Etienne Hendrickx
email: etienne.hendrickx@univ-brest.fr

Mathieu Paquier

Vincent Koehl

Julian Palacino

Ventriloquism effect with sound

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I. STATE OF THE ART

The effect of a spatial disparity between related sound and visual stimuli can be studied in two ways [START_REF] Bertelson | Cross-modal bias and perceptual fusion with auditory-visual spatial discordance[END_REF], either through a localization task, which makes it possible to observe cross-modal biases, or a discordance-detection task, which makes it possible to observe ventriloquism (or perceptual fusion).

A. Cross-modal bias

In a localization task, subjects report the direction of the sound stimulus. Significant shifts in localization towards the visual stimulus were found in many studies [START_REF] Alais | The ventriloquist effect results from near-optimal bimodal integration[END_REF][START_REF] Battaglia | Bayesian integration of visual and auditory signals for spatial localization[END_REF][START_REF] Bertelson | Bayesian integration of visual and auditory signals for spatial localization[END_REF][START_REF] Bertelson | Cross-modal bias and perceptual fusion with auditory-visual spatial discordance[END_REF][START_REF] Hairston | Visual localization ability influences cross-modal bias[END_REF][START_REF] Wallace | Unifying multisensory signals across time and space[END_REF][START_REF] Bermant | Cross-modal bias and perceptual fusion with auditory-visual spatial discordance[END_REF][START_REF] Pick | Sensory conflict in judgments of spatial direction[END_REF][START_REF] Radeau | Adaptation au dplacement prismatique sur la base d'une discordance entre la vision et l'audition[END_REF][START_REF] Radeau | The effect of a textured visual field on modality dominance in a ventriloquism situation[END_REF][START_REF] Warren | Spatial localization under conflict conditions: Is there a single explanation?[END_REF][START_REF] Weerts | The effect of eye position and expectation on sound localization[END_REF]. For example, with a 7 • difference between audio and visual stimuli in the horizontal plane, [START_REF] Bertelson | Cross-modal bias and perceptual fusion with auditory-visual spatial discordance[END_REF] observed that the localization of the sound stimulus by the subjects was shifted 4 • towards the visual stimulus. They also observed a deviation in sound localization of approximately 6.3 • for a 15 • difference between audio and visual stimuli, and observed a deviation of 8.2 • for a difference of 25 • . Such a phenomenon is called cross-modal bias.

The modality specificity hypothesis [START_REF] Welch | Immediate perceptual response to intersensory discrepancy[END_REF][START_REF] Welch | Meaning, attention, and the "unity assumption" in the intersensory bias of spatial and temporal perceptions[END_REF] posits Hendrickx,Paquier,Koehl and Palacino JASA,p. 4 that the sensory modality with the greater precision for the discrimination to be made will dominate the percept with respect to that discrimination. Thus, the visual stimulus influences the percept of the spatial location of the sound stimulus because the visual system spatial precision is in the range of a minute arc (1/60 of a degree) [START_REF] Cavonius | Relationships between luminance and visual acuity in the rhesus monkey[END_REF], while the auditory system precision is equal to or greater than 5 • [START_REF] Recanzone | Comparison of relative and absolute sound localization ability in humans[END_REF] depending on stimulus spectrum and intensity.

In accordance with the modality specificity hypothesis, a predictive model based on maximum-likelihood estimate was successfully used in several studies to estimate the bimodal perception, relying on the precision of the auditory and visual spatial information in unimodal condition [START_REF] Ernst | Humans integrate visual and haptic information in a statistically optimal fashion[END_REF][START_REF] Alais | The ventriloquist effect results from near-optimal bimodal integration[END_REF]. If a visual stimulus is perceived at a position m V with variance σ 2 V , and a sound stimulus at a position m A with variance σ 2 A , then the model predicts that an audiovisual stimulus will be perceived at a position m AV so that:

m AV = σ 2 V σ 2 V + σ 2 A m A + σ 2 A σ 2 V + σ 2 A m V
Thus, the influence of each modality on the localization of the audiovisual stimulus is weighted in proportion to the precision of the modalities in the unimodal condition.

If the visual precision decreases, then the weighting associated with m V decreases and Hendrickx, Paquier, Koehl and Palacino JASA, p. 5 the weighting associated with m A increases: thus the audiovisual stimulus is perceived increasingly close to the sound stimulus. The model therefore suggests that situations might arise where the sound stimulus captures the visual stimulus if the visual stimulus is less salient. This "reverse" ventriloquism was observed by [START_REF] Alais | The ventriloquist effect results from near-optimal bimodal integration[END_REF]. Subjects were required to localize brief light "blobs" or sound "clicks". Light "blobs" could be more or less blurred. With the sharp "blobs", visual localization was good and vision indeed dominated and captured sound. Yet, with the severely blurred "blobs", visual localization was poor and sound captured vision. For less blurred visual stimuli, neither sense dominated and perception followed the mean position between the sound stimulus and the visual stimulus.

On the other hand, if the auditory precision decreases, the visual system will dominate the percept of the spatial location of a sound stimulus even more.

B. Perceptual Fusion or Ventriloquism

In a discordance-detection task, subjects report whether or not they experience perceptual fusion (the so-called ventriloquism effect) of the visual stimulus with the related sound stimulus [START_REF] Jack | Effects of degree of visual association and angle of displacement on the "ventriloquism" effect[END_REF][START_REF] Radeau | Adaptation to auditory-visual discordance and ventriloquism in semirealistic situations[END_REF][START_REF] Thurlow | Certain determinants of the "ventriloquism effect[END_REF], or, in a different version, whether they perceive the visual and sound stimuli as coming from the same or from different location [START_REF] Choe | The "ventriloquist effect": Visual dominance or response bias?[END_REF][START_REF] André | Subjective Evaluation of the Audiovisual Spatial Congruence in the Case of Stereoscopic-3D Video and Wave Field Synthesis[END_REF][START_REF] Werner | Vertical Sound Source Localization Influenced by Visual Stimuli[END_REF][START_REF] Wallace | Unifying multisensory signals across time and space[END_REF]. Studies usually summarize the performance of Hendrickx,Paquier,Koehl and Palacino JASA,p. 6 subjects by reporting the 50%-threshold (the angular difference between related visual and sound stimuli for which subjects still experience fusion -or still perceive the visual and sound stimuli as coming from the same location -half of the time). In some studies, subjects are instead asked to use the ITU-R 5-grade impairment scale (ITU-R BS. 2003) to quantify to what extent the disparity is perceptible and annoying [START_REF] Komiyama | Subjective evaluation of angular displacement between picture and sound directions for HDTV sound systems[END_REF][START_REF] Bruijn | Subjective experiments on the effects of combining spatialized audio and 2D video projection in audio-visual systems[END_REF][START_REF] Melchior | Wave Field Synthesis Hendrickx, Paquier, Koehl and Palacino JASA, p. 48 in combination with 2D video projection[END_REF][START_REF] Melchior | Audiovisual perception using Wave Field Synthesis in combination with augmented reality systems: Horizontal positioning[END_REF][START_REF] Mannerheim | Spatial sound and stereoscopic vision[END_REF]. As shown in Table 1, grades are associated with specific subjective impressions, and experimenters usually report either the threshold for a "perceptible, but not annoying" angular difference [START_REF] Mannerheim | Spatial sound and stereoscopic vision[END_REF] or the threshold for a "slightly annoying" angular difference [START_REF] Melchior | Wave Field Synthesis Hendrickx, Paquier, Koehl and Palacino JASA, p. 48 in combination with 2D video projection[END_REF][START_REF] Melchior | Audiovisual perception using Wave Field Synthesis in combination with augmented reality systems: Horizontal positioning[END_REF]. [START_REF] Komiyama | Subjective evaluation of angular displacement between picture and sound directions for HDTV sound systems[END_REF]) also defines the "acceptable limit of discrepancy" as the midpoint between "perceptible, but not annoying" and "slightly annoying" angular differences. [START_REF] Bertelson | Cross-modal bias and perceptual fusion with auditory-visual spatial discordance[END_REF] and [START_REF] Wallace | Unifying multisensory signals across time and space[END_REF], who carried out a localization and a discordance-detection task at the same time, using 50-msec pulses of either 300 Hz pure tones or broadband noise combined with LED lamps. Both studies found that biases of auditory localization towards the visual stimulus could occur even when fusion was not reported, and that biases were larger when fusion was reported.

C. Previous studies on ventriloquism in azimuth bring out several influencing factors

Numerous studies have investigated ventriloquism in azimuth [START_REF] Lewald | Spatio-temporal constraints for auditory-visual integration[END_REF][START_REF] Komiyama | Subjective evaluation of angular displacement between picture and sound directions for HDTV sound systems[END_REF][START_REF] André | Subjective Evaluation of the Audiovisual Spatial Congruence in the Case of Stereoscopic-3D Video and Wave Field Synthesis[END_REF][START_REF] Wallace | Unifying multisensory signals across time and space[END_REF][START_REF] Jackson | Visual factors in auditory localization[END_REF][START_REF] Thurlow | Certain determinants of the "ventriloquism effect[END_REF][START_REF] Warren | The role of visual-auditory compellingness in the ventriloquism effect: Implications for transitivity among the spatial senses[END_REF][START_REF] Bertelson | Cross-modal bias and perceptual fusion with auditory-visual spatial discordance[END_REF][START_REF] Melchior | Wave Field Synthesis Hendrickx, Paquier, Koehl and Palacino JASA, p. 48 in combination with 2D video projection[END_REF][START_REF] Mannerheim | Spatial sound and stereoscopic vision[END_REF], and all came to the conclusion that the effect decreases with increasing angular difference between the positions of the sound and visual stimuli. Even so, the range of thresholds reported by those studies is wide: from 3 • [START_REF] Lewald | Spatio-temporal constraints for auditory-visual integration[END_REF] to 20 • [START_REF] Komiyama | Subjective evaluation of angular displacement between picture and sound directions for HDTV sound systems[END_REF]. These differences can be explained by several factors: the experience of subjects, the audiovisual temporal disparity, the "compellingness" factor, and attention.

The experience of subjects

In Koimyama's study (1989), subjects had to use the ITU-R 5-grade impairment scale to quantify to what extent the disparity between the mouth of a TV speaker and his voice was perceptible and annoying. With expert subjects, the acceptable limit of the discrepancy was 11

Temporal Disparity

Increasing temporal disparities between sound and image can also decrease the obtained thresholds. Using a 50-ms broadband noise burst followed by a 50-ms illumination of a LED lamp, Wallace measured a 50%-threshold greater than 15 • when the delay was 200ms. However, the 50%-threshold was reduced to about 10 • when the delay was 800 ms [START_REF] Wallace | Unifying multisensory signals across time and space[END_REF].

Compellingness

Ventriloquism also depends on higher level factors, such as whether or not the participant assumes that the stimuli should "go together" [START_REF] Vatakis | Crossmodal binding: Evaluating the unity assumption using audiovisual speech stimuli[END_REF].

Indeed, several studies showed that if the combinations of audiovisual stimuli are perceived as being more meaningful and "compelling", observers will be more likely to treat them as referring to a single audiovisual event [START_REF] Jackson | Visual factors in auditory localization[END_REF][START_REF] Welch | Immediate perceptual response to intersensory discrepancy[END_REF], and therefore to assume that they have a common spatial origin.

For example, [START_REF] Jackson | Visual factors in auditory localization[END_REF] conducted two experiments: in one, the visual stimulus was a puff of steam from a kettle whistle and the sound stimulus was a whistling sound, while in the other, the situation was much more abstract as it consisted of sounds of bells associated with lights. When the disparity between sound and image was equal to 30 • , the whistling sound was still located at the kettle releasing the steam in 97% of the trials, while the sound of bell was located at the light in only 43% of the trials when the disparity between sound and image was equal to 22.5 • .

In one of Thurlow's experiments (1973), a TV monitor was placed in front of the subject, and a loudspeaker was hidden 20 • to the left of the TV monitor. Visual stimuli could either be a speaker reading texts, or a cross in the middle of a circle drawn on a sheet of white paper (the paper was fastened to the front of the TV monitor, with the circle approximating the location of the mouth). In both conditions, the sound stimulus was the voice of the speaker. Subjects were asked to look directly at the mouth of the speaker on the TV screen (or the cross in the middle of the circle) and to turn a stopwatch on whenever they heard speech coming from the direction of the visual stimulus and to turn it off when they did not (the stimulus was 5 minutes long). The average duration during which speech was heard coming from the visual stimulus was 3 minutes and 22 seconds Hendrickx, Paquier, Koehl and Palacino JASA, p. 10 with the TV speaker and this was reduced to 51 seconds with the cross.

In [START_REF] Warren | The role of visual-auditory compellingness in the ventriloquism effect: Implications for transitivity among the spatial senses[END_REF], the dynamic face of a speaker or a static visual stimulus (consisting of a 1 × 2 cm piece of tape placed at the location on the screen where the speaker's mouth would have been) was presented, together with an auditory speech signal with various degrees of spatial discrepancy. Fusion was observed for larger angles with the dynamic face than with the simple static visual spot (from 4.6 • to 3.2 • ), because, according to Warren et al., the combination of the speaker's face and the matching voice was more compelling than the visual spot with a speech signal.

Thus, 50%-thresholds will be greater with realistic sequences such as speech sequences than with arbitrary and non-meaningful combinations of stimuli, such as flashing lights and brief tones.

Attention

Several studies having conducted both discordance-detection and localization tasks suggest that focusing the attention on the spatial location of the sound stimulus makes subjects much more discriminating and thus decreases 50%-thresholds substantially.

Indeed, many subjects reported noticing discrepancies only when they had to localize sound [START_REF] Radeau | Adaptation au dplacement prismatique sur la base d'une discordance entre la vision et l'audition[END_REF][START_REF] Radeau | The effect of a textured visual field on modality dominance in a ventriloquism situation[END_REF] or when they were warned that they might be questioned about the respective origins of the sound and the visual stimuli [START_REF] Bertelson | Cross-modal bias and perceptual fusion with auditory-visual spatial discordance[END_REF]. Bertelson hypothesized that humans tend to ignore the Hendrickx, Paquier, Koehl and Palacino JASA, p. 11 spatial origin of auditory data to the advantage of visual data unless the task forces attention towards it. [START_REF] Thurlow | Certain determinants of the "ventriloquism effect[END_REF] also recommend using discordance-detection tasks instead of localization tasks, as it brings the subjects closer to an everyday life situation and prevents them from becoming excessively discriminating.

However, when [START_REF] Komiyama | Subjective evaluation of angular displacement between picture and sound directions for HDTV sound systems[END_REF] conducted his discordance-detection task, subjects reported that they would probably not have detected audiovisual discrepancies if they had not been asked to judge them. It suggests that even a discordance-detection task may make subjects too discriminating compared with an everyday life situation.

D. Ventriloquism in elevation

Ventriloquism has been extensively examined in the horizontal plane, and to a lesser extent in distance [START_REF] Gardner | Proximity image effect in sound localization[END_REF][START_REF] Mershon | Visual capture in auditory distance perception: Proximity image effect reconsidered[END_REF][START_REF] Agganis | Visual biasing of auditory localization in azimuth and depth[END_REF][START_REF] Zahorik | Auditory and visual distance perception: The proximity-image effect revisited[END_REF][START_REF] Hládek | Ventriloquism effect and aftereffect in the distance dimension[END_REF][START_REF] Bowen | Visual signals bias auditory targets in azimuth and depth[END_REF]. On the other hand, few studies have explored elevation [START_REF] Thurlow | Certain determinants of the "ventriloquism effect[END_REF][START_REF] Werner | Vertical Sound Source Localization Influenced by Visual Stimuli[END_REF].

It has been shown previously that cross-modal biases of auditory localization towards the visual stimulus become larger as the auditory precision decreases. As localization performance is poorer in the vertical plane than in the horizontal plane when stimuli are located on or near the frontal midline, one would expect to observe larger biases in elevation than in azimuth. Indeed, when [START_REF] Makous | Two-dimensional sound localization by human listeners[END_REF] asked subjects to localize broadband stimuli that could vary in both dimensions, the intra-subject variability of Hendrickx, Paquier, Koehl and Palacino JASA, p. 12 responses (i.e. the standard deviation of responses about the mean response location) in the vertical dimension could be as great as 2.5 times that in the horizontal dimension.

If larger biases are obtained in elevation than in azimuth, then, according to [START_REF] Bertelson | Cross-modal bias and perceptual fusion with auditory-visual spatial discordance[END_REF] and [START_REF] Wallace | Unifying multisensory signals across time and space[END_REF] comparative studies between cross-modal bias and ventriloquism, ventriloquism should be observed with larger audiovisual disparities in elevation than in azimuth.

In one of Thurlow's experiments (1973), a TV monitor was placed on the floor, so that the mouth of the speaker on the TV screen was close to 40 • below subjects' ear level.

A hidden loudspeaker was positioned at an angle of 15 • above subjects' ear level. Thus, the total angle between TV speaker and loudspeaker was 55 • . The average duration that speech was heard coming from the TV speaker was about 4 out of 5 minutes. The duration was reduced to 1 minute and 42 seconds when the TV speaker was replaced by the uncompelling cross drawn on a sheet of paper.

In another experiment, the hidden loudspeaker was behind the subjects, at 10 • above their ear level, and the TV speaker was in front of the subjects at an angle of 25 • below ear level. The total elevation difference between TV speaker and hidden loudspeaker was therefore 195 • . The average duration during which speech was heard coming from the TV speaker was about 3 minutes and 20 seconds, that is still two-third of the total duration of the stimulus. The average duration was reduced to 74 seconds with the uncompelling cross.

When Thurlow conducted the experiment with a hidden loudspeaker 60 • to the right of the center of the TV screen (no difference in elevation), however, the average duration that speech was heard coming from the TV speaker was only 52 seconds, that is four times shorter than in the condition with a loudspeaker behind the subjects in spite of the fact that the angular difference between sound and image was reduced from 195 • to 60 • .

Thus, Thurlow's experiments support both the hypothesis that ventriloquism can be observed with larger audiovisual discrepancies in elevation than in azimuth, and the hypothesis that ventriloquism in elevation depends on the compellingness of the combinations of sound and visual stimuli.

In Werner's study (2013), the sound stimulus was either a 30-ms white noise burst or a 6-s anechoic recording of a saxophone, which could be reproduced via either of two virtual loudspeakers reproduced through headphones (using individualised binaural reproductions including acoustic room information). One of the loudspeakers was right in front of the subject (0 • azimuth, 0 • elevation) while the other one was at 25 • above ear level. The visual stimuli were white LEDs positioned in front of the subject (0 • azimuth) along a segment of circle centered at the subject's head, from 10 • below ear level to 35 • above ear level. For each presentation, subjects had to report whether they perceived the audio stimulus below, in-plane, or above the visual stimulus. Note that in this experiment, the sound stimulus was fixed while the visual stimulus was shifted. The estimated Hendrickx, Paquier, Koehl and Palacino JASA, p. 14 50%-threshold was 8 • for the loudspeaker at 0 • elevation, whether the visual stimulus was shifted below or above the loudspeaker. For the second loudspeaker, the 50%-threshold was 10 • when the visual stimulus was shifted below and greater than 10 • when the visual stimulus was shifted above.

Werner concluded that the measured ventriloquism effect had similar magnitudes for elevated stimulus positions as it has in the horizontal plane. Yet, because Werner did not conduct his experiment in azimuth, this assumption is based on comparison with previous studies, whose experimental conditions were different. As ventriloquism is highly dependent on experimental conditions (see I.C), one cannot know whether the obtained similarities of thresholds does not actually result from different test designs.

In Werner's study, many factors may have favored the collection of low 50%-thresholds:

• Subjects were well experienced with listening tests and had been trained. It has been shown that thresholds obtained with experts could be half that obtained with non-expert subjects [START_REF] Komiyama | Subjective evaluation of angular displacement between picture and sound directions for HDTV sound systems[END_REF];

• Sound and image were presented synchronously;

• The combinations of stimuli were not compelling, as they consisted of 30-ms white noise bursts combined with white LEDs. A recording of saxophone was also used, Hendrickx, Paquier, Koehl and Palacino JASA, p. 15 which can seem more realistic. Yet the recording was still associated with the white LEDS, so the combination of sound and image was probably no more compelling in this case;

• The sound stimulus was fixed (at either 0 • or 25 • elevation). Subjects may therefore have learnt where the loudspeakers were located precisely, which made them more accurate when comparing with the position of the visual stimulus.

Had Werner's experiment been conducted in azimuth in the same conditions, thresholds could have been much lower. The results may therefore underestimate the strength of ventriloquism in elevation compared with in azimuth.

E. Summary and aim of the present study

Numerous studies in azimuth have revealed several factors influencing ventriloquism:

the spatial disparity (the effect decreases with increasing angular difference), the temporal disparity (the effect is stronger if the sound and visual stimuli are synchronous), the experience of subjects (experts are more discriminating than naïve subjects) and the "compellingness" factor (the effect is stronger if the combination of the sound and visual stimuli is more realistic).

It has also been shown that ventriloquism is dependent on the auditory system spatial precision (the effect is stronger as the auditory precision decreases). As localization Hendrickx, Paquier, Koehl and Palacino JASA, p. 16 performance is poorer in the vertical plane than in the horizontal plane, 50%-thresholds are expected to be greater in elevation than in azimuth.

Thurlow's studies seem to support this hypothesis, although he did not measure 50%-thresholds so his results cannot be compared with the literature. On the other hand,

Werner did measure 50%-thresholds in the median plane that had similar magnitudes as in previous studies in the horizontal plane. However, this similarity may be rather due to the specificity of his experimental conditions, and only a comparison with 50%-thresholds in azimuth obtained in the same experimental conditions would be truly legitimate.

Several studies also suggest that ventriloquism will be more likely to occur if subjects pay less attention to the spatial location of the sound stimulus. For example, in a real life speech situation, the attention would rather be focused on the semantic content, which may severely reduce subjects' attention to sound localization.

The aim of the present study is to compare ventriloquism in azimuth and in elevation in realistic conditions. It is hypothesized that:

• 50%-thresholds are greater in elevation than in azimuth. Thus, 50%-thresholds were measured for sound stimuli varying in both azimuth and elevation, so that ventriloquism in both dimensions could be compared directly;

• 50%-thresholds can be greater than in Werner's study if the experiment is conducted in conditions that more closely resemble our everyday experience: compelling Hendrickx, Paquier, Koehl and Palacino JASA, p. 17 combinations of stimuli (speech sequences), naïve subjects instead of trained experts and focus of attention on the semantic content of the stimuli.

II. EXPERIMENTAL SETUP A. Stimuli

The program material was the screening of a speaker sitting on a chair on a black background, pronouncing 5-second sentences. The sequences were shot in stereoscopic-3D using a Panasonic AG-3DP1 camera and projected in real size. The choice of stereoscopy was motivated by Ijsselsteijn's findings that stereoscopy increases the sense of presence [START_REF] Ijsselsteijn | Determination of optimal data placement for psychometric function estimation: A computer simulation[END_REF]. It was therefore hypothesized that subjects in the present experiment would assume more easily that the voice and the mouth of the speaker had a common spatial origin if their subjective sensation of "being there" with the speaker was stronger.

The phrases used in the experiment were inspired by the speech corpus used in studies on speech-on-speech masking [START_REF] Martin | Spatial release from speech-on-speech masking in the median sagittal plane[END_REF]. The stimuli consisted of one sentence, in French, following the format "Je m'appelle {nom}, ma couleur préférée est le {couleur} et j'habite à {ville}" ("My name is {name}, my favorite color is {color} and I live in {city}"). There were three possible names (Antoine, Clément, Pierre), three possible colors (Red, Green, Blue) and three possible cities (Bordeaux, Lyon, Marseille). With all possible Hendrickx, Paquier, Koehl and Palacino JASA, p. 18 combinations of names, colors and cities, the sentence could therefore take twenty-seven different forms. The stimuli were recorded in a sound-attenuated room following Bolia's recommendations (2000), with a DPA 4006 microphone connected to a RME Fireface 800.

The microphone was placed 22 cm above the mouth of the speaker so that it would not be in the frame of the camera.

B. Reproduction Setup

The test took place in a sound-attenuated room of dimensions 5.

C. Placement of Loudspeakers

Several studies have obtained left-right symmetry for the ventriloquism effect [START_REF] Werner | Vertical Sound Source Localization Influenced by Visual Stimuli[END_REF][START_REF] Wallace | Unifying multisensory signals across time and space[END_REF] and it was therefore decided to set all the sound stimuli to the right of the visual stimulus.

In the median plane, however, Werner's results ( 2013) suggest an imbalance between positive and negative discrepancies (the obtained 50%-thresholds are likely to be different whether the sound stimulus is shifted above or below the visual stimulus). Nonetheless, only positive elevations (sound stimuli shifted upwards) were studied in order to keep the test within a reasonable duration.

A two-dimensional double pole spherical coordinate system (with θ and φ defined as azimuth and elevation respectively) was used to describe positions of loudspeakers and 50%-thresholds on a 2.40-m sphere centered at the subject's head. Note that this coordinate system differs in its definition of azimuth from the single-pole system that is sometimes used (see [START_REF] Knudsen | Mechanisms of sound localization in the barn owl (Tyto alba)[END_REF] and [START_REF] Middlebrooks | Directional sensitivity of sound-pressure levels in the human ear canal[END_REF] for a discussed comparison between the two systems).

The visual stimulus was displayed on a screen directly in front of the subject, so that Hendrickx, Paquier, Koehl and Palacino JASA, p. 20 the mouth of the speaker corresponded to 0 • azimuth, 0 • elevation, at a distance of 2.40 m.

The sound stimulus could be shifted from the visual stimulus along several circle arcs that were also centered at the subject's head, and whose angle at the visual stimulus with the arc subtending azimuth was noted δ and defined as orientation. In order to keep the test within a reasonable duration, four values were chosen for δ: 0 • (shifting to the right), 45 • (in diagonal), 67.5 • and 90 • (upwards). The four δ-orientations are presented in Fig. 1.

Figure 1: The four δ-orientations along which the sound stimulus could be shifted from the visual stimulus. The orientations were centered at the subject's head. The visual stimulus was fixed (0 • azimuth, 0 • elevation) and is represented by the grey circle.

For each δ-orientation:

• A fusion report refers to a situation where a subject indicates that he perceives the voice and the mouth of the speaker as coming from the same direction;

• The angular difference Ψ is defined as the angle at the subject's head between the visual stimulus (the mouth of the speaker projected right in front of the subject) and the sound stimulus (the voice of the speaker);

• The 50%-threshold Ψ 50% is defined as the value of Ψ for which the percentage of fusion reports is equal to 50% (that is the angular difference Ψ for which the voice of the speaker is perceived as coming from the direction of the mouth half of the time);

• The 50%-threshold Ψ 50% can be broken down into the corresponding azimuth and elevation differences between sound and image: The 50%-threshold azimuth θ 50% and the 50%-threshold elevation φ 50% .

Fig. 2 gives the example of a loudspeaker A positioned along the δ-orientation 67.5 • , with an angular difference of Ψ = 36 • .

Polar coordinates can be calculated from δ and Ψ using the following formulae: Let us suppose that Ψ 50% = 32 • for the δ-orientation 67.5 • . Ψ 50% can be broken down into the corresponding azimuth and elevation differences:

Azimuth : θ A = arcsin(sin Ψ × cos δ) = arcsin(sin 36 • × cos 67.5 • ) ≈ 13 •
θ 50% = arcsin(sin 32 • × cos 67.5 • ) ≈ 11.7 • φ 50% = arcsin(sin 32 • × sin 67.5 • ) ≈ 29.3 •
This means that if a loudspeaker is positioned at azimuth θ = 11.7 • and elevation φ = 29.3 • , fusion will occur 50% of the times when the sound stimulus is reproduced via that loudspeaker.

The values for δ were determined on the basis of an informal test conducted by the four experimenters, which suggested that the 50%-threshold Ψ 50% varies moderately from orientations 0 • to 45 • and more substantially from orientations 45 • to 90 • .

Note that maintaining the loudspeaker locations at constant angles of orientation means that azimuth and elevation variations are constrained as the angular difference Ψ increases along one of the δ-orientations:

• When δ = 0 • , there is no variation in elevation as Ψ increases (horizontal plane);

Hendrickx, Paquier, Koehl and Palacino JASA, p. 24

• When δ = 45 • , azimuth and elevation vary similarly as Ψ increases;

• When δ = 67.5 • , elevation increases faster than azimuth as Ψ increases;

• When δ = 90 • , there is no variation in azimuth as Ψ increases (median plane).

A pilot informal test with six subjects was conducted in order to gain an idea about the general shape of the psychometric functions, from which optimal loudspeaker placement and spacing along each orientation were determined on the basis of recommendations by [START_REF] Lam | Determination of optimal data placement for psychometric function estimation: A computer simulation[END_REF] and [START_REF] Levitt | Transformed up?down methods in psychoacoustics[END_REF]. Levitt, for example, stated that a typical "rule of thumb" is for the experimenter to place the observations so as to roughly cover the range of expected X 10 to X 90 , where X 10 and X 90 are the stimulus levels corresponding in the present study to 10% and 90% of fusion reports.

Loudspeaker locations used in the experiment are presented in Table 2. Note that the seventh loudspeaker of the δ-orientation 90 • had an angular difference Ψ of 137 • , which means it was behind the subjects.

Because of the screen and room configuration, the loudspeakers could not always be placed at an exact distance of 2.40 m from the subject. The maximum distance error was 16% (the loudspeaker right above the subjects, at φ = 90 • ), which falls within the distance discrimination thresholds obtained by [START_REF] Ashmead | Perception of the relative distances of nearby sound sources[END_REF] for a stimulus at 2 m, in a control condition in which intensity was held constant over varying distance. The impact on subjects' answers was, therefore, expected to be negligible.

Orientation δ = 0 • Orientation δ = 45 • Orientation δ = 67.5 • Orientation δ = 90 • Loudsp. θ φ Ψ θ φ Ψ θ φ Ψ θ φ Ψ 1 5 0 5

D. Subjects and Protocol

Eight naïve subjects took part in the experiment (four men and four women, aged 19 to 40 years old). They were financially compensated for their participation, and none of Hendrickx, Paquier, Koehl and Palacino JASA, p. 26 them had particular experience in laboratory listening tests.

A first test (task A "without semantic question") was carried out in which, after each presentation, subjects had to answer the question: "Do the voice and the mouth of the actor come from the same direction?". Once they had given their answer, the next stimulus was automatically played.

An additional test was carried out with questions on the semantic content of the sequences (task B "with semantic questions"): after each presentation, subjects had to report the name, the favorite color and the living place of the speaker before giving their answer to the question on audiovisual coherence. In case of wrong answers, the trial was repeated a bit later.

As recommended by [START_REF] Lam | Determination of optimal data placement for psychometric function estimation: A computer simulation[END_REF], subjects went through thirty trials per loudspeaker for each task. The loudspeakers were presented in a randomized order (so as to appear as unrelated sound stimuli from multiple locations and orientations), with a different randomization for each subject. For each trial, a stimulus was randomly chosen

III. RESULTS

To estimate the psychometric functions, a nonparametric approach was used based on local linear fitting. This method has the benefit of making no assumptions about the true model underlying the data (except its smoothness) while providing better or equal performances compared with common parametric models [START_REF] Zchaluk | Model-free estimation of the psychometric function[END_REF].

For task B, it was decided to remove from data the trials on which subjects answered some semantic questions incorrectly, as the error rate was very low (less than 1% for each subject).

A. Influence of the δ-orientation Fig. 3 presents the 50%-threshold Ψ 50% as a function of the δ-orientation for each subject during task A (without semantic questions). Ψ 50% could not always be determined at δ = 90 • : for subjects B and F, the percentage of fusion reports was greater than 50% for any loudspeaker of the orientation (fusion reports still occurred 85% and 77% of the time respectively when the angular difference Ψ was at its maximum value 137 • ). The value 137 • was chosen for the graph, but fusion might still have occurred more than half of the time for greater angles, maybe even for the whole median plane. function was close to horizontal at the 50%-point, there was very little precision in the Ψ 50% estimate (the confidence interval was [40.6; 107.3]).

It was therefore decided not to use the 50%-thresholds for data obtained at δ = 90 • , but rather to indicate the maximum value of angular difference Ψ for which fusion had been observed to occur more than half of the time. In the case of subject C, the value Ψ = 90 • , corresponding to the sixth loudspeaker of the δ-orientation 90 • was reported. As the psychometric functions were monotonically decreasing for all subjects in this condition, 50%-thresholds are likely to be at values greater than those indicated.

In Fig. 3, 50%-thresholds are already spread out at orientation δ = 0 • , ranging from times greater than other subjects. As δ-orientation increases from 0 • to 45 • , all subjects show a fairly consistent trend, with a moderate increase in 50%-thresholds (mean = +6 • ).

As δ-orientation increases from 45 • to 67.5 • , 50%-thresholds increase faster for all subjects (mean = +10 • , which means that the mean increase is almost twice as much as from δ = 0 • to δ = 45 • , though the difference in orientation is halved). Nonetheless, the rate of this increase varies greatly from one subject to another: for example, the increase is +20 • for subject F whereas it is only +6 • for subjects G. These different rates widen inter-subject variability: at δ = 67.5 • , two subjects (B and F) present much greater thresholds (41 • and 67.5 • to 90 • , 50%-thresholds increase even faster for most subjects, with a greater difference in the rates of increase: +96 • for subject B, but only +12 • for subject G. As a result, widely spread out thresholds are obtained at δ-orientation of 90 • : from 19 • for subject H to 137 • for subjects B and F. Subject H is the only case where, surprisingly, the 50%-threshold decreases by 9.5 • . Note that subjects A, D and E present the same threshold at δ-orientation of 90 • , equal to 43 • . However, this equality is due to our specific definition of threshold in that orientation: the real 50%-thresholds are most likely different from one subject another and may be spread along a range from 43 • (fifth loudspeaker of the orientation) to 90 • (sixth loudspeaker of the orientation).

A similar trend was obtained for task B, which included semantic questions (see Fig. 5), though the shift between δ = 67.5 • and δ = 90 • is less pronounced. Again, some subjects (A, C, D and E) present the same threshold at δ-orientation of 90 • , equal to 34 • , which means that the real 50%-thresholds are most likely different from one subject to another and may actually be spread along a range from 34 • (fourth loudspeaker of the orientation) to 43 • (fifth loudspeaker of the orientation).

In summary, results from both tasks A and B show that :

• 50%-thresholds strictly increase as δ-orientation increases from 0 Wilcoxon tests were carried out to determine whether the task had a significant impact on subjects' responses.

A first test was performed, comparing 50%-thresholds and slopes obtained for δ = {0 • , 45 • , 67.5 • }. It revealed that task had no significant influence (p = 0.976 for Hendrickx, Paquier, Koehl and Palacino JASA, p. 32 50%-thresholds and p = 0.224 for slopes). Another Wilcoxon test was performed for the δ = 90 • orientation, which compared the percentage of fusion reports obtained for each loudspeaker (see Fig. 6). The test was pooled across the seven loudspeakers of the orientation, including results from all subjects, and revealed that there were more fusion reports during the task A "without semantic questions" (p = 0.011), with 64% of fusion reports for task A against 59% for task B "with semantic questions".

C. Influence of azimuth and elevation

Hendrickx, Paquier, Koehl and Palacino JASA, p. 33 Fig. 7 presents the 50%-thresholds Ψ 50% broken down into corresponding azimuth θ 50% and elevation φ 50% for task A.

Changes in azimuth at threshold are quite slight compared to changes in elevation at threshold as δ-orientation increases. A Wilcoxon test, pooled across tasks A and B, even shows that there is no significant difference of azimuth between orientations δ = 0 • and δ = 45 • (p = 0.820). Note that the δ-orientation of 45 • constrains elevation to be equal to azimuth. However, if the study had not been limited to constant orientations, it is likely that 50% thresholds would have been observed at the same azimuth but with greater elevations.

At a certain orientation between δ = 45 • and δ = 67.5 • , the 50%-threshold azimuth θ 50% starts decreasing. Yet, as can be seen on Fig. 7, this decrease is slight compared with the simultaneous increase of the 50%-threshold elevation φ 50% .

Thus, fusion only depends on the azimuth difference between the visual and sound stimuli over a broad range of orientation (from δ = 0 • to at least 45 • ). Beyond 45 • , elevation difference must also be taken into account, yet it requires large changes in elevation compared with azimuth to alter fusion significantly.

IV. DISCUSSION

A. 50%-thresholds are greater in elevation than in azimuth The results of the present study support the hypothesis that 50%-thresholds are greater in elevation than in azimuth : 50%-thresholds were on average four times greater at δ-orientation of 90 • (vertical plane) than at δ-orientation of 0 • (horizontal plane). These results are consistent with Thurlow's previous studies (1973), and also with the localization performance of the auditory system: as spatial precision is poorer in the vertical plane than in the horizontal plane, the influence of the spatial location of the sound stimulus decreases and thus larger angular differences are tolerated. Yet, pronounced inter-subject variability was observed, as 50%-thresholds in the vertical plane ranged from 1.1 to 8 times greater than 50%-thresholds in the horizontal plane depending on the subject. For "oblique directions" (δ-orientation of 45 • and 67.5 • ), the visual and sound stimuli present both azimuth and elevation differences, yet results show that changes in elevation have very little effect on ventriloquism and that 50%-thresholds are mainly determined by the azimuth difference.

B. 50%-thresholds can be large in the vertical plane

It had also been hypothesized that 50%-thresholds in the vertical plane would be greater than in Werner's study if the experimental conditions were changed so as to more closely resemble our everyday experience. In the present experiment:

• Naïve subjects conducted the test instead of experts, and it has been shown that thresholds obtained with non-expert could be as great as twice those with expert Hendrickx, Paquier, Koehl and Palacino JASA, p. 36 subjects;

• The experimenters sought to achieve a high degree of realism for the stimuli (stereoscopic projection of a life-size speaker), assuming that it would substantially increase the compellingness of the combination of sound and visual stimuli. In Thurlow's studies (1973), a compelling combination of sound and visual stimuli could multiply the average duration during which fusion occurred by almost three compared with a non-meaningful combination;

• In the present experiment, sound could come from twenty-eight different locations (while Werner's study only used four loudspeakers). It might therefore have been less easy for the subjects to learn the location of the sound stimuli.

Results show that 50%-thresholds in the vertical orientation were indeed much greater (from 19 • to values greater than 137 • ) than those obtained by [START_REF] Werner | Vertical Sound Source Localization Influenced by Visual Stimuli[END_REF] (between 8 • and 10 • ). The percentage of fusion reports may even have been greater than 50% in the whole median plane for two subjects, as they still reported fusion 85% and 77% of the time even when the sound stimulus was behind them (Ψ = 137 • at δ-orientation of 90 • ). These results are not unexpected: indeed, [START_REF] Thurlow | Certain determinants of the "ventriloquism effect[END_REF] had already observed that fusion was possible in the vertical plane in spite of a 195 • angular difference between the visual and sound stimuli.

C. Variations of attention impact ventriloquism only in the median plane

It had been hypothesized that forcing the subject to focus on the semantic content of the stimuli would increase 50%-thresholds. However, most subjects reported that memorizing the name, the favorite color and the living place of the character was an easy task that did not draw their attention away from spatial disparities. Other subjects reported that the first words "je m'appelle"/"my name is" (which were the same for every sentence) were enough to make their decision on the ventriloquism question and they could therefore focus on the semantic content for the rest of the sentence. Results showed that there was indeed no significant difference between tasks A and B for δ = {0 • , 45 • , 67.5 • }.

However, there were more fusion reports during the task A "without semantic questions" than during the task B "with semantic questions" at δ = 90 • . The trend cannot result from a learning effect, as the order of the tasks was different depending on the subject. It could be hypothesized that forcing the subjects to focus on the semantic content maintains their level of arousal at a higher degree and therefore makes them more discriminating over time.

Although the results contradict the experimenters' hypothesis, they still show that variations in the subjects' attention can change the 50%-thresholds significantly. At δ = {0 • , 45 • , 67.5 • }, those changes are negligible, but it becomes far more influential at δ = 90 • .

D. Different weightings of influencing factors might explain the increase of inter-subject variability as δ-orientation increases

A hypothesis, very similar to a model proposed by [START_REF] Thurlow | Certain determinants of the "ventriloquism effect[END_REF], could explain the observed trends.

Whether a sound stimulus fuses with a visual stimulus or not is a complex decision that depends on several factors such as the location of the sound stimulus, the extent to which a subject assumes that the sound and the visual stimuli should "go together" (compellingness factor) and the extent to which the subject pays attention to the spatial location of the sound stimulus.

The influence of these factors has more or less weight depending on the situation. For example, if the precision of sound localization is poor, then the sound stimulus could come from any one of a large number of locations. If the combination of the visual and sound stimuli is highly compelling, the subjects might assume that the most probable location for the sound stimulus is the same as the visual stimulus. Thus, the influence of the factor "location of the sound stimulus" decreases to the benefit of the "compellingess" factor.

While some factors are fairly consistent across subjects, other factors show large inter-subject variability:

• Localization performance has been shown to be consistent across subjects [START_REF] Makous | Two-dimensional sound localization by human listeners[END_REF]); Hendrickx, Paquier, Koehl and Palacino JASA, p. 39

• The strength of the assumption that a sound stimulus and a visual stimulus should "go together" (compellingness factor) depends on the experience of subjects and on their history with similar situations [START_REF] Warren | The role of visual-auditory compellingness in the ventriloquism effect: Implications for transitivity among the spatial senses[END_REF];

• Attention to the auditory modality has also been shown to vary substantially from one subject to another in previous visual-auditory multisensory tasks [START_REF] Giard | Auditory ? visual integration during multimodal object recognition in humans: A behavioral and electrophysiological study[END_REF].

Thus, if the weight associated with a highly subjective factor (such as compellingness or attention) increases, it would be expected to observe larger inter-subject variability.

In the horizontal plane, localization performance is good. Thus, as long as there is some minimal difference in azimuth between the sound and visual stimuli, whether or not fusion occurs is strongly influenced by the horizontal location of the sound stimulus. This has several consequences:

• 50%-thresholds occur for limited angular differences between the sound and visual stimuli;

• A change in elevation of the sound stimulus has little effect because the lack of precision in vertical localization makes this change an irrelevant spatial cue compared with azimuth;

• The influence of other factors such as compellingness and attention is reduced. Thus, Hendrickx, Paquier, Koehl and Palacino JASA, p. 40 moderate inter-subject variability is shown, and small variations in attention (task A vs. task B) are negligible.

Yet, as δ-orientation increases, there are increasing elevation differences and decreasing azimuth differences between the sound and the visual stimuli. As localization precision is poorer in elevation, the influence of the spatial location of the sound stimulus thus decreases, which has two consequences:

• 50%-thresholds increase;

• The influence of other factors, such as compellingness and variations in attention, increases. As these factors are highly subjective, larger inter-subject variability is observed. It would also explain why the factor "attention" (task A vs. task B) only became significant at δ-orientation of 90 • . Fig. 8 shows the psychometric functions obtained for subject D during task A. The slopes determine how strongly the percentage of fusion reports varies with the angular difference Ψ. A steep slope means that the 50%-threshold clearly separates the angular difference Ψ into two zones: one where fusion always occurs, and one where fusion never occurs. As the slope gets shallower, an interval of "uncertainty" increases around the 50%-threshold, corresponding to a range of angular differences for which subjects' judgments of fusion may change from one trial to another. In Fig. 8, the slopes are steep

V. CONCLUSION

In the present experiment, images of a speaker were presented directly in front of subjects. The voice of the speaker could be reproduced on different loudspeakers, which Hendrickx,Paquier,Koehl and Palacino JASA,p. 42 created disparities between the sound and the visual stimuli. For each presentation, subjects had to indicate whether the voice and the mouth of the speaker came from the same direction (the so-called ventriloquism effect) or not. 50%-thresholds were measured for sound stimuli varying in both azimuth and elevation. Results show that 50%-thresholds were greater in elevation than in azimuth (which is consistent with the localization performance of the auditory system), and could sometimes reach very high values (some subjects still perceived the voice of the speaker on his mouth, even when the sound was reproduced behind them). However, larger inter-subject variability was observed in elevation than in azimuth.

In an additional task, subjects had to answer questions on the semantic content of the stimuli before giving their answer on ventriloquism. As long as some minimal difference in azimuth between the sound and visual stimuli was present, there was no effect of the semantic questions. In the median plane (no difference of azimuth), the effect was significant but contrary to what was expected: 50%-thresholds decreased when subjects had to focus on the semantic content.

Results suggest that:

• In azimuth, fusion is mainly determined by the horizontal location of the sound stimulus relative to the location of the visual stimulus. As sound localization performances in azimuth are precise and similar across subjects, 50%-thresholds and Hendrickx, Paquier, Koehl and Palacino JASA, p. 43 inter-subject variability are moderate compared with in elevation;

• In elevation, sound localization is not precise, and the influence of the location of the sound stimulus decreases substantially to the benefit of subjective factors such as attention or compellingness. Thus, greater 50%-thresholds are obtained (especially if the combination of sound and visual stimuli is realistic) and the inter-subject variabilty increases.

Figure Captions

Table 1. The ITU-R 5-grade impairment scale (ITU-R BS. 2003).

  10×4.40×3.30 m at the University of Brest. The lights were turned off in order to minimize the influence of any visual stimuli. The subject sat at the center of the room. Head position was fixed by a chin clamp. The image was displayed by an Epson EH-TW6000 projector on an acoustically transparent screen, with Epson ELPGS01 3D active glasses. The width and the height of the screen were 130 cm and 73 cm respectively. Playback, commands and data capture were controlled by a software implemented in Max/MSP on a MacBook Pro computer connected to a RME MADIface USB. The system was composed of twenty-eight Amadeus PMX4 loudspeakers fed by a D.O.Tec Andiamo 2.DA MADI to analog converter through Audac DPA154 amplifiers. Each loudspeaker was digitally filtered to compensate for the transfer characteristics of the Hendrickx, Paquier, Koehl and Palacino JASA, p. 19 presentation system. For each presentation, the voice of the speaker was randomly reproduced by one of the loudspeakers at a sound level of about 65 dB (A-weighted).

Figure 2 :

 2 Figure 2: Example of a loudspeaker A with orientation δ = 67.5 • and angular difference Ψ = 36 • .

  out of the twenty-seven possible combinations of names, colours and cities. Each task was divided into two sessions of one hour each and all the subjects completed the two tasks on four different days. Subjects A, B, C and D started with task A while subjects E, F, G and H started with task B. Hendrickx, Paquier, Koehl and Palacino JASA, p. 27

Fig. 4 (Figure 3 :

 43 Fig. 4 (results of subject C at δ = 90 • ) shows another example where the

Figure 4 :

 4 Figure 4: Psychometric function at δ = 90 • for subject C, task A. Points represent data obtained for each loudspeaker.

Figure 5 :

 5 Figure 5: 50%-thresholds Ψ 50% for each subject as a function of the δ-orientation. Task B.

Figure 6 :

 6 Figure 6: Percentage of fusion reports for each loudspeaker at δ-orientation of 90 • , pooled across all subjects.

Figure 7 :

 7 Figure 7: 50%-threshold azimuth θ 50% and elevation φ 50% for subjects A, B, C and D (left) and subjects E, F, G and H (right). Task A. For clarity, results were split between two diagrams. The x-axis corresponds to the δ-orientation 0 • while the y-axis corresponds to the δ-orientation 90 • .

  Hendrickx, Paquier, Koehl and Palacino JASA, p. 41 and quite similar at δ-orientation of 0 • and 45 • . Yet, as δ-orientation increases from 45 • to 90 • , the slope gets shallower. This trend, which has been observed for all subjects, is entirely consistent with the hypothesis that the decision of subjects is being increasingly influenced by fluctuating factors, such as attention, as δ-orientation increases from 45 • to 90 • .

Figure 8 :

 8 Figure 8: Psychometric functions obtained for subject D during task A at each δ-orientation. From left to right : δ = 0 • , δ = 45 • , δ = 67.5 • , δ = 90 • .

Fig. 1 .

 1 Fig. 1. The 4 δ-orientations along which the sound stimulus could be shifted from the

Fig. 2 .

 2 Fig. 2. Example of a loudspeaker A with orientation δ = 67.5 • and angular difference

Fig. 3 .

 3 Fig. 3. 50%-thresholds Ψ 50% for each subject as a function of the δ-orientation. Task A.

Fig. 4 .

 4 Fig. 4. Psychometric functions at δ = 90 • for subject C, task A. Points represent data

Fig. 5 .

 5 Fig. 5. 50%-thresholds Ψ 50% for each subject as a function of the δ-orientation. Task B.

Fig. 6 .

 6 Fig. 6. Percentage of fusion reports for each loudspeaker at δ-orientation of 90 • , pooled

Fig. 7 .

 7 Fig. 7. 50%-threshold azimuth θ 50% and elevation φ 50% for subjects A, B, C and D (left)

Table 1 :

 1

	Impairment	Grade
	Imperceptible	5.0
	Perceptible, but not annoying	4.0
	Slightly annoying	3.0
	Annoying	2.0
	Very annoying	1.0

The ITU-R 5-grade impairment scale (ITU-R BS.

 2003)

  • while it was 20 • with naïve subjects. A comparison of previous studies also shows that the obtained thresholds are usually low with trained subjets (5 -7

• in Melchior et al. (2003), 4 -8 • in Melchior et al. (2006), 6 -8 • in Mannerheim (2011)) while they are always greater than 10 • with naïve subjects (20 • in Komiyama (1989), 18.3 • in André et al. (2014), > 10 • in Wallace et al. (2004)).

Table 2 :

 2

					7.1	7.1	10	4.2	10.2	11	0	10	10
	2	10	0	10	10.5	10.5	15	7.5	18.4	20	0	19	19
	3	14	0	14	13.3	13.3	19	10.7	26.6	29	0	27	27
	4	18	0	18	15.4	15.4	22	13	32.9	36	0	34	34
	5	23	0	23	17.4	17.4	25	16	41.7	46	0	43	43
	6	27	0	27	20	20	29	18.5	50	56	0	90	90
	7	31	0	31	24.6	24.6	36	22.5	67.5	90	0	137	137

Loudspeaker locations, with associated azimuth θ, elevation φ and angular difference Ψ, for the four δ-orientations.

Acknowledgements

The authors would like to thank Pierre Souchar, Baptiste Le Deun, Vincent Mazo and all the subjects from the University of Brest who took part in the subjective experiments. This work was partly funded by the European cross-border cooperation programme INTERREG IV A France (Channel) -England, co-funded by the ERDF, in the context of the Cross Channel Film Lab project, and partly supported by the French National Research Agency (ANR) as a part of the EDISON 3D project (ANR-13-CORD-0008-02) and by the Finistère General Council (29), France.


M L Zanota

L Perier-Camby

F Chauvy

Y Brullé

J M Herri

IMPROVEMENT OF METHANE STORAGE IN ACTIVATED CARBON USING METHANE HYDRATE

Keywords: activated carbon, adsorption, gas storage

The methane storage capacity of dry and wetted activated carbon is evaluated at 1°C in the pressure range . The experiments emphasize the complex influence of the water content. The presence of water decreases the storage kinetics. It decreases also the storage capacity excepted in a domain of water concentration which has not been evaluated precisely but which is located in the range 30-80 % mass of water

INTRODUCTION .

With the massive increase of the urban traffic, coupled with its large contribution to the local pollution in the city centres, natural gas appears to be a favourable alternative to gasoline and diesel. In fact, among the different fuel elements, the methane shows the best ratio H/C which allows to reduce the CO 2 emissions. More, it is a clean fuel with specially low emissions of CO, NO x and particles. As the natural gas resources are enormous, it represents a good alternative to oil in term of energetic independence.

The improvement of the natural gas onboard storage is one of the major parameters to develop this energy. Currently, the natural gas could be stored mainly as compressed gas in pressurised tanks at very high pressure of 20 MPa which can set the engineers a problem of security. It can also be liquefied at -162°C but then requires a cryogenic tank which can hardly be envisaged for onboard applications. The last solution is to store by adsorption on activated carbon for example [START_REF] Lozano-Castello | Advances in the study of methane storage in porous arbonaceous materials[END_REF].

. . (*) Corresponding author : Phone +33 4 77 42 02 92 Fax +33 4 77 49 96 94 E-mail : herri@emse.fr

The storage capacity of the adsorption technology reaches 100 to 140(n)m 3 /m 3 at 3.5 MPa. This value is lower than that obtained in the compressed gas technology which storage capacity is 200 (n)m 3 /m 3 but at a higher pressure of 20 MPa. The storage pressure of the sorption technology is only 3.5 MPa and presents two main advantages : first, it limits the compression work for the tank filling up and allows to connect directly to the existing natural gas distribution network. Secondly, at low pressure, the tank geometry can adopt various shapes in order to adjust it to the vehicle body (polymorphous tanks).

The interest of the adsorption stays only if performances are sufficiently good, i.e. if the available natural gas volume is sufficient and compatible with the city runs. This article deals with a concept that aims to increase the adsorption capacity by coupling it to a gas hydrate formation. In fact, the gas hydrate formation in the remaining free porosity after classical physi-sorption of natural gas on activated carbon should permit to increase the storage capacity [START_REF] Rogers | Hydrates for storage of natural gas[END_REF].

METHANE HYDRATE

For pure methane, only the S I structure is stable. The lattice parameter is 1.203 nm. It is composed of 46 water molecules arranged to form a network of two cavities 5 12 and six cavities 5 12 6 2 . As a result, if all the cavities are occupied by a methane molecule, the theoretical formula of methane hydrate is CH 4 (H 2 O) 5.75 . In the reality, not all the cavities are filled and the methane storage in the hydrate structure is around 170 (n)m 3 /m 3 .

Table 1 shows the equilibrium curve of methane hydrate. (For a more complete description of the hydrate structure and of the thermodynamics, please refer to Sloan [START_REF] Sloan | Clathrate hydrates of Natural Gases[END_REF])

LITTERATURE STUDY

In the purpose to form these compounds to complete the classical adsorption of natural gas on activated carbon, it is strictly compulsory to previously wet the porous media. But, the pre-adsorption of water on activated carbon is known to be a disadvantage because the presence of water generally limits the methane adsorption capacities. The idea of making hydrates in the porosity to enhance the storage capacity has been firstly attempted by Kaneko [START_REF] Kaneko | Nanoclathrate-assited adsorption of supercritical gases in hydrophobic pores[END_REF]. He showed a considerable improvement of the methane storage capacity of wetted activated carbon. He assigned this behaviour to the complementary methane hydrate formation. His experimental results has to be considered carefully because the experimental conditions which was applied (low pressure, ambient temperature) are very far from the classical conditions at which the methane hydrates could form in bulk conditions (see table 1). The concept was then tested and confirmed by Miyawaki [START_REF] Miyawaki | Macroscopic evidence of enhanced formation of methane nanohydrates in hydrophobic nanospaces[END_REF] but the real experimental proof was published by Zhou [START_REF] Zhou | Enhancement of the methane storage on activated carbon by preadsorbed water[END_REF][START_REF] Zhou | Effect of moisture in microporous activated carbon on the adsorption of methane[END_REF]. He presents the influence of water on the storage of methane at pressures from 0.1 to 10 MPa and temperatures from 0 to 8°C. At pressure lower than 4 MPa, Zhou [START_REF] Zhou | Enhancement of the methane storage on activated carbon by preadsorbed water[END_REF] observed a classical result : the presence of water decreases the storage capacities. But for sufficient water quantities and higher pressures, he observed an inversion of the tendency : the higher the water content, the higher the storage capacity.

In this article we give additional proofs showing the influence of water at low and high pressure. We give experimental evidences of the existence of methane hydrates in the activated carbon porosity and that their formation allows to increase the methane storage capacity in comparison to pure adsorption on dry activated carbon in the same conditions of pressure and temperature. We also show that (P,T) conditions of methane storage and release by adsorption associated to the hydrate formation are influenced by the pore size distribution of the activated carbon. We show that the quantity of water pre-sorbed at the carbon surface is a crucial parameter on the storage capacity.

SAMPLE CHARACTERISATION

We present in this study results concerning two commercial activated carbons whose precursor is lingo-cellulose (They are denominated A and B). The porous texture characterisation was obtained by interpretation of physical sorption isotherms of nitrogen at 77K. The mesopore and micropore size distribution has been determined respectively by the BJH method and the Brunauer method. This last method is based on the exploitation of the t diagram, and requires the construction of a particular law giving the t parameter as a function of ρ/ρ 0 . The t parameter is calculated from experiments on a non porous model sample exhibiting a similar surface chemistry. In this study, a black coal has been taken for reference. Table 2

EXPERIMENTS

Experimental device

The set up is composed of a pressurised tank and a ballast reference which operating pressure is up to 10 MPa. The pressurised tank is temperature controlled in the range [-25°C, +80°C] by mean of a cooling jacket. The ballast is directly located into the cooling bath of the thermostat. The pressurised tank is equipped with two sapphire windows (15 cm high, 1.5 cm wide) which allows us to look at the texture of the activated carbon during the methane hydrate crystallization. The total volume of the system is 2.6 litres (including ballast, pressurised tank and pipelines). A Pt 100 temperature probe monitors the temperature in the activated carbon bed.

A Labview program saves continuously the pressure of the pressurised tank and of the ballast, and the temperature. The wetting of the carbon is done by pouring directly the liquid water in the bed under manual mixing. The wetted carbon are then weighed before the adsorption study. The quantity of water poured in the activated carbon is given in weight percentage of the dry carbon mass.

The methane storage capacity is measured by a differential method. The ballast is first filled and its pressure is measured to determine the total number of methane contained inside. Then, the connecting valve between the ballast and the reactor is opened. The temperature increases in the carbon bed due to gas compression, gas adsorption and gas hydrate crystallisation. After a while, the temperature reaches its equilibrium value imposed by the cooling jacket and then the pressure is measured. The knowledge of the volume of the ballast and of the pressurised tank plus the determination of the final equilibrium pressure gives the total amount of methane which has been stored by the activated carbon. The term storing describes the gas adsorption and/or the gas hydrate crystallisation.

We studied pressure between 1 to 8 MPa in order to construct the isotherm of methane sequestration. Temperature is maintained constant at a value of 1°C. The inverse procedure has been used to study the release of the activated carbon bed. The pressurised tank containing the activated carbon bed is emptied by filling back the ballast and the final equilibrium pressure is measured to calculate the total amount of methane which has been released.

RESULTS AND DISCUSSIONS methane storage

Sorption isotherms (1°C) of the sample B is presented on figure 2 as a function of the pressure up to 6 MPa, and as a function of the % mass of the water which has been previously incorporated to the dry activated carbon (from 0 to 32.6 % mass ). The results are consistent with the literature [START_REF] Krooss | Highpressure methane and carbon dioxide adsorption on dry and moistureequilibrated Pennsylvanian coals[END_REF] showing the negative impact of the water : the more the water quantity, the less the methane storage capacity. For sample A, this tendency has also been observed. It is interesting to note that the dry carbons which have been tested can be compared to the sample NC58 tested by Perrin et al [START_REF] Perrin | Improved methane storage capacities by sorption on wet active carbons[END_REF] from the point of view of the massic methane uptakes. Their work must be mentioned here because they evaluated the massic methane uptakes of 5 different activated carbon in the

Pressure (MPa)

Amount of CH4 stored (mol /kg dry carbon) ….

dry carbon moiseture added 5.70 w% moiseture added 13.13 w% moiseture added 32.60 w% same pressure than us. They compared their results with 50 % mass wetted samples. They observed that the methane uptake is dramatically decreased in the presence of 100 % water mass. This is coherent with our results.

But, for higher pressures, and higher water concentration, the tendency is inversed. The isotherm curves present an inflection point and an sudden increase of the storage capacity. The figure 3 presents the storage capacity on sample B for pre-sorbed water quantities higher to 30% mass and pressures up to 8 MPa. At a water content of 32.6% mass , the storage isotherm presents an inflexion point at a pressure of 6-6.5 MPa but it is not enough to increase notably the storage capacity. This inflexion point is more sensitive for water content of 73% mass and appears at lower pressure of 3-3.5 MPa. The storage capacity reaches the performance of the dry activated carbon at a pressure of 6 MPa and higher. For higher concentration of 93% mass of water, the storage performances remains at a very low value.

In first analysis, it appears that the methane storage capacity is very sensitive to the water content and that an optimum exists. The value ot the optimum has not been looked for Figure 3. Effect of water content on the storage of methane in activated carbon sample B at 1°C This analysis is comforted by the experiments performed on sample A which exhibits the same behaviour (figure 4). The sorption capacities according to the pressure and for different quantities of water present an maximum at water concentration of 71 % mass . More, in such a condition, the storage capacity of the wet carbon becomes higher than for the dry carbon for pressures higher than 6-6.5 MPa (increase of about 10% the storage capacity). This increase can be attributed to the hydrate formation in the carbon sample for several reasons. First, the applied conditions (60 bar and 1°C) are favourable to the hydrate formation since the theoretical pressure of formation of methane hydrate in bulk condition at 1°C is 2.9 MPa. Secondly, the visual observation through reactor sapphire windows allows us the direct observation of the hydrate crystals at the surface of the activated carbon. Lastly, the sudden increase of the methane storage capacity is accompanied with a sudden increase of the temperature in the carbon bed. This behaviour is generally associated to the hydrates formation that is a exothermic crystallisation and that fixes methane.

Methane release

The final objective of the end user is not only the methane storage capacity but particularly the methane release capacity. In order to quantify the release capacity, the figure 5 and6 shows the isotherm of storage and release at a temperature of 1°C for samples A and B. (Here the classical term of adsorption and desorption are not appropriated because the adsorption is accompanied with an hydrate formation). The depressurisation curve of methane hydrates formed in sample A, containing 71% mass of water, shows that the hydrates dissociation begins to take place at a pressure 4.5 MPa and finishes at a pressure of 3.2 MPa which is very close to the theoretical dissociation pressure of methane hydrate in bulk conditions (2.9 MPa at 1°C). This dissociation value has to be compared to the pressure at which the hydrates have crystallised in the same experiment, i.e. a pressure of 6-6.5 MPa. So, the storage and release curves present an hysteresis which is very fruitful to analyse. In fact, after their formation at pressure higher than 6 MPa, it is possible to store methane hydrates at a pressure of 4 MPa for example. At this pressure, the storage capacity is 9.7 mole/kg whereas it is 7.5 mole/kg for the dry activated carbon under the same conditions of pressure and temperature. It represents an increase of about 30% of the storage capacity.

As we noted before, at 1°C, the pressure of formation of methane hydrate in bulk conditions is 2.9 MPa whereas it occurs in our experiment at a pressure of 6-6.5 MPa. This could be attributed in first analysis to a delay time in the nucleation of the solid phase. In fact, in other experiments performed in bulk conditions, many authors (see for example [START_REF] Herri | Methane Hydrate Crystallisation Mechanism from In-Situ Particule Sizing[END_REF]) show that the methane hydrate formation in pure water in stirred tank reactor presents the same behaviour : the solution needs to be very supersaturated before the nucleation occurs. This behaviour is explained from a kinetic point of view by referring in first approximation to the simplified model of Volmer which expresses the nucleation rate J as a function of the supersaturation S=P/Peq :

( ) 2 lnS B A J - =
A and B are constants, P is the operating pressure, P eq is the equilibrium pressure. The nucleation rate becomes nil if the operating pressure tends to the equilibrium pressure and increase exponentially as the operating pressure increases. This implies that the question of metastability is a time dependent consideration. For example, in the work of Perrin et al [START_REF] Perrin | Improved methane storage capacities by sorption on wet active carbons[END_REF] on same systems (activated carbon), it is observed hydrate formation at pressure immediately greater than the equilibrium pressure. The reason is they waited for longer time until hydrate appearance (several weeks in some cases).

Such an induction delay imposed by the rate of nucleation is not observed for the dissociation which instantaneously occurs and always takes place at the equilibrium pressure. It is why the experimental procedures to determine the equilibrium curves are always based on the analysis of the dissociation curves. As a consequence, it allows us to determine precisely this equilibrium pressure from the analysis of the releasing curves.

From the point of view of thermodynamic, the Gibbs-Thomson relationship allows to correlate the temperature shift to the size of the pore in which the hydrate crystallisation occurs :

e on dissociati bulk on dissociati r H Cos T T ∆ = ∆ ρ θ γ bulk T is temperature of dissociation in bulk conditions, γ
the surface energy between water and hydrate, ρ the hydrate density, on dissociati H ∆ the enthalpy of hydrate dissociation, e r the radius of the pore and the contact angle between the solid phase and the pore. So, the temperature shift is directly inverse of the pore radius.

The sample A presents a beginning of the dissociation at pressure of 4.5 MPa which corresponds to an equilibrium temperature in bulk condition of 4-5 °C, and so a shift of 3-4°C due to the porosity. The end of the dissociation occurs at 3.2 MPa which corresponds to an equilibrium temperature in bulk condition of 2°C and so a shift of 1°C. In conclusion, the porosity of the sample A introduces a shift of 1 to 3-4 °C on the equilibrium temperature in comparison to the bulk conditions.

The hysteresis of the sample B (figure 6) is wider. The dissociation starts at a pressure which is not easy to measure but ends exactly at the pressure of 2.9 MPa corresponding to the bulk conditions.

The difference between the two samples could be explained by their pore size distribution. Sample A presents a mesoporosity in the range [3.5-4.5 nm] whereas the mesoporosity of the sample B is larger than 15 nm. So, the final equilibrium shift (corresponding the final dissociation point at the lowest pressure) due to the mesoporosity is more important for the sample A than for sample B : the dissociation ends at a lower pressure on sample B than for sample A due to a larger mesoporosity. We can note that such a shift of the equilibrium temperature has been observed for hydrates on other micro-nano systems by Handa and Stupin [10] and Uchida et al [START_REF] Uchida | Dissociation Condition Measurements of Methane Hydrate in Confined Small Pores of Porous Glass[END_REF][START_REF] Uchida | [END_REF], and especially by Perrin el al [START_REF] Perrin | Improved methane storage capacities by sorption on wet active carbons[END_REF] in activated carbon.

CONCLUSIONS

In this study we showed experimentally that methane storage capacities on activated carbon could be increased if water is previously added in large quantity. At lower pressure down to 40 bars, this water decreases the methane storage capacity of the activated carbon. But for higher pressures, the isotherm storage curve presents an inflection point which indicates the formation of hydrate crystals. This crystallisation enhances the performance of the activated carbon from 10 to 30 % mass . This storage capacity is influence by the water concentration which presents an optimum.

The isotherm storage and release curves present an hysteresis. It is necessary to reach high pressure (6-7 MPa) to form hydrates but they can be then stored under a pressure of 4 MPa without dissociating.

  Figure 1. experimental device

Figure 2 .

 2 Figure 2. Effect of water content on the storage of methane in activated carbon B at 1°C

Figure 4 .

 4 Figure 4. Effect of water content on the storage of methane in activated carbon sample A at 1°C

Figure 5 .

 5 Figure 5. Hysteresis measurement for wet activated carbon sample A with 71% mass of presorbed water at 1°C

Figure 6 .

 6 Figure 6. Hysteresis measurement for wet activated carbon sample B with 73% mass of added water at 1°C

Table 1 .

 1 Methane hydrate equilibrium curve

	T [°C]	0	1	2	4	6	8 10 12
	P [MPa] 2.6 2.9 3.2 3.9 4.8 5.9 7.4 9.2

  shows the characterisation of activated carbon A and B.

	sample	Mesoporous diameter (Å)	Microporous diameter (Å)	Surface t (m 2 /g)	Mesoporous volume (cm 3 /g)
	A	35< <45	< 8	1203	0.841
	B	<150	<12	967	0.647
		Tableau 2.Activated carbon characteristics


Myriam Darbouret

Michel Cournil

Jean-Michel Herri

CRYSTALLISATION AND RHEOLOGY OF AN HYDRATE SLURRY AS SECONDARY TWO-PHASE REFRIGERANT FOR AIR-CONDITIONING APPLICATION

Keywords: Rheology, Two-phase flow, Heat transportation, Air-conditioning m Φ Φ, mean, maximum volume fraction [-] ψ : shape factor [-]

HAL is

INTRODUCTION

In the context of the classical refrigerants phase out, phase change materials (PCM) arouse great interests. Indeed, for very low temperature application such as refrigeration, ice-slurries are spread as secondary refrigerants. Concerning hydrates, they have been used as PCM for cold storage for years. The challenge is now to extend this application to cold transportation in a secondary refrigerant loop. In Japan, JFE marketed the first hydrate slurry for air-conditioning. The fluid studied is an aqueous solution of Tetra-ButylAmmonium Bromide ((C 4 H 9 ) 4 NBr) (TBAB). At low temperature this solution crystallises and forms a suspension of semi-clathrate hydrates. After a presentation of the physical properties of such hydrates, we propose hereafter a rheological study of theses TBAB hydrates slurries.

PHYSICAL PROPERTIES OF TBAB HYDRATES

Thermodynamic properties

In a first time, the TBAB hydrates phase diagram was determined experimentally. It is particularly interesting to underline the fact that, at atmospheric pressure, TBAB hydrates are stable for temperatures between 0°C and +12°C. Indeed, in current air-conditioning applications, the cold fluid enters the heat exchanger with a temperature close to +6°C and flow out at about +12°C. This hydrate is therefore a good candidate for air conditioning applications, from a thermodynamic point of view. From the equilibrium diagram, assuming that the thermodynamics equilibrium is reached, one can deduced from temperature the TBAB mass fraction in the liquid phase. The so-called "moment law" (1), gives then a mean of calculating the hydrate mass fraction in the suspension when one knows the values of initial mass fraction of TBAB in the solution ( 0 x ), the mass fraction of TBAB in the liquid phase ( l x ) and the mass fraction TBAB in the hydrate phase ( N x ).

l N l H x x x x x - - = 0
(1) Figure 2 presents an example of the evolution of the slurry composition versus temperature for aqueous solutions of 20% and 35% mass TBAB. The solid line represents the TBAB mass fraction in the liquid phase and the dashed line the hydrate mass fraction. Equations ( 2) and [START_REF] Shimada | Separation of Gas Molecule Using Tetra-n-Butyl Ammonium Bromide Semi-Clathrate Hydrate Crystals[END_REF] give the exchange laws between liquid and solid phase for type A and type B TBAB hydrates.

TBAB hydrates densities

In a second time, the densities of type A and type B hydrates were measured with a pycnometry method consisting in fully crystallising a known mass of TBAB solution. Once hydrates crystallised, hexane was added at the same temperature until the mixture had a precise volume of 10 ml. The mixture is weighted and the hexane volume calculated. The hydrates volume was obtained deducting the hexane volume added. The densities measured for each hydrate type are presented in Table 1. It also gives the mass fraction of TBAB in each hydrate crystal depending on its hydration number. Type B hydrate, with the highest hydration number, is the lightest.

Hydrate type

Kinetics effects during TBAB hydrates crystallisation

Decreasing the temperature of TBAB aqueous solutions, hydrates crystals do not appear as soon as temperature reaches their crystallisation temperature : this is the supercooling phenomenon. Figure 4 presents the evolution with time of the temperature of a 20% mass TBAB aqueous solution flowing in the loop schemed on Figure 5. The three curves correspond to three points of temperature measurement (T1, T2 and T3). The lower temperature is observed in the brushed surface heat exchanger (T1). The successive apparitions of the two hydrate types are evidenced by two successive temperature increases. The slurry leaves then its metastable state for a stable one. On figure 4 are also represented the different fluid natures depending on time and temperature (liquid, type A or type B slurries). When type B hydrates appear, type A hydrates definitively disappear. The magnitude of the supercooling defined as the difference between the theoretical temperature of crystallisation and the minimum temperature reached depends on many factors. For instance it is more likely to be great in a small reactor, or if there is no impurity in the fluid. This supercooling phenomenon is to be avoided or minimized in an industrial context as it represents an additional energy consumption for slurry production. One technique used for example is seeding.

EXPERIMENTAL DEVICE

Set-up description

An "in-situ" experimental method is run here in order to avoid some difficulties due to "ex-situ" methods.

It is an indirect method based on pressure drop and flow rate measurements. The matter of sliding at the wall still remains but we consider here the global apparent behaviour of the fluid which will be the same as in an industrial installation. The experimental set-up is shown in Figure 5. The hydrate slurry is generated in a brushed surface heat exchanger (1) and drained away with the aid of a gear pump (2) specially developed by GOTEC® for ice-slurry technology. After a 0.5 m long pipe, designed to reach an established hydrodynamic regime, the fluid flows through the "rheometer pipe" (3). This is a horizontal cylindrical pipe (L = 1 m; D int = 1.6 10 -2 m) on which the pressure drop between the inlet and outlet is measured with a differential pressure sensor from KELLER® [0-500 mbar] ± 0.1 mbar. The volumetric flow rate is given by a Coriolis flowmeter (4) from MICRO MOTION® [0-500 l/h] (Accuracy : ± 0.5 %). The loop is also equipped with temperature sensors Pt 100 from PROSENSOR (Accuracy : ± 0.1°C) , and with a transparent section in order to observe the flow regime and the slurry appearance. The rotation frequency of the pump can span the range [10 Hz-50 Hz] by the use of a frequency controller.

T5 ∆ ∆ ∆ ∆P1 T1 T3 T2 ∆ ∆ ∆ ∆P2 Q, ρ ρ ρ ρ, T4 T5 T5 ∆ ∆ ∆ ∆P1 T1 T3 T2 ∆ ∆ ∆ ∆P2 Q, ρ ρ ρ ρ, T4 ∆ ∆ ∆ ∆P1 T1 T3 T2 ∆ ∆ ∆ ∆P2 Q, ρ ρ ρ ρ, T4 ∆ ∆ ∆ ∆P1 ∆ ∆ ∆ ∆P1 ∆ ∆ ∆ ∆P1 T1 T3 T2 ∆ ∆ ∆ ∆P2 Q, ρ ρ ρ ρ, T4 T3 T2 T3 T3 T2 T2 ∆ ∆ ∆ ∆P2 ∆ ∆ ∆ ∆P2 ∆ ∆ ∆ ∆P2 Q, ρ ρ ρ ρ, T4 Q, ρ ρ ρ ρ, T4 T5 ∆ ∆ ∆ ∆P1 T1 T3 T2 ∆ ∆ ∆ ∆P2 Q, ρ ρ ρ ρ, T4 T5 T5 ∆ ∆ ∆ ∆P1 T1 T3 T2 ∆ ∆ ∆ ∆P2 Q, ρ ρ ρ ρ, T4 ∆ ∆ ∆ ∆P1 T1 T3 T2 ∆ ∆ ∆ ∆P2 Q, ρ ρ ρ ρ, T4 ∆ ∆ ∆ ∆P1 ∆ ∆ ∆ ∆P1 ∆ ∆ ∆ ∆P1 T1 T3 T2 ∆ ∆ ∆ ∆P2 Q, ρ ρ ρ ρ, T4 T3 T2 T3 T3 T2 T2 ∆ ∆ ∆ ∆P2 ∆ ∆ ∆ ∆P2 ∆ ∆ ∆ ∆P2 Q, ρ ρ ρ ρ, T4 Q, ρ ρ ρ ρ, T4

Procedure description

Experimental tests were performed on TBAB hydrate slurries to characterise their rheological behaviour.

These tests aimed at determining the slurry apparent viscosity for different slurry temperatures, (i.e. for different hydrate contents). At a given temperature, the rotation speed of the pump motor is varied between 10 Hz and 50 Hz following regular steps. These steps are 5 Hz high and last about 30 s. Temperature, volumetric flow rate Q and pressure loss ∆P are continuously recorded. The same procedure is repeated for different slurry temperatures, as the hydrate content slowly increases as temperature decreases.

RHEOLOGICAL BEHAVIOUR OF HYDRATE SLURRIES

In this part we propose to study the rheological behaviour of TBAB hydrate slurries produced in the reactor (fig. 5). We first remind some useful tools for the rheological study and then present the results of the experiments.

Theoretical analysis

We consider a laminar and established flow in a horizontal cylindrical pipe. The pressure drop is linked to the wall shear stress through equation ( 4), derived from a momentum balance. In our case, curves representing pressure drop versus flow rate are straight lines which do not intercept the origin. That why, hereafter we describe the rheological behaviour of slurries through an extrapolated shear stress and an apparent viscosity. The behaviour law of such slurries is then similar to a Bingham fluid law :

      - = 0 0 3 4 1 8 τ τ µ w D U (6)    < = > = - 0 0 0 0 if 0 if τ τ γ τ τ γ µ τ τ & & (7)
The actual existence of such a yield shear stress is not obvious, indeed, one can imagine a very rapid decrease of the viscosity with shear rate for very low shear rate. Nevertheless, in the range of mean velocities explored, the slurry behaves just as this yield stress did exist.

Results

Figure 6 presents some examples of flow curves ( w γ& , w τ ) obtained with TBAB hydrate slurries. These are straight lines which do not intercept the origin. From equation ( 6), one can say that the intercept point is proportional to the extrapolated or yield shear stress. Concerning the slope it is equal to the apparent viscosity of the slurry. This way, one can associate to each volume fraction of hydrate, an apparent viscosity and a yield shear stress. It is to note that for initial mass concentration near 0.40, the hydrate phase diagram (Figure 1) is very flat. This implies that very low temperature variations correspond to significant changes of the hydrate mass fraction. On Figure 6 are represented the three flow curves TBAB hydrate slurries produced with a solution of 35% initial mass concentration of TBAB. With such a solution, the hydrate mass fraction is calculated with poor accuracy because of the temperature probe accuracy (±0.1°C). τ0 = 0,016γ + 1,9 τ0 = 0,016γ + 1,9 τ0 = 0,016γ + 1,9 τ0 = 0,016γ + 1,9 τ0 = 0,044γ + 2,8 τ0 = 0,044γ + 2,8 τ0 = 0,044γ + 2,8 τ0 = 0,044γ + 2,8 τ0 = 0,074γ + 5,2 τ0 = 0,074γ + 5,2 τ0 = 0,074γ + 5,2 τ0 = 0,074γ + 5,2 ) with hydrate volume fraction. This volume fraction is derived from the mass fraction thanks to equation (8).

1 1 1 +         - = Φ H H l H x x ρ ρ (8)
The apparent viscosity of the slurry increases progressively with its load and tends to diverge as the volume fraction of hydrate approaches 60% mass. The apparent viscosity of slurries of type B hydrates seems to diverge for slightly lower mass fraction than type A hydrate. This yield shear stress is the minimum shear stress which leads to the flow of the fluid. In the case of suspensions it is interpreted as the stress necessary to overcome the interaction forces between particles and permit the flow of the suspension. Therefore, the higher volume fraction of particles, the higher yield stress; and the higher strength of interparticle interactions, the higher yield stress.

With Figure 9 the dependence of the yield shear stress with the volume hydrate fraction is highlighted with a log-log representation. We obtain some straight lines of slopes close to 3. It means that the yield shear stress varies like 3 Φ . This phenomenon was already observed and evidenced by Thomas [START_REF] Thomas | Laminar-Flow Properties of Flocculated Suspensions[END_REF] for different metal oxides suspensions. The empirical relations he proposed take into account a shape factor ψ (for nonspherical particles), a particle equivalent diameter p D , and the particle volume fraction:

CONCLUSION

Under atmospheric pressure and temperatures between 0°C and +12°C, aqueous solutions of TBAB can form two types of semi-clathrate TBAB hydrate slurries. Each TBAB hydrate crystal appear after a variable period of metastability and then the thermodynamic equilibrium is regained. In the range of shear rates explored, the rheological behaviour of TBAB hydrate slurries can be described with an apparent viscosity and a extrapolated yield shear stress. This study evidences that TBAB hydrate slurries are transportable until rather high loads of particles (∼ 40% volume). Moreover the Graham et al. model of viscosity for suspensions seems to be appropriate to describe the evolution of the viscosity of the slurries with the volume fraction of particles if two different maximum packing fractions are introduced for the two hydrate types. Concerning the extrapolated yield shear stress, it varies like

NOMENCLATUREA:

  constant [Pa.m 2 ] D: diameter of the pipe [m] D p : particle diameter [m] L: length of the pipe [m] M: molecular weight [g.mol -1 ] N: hydration number [-] ∆P: pressure drop [Pa] Q: volume flow rate [m 3 .s -1 ] H TBAB x x , : TBAB, Hydrate, mass fraction [-] γ& , w γ& : shear rate, wall shear rate [s -1 ] 0 µ , l µ : Apparent, liquid viscosity [Pa.s] hydrate density [kg.m -3 ] w τ , 0 τ : Wall and yield shear stress [Pa]

Figure 1 :

 1 Figure 1: Experimental equilibrium diagram

Figure 2 :

 2 Figure 2: Temperature dependence of the slurry composition x 0 =0.20 and x 0 =0.35.

  Concerning the crystal structure, type A only is well determined and represented on Figure3. Davidson[START_REF] Davidson | Water a comprehensice treatise[END_REF] first gave a description of this semi-clathrate structure. Then Shimada[START_REF] Shimada | Separation of Gas Molecule Using Tetra-n-Butyl Ammonium Bromide Semi-Clathrate Hydrate Crystals[END_REF] published figure3. It is a semiclathrate hydrate as Nitrogen and Brome atoms replace some water molecules. The butyl chains are guests of four unclosed cavities : 3 tetrakaidecahedrons and one pentakaidecahedron. The dotted lines represent bonds which have disappeared from the classical hydrate structure.

Figure 3 :

 3 Figure 3: Structure of type A hydrate.[START_REF] Shimada | Separation of Gas Molecule Using Tetra-n-Butyl Ammonium Bromide Semi-Clathrate Hydrate Crystals[END_REF]

Figure 4 :

 4 Figure 4: Evidence of the supercooling phenomena.

Figure 5 :

 5 Figure 5: Experimental set-up.

  rate, it can be expressed introducing the volume flow rate thanks to the Rabinovitch relation.

Figure 6 :

 6 Figure 6: Flow curves of hydrate slurries (x 0 =0.35)

Figure 7 :

 7 Figure 7: Influence of the hydrate structure on viscosity The experimental viscosities obtained are then compared with the Graham, Steele and Bird [5] model of viscosity which introduces a maximum packing fraction m Φ . When particles in the suspension reach this

Figure 8 :

 8 Figure 8: Influence of the hydrate structure on yield shear stress

Figure 9 :

 9 Figure 9 : Dependence of the yield shears stress with hydrate volume fraction.

Table 1 :

 1

		Hydration	TBAB mass	Density
		number	fraction in
		N (-)	the hydrate x N (-)	ρ H (kg.m -3 )
	A	26	0.41	1082
	B	36	0.33	1067

Physical properties of type A and type B hydrates.

Φ for the two hydrate types. An additional study of the interparticle interaction forces should be interesting in order to go further in the interpretation of the yield shear stress. Lastly, an estimation of the specific heat and fusion enthalpy of such slurries is to be done in order to be able to estimate the COP of an air-conditioning installation running with TBAB hydrate slurries.

ACKNOWLEDGEMENTS

This study is benefits of the financial support of the region Rhône-Alpes in France.

The corresponding viscosity of the suspension is given by (10).

EXTRAPOLATED SHEAR STRESS

Figure 8 presents the dependence of the extrapolated shear stress with the volume hydrate fraction for the two hydrate types. Once again type B hydrate slurries are less transportable as its yield stress are much higher than the ones of type A hydrate slurries.