Thi-Xiu Le

Michel Bornert

Patrick Aimedieu

Baptiste Chabot

Andrew King

Anh-Minh Tang
email: anh-minh.tang@enpc.fr

An experimental investigation on methane hydrate morphologies and pore habits in sandy sediment using synchrotron X-ray computed tomography

Keywords: methane hydrate, sandy sediments, morphology, pore habits, synchrotron X-ray computed tomography

As pore-scale morphologies and spatial distribution (pore habits) of natural gas hydrates in marine sediments considerably affect their physical/mechanical properties, they have extensively been investigated by X-ray computed tomography (XRCT) and especially synchrotron X-Ray computed tomography (SXRCT). While both image spatial and scan temporal resolutions are being improved over time, it is still challenging to distinguish water from methane hydrate in an image due to their low absorption contrast. In this study, methane hydrate formation and growth in wet sand were observed at submicron/micron scale using SXRCT. Saline water (Potassium iodide -KI) was used in order to improve the image contrast. Evolutions of methane hydrate morphologies and distribution at both the pore and sample scales were observed. Results are discussed based on various mechanisms related to material behaviors and experimental conditions, e.g. suction variation during methane hydrate formation, local temperature gradient in the sample, and particularly the interaction of X-rays with the sample. Methane hydrate formation is interpreted as a dynamic process, favoring the Ostwald ripening. Furthermore, morphologies and pore habits of methane hydrates under excess-gas and excess-water conditions are discussed. Some recommendations are finally given for further studies on methane hydrates-bearing sediments via XRCT or SXRCT.

Introduction

Natural gas hydrates (mainly methane hydrates -MH), ice-like compounds of methane gas and water, are most often located in marine and permafrost settings [START_REF] Collett | Natural gas hydrates: A review[END_REF]. They represent a great potential energy resource but also a source of greenhouse gas and geo-hazards [START_REF] Boswell | Current perspectives on gas hydrate resources[END_REF]. Different MH appearances, e.g. nodules/chunks, lenses/veins have been identified in fine-grained sediments [START_REF] Dai | Hydrate morphology: Physical properties of sands with patchy hydrate saturation[END_REF][START_REF] Lei | Laboratory strategies for hydrate formation in fine-grained sediments[END_REF]). Yet, for sandy sediments, MH were found in non-displacive pore habit and at high hydrate saturation, i.e. with a so-called "pore-filling" distribution as defined later [START_REF] Masui | Mechanical Properties of Natural Gas Hydrate Bearing Sediments Retrieved from Eastern Nankai Trough[END_REF][START_REF] Dai | Hydrate morphology: Physical properties of sands with patchy hydrate saturation[END_REF][START_REF] Konno | Permeability of sediment cores from methane hydrate deposit in the Eastern Nankai Trough[END_REF]. Because of technical feasibility limits, only methane hydrate-bearing sands (MHBS) are the actual target for potential methane gas exploration [START_REF] Collett | Natural gas hydrates: A review[END_REF][START_REF] Boswell | Current perspectives on gas hydrate resources[END_REF][START_REF] Le | Methane Hydrate-Bearing Sand -An Energy Resource?[END_REF]. The formation of MH in sandy sediments modifies the microstructure and as a result the physical/mechanical properties of MHBS. Therefore, the study of the microstructure of MHBS is essential for the interpretations of geophysical data and reservoir-scale simulations in the scope of methane gas production [START_REF] Gabitto | Physical properties of gas hydrates: A review[END_REF].

While recent technical developments permit to extract intact methane hydratebearing cores from natural settings, preserving their in situ pressure-temperature conditions, and to efficiently extrude such samples into triaxial cells for mechanical characterization [START_REF] Priest | PCATS Triaxial: A new geotechnical apparatus for characterizing pressure cores from the Nankai Trough, Japan[END_REF][START_REF] Yamamoto | Overview and introduction: Pressure core-sampling and analyses in the 2012-2013 MH21 offshore test of gas production from methane hydrates in the eastern Nankai Trough[END_REF][START_REF] Yoneda | Mechanical properties of hydrate-bearing turbidite reservoir in the first gas production test site of the Eastern Nankai Trough[END_REF][START_REF] Yoneda | Pressure-core-based reservoir characterization for geomechanics: Insights from gas hydrate drilling during 2012-2013 at the eastern Nankai Trough[END_REF], these procedures are still highly challenging and improvements are still needed to increase the proportion of successful sample extractions. That explains why most of the existing experimental works focus on synthetic samples produced in the laboratory. Various methods have been proposed to form methane hydrates in sandy sediments in the laboratory. Comparisons between seismic velocities measured on real samples and those calculated via conceptual models have been used to indirectly assess the MH pore habits in sandy sediments (Dvorkin & Nur, 1996&1998;[START_REF] Helgerud | Elastic-wave velocity in marine sediments with gas hy-drates: Effective medium modeling[END_REF][START_REF] Dvorkin | Introduction to Physical Properties and Elasticity Models[END_REF]. Four idealized arrangements of MH at the pore scale in sediment, referred to as "pore habits", have been considered: "graingrain contact cementing", "mineral coating cementing", "load-bearing" and "porefilling" [START_REF] Dvorkin | Introduction to Physical Properties and Elasticity Models[END_REF]. MH were supposed to be located at the contacts of sand grains (grain-grain contact cementing) when the excess-gas or the ice-seeding methods are used to produce them [START_REF] Waite | Methane hydrate formation in partially water-saturated Ottawa sand[END_REF][START_REF] Priest | A laboratory investigation into the seismic velocities of methane gas hydrate-bearing sand[END_REF]. Loadbearing MH were inferred in sandy sediments when the excess-water method was adopted [START_REF] Priest | Influence of gas hydrate morphology on the seismic velocities of sands[END_REF]. Finally, MH initially formed following the excess-gas method (with grain-grain contact cementing morphology), were supposed to be redistributed within the pore space between sand grains (i.e. "pore-filling" morphology) when excess methane gas was replaced by water. This method is referred to as "water saturation", and can be done with or without an additional temperature cycle [START_REF] Choi | Laboratory formation of noncementing hydrates in sandy sediments[END_REF][START_REF] Le | Effect of temperature cycle on mechanical properties of methane hydrate-bearing sediment[END_REF].

As MH morphologies and pore habits considerably affect physical/mechanical behaviors of MHBS [START_REF] Waite | Physical properties of hydrate-bearing sediments[END_REF]Lei et al., 2019a), their direct observation at pore scale is of major importance. X-ray computed tomography (XRCT) has been used in several studies to investigate the microstructure of gas hydrate-bearing sediments, mostly under excess-gas conditions. The spatial resolution of image has been well improved over time [START_REF] Yang | Microstructure Observations of Natural Gas Hydrate Occurrence in Porous Media Using Microfocus X-ray Computed Tomography[END_REF][START_REF] Zhao | Microstructural characteristics of natural gas hydrates hosted in various sand sediments[END_REF]Lei et al., 2019a).

In addition, hydrate growth and pore habits in sediments at the pore scale were followed by 4D time-lapse imaging thanks to the higher temporal resolution of synchrotron X-Ray computed tomography (SXRCT) [START_REF] Chaouachi | Microstructural evolution of gas hydrates in sedimentary matrices observed with synchrotron X-ray computed tomographicmicroscopy[END_REF][START_REF] Kerkar | Direct observations of three dimensional growth of hydrates hosted in porous media[END_REF][START_REF] Kerkar | Imaging methane hydrates growth dynamics in porous media using synchrotron X-ray computed tomography[END_REF]. However, the contrast between water and methane hydrate in a XRCT image is rather poor so that it is challenging to distinguish both phases. Indeed the grey level in an XRTC image reflects the material X-ray attenuation difference and mainly depends on the material density and atomic number. That is why other types of gas or saline water solutions have been used in most studies to enhance the XRCT/ SXRCT image contrast [START_REF] Kerkar | Direct observations of three dimensional growth of hydrates hosted in porous media[END_REF][START_REF] Kerkar | Imaging methane hydrates growth dynamics in porous media using synchrotron X-ray computed tomography[END_REF][START_REF] Chaouachi | Microstructural evolution of gas hydrates in sedimentary matrices observed with synchrotron X-ray computed tomographicmicroscopy[END_REF][START_REF] Sahoo | Laboratory Insights Into the Effect of Sediment-Hosted Methane Hydrate Morphology on Elastic Wave Velocity From Time-Lapse 4-D Synchrotron X-Ray Computed Tomography[END_REF]. To this respect, it should be noted that the methane hydrate formation phase boundary is shifted depending on the concentration of salt in the water (Sloan, 2008) and that salt exclusion during the hydrate formation results in a salt concentration increase in the remaining water [START_REF] Chen | Pore-scale evidence of ion exclusion during methane hydrate growth and evolution of hydrate pore-habit in sandy sediments[END_REF]. Furthermore, morphologies of gas hydrates depend on the type of gas used. [START_REF] Chen | Ostwald ripening changes the pore habit and spatial variability of clathrate hydrate[END_REF], observed via XRCT Ostwald ripening-type changes of the spatial distribution in the pores space of sediments of Xenon hydrate formed following the excess-gas method, at both the pore and sample scales. Lei et al. (2019b) observed similar water migration during the formation of carbon dioxide hydrate in sediments.

However, their image spatial resolution was low, with a voxel size larger than 10 µm.

Discontinuous water migrations during MH formation in wet sand with saline solution (10 wt% of Sodium Bromide -NaBr) were observed by Nikitin et al. (2019) who used SXRCT imaging at higher image spatial resolution (voxel size was about 2 µm) and higher temporal resolution.

In order to mimic natural MHBS in saline water saturated media, [START_REF] Kerkar | Imaging methane hydrates growth dynamics in porous media using synchrotron X-ray computed tomography[END_REF] formed MH in saline water saturated media (5 wt% of BaCl 2 ) following the excesswater method. Patchy methane hydrate distributions and heterogeneous hydrate accumulations were observed via SXRCT. However, the image interpretation was based on standard filtering and segmentation methods to compensate for low image resolution (voxel size = 7.5 µm), making direct observations of MH morphologies and pore habits delicate. Recently, methane hydrate morphologies and pore habits in sandy sediments, initially under excess-gas conditions and then subjected to saline water injection, or directly under excess-water conditions, were investigated at high image spatial resolution (about 2 µm) by Lei et al. (2019a). An XRCT technique developed by Lei et al. (2018), taking advantage of both X-Ray attenuation and phase contrasts, was used to improve image contrast. However, due to the low temporal resolution of XRCT, the kinetics of methane hydrate formation could not be fully observed.

In the present study, the progressive formation and the evolution of methane hydrates under excess gas conditions were observed by using time resolved SXRCT imaging with submicron/micron voxel size. MH morphologies and pore habits, together with water migrations, at both pore and sample scales, were investigated.

Saline water (Potassium iodide -KI) was used. Experimental conditions are detailed in section 3, while section 4 summarizes main observations. Morphologies and pore habits of MHs under excess-gas conditions and under saline water conditions are discussed in section 5, where some recommendations are also formulated for further studies on MH via XRCT/SXRCT imaging.

Experimental method

Materials

The sediment used in this study was Fontainebleau silica sand (NE34), which consists of poor-graded sub-rounded quartz grains whose diameter ranges from 100 to 300 micrometers. Saline solution (3.5 % of KI by weight) and methane gas with standard purity of 99.995 % were used.

Experimental setup and imaging conditions

Figure 1 provides a sketch of the experimental setup used in this study, while figure 2 shows a picture of it. Wet sand was manually compacted into an aluminum tube with an outside diameter of 6.45 mm, a thickness of 0.89 mm and a total length of about 200 mm. The sample temperature was controlled by cooled air circulated at a constant flow rate through a Poly-methyl-methacrylate (PMMA) tube, with an outside diameter of 23 mm and a thickness of 2 mm, from its top to its bottom. Note that the PMMA tube was fixed during CT scan and that the aluminum tube freely rotated inside it. The air temperature at the air inlet and outlet was measured with two thermocouples inserted into the PMMA tube. It should be noted that a preliminary experiment, with additional thermocouples in the wet sand inside the aluminum tube and on the latter, showed an identical temperature at the same height in the PMMA tube, the aluminum tube and in the sand at the center of the aluminum tube. As for the gas pressure control, a small methane gas bottle (internal volume of 40 mL) associated with a pressure reducer was connected to the gas inlet at the lower end of the aluminum tube. This ensured a constant methane gas pressure of 7 MPa (±0.1 MPa) in the sample during the MH formation and the SXRCT scans.

SXRCT scans were performed at the PSICHE beamline of the French Synchrotron SOLEIL. A pink X-ray beam with a mean energy of 44 keV was used. X-rays were converted into visible photons by means of a 50µm thick LuAg scintillator crystal, which was observed with a Hamamatsu ORCA camera equipped with a 2048x2048 pixels CCD sensor, with a pixel size of 6.5µm, through an optical microscope based on a objective lens from Mitutoyo. Two types of scans were performed as shown in Figure 1. The high-resolution scans were focused on two central zones (Z0_HR, Z1_HR), marked with a green line. They were 1.75 mm in height and 1.75 mm in diameter and had a voxel size of 0.9 µm. The 180° scan duration was 12 minutes (0.2 hour). The low-resolution scans, marked with a blue line were 3.47 mm in diameter and 1.75 mm in height. They were performed to investigate MH distribution all along the sample height. Their voxel size was 1.8 µm and the scan duration was 15 minutes (0.25 hour). Note that the same objective lens was used for both scans.

In the low-resolution scans pixels of the camera were 2x2 binned but scans were performed over 360 degrees to virtually double the 1024x1024 image resolution of the binned sensor along the horizontal direction. The PyHst software (https://software.pan-data.eu/software/74/pyhst2) was used to reconstruct the 3D images. The Paganin's filter option was activated and its parameters were optimized to limit the phase contrast at the interfaces so that gray levels within each phase in the image remained almost homogeneous. Therefore, contrast in the obtained SXRCT images depended mainly on the difference of X-ray material attenuation. The brightness of the different phases in the images reflects the material density, with the following order ranging from brighter to darker: sand > saline water > methane hydrate > methane gas.

Test procedure

Wet sand was manually compacted into the aluminum tube. The average porosity was about 0.40. The initial moisture content and the average water degree of saturation were evaluated to about 15% and 60%, respectively. After the installation of the system (Figure 1) onto the rotation table of the beamline, residual air was removed from the aluminum tube by using a vacuum pump prior to the application of methane gas at a pressure of 7 MPa. Afterward, MH were formed by circulating cooled air to reduce the temperature inside the PMMA tube from room temperature down to 1-2 °C. The first CT scan was performed when the temperature measured by the first thermocouple (shown in Figure 1) reached the target temperature T = 2 °C.

The temperature measured by the second thermocouple was then 4 °C. The distance between the two sensors being about 150 mm, the average temperature gradient along the tube was thus 0.013 °C/mm. Figure 3 shows the type and position of the scans performed to follow the MH formation as a function of time, with t = 0 corresponding to the moment when the temperature of the cell reached the target value. During the first 17 hours, high-resolution scans were performed continuously and alternatively at the positions Z0_HR and Z1_HR. That allowed us to follow the growth of MH at grain scale in these zones. Afterwards, low-resolution scans at various positions (from Z-7 to Z9) were performed in order to investigate the MH distribution at sample scale.

Results

The vertical cross-section through the 3D image of zone Z0_HR recorded at the beginning of the test shown in Figure 4a and Figure 5a shows that water was located at contacts between sand grains because of capillary suction. Menisci at the interfaces between the liquid phase (water, intermediate grey level in figure 5 and yellow/green color in figure 5) and the gas phase (methane gas, dark grey in figure 4 or blue color in figure 5) can be easily identified. At t=0.58 h after the application of methane hydrate formation conditions (Figure 4b), methane hydrates were already formed and took the form of small needle-shaped MH crystals, called "filaments" in the following, located at the surface of grains or at the interface between water and gas (Figure 4b). The volume of liquid at the grain contacts was reduced compared to that shown in Figure 4a (vertical cross section are taken at the same position in the 3D image). This can be explained by the formation of methane hydrates in this zone but also in other zones (outside of the observed zone) which absorbed water. Note that no MH layer (which may have been already formed at grain surfaces and at water/ gas interfaces) could not be clearly evidenced, probably because of both their thin thickness and the partial volume effect of CT images. In these 2D cross-sections, some MH seem to be suspended in pore space but in reality they are all connected to either water/gas interfaces or grain surfaces, as evidenced when one browses the full 3D image. Unfortunately, no additional scan has been conducted between t = 0 and t = 0.58h to investigate the very beginning of MH formation. Figures 4c and4d show MH morphologies and pore habits in zone Z0_HR at t = 4 and 4.5 h, respectively. MH filaments became bigger and thicker over time at grain surfaces and gas/water interfaces. Coarser nodular MH crystals with similarly increasing size can also be observed. Furthermore, two different grey levels can clearly be observed in the water/hydrate areas: darker areas correspond to hydrates (or hydrate rich zones) while the brighter ones correspond to saline water, whose brightness indeed increases due to ion exclusion during MH growth [START_REF] Chen | Pore-scale evidence of ion exclusion during methane hydrate growth and evolution of hydrate pore-habit in sandy sediments[END_REF]. These areas appear respectively in light blue and yellow/orange colors in the false color representation in figure 5b. Hydrates seem to be preferentially located in the outer areas, at the interface between gas and water.

Images of the same vertical cross-section through zone Z1_HR at t = 3.8, 4.3, 8 and 12.4 h are shown in Figure 6. At t = 3.8 h (Figure 6a), MH nodular crystals/filaments and layers can be observed at grain surfaces and at gas/water interfaces. However, it seems that the MH saturation (volume of MH divided by the volume of void) was significantly lower than the average initial water saturation (i.e. 60 %). At t = 4.3 h, water and MH hydrates invaded the pore space on the top of the image while MH in the other zones were barely changed (Figure 6b and Figure 7a). At t = 8 h (Figure 6c), on the top of the image, additional MH were formed inside the pore space filled with water, corresponding to a pore-filling habit. Actually, the gray level of these zones changed from a bright level (corresponding to water) to a darker gray level (corresponding to MH). In the other zones of the image where pore spaces were filled with methane gas, MH continued to grow with respect to the image obtained at t = 4.3 h (Figure 6b). Additional grow of MH in both highly or moderately saturated pore spaces in zone Z1_HR were observed from 8 to 12.4 hours (see Figures 6c,6d and Figure 7b).

From 8 hours, the lower part of zone Z1_HR which is shared with zone Z0_HR (red boxes in Figures 6c and6d) was perturbated by some intense ring artefacts (which indeed appear as rings in transverse cross-sections). Indeed, the PMMA tube which does not rotate during the scans is continuously irradiated at the same position for a given vertical position of the sample, with some overlap for scans of zones Z0 and Z1. More precisely, Figure 8 shows the images over the zone Z0_HR at subsequent times t = 12.2, 13.4 and 16.3 h. At t = 12.2 h (Figure 8a), large MH can be observed but now the whole image was influenced by such ring artefacts. We checked the PMMA tube and noted that the zone crossed by the X-ray beam, of square shape delimited by adjusted slits, was strongly damaged throughout the whole thickness of the tube: the initially transparent PMMA became a heterogeneous porous material.

As stated above, in the used experimental setup, the PMMA tube was fixed during the scans, with the aluminum tube rotating inside it. As a consequence, the same PMMA zone has been continuously irradiated during all previous scans at the same height and the accumulated irradiation would have caused such damage, even more intensively in the overlapping areas. The PMMA tube was then manually rotated so that the X-ray beam no longer passed through the damaged zone to avoid such intense ring artefacts during the subsequent scans. The image obtained at t = 13.6 h (Figure 8b) shows no more such ring artefacts. However, the proportions of MH and water were well reduced compared to time t = 12.2 h. This trend was confirmed by the image obtained at t = 16.3 h (Figure 8c) where MH can no longer be observed in this zone. Only a small quantity of water remained at grain contacts. The comparison with Figure 4 shows that there were no large relative motions of the grains. However some small relative motions can be qualitatively observed when images are compared in details, showing that MH formation and dissolution may induce grain motion. A quantitative analysis of the latter, for instance with adapted discrete digital volume correlation techniques, is left for further investigations. For the purpose of the qualitative discussion of the present study, such motions will be neglected. It should however be noted that such small motions make it difficult to quantify MH saturation by simple image subtraction techniques.

The results obtained in zone Z1_HR at t = 13.6 and 16.5 h are shown in Figure 9.

The ring artefacts observed at t = 12.4 h (Figure 6d) were no longer observed at t = 13.6 h (Figure 9a). Furthermore, the quantity of MH and water seems to decrease at the bottom similarly to what was observed in zone Z0_HR (Figure 8). This reduction trend is confirmed by the image obtained at t = 16.5 h where MH could no longer be observed in the lower half part of the image (Figure 9b). Moreover, as in zone Z0_HR

shown in Figure 8c, only a small quantity of water was found at grain contacts in this area. These observations in both ZR0_HR and ZR1_HR zones suggest that MH under local excess-water conditions as in the top part of the images were more stable than MHs under local excess-gas conditions as in the lower part of the image.

For a better understanding of the observed results, which suggests a strong macroscopic heterogeneity of MH volume fraction in the sample, scans at a lower resolution (voxel size: 1.8 µm) were used to enlarge the horizontal size of the investigated area of a single scan. The larger scanned zone was then 1.75 mm in height (limited by sensor size and X-ray beam height) and 3.47 mm in diameter for each scan. Furthermore, several scans were superposed to explore the sample along its length. But due to the limited beamline time, the pitch between subsequent scans was double their height (i.e. scans at intermediate heights were skipped), as shown in Figure 1. These scans were performed along the sample over a distance of 290 mm in total, with zones labelled from Z-7 to Z9 (see Figure 1 and Figure 3).

Figure 10 shows the images obtained in zones Z-1 (t = 19.2 h), Z0 (t = 21.5 h), Z1 (t = 19.5 h). The observation of the common zone of the three scans show that MH and water distributions did not change significantly during these scans. For this reason, the images were merged into a bigger image of 3.47 mm in width and 5.15 mm in height. The red box corresponds to the zones Z0_HR and Z1_HR scanned at high resolution previously. It is obvious that in the central zone (i.e. the top of zone Z-1_HR, the whole zone Z0_HR and the bottom of zone Z1_HR), no hydrates were present and the quantity of water was really small. Both MH and water in much larger amount were found in the periphery zones. Furthermore, it seems that the top of zone Z1 and the bottom of zone Z-1 have similar pore space distribution, with MH mixed with saline water together with some gas pockets. However, the quantity of MH was larger at the top of zone Z1 compared to that at the bottom of zone Z-1 which contained more water (Figure 10 and Figure 11a,c). Note that a slight ring artefact was found in the center of the images, as commonly observed in XRCT images.

Figure 12 shows vertical cross-section through images recorded at positions Z-3, Z-5 and Z-7, with details provided in Figure 13 in false colors. In some areas in these images, the granular medium was still under local gas-saturated conditions. MH were found in form of nodular crystals and layers around sand grains and at water/gas interfaces. On the other hand, in some local areas saturated with water (mostly in zones Z-3 and Z-5), some round MH particles were found.

Images of zones Z3, Z5, Z7 and Z9 are shown in Figure 14 and Figure 15. It shows that methane gas, methane hydrates and saline water were mixed in the pore space of all these zones.

Figure 16 presents some examples of images showing various MH morphologies and pore habits. Their corresponding gray level histograms are shown in Figure 17, with a maximum count of grey level (corresponding to sand grains) of each image normalized to 1. Gray level ranges for the four phases in Figure 17 overlap as a combined consequence of partial volume effect and image noise. Both the images and their corresponding gray level histograms confirm that MH were in local gassaturated conditions in Figure 16a, under local excess saline water conditions with some methane gas bubbles in Figure 16b and in local excess water-saturated conditions in Figure 16c. MH were found in angular nodular crystal or layer forms around sand grains and at water/ gas interfaces in local gas-saturated zones in figure 16a while they mainly took the form of round particles mixed in saline water in excess-water zones in Figure 16a, Figure 16b and in the whole Figure 16c. It seems that round MH particles of 20-30 µm were found mixed heterogeneously with saline water to create local saline water-saturated zones (pore-filling/load-bearing habit).

Discussions

These aforementioned results show multiple water migration mechanisms at the grain scale during MH formation in sandy sediment following the excess-gas method.

That results in heterogeneous MH distributions at both pore and sample scales. Note that the excess-gas method is a common method used to create synthetic MHBS in laboratory for both macroscopic characterizations (Miyazaki et al., 2011a & b;[START_REF] Hyodo | Mechanical and dissociation properties of methane hydrate-bearing sand in deep seabed[END_REF][START_REF] Le | Effect of temperature cycle on mechanical properties of methane hydrate-bearing sediment[END_REF][START_REF] Le | Kinetics of methane hydrate formation and dissociation in sand sediment[END_REF] and pore-scale observations by means of XRCT or SXRCT [START_REF] Chaouachi | Microstructural evolution of gas hydrates in sedimentary matrices observed with synchrotron X-ray computed tomographicmicroscopy[END_REF]Lei et al., 2019a).

Water and/or gas hydrate movement during gas hydrate formation were observed by XRCT/SXRCT [START_REF] Chen | Ostwald ripening changes the pore habit and spatial variability of clathrate hydrate[END_REF]Lei et al., 2019a&b;Nikitin et al., 2019). [START_REF] Chen | Ostwald ripening changes the pore habit and spatial variability of clathrate hydrate[END_REF] observed a hydrate coarsening over some ten days which was explained by the reduction of the specific interfacial surfaces (Ostwald ripening). XRCT experiments were performed with Xenon hydrates while methane hydrate growth on water droplets was observed with optical microscopy. However, no water migration was observed. In the work of Lei et al. (2019b), fast water migration was found after MH nucleation, became slower after 24 h and water remained stable after 81 h. In addition, progressive methane hydrate migrations were observed by XRCT scans over the whole duration of the test. Lei et al. (2019a) observed CO 2 hydrates forming preferentially toward the periphery of the sample. In addition, sediment particles moved toward the sample center. These two phenomena were explained by cryogenic suction governed by temperature gradient generated during gas hydrate formation. Furthermore, Nikitin et al. (2019) performed SXRCT scans to observe MH formation in sandy sediment and found multiple fast water movements. That once again was explained by cryogenic suction.

In the present study, water was observed to move out of zone Z0_HR at 0.58 h (Figure 4). However, it migrated into zone Z1_HR at 3.8 h (Figure 6). In addition, both methane hydrates and water were moved out of zone Z0_HR (at t = 13.4 h, Figure 8b) and the bottom of zone Z1_HR (at t = 13.6 h, Figure 9a). The two first events would be explained by the cryogenic suction governed by a local temperature gradient during the MH formation. Vertical temperature gradient was obvious (about 0.013 °C/mm). Furthermore, both events could be interpreted as Haines jumps (i.e. sudden jumps of the fluid interfaces accompanied by fluid redistribution and a transient pressure response) when pressure-volume response was multi-value across pore throats due to the MH formation [START_REF] Sun | Haines jumps: Pore scale mechanisms[END_REF]. It should be noted that Haines jumps are fast phenomena and that their dynamic evolution could not be captured by our high-quality images with limited temporal resolution (12'-15' for one image). As a small quantity of small methane hydrates might be mixed in pore space with methane gas and saline solution, they could be moved together with the saline solution if they are not attached to grains or if their connection with grains is weak enough. The third event (MH and water disappearance) can be explained by the Haines jump mechanism and/or the energy supplied by X-rays that locally heated the sample. This X-ray-induced heating has been evidenced by some theoretical models and experiments when studying biological molecules with macromolecular crystallography [START_REF] Helliwell | Synchrotron X-radiation protein crystallography: Instrumentation, methods and applications[END_REF][START_REF] Kriminski | Heat transfer from protein crystals: Implications for flash-cooling and X-ray beam heating[END_REF][START_REF] Wallander | Simulated sample heating from a nanofocused X-ray beam[END_REF][START_REF] Warren | Direct measurement of X-rayinduced heating of microcrystals[END_REF]. These works showed that the increase of temperature induced by X-rays depended not only on the absorbed energy but also on the heat transfer to the surrounding medium. In the present study, zones Z0_HR and Z1_HR were exposed to X-rays continuously during the first twelve hours. Actually, within a beam power of 0.118 W/mm 2 , the volume fractions of quartz, saline water and air are 0.60, 0.24 and 0.16, respectively, the heat flux provided to the this zone was estimated at 0.0015 W/mm 3 . By considering a simplified one-dimensional heat diffusion along the sample's axis, the maximum temperature increase (related to beam-induced heating) was estimated at 4 °C. That could explain the MH dissociation in these zones as shown in Figure 10. In addition, most of the water released after MH dissociation can reasonably be assumed to have moved to other zones for further MH formation. The zone Z0_HR was more sensitive to beam-induced heating than the zone Z1_HR because the zone Z0_HR was exposed to X-rays 2 hours before the scans were switched between these two zones.

Furthermore, the temperature in the zone Z1_HR was slightly lower than that in the zone Z0_HR due to the vertical temperature gradient. MH still existed at the periphery of the zone Z0 (Figure 10). That could be explained by the existence of a radial temperature gradient, which was negligible for the case of wet sand in the preliminary test without MH as aforementioned, but could exist in the case of MH formation as the tube periphery was in direct contact with cooled air: the MH formation can increase sample temperature locally because it is an exothermic process and this increase of temperature in the zones nearby the tube periphery could be compensated more easily by cooled-air circulation than in the center of the tube. In addition, X-rays irradiated continuously the central part of the sample, and only intermittently the periphery. Besides, it seems that zones Z-3, Z-5 and Z-7 corresponded to the expected excess-gas media (Figure 11 and Figure 12) while the zones Z3, Z5, Z7 and Z9 (situated at higher positions) were modified due to multiple water migrations during the MH formation (Figure 14 and Figure 15). That can be explained by the vertical temperature gradient and water condensation which favored the MH formation on the top of the sample. That can also be related to the stochastic nature of Haines jump, the unstable nature of the MH formation and/or the temperature increase induced by X-ray irradiation.

The MH formation naturally is a dynamic process that favored Ostwald ripening as well as the appearance of local excess-water conditions. However, it seems that sample temperature gradient and X-rays-induced heating favored more water migrations. It should be noted that the ratio of sample height/diameter is generally close to two for macroscopic tests (e.g. triaxial tests) while it is much larger for XRCT/SXRCT studies. That involves important vertical temperature gradients.

Temperature control shows an important role for MH stabilization. Furthermore, studies on MH should pay attention to the interaction of X-rays and the sample (beam-induced heating).

To mimic natural methane hydrate-bearing marine sediments, the dissolved gas method is considered as a good method. However it is time consuming, especially at high hydrate saturation, due to the low solubility of methane gas in water [START_REF] Spangenberg | Pore space hydrate formation in a glass bead sample from methane dissolved in water[END_REF]. The water-excess method, proposed by [START_REF] Priest | Influence of gas hydrate morphology on the seismic velocities of sands[END_REF], was supposed to create load-bearing MH in sandy sediments at hydrate saturation lower than 40%, according to sonic wave velocity measurements. However, MH were observed to be formed heterogeneously inside these samples via XRCT [START_REF] Kneafsey | Examination of Hydrate Formation Methods: Trying to Create Representative Samples[END_REF]. Note that pore-filling MH begin bridging sediment grains and behaving as load-bearing distributions when MH saturation exceeds 25 -40 % [START_REF] Waite | Physical properties of hydrate-bearing sediments[END_REF]. [START_REF] Kerkar | Imaging methane hydrates growth dynamics in porous media using synchrotron X-ray computed tomography[END_REF] confirmed patchy methane hydrate distribution and heterogeneous accumulations with XRCT at higher image spatial resolution. Via measurements of sonic wave velocities, MH created following the excess-gas method were supposed to be converted/redistributed from the grain contacts to the pore space between grains when sample was saturated with water (with or without an additional temperature cycle) [START_REF] Choi | Laboratory formation of noncementing hydrates in sandy sediments[END_REF][START_REF] Le | Effect of temperature cycle on mechanical properties of methane hydrate-bearing sediment[END_REF]. In the work of Lei et al. (2019b), the effect of water injection on this conversion/redistribution of MH was confirmed by XRCT scans at high image spatial resolution. Furthermore, the obtained images showed round MH particles under excess-water conditions. In the present study, MH were initially formed following the excess-gas method. However, after multiple water migrations, MH in both local excess-gas and local excess-water media were observed in the sample. MH in local excess-gas media were in cementing forms (mineral-coating and/or grain-contacts) while round MH particles were mixed with water in the pore space under local excess-water conditions (Figure 10). The faster MH formation under excess-gas conditions could explain why methane hydrates were less stable than that under excess-water conditions where MH were formed slowly (mostly via methane gas diffusion). These observations confirmed the pore-filling/load-bearing distribution of MH in excess-water media (round MHs particles mixed with water in the pore space of porous media) that are being widely used for numerical simulations [START_REF] Waite | Methane hydrate formation in partially water-saturated Ottawa sand[END_REF][START_REF] Waite | Physical properties of hydrate-bearing sediments[END_REF]. It is supposed that MH distribution at the grain scale of MHBS after the water saturation at low MH saturation and after the temperature cycle in the work of [START_REF] Le | Effect of temperature cycle on mechanical properties of methane hydrate-bearing sediment[END_REF][START_REF] Le | Kinetics of methane hydrate formation and dissociation in sand sediment[END_REF] looks alike and resembles to natural MHBS.

Conclusions

In the present work, methane hydrate-bearing sand was created first by pressurizing methane gas (at 7 MPa) in wet sand (with saline water, KI 3.5 wt%), followed by decreasing the sample temperature (excess-gas method). SXRCT scans were used to observe the MH formation. The following conclusions can be drawn:  MH were initially formed following the excess-gas method. However after multiple water migrations in the sample, both local excess-gas and local excess-water media can co-exist. Water migrations can modify MH morphologies and pore habits in the pore space. The MH distribution was heterogeneous at the grain scale as well as the sample scale.

 Under local excess-water conditions, round MH particles were found mixed with water in the pore space (pore-filling/load-bearing habit) while MH cement sand grains under local excess-gas conditions (grain-grain contacts and/or mineral-coating). Actually, pore-filling and load-bearing models could be used to simulate MH, at the grain scale in synthetic sandy sediments, under excesswater conditions as well as natural MHBS for numerical studies on physical/mechanical behaviors of MHBS.

 MH formation in porous media is naturally a dynamic process. However, it seems that sample temperature gradient and X-ray-induced heating favor more water migrations during the MH formation observed by XRCT/SXRCT.

Figure 1 .

 1 Figure 1. Experimental setup showing pressure and temperature controls for SXRCT tests and the positions of the low-and high-resolution CT scans.

Figure 2 .

 2 Figure 2. Picture of the experimental setup (left: on a laboratory CT scanner; right: on the Psiché beamline)

Figure 5 .

 5 Figure 5. Details of yellow boxes in Figure 4a&d.

Figure 6 .

 6 Figure 6. Vertical cross-section through Z1_HR: (a) t = 3.8 h; (b) t = 4.3 h; (c) t = 8 h; (d) t = 12.4 h.

Figure 7 .

 7 Figure 7. Details of yellow boxes in Figure 6b&d.

Figure 8 .

 8 Figure 8. Vertical cross-section through Z0_HR: (a) t = 12.2 h; (b) t = 13.4 h; (c) t = 16.3 h.

Figure 9 .

 9 Figure 9. Vertical cross-section through Z1_HR: (a) t = 13.6 h; (b) t = 16.5 h.

Figure 10 .

 10 Figure 10. Vertical cross-section through Z1 (t = 19.5 h), Z0 (t = 21.5 h), and Z-1 (t = 19.2 h). Image dimensions: 3.47 mm x 5.15 mm.

Figure 11 .

 11 Figure 11. Details of yellow boxes in Figure 10.

Figure 12 .

 12 Figure 12. Vertical cross-section through Z-3 (a, t = 19.0 h), Z-5 (b, t = 18.8 h), and Z-7 (c, t = 18.5 h). Image dimensions: 3.47 mm x 1.75 mm.

Figure 13 .

 13 Figure 13. Details of yellow boxes in Figure 12 a,b,c.

Figure 14 .

 14 Figure 14. Vertical cross-section through Z9 (a, t = 20.5 h), Z7 (b, t = 20.2 h), Z5 (c, t = 20 h) and Z3 (d, t = 19.7 h). Image dimensions: 3.47 mm x 1.75 mm.

Figure 15 .

 15 Figure 15. Details of yellow boxes in Figure 14 a,b,c,d.

Figure 16 .

 16 Figure 16. Possible morphologies and pore habits of MHs: (a) image in Z-3 (t = 19 h); (b) image in Z1 (t = 19.5 h; (c) image in Z-1 (t = 19.2 h).

Figure 17 .

 17 Figure 17. Normalized histograms of images in Figure 10 (a, b, c).

Acknowledgements

The present study was funded by the French National Research Agency via the project HYDRE "Mechanical behavior of gas-hydrate-bearing sediments" -ANR-15-CE06-0008. The authors would also like to express their great thanks to Synchrotron Soleil for access to the Psiché beamline via the Proposal 20181629 "Morphology and evolution of methane hydrates in granular sediment". The technical support from Marine Lemaire and Emmanuel Delaure was highly appreciated. We also would like to thank Ross Brown (IPREM) for our interesting discussions.


Dr Thi Xiu Le

Dr Patrick Aimedieu
email: patrick.aimedieu@enpc.fr

Dr Michel Bornert
email: michel.bornert@enpc.fr

Baptiste Chabot
email: baptiste.chabot@enpc.fr

Dr Andrew King
email: king@synchrotron-soleil.fr

Anh Minh

Dr Anh Minh Tang

New X-Ray Microtomography Setups and Optimal Scan Conditions to Investigate Methane Hydrate-Bearing Sand Microstructure

Keywords: Methane hydrate-bearing sand, X-ray computed tomography (XRCT), synchrotron XRCT, experimental setups, scans conditions, high pressure, low temperature

published or not. The documents may come

Introduction

Methane hydrates (MHs), being solid ice-like compounds of methane gas and water, are naturally formed at high pressure and low temperature in marine and permafrost settings. They are being considered as an alternative energy resource but also a source of geo-hazards and climate change [START_REF] Collett | Natural gas hydrates: A review[END_REF]. Depending on the characteristic particle size and the effective stress, different morphologies and pore distribution within natural sediments of methane hydrates, such as nodules/chunks, lenses/veins or pore-filling have been identified [START_REF] Boswell | Gas hydrate accumulation types and their application to numerical simulation[END_REF][START_REF] Dai | Hydrate morphology: Physical properties of sands with patchy hydrate saturation[END_REF]).

In the scope of methane gas production from methane hydrate-bearing sediments, currently, due to technical feasibilities, only pore-filling MHs at high hydrate saturation in sandy sediments are being considered. Most experimental works concern laboratory tests on synthetic samples because of challenges to get cored-intact methane hydrate-bearing sediment samples. In the objective of creating synthetic pore-filling methane hydrates in sandy sediments (to mimic natural sediments), different methods have been proposed such as the excess-gas, ice-seeding, or excess-water methods [START_REF] Clayton | The effects of disseminated methane hydrate on the dynamic stiffness and damping of a sand[END_REF][START_REF] Priest | Influence of gas hydrate morphology on the seismic velocities of sands[END_REF][START_REF] Waite | Methane hydrate formation in partially water-saturated Ottawa sand[END_REF]). However, by using seismic wave velocities [START_REF] Chand | Elastic velocity models for gas-hydrate-bearing sediments -A comparison[END_REF][START_REF] Dvorkin | Introduction to Physical Properties and Elasticity Models: Chapter 20[END_REF][START_REF] Dvorkin | Elasticity of marine sediments: "Rock physics modeling[END_REF][START_REF] Dvorkin | Elasticity of high-porosity sandstones: Theory for two North Sea data sets[END_REF][START_REF] Helgerud | Elastic-wave velocity in marine sediments with gas hy-drates: Effective medium modeling[END_REF], MHs are believed to exist in four idealized arrangements or "pore-habits": cement, with graingrain contacts; cement, with mineral coating; load-bearing and pore-filling. Physical and mechanical properties of sediments containing MHs depend considerably on methane hydrate morphologies and distribution within the pore space, which are thus of the essence for interpretation of geophysical data and reservoir-scale simulations in the scope of methane gas production [START_REF] Taleb | Hydromechanical Properties of Gas Hydrate-Bearing Fine Sediments From In Situ Testing[END_REF][START_REF] Le | Effect of temperature cycle on mechanical properties of methane hydrate-bearing sediment[END_REF][START_REF] Nguyen-Sy | A model to predict the elastic properties of gas hydrate-bearing sediments[END_REF][START_REF] Alavoine | Fast Fourier transform-based homogenisation of gas hydrate bearing sediments[END_REF][START_REF] Taleb | Seafloor depressions on the Nigerian margin: Seabed morphology and sub-seabed hydrate distribution[END_REF]. Therefore, pore-scale observations of MH morphologies and pore-habits in sandy sediments are crucial. Laboratory X-ray computed tomography (XRCT) and Synchrotron X-Ray Computed Tomography (SXRCT) have been extensively used to investigate the 3D microstructure of gas hydrate-bearing sediments (Chaouachi et al. 2014[START_REF] Kerkar | Direct observations of three dimensional growth of hydrates hosted in porous media[END_REF]; [START_REF] Kerkar | Imaging methane hydrates growth dynamics in porous media using synchrotron X-ray computed tomography[END_REF][START_REF] Ta | Observations of pore-scale growth patterns of carbon dioxide hydrate using X-ray computed microtomography[END_REF][START_REF] Zhao | Microstructural characteristics of natural gas hydrates hosted in various sand sediments[END_REF]. Studying synthetic methane hydrate-bearing sand (MHBS) with these techniques is really challenging due to not only the need of special experimental setups (i.e. high pressure and low temperature should be maintained) but also to the poor image contrast between methane hydrate and water, which depends mainly on the difference of material density and atomic number. To improve XRCT/SXRCT image contrast, other gas/fluid (Tetrahydrofuran-THF, Carbon dioxide-CO 2 or Xenon-Xe) and/or saline water solutions (Sodium chloride-NaCl, Barium chloride-BaCl 2 , Potassium iodide-KI) have been used (Chaouachi et al. 2014[START_REF] Kerkar | Direct observations of three dimensional growth of hydrates hosted in porous media[END_REF][START_REF] Kerkar | Imaging methane hydrates growth dynamics in porous media using synchrotron X-ray computed tomography[END_REF][START_REF] Ta | Observations of pore-scale growth patterns of carbon dioxide hydrate using X-ray computed microtomography[END_REF][START_REF] Chen | Ostwald ripening changes the pore habit and spatial variability of clathrate hydrate[END_REF]. By using gas/fluid different from methane, experimental setups are less complicated. For instance, there is no need of pressure control for the THF hydrate (THF hydrate can be formed at atmospheric pressure) while lower pressure and/or higher temperature are needed for studies of CO 2 or Xe hydrates. Note that gas hydrate morphology depends on the type of gas/fluid used. Furthermore, the phase boundary of methane hydrate formation is shifted depending on salt concentration contained in water [START_REF] Sloan | Clathrate Hydrates of Natural Gases[END_REF] and salt exclusion during gas hydrate formation increases the salt concentration in the remaining water.

Concerning XRCT image, spatial resolution mainly depends on the distances between the source, the object and the detector. Complex experimental setups of MHBS studies usually limit the image spatial resolution to avoid the collision between the source, the experimental setup and the detector. Morphologies and pore habits of methane hydrate formed in sandy sediments following the excess-gas method (MHs are formed by injecting methane gas into an unsaturated sandy sediment) have been investigated previously by [START_REF] Yang | Microstructure Observations of Natural Gas Hydrate Occurrence in Porous Media Using Microfocus X-ray Computed Tomography[END_REF] and [START_REF] Zhao | Microstructural characteristics of natural gas hydrates hosted in various sand sediments[END_REF]. Within voxel size of 25 µm, it was impossible to directly observe MHs as the voxel size was in the same order of magnitude as the size of the largest MH crystals. By using a conventional segmentation method based on gray levels (which are, as a first approximation, proportional to material density), methane hydrates were found to be formed at gas-water interfaces, floating between sand grains without coating grain surfaces (a water layer was found to envelop grain surfaces). However, image noise and partial volume effect (gray levels of voxels at interfaces of different phases are intermediate between the gray levels of the different phases) did influence the segmentation and the attributed phases (morphologies and pore habits of methane hydrates).

Note that reported XRCT scans were usually performed at the end of the gas hydrate formation process in sandy sediments as the scanning time is long (several hours).

Within the high temporal resolution of SXRCT (a few minutes), the formation and growth of gas hydrate in sandy sediments could be captured over time.

In the present study, three experimental setups have been developed in the objective of investigating pore-scale morphologies and pore habits of MHs in sandy sediments via XRCT and SXRCT. Their designs aim at improving the image contrast and the image spatial resolution. As CT images can hardly differentiate pure water from methane hydrate, saline water (i.e. KI solution) was used to better distinguish the liquid phase and methane hydrate when both coexist. Furthermore, efforts have been made to enhance the image spatial resolution in order to distinguish methane hydrate from the liquid phase (either tap or saline water) on the basis of their morphology (regular water menisci or more complex geometry of MH). In the following sections, the optimization of XRCT scan conditions for MHBS is first described. Afterwards, the three experimental setups and their corresponding advantages and drawbacks are discussed.

Optimization of scan conditions

Absorption XRCT and SXRCT consist in exposing an object to X-rays from multiple orientations (by rotating the sample in this study) and measuring the intensity decrease for all source-detector paths. Gray levels of the obtained radiographic images, after calibration, quantify the attenuation of the sample, i.e. reflect the proportion of X-rays absorbed/scattered as they pass through the object. More precisely, X-ray attenuation follows a Beer-Lambert type law (Swinehart 1962), which involves the linear attenuation coefficient (). Different phases in the object can be well distinguished if their attenuation coefficients are significantly different from each other. Indeed,  is a function of the energy of X-rays. In a polychromatic setup (as for XRCT), the gray levels of the image result from a complex average of , which is relative to the used energy range. [START_REF] Lei | Pore-Scale Visualization of Methane Hydrate-Bearing Sediments With Micro-CT[END_REF] used potassium iodide solutions and in-line propagation-based phase-contrast CT analysis of X-ray attenuation and diffraction for pore-scale visualization of MHBS with XRCT. In the present study, theoretical ratios of  of different phases (methane gas, pure water, methane hydrate, saline water, quartz) are first calculated in order to quantify the induced contrast between phases on the image gray scale (see Figure 1). For the considered materials, sand grains are the most absorbing objects while methane gas is the least absorbing. We thus plot the absorption of the other phases (water, MHs and saline water) in a normalized scale where 1 corresponds to grains and 0 corresponds to gaz. The XCOM program established by the National Institute of Standards and Technology (NIST XCOM) provides the mass attenuation coefficients (µ/ρ) of various compounds for various values of photon energy. These data allowed plotting the curves corresponding to water/quartz and methane hydrate/quartz shown in Figure 1. For the saline solutions (i.e. Potassium iodide KI), the value of the mass attenuation coefficient of the solution is obtained according to a simple addition:

(1) where w i is the mass proportion of the component i (water or salt) and  is the unit mass, being for water and Potassium iodide (KI) equal to 1 and 3.12 (Mg/m 3 ), respectively. The results obtained for the KI solution of 2, 3.5 and 5 wt% are also plotted in Figure 1. Note that the adopted density of quartz, methane gas, methane hydrate and water is 2.65, 0.0007, 0.9 and 1 Mg/m 3 respectively.

Figure 1 shows that, for the whole considered energy range (10-200 keV, which corresponds to typical energies considered in a laboratory XRCT setup), there is almost no difference between the ratio of pure water/quartz and that of methane hydrate/quartz (red and black curves). The difference in gray level of these two phases is in the order of image noise (which typically varies from 2 % to 10 % of gray level range). That explains the difficulty in distinguishing methane hydrate from water in a XRCT image. For the case of KI solutions (blue curves), their ratios are significantly different from that of methane hydrate in the range of photon energy higher than 33 keV where an absorption edge is observed. At a concentration of 5 % for KI, the maximum ratio is close to 1 (i.e. saline solution absorbs almost as quartz)

while at 2 % of concentration, the increase in contrast (allowed by the KI solution) is moderate. Therefore, saline water of 3.5 % of KI by weight was chosen in this study so that saline water can be optimally distinguished from both methane hydrate and sand grain. More precisely, for energies between 33 and 60 keV, the gray level of saline solution would be at equal distance from quartz and MH, optimizing the image contrast. Note that the laboratory XRCT source is a polychromatic source with a wide energy spectrum with a maximal energy corresponding to the prescribed electron beam acceleration voltage. However, its maximum intensity, due to the Bremsstrahlung effect, is somewhat below that maximum. Furthermore, to avoid beam hardening artifacts in XRCT images and more specifically to reduce X-rays bellow 33 keV, a copper filter (Cu) was used to eliminate low energy X-rays. Relative transmission of X-ray intensity exp(-µ Cu x t Cu -µ Al x t Al ) of two cases of copper thickness (t Cu ), is also shown in Figure 1 (Aluminum tube thickness, t Al is 2 x 0.89 mm). In the present study, a Cu filter with a thickness of 0.1 mm was used for the scans to preserve a higher X-ray flux in the energy range of 30 -100 keV where the linear attenuation coefficient ratio of the KI solution at 3.5 wt% is well separated from that of methane hydrate.

Preliminary scans at abovementioned optimized conditions (acceleration voltage of source was 80 or 100 keV; 0.1 mm thick Cu filter) were done. Typical close views of cross sections of 3D images obtained on mixtures of dry sand with either pure water or saline water compacted in an aluminum tube (exterior diameter, d ext. = 6.45 mm; thickness, t = 0.89 mm) are shown in Figure 2. For the case of sand wetted with pure water, Figure 2a, the mean gray levels of each phase were determined from the gray level profiles along the yellow line in Figure 2a, plotted in Figure 3a: G a = 21100 (for air, A); G q = 22700 (for quartz, Q); G w = 21600 (for pure water, W). Similarly, for the case of sand wetted with saline water (Figure 2b), Figure 3b shows: G a = 12400; G q = 14150; G sw = 13400 (saline water, SW). The ratios of water, R w/q and of saline water, R sw/q were calculated as follows:

R w/q = (G w -G a )/(G q -G a )
(2)

R sw/q = (G sw -G a )/(G q -G a ) (3)
According to profiles shown in Figure 3, R w/q is equal 0.3 while R sw/q equal 0.6.

Furthermore, it is expected that the ratio of methane hydrate/quartz is close to that of water/quartz. These scan conditions should be then appropriate for MHBS scans, with an optimal contrast between air, MH, saline water and quartz (relative gray levels equal 0, 0.3, 0.6, and 1, respectively).

Unlike conventional laboratory XRCT, the so-called "pink beam" SXRCT makes use of a narrower energy spectrum, which is more concentrated around a mean energy.

Details of effective linear attenuation coefficient has been defined in the work of [START_REF] Lei | Pore-Scale Visualization of Methane Hydrate-Bearing Sediments With Micro-CT[END_REF]. Preliminary SXRCT scans (typical cross sections shown in Erreur ! Source du renvoi introuvable.) were performed at the Psiche beamline at the French synchrotron SOLEIL [START_REF] King | Tomography and imaging at the PSICHE beam line of the SOLEIL synchrotron[END_REF]) run in pink mode with a mean energy of 44 keV. R w/q and R sw/q are 0.25 and 0.6 respectively (Figure 5). These values are close to the theoretical estimations at 44 keV (see Figure 1). Note that the Paganin filter [START_REF] Paganin | Simultaneous phase and amplitude extraction from a single defocused image of a homogeneous object[END_REF], designed to account for and partly correct phase contrast artifacts, has been used during the image reconstruction. It can also be noticed from profiles in Figures 3 and5 that noise levels are significantly lower in SXRCT images than in XRCT ones.

Experimental setup investigations

Materials and methodology

The sediment used in this study was Fontainebleau silica sand (NE34). To maintain low temperature, cooled air was circulated around the aluminum tube.

Compressed air was cooled down by using a combination of chilled water (controlled by a cryostat) and a heat exchanger. Cooled air temperature, as well as sample temperature, were controlled via the compressed air flow rate (by imposing a compressed air pressure). Note that air was chosen instead of liquids for the temperature control to avoid additional X-ray absorption. In addition, preliminary experiments with wet sand showed an identical temperature (measured by thermocouples) in the air, outside of the aluminum tube, and that in the wet sand, at the center of the aluminum tube, at the same height.

Methane gas was injected into the sample to maintain a high methane gas pressure.

It is supposed that methane gas pressure is constant in a closed system once the MH formation is finished (no need of additional methane gas for further MH formation). Therefore, at the end of the MH formation when the media are supposed to be stable, there is no need to control methane gas pressure during the XRCT scans. However, when the purpose is to follow the MH formation over time by SXRCT scans, methane gas pressure needs to be controlled and maintained constant during the whole process.

The above thermal and pressure conditions were maintained during the laboratory XRCT scans, which lasted about 12 hours each to avoid MH dissociation. A generic view of various experimental setups developed in this purpose is shown in Figure 6.

The sample was fixed on a turntable for scans. An Ultratom micro-tomography setup, from RX Solutions, using either a Hamamatsu L10801 micro-focus reflection ( 230keV) or a Hamamatsu L10712 nano-focus (160 keV) transmission X-ray source together with a Paxscan Varian 2520V flat-panel imager (1920x1560 pixels 2 , pixel size of 127 µm), was used for the laboratory XRCT scans. At an optimized Source Detector Distance (SDD), governed by the divergence of the X-Ray cone-beam of the X-Ray source in use, a smaller Source Object Distance (SOD) would provide a higher spatial resolution (or a smaller voxel size).

Furthermore, SXRCT scans were performed at the Psiche beamline at the French synchrotron SOLEIL [START_REF] King | Tomography and imaging at the PSICHE beam line of the SOLEIL synchrotron[END_REF]) with a mean energy of 44 keV. Voxel size was 0.9 µm and the scan time 12-15 minutes. Paganin filter was optimized to limit the phase contrast at the interfaces between constitutive phases so that gray level of each phase in the images remains almost homogenous (apart from noise).

In the present study, three setups have been developed. The details of each of them, their advantages and drawbacks and the obtained results are presented in the following sections.

Experimental setup No. 1

Figure 7 shows the first setup used for XRCT scans of MHBS. A poly-methylmethacrylate tube (PMMA tube; exterior diameter, d ext = 24 mm; thickness, t = 3.5 mm) was fixed around the aluminum tube for the cooled-air circulation from its bottom to its top. A manometer was fixed at the top of the aluminum tube to monitor methane gas pressure in the tube. The aluminum tube height was chosen to avoid collision between the manometer and the X-ray source during the scan (the distance from the turntable to the top of the aluminum tube is 430 mm, see Figure 7). Note that both XRCT sources available on the Ultratom setup can be used. A thermocouple was installed between the aluminum tube and the PMMA one at the middle of its height.

Methane gas at 7 MPa was injected during the MH formation by a pressure controller, which was connected to a gas flowmeter. These conditions were maintained during two days for the MH formation. At the end of the MH formation, pressure controller and gas flowmeter were removed, and all the valves were closed prior to the transportation of the whole system to the XRCT room.

A cooling gel was wrapped around the PMMA tube during the cell transportation (which lasted about five minutes during which the cooled-air circulation had to be cut off) to avoid MH dissociation. The cooled-air circulation around the aluminum tube was reset as quickly as possible once the cell was installed inside the XRCT room.

Sample pressure and temperature were verified before the scan. The Source Object Distance (SOD) was limited by the exterior diameter of the PMMA tube (SOD  20 mm to maintain a security distance of 8 mm). Dry compressed-air flow was shifted towards the PMMA tube to avoid water condensation during scans (anticondensation system). Both aluminum and PMMA tubes were rotated together to maintain sample temperature during the scan. The soft tube bringing cooled air from the heat exchanger to the PMMA tube needed to be flexible and long enough to rotate with the PMMA tube.

Twelve tests have been performed with this setup, among which however, only a few gave images exhibiting good enough quality to be used to characterize microstructure (about 40 %). Indeed, it turned out that the cell slightly vibrated during the scans because of the turbulent cooled-air flow. These vibrations induced fluctuations of the CT geometry whose amplitude were too large for an accurate CT reconstruction. The obtained 3D images were thus blurred, with very unsharp edges.

An example of an unsuccessful scan is shown in Figure 8. Gray levels within the constitutive phases, including grains, were not homogenous. MH morphology observation was then impossible. An example of a successful scan is shown in Figure 9 (voxel size was 5 µm). The image shows an assembly of sand grains (light gray), the pore space filled with methane gas (black) and methane hydrates (gray).

MHs can be observed at grain contacts and also on grain surfaces. The mean gray level of each phase was determined from the gray level profiles (as illustrated in Erreur ! Source du renvoi introuvable.10): G a = 22500 (for air, A); G q = 33000 (for quartz, Q) and G mh = 26500 (for methane hydrate, MH). The ratio R mh/q is equal to 0.38, similar to the expected ratio. Furthermore, the standard deviations of the quartz and methane gas phases are close (700). Signal to noise ratio (SNR) was estimated at (33000 -22500)/700 = 1/0.067.

Experimental setup No. 2

In order to improve the image spatial resolution, the setup No. 2 (shown in Figure 11) has been designed. First, to further reduce the SOD, the PMMA tube (used in the setup No. 1) was removed. The nano-focus source was used instead of the microfocus one, and the aluminum tube was placed closer to it during the scans: SOD was 8 mm instead of 20 mm in the setup No. 1. A Polyvinyl Chloride (PVC) support was fixed to the source and enveloped the aluminum tube. Temperature control was ensured by a circulation of cooled air inside this PVC support, again from the bottom to the top. A thin Kapton film was used to thermally isolate the source (and in particular its thin window) and to protect it from the cooled air. Within this system, only the aluminum tube was rotated during the scans while the PVC support was fixed. A smaller air flow rate (compressed air pressure was about 200 kPa compared to 360 kPa for the setup No. 1) was needed to maintain a similar sample temperature. Actually the heat flux from ambient air through the soft tube walls, between the heat exchanger and the cooled-air inlet, was lower (in particular because of a shorter soft tube length). In addition, the manometer was fixed at the bottom of the cell and the aluminum tube height was reduced to 320 mm (this minimal length being constrained by the diameter of the nano-focus source). These modifications allowed significantly reducing the amplitude of the vibrations of the aluminum tube during scans.

Methane hydrates were equally formed in sandy sediments in the laboratory then transported to the XRCT room for scans. The PMMA tube (used for setup No. 1) was placed around the aluminum tube to initially form MHs. Compared to the setup No. 1, the installation of the cell in the XRCT room was more complicated as cooled air can only be circulated when the aluminum tube was enveloped by the PVC support.

Sample temperature was maintained by a cooling gel wrapped directly around the aluminum tube during its installation. A thermocouple, fixed on the PVC support (see Figure 11), was used to measure the sample temperature close to the scanned zone.

As for the first setup, among the ten scans preformed with the second setup, only a few provided images with good quality (about 40 %), again because of cell vibrations.

An example of successful result is shown in Figure 12 (voxel size was 3.5 µm). MH was more difficultly distinguished from methane gas even with a better image spatial resolution compared to the setup No. 1 (see Figure 9), because in particular of a poorer signal to noise ratio. R mh/q and SNR were estimated at 1/3 and 1/0.085 respectively (Figure 13).

Another possible reason, to explain the heterogeneity of gray levels in the phases, is related to the heterogeneous and porous structure of the PVC support. Indeed, Xrays passed through a thin PVC layer serving for thermal isolation before being captured by the detector. During the calibration stage of the CT scans, which consists in recording various radiographs without sample, the PVC layer crossed by X-rays is not exactly at the same position as during the scans with the sample, which induces additional artifacts. For a further development of setup No. 2, another, more homogeneous material (such as PMMA) should be used between aluminum tube and detector. Actually, PVC was chosen in this study because manufacturing the complex-shaped support with PVC was easier (compared to PMMA).

Experimental setup No. 3

Within the two first setups, methane hydrates were first formed outside the tomography room and XRCT scans were performed only when the MH formation was stabilized. During the scans, the cell was closed and the temperature was maintained. Setup No. 3 was primarily developed for SXRCT scans which allow one to continuously follow the formation and evolution of MHs. For this reason, methane gas needs to be supplied and its pressure to be monitored during the scans.

Figure 14 shows the schematic view and a picture of the setup No. 3. A small methane gas bottle (volume of 40 mL) was connected to the methane gas inlet of the cell via a pressure reducer, which reduced the methane gas pressure from 13 MPa inside the bottle to 7 MPa at the gas inlet. This system was used to maintain methane gas pressure in the sample constant at 7 MPa (±0.1 MPa) during the MH formation and scans.

Cooled air was circulated between the aluminum and a PMMA tube, similar to the one used in the setup No 1 but somewhat smaller and thinner (exterior diameter, d ext = 23 mm; thickness, t = 2 mm), for the temperature control. The cooled-air inlet was, in this setup, at the top of the PMMA tube. The PMMA tube was fixed at its top and thus did not rotate during the scans. The compressed air pressure was in the same order as that used for the setup No. 2. In addition, the aluminum tube height was reduced to 180 mm. Two thermocouples, inserted into the PMMA tube to measure the air temperatures close to the air inlet and outlet, showed a rather stable temperature difference of 1.5 -2.0 °C during the scans.

Figure 15 shows a preliminary result obtained by XRCT, with a voxel size of 4 µm.

The micro-focus source was used because the geometry of the tube does not allow high resolution. This 15-hour scan was started 28 hours after the start of the experiment, during which temperature and pressure were controlled, when the formation of MH was considered to be stabilized. MH morphologies (crystals/layers) were clearly observed over grain surfaces. Furthermore, R mh/q and SNR were 0.3 and 1/0.095 respectively (Figure 16). It can be seen that the R mh/q and SNR were in the same order for the three experimental setups. The difference was that successful scan ratios were lower for the two first setups due to cell vibration while this problem was well resolved by using the third one: all five XRCT tests were successful. The setup No. 3 is however not compatible with higher resolution XRCT imaging because of the large diameter of the PMMA tube.

The setup No. 3 was also successfully used to perform SXRCT scans. An example is shown in Figure 17 (voxel size was 0.9 µm). Really small hydrate particles, formed at the sand grains surface, can be clearly observed. R mh/q , R sw/q and SNR were 0.27, 0.73 and 1/0.080, respectively (Figure 18). The ratios (R mh/q , R sw/q ) calculated on the image are close to the theoretical ones. A small increase of salt concentration in the remaining saline water during the MH formation caused a slightly higher R sw/q value. Furthermore, within the high temporal resolution of SXRCT, the evolution of methane hydrate formation could be followed with time. Figure 19 provides vertical crosssections through the sample (note that previously shown cross-sections were horizontal) at a same position at various times. Water was initially located at the contacts of sand grains because of the capillary suction (Figure 19a). The air-water interface can be easily identified by the concave meniscus. At 0.8 h from the application of MH formation conditions, these interfaces became irregular and the concave meniscus disappeared. In addition, a thin layer (of water or methane hydrate) appeared on the surface of the grain. As water and methane hydrate have similar gray levels and cannot be distinguished by gray levels, the evolution of their morphology can be used. Actually, irregular interface between the gas phase and water or hydrate phase suggests that this later became a rigid phase (i.e. methane hydrate). Besides, the thin layer appeared on the sand grain surface should correspond to methane hydrate as suggested by [START_REF] Chaouachi | Microstructural evolution of gas hydrates in sedimentary matrices observed with synchrotron X-ray computed tomographic microscopy[END_REF]. It should be noted that some water was moved out of this area between t = 0.3 -0.8 h. We can then expect that at 0.8 h, methane hydrate was formed at methane gas/water interfaces and at the sand grain surface; MH layers became thicker with time as shown in the Figure 19.

Lists of figures

  Classified as SP according to the Unified Soil Classification System (USCS), it consists of quartz grains having a diameter ranging from 100 to 300 microns. Tap water and saline solution (KI with concentration of 3.5 %) were used for the test. Standard purity of the used methane gas was 99.995 %. The characteristics of tap water provided by the supplier are: total chlorine 0.48 mg(Cl 2 )/L; pH 7.7; electrical conductivity (at 25 °C) 609 S/cm; total iron < 10 g/L; total aluminum 53 g/L. In the present work, we consider that the salinity and the total dissolved solids in the tap water are negligible.Moist sand was first compacted by tamping in layers into an aluminum tube (exterior diameter, d ext = 6.45 mm; thickness, t = 0.89 mm). Aluminum was chosen instead of beryllium as used in other studies (e.g.[START_REF] Lei | Pore-Scale Visualization of Methane Hydrate-Bearing Sediments With Micro-CT[END_REF] to facilitate the manipulation because of the toxicity of beryllium. The initial water content was fixed in the range between 10-15 % with an accuracy of 0.1%. In the present work, we consider that the initial water content does not influence the quality of the obtained images. The average porosity (volume of gas and liquid phases divided by total volume of the sample) was estimated at 0.40 by segmenting several 3D images obtained on the samples at various locations (see Le 2019, for more details about the segmentation technique). Both high pressure and low temperature (2-3 °C; 7 MPa) were maintained for the MH formation.

Figure 1 .

 1 Figure 1. Linear attenuation coefficient ratio between phases, and X-Ray

Figure 2 .

 2 Figure 2. XRCT images of unsaturated sand with (a) pure water; (b) saline water. 549

Figure 4 .

 4 Figure 4. SXRCT images of unsaturated sand with (a) pure water; (b) saline water.

Figure 5 .

 5 Figure 5. Gray level profiles along yellow lines in Figure 4: (a) water/quartz; (b) saline

Figure 6 .

 6 Figure 6. Experimental setup principles for XRCT scans of MHBS. SOD: Source

Figure 7 .

 7 Figure 7. Experimental setup No. 1: (a) Schematic view; (b) picture.

Figure 8 .

 8 Figure 8. Example of image of an unsuccessful scan due to the cell vibration,

Figure 9 .

 9 Figure 9. Example of image of MHBS obtained with the setup No. 1. Voxel size: 5µm.

Figure 10 .

 10 Figure 10. Gray level profile along yellow line in Figure 9.

Figure 11 .

 11 Figure 11. Experimental setup No. 2: (a), (b) Schematic view; (c) picture.

Figure 12 .

 12 Figure 12. Example of image of MHBS obtained with the setup No. 2. Voxel size: 3,5

Figure 13 .

 13 Figure 13. Gray level profile along yellow line in Figure 12.

Figure 14 .

 14 Figure 14. Experimental setup No. 3: (a) Schematic view; (b) picture.

Figure 15 .

 15 Figure 15. Example of XRCT image of MHBS obtained with the setup No. 3. Voxel

Figure 16 .

 16 Figure 16. Gray level profile along yellow line in Figure 15.

Figure 17 .

 17 Figure 17. Example of SXRCT image of MHBS obtained with the setup No. 3. Voxel

Figure 18 .

 18 Figure 18. Gray level profile along yellow line in Figure 17. 601

Acknowledgement

The authors would like to express their great appreciation to the French National Research Agency for funding the present study, which is part of the project HYDRE "Mechanical behavior of gas-hydrate-bearing sediments" -ANR-15-CE06-0008.

SXRCT images were recorded at the Psiche beamline of Synchrotron Soleil in the context of proposal 20181629.

We also would like to express our sincere thanks to Marine Lemaire and Emmanuel Delaure for their technical support.

Discussions and recommendations

Three experimental setups were developed for pore-scale morphology and pore-habit investigations of MHs in sandy sediments via XRCT and SXRCT. The image spatial resolution was well improved by using SXRCT instead of XRCT. However, SXRCT scans are costly and access time is very limited. Furthermore, by using saline water, methane hydrates could be well distinguished from the remaining water during the MH formation (Figure 17) while for the case of tap water (e.g. Figure 19), methane hydrates and water could only be distinguished from each other via the kinetics of MH formation (MH crystals or layer were grown over time) or via the interface roughness (smooth interface between liquid and gas due to interfacial tension).

However, due to the shift of the phase boundary of methane hydrate formation for saline solution, the sample temperature needed to be maintained at a lower temperature compared to that for water (1-2 °C lower at 7 MPa).

In previous studies where gas hydrate morphology in sediments were investigated, other gas/fluid (THF or Xenon) was used to facilitate the gas hydrate formation because only temperature control [START_REF] Kerkar | Direct observations of three dimensional growth of hydrates hosted in porous media[END_REF] or pressure control (Chen and Espinoza 2018) was required. In the present work, as methane hydrates were investigated, both low temperature and high pressure were required. Furthermore, in order to maintain a low temperature, liquid was usually used in previous studies [START_REF] Chaouachi | Microstructural evolution of gas hydrates in sedimentary matrices observed with synchrotron X-ray computed tomographic microscopy[END_REF][START_REF] Ta | Observations of pore-scale growth patterns of carbon dioxide hydrate using X-ray computed microtomography[END_REF][START_REF] Zhao | Microstructural characteristics of natural gas hydrates hosted in various sand sediments[END_REF][START_REF] Le | Kinetics of methane hydrate formation and dissociation in sand sediment[END_REF]. That would avoid the system vibration induced by air flow, as observed in the present work.

However, X-ray absorption of water would decrease the image's quality. Furthermore, voxel size in XRCT images, in these studies, was quite large, in a range of 20 µm to 30 µm due to complex and bulky experimental setups, which were required to control both temperature and pressure [START_REF] Ta | Observations of pore-scale growth patterns of carbon dioxide hydrate using X-ray computed microtomography[END_REF][START_REF] Yang | Microstructure Observations of Natural Gas Hydrate Occurrence in Porous Media Using Microfocus X-ray Computed Tomography[END_REF][START_REF] Zhao | Microstructural characteristics of natural gas hydrates hosted in various sand sediments[END_REF]. Within such resolution, small particles of MHs could not be observed. Furthermore, the partial volume effect was important. In the present work, a voxel size of 4 µm was obtained by the setup No. 3 with a very good image's quality, even in a laboratory CT setup, MH morphologies (crystals, layers) were thus clearly observed.

Besides, [START_REF] Lei | Pore habit of methane hydrate and its evolution in sediment matrix-Laboratory visualization with phasecontrast micro-CT[END_REF] used a Peltier plate for temperature control. Yet, a temperature gradient of 4 °C was measured between the top and bottom of the sample (about 54 mm height), i.e. 0.08 °C/mm. By using cooled air in this study, the temperature gradient over 150 mm of the tube height was about 2 °C, i.e. 0.013 °C/mm which favors the homogeneity of MH formation in the sample. Moreover, by using a small methane gas bottle in this study, associated with a pressure reducer, methane gas pressure was maintained constant during the whole MH formation process.

Among the three experimental setups developed in the present study, the third one was the most optimized. Actually, the aluminum tube height was shortened to minimize the vibration induced by the air flow. The setup No. 2 has the best spatial resolution for XRCT scans (voxel size equals to 3.5 µm) but its experimental procedure is the most delicate. Besides, the setup No. 2 was compatible only with the Nano-focus source while the two others can be used for all types of X-ray source.

Concerning the pressure control system, the sample can be disturbed during the system transportation to the XRCT room in the case of the two firsts setups.

However, it avoids occupying the room during a long period. The setup No. 3 (using a small methane gas bottle) is the best choice for SXRCT scans. It however requires a setup compatible with large and heavy samples, as the one available on the Psiche beamline.

Conclusions

The paper describes the scan condition optimizations and the developments of special experimental setups to investigate pore-scale morphologies and pore-habits of MHBS via XRCT and SXRCT.

Based on theoretical attenuation coefficient ratios between phases, XRCT scan conditions were optimized (scan energy, filter thickness and saline water solution).

Preliminary XRCT and SXRCT scans performed on compacted sand wetted with pure water or saline water confirmed the theoretical estimations.

Afterward, three experimental setups were developed in the objective of improving the image spatial resolution for pore-scale morphology and pore-habit investigations of MHs in sandy sediments via XRCT and SXRCT. The details of temperature and gas pressure controls were presented. The results obtained for each experimental setup allowed evaluating its performance to observe the morphologies and porehabits of MHBS. The experimental setup No. 3 seems to be the most appropriate.

Sample temperature was controlled by circulating cooled air between the aluminum and the PMMA tube which is fixed at its top. Attention was paid to minimize the cell vibration induced by cooled air flux.

The choices of temperature and pressure controls presented in the present work can be useful for further studies on MHBS as well as other geo-materials involving a control of temperature and/or gas pressure during XRCT/SXRCT scans.


Raphaël P A Perez
email: raphael.perez@cirad.fr

Rémi Vezy

Loïc Brancheriau

Frédéric Boudon

François Grand

Doni Artanto Raharjo

Jean-Pierre Caliman

Jean Dauzat

Toward a functional-structural model of oil palm accounting for architectural plasticity in response to planting density

Keywords: FSPM, Lidar, phenotypic plasticity, plant architecture, planting density

Functional-structural plant modelling approaches (FSPM) open the way for exploring the relationships between the 3D structure and the physiological functioning of plants in relation to environmental conditions. FSPMs can be particularly interesting when dealing with perennial crops like oil palm, for which research on innovative management practices requires long and expensive agronomic trials. The present study is part of the PalmStudio project, which aims at developing a FSPM for oil palm capable of conducting virtual experiments to test the relevance of innovative management practiceds and/or design ideotypes.

We propose a methodological approach which integrates architectural responses to planting density in an existing oil palm FSPM (Perez et al. 2018a b). Combining standard field phenotyping with Lidar-based derived measurements, we manage to evaluate the phenotypic plasticity of the main parameters required for the calibration of the 3D plant model. LiDAR scans were processed using the PlantScan3D software [START_REF] Boudon | Quantitative assessment of automatic reconstructions of branching systems obtained from laser scanning[END_REF] to derive phenotypic traits of leaf geometry that were compared to labour-intensive measurements. Density-based allometries of leaf geometry and biomass are then derived from the observed variations in phenotypic traits and integrate into the FSPM.

Our results illustrate the accuracy and the efficiency of Lidar-based phenotyping of leaf geometrical traits. In average, we find less than 3% of difference in leaf dimensions (i.e. rachis length) in comparison with traditional hand-made field measurements. The fast and efficient measurements of usually labour-intensive traits such as leaf curvature allowed estimating the plasticity of leaf geometry in response to density. We find that the main traits affected by density were leaf dimensions (up to 15% and 25% of increase in rachis length and petiole length respectively) and curvature (15% of increase in leaf erectness-related parameter), whereas other structural traits like the number of leaflets per leaf remained unchanged. Simple density-based allometric relationships were then modelled and combined with the existing allometric-based 3D oil palm model VPalm (Perez et al. 2018a). These data also enable the development and the integration in VPalm of a biomechanical model simulating leaf curvature.

The methodology presented in this study paves the way for a rapid integration of phenotypic plasticity in FSPMs. Our FSPM is now able to estimate how planting density affect not only plant architecture but also functional processes such as carbon assimilation and transpiration. Ongoing research aims at coupling the current FSPM with a carbon allocation model [START_REF] Pallas | Using plant growth modeling to analyze C source-sink relations under drought: inter-and intraspecific comparison[END_REF] to simulate the retroactions of functioning processes on plant architecture together with environmental and agronomic conditions.


Jean-François F Barczi
email: barczi@cirad.fr

Yves Caraglio

Eric-André Nicolini

Hervé Rey

Alexandre De

Herve Rey

Alexandre Haldat

Modelling and simulating tree growth dynamics including both

Keywords: architecture, biomass, plasticity, whole plant, FSPM

come   L'archive ouverte pluridisciplinaire

Introduction

Tree structural and biomass growth studies are mainly carried out on shoot compartment. Root compartment is usually taken apart due to the difficulties on measuring and observing it, especially when considering root growth. AMAP team is already leading experimental studies including both compartments through field experiments and observations. AMAP also provides shoot or root models and simulators of tree architecture and biomass production applied to many agronomic and forest species. It now becomes very critical to study tree structural plasticity according to global climate change. For this purpose, both shoot and root systems have to be considered at the same time since they play collaborative roles dedicated to climate traits (water availability for roots and light or carbon availability for shoots). We propose a whole-plant model and its simulator (RoCoCau) with a linkable external module (TOY) to represent shoot and root compartments dependencies and thus tree structural plasticity when facing various aerial and edaphic environments.

Literature shows this plasticity but generally at one moment of the tree life cycle. One of the main issue of such a tool is to understand how this balance is managed according to tree development (structure maintenance vs space exploration).

Materials and Methods

RoCoCau is made of the association of AmapSim (Barczi et al 2008) and DigR (Barczi et al 2018) to represent shoots and roots. The software simulation environment makes it possible to plug an external functional module to the core structure simulator. We propose the module (TOY) that roughly models the dependency between the two compartments. This dependency remains in (i) biomass production that needs water uptake through roots, carbon and light uptake through leaves and in (ii) biomass partitioning to control development and growth of both compartments in order to preserve a balanced uptake capacity on water, carbon and light.

Results and Discussion

We have been applying RoCoCau to eucalyptus root/shoot systems that were previously modeled to check its accuracy to mimic realistic whole tree growth dynamics (figure 1). We then plugged the TOY model to RoCoCau and tried some environmental stresses (water, carbon and light) applied on the same simple tree architecture with different responses capabilities (light-demanding, shade-tolerant, drought tolerant or not). Figure 2 shows optimal environment, water and light stresses applied on the same theoretical species. This situations result in different global plant sizes but also in different shoot/root balances. For each situation, we extracted data along simulations to show how much water, light and carbon were collected and what was the consequence on growth rate change for both root and shoot compartments. It is then possible to monitor tree plasticity according to environmental change. The model has a good quantitative response in accordance to knowledge about tree plasticity. The proportion of root biomass is favored under drought conditions or more generally when trees grow on bad soil ( Leuschner et al, 2001). In such stressed environment, stems show frequently a reduced leafy area (Kozlowsky & Pallardy 2002). In shade environment, trees invest more in leaf surface in order to increase light foraging capacity (Poorter & Nagel 2000). Simulations show a permanent balance of both root and shoot system with regulation of architecture and resource capture (leaves, fine roots) according to the species capabilities facing different environmental stresses.

For now, only an in silico study was carried out. It is now necessary to get field data to try TOY calibration. For this purpose some measurements are carried out into the FTC2 experimental device where 4 tropical species are grown in french Guyana. Tree individuals are regularly extracted and measured to feed a database used to train a neural network at TOY parameters calibration.

Conclusion

The simulation of the RoCoCau structural model linked with the TOY functional model allows to test hypothesis on tree plasticity facing environmental change. RoCoCau offers a good botanical accuracy at representing both shoot and root architectural dynamics. TOY includes main physiological processes to get water, light and carbon and to produce biomass that will be shared between the two compartments in a way that permanently controls the balance of their shoot and root foraging capabilities.

  figure 1. « realistic» simulation(RoCoCau) figure2. same default plant species growing in optimal environment, with water stress and with light stress (RoCoCau+TOY)