D Salze

O Belcourt

F Lannuzel

Experimental study of interactions between uranium and nalkanes in hydrothermal conditions (500 bar, 200°C)

Keywords: n-alkane, uranium, oxidation, hydrothermal conditions, pyrolysis

Organic matter is commonly involved in uranium deposits by reducing and alteration processes. An experimental study of the pyrolysis of linear n-alkanes at 200°C, 500 bar for 2 months in presence of water and/or uranium were carried out. These experiments reveal that the initiation mechanism of the reaction pathway is the reduction of uranium and the oxidation of organic matter and that the oxidation of n-alkanes produces different compounds (aldehydes, alcohols, ketones, carboxylic acids, esters) in different configurations and proportions by auto-oxidation and free-radical reactions. Another parameter observed during the experiments is the increase of the oxidation process the longer the aliphatic chain is. The pyrolysis of n-octane particularly revealed the role of water as an oxidizing agent instead of auto-oxidation mechanisms.

INTRODUCTION

The affinity of uranium and other metals of economic interest for carbon compounds and organic materials especially is such that it has been proposed as a criterion for prospecting [START_REF] Mossman | Carbonaceous substances in mineral deposits: implications for geochemical exploration[END_REF]. Carbonaceous material is frequently observed in uranium field, which raises the question of the role played by carbon compounds in the formation of some deposits.

Naturally occurring carbonaceous organic materials such as coals are known to have played important roles in controlling uranium concentrations within the different stages of the sedimentary cycle [START_REF] Kish | Uraninite-Albite Veins from the Mistamisk Valley of the Labrador Trough, Quebec[END_REF][START_REF] Cai | Biogenic and petroleum-related ore-forming processes in Dongsheng uranium deposit, NW China[END_REF][START_REF] Cuney | The extreme diversity of uranium deposits[END_REF]. The relationship between organic compounds and uranium show that these interactions are various: transport, remobilization, reduction, concentration, and preservation [START_REF] Landais | Analyse des matières organiques associées aux minéralisations uranifères: implications genetiques[END_REF].

Most uranium deposits associated with carbon compounds are generally formed at relatively low or moderate temperatures (<350 °C). This is the case of roll-front type deposits of Dongsheng in China [START_REF] Cai | Biogenic and petroleum-related ore-forming processes in Dongsheng uranium deposit, NW China[END_REF][START_REF] Cai | Petroleum-related origin for sandstone-hosted uranium deposits in the Dongsheng area, Ordos Basin (China)[END_REF], deposits of Oklo in Gabon [START_REF] Cortial | Ma.)) et leurs kérogènes: Relations avec les minéralisations uranifères[END_REF][START_REF] Cortial | Characterization of organic matter associated with uranium deposits in the Francevillian formation of Gabon (lower proterozoic)[END_REF][START_REF] Gauthier-Lafaye | Les gisements d'uranium du Gabon et les réacteurs d'Oklo : modèle métallogénique de gîtes a fortes teneurs du protérozoïque inférieur[END_REF][START_REF] Nagy | Organic matter and containment of uranium and fissiogenic isotopes at the Oklo natural reactors[END_REF][START_REF] Nagy | Role of organic matter in the Proterozoic Oklo natural fission reactors, Gabon, Africa[END_REF][START_REF] Mossman | Hydrocarbon Habitat of the Paleoproterozoic Franceville Series, Republic of Gabon[END_REF][START_REF] Mossman | Petrography and paragenesis of organic matter associated with the natural fission reactors at Oklo, Republic of Gabon: a preliminary report[END_REF][START_REF] Mossman | Geochemistry of Organic-Rich Black Shales Overlying the Natural Nuclear Fission Reactors of Oklo, Republic of Gabon[END_REF][START_REF] Mossman | Black shales, organic matter, ore genesis and hydrocarbon generation in the Paleoproterozoic Franceville Series, Gabon[END_REF] and Lodève in France [START_REF] Capus | Observation de bitumes uranifères à Cerilly (Allier) et à Lodève (Hérault) : implications métallogéniques[END_REF][START_REF] Capus | Matières organiques et minéralisations uranifères: exemple des bassins permo-carbonifères de l'Aumance (Allier) et de Lodève (Hérault)[END_REF][START_REF] Landais | Relation uranium -matière organique dans deux bassins permiens français : Lodève (Hérault) et Cérilly-Bourbon-l'Archambault (Allier)[END_REF].

The relationship between uranium and organic matter is observed both at deposits scale and at molecular scale where chemical bonds were established between certain functional groups of organic compounds and uranium atoms [START_REF] Landais | Analyse des matières organiques associées aux minéralisations uranifères: implications genetiques[END_REF].

This work aims to better understand the intimate interaction reactions between uranium and organic compounds under conditions of temperature and pressure corresponding to the fields of organic diagenesis and low temperature hydrothermalism.

Several experiments have been performed with models compounds representing the mineral phase and the organic compounds. The use of such simplified systems allows good control of the experimental conditions and to propose reaction mechanisms.

A first set of experiments designated as reference that involves organic compounds alone was performed to evaluate their stability in the absence of uranium in the chosen experimental conditions. Then, a second set were carried out in the same conditions but in the presence of uranium under solid form. Comparison of these two sets of experiments will allow a better understanding of: i) the role of the compounds resulting from the decomposition of the organic matter in the reduction of uranium;

ii) the effect of uranium on the organic compounds;

iii) Determining the dominating reactions between reduction of uranium, solubility and modification of the organic compounds.

MATERIAL AND METHOD

Confined pyrolysis

Experiments were performed at high pressures using confined pyrolysis. This technique first used in geochemistry for mineral syntheses and simulation of hydrothermal metamorphism [START_REF] Poty | Solution-mineral equilibria in the system MgO-SiO2-H2O-MgCl2 at 500°C and 1 kbar[END_REF][START_REF] Nguyen-Trung | Contribution à l'étude expérimentale du système Mg-SiO2-HCl-H2O. Facteurs contrôlant les minéralisations sulfurés de Nickel[END_REF] found applications in organic geochemistry [START_REF] Hryckowian | Experimental studies of anthracite coals at high pressures and temperatures[END_REF][START_REF] Marsh | The carbonisation of anthracene and biphenyl under pressures of 300 MNm (3 kbar)[END_REF][START_REF] Bostick | Time as a factor in the thermal metamorphism of phytoclasts (coaly particles)[END_REF][START_REF] Monthioux | Comparison between natural and artificial maturation series of humic coals from the Mahakam delta, Indonesia[END_REF][START_REF] Landais | Pyrolysis of organic matter in cold-seal pressure autoclaves. Experimental approach and applications[END_REF][START_REF] Ungerer | State of the art of research in kinetic modelling of oil formation and expulsion[END_REF]. Confined pyrolysis allows working in a range of pressure and temperature similar as those that can be found in sedimentary basins.

The loading of the gold cells (40 mm in length, 5 mm in diameter and 0.5 mm in thickness) was made under helium atmosphere (purity 99.9999%) The reactors were sealed by arc welding while the sample was refrigerated by a cold nitrogen flow. The gold cells were then loaded and heated under pressure in stainless steel autoclaves. Special care was taken to avoid oxygen concentration in the gold cells because oxygen speeds up the reactivity [START_REF] Engel | Etude expérimentale de l'influence accélératrice de traces d'oxygène sur la pyrolyse en phase gazeuse de quelques hydrocarbures saturés[END_REF][START_REF] Martin | La décomposition thermique du propane: II. -Étude expérimentale de la pyrolyse du propane en présence de traces d'oxygène[END_REF][START_REF] Niclause | LA PYROLYSE DU PROPANE ET DE L'ISOPENTANE: INFLUENCE DE TRACES D'OXYGÈNE ET EFFETS DE PAROIS[END_REF].

Choice of the organic compounds

The organic compounds used in these experiments are different n-alkane with different lengths (see table 1) in order to study the influence of this parameter on the different reactions. The individual pyrolysis of each of these compounds in different experimental conditions has been very widely studied [START_REF] Voge | Thermal Cracking of Higher Paraffins[END_REF][START_REF] Dente | Mathematical Modelling of Pyrolysis Reactions[END_REF][START_REF] Baronnet | Industrial problems and basic research in pyrolysis and oxidation reactions[END_REF].

Choice of the uranium carriers

Many authors have highlighted the role of reducing agent of the organic matter on uranium and on the hydrothermal deposition of deposits [START_REF] Moore | Extraction of uranium from aqueous solution by coal and some other materials[END_REF][START_REF] Landais | Organic matter in hydrothermal ore deposits[END_REF][START_REF] Nakashima | Experimental study of mechanisms of fixation and reduction of uranium by sedimentary organic matter under diagenetic or hydrothermal conditions[END_REF][START_REF] Nakashima | Precipitation kinetics of uranium by sedimentary organic matter under diagenetic and hydrothermal conditions[END_REF]. It has been shown that uranium is brought by the fluids under the state of oxidation VI in the form of uranyl complex. In contact with organic matter, uranium is reduced and mineralized.

In order to highlight the role of organic matter in the precipitation of uranium and particularly associated reactions uranium VI oxide UO 3 has been selected as reactants.

Experimental study of the four experimental series

Four experimental series were carried out in order to highlight the mechanisms of interaction between uranium and the organic compounds. The first two series correspond to a frame of reference to control experiments with an organic compound exclusively (first serie) or with deuterated water (second serie). It was established in order to determine the stability and the behaviour of the organic compounds under our experimental conditions and to show experimentally the reactional complexity which can exist in the pyrolysis of certain organic molecules under the conditions close to the formation of a uranium deposit.

The third serie simulates the reaction between an organic compound and solid uranium. The uranium VI oxide UO 3 allows the study of the reactions of uranium at the solid state. These reactions using solid uranium are not the same as the reactions occurring during the formation of a uranium deposit where uranium is transported to the trap via an aqueous fluid. However, reactions of this type between a solid containing some uranium and the organic compound are taken into account when the latter remobilise uranium in order to transport it as it is considered by [START_REF] Capus | Matières organiques et minéralisations uranifères: exemple des bassins permo-carbonifères de l'Aumance (Allier) et de Lodève (Hérault)[END_REF] [START_REF] Capus | Matières organiques et minéralisations uranifères: exemple des bassins permo-carbonifères de l'Aumance (Allier) et de Lodève (Hérault)[END_REF] in the deposit of Lodève. The solubility of the uranium is also studied in the organic liquid phase of our experiments involving a series of possible reactions that it is also necessary to take into account. The comparison with the frame of reference allows the characterization of the reactions specific to the interactions between the organic compounds and uranium.

The fourth serie of experiments is a ternary system with organic compound, solid uranium (UO 3 ) and deuterated water to simulate the mechanism of interaction under the conditions close to the formation of a uranium deposit.

The reactants were composed of 1 cm 3 of organic compound (99.5% purity obtained from Fluka and used as received) for reference without deuterated water and organic compound-uranium experiments and 0,5 cm 3 of organic compound and 0,5 cm 3 of deuterated water (D2O, ultra-pure water) for reference experiments with water and ternary solution experiments. For the organic compound-uranium-(D2O) experiments, the gold cells were loaded with 0.6 g of UO 3 (table 1).

ANALYTICAL

Extraction

Liquid phase

After pyrolysis, gold capsules were pinched at one end and placed in contact with a vial allowing the recovery of the liquid phase. A large part of the liquid phase is carried along by the gas flowing out of the capsule. This flow is directed towards the vial specified for the organic liquid phase. When the capsule is no longer in pressure it is completely opened in order to recover the remaining liquid phase. The aqueous phase is removed using a glass pipette and placed in the aqueous liquid vial. The two liquid phases are then centrifuged to remove suspended particles.

Solid phase

The recovering step of the solid phase is performed immediately after the liquid one. The second end of the capsule is open using a cutter and the solid is recovered.

Gaz chromatography -mass spectrometry

The samples were analyzed by a gas chromatograph (Hewlett-Packard HP 6890) coupled to a mass spectrometer (Hewlett-Packard HP 5972) using a split/splitless injector, a 60 m DB-5 J & W, 0.25 mm i.d., 0.1 mm film fused silica column. Two different temperature programs were used according to the injection mode:

Split injection mode : 70°C-130°C with 15°C/min, 130°C-300°C with 3°C/min followed by an isothermal stage at 300°C during 15 min with, constant flow of helium of 1 ml/min.

Splitless injection mode: 70°C-130°C with 15°C/min, 130°C-300°C with 3°C/min followed by an isothermal stage at 300°C during 15 min with, constant flow of helium of 1 ml/min.

The mass spectrometer was operated in the electron ionization (EI) mode at 70 eV ionization energy and mass spectra were scanned from 50 to 500 Da using a quadrupole detector. Data were acquired and processed using the Agilent ChemStation software. Compounds were identified by comparison of their mass spectra with published spectra and those from the Wiley275 database, or by interpretation of MS fragmentation patterns.

Derivatization (sylylation)

Because of the presence of alcohols and carboxylic acids in the extracts, a silylation step was carried out in order to improve the chromatographic resolution. The organic solutions were diluted in a flask at a concentration of 4mg/ml with a sylilating reagent (BSTFA + TMCS 99.1, Supelco). To accelerate the reaction, the flasks were heated up to 50 ° C for 15 minutes.

Then, 0.5 ml of the solution was introduced into the chromatograph injector in splitless mode. All the samples were run with and without sylylation to identify hydrocarbons and oxygenated products separately.

RESULTS

Reference System (organic compounds pyrolysed alone or with water)

The 7 reference n-alkanes were pyrolyzed alone or with deuterated water. The products of reactions were analyzed by GC-MS. The chromatograms of these 2 series of experiments do not show the formation of pyrolysis products. One organic compound is shown for illustration (figure1). This is consistent with previous studies indicating that the temperature of 200°C is too low to observe any advancement of the reaction [START_REF] Poutsma | Fundamental reactions of free radicals relevant to pyrolysis reactions[END_REF][START_REF] Bounaceur | Modeling of hydrocarbons pyrolysis at low temperature. Automatic generation of free radicals mechanisms[END_REF][START_REF] Ding | A Reactive Molecular Dynamics Study of n-Heptane Pyrolysis at High Temperature[END_REF][START_REF] Liu | Molecular dynamics simulation of the high-temperature pyrolysis of methylcyclohexane[END_REF]. 4.2 Experiments with binary mixture: uranium UO 3 (solid) + n-alkane

Analyses of the liquid organic phase by GC-MS

These compounds were pyrolyzed for 2 months at 500 bar, 200°C in the presence of UO 3 and the results are summarized in table 2.

-n-pentane

The analysis of the products of reaction of n-pentane in the presence of UO 3 did not show any formation of organic compounds. Furthermore uranium still had a yellow color at the end of the experiment, corresponding to the form of uranium trioxide UO 3 .

-

n-hexane

The experiments with n-hexane reveal the presence of a secondary alcohol (n-hexanol)

having the same number of carbon as hexane. However the position of the hydroxyl group could not be specified (figure 2).  Oxygenated compounds with aliphatic chain shorter than the reactant:

Carboxylic acids show chain lengths ranging from 5 to 8 carbon atoms (from the pentanoic acid to the octanoic acid). The presence of carboxylic acids with shorter aliphatic chains (between C 1 and C 4 ) is possible but cannot be detected by the analysis technique (column not adapted for the light polar compounds).

 Oxygenated compounds with aliphatic chains longer than n-octane:

Analysis of the same organic solution resulting from n-octane pyrolysis but this time by GC-MS in "splitless" mode after silylation confirms the presence of carboxylic acids and alkanols with a higher chromatographic resolution. In addition, another series of compounds in lower concentration is observed (figure 3). Because the initial reagent (n-octane) is not detected (solvent delay), it is then possible to inject it at higher concentration and thus to detect compounds in very low abundance.  Oxygenated compounds with aliphatic chain shorter than the reactant. These compounds correspond to carboxylic acids containing 5 to 12 carbon atoms. It has not been possible to detect acids with shorter chains in GC-MS with the analytical conditions used.

 Oxygenated compounds with aliphatic chains longer than the initial reactant. These compounds are combined into groups of 5 isomers, each of these groups containing the same number of carbon atoms (from 15 to 24 carbon atoms).  oxygenated compounds with aliphatic chains shorter than the initial product: carboxylic acids containing 4 to 14 carbon atoms for n-tetradecane and 4 to 16 carbon atoms for n-hexadecane (observed in mode of injection "splitless"), n-alkanes with chains shorter than the initial product, corresponding to n-alkanes containing 8 to 13 carbon atoms for the tetradecane and 7 to 14 carbon atoms for hexadecane are also present.

 oxygenated compounds with aliphatic chains longer than the initial product. This  Compounds of shorter aliphatic chains represented by carboxylic acids. The number of carbon in the aliphatic chains of these acids lies between 5 (the lighter compounds are not observable under the analytical conditions used) and numbers of carbon of n-initial alkane.

Like ketones, the carboxylic acids show a shift of mass of 1 or 2 units revealing an exchange of 1 or 2 hydrogen by one or 2 deuterium.

 Compounds with longer aliphatic chains than starting products. Esters, highlighted during the experiments n-alkanes -UO 3 are also observed in the case of the ternary mixtures. Just like the ketones and the carboxylic acids, these esters present a shift of mass of one or two units. For a given ester, the abundance relating of isomer to a deuterium atom is lower than that with two deuterium atoms suggesting a preferential production of the configuration with two deuterium atoms.

Table 2 summarizes the products of the ternary experiment including various esters observed or deduced (due to limitations from our analytical conditions) for the different n-alkanes used. All the reactions products for the four series of experiments are resumed in a master table

C8H18 C8H18 C12H26 C7H16 C11H24 C9H20 C9H20 C9H20 C13H28 C8H18 C12H26 C10H22 C10H22 C9H20 C13H28 C11H24 C11H24 C10H22 C14H30 C5H10O2 C5H10O2 C5H10O2 C12H24O2 C4H8O2 C11H22O2 C4H8O2 C11H22O2 C6H12O2 C6H12O2 C6H12O2 C5H10O2 C12H24O2 C5H10O2 C12H24O2 C7H14O2 C7H14O2 C7H14O2 C6H12O2 C13H26O2 C6H12O2 C13H26O2 C8H16O2 C8H16O2 C8H16O2 C7H14O2 C14H28O2 C7H14O2 C14H28O2 C9H18O2 C9H18O2 C8H16O2 C8H16O2 C15H30O2 C10H20O2 C10H20O2 C9H18O2 C9H18O2 C16H32O2 C11H22O2 C10H20O2 C10H20O2 C12H24O2 C12H24O2 C19H38O2 C15H30O2 C22H44O2 C15H30O2 C22H44O2 C20H40O2 C27H54O2 C13H22O2 C13H22O2 C20H40O2 C16H32O2 C23H46O2 C16H32O2 C23H46O2 C21H42O2 C28H56O2 C14H28O2 C14H28O2 C17H34O2 C24H48O2 C17H34O2 C24H48O2 C22H44O2 C29H58O2 C15H30O2 C15H30O2 C18H36O2 C18H36O2 C25H50O2 C23H46O2 C30H60O2 C16H32O2 C16H32O2 C19H38O2 C19H38O2 C26H52O2 C24H48O2 C31H62O2 C17H34O2 C20H40O2 C20H40O2 C27H54O2 C25H50O2 C32H64O2 C18H36O2 C21H42O2 C21H42O2 C26H52O2 n -a l
* C12H23DO2 C12H22D2O2 C14H27DO2 C14H26D2O2 C16H31DO2 C16H30D2O2 C18H35DO2 C18H34D2O2 C20H39DO2 C20H38D2O2 C13H25DO2 C13H24D2O2 C15H29DO2 C15H28D2O2 C17H33DO2 C17H32D2O2 C19H37DO2 C19H36D2O2 C21H41DO2 C21H40D2O2 C14H27DO2 C14H26D2O2 C16H31DO2 C16H30D2O2 C18H35DO2 C18H34D2O2 C20H39DO2 C20H38D2O2 C22H43DO2 C22H42D2O2 C15H29DO2 C15H28D2O2 C17H33DO2 C17H32D2O2 C19H37DO2 C19H36D2O2 C21H41DO2 C21H40D2O2 C23H45DO2 C23H44D2O2 C16H31DO2 C16H30D2O2 C18H35DO2 C18H34D2O2 C20H39DO2 C20H38D2O2 C22H43DO2 C22H42D2O2 C24H47DO2 C24H46D2O2 C19H37DO2 C19H36D2O2 C21H41DO2 C21H40D2O2 C23H45DO2 C23H44D2O2 C25H49DO2 C25H48D2O2 C20H39DO2 C20H38D2O2 C22H43DO2 C22H42D2O2 C24H47DO2 C24H46D2O2 C26H51DO2 C26H50D2O2 C23H45DO2 C23H44D2O2 C25H49DO2 C25H48D2O2 C27H53DO2 C27H52D2O2 C24H47DO2 C24H46D2O2 C26H51DO2 C26H50D2O2 C28H55DO2 C28H54D2O2 C27H53DO2 C27H52D2O2 C29H57DO2 C29H56D2O2 C28H55DO2 C28H54D2O2 C30H59DO2 C30H58D2O2 C31H61DO2 C31H60D2O2 C32H63DO2 C32H62D2O2

Same compounds than in serie 03

Same compounds than in serie 03 with substitution of one or two hydrogen by one or two deuterium

Same compounds than in serie 03

Same compounds than in serie 03 with substitution of one or two hydrogen by one or two deuterium

Same compounds than in serie 03 with substitution of one or two hydrogen by one or two deuterium

proposed in an annex (Annex 1)

Dominant reactions

Analysis by GC-MS enables the percentage of product formed to be qualitatively determined by the ratio between the abundance of the initial reagent at the end of the experiment and the abundance of products. Table 3 shows that 85.07% of the reagent is still present at the end of the experiment in the presence of D 2 O compared to 88.21% in the deuterated waterfree experiment. However, there are only 0,14% esters formed in the presence of D 2 O compared to 0,55% in waterless experiments.

DISCUSSION

No organic matter except the initial reagent (and contaminants) is observed in the reference experiments. The different n-alkanes are stable under these conditions or their conversion is too weak to be observed regardless their chain length.

For the experiments of n-alkane pyrolysis in the presence of uranium, the formation of oxygenated products with aliphatic chain length increase has been shown for all the nalkanes studied. Moreover, the more the length of the n-alkane chain increases, the more we observe products of pyrolysis and the more the conversion is important.

We have chosen to focus the first part of our discussion on the n-octane because it is the first reagents showing the formation of oxygenated products and a chain length increase.

The conversion of n-octane becomes observable when it is pyrolyzed in the presence of uranium. The presence of deuterated water alone does not cause changes in the initial reagent indicating that the presence of uranium speed-up existing reaction and/or induces new reactions.

5.1 Reactivity of the mixture n-octane -uranium

Initiation of the mechanism

The presence of uranium in the reaction medium is most likely the cause of the initiation of reactions leading to the high diversity of degradation products observed. The redox mechanism is the mechanism of initiation of the reaction process: the reduction of uranium releasing oxygen atoms on the one hand and the oxidation of organic compound generating free radicals on the other hand (figure 7 (1). The numbers in parentheses indicate the reaction in Figures 7 to 10.). [START_REF] Landais | Organic geochemistry of sedimentary uranium ore deposits[END_REF] [START_REF] Landais | Organic geochemistry of sedimentary uranium ore deposits[END_REF] summarizes the oxidation of organic matter during the reduction of uranium by the following chemical reaction:

2(RH)+UO 2 2+  2R° + 2H + + UO 2
The release of oxygen atoms into the reaction medium makes the latter oxidizing. The contact between oxygen atoms and n-alkane boosts auto-oxidation processes and trigger oxidation of the n-alkane.

Radical mechanism

Mechanism involving free radicals generated from n-alkanes in auto-oxidation processes are well described in literature [START_REF] Glaude | Modelling of n-heptane and iso-octane gas phase oxidation at low temperature by using computer-aided designed mechanisms[END_REF][START_REF] Glaude | Construction and simplification of a model for the oxidation of alkanes[END_REF][START_REF] Faure | Low temperature air oxidation of n-alkanes in the presence of Na-smectite⋆[END_REF]. Especially, Faure et al. ( 2003) [START_REF] Faure | Low temperature air oxidation of n-alkanes in the presence of Na-smectite⋆[END_REF] have studied in detail the low temperature air oxidation of n-alkanes in the presence of Na-smectite. Their results achieved with a different substrate are very similar to those presented here.

In the case of n-octane, the free radicals can be generated during the oxidation reaction by metathesis and locate into four different positions (R°) (Figure 7 (1)).

Radicals (R°) then react with molecular oxygen and form peroxide radicals (ROO°) (Figure 7 (2)) inducing there after successive radical reactions. Then peroxide radicals stabilize into In the experiment with deuterated water there is no shift of mass for the alkanols unlike for the esters, carboxylic acids and ketone where there is a shift of mass of one or two unit(s)

which indicates an involvement of water as an oxidizing agent ((3), ( 4), ( 9) and ( 10)) replacing auto-oxidations of n-octane by an oxidation by deuterated water. The deuterated water being an abundant compound of the medium, the probability that one of the free radical compounds interacts with water is high, leading to incorporation of deuterium in organic compounds, in contrast with the experiments without water where the latter is only a marginal product. Moreover, having deuterium atoms in the alkyl chain, due to an isomerization reaction in which a hydrogen atom of the chain is exchanged with the deuterium atom of a functional group, suggests the use of water as an oxidizing agent.

The assumption of a neutralization related to the presence of water as a reactive component of the ester-forming reaction can be considered due to the fact that the reaction with noctane has a higher yield in the presence of water but a smaller quantity of products formed.

Extension of n-octane oxidation mechanisms in the presence of uranium to others organic compounds

Salze (2008) [START_REF] Salze | Etude des interactions entre uranium et composés organiques dans les systèmes hydrothermaux[END_REF] obtained similar compounds after the pyrolysis of n-alkanes, n-dec-1-ene and butyl-cyclohexane. The hypothesis of a reaction pathway identical to that of n-octane can be proposed: i) Oxidation of organic compounds by uranium to form alkanols then carboxylic acids and ketones. ii) Addition reactions leading to the formation of esters for nalkanes reagents.

The low abundance of these ester molecules relative to the oxygenated molecules in GC-MS analyses results in a low yield of these addition reactions against oxidation-reduction reactions leading to the formation of alkanols, ketones and carboxylic acids (Table 2).

The duration of our experiments is too short to involve the role of radiolysis. [START_REF] Schlepp | Réactivité des bitumes d'enrobage des déchets ultimes. Comparaison avec un analogue naturel[END_REF] [44] attributed the changes in organic matter of Lodève deposit to the effect of radiolysis alone. In this study it was shown that the oxidation of the organic matter occurred in the short term (less than 2 months at 200°C and 500 bar). [START_REF] Faure | Low temperature air oxidation of n-alkanes in the presence of Na-smectite⋆[END_REF] showed the catalytic role of clays on the thermal degradation of hydrocarbons at low temperature.

Thus, the oxidative processes studied in this present work seem to have an important role in hydrocarbon degradation. However, this degradation does not seem to be the result of a single process but of a combination of processes such as oxidative processes, radiolysis and catalytic phenomena.

When comparing this study carried out in the presence of an oxidizing medium with other works investigating the thermal cracking of alkanes [START_REF] Jackson | Temperature and pressure dependence of n-hexadecane cracking[END_REF], some similarities can be found: mechanisms involved are of free-radical type leading to products both smaller and larger than the starting material. But reactions are very different leading here to oxygenated compounds. [START_REF] Weres | Hydrous pyrolysis of alkanes, alkenes, alcohols and ethers[END_REF] have studied the hydrous pyrolysis of alkanes in presence of clay. They have reported that adding water shifted the process to a free radical mechanism and eliminated the catalytic effect of clay. Experiments carried out here with water and uranium do not exhibit the same inhibition effect of water probably because uranium and clay have a different reactivity.

CONCLUSIONS

This paper presents the first steps of the chemical behaviour of uranium in the ternary system Uranium -Organic Matter -D 2 O under conditions close to the genesis of a uranium deposit. The study of organic compounds and their evolution revealed several phenomena: i)

The following redox reaction (reduction of uranium and oxidation of organic matter) is the initiation mechanism of the reaction pathway and generates free radicals. ii) The oxidation of n-octane leads to the production of alcohol, ketones, aldehydes, carboxylic acids and esters molecules in different configurations and proportions. iii) The reactions with n-alkanes made it possible to show an increase in the phenomenon of gradual oxidation of the organic matter starting from the compound C6. The parameter of increase in the aliphatic chain is a major factor of the increase in the oxidizing ability of the medium on the organic compound in balance with uranium trioxide.

The reaction model of n-octane passing through radical, oxidation and addition reactions could be extended to all compounds studied.

 3 

 3 The first serie of experiments corresponds to the pyrolysis of organic compound exclusively  The second serie of experiments corresponds to the pyrolysis of organic compounds with deuterated water  The third serie of experiments corresponds to the pyrolysis of organic compound with solid uranium under the state of oxidation UO The fourth serie of experiments corresponds to the pyrolysis of organic compound with solid uranium under the state of oxidation UO 3 and deuterated water The experimental conditions of all the experiments were 473K (200°C), 50MPa (500 bar) for 2 months.

Figure 1 :

 1 Figure 1 : Chromatograms (split mode) of pyrolysis's at 200°C, 500 bar for 2 months: a)

Figure 2 :

 2 Figure 2: Chromatogram of the pyrolyzed n-hexane + UO 3 at 200°C, 500 bar for 2 months -n-octane

Figure 3 :

 3 Figure 3: GC-MS Chromatogram (Split and splitless mode) of the pyrolysis of the mixture n-octane + UO 3 at 200°C, 500 bar for 2 months. C n -CA: Carboxylic Acid with n carbons -n-dodecane

O 2 .

 2 They were identified on the basis of their mass spectrum with the assistance of the Wiley data base. They present the same mass spectrum before and after silylation suggesting the absence of the hydroxyl function in their structure. The figure4proposes a structure for these various esters.

Figure 4 :

 4 Figure 4: GC-MS Chromatogram (Split mode) of the pyrolysis of the solution n-dodecane + UO 3 at 200°C, 500 bar for 2 months. C n -CA: Carboxylic Acid with n carbons --n-tetradecane and n-hexadecane

Figure 5 :

 5 Figure 5: Chromatograms (Split mode), a) n-tetradecane and b) n-hexadecane pyrolyzed with

Figure 6 :

 6 Figure 6: Chromatogram of the products after pyrolysis of the n-tetradecane in the presence of D 2 O and uranium at 200°C, 500 bar (Split). Cn-CA: Carboxylic Acids with n carbons

hydroperoxide (Figure 7 ( 3 )

 73 ) by incorporation of a hydrogen atom and production of other free radicals. From this point three sets of reactions corresponding to the creation of the three different families of detected compounds can occur. The first set, preservation of the aliphatic chain (corresponding to compounds having preserved the same number of carbon that the initial n-alkane) is described in[START_REF] Faure | Low temperature air oxidation of n-alkanes in the presence of Na-smectite⋆[END_REF] [START_REF] Faure | Low temperature air oxidation of n-alkanes in the presence of Na-smectite⋆[END_REF]. Formation of hydroperoxide and homolytic cleavage leads to the formation of alcohol then ketones with all the position isomers we observed in our chromatograms (figure7 and 8).

Figure 7 :Figure 8 :

 78 Figure 7: Reaction pathway showing the secondary alcohol formation

Figure 9 :

 9 Figure 9: Reaction pathway showing the formation of the carboxylic acidsThe third set of reactions corresponds to an increase of the length of the aliphatic chain and

Figure 10 :

 10 Figure 10: Reaction pathway showing the formation of esters 5.1.3 Reactivity of mixture N-octane -uranium-D 2 O

Table 1 Summary of experiments performed and reagents and quantities used SERIE 01 SERIE 02 Reference experiments without water Reference experiments with water Name of the compound Formula Chemical Formula Molecular weight (g.mol -1 ) Volume of organic compound (cm 3 ) Volume of organic compound (cm 3 ) Volume of water (cm 3 )

 1

	n-pentane	C5H12	72.15	1	0.5	0.5
	n-hexane	C6H14	86.18	1	0.5	0.5
	n-octane	C8H18	114.23	1	0.5	0.5
	n-decane	C10H22	142.28	1	0.5	0.5
	n-dodecane	C12H26	170.33	1	0.5	0.5
	n-tetradecane	C14H30	198.39	1	0.5	0.5
	n-hexadecane	C16H34	226.44	1	0.5	0.5

SERIE 03 SERIE 04 Binary system organic compound-uranium Ternary system organic compound-uranium-deuterated water Name of the compound Formula Chemical Formula Molecular weight (g.mol -1 ) Weight of solid uranium (g) Volume of organic compound (cm 3 ) Weight of solid uranium (g) Volume of organic compound (cm 3 ) Volume of water (cm 3 )

	n-pentane	C5H12	72.15	0.6	0.5	0.6	0.5	0.5
	n-hexane	C6H14	86.18	0.6	0.5	0.6	0.5	0.5
	n-octane	C8H18	114.23	0.6	0.5	0.6	0.5	0.5
	n-decane	C10H22	142.28	0.6	0.5	0.6	0.5	0.5
	n-dodecane	C12H26	170.33	0.6	0.5	0.6	0.5	0.5
	n-tetradecane	C14H30	198.39	0.6	0.5	0.6	0.5	0.5
	n-hexadecane	C16H34	226.44	0.6	0.5	0.6	0.5	0.5

  These compounds are gathered in isomer triplets with carbon number ranging from 12 to 16 with the following formulas: C 12 H 24 O 2 , C 13 H 22 O 2 , C 14 H 28 O 2 , C 15 H 30 O 2 , C 16 H 32 O 2 .

  These compounds were identified as esters with the following formulas: C 15 H 30 O 2, C 16 H 32 O 2, C 17 H 34 O 2, C 18 H 36 O 2, C 19 H 38 O 2, C 20 H 40 O 2, C 21 H 42 O 2, C 22 H 44 O 2 , C 23 H 46 O 2 , C 24 H 48

  time, these compounds combine in group of 6 isomers containing 15 to 27 atoms of carbon for the tetradecane and 7 isomers (6 and 7 being partially coeluted on the chromatograms) containing 20 to 32 carbon atoms for n-hexadecane. As for n-dodecane, these compounds were identified out of esters of empirical formulas (C 15 H 30 O 2, C 16 H 32 O 2, C 17 H 34 O 2, C 18 H 36 O 2, C 19 H 38 O 2, C 20 H 40 O 2, C 21 H 42 O 2, C 22 H 44 O 2 , C 23 H 46 O 2 , C 24 H 48 O 2, C 25 H 50 O 2, C 26 H 52 O 2 , C 27 H 54 O 2 for ntetradecane and C 20 H 40 O 2, C 21 H 42 O 2, C 22 H 44 O 2 , C 23 H 46 O 2 , C 24 H 48 O 2, C 25 H 50 O 2, C 26 H 52 O 2 , C 27 H 54 O 2 , C 28 H 56 O 2, C 29 H 58 O 2, C 30 H 60 O 2 , C 31 H 62 O 2 , C 32 H 64 O 2 for n-hexadecane).

Table 2 :

 2 Summary table compiling the compounds detected in the experiments of series 03 and 04. For series 01 and 02, the reaction products were similar to reactants. Compounds in italics* were not detected but deduced

	Reactants	n -penta ne (C5H12)	n -hexa ne (C6H14)
	n -a l ka nes	C5H12	C6H14	C8H18			C14H30	C16H34
	n -a l ka nones			C8H16O	C10H22O	C12H24O	C14H28O	C16H32O
	n -a l ka nol s		C6H14O	C8H18O	C10H24O	C12H26O	C14H30O	C16H34O
					C8H18

  * C 9 H 16 D 2 O 2 * C 11 H 21 DO 2 * C 11 H 20 D 2 O 2 * C 13 H 25 DO 2 * C 13 H 24 D 2 O 2 * C 15 H 29 DO 2 * C 15 H 28 D 2 O 2 * C 17 H 33 DO 2 * C 17 H 32 D 2 O 2 * C 10 H 19 DO 2 * C 10 H 18 D 2 O 2 * C 12 H 23 DO 2 * C 12 H 22 D 2 O 2 * C 14 H 27 DO 2 * C 14 H 26 D 2 O 2 * C 16 H 31 DO 2 * C 16 H 30 D 2 O 2 * C 18 H 35 DO 2 * C 18 H 34 D 2 O 2 * C 11 H 21 DO 2 * C 11 H 20 D 2 O 2 * C 13 H 25 DO 2 * C 13 H 24 D 2 O 2 * C 15 H 29 DO 2 * C 15 H 28 D 2 O 2 * C 17 H 33 DO 2 * C 17 H 32 D 2 O 2 * C 19 H 37 DO 2 * C 19 H 36 D 2 O 2

	ka nes
	n -a l ka nones
	n -a l ka nol s
	n-a l ka nes
	Ca rboxyl i c
	a ci ds
	C 9 H 17 DO 2

Table 3 :

 3 Percentage calculated by measuring by GC-MS the abundance of products formed atthe end of the experiment at 200°C, 500 bar (ca: carboxylic acid, al: alcohol, ke: ketone).

	Experiment	Initial reactant (%)	Oxygenated products (%)	ca+al+ke (%)	Esters (%)
	n-pentane + UO3 2 months	100,00	0,00	0,00	0,00
	n-pentane + UO3 + D2O months	100,00	0,00	0,00	0,00
	n-hexane + UO3 2 months	100,00	0,00	0,00	0,00
	n-hexane+ UO3 + D2O 2 months	87,45	12,55	12,55	0,00
	n-octane + UO3 2 months	88,21	11,79	11,24	0,55
	n-octane + UO3 + D2O 2 months	85,07	14,93	14,79	0,14
	n-decane+ UO3 2 months	99,82	0,18	0,18	0,00
	n-decane+ UO3 + D2O months	99,56	0,44	0,44	0,00
	n-dodecane + UO3 2 months	85,61	14,39	13,36	1,03
	n-dodecane + UO3 + D2O 2 months	84,83	15,17	14,61	0,56
	n-tetradecane + UO3 2 months	84,14	15,86	14,60	1,27
	n-tetradecane + UO3 + D2O 2 months	86,52	13,48	11,84	1,64
	n-hexadecane + UO3 2 months	90,95	9,05	8,31	0,74
	n-hexadecane + UO3 + D2O 2 months	84,95	15,05	14,17	0,88

Acknowledgments

We thank M. Cuney and P. Faure for their technical and scientific assistance. This work was supported by Areva.


L Aprin

P Mercier

L Tadrist

Experimental analysis of local void fractions measurements for boiling hydrocarbons in complex geometry

Keywords: boiling flow, hydrocarbons, tube bundle, void fraction, flow map, statistical analysis

The present paper is part of a research program on two-phase flows and heat transfer studies in tube bundles. An experimental study was carried out to analyse the void fraction for vertical two-phase flows.

Boiling across a horizontal tube bundle for three hydrocarbons (n-pentane, propane and iso-butane) under saturated conditions is investigated. The experiments were performed on a tube bundle with 45 plain copper tubes of 19.05 mm outside diameter in a staggered configuration with a pitch to diameter ratio of 1.33. An optical probe has been developed to determine the local void fraction at the minimum cross section between the tubes.

The void fraction for the three hydrocarbons was found to be significantly less than the homogeneous prediction, and correlated well with the Zuber and Findlay (1965) model. A statistical analysis using Probability Density Functions (PDF) was performed to characterise the flow regimes. Two different flow regimes have been identified in the bundle, namely a "bubbly" and an "annular-dispersed" flow. A transition zone was evidenced by analysing the bubble size distribution. A comparison with the only preexisting map, established for adiabatic air-water flow, shows that the transitions between the flow regimes do not correspond to our results in boiling case.

1

Introduction and literature survey

The process industry using heat exchangers with a fluid evaporating across a tube bundle, are numerous.

These exchangers like kettle reboilers, flooded evaporators or steam generators are widely used in chemical industries and in nuclear power plants. The design of such equipment is not always adapted to the phenomenology of the two-phase flow in the tube bundle, and the currently used correlations do not take into account all the complexity of this problem [START_REF] Webb | Correlation of convective vaporization on banks of plain tubes using refrigerants[END_REF]).

Existing models are limited to some given cases of bundle geometries and working fluid with moderate to high mass velocities (mainly refrigerants and adiabatic air-water flow, [START_REF] Jensen | Boiling heat transfer mechanisms in a horizontal tube bundle[END_REF], [START_REF] King | Local heat transfer and flow pattern distributions in kettle reboiler. Twophase flow modelling and experimentation[END_REF] and [START_REF] Rahman | An interfacial friction factor correlation for shell-side vertical two-phase cross-flow past horizontal inline and staggered tube bundles[END_REF]). This lack of data for industrial equipment at typical operating conditions results in an increase in the safety margins, and hence an over-sizing of the heat exchangers. Finally, to improve the energy effectiveness of such equipment requires a better understanding of the two-phase flow across the tube bundle. Obtaining a precise flow regime map for boiling flows in tube bundles is thus essential to optimise the heat transfer design and to predict the two-phase flow-induced vibrational phenomena.

Two-phase flow patterns inside tubes

Boiling flows are more complex than single phase flows thus a more detailed analysis is necessary to understand the heat transfer mechanisms and to build predictive methods. Heat transfer under boiling conditions depends strongly on several parameters: the temperature difference between the wall and the fluid, the fluid properties and the wall geometry. It has been shown that for boiling two-phase flow in tubes, the knowledge of flow regimes is key to predicting the pressure and heat transfer [START_REF] Hewitt | Annular two-phase flow[END_REF]. The purpose is not to summarise all the studies realised in the past but rather to show the detection flow methods and the complexity of flows in the vertical tube case.

A two dimensional representation is generally used for a flow map. The coordinate system changes according to the authors and there is currently no agreement on the best system. The first flow pattern was proposed by [START_REF] Baker | Simultaneous flow of oil and gas[END_REF] who defined by visual observations the transitions based on the superficial gas and liquid velocitiesFlow patterns such as bubble, slug, annular and spray were observed. A significant change in flow mechanisms in a large pipe was suggested since the pressure drops were less than those predicted by the Lockhart-Martinelli's correlation (1949). Hewitt and Roberts' map (1969) is the most widely used flow map for air-water and steam-water flows. [START_REF] Bennet | Flow visualisation studies of boiling at high pressure[END_REF] steam-water results were also represented in the Hewitt and Roberts' flow regime map. They performed experiments with steam-water mixtures flowing in a pipe. Taitel and Dukler (1977) compared the Hewitt and Roberts' technique to the Govier and Aziz method (1972) and also to [START_REF] Oshinowo | Vertical two-phase flow. Part I. Flow pattern correlations[END_REF]. These comparisons revealed large discrepancies in the general trends of the transitions between flow regimes. These differences can be explained by the "subjective" definitions of the flow regimes and the single representation for several transitions. In order to identify two-phase flow regimes in an objective manner, [START_REF] Zuber | The interrelation between void fraction fluctuations and flow patterns in two-phase flow[END_REF] performed a statistical analysis of X-ray void fraction measurements for vertical air-water flow in a narrow rectangular channel. The Probability Density Functions (PDF) of void fraction fluctuations was successfully used to identify the bubbly, slug and annular flow regimes. [START_REF] Zürcher | Development of a diabatic two-phase flow pattern map for horizontal flow boiling[END_REF] and [START_REF] Thome | Two phase flow pattern map for evaporation in horizontal tubes: Latest version[END_REF] performed two-phase flow pattern map for evaporation in tubes.

In summary, it appears that even for a simple geometrical configuration, the precise determination of flow regimes is very complex. Most of the proposed flow maps are specific because they are based on visual observations and/or under specific adiabatic conditions. Only [START_REF] Zuber | The interrelation between void fraction fluctuations and flow patterns in two-phase flow[END_REF] have used a quantitative method to identify flow patterns. The theoretical approach of Taitel and Dukler (1977) for flow regime transitions is original; nevertheless this approach is difficult to extrapolate for complex geometries and flows.

Two-phase flow patterns in tube bundle

The main difficulty in the thermal design of horizontal reboilers is the determination of the heat transfer coefficient on the external side tube. The distribution of heat transfer coefficients presents a strong variation according to the position in the bundle [START_REF] Cornwell | An experimental study of the effects of fluid flow on boiling within a kettle reboiler tube bundle[END_REF]). In order to improve and optimise such equipments more information on two phase flow distribution in tube bundles are needed.

Only few experimental studies deal with vertical two-phase flow across a tube bundle. These investigations are based on visual observations because measurements are difficult to develop. [START_REF] Grant | Pressure drop on the shell-side of a segmentally baffled shell-and-tube heat exchanger with vertical two-phase flow[END_REF] were the first to describe the flow pattern in a tube bundle. They used a segmentally baffled transparent heat-exchanger of rectangular cross section with 39 unheated tubes of 19 mm outer diameter. Tubes were arranged in a staggered configuration of an equilateral triangular orientation (p/d=1.25). They performed their investigations with vertical adiabatic air-water flow. Three flow patterns were visualised: bubbly, intermittent and dispersed flows. A flow regime map was proposed by Grant and Murray based on dimensionless superficial velocities given by [START_REF] Bell | Interpretation of horizontal intube condensation heat transfer correlations with two-phase flow regime map[END_REF]. [START_REF] Kondo | Experimental investigation of air water two-phase upflow across horizontal tube bundles-Part I flow pattern and void fraction[END_REF] have studied vertical adiabatic air-water flow in three different staggered tube bundles. A quick-closing valves technique was used to measure averaged void fractions. Visual observations were performed with high speed video camera for a better identification of flow regimes.

They observed bubbly, slug, froth and spray flows. They also provide information on bubble sizes and frequencies, and observed flow patterns dependant only on the air mass flow and the pitch to diameter ratio (p/d). [START_REF] Ulbrich | Vertical, upward gas-liquid two-phase flow across a tube bundle[END_REF] carried out an experimental investigation of air and water flow across a tube bundle with 10 rows of 5 tubes with 20 mm outside diameter. The tubes were arranged in a square in-line layout with a 1.5 p/d ratio. The mean void fraction was measured by using a conductivity method. Flow regimes were determined by a combination of visual observations using both a video camera and observing the pressure drop fluctuations between the second and the ninth rows. Three flow patterns were identified (bubbly, intermittent and dispersed flows) and a flow map based on gas and liquid superficial velocities was proposed. [START_REF] Noghrehkar | Investigation of two phase flow regimes in tube bundles under cross-flow conditions[END_REF] recently studied a vertical air-water flow across a tube bundle. Experiments were conducted using staggered and in-line tube bundles with the same pitch-to-diameter ratio (p/d=1.47). A resistivity probe was used to access the local void fraction. A probability density function (PDF) of void fraction fluctuations was used as an objective statistical method to determine three different flow regimes (bubbly, intermittent and annular flow) and the associated transitions. A flow regime map was proposed for each bundle. Similar results were observed for the two geometries. However, for the staggered arrangement the bubbly-intermittent transition occurs at higher gas flow rates.

The only study in boiling conditions was reported by [START_REF] Hahne | Local void fraction measurements in finned tube bundles[END_REF]. R-11 refrigerant fluid was used and experiments were carried out with low-finned tubes arranged in staggered and in-line configurations.

The authors performed local void fraction measurements with an optical probe. Probability density histograms were realised to identify flow patterns for in-line tube bundles. A bubbly flow regime was mainly observed in the bundle, and a slug flow regime was only detected at the bundle exit. The authors suggest that the combination of a narrow gap and fins may divide large vapour slugs into smaller ones.

Void fraction model in tube bundle

The knowledge of void fraction, and gas and liquid velocities are fundamental in the prediction of the thermal hydraulic characteristics in reboilers [START_REF] Gebbie | Void fraction distributions in a Kettle reboiler[END_REF]). Several authors used a void fraction parameter in their heat transfer correlations for tube bundles [START_REF] Leong | Heat transfer coefficients in a reboiler tube bundle[END_REF]Cornwell (1979), Polley et al. (1980), [START_REF] Palen | Circulation boiling model for analysis of kettle and internal reboiler performance[END_REF] or [START_REF] Whalley | A simple method for calculating the recirculating flow in vertical thermosyphon and kettle reboiler[END_REF]). All these approaches were limited because of the lack of existing suitable void fraction models. [START_REF] Kondo | Experimental investigation of air water two-phase upflow across horizontal tube bundles-Part I flow pattern and void fraction[END_REF] performed void fraction measurements in vertical air-water upflow. Their experiments were realised at low mass velocities (m L <5 kg.m -2 .s -1 ). They found that the void fraction depends only on the superficial gas velocity. [START_REF] Schrage | Two-phase pressure drop in vertical crossflow across a horizontal tube bundle[END_REF] carried out experiments for adiabatic air-water flow using quick-closing valves. They measured the mean void fraction for an in-line plain tube bundle arranged in square layout. The authors proposed a new void fraction correlation based upon the Froude number. [START_REF] Dowlati | Pitch-to-diameter effect on two-phase flow across an in-line tube bundle[END_REF]Dowlati et al. ( , 1992aDowlati et al. ( , 1992b[START_REF] Dowlati | Measurement of void fraction and pressure drop in flow boiling of R-113 across horizontal tube bundles[END_REF][START_REF] Dowlati | Two-phase crossflow and boiling heat transfer in horizontal tube bundles[END_REF] measured the void fraction using a gamma densitometry technique for air-water and R-113 refrigerant flow with in-line and staggered tube bundles. As in Schrage's experiments, a higher void fraction is obtained when the total mass flux is increased at fixed qualities. The authors mentioned that the homogeneous model over predicts the experimental data. A void fraction correlation based on Zuber and Findlay's (1965) drift flux model was proposed. This model was independent of the pitch-to-diameter ratio. The Zuber and Findlay's parameters obtained for air-water flow differ from those of R-113 flows. [START_REF] Roser | Modélisation thermique de bouilleurs à tubes horizontaux. Etude numérique et validation expérimentale[END_REF] performed void fraction measurements using an optical probe for n-pentane boiling flow in a staggered tube bundle. A large discrepancy between the measured values and the homogeneous model was also observed. The Zuber and Findlay's parameters were deduced by fitting the experimental data. More recently, [START_REF] Feenstra | An improved void fraction model for two-phase crossflow in horizontal tube bundles[END_REF] proposed a void fraction model for upward cross-flow through a horizontal tube bundle with the use of the two phase velocities. [START_REF] Consolini | Void fraction and two-phase pressure drops for evaporating flow over horizontal tube bundles[END_REF] used this correlation for pressure drop prediction, and found good performances with their results.

The literature survey clearly shows a lack of comprehensive analysis of flow regimes. The majority of investigations were performed with adiabatic two-phase flows. This situation could be rather different in boiling conditions. In fact, the thermohydraulic parameters vary throughout the tubes bundle and the vapour is produced on the surface tubes which is not encountered in adiabatic flows. Understanding the behaviour of two-phase flows under boiling conditions in complex geometries, cannot be done successfully by just a visual approach, or a global parameter analysis alone.

Strategy of the present analysis

In boiling conditions all parameters vary along the tube bundle. For a better understanding of the twophase flow mechanisms, local measurements of parameters are required.

Local flow parameters, such as the vapour and liquid velocities, the mass quality and the void fraction vary along the tube bundle. Hence, the use of local and precise instrumentation is necessary. The lack of experimental studies on the local void fraction in a tube bundle shows the weaknesses and the limits of the previous investigations. The majority of investigations were performed with adiabatic two-phase flows and the heat transfer mechanisms were not tackled. [START_REF] Hahne | Local void fraction measurements in finned tube bundles[END_REF] used boiling conditions only for R-11 refrigerant. Physical properties play an important role in the thermal hydraulic performance of two-phase flows. Consequently Hahne's results are limited and cannot be directly applied to actual fluids used in the process industry.

The objectives of this work are to characterise the two-phase flow patterns outside horizontal tube bundles, to establish original flow maps and finally, to propose an interpretation of the transitions found between flow regimes. The present work is realised with three hydrocarbons n-pentane, propane and isobutane, at different working conditions (Table 2), leading to large variations in the physical properties (Table 1). An original data bank is gathered. This will be used for the analysis of the two-phase flow and the heat transfer in tube bundles. This paper focuses on the local void fraction behaviour to determine flow regimes, and to propose a flow map under boiling conditions. The analysis is based on local void fraction measurements. An optical probe system was chosen because of its simplicity, its precision and its compatibility with hydrocarbon fluids. The local void fraction measurement was performed at a central position in the tube bundle. To observe all the possible flow regimes at this unique position, several mass flow velocities and heat flux were investigated.

2

Experimental set-up and procedure

The test loop

The hydrocarbon closed loop composes; a test section, a condenser, a cooler and a liquid pump (Figure 1). The test section is representative of an industrial reboiler, but differs by the presence of two vertical walls confining the flow. Half round solid tubes are stuck on the inner walls to prevent flow bypasses.

This device avoids internal shell-side re-circulations and allows a precise control of the total mass flow rate through the bundle. The hydrocarbon is pumped from the shell, then subcooled and re-enters the test section at saturated conditions. The hydrocarbon mass flow rate M 2L is controlled by a variable speed pump PM201 up to 1 kg.s -1 . The vapour leaving the boiler at the top is condensed, and returned to the shell where it mixes with the liquid pouring over the wall (Figure 1). The vapour mass flow rate M 2G produced in the bundle is measured downstream of the condenser. Liquid and vapour flow rates are measured by flowmeters allowing determination of the vapour quality at the test section exit. For each experiment, we compared the vapour quality at the test section exit measured at the condenser to the values obtained by heat balance on the hot side. The maximum deviations for these two values do not exceed 5%. This procedure was applied systematically for checking the validity of our measurements.

This configuration reduces the two-phase flow instabilities, allowing the loop to run at low mass fluxes, which are typical operating conditions for industrial reboilers. Most equipment operates in natural convection (or "thermosiphon") mode, rather than in forced convection as considered in the present work.

The present experiments use forced convection because it eliminates circulation instabilities (if the circulation rate is higher than would be achieved by thermosiphon action) and allows to precisely calculating the quality of the two phase flow. The bundle is arranged in a staggered layout with a pitch-todiameter ratio (p/d=1.33). The tubes are 500 mm long with an inner diameter of 15.7 mm and an outer diameter of 19.05 mm. All of the copper tubes have been polished on the outer surface with an average roughness of 0.4 µm.

To produce vapour, hot water-glycol flows inside the tubes. Nine groups of tubes (a control volume) are fed at the same mass flow rate and inlet temperature conditions (Figure 2a). A heat balance is performed for each control volume using the measurement of water-glycol solution mass flow rate M 1 and the inlet and outlet temperatures (T 1in (j), T 1out (j)) (Figure 2a).

On the hydrocarbon side, the measured quantities are the flow temperatures at every second row of tubes (T 2 (1)…T 2 ( 9)), the pressure drop ∆p between the top and the bottom of the bundle and the local void fraction. The entrance conditions of the fluid are known from the recorded temperature T 2 (0), pressure p(0) and mass flow rate M 2L (Figure 2a). The nominal ranges of experimental conditions covered in this investigation are listed in Table 1. The calculation of uncertainties was evaluated for all the operating conditions. It was founded that the temperature uncertainties were less than 0.5K. The pressure level and mass flux uncertainties were less than 5% and the void fraction were less than 1%. Using the method proposed by [START_REF] Moffat | Describing the uncertainties in experimental results[END_REF], the maximum uncertainties in vapour quality, heat transfer coefficient and heat flux were less than 25% for all the operating conditions.

Optical fibre probe

The void fraction measurement system is composed by an optical probe, a transmitter and an infra-red light detector (Figure 3b). The optical system is made up of a silica optical fibre with only one connector on the whole length. The optical fibre is held in a 2 mm diameter rigid sheath, and ended by a sapphire point of 0.4 µm in diameter (Figure 3a). Its tip is cone-shaped to allow the precise detection of bubbles with a minimum diameter of 80 µm. The choice of the sapphire point is justified by its greater robustness, which is necessary in the industrial environment. The local void fraction ε is measured at three positions on an inclined line between the tubes, along which the optical probe can move within an accuracy of 0.05 mm. The three measurements are equidistant to 2.1 mm around the central position 2 (Figure 2b). The void fraction recording is based on the difference of refraction index between the liquid and the vapour.

The signal coming from the emission diode is sent continuously by the optical fibre. When the tip of the probe is in the liquid, the signal is refracted and the detector gives a low voltage level. On the contrary, when the probe is in the vapour, the signal is reflected and returns to the reception diode which gives a high voltage level. An electronic circuit converts the direct signal coming from the detector into a TTL square signal. Analogous and digital signals are visualised simultaneously on an oscilloscope and this makes the quality control of the measurements possible. The gain of the detector is fixed to have a difference of 6V between the high and the low levels of the analogous signal; the detection threshold of a bubble is fixed at 0.77 V. Under these conditions, the observed noise is always lower than 0.4 V. The duration of all the high level signals is summed to determine the total time t G during which the probe detects the vapour. The void fraction ε is defined as the ratio of t G time over the total recording time T R :

R G T t = ε (1)
The measuring system used for the n-pentane [START_REF] Roser | Modélisation thermique de bouilleurs à tubes horizontaux. Etude numérique et validation expérimentale[END_REF]) and propane allowed a recording time of 6.4 s. This value corresponds to the maximum capacity of the buffer memory of the acquisition card working at a sampling rate of 5 kHz. For the iso-butane data, the sampling rate was 2 kHz without any notable loss of information with a total recording time of 160 s. A PC-based data acquisition system with a National Instrument NI-PCI-6013 high speed A/D data acquisition board and LabView software was used to record the digital signal of the void fraction from the optical probe.

Data analysis

If P(ε) is the probability that the void fraction, ε, is less than some specific value, then dP(ε)/dε=p(ε)

represents the probability per unit void fraction that the void fraction lies between the values of ε and ε+dε. During the total time recording T R , the void fraction and the time scale can be divided into equal increments of ∆ε and ∆t respectively. The void fraction appears n i times between ε i and ε i +dε i . If N is the number of ∆t windows for the total time recording T R , we have:

∑ = ∆ = ∆ i n k R k G i i i T t N n 1 , 1 ε ε (2)
In the case of bubbly flow, a large ratio n i /N occurs at low void fraction while a smaller ratio exists for higher values of the void fraction. The ratio Σ(∆t/T) represents the probability that the void fraction lies within the given interval, bounds around ε i . Then the PDF can be given by:

∑ = → ∆ ∆ i i n k k G i R t T 1 , 0 1 lim ε ε (3)
If ∆t is small enough, the PDF can be evaluated by using the left or right hand side of equation ( 2). In the present investigation, the PDF has been carried out on the instantaneous digital signal of the local void fraction. The digital signal is cut in 8000 ∆t windows (Figure 4), and the partial void fraction in each window is calculated by (1) ( )

t t t j G j ∆ = , ε (4)
The amount n i of partial void fraction ε j (t) for each interval ∆ε is added up n i =n i +1 when ε i <ε j <ε i +∆ε i .

Finally, the PDF i relative to the void fraction interval ∆ε i is defined by: 20

... 1 = ∆ = i N n PDF i i ε ε (5)
The void fraction scale is divided into 20 intervals (∆ε=0.05) and the total recording time into 8000 ∆t windows.

Choice of the ∆t duration sample determination

The PDF shapes are closely related to the windows duration ∆t. To investigate this, an analysis of its influence has been realised. In fact, the ∆t window implemented must be large to visualise high void fraction time variations and also sufficiently small so as to have variations of the instantaneous void fractions. The choice of the ∆t parameter is consequently difficult to evaluate. As a result, a quantitative method must be implemented to determine the value of this window in order to realise a quantitative analysis of the flow patterns.

To obtain a quantitative value of ∆t, an analysis of the instantaneous cross-correlation void fraction functions R x,x (τ) was performed.

( ) ( ) ( ) τ ε ε τ + ⊗ = t t R xx (6)
This approach allows us to pin-point the time at which the signals are no longer correlated and hence to achieve a better evaluation of the characteristic times. Figure 6 presents a representative sample of the results obtained for the three hydrocarbons at various operating conditions. It can be noticed that the signals differ from one fluid to another, and also for different operating conditions. The iso-butane and the n-pentane signals are no longer correlated for times above 0.01s and for propane approximately 0.02s.

To simplify the systematic analysis we chose the same time interval for the three hydrocarbons corresponding to the highest value deduced from the cross correlation function, 0.02s. This choice is not unique.

Characterisation of the flow regimes by statistical analysis

To complete this approach a statistical analysis has also been realised. The latter is based on the determination of the higher moments (second, third and fourth) to allow an interpretation of the void fraction variation according to different flow regimes.

The general form of the moments (r>2) of a PDF is given as:

( ) [ ] ∑ = - = N i r i r Z x t Z N M 1 , 1 (7)
The first moment M 1 , equal to zero, provides the arithmetic mean value of the variable Z. The second moment M 2 is the root-mean square deviation from the mean value. The third moment M 3 allows the evaluation of the curve's asymmetry around the mean value. And finally, the fourth moment M 4 represents the distribution concentration around a peak.

The skewness coefficient C M3 =M 3 /M 2 3/2 and kurtosis coefficient C M4 =M 4 /M 2 2 are used to characterise the probability density histograms as illustrated in Figure 7 and Figure 8. Figure 7a proposes a schematic histogram with a positive coefficient of skewness which means that many events N occur at small values of the variable. Figure 7b gives a Gaussian distribution of events and, in Figure 7c, a negative coefficient of skewness indicates a great number of events at high values of the variable.

In the case of a Gaussian distribution (or normal law), odd moments are zero and even moments are calculated by: ( )

n n M n n M ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ = 2 ! ! 2 2 2 (8)
The schematic histograms for different coefficients of kurtosis C M4 are presented in Figure 8. In the case of a Gaussian distribution of a variable, C M4 is equal to 3(Figure 8b). For C M4 >3 a great number of events occur in a region around the peak (Figure 8a). For C M4 <3, the events are spread as a large range around the peak (Figure 8c).

A statistical study will be performed so as to characterise the flow regimes. The analysis of the third and fourth order moments will help, and can be used to obtain information on the size of the bubbles through the C M3 coefficient, and also on their distributions in the flow with the C M4 coefficient.

4

Results and discussion

Local mean void fraction analysis

Global thermal conditions of reboilers are partially governed by hydraulic conditions at the tube scale. In order to characterize the two-phase flow in the bundle, we compared the experimental data of the void fraction for each hydrocarbon with the Homogeneous Model (HM). The mean void fraction was calculated by an average of positions 1, 2 and 3 between the tubes (Figure 2b). These three positions have been selected because of their location in the main flow between the tubes at the minimum cross section.

Figure 9 compares the homogeneous model with the experimental results for each hydrocarbon, at the same mass velocity based on the minimum cross-section (m 2L =15 kg.m -2 .s -1 ). The experimental values are significantly lower than the prediction of the homogeneous flow model where the slip factor is not considered. This over-prediction is found for the three hydrocarbons and all the operating conditions investigated. The comparison of the hydrocarbon measurements reveals that the void fraction for npentane is higher than for the two other fluids. This is due to a lower operating pressure inducing a larger density ratio (ρ L /ρ G ) for n-pentane. This is in accordance with the [START_REF] Martinelli | Prediction of pressue drop during forced-circulation boiling of water[END_REF] investigation. It shows that for a given vapour quality a decrease in operating pressure for steam-water leads to an increase in void fraction. [START_REF] Dowlati | Measurement of void fraction and pressure drop in flow boiling of R-113 across horizontal tube bundles[END_REF] have also observed this trend for R-113 boiling flow in a staggered tube bundle. On Figure 9, propane and iso-butane give approximately the same void fraction results since their physical properties are similar at the same operating pressure.

To take into account the void fraction variations in terms of the physical properties, the drift flux model has been applied to our results for the three hydrocarbon fluids. Initially developed by Zuber and Findlay (1965), this model suggests that the average gas velocity U G is linearly related to the superficial velocity j as, ( )

⎪ ⎪ ⎩ ⎪ ⎪ ⎨ ⎧ - + = = + = L L G L G L G Gj G x m x m j x m U with U j C U ρ ρ ε ρ 1 . . . . 2 2 2 0 (9)
where C 0 represents the void fraction distribution parameter and U Gj is the drift velocity. In Figure 10 the results for n-pentane, propane and iso-butane are plotted.

Using a linear regression, the following fitted curve was obtained with an average deviation of 20% for the three hydrocarbons:

23 . 0 047 . 1 + = j U G ( 10
)
The fact that C 0 is different from unity and U Gj is different from zero, clearly indicates that the homogeneous model fails. The obtained value of C 0 (1.047) is similar to the values obtained by Dowlati et al. (1992[START_REF] Dowlati | Measurement of void fraction and pressure drop in flow boiling of R-113 across horizontal tube bundles[END_REF] for air-water (1.104) and R-113 (1.076). On the contrary, the value of U Gj (0.23) is lower than those obtained by Dowlati et al. (1992[START_REF] Dowlati | Measurement of void fraction and pressure drop in flow boiling of R-113 across horizontal tube bundles[END_REF] for air-water flow (0.33) and R113-boiling flow (0.85).

Equation 10 correlates all our experimental data bank. The Zuber and Findlay's approach (1975) leads to a single relation for the whole of the investigated operating conditions (fluid, pressure, mass flow rate and heat flux). This representation doesn't show the differences in the fluid flow behaviour. To overcome this deficiency another approach must be implemented.

PDF description

To determine the flow regimes for convective boiling in a staggered bundle, the PDF method associated with moments of higher orders was developed and applied on hydrocarbon void fraction recordings. This method was used for the first time by [START_REF] Zuber | The interrelation between void fraction fluctuations and flow patterns in two-phase flow[END_REF] to obtain a quantitative representation of the flow patterns in a narrow rectangular channel. It was also used successfully thereafter by [START_REF] Hahne | Local void fraction measurements in finned tube bundles[END_REF] to analyse the flows regimes of refrigerants in pool boiling conditions outside a bundle of finned tubes, and by Noghrekhar et al. (1999) for adiabatic air-water flows on smooth tubes bundle in both a square and a staggered configuration.

Figure 11 represents three typical PDF of the local void fraction obtained with iso-butane and their associated void fraction signals. The PDF data showing a single peak at low void fractions, is obtained for signals of events of short time duration; they represent bubbly flow (Figure 11a). Conversely, the PDF data showing one peak at high void fractions is obtained for signals of events with high time duration; they represent annular-dispersed flow (Figure 11c). Between these two regimes, an intermittent regime can be identified as a combination of the two others. The void fraction time series is composed of two types of signals: high time duration of the void fraction (characteristic of annular-dispersed flow) and small time duration of void fraction (characteristic of the bubbly flow). On the corresponding PDF, two peaks are found: one at low void fraction for small bubbles and one at high void fraction for large bubbles (Figure 11b). Nevertheless, qualitative comparison between PDF curves is not satisfactory. A quantitative study must be undertaken using statistical tools.

Sensitivity of PDF to operating conditions

The analysis of the PDF variations according to the hydrocarbon mass velocity rate and the heat flux were performed in order to understand the flow regime evolution as well as the mechanisms leading to the transitions. In the case of a two-phase-flow in a confined and tortuous space, two physical mechanisms support the creation of the flow regimes: the fragmentation and the coalescence of the bubbles.

Fragmentation breaks up and divides large vapour slugs into smaller ones, and coalescence results from the gathering of small bubbles into a large vapour slug. Figure 12 shows for each flow regime the evolution of a PDF with increasing mass flow rate for a given heat flux. For bubbly flow (Figure 12a), the peak which appears at ε=0.2 for m 2L =31 kg.m -2 .s -1 is attenuated and moves to a higher values for higher mass flow rates. For the three regimes, an increase in mass flow rate causes a reduction of the number of events at low void fractions and an increase at large void fraction (Figure 12a-b-c). The tube bundles compactness in a staggered configuration obliges the bubbles to coalesce to form large vapour slugs of significant size. This interpretation differs from Hahne's one (1990) probably because of the use of finned tubes in his study.

In addition, we noticed a strong influence of the heat flux on PDF curves. Comparison of the different curves on Figure 12a-b-c shows that for the same massflow rate (m 2L =39 kg.m -2 .s -1 ) an increase of the heat flux causes more important changes in the flow regimes than the increase of the hydrocarbon flow.

As the heat flux increases, bubbles forming on the tubes are more numerous. When they separate from the wall, they tend to join and coalesce with the vapour already present in the main flow. The quantity of vapour produced is more important at higher heat flux, the coalescence will be enhanced and the flow transition will occur earlier than for adiabatic two-phase flow.

Characterisation of flow regimes

The previous analysis shows the difficulty to separate and to characterise the different flow regimes with only the use of the PDF curves. This is why a statistical analysis based on the local void fraction measurements was also performed. The approach consists in analysing the void fraction signal with moments of order 3 and 4. The variations of these moments allow the PDF shape and consequently the flow regimes to be defined.

In Figure 13 the standard deviation from the mean value of void fraction is presented for all operating conditions and for the three hydrocarbons. As we can see, the whole of the void fraction range is covered from 0 to 1. Almost all the M 2 values are grouped together in the same curve. The fitted curve presents a parabolic shape. Propane and n-pentane appear respectively at low and high void fractions. For iso-butane it was possible to carry out measurements on a broader range of void fractions. The M 2 coefficient has a maximum value of 0.35 for the void fraction value of 0.5. A low value of M 2 represents a flow regime where the vapour structures (bubbles or slugs) have the same size. Conversely, large values of M 2 reveal the existence of both small and large vapour structures. The comparison between the hydrocarbons shows some differences. The propane experiments were located at low void fractions, while the n-pentane experiments were located at high void fractions. The iso-butane experiments covered all the void fraction range.

In Figure 14 the kurtosis coefficient C M4 is plotted for all of the data; a C M4 value larger than 3 means that all the events are concentrated around the mean value (Figure 8a). For a low void fraction (ε<0.35), almost all the tests of propane and some of the iso-butane tests (those at a low heat flux and a low mass flow rate) present a C M4 value larger than 3. According to the previous analysis (Figure 13 and Figure 14)

we assume that these regimes are composed of small bubbles of similar size. For high void fraction measurements (ε>0.56), C M4 values of n-pentane and iso-butane are larger than 3. The flow is composed of vapour slugs of the same size. It should be noted that it is difficult to precisely evaluate the width of the transition zone because the minimum values of C M4 are close to 3. However, for 0.35<ε<0.56 (which comprises most of the iso-butane results) the coefficient is around 3 and confirms that these flows include a large variety of events distributed according to a normal law.

In Figure 15 the coefficient of skewness C M3 is presented for all the fluids investigated. For void fraction lower than 0.35, the coefficient is clearly positive. According to Figure 7a the PDF data presents a peak for low void fractions; this means that there is a large number of small bubbles present in the flow. For a higher void fraction (0.35<ε<0.56), the coefficient is around zero (-0.5<C M3 <0.5). The flow is composed of bubbles of different sizes distributed according to a Gaussian curve (Figure 7b). This flow regime is assumed to be representative of an intermittent regime due to the alternative presence of small and large bubbles. For void fractions higher than 0.56, the coefficient is negative and drops quickly. According to Figure 7c, this indicates a great number of events at high void fractions, representative of an annulardispersed flow.

In summary, the flow regimes can be separated in the following way:

-Bubbly flow regime for a void fraction lower than 0.35, -Annular -dispersed flow regime for a void fraction higher than 0.56, -Intermittent flow regime for a void fraction varying in a range between 0.35 and 0.56.

Flow regime descriptions and flow map

The statistical analysis highlighted three flow patterns. To obtain more information on two-phase flow regimes, an analysis of the mean bubble diameter B d was performed. This diameter is calculated as:

G B B U t d . = (11)
The average time B t of flowing bubbles has been evaluated as,

N t n t N i i i B ∑ = = 1 (12)
Where n i is the number of bubbles which have a duration time t i , and N is the total number of time data recorded. G U is the mean real vapour velocity :

ε ρ . . 2 G L G x m U = (13)
Figure 16 shows the evolution of the average bubble size for the three hydrocarbons. For void fractions lower than 0.35, the mean bubble diameter is lower than the minimum space between the tubes (Figure 2b). When the bubbles reach a critical size, which corresponds to the minimum space between the tubes, the flow becomes chaotic. Alternative passages of small and large vapour structures occurs, this corresponds to the two peaks of the intermittent regime (Figure 11b). For a higher mean void fraction the bubbles are bigger and close to each other, the interfaces between the vapour slugs breaks and a continuous vapour phase, in which liquid droplets can be involved, is generated. This annular-dispersed flow, which appears for void fractions higher than 0.56, presents an average size of bubble ranging between 2.5 and 7 times the tubes clearance.

These flow regime results could be interpreted using the fluid physical properties. The propane whose vapour density is most significant for the given operating conditions, mainly produces a bubbly flow regime. Conversely, n-pentane which has the lower vapour density for the operating conditions used is exclusively located in the annular-dispersed flow regime. Iso-butane which has vapour densities ranging in-between propane and n-pentane, covers all of the three flow regimes.

As in the case of convective boiling inside a tube, the flow structure outside of a tube bundle is controlled by the heat flux, the hydrocarbon mass flow rate and the physical properties. However, the effects of the obstacles and the tortuosity will induce flow transitions at lower void fractions. In a tube bundle, the extent of the transition zone is partly due to the agitation and the dynamic effects of the two-phase flow which tends to divide larger vapour slugs in smaller ones, and then increases the transition zone between the bubbly and the annular-dispersed flow.

Figure 17 is a schematic representation of the two flow regimes.

Bubbly flow is characterized by a vapour phase distributed as discrete bubbles in the continuous liquid phase (Figure 17a). These bubbles initially detaching from nucleation sites on tube walls. [START_REF] Kondo | Experimental investigation of air water two-phase upflow across horizontal tube bundles-Part I flow pattern and void fraction[END_REF] and [START_REF] Ulbrich | Vertical, upward gas-liquid two-phase flow across a tube bundle[END_REF] noted that bubbles have a uniform size with a characteristic diameter lower than the space between the tubes.

Annular-dispersed flow is characterised by a continuous gas phase in which the liquid droplets are carried (Figure 17b). The larger fraction of the flow area in a tube bundle is occupied by the vapour phase in the form of channels between the tubes. The liquid phase mainly occupies the recirculation zone between the tubes, and has an irregular movement with surface waves on the tube walls.

Intermittent flow is characterized by a superposition of bubbly and annular-dispersed flows.

The few established flow regimes found compared to those obtained for two-phase flows in vertical tubes, is mainly due to the presence of tubes whose effect is to confine a flow in a complex geometry. The experimental data were first compared to the flow map proposed by [START_REF] Noghrehkar | Investigation of two phase flow regimes in tube bundles under cross-flow conditions[END_REF]. These authors evidenced the transition zone for a staggered tube bundle (p/d=1.47) in adiabatic conditions (airwater mixture) as shown in dashed lines on Figure 18. As we can see on this figure, the flow transitions proposed by these authors differ highly from our flow boiling conditions. The main differences are:

-The transitions for flow boiling conditions are moved towards lower superficial vapour velocity.

-In flow boiling the transitions depend only on vapour velocities, liquid velocities do not play a role.

-The width of the transition zone between the bubble and annular-dispersed flows is significantly smaller for boiling flow (superficial gas velocity between 0.15 and 0.35) compared to adiabatic two-phase flow (between 0.45 and 3.9).

These differences might be explained by the fact that in adiabatic conditions the two-phase flow is organized from the bottom of the bundle and only influenced by the geometrical configuration of the tube bundle. In flow boiling conditions the vapour is generated on the tube wall, and all along the bundle. This effect combined with the complex geometry of the obstacles (tubes bundle) involves large disturbances of the two-phase flow. This leads to a shift in the transition zone towards smaller void fractions.

As a result, a new flow regime map is proposed for flow boiling in tube bundles. The limits between the flow regimes are determined according to the constant superficial vapour velocities j G (Figure 18). The limits between bubbly and intermittent flow are j G =0.15± 0.03 m.s -1 , and between intermittent and annular-dispersed flow are j G =0.35± 0.03 m.s -1 . The error uncertainties in both the vapour quality and the mass flowrate are included in the data range and limits.

Conclusions

Two-phase flow patterns in a staggered tube bundle were investigated for three hydrocarbons at boiling conditions. The experimental device and the local instrumentation implemented appears well adapted to the analysis of boiling outside horizontal tube bundles. A method of the local void fraction analysis in such a complex geometry was successfully developed. Three hydrocarbons were explored under several operating conditions (pressure, heat flux and massflow rate). In this study a quantitative method for the determination of flow structures for boiling conditions outside horizontal tube bundle has been proposed.

The correlation of Zuber and Findlay (1965) was applied to the void fraction data with a good agreement and a unique relationship between j G and U G was obtained for the three fluids. This correlation is rather directed towards practical applications, and does not provide a comprehensive analysis of two-phase flow phenomena.

The statistical analysis of the void fraction signals allows a clear identification of two regimes bubbly and annular-dispersed flow, separated by an intermediate regime. The latter corresponds to the superposition of the two main modes. The statistical analysis showed that, for the investigated conditions, propane flows are mainly bubbly and n-pentane flows are mainly annular-dispersed. For iso-butane both bubbly and annular-dispersed regimes are evidenced. The transitions between these regimes were identified and correspond to void fraction thresholds. Bubbly flow is found for void fraction values lower than 0.35 while annular-dispersed flow is found for values higher than 0.56.

A flow map based on the superficial vapour and liquid velocities (j G , j L ) has been proposed for tube bundles with a pitch-to-diameter ratio equal to 1.33. It has been shown that the transition regimes were found for a superficial vapour velocity of 0.15 ± 0.03 m.s -1 and 0.35 ± 0.03 m.s -1 . The study showed the major roles of the fluid physical properties such as the liquid and vapour densities on the regimes. The proposed flow map covers a large range of operating conditions for three hydrocarbons at different operating conditions. Moreover, it will be interesting to analyse the validity of the proposed map with other fluids such as non-hydrocarbon fluids.

Future works must be directed towards the influence of the geometrical parameters. It seems that the space between the tubes is a dominating parameter, not on the nature of the flow regimes but on the transition between these regimes.

Based on the present flow regime map, the heat transfer and pressure drop laws must be established. An investigation will be carried out to highlight the existing relationship between the thermohydraulic laws and the flow regime map. Figure 6 Cross correlation functions for various hydrocarbons -n-pentane (p=0.3 bar, q=44 kW.m -2 , m 2L =44 kg.m -2 .s -1 ); propane (p=6 bar, q=6 kW.m -2 , m 2L =15 kg.m -2 .s -1 ); iso-butane (p=4 bar, q=52 kW.m -2 , m 2L =46 kg.m -2 .s -1 ). Figure 14 The kurtosis coefficient of local void fraction for three hydrocarbons on a staggered tube bundle. This coefficient measures the concentration of experimental values around a peak. We confirm that for bubbly flow (small void fraction), and annular-dispersed flow (high void fraction) the PDF is

represented by a single peak as shown on Figure 8a-c. In the intermittent regime, the PDF presents two peaks representative of a Gaussian distribution of small and large vapour bubbles (Figure 8b)

Figure 15 The skewness coefficient of local void fraction for three hydrocarbons on a staggered tube bundle. This coefficient measures the asymmetry of the PDF. We confirm that for bubbly flow (small void fraction), and annular-dispersed flow (high void fraction) the PDF is non symmetric as shown on Figure 7a-c. In the case of intermittent regime, the PDF is symmetric around the mean void fraction (Figure 7b)

Figure 16 Mean bubble diameter vs. mean void fraction for propane, iso-butane and n-pentane in boiling conditions. This figure shows the importance of tube clearance for the organization of the flow regime. ). The dashed lines represent the transitions obtained by [START_REF] Noghrehkar | Investigation of two phase flow regimes in tube bundles under cross-flow conditions[END_REF] with adiabatic results.

Table 1 Physical properties of n-pentane, propane and iso-butane for the operating conditions used in the present investigation. The physical properties have been calculated at saturation temperature with REFPROP 6.01 software.

Table 2 Operating conditions for the three hydrocarbons used in the present investigation. A broad range of the operating conditions is covered. This constitutes a unique database of flow boiling in a tube bundle. 9 9 heat flux q [kW.m -2 ] 13 ≤ q ≤ 44 3 ≤ q ≤ 53 10 ≤ q ≤ 52 Table 2

COOLER

2L T 2 (0) p(0) T 2 (1) T 2 (2) T 2 (3) T 2 (4) T 2 (5) T 2 (6) T 2 (7) T 2 (8) T 2 (
2L T 2 (0) p(0) T 2 (1) T 2 (2) T 2 (3) T 2 (4) T 2 (5) T 2 (6) T 2 (7) T 2 (8) T 2 (
ε (t) ε =82,5 % ε =42,5 % ε =77,5 % ε =47,5 % ε =57,5 % ε =57,5 %

Iso-butane

  Figure 5 a,b,c show the PDF of the recorded signal for three different mean void fractions by using several ∆t values. It is clearly shown that a decrease of the time scale ∆t from 0.5 s to 0.005 s induces significant modifications of the normalised PDF function. For the smallest values of time cut, all the curves present an increase for low void fraction values and also for high values. For the highest time cuts (0.5s) the curves normally present an accentuation of the peak around the mean void fraction.

Figure 1

 1 Figure 1 Sketch of the experimental apparatus. (a) Boiling two-phase flow installation, (b) tube bundle test section.

Figure 2

 2 Figure 2 Sketch of the tube bundle test section with measured quantities (a) and location of void fraction measurements with an optical probe system (b).

Figure 3

 3 Figure 3 Void fraction measurements system (a) sectional of the optical probe tip and (b) diagram of the fibre optical system.

Figure 4

 4 Figure 4 Typical instantaneous void fraction variation signal versus time, and time windows method used for statistical analysis.

Figure 5

 5 Figure 5 Influence of the time duration sample variations on PDF data for regimes, (a) Bubbly flow, (b) intermittent flow, and (c) annular-dispersed flow.

Figure 7

 7 Figure 7 Schematic histograms for the three different coefficients of skewness C M3 .

Figure 8

 8 Figure 8 Schematic histograms representation for the three different coefficients of kurtosis C M4 in the case of a Gaussian function of void fraction.

Figure 9

 9 Figure 9 Local mean time void fraction profile versus vapour quality. A comparison of the experimental data with the homogenous model for boiling hydrocarbons.

Figure 10

 10 Figure 10 Vapour velocity versus total superficial velocity for the three hydrocarbons propane, iso-butane and n-pentane. Analysis of the experimental data with the drift flux model. The points are deduced for each experiment. U G is deduced from the local measurement (liquid massflow rate m 2L , vapour quality x, void fraction ε, vapour density ρ G ). The curve is obtained by fitting the experimental points. The Zuber and Findlay's coefficients are then deduced (C 0 =1.0466, U Gj =0.23).

Figure 11

 11 Figure 11 Typical probability density function of the local void fraction signal for the three regimes (a) bubbly flow, (b) intermittent flow, (c) annular-dispersed flow for iso-butane boiling in a staggered tube bundle. The operating conditions are displayed on each graph. A sample of the void fraction time signal is also shown.

Figure 12

 12 Figure 12 Probability Density Function variation of local void fraction signal for (a) bubbly flow, (b) intermittent flow, (c) annular-dispersed flow for iso-butane boiling on a staggered tube bundle.

Figure 13

 13 Figure 13 Variation of M 2 coefficient of local void fraction for three hydrocarbons on a staggered tube bundle. The points are deduced from the experimental values of void fraction signal. Far from the intermittent regime, i.e. for bubbly and annular-dispersed flow, the RMS decreases.

Figure 17

 17 Figure 17 Sketch of the two flow regimes proposed for boiling conditions outside a tube bundle. (a) Bubbly flow. (b) Annular-Dispersed f low.

Figure 18

 18 Figure18Flow regime map for a staggered tube bundle in hydrocarbon flow boiling conditions. The two vertical lines represent transitions between the flow regimes (bubbly flow for j G <0.15 ± 0.03 m.s -1 , annular-dispersed flow for j G >0.56 ± 0.03 m.s -1 and intermittent flow for 0.15 ± 0.03 <j G < 0.56± 0.03 m.s - 1

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Fluid