Arnaud Germaneau
email: arnaud.germaneau@univ-poitiers.fr

PhD Tanguy Vendeuvre

MD, PhD Alexandre Delmotte

Cyril Samuel D'houtaud

Louis Brèque

Pascal Petureau

Jean-Christophe Doumalin

Fabrice Dupré

Philippe Brémand

Maxy

MD S D'houtaud

MD C Brèque

PhD L Petureau

PhD P Doumalin

PhD J.-C Dupré

PhD F Brémand

PhD P Maxy

J P Richer

MD, PhD P Rigoard

Should we recommend occipital plate fixation using bicortical screws or inverted occipital hooks to optimize occipito-cervical junction fusion? A biomechanical study combining an experimental and analytical approach

Keywords: occipital bone, occipito-cervical fusion, mark tracking, 3D measurements, biomechanics

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

Introduction

Surgical occipito-cervical fusion is required when cranio-cervical junction stability has been compromised [START_REF] Winegar | A systematic review of occipital cervical fusion: techniques and outcomes: a review[END_REF] characterized by excessive laxity or mobility. This condition can result from various degenerative [START_REF] Goel | Craniovertebral instability due to degenerative osteoarthritis of the atlantoaxial joints: analysis of the management of 108 cases[END_REF], tumoral [START_REF] George | Bone tumors at the cranio-cervical junction. Surgical management and results from a series of 41 cases[END_REF][START_REF] Zimmermann | Palliative occipito-cervical stabilization in patients with malignant tumors of the occipito-cervical junction and the upper cervical spine[END_REF], traumatic [START_REF] Vaccaro | Indications for surgery and stabilization techniques of the occipitocervical junction[END_REF], inflammatory [START_REF] Grob | Occipitocervical fusion in patients with rheumatoid arthritis[END_REF], infectious [START_REF] Shukla | Management of craniovertebral junction tuberculosis[END_REF] or congenital diseases [START_REF] Giussani | Severely symptomatic craniovertebral junction abnormalities in children[END_REF].

Stabilization can be achieved by performing a posterior instrumentation between the horizontal part of the occipital bone and the cervical spine to bridge the instability area [START_REF] Vaccaro | Indications for surgery and stabilization techniques of the occipitocervical junction[END_REF]. The choice of multilevel articular screws at the cervical level has rapidly reached a consensus, as a compelling technique has been developed to implant screws safely at the facet level, thereby ensuring distal stabilisation anchorage [START_REF] Sasso | Occipitocervical Fusion with Posterior Plate and Screw Instrumentation -a Long-Term Follow-up-Study[END_REF].

By contrast, at the occipital level, the choice of site and implant type since first indications has been controversial. The anatomical particularities of this region can partially explain why so many types of implants have been developed by industry to provide adequate anchorage at the proximal occipital level. The median external occipital protuberance (EOP) is the thickest part of the occiput. From this anatomical landmark and the underlying median external crest joining EOP to the foramen magnum, occipital bone thickness decreases laterally and inferiorly in a radial fashion [START_REF] Papagelopoulos | Biomechanical evaluation of occipital fixation[END_REF]. EOP underlying projection is frequently associated with the convergence of major venous sinuses [START_REF] Roberts | Quantitative anatomy of the occiput and the biomechanics of occipital screw fixation[END_REF][START_REF] Wolfla | Anatomical, biomechanical, and practical considerations in posterior occipitocervical instrumentation[END_REF][START_REF] Zipnick | Occipital morphology: an anatomic guide to internal fixation[END_REF]. A recent study reported that a contact between venous structures and the internal occipital crest has been found for 37% of the study population [START_REF] Kobayashi | Anatomical study of the occipital sinus using contrastenhanced magnetic resonance venography[END_REF].

From a mechanical point of view, proximal occipital stability of the fixation is usually ensured by bi-cortical occipital screws implanted through one median or two lateral occipital plate(s) [START_REF] Heywood | Internal fixation for occipito-cervical fusion[END_REF][START_REF] Roberts | Quantitative anatomy of the occiput and the biomechanics of occipital screw fixation[END_REF][START_REF] Wolfla | Anatomical, biomechanical, and practical considerations in posterior occipitocervical instrumentation[END_REF]. The variability of occipital bone local thickness combined with the anatomy of dural sinuses, should considerably influence the perimeter of a safe working area and the length of occipital screws. This can potentially affect fixation strength and stiffness and entailing but also operative risks (massive haemorrhage, air embolism, Cerebro-Spinal Fluid -CSF) leak and direct cerebellar tissue injury [START_REF] Ebraheim | An anatomic study of the thickness of the occipital bone: implications for occipitocervical instrumentation[END_REF][START_REF] Heywood | Internal fixation for occipito-cervical fusion[END_REF][START_REF] Korovessis | Posterior compact Cotrel-Dubousset instrumentation for occipitocervical, cervical and cervicothoracic fusion[END_REF][START_REF] Wolfla | Anatomical, biomechanical, and practical considerations in posterior occipitocervical instrumentation[END_REF]. For that, it seems important to be able to study the mechanical behavior at the interface between bone and implant by identifying stiffness of fixations (ratio between loading moment to impose movement and range of angular variation).

Given this challenge, surgical implant design has evolved in three new directions: (i) A surgical technique consisting in implanting an inverted occipital hook clamp on each side, inserted through a burr hole was developed in 1998 [START_REF] Faure | Invertedhook occipital clamp system in occipitocervical fixation[END_REF][START_REF] Faure | Occipitocervical fixation with a single occipital clamp using inverted hooks[END_REF] and recently used for occipito-cervical arthrodesis for young and small children [START_REF] Odent | Internal fixation with occipital hooks construct for occipito-cervical arthrodesis. Results in 14 young or small children[END_REF], as a potential alternative to optimize occipito-cervical fixation.

Using this technique, dura mater, venous and parenchyma structures seem to be better controlled during surgical intervention. Concerning the mechanical behavior, the hooks would propose a significant contact surface to transmit forces involved by neck movements to the occipital bone.

(ii) In another direction, industry has provided more screws with smaller pitch to increase bone interfacing and to decrease contact pressure between bone and implant. Historically, screws have progressively replaced hooks because of their higher resistance in pull-out [START_REF] Haher | Occipital screw pullout strength: a biomechanical investigation of occipital morphology[END_REF] and lower iatrogenic positioning. The association of using screws and lateral plates could provide a better stiffness [START_REF] Anderson | Biomechanics of occipitocervical fixation[END_REF] by decreasing load arm because of screw alignment with cervical implants. The risk of lesioning a venous sinus appears lower but dural lesion and cerebellar wounds have been described and associated lower bone thickness at this level [START_REF] Kobayashi | Anatomical study of the occipital sinus using contrastenhanced magnetic resonance venography[END_REF][START_REF] Zipnick | Occipital morphology: an anatomic guide to internal fixation[END_REF].

Conceptually, the use of bi-cortical screws should offer higher mechanical strength but according to some authors [START_REF] Haher | Occipital screw pullout strength: a biomechanical investigation of occipital morphology[END_REF][START_REF] Papagelopoulos | Biomechanical evaluation of occipital fixation[END_REF], simple cortical screws have produced good results in terms of mechanical response and mitigated risks of lesioning adjacent structures (venous sinus, dura mater, cerebellum).

(iii) Some authors tend to favour a median positioning of one single occipital plate [START_REF] Antar | Additional Surgical Method Aimed to Increase Distractive Force during Occipitocervical Stabilization : Technical Note[END_REF] instead of two laterally. Indeed a correlation exists between bone thickness, screw length and pull-out strength [START_REF] Haher | Occipital screw pullout strength: a biomechanical investigation of occipital morphology[END_REF][START_REF] Hurlbert | A biomechanical evaluation of occipitocervical instrumentation: screw compared with wire fixation[END_REF][START_REF] Wolfla | Anatomical, biomechanical, and practical considerations in posterior occipitocervical instrumentation[END_REF]. A proper anchorage in this region would require a significant length of screws to provide optimal stability. However, this positioning could lead to a higher risk of venous bleeding related to median occipital venous sinus [START_REF] Kobayashi | Anatomical study of the occipital sinus using contrastenhanced magnetic resonance venography[END_REF][START_REF] Zipnick | Occipital morphology: an anatomic guide to internal fixation[END_REF]. A frontal shift between median occipital implants and cervical implants could decrease stiffness by increasing load arm, in particular for rotation movements [START_REF] Anderson | Biomechanics of occipitocervical fixation[END_REF]. Therefore, some clinicians do recommend this medial occipital zone and the insertion of screws as long as possible to maximize stability and ensure a durable stable mechanical response. This strategy is however linked to a higher risk of median occipital venous sinus damage for these anatomical reasons.

Overall, the choice of occipital implant and implant site can therefore be difficult for the surgeon. To determine the best compromise in terms of clinical benefits/surgical risks balance and surgical stability, the goal of this study was to provide a biomechanical analysis and a comparison of the four most used devices dedicated to occipito-cervical junction fusion. A two-step combined methodology was envisaged: An initial analytical mechanical model was developed as a pre-requisite to define contact pressure, corresponding to mechanical stress transmitted to the bone, involved by implants at the screw site or plate interface. This theoretical approach, presented in this article, describes the determination of contact pressure for various implants in order to analyse the mechanical effects according to the interface and the bone thickness and to predict the risk of bone damage or fracture for imposed loadings. As a second step, we designed an experimental study to analyse the biomechanical behaviour of occipital implants on human cadaveric specimens. We developed a specific experimental loading setup coupled with a non-contact analysis by using an optical method to measure displacement fields and to analyse mechanical behaviour. The experimental approach describes a complete mechanical analysis of occipital fixations by evaluating their stiffness from the relationships between mobility (displacement / angle variations) and loadings (imposed moment for flexion-extension movements) and by identifying their mechanical strength from pull-out tests.

Methods

Specimen preparation

Twenty-four anatomical fresh frozen skulls were prepared (Laboratory of anatomy, Université de Poitiers -n°DC-2019-3704). After thawing, skulls were extracted and cleared of soft tissue. In each one, the calvaria was sawed and the brain and soft tissues were removed. Anterior skull structures including the mandible were removed too. Then cervical vertebras were substituted by a metallic plate (Figure 1) on which load was applied.

For each skull, superior sawed part was potted in rigid polyurethane resin. Fixations were achieved using 3mmdiameter rod. The straight side of the rod was fixed to cervical spine and the other extremity was fixed to the occipital bone with implants and a plate. Different implants were studied: screws directly implanted in the bone or hooks (Figure 2). The specimens were distributed among four groups, each one corresponding to one type of implant (Figure 2): lateral plates + large pitch screw (LP+LPS), lateral plates + hooks (LP+H), lateral plates + small pitch screws (LP+SPS) and median plate + small pitch screws (MP+SPS). Diameter of screws implanted in the skull was 4mm and the length was adapted to the local thickness of the bone. To achieve the fixation using hooks, a burr hole of 10mm diameter was drilled on both sides of the external occipital crest. The specimens were distributed among the four groups with homogeneity in sex and age (Table 1). Bone thickness was also measured with a specific gauge just after hole drilling. We can observe a higher value of standard deviation of -6 -bone thickness in the group MP+SPS due to implantation of 2 screws in the occipital crest (high bone thickness) and 2 screws on both sides.

Analytical model

An analytical approach was performed to establish theoretical mechanical response of implants and to determine contact pressure between bone and implants by considering similar loading and boundary conditions than the ones imposed by the experimental setup presented in Figure 1. Determination of contact pressure provides an evaluation of mechanical stress transmitted between implants and bone during a movement of the occipitocervical junction. Mechanical loadings (force F and moment M) and pressures (p) are supposed to be homogeneous distributed in the contact areas of fixations. Relationships allowing the estimation of contact pressure are presented in the Table 2. Fixations by screws are essentially ensured by the contact between implants and cortical bone (highlighted in red in the figure presented in the Table 2). In the lateral area, occipital bone is principally constituted by cortical bone and mechanical loadings are supposed to be homogeneously distributed along the thread on the whole thickness of the bone. Concerning median fixation, there is a significant part of cancellous bone and pressure involved by loading applied on the fixation cannot be supposed homogeneously distributed along all the length of the thread. For this latter case and according to the observation of cadaveric specimens, a coefficient from the ratio between thicknesses of cortical bone and cancellous bone was considered to estimate contact pressure involved by load transmission in screws.

Concerning fixations by hooks, two situations were considered to determine contact pressure:

-If the hook size exactly corresponds to the thickness bone (Table 2 (b1)): the pressure is supposed to be uniformly distributed on the contact surface between hook and bone.

-If there the hook size does not exactly correspond to bone thickness (Table 2 (b2)): a slightly larger hook is chosen and contact area between bone and hook is localized and corresponds to a line. In this case, Hertz theory [START_REF] Johnson | Contact mechanics[END_REF] can be used to determine contact pressure, we assumed an elastic behaviour for materials, mechanical characteristics are given in Table 2. [START_REF] Boruah | Influence of bone microstructure on the mechanical properties of skull cortical bone -A combined experimental and computational approach[END_REF] -8 -Table 2: Evaluation of contact pressure according to the type of implant and contact areas

Experiments

Load was applied directly on the metallic vertebra with a classical tensile test setup (Figure 1) to study mechanical effects linked to flexion-extension movements. Moments ( ) were imposed by a force ( ) with a level arm between the load axis to the point of force application (distance between noted ). Free linear rail guides were employed to maintain direction of the force during the loading (Figure 1) and to make free the displacements along the other directions. The imposed moment can be deduced from the force controlled by the loading setup: ∧ (values of forces and moment are given by norms of the vectors, noted F and M).

A 3D mark tracking method [START_REF] Germaneau | A novel approach for biomechanical spine analysis: Mechanical response of vertebral bone augmentation by kyphoplasty to stabilise thoracolumbar burst fractures[END_REF] was employed to measure displacement components during the mechanical loading on the full surface of the posterior, on the fixations and on the rods and also on the metallic vertebra to compute the imposed moment value (M). This method enables to measure 3D displacements of marks (natural or artificial) deposed on surfaces from a stereoscopic vision and the use of two CCD cameras (Figure 3-a) to obtain evolution of mark positions in the space.

To determine the range of motion of the bone according to the metallic vertebra and the applied loading, three orthogonal local bases were defined (Figure 3-b): a reference one on the metallic vertebra (noted B0), on second one on the plate fixed on the bone (B1) and the last one on the bone close to the plate (B2). Thus, angle variations ( ) between each base were measured according to the imposed load allowing determination of -9 -stiffness values ( ) of the fixations (variations between B0 and B2) and the implants (variations between B1 and B2) from identification of a linear relationship ( . ).

For biomechanical tests on the cranio-cervical junction, alternating sequences of flexion/extension moments of ±2.5N.m can be usually applied [START_REF] Richter | Biomechanical evaluation of a new modular rod-screw implant system for posterior instrumentation of the occipito-cervical spine: in-vitro comparison with two established implant systems[END_REF][START_REF] Wolfla | Anatomical, biomechanical, and practical considerations in posterior occipitocervical instrumentation[END_REF] but imposed moment values can be much higher in case of dynamic loading during sport practice or collision [START_REF] Cazzola | Cervical Spine Injuries: A Whole-Body Musculoskeletal Model for the Analysis of Spinal Loading[END_REF]. To test mechanical behavior of fixations in severe conditions, each specimen was cyclically loaded ramping from -6N.m to +6N.m for flexion-extension movement. To impose these values, loading was in real-time controlled and imposed with a speed of 15mm/min. Motion fields were measured by 3D mark tracking technique with a frequency of 0.5Hz and with an accuracy lower than 0.05mm for displacements and 0.1° for angles.

After cyclic loadings, pull-out tests were performed by imposing a ramp extension loading up to bone fracture in order to identify the limit values of moments and angles according to the type of implant and the bone thickness.

Statistical analysis

Comparison of mechanical responses were performed from variance analyses to evaluate differences in the experimental measurements. Non-parametric ANOVA (Kruskall-Wallis) and multiple comparison testing (Dunn) [START_REF] Altman | Parametric vs non-parametric methods for data analysis[END_REF] to test statistical differences between specimens about stiffness, contact pressure or moment value for pull-out. All statistical analyses were done at a significance level (p-value) equal to 0.05.

-10 -

Results

Analytical model

From analytical approach, pressures were computed from relationships given in Table 2 and by considering a bone thickness of 4mm for lateral implants and 10mm for median positioning. Imposed loading went up to 100N, involving a maximal moment of 6N.m. Figure 4 shows theoretical evolution of contact pressure between implants and bone for the four types of fixations. Among fixations by screws, solution with median plate involves the highest contact pressure (25MPa for a moment of 6N.m). Concerning lateral plates, pressure with SPS is lower than pressure involved with LPS (respectively 16 and 20MPa). For fixations by H, contact pressure is very low if an exact contact is considered (if bone thickness and hook dimension are equal, corresponding to an optimized hook). If bone thickness and hook dimension are not similar, Hertz theory shows a significant increasing of the contact pressure, up to 35MPa for a moment of 6N.m. To complete this preliminary observation, specific contact pressures for each specimen were computed by considering their real values of bone thickness and implant dimensions to determine contact pressure evolution from the relationships and parameters given in Table 2. Figure 5 shows distribution of contact pressures between implants and bone for all the specimens of the four types of fixations and for a moment equal to 6N.m. For fixations by IH, only two values were obtained corresponding to optimized or non-optimized contacts which lead to a large range of pressure between 1 and 18MPa. Contact pressures observed SPS were similar for median or lateral positioning (7-12MPa). Fixations by LPS involved the highest values . Comparison between the four groups from a statistical analysis highlighted one significant difference between fixations by LP+LPS and fixations by LP+SPS. Flexibility curves were approached by linear approximation to identify stiffness coefficients for each specimen.

Figure 7-a shows distribution of global stiffness values measured between bases B0 and B2. Fixation system by MP+SPS seemed to be less rigid than LP whatever the implant. This can be explained by the geometry of MP involving the deformation of fixations with rods. Statistical analysis did not show any significant difference for the global stiffness of fixation.

Figure 7-b shows distribution of implant stiffness values. Fixations by LP+SPS gave stiffness with a wide range but values were largely higher than the other fixations. Range values of stiffness were more limited for the others implants. Fixations by H were slightly less rigid than implants by screws. Mechanical responses of LPS in lateral position and SPS with median plate were similar. One significant difference was revealed by the statistical analysis between SPS and H. Differences were also observed between LP+SPS and the two other implants but the significant threshold value was not reached.

Discussion

Flexion-extension tests

The study of stiffness values measured between cervical vertebra and occipital bone (B0 vs B2) did not reveal any significant statistical difference among the four groups. From a clinical point of view, these results do not reveal any difference about mechanical behaviour of the junction constituted by rods and implants. This global stiffness did not characterize stiffness implants but is essentially linked to the mechanical response of the rods and the fixation between rods and implants. This can explain the response given by fixation by MP+SPS. MP was linked on the occipital bone by screws and rods were assembled on the plate with other screws on small butterfly extremities, which could be deformed under loading. This double system of fixation and deformation of plate involved globally a more flexible fixation.

Concerning analysis of local stiffness of implants (B1 vs B2), a difference was observed between fixation by screws and fixation by hooks. A statistical significant difference was observed on fixations with lateral plates, between SPS and H. This observation of less stiffness on hooks was linked to the thickness differences of occipital bone and hook size. This was confirmed by the analytical model using theoretical approach of contact -14 -pressure. If the hook dimension is equal to the bone thickness, the contact pressure is low and the stiffness should be high. This was observed on some specimens among the fixations by hooks in the tested specimens.

Concerning surgery complication ratio, a retrospective study on the comparison between rigid (e.g. screws with plate or rods) and non-rigid (e.g. sublaminar wiring or bone grafting) osteosynthesis systems of the occipitocervical junction showed superiority of rigid systems from a clinical point of view [START_REF] Garrido | Rigid versus nonrigid occipitocervical fusion: a clinical comparison of short-term outcomes[END_REF].

However, complications appearing among non-rigid systems were less important. Non-rigid systems were different to the ones studied in the present work and were constituted by rods fixed to the bone by threads.

Analytical model

An analytical approach was proposed in this study to determine contact pressure involved in each type of fixation. This analysis revealed a significant difference for LP between LPS and SPS. This difference was due to the pitch dimension of each type of screw. SPS with a smaller pitch (1mm vs 1.8mm) offered a larger surface for load distribution involving a lower contact pressure. Thus, stress distribution in the bone remains lower with this type of implant offering a better ability to allow higher loadings due to movements of the head.

According to this analytical model, the best solution for a low contact pressure and a low stress distribution in the bone would be fixation by IH. For that, the necessary condition requests the same dimension between hook and bone thickness. If dimensions are not exactly the same, loading are transferred from a contact line involving mobility and a significant increasing of contact stress which can lead to local damages in the bone.

Analytical approach constitutes an original solution to give the mechanical response of occipital implants. The literature does not reveal any study similar with this model. The comparison with the experimental data showed great correlation of the results. The bone dimensions and thickness can be considering from the analytical approach that constitutes a great predictive model of mechanical behaviour of implant to determine contact pressure and stress distribution generated in bone tissues. Thus, it could be possible to adapt the best stabilisation solution in accordance between local bone density / thickness and pressure generated by implant.

Pull-out tests

Pull-out tests revealed a significant difference between LP+SPS and MP+SPS. For both fixations, implant was similar, only nature of the bone was different: bone thickness is higher in the median region but is constituted by cancellous bone whereas lateral region is thicker but with compact bone. The choice of median plate is based on the higher bone thickness but results obtained in the present case are not in accordance with previous observations [START_REF] Richter | Biomechanical evaluation of a new modular rod-screw implant system for posterior instrumentation of the occipito-cervical spine: in-vitro comparison with two established implant systems[END_REF][START_REF] Winegar | A systematic review of occipital cervical fusion: techniques and outcomes: a review[END_REF]. Anatomical studies [START_REF] Haher | Occipital screw pullout strength: a biomechanical investigation of occipital morphology[END_REF] have shown that thickness of cortical bone of external table is larger close to the external occipital protuberance but also that cancellous bone is proportionally present in this area. SPS with a small pitch are well adapted for screwing in compact bone but not optimized for cancellous bone. Thus, implanting cannot benefit of the whole bone thickness, only cortical bone is really solicited by this type of screw.

Furthermore, during pull-out tests, moment imposed by cervical vertebra involved a rotation loading on the occipital fixation corresponding to a tensile loading only on the screw closer to vertebra. In the case of lateral plates, this loading is distributed on both sides and so on the two implants contrary to only one implant for median plate. Finally, the choice to distribute implant areas at each side of the protuberance in compact bone with adapted SPS would provide a stronger implanting in the occipital bone.

Pull-out tests on fixations by hooks gave results in accordance with analytical approach. This solution should

give the most robust anchorage but measured moment values for bone fracture were lower compared to results obtained with SPS (Figure 8-a) but similar if the thickness was considered (Figure 8-b). As commented in the analytical study, this can be due to the difference between hook dimension and bone thickness. Implanting technique of IH requires a burr hole with a sufficient diameter to allow hook positioning in a region where bone thickness decreases. This technique could weaken occipital bone involving locally a lower strength, which could be amplified if hook dimension and bone thickness are different.

Limitations

The main limitation of this work is that experiments were performed on cadaveric specimens with a mean age of 72.5 years. Even if the protocol of this study does already include a larger sample size than the other studies available in the literature, the number of samples could be a limitation and it might be great to increase it. It was verified that the tested specimens were pathology-free and this mean age corresponds to the mean ages of specimens tested in the few other available studies.

This type of experimental approach is necessary to validate numerical or analytical models. Another limitation of the present study was the measurement resolution of the contact pressure between bone and implant. The bone thickness which was measured with a specific surgical gauge with a resolution of 0.1mm giving a sensitivity of 0.3MPa for contact pressure evaluation. This approach was very interesting because it gave relevant results for contact stress analysis but it did not allow evaluation of micro-contact pressure. However, the advantage of this

Figure 1 :

 1 Figure 1: Experimental setup and specimen preparation

Figure 3 :

 3 Figure 3: Measurements of displacements and angles: (a) 3D mark tracking setup; (b) Definition of reference bases for measurements of angular mobility.

Figure 4 :

 4 Figure 4: Evolution of contact pressure according to imposed moment for the four types of implants

Figure 5 :

 5 Figure 5: Distribution of theoretical contact pressure involved on implants according to the type of fixation

Figure 6 :Figure 8

 68 Figure 6: Evolutions of angular mobility for one specimen of each group between metallic vertebra and bone (a) and between plates and bone (b)

Figure 8 :

 8 Figure 8: Distribution of moment values for pull-out (a) and ratio between moment value for pull-out and bone thickness (b)

Table 1 :

 1 Specimen distribution according to sex and age

	Lateral Plate (LP); (e) Median Plate; (f) Rod
	Fixation	Mean age (years)	Sex-ratio	Bone thickness (mm) Mean (SD)
	LP+LPS	71.66	3H/3F	5.3 (0.9)
	LP+H	71.33	3H/3F	4.0 (0.9)
	LP+SPS	74.33	4H/2F	6.9 (1.4)

in vitro design is that the stabilization devices are directly used adequately with anatomical considerations. Furthermore, biomechanical observations and conclusions can be directly clinically transposable by surgeons.

Conclusion

This paper, by focusing on a biomechanical analysis of occipito-cervical fusion, compares four types of occipital implants using an analytical approach combined with experiments on anatomical specimens lead with a specific loading setup and 3D optical measurement method. Proximal stability of occipito-cervical fixation is not only insured by the choice of anatomical site of implantation of occipital screws and plate (conditioned by occipital bone thickness) but is directly influenced by the type of implants. The association of two lateral plates fixed to the occipital bone with small pitch screws appears to ensure an optimal compromise in terms of biomechanical stability and bone/implant/device interfacing. The analytical approach proposed in this work can be considered as an interesting tool to predict mechanical behaviour and stress distribution generated by implant at the level of occipital bone.

Acknowledgements

The authors would like to thank gratefully Medtronic for providing us the surgical implants and wish to thank Jeffrey Arsham, an American translator, for rereading and correction of the original English-language manuscript.


Rafik Mallek

Christelle Miqueu

Matthieu Jacob

Pascal Le Mélinaire

Christophe Dicharry
email: christophe.dicharry@univ-pau.fr

Effect of porous activated carbon particles soaked in cyclopentane on CP-hydrate formation in synthetic produced water

Keywords: Water desalination, produced water, hydrate-based desalination process, cyclopentane hydrate Cyclopentane PACP: Porous activated carbon particles HBD: Hydrate-based desalination

Hydrate-based desalination (HBD) could be an interesting alternative to more conventional processes for desalinating high-salinity waters such as those produced during oil & gas extraction. The present study investigates the hydrate formation stage of a recently patented HBD process, in which porous activated carbon particles (PACP) are used as guest (here cyclopentane (CP)) reservoirs and carriers for hydrate formation. The effects of the CP content (0.5 to 1 g of CP per gram of PACP), of the PACP particle size (400 and 700 µm), the stirring rate (0 to 360 rpm), and the salinity of the synthetic produced water (3.5 to 16 wt% NaCl) on hydrate formation were investigated in batch reactor experiments. The results showed that the CP-soaked PACP drastically enhanced both the hydrate formation kinetics and the water-to-hydrate conversion, even in the case with the highest water salinity (16 wt% NaCl). The best compromise (high kinetics and conversion) was obtained with the largest particle diameter (700 µm) loaded with 0.8 g of CP per gram of PACP. Stirring increases the

Introduction

The oil and gas industry handles large volumes of water (three barrels of water for one of oil [START_REF] Abousnina | An overview on oil contaminated sand and its engineering applications[END_REF]) which is produced as a byproduct during oil and gas extraction. Produced water (PW) generally contains many organic and inorganic compounds, including oil droplets, chemical additives and various salts at different concentrations. The TDS (total dissolved solids) of PW, which represents the total concentration of dissolved matters (inorganic salts and organic matter) in water, varies between 0.1 and 28.5 wt% depending on the nature of the reservoir and the resource produced [START_REF] Benko | Produced water in the Western United States: Geographical distribution, occurrence, and composition[END_REF]. Cha and Seol [START_REF] Cha | Increasing gas hydrate formation temperature for desalination of high salinity produced water with secondary guests[END_REF] reported an average TDS of 8.2 wt% for PW, calculated based on the 58,707 entries of a database of oil and gas fields provided by the United States Geological Survey (USGS). Produced water is either injected into disposal wells, reinjected into the producing reservoir (to sustain reservoir pressure), or discharged into surface water bodies (very often into seawater). Reinjection of PW is the preferred management option since it offers a dual benefit: enhanced oil production and a lesser environmental impact (mainly lower water consumption and a lower impact on surface water quality and related ecosystems). Reinjected and discharged PW can be desalinated to avoid possible compatibility issues with formation water, to enhance oil production [START_REF] Nair | Membrane performance analysis for smart water production for enhanced oil recovery in carbonate and sandstone reservoirs[END_REF] or to meet local regulations.

Nowadays, medium-salinity waters such as seawater (3.5 wt%) are generally treated using reverse osmosis processes, which have a high salt-removal efficiency (> 99%) and a relatively low production cost (0.45 -0.92 USD/m 3 water) [START_REF] Babu | A Review of clathrate hydrate based desalination to strengthen energy-water nexus[END_REF]. However, desalting complex effluents such as PW using reverse osmosis requires heavy and costly pretreatment (coagulation, microfiltration, etc.) of the feed water, which must be free of solid particles, organic matter, oil, etc. to protect the membranes [START_REF] Çakmakce | Desalination of produced water from oil production fields by membrane processes[END_REF]. Moreover, reverse osmosis is reported as ineffective in desalinating water with a TDS greater than 4.3 wt% [START_REF] Younos | Overview of desalination techniques: Overview of techniques[END_REF], a range in which PW is generally situated.

Hydrate-based desalination (HBD) processes could potentially be used to treat this type of water [START_REF] Cha | Increasing gas hydrate formation temperature for desalination of high salinity produced water with secondary guests[END_REF][START_REF] Fakharian | Desalination of high salinity produced water using natural gas hydrate[END_REF]. Once the hydrates have formed, the hydrate crystals are separated from the remaining brine solution, in which salts are concentrated. The separated crystals are then dissociated and desalinated water is obtained [START_REF] Babu | A Review of clathrate hydrate based desalination to strengthen energy-water nexus[END_REF]. The slow kinetics of hydrate formationvery often due to the limited contact area between the water phase and the hydrate former (which generally has a very low solubility in water), thus limiting the mass transfer between the two phases -are considered as one of the main obstacles to the large-scale development of hydrate-based processes [START_REF] Babu | A Review of clathrate hydrate based desalination to strengthen energy-water nexus[END_REF][START_REF] Ho-Van | Cyclopentane hydrates -A candidate for desalination?[END_REF]. Hydrate formation can be promoted by mechanical stirring of the phases for example, but this increases energy consumption and costs, and/or by adding surfactants known to act as hydrate promoters [START_REF] Gayet | Experimental determination of methane hydrate dissociation curve up to 55MPa by using a small amount of surfactant as hydrate promoter[END_REF], but their use induces additional costs and contaminates the desalinated water. In an attempt to overcome these issues, a new hydratebased desalination process, called BGH's process in this paper, was recently developed and patented [11]. This process is based on the HBD concept, but with the added innovation of using porous activated carbon particles (PACP) soaked in cyclopentane (CP), which can form gas hydrates at atmospheric pressure.

There are few studies on HBD desalination using CP as guest or co-guest molecules in the literature [START_REF] Cha | Increasing gas hydrate formation temperature for desalination of high salinity produced water with secondary guests[END_REF][START_REF] Ho-Van | Cyclopentane hydrates -A candidate for desalination?[END_REF][START_REF] Zheng | Effects of cyclopentane on CO2 hydrate formation and dissociation as a co-guest molecule for desalination[END_REF][START_REF] Han | Investigation of salt removal using cyclopentane hydrate formation and washing treatment for seawater desalination[END_REF][START_REF] Han | Enhanced efficiency of salt removal from brine for cyclopentane hydrates by washing, centrifuging, and sweating[END_REF][START_REF] Corak | Effect of subcooling and amount of hydrate former on formation of cyclopentane hydrates in brine[END_REF][START_REF] Li | Promotion effect of graphite on cyclopentane hydrate based desalination[END_REF][START_REF] Ling | Desalination and Li+ enrichment via formation of cyclopentane hydrate[END_REF][START_REF] Babakhani | Phase equilibrium measurements and modelling of mixed cyclopentane and carbon dioxide hydrates in presence of salts[END_REF]. The influence of added particles -mainly graphite, silica sand and activated carbon -on hydrate formation has been investigated in different contexts (water desalination, methane storage, flow assurance, etc.) [START_REF] Linga | A Review of reactor designs and materials employed for increasing the rate of gas hydrate formation[END_REF][START_REF] Baek | Inhibition effects of activated carbon particles on gas hydrate formation at oil-water interfaces[END_REF]. Graphite and silica sand particles were found to promote hydrate formation kinetics [START_REF] Li | Promotion effect of graphite on cyclopentane hydrate based desalination[END_REF][START_REF] Linga | A Review of reactor designs and materials employed for increasing the rate of gas hydrate formation[END_REF][START_REF] Babu | Morphology of methane hydrate formation in porous media[END_REF], whereas activated carbon was reported to be a kinetic hydrate inhibitor [START_REF] Baek | Inhibition effects of activated carbon particles on gas hydrate formation at oil-water interfaces[END_REF] or promoter [START_REF] Linga | A Review of reactor designs and materials employed for increasing the rate of gas hydrate formation[END_REF][START_REF] Babu | Morphology of methane hydrate formation in porous media[END_REF][START_REF] Siangsai | Investigation on the roles of activated carbon particle sizes on methane hydrate formation and dissociation[END_REF][START_REF] Siangsai | Improved methane hydrate formation rate using treated activated carbon and tetrahydrofuran[END_REF][START_REF] Yan | Experimental and modeling study on hydrate formation in wet activated carbon[END_REF]. To the best of our knowledge, no study has ever used porous particles as both a reservoir and a carrier of the guest molecules for hydrate formation.

The present work is an experimental study of the effect of CP-soaked PACP on hydrate formation in synthetic PW. Sodium chloride (NaCl) is used as a model salt to prepare the PW. This choice is justified by the fact that NaCl represents the highest salt fraction in real PW [START_REF] Benko | Produced water in the Western United States: Geographical distribution, occurrence, and composition[END_REF].

Effectively, referring to the USGS database, Cha and Seol reported that the average sodium chloride content in real PW is 70% higher than those of the other main mineral salts present [START_REF] Cha | Increasing gas hydrate formation temperature for desalination of high salinity produced water with secondary guests[END_REF]. This article does not look into the hydrate recovery and dissociation steps and focuses only on the hydrate formation stage of BGH's process. It investigates the effects of the presence of CP-soaked PACP, of the CP-loading rate of the PACP, of particle size, the stirring rate, and salinity on the hydrate formation kinetics and water-to-hydrate conversion.

Prior to this though, preliminary experiments were performed without PACP to evaluate the thermodynamic and kinetic effects of NaCl on CP-hydrate formation.

MATERIALS AND METHODS

Materials and Apparatus

Cyclopentane (CP) (purity of 97%) was purchased from Sigma Aldrich. Deionized water (resistivity of 18.2 MΩ.cm) was produced by a Purelab laboratory water-purification system. Sodium chloride (NaCl) (purity of 99.5%) was supplied by Acros Organics. Two grades of porous activated carbon particles (PACP), G-BAC-G70R and A-BAC-SP, supplied by Keruha GmbH (Germany) were used in the hydrate formation experiments. According to the supplier, they have the same pore size distribution (PSD) and porosity, but different mean particle diameters (700 and 400 µm respectively). Their particle size distributions are provided as supplementary material (Figure S1). Their specific surface area is between 1,100 and 1,300 m 2 /g. Plastic syringes (3-mL capacity) and cellulose acetate syringe filters (0.8-µm mesh size), used to take and filter samples of the aqueous solution, were purchased from Sodipro.

The amounts of NaCl required to prepare the PW were weighed using a precision balance with an uncertainty of ± 0.001 g.

The effect of NaCl concentration on the CP-hydrate equilibrium temperature was studied using a set of glass flasks, each with a capacity of 30 mL, and two Julabo F32 cryostats using ethane-diol as a refrigerant fluid.

The effect of NaCl concentration on the hydrate growth rate at the water/CP interface was evaluated using a sealed cylindrical glass cell of 3 cm in diameter and with a capacity of 30 mL placed in a cylindrical metal-jacketed vessel, through which ethane-diol was circulated to control the temperature. The water/CP interface was observed using a binocular magnifier (Wild Heerbrugg) fitted with a CCD camera (IDS UI124xSE-C) and positioned above the glass cell. The cell was backlit by an LED light table (Edmund Optics). The snapshots of the interface were recorded on a PC at regular intervals using a lab-made program.

The experiments based on BGH's process were conducted in two similar jacketed glass reactors with a 1-L capacity (Figure 1). Each reactor was fitted with a mechanical stirrer with a 4-bladed glass double propeller-stirrer shaft. A Lauda cryostat (RE 1050 G), using a silicone oil (Kryo 51) as a refrigerant, was used to control the temperature inside the reactors. The reactor temperature, measured using a PT100 temperature sensor (± 0.15°C uncertainty), was recorded by a data logger and a computer at regular intervals. The reactors have several inlets and outlets: the former were used to introduce the products (brine, PACP) when preparing the hydrate formation experiment, and the latter to collect the brine samples for refractive index measurement during the experiment.

The refractive index nD (at a wavelength of 589.3 nm) of the collected brine samples was measured using an Anton Paar refractometer (Abbemat 3200) with an accuracy of ± 0.0001.

The sample salinity was then deduced using a previously determined "nD -[NaCl]" calibration curve (see eq. 2 in the Procedures section).

Preliminary investigation

The aim of the preliminary experiments without PACP was to analyze the effect of NaCl concentration on both the CP-hydrate equilibrium temperature and growth rate. Moreover, they served to choose the initial experimental conditions (initial water salinity; initial experimental temperature), referred to as the "starting points" in the chapters below, for testing BGH's process.

Effect of NaCl concentration on the CP-hydrate equilibrium temperature

Fourteen flasks, each containing 2 g of CP, 18 g of water with different NaCl concentrations between 0 and 23 wt%, and a small rod (to help mix the fluids), were prepared, split into two concentration groups (group#1 (< 10 wt% NaCl) and group#2 (> 10 wt% NaCl)), and placed in two cryostats. Group#1 and group#2 were cooled down to -10°C and -22°C respectively and maintained at these temperatures for 24 hours to form ice. The ice was then melted by increasing the bath temperature to -4 and -18°C for group#1 and #2 respectively in order to trigger hydrate formation. The flasks were shaken manually at regular intervals over the course of 16 hours to promote the formation of CP hydrates. The bath temperature was then increased to 0 and -14°C for group#1 and #2 respectively. These temperatures were 1°C lower than the lowest CP-hydrate equilibrium temperatures at NaCl concentrations of 10 wt% and 23 wt% found in the literature [START_REF] Ho-Van | Experimental study and modelling of cyclopentane hydrates in the presence of NaCl, KCl and a mixture of NaCl -KCl[END_REF][START_REF] Kishimoto | Crystal growth of clathrate hydrate at the interface between seawater and hydrophobic-guest liquid: effect of elevated salt concentration[END_REF][START_REF] Zylyftari | Salt effects on thermodynamic and rheological properties of hydrate forming emulsions[END_REF][START_REF] Delroisse | Effect of a hydrophilic cationic surfactant on cyclopentane hydrate crystal growth at the water/cyclopentane interface[END_REF].

The CP-hydrate equilibrium temperatures were determined using a "step-heating method" [START_REF] Tohidi | Improving the accuracy of gas hydrate dissociation point measurements[END_REF], which consists in applying a stepwise heating method combined with a sufficiently long equilibrium time at each step. In our experiments, the bath temperature was increased by steps of 0.2°C and maintained at the new temperature for 4 to 12 hours. The bath temperature was monitored using a PT100 probe (± 0.15°C uncertainty). The presence of CP hydrates in the flasks was visually checked at each step. If CP hydrates were still present, the flask was manually shaken before the next temperature increase. When only a small amount of CP hydrates remained, the temperature step was reduced to 0.1°C. The process was repeated until the last CP-hydrate crystals had melted. The CP-hydrate equilibrium temperatures were calculated as the arithmetic mean of the last two temperatures (before and after the last CPhydrate crystals had melted). Any uncertainties regarding the measured equilibrium temperatures were evaluated as the sum of PT100 uncertainty (± 0.15°C) and either ± 0.05°C, for the temperature step of 0.1°C, or ± 0.1°C if the CP-hydrate crystals had melted, before the temperature step was reduced from 0.2 to 0.1°C.

Effect of NaCl concentration on the CP-hydrate growth rate

Nine aqueous solutions with different NaCl concentrations (0, 1, 2, 3.5, 4, 6, 8, 10, and 16 wt%) were prepared. 20 mL of NaCl solution and 4 mL of CP were transferred to the cylindrical glass cell. The latter was placed in the metal-jacketed vessel and covered with a petri dish to limit CP evaporation. The temperature of the system was set such as to obtain the desired subcooling. Two different subcoolings (2°C and 6°C) were investigated: at 6°C, the lateral hydrate growth rates of all the different NaCl preparations were measured, whereas at 2°C, they were measured only for NaCl concentrations of 0, 3.5, 10, and 16 wt%. Hydrate crystallization was triggered by seeding the system with a few CP-hydrate crystals prepared beforehand. Because of their intermediate density, the seeds settled at the water/CP interface.

The binocular magnifier was then focused on the crystals located on the flat part of the interface (around the vertical shaft of the cell). The lateral hydrate growth rate (GR) was evaluated by measuring the distance covered by the hydrate crystallization front at the water/CP interface in a given growth direction on two snapshots taken at different times.

Three measurements were performed, each on a different point of the crystallization front, and the mean GR value was calculated. The GR uncertainty was calculated as the deviation from the mean GR value. The uncertainty of the imposed subcooling was ± 0.3°C.

Hydrate formation experiments in BGH's process

The study investigated the effects of the presence and absence of PACP at different stirring rates and, in the case of the system with PACP, the effect of the CP-loading rate, the PACP size and water salinity on the CP-hydrate formation kinetics and the total amount of hydrates formed.

For this purpose, a series of experiments was carried out using the glass reactors. Synthetic water was first introduced into the reactors and cooled down to the experiment temperature.

Stirring was started and set to the target rate (0, 180, or 360 rpm). Alongside that, CP -or PACP soaked in CP -were cooled in a freezer for 16 hours to -0.5°C and 0.5°C respectively, before being introduced into the reactors. This procedure was used to prevent hydrate crystallization before the system temperature reached the target experiment temperature. Note that, to avoid moisture crystallizing on the soaked PACP -which could trigger hydrate formation before the PACP were introduced into the reactors -they were not cooled to negative temperatures in the freezer. If they had been, it would have been impossible to evaluate the effect of PACP on induction time since hydrate formation would have been spontaneous.

The hydrate formation kinetics were quantified based on the induction time for hydrate crystallization tind and the relative water-to-hydrate conversion rate determined one hour after the onset of hydrate crystallization:

-tind was calculated as the time elapsed from the moment when CP or the soaked PACP were introduced into the reactor to the start of temperature increase due to hydrate crystallization.

Note that when hydrate crystallization did not occur in the first two hours, it was triggered by seeding the system with a few CP-hydrate crystals prepared beforehand. Moreover, tind was measured only in the experiments where the effect of PACP and the stirring rate were investigated. In the other experiments, hydrate crystallization was systematically initiated by seeding the system with a few CP-hydrate crystals.

was calculated as = ∆ ∆

, where ∆t = 1h and WHC is the waterto-hydrate conversion, WHC , the maximum value of WHC that should be obtained, either when all the CP initially present in the system is converted to hydrates or when the system reaches the CP-hydrate equilibrium curve (Figure 2). Note that in all the experiments of this study, water was in excess since the molar ratio of water to CP is 30:1, which is greater than the stoichiometric water to CP molar ratio for complete conversion to hydrate (17:1). (Eq.1)

[./ 0] was obtained from the refractive index (nD) measurement of the NaCl solution sample collected at time t and using the following "nD -[NaCl]" calibration equation (Equation 2):

[./ 0] = 564.55 ?@ -752.49 (Eq. 2)

The nD measurements were performed at 20°C. The samples collected were filtered to remove any suspended solids (hydrate crystals, PACP or impurities) before measuring nD.

We checked that the use of filters and the solubility of CP in water (86 mg/L at 10°C [START_REF] Cha | Increasing gas hydrate formation temperature for desalination of high salinity produced water with secondary guests[END_REF]) did not impact the nD values obtained. A check was also run to make sure that NaCl did not adsorb on the PACP at the salinities used (3.5, 10, and 16 wt%).

Effect of PACP and stirring rate on CP-hydrate formation

The CP-hydrate formation experiments -without and with G-BAC-G70R loaded with 0.8 g of CP per gram of PACP -were conducted at the starting point 1 (3.5 wt% NaCl; -0.5°C) and at stirring rates of 0, 180, and 360 rpm for 78 hours. For these experiments, 777.2 g of a NaCl solution (750 g of deionized water and 27.2 g of NaCl) and 100 g of CP -or 125 g of PACP soaked in 100 g of CP -were introduced into each reactor where the temperature was set to -0.5°C. Stirring started once the system temperature had reached the target temperature.

Effect of the CP-loading rate of PACP on CP-hydrate formation

The CP-hydrate formation experiments were conducted using G-BAC-G70R loaded with 0.5, 0.65, 0.8, and 1 g of CP per gram of PACP, at the starting point 1 (3.5 wt% NaCl; -0.5°C) for 24 hours. 0.8 g of CP per gram of PACP was the loading rate typically used by the start-up BGH in its tests to work out its HBD process. Note that at this CP-loading rate, the particles were wet and stuck together, which suggests that both their pores and external surface were saturated with CP. The other loading rates used in the present study were chosen such as to evaluate the effect of this parameter on the hydrate formation kinetics and water-to-hydrate conversion over a range on either side of this value. For the CP-hydrate formation experiments, 777.2 g of a NaCl solution (750 g of deionized water and 27.2 g of NaCl) and 125 g of PACP soaked in 62.5, 81.25, 100 and 125 g of CP respectively were introduced into each reactor where the temperature was set to -0.5°C. A stirring rate of 180 rpm was used.

Effect of the size of PACP on CP-hydrate formation

The CP-hydrate formation experiments were conducted using G-BAC-G70R (mean particle diameter of 700 µm) and A-BAC-SP (mean particle diameter of 400 µm) loaded with 0.8 g of CP per gram of PACP, at the starting point 1 (3.5 wt% NaCl; -0.5°C) for 24 hours. For these experiments, 777.2 g of a NaCl solution (750 g of deionized water and 27.2 g of NaCl) and 125 g of PACP soaked in 100 g of CP were introduced into each reactor where the temperature was set to -0.5°C. A stirring rate of 180 rpm was used.

Effect of water salinity on CP-hydrate formation

In this part of the study, the CP-hydrate formation experiments were performed at two additional starting points defined as starting point 2 (10 wt% NaCl; -4.9°C) and starting point 3 (16 wt% NaCl; -9.5°C) for 24 hours. Although the operating points 1, 2 and 3 have different temperatures, they have the same initial subcooling of 6°C. The PACP used were G-BAC-G70R loaded with 0.8 g of CP per gram of PACP. A stirring rate of 180 rpm was used.

RESULTS AND DISCUSSION

Effect of NaCl on CP-hydrate formation

Effect of NaCl concentration on the CP-hydrate equilibrium temperature

The CP-hydrate equilibrium temperatures obtained at the different NaCl concentrations investigated (0 to 23 wt%) are plotted in Figure 3 and the measured values are given in Table 1. As expected, the increase in water salinity resulted in a decrease of the CP-hydrate

Effect of NaCl concentration on the CP-hydrate growth rate

In these experiments, CP-hydrate formation and growth occurred at the (quiescent) water/CP interface. A thin hydrate layer ended up covering the entire water/CP interface (~7.1 cm 2 ) available. Once the latter was totally covered, the hydrate growth stopped. Consequently, only a very small amount of hydrates formed in the system compared to the volume of NaCl solution (20 mL). This implies that the water salinity remained almost constant and that the We can see that both the NaCl concentration and the imposed subcooling drastically affect the hydrate growth rate. The latter decreases as the water salinity at a given subcooling increases and rises with the subcooling at a given salinity. The subcooling acts as a driving force and NaCl as a kinetic inhibitor for hydrate formation (in addition to its thermodynamic inhibitor effect (section 3.1.1)). According to the results shown in Figure 4, a high subcooling must be chosen to obtain a high hydrate growth rate in a hydrate-based desalination process.

Consequently, in all the hydrate formation experiments performed, a subcooling of 6°C was chosen so that the system was deep inside the hydrate stability zone but remained outside the ice stability zone (see the three starting points in Figure 3). However, it is important to keep in mind that i) the introduction of the soaked PACP into the reactor, ii) the exothermicity of hydrate crystallization and, iii) the consumption of water molecules (by the growing hydrate phase) -which causes an increase in the salinity of the remaining liquid water and thus a decrease in the CP-hydrate equilibrium temperature -caused the subcooling to drop during the hydrate formation experiments. Considering these effects, we determined that the minimum subcoolings reached during the experiments performed at the starting points 1, 2 and 3 were 3.9, 4.1, and 5.1°C respectively. Note that the decrease in the imposed subcooling was mainly due to the exothermicity of the crystallization and the increase in salinity and not to the introduction of the soaked PACP into the reactor.

Hydrate formation experiments in BGH's process 3.2.1 Effect of PACP and the stirring rate on CP-hydrate formation

The effects of the absence and presence of PACP (G-BAC-G70R loaded with 0.8 g of CP per gram of PACP) and of the stirring rate on CP-hydrate formation are shown in Figure 5 and Table 2. For ease of comparison, data in Figure 5 are presented with a common base time t = 0, which corresponds to the onset of hydrate crystallization (whether the crystallization occurred spontaneously or had to be triggered by adding a few CP-hydrate crystals).

Table 2.

Values of the induction time, the relative water-to-hydrate conversion rate and the final relative water-to-hydrate conversion (at t = 78 h) for the systems with and without PACP (G-BAC-G70R loaded with 0.8 g of CP per gram of PACP) and different stirring rates. The initial conditions for these experiments correspond to starting point 1 (Figure 3). For all the experiments performed without PACP, hydrate crystallization never occurred spontaneously in the first two hours the system spent at the target temperature of -0.5°C (i.e.

the induction time tind was greater than two hours). With PACP, tind lasted just a few minutes for one third of the experiments performed and more than 2 h for the others. The presence of PACP therefore increases the probability of early hydrate crystallization. The large number of nucleation sites provided by the PACP may explain this result. The stirring rates investigated do not affect the trend observed for tind.

is much higher for the system with PACP than without at a given stirring rate, and stirring increases in both systems. The increased contact area between water and CP, due either to the PACP (soaked in CP) or to the stirring of the system or both, can explain the trend observed. As expected, for the systems without PACP, a higher stirring rate ensures more efficient mixing of water and CP and thus a greater interface between the two phases. In the presence of PACP, the stirring causes dispersion of the particles, which tend to agglomerate in the water phase when no stirring is applied. However, in this case, the contact area between water and CP is predominantly controlled by the external specific surface area of the particles (in which CP is adsorbed), which does not vary with the agitation. This is why changes very little when the stirring rate is increased from 180 to 360 rpm.

is much higher for the system with PACP than without at the stirring rates of 0 and 180 rpm. There is quite a spectacular difference in the values obtained for the quiescent systems (0 rpm), where is around 0 and 47.4% for the system without and with PACP respectively, 78 hours into the experiment. This is due to the difference in the size of the contact area between the water and the CP where hydrate formation and growth take place. Without PACP, the contact area is about 80 cm² (the cross-section of the glass reactor), whereas with PACP it is at least 11,000 cm² (the total external surface area of the particles).

Moreover, the variation of with the stirring rate displays an opposite trend according to whether or not PACP are present: increases with the stirring rate in the systems without PACP and decreases in other cases. For the former, the increase in the contact area between water and CP with stirring explains the trend observed. For the latter, the reason why decreases as the stirring rate increases remains unclear. One of the reasons might be that the increase in the initial hydrate growth rate caused by the mixing leads to the early formation of an impermeable hydrate crust at the surface of the PACP, which limits (or stops) the hydrate formation process. Corak et al. [START_REF] Corak | Effect of subcooling and amount of hydrate former on formation of cyclopentane hydrates in brine[END_REF] observed a similar tendency in their research on CP-hydrate formation in brines (3 wt% NaCl solutions). They reported that faster hydrate crystallization led to a greater amount of encapsulated CP and thus a smaller amount of hydrates (since the encapsulated CP is unavailable for hydrate formation).

An important finding in this section is that the CP-soaked PACP both increases the hydrate formation kinetics and "supplies" the hydrate reaction with CP. Note that the kinetic enhancement of hydrate formation observed in the presence of the PACP is consistent with the results reported by other authors for submillimetric particles, which were obtained mainly within the context of methane storage [START_REF] Babu | Morphology of methane hydrate formation in porous media[END_REF][START_REF] Siangsai | Investigation on the roles of activated carbon particle sizes on methane hydrate formation and dissociation[END_REF][START_REF] Siangsai | Improved methane hydrate formation rate using treated activated carbon and tetrahydrofuran[END_REF][START_REF] Yan | Experimental and modeling study on hydrate formation in wet activated carbon[END_REF].

In the following sections, the effect of the PACP CP-loading rate, PACP size and water salinity on and will be investigated. Because remains almost constant for the systems with PACP after around 20 hours of experimentation (see Figure 5), 24 hours was chosen as the duration for all the following experiments. A stirring rate of 180 rpm was chosen to ensure homogeneity of the system during the experiments. Moreover, hydrate crystallization was triggered by seeding the system with a few CP-hydrate crystals.

Effect of the CP-loading rate of PACP on CP-hydrate formation

The effect of the CP-loading rate on CP-hydrate formation is illustrated in Figure 6, and the corresponding values of and are given in Table 3. The points for the different CP-loading rates overlap for the first three hours of the experiment (Figure 6) meaning that hardly depends on CP-loading (Table 3). About five hours into the experiments, the variation rate of decreases for all the systems (Figure 6). At the end of the experiments (24 h), we can see that significantly increases with the CP-loading rate when the latter is lower than or equal to 0.8 g of CP per

gram of PACP (Table 3). This can be explained by the increase in the amount of CP available for hydrate formation. However, a further increase in the CP-loading rate (to 1 g of CP per gram of PACP) causes to drop. This decrease, due to the normalization of WHC, indicates a reduction in the ratio of the CP converted to hydrates to the CP present in the system. The main possible reason for this behavior is given below. When preparing the PACP, soaked in 1 g of CP per gram of PACP, some of the CP added was not adsorbed by the PACP but remained as a free liquid phase. Note that free liquid CP was not observed at the lower CP-loading rates used, which suggests that the maximum loading rate of PACP is approximately 0.8 g of CP per gram of PACP. When the PACP prepared with 1 g of CP per gram of PACP are added to the NaCl solution, the excess CP is dispersed as droplets in the bulk phase by agitation (180 rpm). Because the agitation used is not very vigorous, the increase in the water/CP interface caused by the excess CP in the bulk phase is small compared to the interface between the CP adsorbed in the PACP and the water. The amount of hydrates formed therefore increases less significantly than the amount of CP added, and decreases as a consequence.

The results obtained in this section show that the optimal rate for loading PACP with CP in order to obtain high hydrate formation kinetics and conversion is around 0.8 g of CP per gram of PACP.

Effect of water salinity on CP-hydrate formation

In Figure 8 and Table 5, the results of the CP-hydrate formation experiments conducted with the 700-µm PACP (loaded with 0.8 g of CP per gram of PACP) at concentrations of 10 and 16 wt% NaCl (starting points 2 and 3 in Figure 3) are shown and compared with those obtained in experiments using 3.5 wt% NaCl (given in paragraph 3.2.1). Table 5. Values of the relative water-to-hydrate conversion rate and the final relative waterto-hydrate conversion (at t = 24 h) for the system with PACP (G-BAC-G70R loaded with 0.8 g of CP per gram of PACP). The initial conditions for these experiments correspond to starting points 1, 2 and 3 (see Figure 3). The stirring rate is 180 rpm. The points obtained at time t for NaCl concentrations of 3.5 and 10 wt% are very similar (Figure 8). Consequently, and have roughly the same values for both concentrations (Table 5). This very interesting result suggests that the PACP soaked in CP "cancel" the kinetic inhibition effect of NaCl (demonstrated in paragraph 3.1.2) for low to moderate salt concentrations. However, both and significantly decrease in the system with 16 wt% NaCl. We saw in paragraph 3.1.2 that the kinetic inhibition effect of NaCl on CP-hydrate formation is much stronger with 16 wt% NaCl than with 3.5 and 10 wt% NaCl. In actual fact, the hydrate growth rate (measured at the water/CP interface) with 16

wt% NaCl was 5 times lower than the growth rate with 10 wt% NaCl and 19 times lower than the one with 3.5 wt%. We can therefore infer that above a certain salinity, the presence of PACP is no longer able to "cancel" the kinetic inhibition effect of NaCl.

In their work on the desalination of PW using natural gas hydrates, Fakharian et al. [START_REF] Fakharian | Desalination of high salinity produced water using natural gas hydrate[END_REF] did not observe any hydrate formation in waters with a TDS higher than 160 g/L (i.e. 13.7 wt% of salts). In the present study, we succeeded in forming hydrates in water with 16 wt% NaCl.

This illustrates another beneficial effect of using PACP soaked in CP.

Conclusion

This study demonstrates that using PACP soaked in CP significantly enhances hydrate formation kinetics and water-to-hydrate conversion. So, they act both as a kinetic promoter and a CP reservoir for hydrate formation. Combining PACP and stirring increases the formation kinetics but unexpectedly reduces the final water-to-hydrate conversion. The formation kinetics and water-to-hydrate conversion increase with the CP-loading rate of the PACP and then level off (or even slightly decrease) above a given loading rate (0.8 g CP per gram of PACP in our case). It was found that the smaller PAC particles induce higher hydrate formation kinetics but a lower final conversion. It is interesting to note that the use of PACP soaked in CP makes it possible to overcome the kinetic inhibition effect of NaCl for salinities of up to 10 wt%. Above this value, PACP still enhance hydrate formation but both the formation kinetics and the conversion decrease (compared to lower salinities).

BGH's process, which cleverly combines the use of a guest molecule (CP) forming hydrates at atmospheric pressure, and guest-soaked porous particles that promote hydrate formation and growth, appears as a promising desalination method. Nevertheless, the final water-to-hydrate conversion needs to be improved since more than one half of the CP adsorbed in the PACP is not converted to hydrates (see Tables 2 and5). Possible reasons for this behavior might be the formation of an impermeable hydrate layer on the PACP surface that blocks the contact between CP and water, and/or a fraction of CP tightly trapped in the pores of the PACP making it unavailable for hydrate formation. Further enhancement of the hydrate formation kinetics would also be advantageous in view of an industrial application of this desalination process. These points are currently under investigation.

Figure 1 .

 1 Figure 1. Experimental set-up for CP-hydrate formation: a) 1-L reactor, b) mechanical stirrer,

Figure 2 .

 2 Figure 2. Experimental procedure to determine the relative water-to-hydrate conversion rate

  equilibrium temperatures. Our experimental values are consistent with those published by Ho-Van et al.[START_REF] Ho-Van | Experimental study and modelling of cyclopentane hydrates in the presence of NaCl, KCl and a mixture of NaCl -KCl[END_REF], Delroisse et al.[START_REF] Delroisse | Effect of a hydrophilic cationic surfactant on cyclopentane hydrate crystal growth at the water/cyclopentane interface[END_REF], Zylyftari et al.[START_REF] Zylyftari | Salt effects on thermodynamic and rheological properties of hydrate forming emulsions[END_REF] and Kishimoto et al.[START_REF] Kishimoto | Crystal growth of clathrate hydrate at the interface between seawater and hydrophobic-guest liquid: effect of elevated salt concentration[END_REF] (see Figure3). More precisely, they range between the equilibrium points found in Ho-Van et al.'s study, determined by what they called rapid and slow processes. Ice equilibrium temperatures for the same range of NaCl concentrations are also shown in Figure3. The starting points used for the hydrate formation experiments conducted in the glass reactors should be chosen in the region between the CP-hydrate and ice[START_REF] Cohen-Adad | Alkali Metal and Ammonium Chlorides in Water and Heavy Water (Binary Systems)[END_REF] curves.

Figure 3 .

 3 Figure 3. CP-hydrate and ice equilibrium temperatures as a function of NaCl concentration.

  imposed subcooling varied very little during hydrate formation. The measured lateral hydrate growth rate at the NaCl concentrations investigated (0 to 16 wt%) and the subcoolings of 2 and 6°C are shown in Figure4. Images showing the morphology of the CP-hydrate crystals formed are provided as supplementary material (FigureS2). The CP-hydrate crystal morphology was found to depend essentially on the imposed subcooling. The lateral hydrate growth rate values obtained at these subcooling conditions are consistent with those measured by Kishimoto et al.[START_REF] Kishimoto | Crystal growth of clathrate hydrate at the interface between seawater and hydrophobic-guest liquid: effect of elevated salt concentration[END_REF] at around the same subcoolings.

Figure 4 .

 4 Figure 4. Measured lateral growth rate of CP-hydrates formed at the water/CP interface, at

Figure 5 .

 5 Figure 5. Effect of PACP (G-BAC-G70R loaded with 0.8 g of CP per gram of PACP) and the

Figure 6 .

 6 Figure 6. Effect of the CP-loading rate of PACP (G-BAC-G70R) on the relative water-to-

Figure 8 .

 8 Figure 8. Effect of water salinity on the relative water-to-hydrate conversion. The PACP (G-

Table 1 .

 1 CP

		-hydrate equilibrium temperatures (Teq) measured at different NaCl
	concentrations ([NaCl])
	[NaCl] a	0	1	2	3.5	5	8	10
	(wt%)
	Teq (°C)	7.13 ±	6.72 ±	6.18 ±	5.53 ±	4.56 ±	2.78 ±	1.15 ±
		0.20	0.20	0.25	0.19	0.26	0.24	0.21
	[NaCl] a	12	14	16	18	20	22	23
	(wt%)
	Teq (°C)	-0.05 ±	-1.63 ±	-3.47 ±	-5.3 ±	-7.78 ±	-9.85 ±	-11.37 ±
		0.20	0.20	0.20	0.19	0.18	0.20	0.20

a : ± 0.01 wt%

Table 3 .

 3 Values of the relative water-to-hydrate conversion rate and the final relative water-

	to-hydrate conversion (at t = 24 h) for the systems with PACP (G-BAC-G70R) at different
	CP-loading rates. The initial conditions for these experiments correspond to starting point 1
	(see Figure 3). The stirring rate is 180 rpm.
	CP-loading rate	0.5	0.65	0.8	1
	(gram of CP per
	gram of PACP)
	(% / h)	6.6 ± 2.2	8.4 ± 1.6	8.2 ± 1.3	6.5 ± 1.1
	(%)	23.1 ± 1.9	33.0 ± 2.6	40.9 ± 2.6	36.7 ± 0.6

Table 4 .

 4 Values of the relative water-to-hydrate conversion rate and the final relative water-

	to-hydrate conversion (at t = 24 h) for the different sizes of PACP (G-BAC-G70R (700 µm)
	and A-BAC-SP (400 µm)) loaded with 0.8 g of CP per gram of PACP. The initial conditions
	for these experiments correspond to starting point 1 (see Figure 3). The stirring rate is 180
	rpm.
	Particle size	400	700
	(µm)	(A-BAC-SP)	(G-BAC-G70R)
	(% /h)	11.4 ± 0.6	8.2 ± 1.3
	(%)	33.7 ± 0.9	40.9 ± 2.6

Acknowledgements

This research was financially supported by Total. The authors would like to thank Frédéric Plantier and Manuel Ildefonso (UPPA), and Patrick Baldoni-Andrey, Hervé Nabet, and Stéphane Nowe (Total) for their valuable scientific input and discussions. Joseph Diaz (UPPA) is gratefully acknowledged for his technical assistance. Christelle Miqueu would like to acknowledge the E2S UPPA hub "Newpores" supported by the French Investissements d'Avenir program managed by the ANR (ANR-16-IDEX-0002).

Effect of the size of PACP on CP-hydrate formation

The values obtained for the 400-µm PACP (A-BAC-SP) were higher than those obtained with the 700-µm PACP (G-BAC-G70R) at the beginning of the hydrate formation experiment, but then became lower after about 5 hours (Figure 7). is therefore higher in the case of the smaller particles and is higher in the case of the larger ones (Table 4). Because these PACP have the same PSD and the same porosity, the difference in the obtained can probably be explained by the difference in the external specific surface area of the particles. Smaller particles effectively have a larger external specific surface area, which provides a higher water/CP contact area and more nucleation sites. Consequently, a higher hydrate growth rate can be expected. However, is higher when using 700-µm PACP, i.e. in the system with the PACP that offer the smaller water/CP contact area. A possible explanation might be that the slower initial hydrate growth rate ( ) obtained with these PACP delays or limits the formation of an impermeable hydrate crust on the CP layer at the PACP surface. The CP transfer is sustained, and a greater amount of hydrates forms. Note that the trends observed here for the effect of the PACP size on are consistent with those reported by Li et al. in their study on the promotion effect of graphite on CP-hydrate formation [START_REF] Li | Promotion effect of graphite on cyclopentane hydrate based desalination[END_REF]. The authors observed that the water-to-hydrate conversion was initially faster and then increased more slowly for the smallest particles than for the largest ones.