Norwegian Nautical NT10 (2009), No.514 INT 174 ational Bathymetric Chart of the ophysical Research Letters, doi:

The authors would like to thank Institute of Marine Research, Norw of the R/V GO SARS and R/V assistance and cooperation. The re results has been supported by AC Change, Economy and Society), European Union under Grant Agre the Ocean of Tomorrow call of the Seventh Framework Programme.

V. REFEREN


For this pressure range, existing experimental methods show some drawbacks (see Table 1).

Here, we present a new apparatus based on static analytic method with improved sampling mechanisms.

  Apparatus Description ROLSI TM capillary sampler [1] : • In-situ sampling • Small sample volume (several μL per sample) • On-line analysis by gas chromatograph (GC) But…driving force needed: P cell >P carrier gas (≈3 bar) 6PV: 6-port sample injection valve; C: carrier gas; EC: equilibrium cell; GC: gas chromatograph; LS: liquid ROLSI TM sampler; MS: magnetic stirrer; PP: platinum resistance thermometer probe; PT: pressure transducer; PVT: PVT chamber; SL: Sample Loop; V i : valve; VP: vacuum pump; VS: vapor ROLSI TM sampler. Improvements • For liquid phase: a small variable volume chamber (PVT) equipped with a piston for compression (Patent application is ongoing [2]) • For vapor phase: a 6-port sample injection valve implanted in the transfer line  Experimental Results* n-Butane (1) + Ethanol (2). (○) this work at 323.22 K; (△) static-synthetic method at 323.75 K [3]; (□) static-analytic method without the improvements at 323.25 K [4]. Diethyl sulfide (1) + Ethanol (2). (○,•) this work at 343.13 K; (□) circulation still at 343.15 K [5]. Diethyl sulfide (1) + n-Butane (2). (○) this work at 317.62 K and 343.14 K; (□) staticsynthetic method at 343.15 K [6] (y calculated by SRK EoS [7]). 1-Pentanethiol (1) + 1-Pentanol (2). (○,•) this work at 372.75 and 392.72 K. *Experimental were correlated through Wilson model [8] with SRK EoS [7] Liquid-Equilibrium (VLE) data are of great importance in chemical engineering. Experimental data combined with appropriate thermodynamic models are essential for the design and optimization of separation processes. In most industrial applications, operating conditions vary from low (< 1 bar) to moderate (1 -10 bar) pressures.

Fan Zhang 1,2 , Pascal Théveneau 1 , Xavier Canet 2 , Elise El Ahmar 1 , Chien-Bin Soo 2 , Pascal Rousseaux 2 , Christophe Coquelet 1 1. Mines ParisTech, PSL -Research University, CTP -Centre Thermodynamique des Procédés, 35 rue St Honoré, 77305 Fontainebleau Cedex, France 2. PROCESSIUM, CS 52132, 62 Boulevard Niels Bohr, 69603 Villeurbanne Cedex, France 10

  two ROLSI TM capillary samplers was presented. The proposed improvements allow ROLSI TM to perform in-situ sampling even at P < P carrier gas . The apparatus has shown comparable performances to existing methods, while showing some advantages. Two binary systems of interest were investigated.

th European Congress of Chemical Engineering Sept. 27 th -Oct. 1 st 2015 Nice, France Contact: fan.zhang@mines-paristech.fr Introduction  A new static-analytic apparatus equipped New systems are expected to be investigated for various applications in chemical engineering. The liquid sampling mechanism is expected to be used for liquid-liquid equilibrium measurement.  Conclusion & Perspective  Reference [1]: Armines, French Patent No. 2853414, 2003 [2]: Armines. French Patent Application No. 1460309, 2014 [3]: T. Holderbaum et al., Fluid Phase Equilib., 63(1991)219 [4]: C.-B. Soo et al., Fluid Phase Equilib., 286 (2009) 79 [5]: E. Sapei et al., Fluid Phase Equilib., 301 (2011) 200 [6]: C. Dell'Era et al. Fluid Phase Equilib. 291 (2010) 180 [7]: G. Soave, Chem. Eng. Sci. 27 (1972) 1197 [8]: G.M. Wilson, J. Am. Chem. Soc. 86 (1964) 127

Table 1 .

 1 Common experimental methods in low and moderate pressure range


Jean-Philippe Guillemin

Peggy Lamy

Gérard Thomas

Olivier Bonnefoy

Micro-Nano : des comportements différents, des procédés à adapter

L'arrivée de nanomatériaux parmi les différents matériaux utilisés en pyrotechnie pose de nombreux problèmes de mise en oeuvre. En effet, leurs propriétés texturales particulières ne permettent pas de les utiliser comme des matériaux classiques. Il est impératif d'adapter les procédés de mise en oeuvre habituels. Pour obtenir l'adéquation de ces nouveaux matériaux et de nos procédés, des études spécifiques du comportement des nanomatériaux au cours des procédés de mise en oeuvre par coulée ont été réalisés. L'observation des écarts de comportement des nanomatériaux par rapport aux "micro-matériaux" pour une même nature chimique et des conditions identiques de mise en oeuvre permet d'établir des lois de comportement spécifiques, fonction de la taille des particules manipulées. Les mentalités, comme les procédés, doivent évoluer et prendre en compte l'élévation de surface spécifique qu'offre le passage à l'échelle nanométrique. Ainsi un chargement moindre en nanomatériaux ne sera pas forcement synonyme de lacunes sur les caractéristiques du produit fini (propriétés mécaniques ou pyrotechniques). Deux questions peuvent alors se poser : faut-il adapter les formulations aux procédés , en prenant en compte les caractéristiques des matières premières ou bien adapter des procédés devant supporter des taux de chargement élevés en nanomatériaux ? Le manque de connaissance et le recul sur le comportement des nanomatériaux sont un frein à leur intégration dans des composés pyrotechniques mais les propriétés exhibées laissent présagées d'un grand intérêt en vue de l'optimisation des propriétés des composés fabriqués.

Introduction

Les matériaux énergétiques mis en oeuvre par coulée-fondue peuvent être définis comme un ensemble biphasique composé d'une phase liquide (2,4,6 -trinitrotoluène et cires fondues) et d'une phase solide (matériaux pulvérulents actifs ou inertes). La composition massique de ces "pâtes" (avec des taux de chargement supérieurs à 50%) est telle que la texture du produit se rapproche de celle d'un béton présentant un seuil d'écoulement, c'est-à-dire une contrainte critique à partir de laquelle le matériau commence à s'écouler. Actuellement, la formulation des explosifs secondaires se base sur une démarche thermodynamique où les propriétés détoniques, calculées à partir des taux de chargement des matières premières, sont prioritaires. Cette recherche des caractéristiques pyrotechniques du produit final ne prend pas en compte l'étape de mise en oeuvre et abouti à des problèmes d'élaboration (difficulté de malaxage, mauvaise coulabilité) difficiles à résoudre. Cet article montrera l'évolution du comportement à l'écoulement d'un mélange biphasique liquide/solide en utilisant un matériau pulvérulent sous deux configurations différentes (micrométrique et nanométrique). La rhéologie de ces mélanges contribuera à l'étude de cette évolution. Les résultats présentés rendront compte du besoin d'adaptation des procédés en fonction du changement d'échelle des matériaux utilisés.

Rhéologie des matériaux énergétiques

La caractérisation de l'écoulement d'un matériau passe par l'étude de ses caractéristiques rhéologiques (terme inventé par Bingham, en 1929, pour définir l'écoulement des corps sous l'effet des déformations et des contraintes qui leurs sont appliquées). Le comportement de la matière s'exprime en général sous forme d'un rhéogramme (évolution de la contrainte de cisaillement en fonction de la vitesse de cisaillement). Grâce au rhéogramme, différents modèles empiriques peuvent caractériser les propriétés d'écoulement du matériau [1]. Les modèles succeptibles de représenter les matériaux énergétiques sont définis ci-dessous : le modèle newtonien : Par souci de confidentialité la nature physico-chimique de la cire et du dispersant ne sera pas développée. Dans le cadre de cette étude, ces deux produits sont employées comme agents de dispersion afin d'éviter les problèmes de sédimentation ou d'agglomération qui pourraient compromettre la qualité des mesures rhéologiques. La matrice, constituée des cires, a une masse constante tout au long de l'étude. Ces cires sont portées à leur température de transition vitreuse, puis l'aluminium pulvérulent est introduit à différentes fractions volumiques. Le mélange est ensuite homogénéisé puis introduit dans le godet du rhéomètre à l'aide d'une seringue.

Matériaux et techniques expérimentales

Technique expérimentale

Les mesures en cisaillement simple ont été effectuées à une température de 85°C +/-0.1°C. Un rhéomètre rotatif à vitesses imposées (Rheomat 30, Contrave), est utilisé pour l'obtention des rhéogrammes. Afin d'être dans un domaine présentant une large plage de cisaillement, le système de mesure retenu est en configuration coaxiale avec les dimensions suivantes : diamètre du godet = 19.99 mm, diamètre du corps de mesure = 18.96 mm, hauteur du corps de mesure = 23.49 mm.

Résultats et discussion

Comportement à l'écoulement de l'aluminium micrométrique Les courbes d'écoulement des mélanges chargé en aluminium micrométrique et de la matrice seule sont représentées figure 1.

Conclusion

L'étude rhéologique de l'aluminium a mis en évidence les différences de comportement à l'écoulement selon qu'il soit micrométrique ou nanométrique. Alors que l'aluminium micrométrique ne présente pas de contrainte seuil pour des fractions volumiques inférieures à 20%, l'aluminium nanométrique prend les caractéristiques d'un fluide à contrainte critique pour des pourcentages volumiques plus faible (dès 10%). L'utilisation de ces nanomatériaux dans le procédé de coulée fondue apportera donc des problèmes d'écoulement . Par contre l'élévation de surface spécifique qu'offre l'entité nanométrique est un avantage du point de vue pyrotechnique. En effet la surface d'échange d'une nanoparticule d'aluminium est 75 fois plus importante que la particule micrométrique. Ainsi si l'on souhaite conserver le procédé de coulée fondu, il est primordial d'adapter les proportions des produits introduits en fonction de leur nature. "Mettre moins pour faire plus" serait donc la philosophie à adopter pour bénéficier des propriétés prometteuses des nanomatériaux.

Bibliographie

[1] Couarraze G, Grossiord J.L., Initiation à la Rhéologie, TEC, (2000), 63pp

[2] Tattersall, G.H., Banfill, P.F.G., The rheology of fresh concrete, Pitman, (1983), 356pp

[3] Barnes, H.A., A handbook of elementary rheology, Institute of Non-Newtonian Fluids Mechanics, University of Wales, (2000), 200pp

  la structure n paramètre adimensionnel compris entre 0 et 1 et pouvant être considéré comme une indice de structure.

Figure 1 :

 1 Figure 1 : évolution du comportement rhéologique en fonction du pourcentage volumique en aluminium micrométrique

Figure 2 :Figure 3 :

 23 Figure 2 : évolution du comportement rhéologique en fonction du pourcentage volumique en aluminium nanométrique

Matériaux Les aluminium micrométriques et nanométriques sont fournis respectivement par les sociétés Ecka granules et Technanogy. Leurs caractéristiques physico-chimiques sont données dans le tableau 1. Le diamètre moyen est évalué par granulométrie laser

	(Malvern
	Mastersizer 2000). Les surfaces spécifiques sont déterminées par adsorption/désorption
	d'azote (Micromeretics) et la forme des particules est visualisée par microscopie électronique
	à balayage.

Tableau 1 :

caractéristiques physico-chimiques des produits utilisés

	Produit densité réelle	diamètre	Surface	Forme des
		(g/cm 3 )	moyen	spécifique (m²/g)	particules (MEB)
	Al nano	2,7	50 nm *	35-39 *	Sphère
	Al micro	2,7	12,3 µm	0,49 +/-0,02	Sphère
	Cire	1,02
	Dispersant	0,947

* données fabricant

Tableau 2 : caractéristiques rhéologiques du mélange Cire/Dispersant/Al micro %V en Al micro τ c (Pa

		)	K	n	R 2
	45	4,07312 0,69117 0,9992 0,99862
	37	2,0923 0,18194	1	0,99952
	22	0	0,12102	1	0,99973
	0	0	0,04856	1	0,99587

Le modèle Herschel-Bulkley est bien adapté (R²>0.99) pour l'ensemble des courbes. Quelque soit le volume occupé par l'aluminium micrométrique, l'indice de structure n reste constant et est à peu près égal à 1 et pour un pourcentage volumique inférieure à 22% la contrainte seuil est négligeable. Lorsque le volume en aluminium augmente (37 et 45%) une contrainte seuil assez faible apparaît. Pour les concentrations élevées en aluminium micrométrique le comportement rhéologique de ces mélanges correspond à comportement de Bingham. C'est-à-dire que, contrairement au modèle de Herschel-Bulkley, la viscosité devient indépendante de la vitesse de cisaillement après que la contrainte seuil soit dépassée. Pour des mélanges où la proportion volumique est élevée, la structure du mélange est telle que pour des cisaillements très faibles, des zones de contact intergranulaires peuvent se former et bloquer de façon éphémère le mouvement du fluide.

Différence de comportement entre l'aluminium nanométrique et micrométrique.

  Pour un mélange chargé à 34% en volume en aluminium nanométrique, la texture du mélange devient sableuse et les mesures rhéologiques deviennent difficilement réalisables (problème de remplissage du godet, incertitude sur les mesures trop importante). La démarche expérimentale fut donc d'étudier l'évolution du comportement rhéologique d'un mélange cire/dispersant/aluminium nanométrique en faisant varier progressivement la quantité d'aluminium nanométrique. Les rhéogrammes en fonction des différents pourcentages volumiques en aluminium nanométrique sont représentés figure 2.

		800
		700
		600
		500
										34 %
	τ (Pa)	300 400								27 % 13 % 10%
										7 %
		200
		100
		0
		0	100	200	300	400	500	600	700	800
						γ (s -1 )

  Alors que l'aluminium micrométrique présente des variations négligeables des paramètres rhéologiques (τ c , K et n), le comportement à l'écoulement des mélanges cire/dispersant/Al nano diffère au delà d'une fraction volumique en aluminium nanométrique supérieure à 10%. Les valeurs de contrainte seuil ou de consistance des mélanges chargés aluminium nanométrique peuvent s'expliquer de la façon suivante : l'aluminium nanométrique se présente sous forme d'agglomérat. Des mesures au granulomètre laser ont fait ressortir des tailles moyennes de particule de 64 µm pour l'entité nanométrique. Il s'agit en fait du diamètre d'un ensemble de particule représenté par une sphère. Lorsque des ultrasons sont appliqués, ce diamètre diminue mais la taille des particules d'aluminium nanométrique (50 nm) n'est pas détecté par l'appareil même pour un apport énergétique important en ultrason. L'aluminium nanométrique aura donc tendance à se trouver sous forme d'agglomérat même en présence d'un dispersant. Lorsque des particules sont agglomérées au sein d'une suspension, les agglomérats emprisonnent une certaine quantité de liquide. Ce liquide ne peut se déplacer librement : il se déplace avec les agglomérats comme si l'ensemble (particules agglomérées + liquide emprisonné) était un solide. Tout se passe donc comme si la suspension formée d'agrégats contenait moins de liquide que la quantité prévue, et plus de solide. Elle présente donc une contrainte seuil et une viscosité plus élevées, à concentration égale, qu'une suspension correctement dispersée. Evidemment des clichés au microscope électronique à transmission permettront ou non de vérifier l'hypothèse précédemment énoncée.


Stefano Langé
email: stefano.lange@polimi.it

Laura A Pellegrini

Paolo Stringari
email: paolo.stringari@mines-paristech.fr

Christophe Coquelet

EXPERIMENTAL DETERMINATION OF THE SOLID-LIQUID-VAPOR LOCUS FOR THE CH 4 -CO 2 -H 2 S SYSTEM AND APPLICATION TO THE DESIGN OF A NEW LOW-TEMPERATURE DISTILLATION PROCESS FOR THE PURIFICATION OF NATURAL GAS

The discovery of new natural gas reservoirs with high CO 2 and/or H 2 S content and the increasing energy demand compel industries to design new process solutions for the profitable exploitation of these kinds of gas reserves. Low temperature technologies have been studied to this purpose, showing higher performances and economic profitability when the CO 2 content in the natural gas stream is high. Since in low-temperature processes for natural gas upgrading a solid phase can be formed, experimental data are necessary to determine pressure, temperature and phase compositions when phase equilibrium involves the presence of a solid phase. In this way, it is possible to properly set up a model to predict the conditions for solid formation and define the optimal process operating conditions. Literature data for phase equilibria involving a solid phase in the CH 4 -CO 2 -H 2 S system are few. In this work experimental TPxy data have been obtained for defining the maximum temperature at which SLVE exists for different compositions of the CH 4 -CO 2 -H 2 S system. A proper experimental procedure has been designed to obtain these measurements and data have been compared with the results obtained with a suitable thermodynamic model. Moreover, an example of the application of these experimental data and their thermodynamic modeling to the validation of a new process for the low-temperature purification of natural gas is proposed. A preliminary assessment of the profitability of the proposed process solution in comparison with more traditional MDEA units, industrially used for the sweetening of natural gas, has been carried out.

Introduction

Natural gas is a resource that is widely used nowadays in different industrial sectors. Its main uses are related to the production of energy (38 %) and to the industrial sector (60 %) [START_REF] Bp | BP Energy Outlook 2030[END_REF]. In recent years, natural gas has started to be used also in the transportation sector, though this use just covers a small portion of the natural gas production [START_REF] Bp | BP Energy Outlook 2035[END_REF].

The global energy demand is expected to grow rapidly in the next twenty years. Primary energy consumption is expected to rise by 41% in 2035, with a great contribution coming from growing emerging economies. Among fossil fuels sources, natural gas demand is expected to have the most rapid growth [START_REF] Bp | BP Energy Outlook 2035[END_REF]. Recent studies about geographical distribution of remaining discovered gas reserves have demonstrated that 40% of the actual remaining natural gas reserves are sour and/or with high carbon dioxide content [START_REF] Carrol | New Challenges & Solutions in Designing Large Sour Gas Projects[END_REF][START_REF] Burgers | Worldwide Development Potential for Sour Gas[END_REF]. Carbon dioxide content can vary between 15 % and 70 % [START_REF] Burgers | Worldwide Development Potential for Sour Gas[END_REF] and the hydrogen sulfide concentration can reach 15 % [START_REF] Rojey | Natural Gas Production Processing Transport[END_REF]. Some examples of real gas fields compositions are given in Table 1. Kapuni (New Zeland) 43.8 - [START_REF] Rojey | Natural Gas Production Processing Transport[END_REF] Bearberry (Canada) 5 90 [START_REF] Scherbinin | Shell Experience in Sour Gas Fields[END_REF] Harweel Cluster (Oman) 20 5 [START_REF] Scherbinin | Shell Experience in Sour Gas Fields[END_REF] La Barge (USA) 65.9 5 [START_REF] Parker | CO2 Management at ExxonMobil's LaBarge Field[END_REF] Natural gas must be purified to commercial grade to be suitable for the market and for subsequent utilization. Several techniques are available for the upgrading of natural gas streams. Mostly physical absorption and chemical scrubbing with amine solutions have been widely applied for the purification of streams in the natural gas industry [START_REF] Kohl | Gas Purification[END_REF]. However, this latter technology is energy intensive, particularly when carbon dioxide content in the feed gas is high [START_REF] Swattanapong | Behavior of Reboiler Heat Duty for CO 2 Capture Plants Using Regenerable Single and Blended Alkanolamines[END_REF]. Typically, a limit value for the concentration of CO 2 , in the natural gas stream to be purified, that gives the trade-off between the purification by means of amine scrubbing and low-temperature processes is 20 mol% [START_REF] Lallemand | Highly Sour Gas Processing: H 2 S Bulk Removal With the Sprex Process[END_REF]. In this scenario, natural gas producers need new process solutions to allow the profitable exploitation of low quality hydrocarbon gas reserves, which, until some years ago, were not considered suitable for commercialization. The new process solutions for the natural gas upgrading must be able to remove carbon dioxide and hydrogen sulfide, together with other impurities, to meet commercial specification, while decreasing the overall production costs in comparison with more standard technologies [START_REF] Northrop | The CFZ TM process: A Cryogenic Method for Handling High-CO 2 and H 2 S Gas Reserves and Facilitating Geosequestration of CO 2 and Acid Gases[END_REF].

Several technologies have been proposed in literature for the low-temperature purification of natural gas: the Rectisol process [START_REF] Hochgesand | Rectisol and Purisol[END_REF], the Ryan-Holmes process [START_REF] Holmes | Pilot tests prove out cryogenic acid-gas/hydrocarbon separation processes[END_REF][START_REF] Holmes | Cryogenic distillative separation of acid gases from methane[END_REF][START_REF] Holmes | Distillative separation of carbon dioxide from light hydrocarbons[END_REF], the CFZ TM process [START_REF] Haut | Development and application of the controlled-freeze-zone process[END_REF][START_REF] Valencia | Method and apparatus for separating carbon dioxide and other acid gases from methane by the use of distillation and a controlled freeze zone[END_REF][START_REF] Valencia | Method and apparatus for cryogenic separation of carbon dioxide and other acid gases from methane[END_REF][START_REF] Valencia | Bubble cap tray for melting solids and method for using same[END_REF], the Cryocell ® process [START_REF] Amin | The Cryocell: an Advanced Gas-Sweetening Technology[END_REF], the Sprex ® process [START_REF] Lallemand | Highly Sour Gas Processing: H 2 S Bulk Removal With the Sprex Process[END_REF] and, recently, a new process based on a dual pressure distillation unit [START_REF] Pellegrini | Process for the removal of CO 2 from acid gas[END_REF]. Other applications of low-temperature processes are available also for the biogas upgrading, particularly the antisublimation process [START_REF]EReIE CRYO-PUR Project[END_REF] which operates around the atmospheric pressure. In all these low-temperature purification processes it is of paramount importance to properly assess the thermodynamic conditions at which a solid phase can appear.

To allow reliable process design and optimization, suitable thermodynamic models are needed. In the meantime experimental data are required to properly set up equations of state for phase equilibrium calculations. The development of accurate thermodynamic model is essential for the calculation of transport, heat and mass transfer properties. Since in low-temperature processes for natural gas upgrading a solid phase can be formed, experimental data are necessary to determine pressure, temperature and phase compositions of phase equilibria involving a solid phase, consisting mainly of CO 2 . In this way it is possible to properly set up a model to predict the conditions for solid formation and choose the optimal process operating parameters, depending on the adopted technology. Literature data for the binary CO 2 -CH 4 [START_REF] Donnelly | Phase Equilibria in the Carbon Dioxide-Methane System[END_REF][START_REF] Davis | Solid-Liquid-Vapor Phase Behavior of the Methane-Carbon Dioxide System[END_REF][START_REF] Im | Phase Equilibrium of Carbon Dioxide and Light Paraffins in Presence of Solid Carbon Dioxide[END_REF][START_REF] Shen | Determination of CO 2 Solubility in Saturated Liquid CH 4 + N 2 and CH 4 + C 2 H 6 Mixtures above Atmospheric Pressure[END_REF][START_REF] Cheung | Solubility of Carbon Dioxide and Hydrogen Sulfide in Liquid Hydrocarbons at Cryogenic Temperatures[END_REF][START_REF] Boyle | Solid-Liquid Equilibrium Data Collection[END_REF][START_REF] Brewer | Freezing Points of Binary Mixtures of Methane[END_REF][START_REF] Sterner | Phase Equilibria in the CO 2 -Methane Systems[END_REF][START_REF] Knapp | Solid-Liquid Equilibrium Data Collection[END_REF][START_REF] Streich | N 2 Removal from Natural Gas[END_REF][33][START_REF] Brady | Water-Hydrocarbon Liquid-Liquid-Vapor Equilibrium Measurements in 530 Degrees F[END_REF][START_REF] Sparks | Water Content of NGL in Presence of Hydrates[END_REF], CO 2 -H 2 S [START_REF] Sobocinski | Heterogeneous Phase-Equilibria of the Hydrogen Sulfide-Carbon Dioxide System[END_REF][START_REF] Chapoy | Vapour-Liquid Equilibrium Data for the Hydrogen Sulphide (H 2 S) + Carbon Dioxide (CO 2 ) System at Temperatures from 258 to 313[END_REF] and CH 4 -H 2 S [START_REF] Kohn | Heterogeneous Phase Equilibria of the Methane-Hydrogen Sulfide System[END_REF][START_REF] Cheung | Solubility of Carbon Dioxide and Hydrogen Sulfide in Liquid Hydrocarbons at Cryogenic Temperatures[END_REF] system are available to define the PT, the Tx or the Ty diagrams for SLE, SVE or SLVE loci. On the contrary, experimental data for phase equilibria involving a solid phase in the CH 4 -CO 2 -H 2 S ternary system are few and almost only PT data [START_REF] Robinson | The Behavior of CH 4 -CO 2 -H 2 S Mixtures at Subambient Temperatures[END_REF][START_REF] Théveneau | Recherche de la température de formation d'une phase solide pour cinq systèmes méthane -dioxyde de carbone -sulfure d'hydrogène[END_REF].

The aim of this work is to provide experimental TPxy data for defining the maximum temperature at which SLVE exists for different compositions of the CH 4 -CO 2 -H 2 S system. A proper experimental procedure, based on a synthetic non-visual technique, has been designed to allow these measurements. The procedure has been validated against available experimental data for the SLV locus of the binary CH 4 -CO 2 mixture and subsequently applied to the study of the SLV loci of the ternary system. The obtained experimental results have been used to tune the thermodynamic model parameters and the results have been applied to the validation of the optimized process layout of the dual-pressure low-temperature distillation process [START_REF] Pellegrini | Process for the removal of CO 2 from acid gas[END_REF]. A preliminary assessment of the profitability of the studied process solution, in comparison with more traditional MDEA units, has been carried out by defining a proper merit index function that describes the trade-off between the two technologies in terms of energy costs, depending on the geographic area where the gas reserve is located.

Apparatus

The equipment used in this study is similar to the one developed by Baba Ahmed and De

Stefani [START_REF] Stefani | Experimental Determination of Carbon Dioxide and Nitrous Oxide Co-Solubility in Liquid Oxygen[END_REF][START_REF] Stefani | Solubility Measurements for Carbon Dioxide and Nitrous Oxide in Liquid Oxygen at Temperatures Down to 90[END_REF] and used by Courtial et al. for GPA project 052 developed for solubility measurement of CO 2 into liquid oxygen in static analytic mode [START_REF] Courtial | Research Report 219 -Methanol Distribution (as a contaminant) in Fractionation Products and Freeze Out Boundaries[END_REF]. For this study, the equipment and experimental procedure were modified. The experimental facility used in this work is presented into two configurations (Fig. 1): a first one (Fig. 1a) used for the determination of the SLV locus of the CH 4 -CO 2 binary mixture and a second one (Fig. 1b) adapted to perform the same kind of experiments on the ternary CH 4 -CO 2 -H 2 S system. The binary mixture has been considered in order to design the experimental procedure and to test its reliability against the literature available experimental data. The equilibrium cell is heated by means of an electric resistance, regulated by a Fuji electric PXR PID temperature controller. The cell is inserted in a liquid nitrogen cryostat. The mixing in the cell is provided by means of a magnetic stirrer. A 16

MPa PTX611 Druck pressure transducer is used to measure the internal pressure and two platinum probes are used to measure the temperatures in the upper and lower part of the cell.

Capillary samplers (ROLSI TM , Armines' Patent) are used for sampling the mixture that is sent through a temperature-controlled transfer line to the gas chromatograph for the composition analysis. The samplers' capillaries and the pressure transducer tube are insulated and heated by a temperature regulator to avoid solidification and condensation during operations, since otherwise they are exposed to the nitrogen vapor from the cryostat. The pressure in the feed line is measured by means of a 20 MPa PTX611 Druck pressure transducer. In the configuration used for the ternary system investigation, two gas reservoirs have been used to charge the methane/carbon dioxide mixture and the hydrogen sulfide. The purge system is equipped with a vacuum pump. For experiments involving H 2 S, a nitrogen line has been installed to clean the equipment and the purge line is connected to a column containing a saturated solution of NaOH and provided with a magnetic stirrer. The acquisition system and the gas chromatograph are connected to a computer for data collection. The gas chromatograph is a Perichrom PR 2100 type and the column is a Porapak Q, 80/100 mesh, 1/8" external diameter and 2 mm internal diameter made in Silcosteel. The composition is determined by means of the analysis of samples using a carefully calibrated Thermal Conductivity Detector (TCD).

Liquid Nitrogen (LN2) LN2 CO2/CH4 V 1 V 6 Vacuum pump V 3 V 2 Cryostat V 5 V 4

Temperature probes

Gas chromatograph Acquisition 20 MPa Transducer 16 MPa transducer

E C V 10 Rolsi TM samplers CO2/CH4 reservoir Purge H2S V 8 H2S reservoir 7 V N2 purge V 9 NaOH Liquid Nitrogen (LN2) LN2 CH4 V 1 V 6 Vacuum pump V 3 V 2 Cryostat V 5 V 4

Temperature probes

Gas chromatograph Acquisition 20 MPa Transducer 16 MPa transducer

E C V 8
Rolsi TM samplers CO2 Purge

Materials

Methane (CAS: 74-82-8) has been supplied by Messer, with a purity of 99.995 vol%. Carbon dioxide (CAS: 124-38-9) and hydrogen sulfide (CAS: 7783-6-4) have been supplied by Air

Liquide, with a purity of 99.995 and 99.5 vol% respectively. For the experiments with the ternary mixture, two gas cylinders of a binary CH 4 -CO 2 mixture have been used to keep constant the ratio between the number of moles of methane and carbon dioxide in the global composition at different mol% of hydrogen sulfide. The supplier of these cylinders is Air Liquide and the content of carbon dioxide is 70 and 40 mol% (as specified by the supplier) at 41 and 65 bar respectively.

Calibrations

The 16 MPa PTX611 Druck pressure transducer has been calibrated using a GE PACE5000 automated pressure indicator as reference. The pressure range used for calibration is 1-67 bar (calibration uncertainty u(P) = 0.1 kPa). The temperature sensors have been calibrated for reproducing the triple point [START_REF] Huber | NIST Standard Reference Database 23, Reference Fluid Thermodynamic and Transport Properties-REFPROP, Version 9.0[END_REF] of CO 2 , N 2 O and R134a, to cover all the temperature range used for SLV measurement. The temperature range used from calibration is 169.85 K-216.59 K (calibration uncertainty u(T) = 0.015 K). The composition analysis has been carried out using a TCD to determine the composition of both liquid and vapor phases. The TCD has been calibrated correlating the peak surface of the output signal to the known amount of moles supplied to the injector through an Evol XR electronic automated syringe. The maximum calibration uncertainties for the vapor phase mole fractions are u(y, k = 2): 0.011 for CH 4 , 0.011 for CO 2 and 0.009 for H 2 S and maximum calibration uncertainties for the measurements of the liquid phase mole fractions are u(x, k = 2): 0.009 for CH 4 , 0.018 for CO 2 and 0.017 for H 2 S.

Experimental procedures

Firstly the equilibrium cell is loaded to obtain a desired global composition. The magnetic stirrer is turned on to avoid diffusivity effect. Once the equilibrium cell is loaded, the cryostat is filled with liquid nitrogen for the half of its volume, to avoid the contact between the metallic part of the equipment and the liquid nitrogen. The temperature of the cell is decreased 5 °C to 10 °C lower than the estimated triple point of the mixture.

During the cooling step, when solid CO 2 starts to form, a change in the slope of the pressure vs.

temperature in the cell can be noticed. Once the set temperature is achieved and system temperature and pressure are stable, the system is heated up. The regulation can be difficult due to the high temperature difference between the cell and the boiling liquid nitrogen in the cryostat.

The heating rate plays a significant role in the determination of the triple point where the solid decomposition occurs. High heating rates take the system to be overheated, with a consequent shift in the effective triple point. Moreover dynamic effects during heating may occur. In this way a step procedure is preferable, since it lets the system to evolve through equilibrium conditions.

The number of steps must be properly selected to allow the triple point calculation. In general it is a good practice to select a 10 °C range across the desired triple point and perform steps every 1 °C. Stable conditions for the system at each step must be assured. Every ramp lasts 30 min and each temperature soak is maintained for 1 h. In this way also the heating rate during each ramp is low and dynamic effects are minimized during temperature step changes. This procedure is equal to a slow heating (Fig. 2), but it is more controllable since, under dynamic conditions, the slow heating can be achieved only when the liquid nitrogen level in the cryostat is high. The sensitivity of the system to the dynamics of the boiling liquid nitrogen is high. High levels of liquid nitrogen allow slow heating, but, as the level decreases, it is not possible to properly control the heating rate anymore. Collected temperatures and pressures in the cell are used to determine the equilibrium temperature and pressure on each soak. The temperature considered is the average between the temperatures measured on the top and on the bottom of the cell. The average value of temperature and pressure are reported on a PT diagram and two linear regressions are performed across the slope change in the PT trend. The triple point is then calculated as the intersection between the two lines (Fig. 2b). Once determined, the temperature is brought down, close to the triple point (typically 0.5 °C higher to avoid possible solid formation). Composition analysis can be performed once the system reaches stable conditions and temperature and pressure are close to the triple point.

The repeatability of the measurements and the rigorous check of the system effective equilibrium conditions have been checked by performing different sampling campaigns (at stable temperature and pressure) for both the liquid and vapor phases composition analysis for the same equilibrium point several times and at different periods during the day.

For the loading of the ternary mixture in the cell, first H 2 S is loaded or directly into the cell at a pressure lower than the vapor pressure at atmospheric conditions, or, if necessary, by means of the H 2 S reservoir. The number of added moles can be calculated and so, knowing the pressure of the binary CO 2 -CH 4 gas cylinders, the mixture reservoir volume and the ambient temperature, the correct number of moles of the binary mixture can be added in the cell to obtain per each cylinder four points at 20 mol%, 15 mol%, 10 mol% and 5 mol% of H 2 S in the global composition.

Experimental results

Validation of the procedure on the CH 4 -CO 2 SLV locus

The obtained results for the TPxy measurements on the SLV locus of the CH 4 -CO 2 mixture are reported in Figures 345. The estimated uncertainties (U), calculated according to the standards [START_REF] Taylor | Guidelines for evaluating and expressing the uncertainty of NIST measurement results[END_REF][START_REF] Stringari | Study OF Factors Influencing Equilibrium and Uncertainty in Isochoric Hydrate Dissociation Measurements[END_REF], for the measured solid dissociation points is U(T, k = 2) = 0.11 K and U(P, k = 2) = 10.6 kPa, while for the vapor and liquid phase compositions the maximum uncertainties have been presented in section 4. To test the reliability of the studied procedure, results obtained for the binary methane-carbon dioxide mixtures have been compared to literature data and to results obtained with the Yokozeki equation of state [START_REF] Yokozeki | Analytical Equation of State for Solid-Liquid-Vapor Phases[END_REF] with the parameters presented in reference [START_REF] Stringari | An Equation of State for Solid-Liquid-Vapor Equilibrium Applied to Gas Processing and Natural Gas Liquefaction[END_REF]. The thermodynamic model will be discussed in the next section. [START_REF] Davis | Solid-Liquid-Vapor Phase Behavior of the Methane-Carbon Dioxide System[END_REF] are more reliable than the ones by Donnelly and Katz (1954) [START_REF] Donnelly | Phase Equilibria in the Carbon Dioxide-Methane System[END_REF], which show a significant deviation from the main data trend.

Application of the procedure on the TPxy measurements on the SLV locus of the CH 4 -CO 2 -H 2 S system

The results obtained for the CO 2 -CH 4 mixture have demonstrated the feasibility and the reliability of the procedure. The method has been applied to the ternary mixture to study the shape of the SLV locus. The results of the experimental study for the ternary CH 4 -CO 2 -H 2 S mixtures are reported in Figures 678. The maximum uncertainty on the measured solid dissociation temperature is U(T, k = 2) = 0.19 K and the one for the pressure is U(P, k = 2) = 12.7 kPa. The maximum uncertainties of the vapor and liquid phase compositions have been discussed in section 4. Fig. 6 shows the temperatures and pressures at which the measurements have been carried out with respect to pure components and binary mixtures phase boundaries. Results related to TPxy data have been discussed by comparison with the thermodynamic model results. In the system methane-hydrogen sulfide a quadruple point is present and, moreover, a liquid-liquid-vapor and a solid-liquid-liquid loci are present. This introduces the possibility of a quadruple point line, a solid-liquid-liquid and a liquid-liquid vapor surfaces in the system. Moreover, the binary carbon dioxide-hydrogen sulfide system presents a eutectic point in the solid liquid vapor locus. These complex behaviors may occur also in the ternary system.

The obtained experimental data falls in a region of T and P away from the one where complex phase behavior may occur. From the graphs (Fig. 78), it can be noticed that the measured points are really the triple points of the ternary mixture. For these points the phase diagram is quite simple.

Thermodynamic model

The and CH 4 -H 2 S.The detailed description of the model can be found in literature [START_REF] Stringari | An Equation of State for Solid-Liquid-Vapor Equilibrium Applied to Gas Processing and Natural Gas Liquefaction[END_REF][START_REF] Riva | Solid-Liquid-Vapor Equilibrium Models for Cryogenic Biogas Upgrading[END_REF].

Calculations of phase equilibria are performed using a Fortran routine for the Gibbs free energy minimization. For the binary CH 4 -CO 2 mixture the model has been already validated against experimental data [START_REF] Stringari | An Equation of State for Solid-Liquid-Vapor Equilibrium Applied to Gas Processing and Natural Gas Liquefaction[END_REF][START_REF] Riva | Solid-Liquid-Vapor Equilibrium Models for Cryogenic Biogas Upgrading[END_REF]. Pure compound thermophysical properties have been taken from NIST (REFPROP 9) [START_REF] Huber | NIST Standard Reference Database 23, Reference Fluid Thermodynamic and Transport Properties-REFPROP, Version 9.0[END_REF], while pure compound parameters for the EoS have been taken from literature for CO 2 and CH 4 [START_REF] Stringari | An Equation of State for Solid-Liquid-Vapor Equilibrium Applied to Gas Processing and Natural Gas Liquefaction[END_REF], while for H 2 S they have been obtained by regression, according to [START_REF] Stringari | An Equation of State for Solid-Liquid-Vapor Equilibrium Applied to Gas Processing and Natural Gas Liquefaction[END_REF], against auxiliary values (obtained using REFPROP 9 [START_REF] Huber | NIST Standard Reference Database 23, Reference Fluid Thermodynamic and Transport Properties-REFPROP, Version 9.0[END_REF]) for the VLE, SLE and SVE of the pure compound. The considered objective function is:

𝐴𝐴𝐷% = 100 𝑁𝑃𝑇 𝑒𝑞 𝑃 𝑗 ,𝑒𝑞 𝑐𝑎𝑙𝑐 -𝑃 𝑗 ,𝑒𝑞 𝑒𝑥𝑝 𝑃 𝑗 ,𝑒𝑞 𝑒𝑥𝑝 𝑁𝑃𝑇 𝑒𝑞 𝑗 =1 𝑒𝑞 = 𝑆𝑉𝐸, 𝑉𝐿𝐸, 𝑆𝐿𝐸 (1)
The highest value of the AAD% is about 8.6 % for the solid-vapor branch of the H 2 S PT diagram.

The values of the binary interaction parameters for the CH 4 -H 2 S and CO 2 -H 2 S mixtures have been obtained by regression considering literature available experimental data. For the CH 4 -H 2 S system VLE [START_REF] Kohn | Heterogeneous Phase Equilibria of the Methane-Hydrogen Sulfide System[END_REF][START_REF] Reamer | Phase Equilibria in Hydrocarbon Systems[END_REF][START_REF] Coquelet | Phase Equilibrium Data for the Hydrogen Sulphide + Methane System at Temperatures from 186 to 313 K and Pressures up to About 14 MPa[END_REF], SLE [START_REF] Cheung | Solubility of Carbon Dioxide and Hydrogen Sulfide in Liquid Hydrocarbons at Cryogenic Temperatures[END_REF] and LLE [START_REF] Coquelet | Phase Equilibrium Data for the Hydrogen Sulphide + Methane System at Temperatures from 186 to 313 K and Pressures up to About 14 MPa[END_REF] experimental data have been considered , while for the binary CO 2 -H 2 S system SLVE experimental data [START_REF] Sobocinski | Heterogeneous Phase-Equilibria of the Hydrogen Sulfide-Carbon Dioxide System[END_REF] have been used for parameters regression. The agreement between model results and considered experimental data for the former binary system is good, while for the latter system a good representation of the liquidus curve and a less accurate representation of the solid-vapor curve have been obtained on the SLV locus. Due to the less accuracy in binary interaction parameters for the representation of the SLV locus of the CO 2 -H 2 S system, the eutectic point [START_REF] Sobocinski | Heterogeneous Phase-Equilibria of the Hydrogen Sulfide-Carbon Dioxide System[END_REF] is overestimated in terms of temperature and pressure. In this way, its solid-solid-liquid line (Fig. 6), which starts from the eutectic point, is shifted at higher temperatures. For the process validation (see next section) this is not a problem, since the overestimation of the CO 2 -H 2 S eutectic point, in terms of temperature and pressure, let the model to be more conservative. The binary interaction parameters have been obtained by minimizing the following objective function:

𝑓 𝑜𝑏𝑗 = 1 𝑁𝑃𝑇 𝑥 𝑗 𝑐𝑎𝑙𝑐 -𝑥 𝑗 𝑒𝑥𝑝 𝑁𝑃𝑇 𝑗 =1 (2)
where x is the mole fraction of the lighter compound of the binary mixture in each phase at equilibrium. The agreement between the experimental data and the model results for the ternary system is shown in Figure 9. The agreement between calculated and experimental data is quite good and values of AAD%s are less than 7%.

Application to the low-temperature distillation process

The new process for the low-temperature purification of natural gas has been studied at Politecnico di Milano [START_REF] Pellegrini | Process for the removal of CO 2 from acid gas[END_REF]. The process is based on a dual pressure (approximately 40/50 bar) low-temperature distillation operation, designed to bypass the SLV locus of the CH 4 -CO 2 binary mixture through a proper thermodynamic pathway. In this work an optimized process layout has been taken into account (Fig. 10). The gas stream to be purified ( 1) is fed to the high pressure (HP) section T-1 at its dew point; in this first part of the distillation unit, the natural gas feed is separated into two streams: a bottom one (2) with a high CO 2 content and a top product flow (3) rich in methane. The top product stream (3) from the HP section is split into two streams: the first one (3h) is heated (4h) and expanded (5h) to the low pressure (LP) section pressure; the second one (3c) is cooled (4c) so that after expansion it is at its bubble point at 40 bar (5c). The superheated gas stream is fed at the bottom of the LP section while the liquid feed is sent few theoretical trays above the bottom of the LP section. In the LP distillation section a top product methane gas stream at commercial grade is obtained, while the bottom liquid stream (6) rich in methane is pumped back to the HP section (stream 7) to provide the reflux.

The condenser is a full-reflux condenser and the top product stream ( 8) is obtained as gas.

The rationale of the process to avoid the solid CO 2 formation is the bypass of the maximum of the SLV locus of the methane-carbon dioxide system.

In the HP section the separation is limited by the critical point of the mixture, that does not allow to reach the commercial grade for the methane stream. So the mixture must be depressurized To avoid the frosting of carbon dioxide at the inlet of the LP section, the stream must be heated at 50 bar before expansion. The limiting condition to frosting is the dew point of stream 5h at 40 bar. For safety reasons, it is suggested to keep the temperature of this stream 5-6 K over its dew point at 40 bar, without forming a solid phase. In this way the presence of dry ice is avoided in all the parts of the process. From the top of the LP section, a methane stream at commercial specification is obtained, while the bottom liquid stream rich in methane is pumped back to 50 bar and sent to the top of the HP section few theoretical trays over the feed tray. To avoid the freezing at the outlet of the LP section, the CO 2 content in this stream must be kept at about 8 mol%, so that the LP section of the distillation unit operates in the liquid-vapor region under the low-temperature triple point at 40 bar.

The process has been studied using the commercial process simulator Aspen Hysys ® v7.3 [START_REF]Aspen HYSYS ®[END_REF].

The feed stream has a CO 2 content from 5 to 65 mol% and a hydrogen sulfide content from 0 to 15 mol% per each value of the CO 2 mole fraction. The methane content in the feed stream is the balance. The composition range has been defined in order to cover the largest possible field of real gas compositions, to better assess the performances of the proposed solution in different existing cases.

As process specifications, the methane content in the HP section bottom stream (2) has been fixed at 0.01 mol%, to enhance the hydrocarbon recovery of the process unit, while for the purity of the produced gas (stream 8) classical specifications for H 2 S and CO 2 contents in pipelinequality gas have been adopted [START_REF] Northrop | The CFZ TM process: A Cryogenic Method for Handling High-CO 2 and H 2 S Gas Reserves and Facilitating Geosequestration of CO 2 and Acid Gases[END_REF][START_REF] Mokhatab | Handbook of Natural Gas Transmission and Processing[END_REF].

To show the potentiality of the thermodynamic study previously illustrated for the design and validation of low-temperature distillation process, the thermodynamic model validated against obtained and literature experimental data has been used to draw SLE lines for the ternary system at fixed contents of hydrogen sulfide in the global composition. Since under 50 bar solidification occurs at triple point and its simple graphical representation may be difficult for ternary systems, an alternative procedure has been adopted. Considering the slope of the SLE curves of pure compounds it is possible to notice that it is highly steep: small variations of temperature can lead to high variations of pressure. Moreover, the phase behavior of condensed phases is not strongly influenced by the pressure in the range of medium-low pressures. Therefore, to check the possible formation of a solid phase in the process involving ternary mixtures, the SLE diagram at 50 bar has been used, with a liquid phase having hydrogen sulfide contents from 0 up to 15 mol% as considered in the gas feed stream of the studied process. Column liquid phase composition profiles normalized on their H 2 S contents have been plotted against SLE curves (Fig. 11) to check possible crosses with the solid-liquid equilibrium lines. It has to be pointed out that the hydrogen sulfide mole fraction varies, tray by tray, in the two sections of the distillation units. Results show that no intersection between SLE lines and distillation curves occurs. Moreover, the process lines do not cross the SLE locus of pure CH 4 -CO 2 system as well, remaining far away from freezing conditions in both the HP and LP sections. Moreover, the eutectic behavior of the system is highlighted. At high contents of hydrogen sulfide, the SLE lines become representative of a SLLE line (dashed).

The profiles along the LP section of the process are close to these lines, however the amount of H 2 S in the liquid phase in this section of the process is really small (since the biggest part of H is removed in the HP section); indeed no liquid-liquid immiscibility occurs in this part of the process. No solid phase is formed in the presence of hydrogen sulfide in the process gas feed.

It is possible to build a merit-index function to show the profitability of the low-temperature process respect to more traditional MDEA units [START_REF] Pellegrini | A New Cryogenic Technology for Natural Gas Sweetening[END_REF]. The details of a preliminary technoeconomic evaluation can be found elsewhere [START_REF] Langè | Purification of Natural Gas by means of a New Low Temperature Distillation Process[END_REF]. The comparison has been carried out in terms of energy expenses for the two processes, showing the relative trade-off between the two technologies depending on the geographic area where the gas reserve is located. The breakeven point is established depending on the ratio between the price of the fuel gas and the price of electricity (Fig. 12): fuel gas is used to produce steam for MDEA regenerator reboiler, while electric energy is consumed to drive the compressors of the refrigeration cycle for the lowtemperature purification process. and the presence of these substances may influences the phase behavior of natural gas mixtures.

As future developments for this work, new experimental investigations will be done to study the effect of the mentioned compounds on the ternary system object of this work, in order to better understand the complex phase behavior of mixtures of interest for the natural gas industry in a large region of temperatures and pressures and to better investigate the proposed process solution for the purification of real gas streams, considering all the components of a typical natural gas feed.

Figure 1 .

 1 Figure 1. Flow diagram of the equipment used for a) TPxy solid apparition measurements for the CH 4 -CO 2 system and b) TPxy solid apparition measurements for the CH 4 -CO 2 -H 2 S system.

Figure 2 .

 2 Figure 2. a) Definition of the experimental procedure and b) example of triple point calculation from PT data.

Figure 3 .

 3 Figure 3. Comparison among literature data for the TP SLV locus of the CH 4 -CO 2 mixture, experimental data obtained in this work and results obtained with the Yokozeki EoS [49] for SLV calculation.

Figure 4 .

 4 Figure 4. Comparison among literature data for the Tx SLV locus of the CH 4 -CO 2 mixture, experimental data obtained in this work and results obtained with the Yokozeki EoS [49] for SLV calculation.

Figure 5 .

 5 Figure 5. Comparison among literature data for the Ty SLV locus of the CH 4 -CO 2 mixture, experimental data obtained in this work and results obtained with the Yokozeki EoS [49] for SLV calculation.

Figure 6 .

 6 Figure 6. PT projections of the CH 4 -CO 2 , CO 2 -H 2 S and CH 4 -H 2 S systems with experimental TP measurements for the CH 4 -CO 2 -H 2 S system. : experimental data obtained in this work; : SLV locus of the binary CH 4 -CO 2 system; : SLV and SSL loci of the binary CO 2 -H 2 S system; : SLV, VLL, SLL, SSL and lowtemperature critical line of the binary CH 4 -H 2 S system; : PT diagram of pure CH 4 ; : PT diagram of pure CO 2 ; : PT diagram of pure H 2 S.

Figure 7 .Figure 8 .

 78 Figure 7. Phase equilibrium for the CH 4 +CO 2 +H 2 S system. The graphs from a) to d) show the evolution of the phase diagram when progressive amounts of H 2 S are added to a mixture of CH 4 +CO 2 with a mole ratio of about 0.4/0.6. : experimental tie line for the ternary CH 4 -CO 2 -H 2 S mixture; : global composition and -: model results. From a) to d) the H 2 S molar fraction in the global composition is about: 0.20, 0.15, 0.10 and 0.05 respectively.

Figure 9 .

 9 Figure 9. Model performances (Yokozeki, 2003 with binary interaction parameters obtained in this work) for the prediction of SLV composition for the ternary CH 4 -CO 2 -H 2 S mixture.

Figure 10 .

 10 Figure 10. Process flow diagram for the new low-temperature distillation process [21].

  slightly under the critical pressure of pure methane, avoiding huge recompression costs. At 50 bar the SLE and the VLE surfaces are completely divided, thus no solidification during distillation operation may occur. Solidification inside distillation units can occur only at triple point. During the cooling at 50 bar of the split part of stream 3 (HP section top product) the SLE is never crossed, so the operation is performed without freezing of the mixture. On the other hand, stream 4c arrives at 40 bar without crossing the SLV locus during the expansion. The part of stream 3 that goes to the intermediate heat exchanger (stream 3h) cannot be fed to the LP section without superheating, otherwise the produced stream at 40 bar can form a solid phase in the solid-vapor region at 40 bar.

Figure 11 .

 11 Figure 11. SLE lines at 50 bar for the ternary CH 4 -CO 2 -H 2 S system and check of the possible formation of a solid phase in the process involving the ternary system.

Figure 12 .

 12 Figure12. Breakeven point loci obtained as functions of costs of gas and electricity, and the acid gas contents in natural gas. Trade-off for different geographic areas is highlighted.

Table 1 .

 1 H 2 S and CO 2 contents in some natural gas fields

	Field	CO 2 [vol%] H 2 S [vol%] Reference
	Lacq (France)	9.3	15.3	[5]
	Uch (Pakistan)	46.2	-	[5]

  thermodynamic model used to describe experimental data for both binary CH 4 -CO 2 and ternary CH 4 -CO 2 -H 2 S mixtures is based on the Yokozeki EoS (2003) for SLV calculations [48-

49] (Eq. 1). The model has been set up for this work according to the procedure described by

Stringari et al. (2014)

[START_REF] Stringari | An Equation of State for Solid-Liquid-Vapor Equilibrium Applied to Gas Processing and Natural Gas Liquefaction[END_REF]

for both pure compounds and binary mixtures of CH 4 -CO 2 , CO 2 -H 2 S

Conclusions

In this work experimental TPxy data have been obtained for defining the maximum temperature at which SLVE exists for different compositions of the CH 4 -CO 2 -H 2 S system. A proper experimental methodology, based on a synthetic non-visual technique, has been developed. The procedure has been validated performing TPxy measurements on the SLV locus of the binary CH 4 -CO 2 mixture and comparing the obtained results with literature available data.

The obtained experimental results have been used to properly check the reliability of the Yokozeki SLV EoS applied to ternary mixtures of CH 4 -CO 2 and H 2 S, used in this work for the thermodynamic modeling. The model has been used to design phase diagrams and SLE lines for the ternary system. The obtained results have been applied for the thermodynamic validation of a new low-temperature distillation process for the purification of natural gas. This work highlights the importance and the effectiveness of the thermodynamic work applied to process design and simulation and the potential of coupling the two approaches to solve industrial problems: the obtained experimental data have been of paramount importance to properly investigate the reliability and the performances of the Yokozeki SLV EoS applied to mixtures of interest for natural gas. Complex phase behaviors, like the presence of a eutectic point in the SLE lines, have been shown. Improvements made on the thermodynamic model of these systems have been fundamental to properly investigate the possibility of solid phase formations in a low-temperature distillation process for the purification of natural gas, allowing the rigorous check on freeze-out problems in the system. The comparison of column liquid phase composition profiles, calculated from process simulations, and the obtained SLE lines has shown that no solid phase is formed at process operating conditions, demonstrating that the process is able to purify, to commercial


Mojdeh Rastgoo

Guillaume Lemaître

Joan Massich

Olivier Morel

Franck Marzani

Rafael Garcia
email: rafael.garcia@udg.edu

Fabrice Meriaudeau

Guillaume Lemaitre

Tackling the Problem of Data Imbalancing for Melanoma Classification

Keywords: IMBALANCED, CLASSIFICATION, MELANOMA, DERMOSCOPY

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

INTRODUCTION

Malignant melanoma is the deadliest type of skin cancer, accounting for the vast majority of skin cancer deaths (American-Cancer-Society, 2014). According to latest reports, melanoma causes over 20,000 deaths annually in Europe [START_REF] Forsea | Melanoma incidence and mortality in europe: new estimates, persistent disparities[END_REF]. In 2014, the American Cancer Society also reported that the number of new diagnosed cases is 76,100 with 9710 estimated deaths (American-Cancer-Society, 2014). Nevertheless, melanoma is the most treatable kind of cancer if diagnosed early.

Melanoma is clinically diagnosed through visual inspection and deep analysis of the lesion, using clinical imaging techniques such as dermoscopic imaging. The clinical diagnosis of early stage melanoma is commonly based on the "ABCDE" rule [START_REF] Abbasi | Early diagnosis of cutaneous melanoma: revisiting the abcd criteria[END_REF], defined as Asymmetry, irregular Borders, variegated Colors, Diameters greater than 6 mm and its Evolution over time. These inspections and analysis are challenging since, first different lesions such as melanoma and dysplastic nevi share similar characteristics in terms of "ABCD" and second the necessity to perform patient follow-up over the years. Therefore, the research communities have dedicated their efforts to develop computerized lesion analysis algorithms for classification of melanoma lesions.

When studying skin lesions, akin to other medical applications, the percentage of malignant cases is far less when compared with benign cases. This problem is frequently referred as "class imbalance" problem [START_REF] Prati | Data mining with imbalanced class distributions: concepts and methods[END_REF] and has been encountered in multiple areas such as telecommunication managements, bioinformatics, fraud detection, and medical diagnosis. Imbalanced data substantially compromises the learning process since most of the standard machine learning algorithms expect balanced class distribution or an equal misclassification cost [START_REF] He | Learning from imbalanced data[END_REF].

Medical data are prone to such drawbacks due to the fact that the portion of diseased samples or patients is far lower than healthy cases. Furthermore, the detection and classification of minority malignant cases are highly essential so that the Sensitivity (SE) of developed algorithms need to be maximized. Consequently, the problem of imbalanced data is usually addressed by employing different techniques which do not impair the topology of the data. Despite the fact that classification of malignant melanoma has been extensively studied (Rastgoo et al., 2015a), up to our knowledge, only few works tackled the issue implied by imbalanced dataset [START_REF] Barata | Two systems for the detection of melanomas in dermoscopy images using texture and color features[END_REF][START_REF] Celebi | A methodological approach to the classification of dermoscopy images[END_REF]. Barata et al. generate new synthetic samples by adding a Gaussian noise with fixed parameters to the samples belonging to the minority class [START_REF] Barata | Two systems for the detection of melanomas in dermoscopy images using texture and color features[END_REF]. Celebi et al. and Capdehourat et al. over-sampled their dataset using Synthetic Minority Over-sampling TEchnique (SMOTE) [START_REF] Chawla | Smote: synthetic minority oversampling technique[END_REF] to improve the SE of their algorithm [START_REF] Celebi | A methodological approach to the classification of dermoscopy images[END_REF][START_REF] Capdehourat | Pigmented skin lesions classification using dermatoscopic images[END_REF].

This paper provides an insight to the specific problem of classification of imbalanced dataset for malenoma. To proceed, we review different techniques proposed by the machine learning community and compile a comprehensive quantitative evaluation. The rest of this paper is organized as follows: an overview of the classification framework designed to investigate data balancing techniques is presented in Sect. 2. The balancing strategies are explained in depth in Sect. 3 and the validation and classification are discussed in Sect. 4. A quantitative evaluation is discussed in Sect. 5 followed by a concluding section.

MATERIAL AND METHODS

Figure 4 illustrates and summarizes the experiment designed to explore the data imbalance problem during the classification of dermoscopic images. The experimentation is based on the works presented in (Rastgoo et al., 2015a[START_REF] Rastgoo | Ensemble approach for differentiation of malignant melanoma[END_REF] and follows a cross-validated classification evaluation framework. Details of the dataset used for the experiments are given in Sect. 2.1. The extracted features correspond to the highest performing subset of features according to the latter mentioned studies and are presented in Sect. 2.2.

Dataset

In order to allow future comparisons, we choose to work with the only public dermoscopic dataset PH 2 [START_REF] Barata | Two systems for the detection of melanomas in dermoscopy images using texture and color features[END_REF]. This dataset is acquired at Dermatology Service of Hospital Pedro Hispano, Matosinhos, Portugal [START_REF] Barata | Two systems for the detection of melanomas in dermoscopy images using texture and color features[END_REF] with Tuebinger Mole Analyzer system with a magnification of 20×. The 8-bits RGB color dermoscopic images were obtained under the same conditions with a resolution of 768 px × 560 px. This dataset contains 200 dermoscopic images divided into 160 benign and dysplastic and 40 melanoma lesions. In terms of Ground Truth (GT), histological diagnosis and segmentation of the lesions are provided.

Due to an imbalance limitation of one of the techniques here studied, the experimentation is conducted on a data subset with an imbalance ratio of 1:3. Thus, the subset is composed of 39 melanoma and 117 benign and dysplastic lesions, randomly selected. Figure 1 shows three samples of this dataset, representing melanoma, dysplastic, and benign lesion, respectively.

Feature extraction

The color variance and histogram (C 1 ) descriptor contains the mean and variance of the color channels {R, G, B, H, S, V, L, A, B} and a 42 bins histogram for each channel of the set {R, G, B}. Thus, the final descriptor is made of 144 features. The opponent color space angle and hue histogram (C 2 ) is a robust and rotation invariant feature descriptor derived from the RGB channels [START_REF] Van De Weijer | Coloring local feature extraction[END_REF], such that: where d denotes the spatial coordinates of (x, y) and R d , G d , B d denote the first order derivatives of RGB channels with respect to the coordinates. This color descriptor is built by taking a 42 bins histogram for the opponent angle θ O d and the hue channel (H), for a final descriptor size of 84 dimensions.

H = arctan √ 3 (R -G) R + G -2B , θ O d = arctan √ 3 R d -G d R d + G d -2B d , (1)
Completed Local Binary Pattern (CLBP) (T 1 ) is a completed modeling of Local Binary Pattern, especially designed for texture classification [START_REF] Guo | A completed modeling of local binary pattern operator for texture classification[END_REF]. This descriptor encodes the magnitude and sign differences of the central pixel with its neighbors and the grey level of the central points in the local patterns rather than only the sign differences (see Fig 2). The sign CLBP S , magnitude CLBP M , and central grey level CLBP C binary pattern are created by encoding the local distance components and the central grey levels to binary patterns. The CLBP are calculated for each pixel in a given image and the final descriptor is defined as their histogram.

The rotation invariant, uniform, and normalized CLBP features is calculated considering a radius of 24 px. The descriptor is composed of 26 dimensions.

Gabor filter (T 2 ) is a linear filter which is defined as a modulation of a Gaussian kernel with a sinusoidal wave. This filter is formulated in Eq. ( 2) as two Gaussians with standard deviations of σ x and σ y that vary along x and y axes and it is modulated by a complex sinusoidal with a wavelength of λ.

Here θ represents the orientation of the Gabor filter, ψ is the phase offset and s is the scale factor. The filter bank is created using six different orientations equally spaced in the interval [0, π], along 4 scales with a downsizing factor of 2:

g(x, y) = exp - x 2 2σ 2 x + y 2 2σ 2 y cos 2π x λ + ψ , (2)
where

x = s (x cos θ + y sin θ) , y = s (-x sin θ + y cos θ) .
The final descriptor is composed 48 feature dimensions.

BALANCING STRATEGIES

Considering a binary classification problem, the class with the smallest number of samples is defined as the minority class and its counterpart is defined as the majority class. The problem of data balancing corresponds to equalize the number of samples of both the minority and majority classes. This task can be achieved in either data or feature space.

Data space sampling

Data space sampling is related with the generation of new synthetic samples by modifying the original data ahead of any feature extraction processes. Over-Sampling (OS) is performed on the original dataset by generating synthetic melanoma images based on two types of deformation [START_REF] Rastgoo | Ensemble approach for differentiation of malignant melanoma[END_REF]. Furthermore, cubic b-spline interpolation is used with both methods to approximate non-integer points in the image. These deformations are considered since they are more likely to occur, due to non-planar surface of some body parts, skin wrinkles, camera rotation, and position. A synthetic example illustrating the results of these deformation is presented in Fig. 3.

Feature space sampling

Three strategies can be employed to overcome the problem of imbalanced dataset: (i) Under-Sampling (US), (ii) OS, and (iii) a combination of both. The following sections give an overview of the techniques used to tackle this issue.

Under-Sampling

Considering the problem of imbalanced, US is performed such that the number of samples of the majority class is reduced to be equal to the number of samples of the minority class. The following methods are considered to perform such balancing.

Random Under-Sampling (RUS) is performed by randomly selecting without replacement a subset of samples from the majority class such that the number of samples is then equal in both minority and majority classes. Tomek Link (TL) can be used to undersample the majority class of the original dataset [START_REF] Tomek | Two modifications of cnn[END_REF]. Let define a pair of Nearest Neighbour (NN) samples (x i , x j ) such that their associated class label y i = y j . The pair (x i , x j ) is defined as a TL if, by relaxing the class label differentiation constraint, there is no other sample x k defined as the NN of either x i or x j . US is performed by removing the samples belonging to the majority class and forming a TL. It can be noted that this US strategy does not enforce a strict balancing between the majority and the minority classes.

Clustering Under-Sampling (CUS) refers to the use of a k-means to cluster the feature space such that k is set to be equal to the number of samples composing the minority class. Hence, the centroids of these clusters define the new samples of the majority class.

NearMiss offers three different methods to under-sample the majority class [START_REF] Mani | knn approach to unbalanced data distributions: a case study involving information extraction[END_REF].

In NearMiss-1 (NM1), samples from the majority class are selected such that for each sample, the average distance to the k NN samples from the minority class is minimum. NearMiss-2 (NM2) diverges from NM1 by considering the k farthest neighbours samples from the minority class. In NearMiss-3 (NM3), a subset M containing samples from the majority class is generated by finding the m NN from each sample of the minority class. Then, samples from the subset M are selected such that for each sample, the average distance to the k NN samples from the minority class is maximum. In our experiment, k and m are fixed to 3.

Neighborhood Cleaning Rule (NCR) consists of applying two rules depending on the class of each sample [START_REF] Laurikkala | Improving identification of difficult small classes by balancing class distribution[END_REF]. Let define x i as a sample of the dataset with its associated class label y i . Let define y m as the class of the majority vote of the k NN of the sample x i . If y i corresponds to the majority class and y i = y m , x i is rejected from the final subset. If y i corresponds to the minority class and and y i = y m , then the k NN are rejected from the final subset. In our experiment k is fixed to 3.

Over-Sampling

In the contrary, the data balancing can be performed by OS in which the new samples belonging to the Features Color Texture Combined SMOTE is a method to generate synthetic samples in the feature space [START_REF] Chawla | Smote: synthetic minority oversampling technique[END_REF]. Let define x i as a sample belonging to the minority class. Let define x nn as a randomly selected sample from the k NN of x i , with k set to 3. Therefore, a new sample x j is generated such that

C 1 C 2 C 1,2 T 1 T 2 T 1,2 T 1 ,C 1,2 T 2 ,C 1,2 T 1,2 ,C
x j = x i + σ (x nn -x i ),
where σ is a random number in the interval [0, 1].

Combination of OS and US

Subsequently, OS methods can be combined with US methods to clean the subset created. In that regard, two different combinations are tested.

SMOTE + TL are combined to clean the samples created using SMOTE [START_REF] Batista | Balancing training data for automated annotation of keywords: a case study[END_REF]. SMOTE over-sampling can lead to overfitting which can be avoided by removing the TL from both majority and minority classes [START_REF] Prati | Data mining with imbalanced class distributions: concepts and methods[END_REF]. SMOTE + Edited Nearest Neighbour are combined for the same aforementioned reason [START_REF] Batista | A study of the behavior of several methods for balancing machine learning training data[END_REF].

CLASSIFICATION

The classification is performed using a Random Forests (RF) classifier. RF is an ensemble of decision trees [START_REF] Breiman | Random forests[END_REF] which generalizes the classification process by applying two types of randomization: at the tree level, each tree is fed by a bootstrap made of S samples built from the original data of size S such that S = S , and at the node level, a subset of feature dimensions m is randomly selected from the original dimension M such that m = √ M. The trees in RF are grown to their maximum length without any pruning. Each tree in the ensemble casts a unit vote in the final prediction and the final prediction is based on combination of all the votes. RF is used with 100 un-pruned trees and the original feature dimension of size M = {144, 84, 228, 26, 48, 74, 254, 276, 302}

Validation

We used a 10-fold cross-validation scheme to validate our classifier with stratified sampling. However, differently from the usual 10-fold cross-validation, 8 folds were kept for training and 2 folds for testing at each iteration. The training set is balanced using previously described imbalanced techniques. The classification performance are reported in terms of average SE (TPR) and Specificity (SP) (TNR) over 10 runs of cross-validation. The visual and analytic interpretation of these evaluation measures are depicted in Fig. 5.

To select the best performance, similarly to [START_REF] Barata | Towards an automatic bag-of-features model for the classification of dermoscopy images: The influence of segmentation[END_REF] we consider to evaluate the results based on a cost function, which defines the trade off between SE and SP. This function is formulated as:

C = c 10 (1 -SE) + c 01 (1 -SP) c 10 + c 01 , (3)
where, c 10 and c 01 are the costs of incorrectly classifying a melanoma and non-melanoma lesions, respectively. In cancer classification such as melanoma, correctly identifying the cancer lesions has high importance (i.e., high SE). Thus incorrect classification of melanoma is not desired and c 10 is a greater error and evidently more costly and should be penalized more.

In order to achieve a high SE without significantly reducing the value of SP, Barata et al. proposed to set c 10 = 1.5 × c 01 and c 01 = 1 [START_REF] Barata | Towards an automatic bag-of-features model for the classification of dermoscopy images: The influence of segmentation[END_REF]. We considered the same configuration for our cost function.

EXPERIMENTAL RESULTS

The classification results are reported in Table 1 using the aforementioned features, the RF classifier, and the different imbalancing techniques presented in Sect. 3 and Sect. 4. Table 1 can be divided into three main parts representing the results using imbalance data (IB), the balancing in the data space OS and the balancing in the feature space. These strategies are separated by a double horizontal line. The strategies performed in the feature space are subdivided into either OS or US or a combination of OS follow by US (see horizontal dashed line in Table 1).

In this table, based on the previously defined cost function, the best performance for each feature set are highlighted in the shaded cells. and their combination with OS techniques outperform the OS techniques. Due to the characteristics similarities of melanoma and dysplastic lesions, it is expected to have correlated feature space among melanoma and dysplastic lesions. Subsequently, the miss-leading samples could be removed using US and lead to better performance. Specifically to our purpose, NM2 algorithm with the combination of all the features (T 1,2 C 1,2 ) with the lowest cost value, achieve the highest SE and SP of 91.2% and 81.7%. Using the same feature combination, RUS achieve the second lowest cost with SE and SP of 92.5% and 78.3%, respectively. The NM2 algorithm also achieve the third lowest cost with combination of Gabor and color features (T 2 ,C 1,2 ) with SE and SP of 92.5% and 77.5%, respectively. Focusing only on OS techniques, OS in data space outperforms the techniques performing in feature space.

Balancing techniques

Classification cost, C C 1 C 2 C 1,2 T 1 T 2 T 1,2 T 1 ,C 1,2 T 2 ,C 1,2 T 1,2 ,C
A - + P + - A - + P- P + - A - + P + - A - + (
Comparing the color features, opponent color angle and hue histogram feature descriptor, C 2 , has a better performance than well-used color statistics, C 1 . In texture domain, Gabor descriptor, T 2 , outperforms CLBP features, T 1 . Finally, the combination of color and texture features outperforms any other feature combination.

CONCLUSION

In this paper, we analyzed the impact of data balancing techniques for the classification of malignant melanoma. Therefore, we presented an extensive comparison of twelve OS and US techniques in both feature and data space. These techniques were evaluated on the only public dermoscopic dataset, the PH 2 dataset, in order to provide a chance for future comparison. The obtained results particularly highlight the advantage of balancing the training set over using the original data, particularly for the methods based on US (NM2, NCR) and combination of OS and US in feature space. Furthermore, OS in data space outperforms the techniques performing in the feature space. This study also showed that combining color and texture features will lead to better performance.

Figure 1 :

 1 Figure 1: Samples of PH 2 dataset, representing melanoma, dysplastic and benign lesions, respectively.

Figure 2 :

 2 Figure 2: CLBP descriptor process, (a) represents an example on how local distances, sign and magnitude components are calculated and (b) shows an overall view of CLBP process.

Figure 3 :

 3 Figure 3: Data space transformation: (a) original synthetic data, (b) RDGM deformation, (c) BD deformation.

Figure 4 :

 4 Figure 4: Framework outline

  a) Confusion matrix with truly and falsely positive samples detected (TP, FP) in the first row, from left to right and the falsely and truly negative samples detected (FN, TN) in the second row, from left to right. and Specificity evaluation, corresponding to the ratio of the doted area over the blue area.

Figure 5 :

 5 Figure 5: Evaluation metrics: (a) confusion matrix, (b) Sensitivity -Specificity

Table 1 :

 1

The obtained results with different balancing techniques for color and texture features using a RF classifier. The first and second highest results for each feature set are highlighted in dark and lighter gray colors, respectively.

Table 2

 2

	shows the

Table 2 :

 2 The classification costs, C for different balancing techniques and feature sets.