Mateusz Sitarz

Katarzyna Szkliniarz

Jerzy Jastrzębski

Jaroslaw Choiński

Arnaud Guertin

Ferid Haddad

Andrzej Jakubowski

Kamil Kapinos

Maciej Kisieliński

Agnieszka Majkowska

Jarosław Choiński

Etienne Nigron

Malihe Rostampour

Anna Stolarz

Agnieszka Trzcińska

Rafał Walczak

Jolanta Wojtkowska

Wiktor Zipper

Aleksander Bilewicz

Production of Sc medical radioisotopes with proton and deuteron beams

Keywords: proton and deuteron beams, 43,44,47 Sc radioisotopes, radioisotope production

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INTRODUCTION

In a recent publication [START_REF] Szkliniarz | Production of medical Sc radioisotopes with an alpha particle beam[END_REF] we presented information on the production efficiency and the isotopic purity of positron emitting Sc radioisotopes ( 43 Sc, 44g Sc and 44m Sc) formed using an alpha particle beam of energy up to 30 MeV. We also presented there in detail the motivation and history of the investigation of the positron emitters 43 Sc and 44 Sc. In the present paper we extend this study to two other possible production routes using a proton and deuteron beams. We also extend these studies to the prospective therapeutic 47 Sc radioisotope which may be formed using a proton beam. The production efficiency, isotopic purity and possible medical applications of Sc radioisotopes were previously studied in a number of works using proton [START_REF] Bartoś | New separation method of no-carrier-added 47 Sc from titanium targets[END_REF][START_REF] Krajewski | Cyclotron production of 44 Sc for clinical application[END_REF][START_REF] Severin | Cyclotron Produced 44g Sc from Natural Calcium[END_REF][START_REF] Müller | Promises of cyclotron-produced 44 Sc as a diagnostic match for trivalent β-emitters: in vitro and in vivo study of a 44 Sc-DOTA-folate conjugate[END_REF]2014;[START_REF] Hoehr | 44g Sc production using a water target on a 13 MeV cyclotron[END_REF][START_REF] Hernandez | 44 Sc: An Attractive Isotope for Peptide-Based PET Imaging[END_REF][START_REF] Van Der Meulen | Cyclotron production of 44 Sc: From bench to bedside[END_REF][START_REF] Valdovinos | Separation of cyclotron-produced 44 Sc from a natural calcium target using a dipentylpentylphosphonate functionalized extraction resin[END_REF][START_REF] Singh | Scandium-44 DOTATOC PET/CT: first in-human molecular imaging of neuroendocrine tumors and possible perspectives for theranostics[END_REF], Domnanich et al. 2016a, 2016b, 2017a, 2017b) deuteron [START_REF] Kuhn | Production of the medically interesting radioisotopes 44,44m Sc and their radioactive byproducts via deuteron and alpha-particle induced nuclear reactions on natural Ca and K[END_REF][START_REF] Huclier-Markai | Optimization of reaction conditions for the radiolabeling of DOTA and DOTA-peptide with 44m/44 Sc and experimental evidence of the feasibility of an in vivo PET generator[END_REF]Alliot et al., 2015aAlliot et al., , 2015b;;Duchemin et al., 2015) and alpha particle beams [START_REF] Kupsch | Verfahren zur Gewinnung von radionuklidisch reinem Scandium-43[END_REF][START_REF] Kuhn | Production of the medically interesting radioisotopes 44,44m Sc and their radioactive byproducts via deuteron and alpha-particle induced nuclear reactions on natural Ca and K[END_REF][START_REF] Coenen | Development of the non-standard PET radionuclides 43,44g Sc and 45[END_REF][START_REF] Nagatsu | A study on remote production of 43 Sc from nat CaO target via the nat Ca(α,x)-reaction[END_REF][START_REF] Walczak | Cyclotron production of 43 Sc for PET imaging[END_REF][START_REF] Szkliniarz | Medical Radioisotopes Produced Using the Alpha Particle Beam from the Warsaw Heavy Ion Cyclotron[END_REF][START_REF] Szkliniarz | Production of medical Sc radioisotopes with an alpha particle beam[END_REF].

The 43 Sc and 44 Sc radioisotopes, thanks to their relatively long half-lives (3.89 h and 3.97 h, respectively), may constitute an attractive alternative in Positron Emission Tomography to the currently employed 18 F with a half-life of only 110 min. In particular, in spite of poorer positron tomography resolution [START_REF] Bunka | Imaging quality of 44 Sc in comparison with five other PET radionuclides using Derenzo phantoms and preclinical PET[END_REF] with these radioisotopes, their production using a single facility and subsequent distribution to hospitals not possessing a cyclotron and/or radiopharmaceutical synthesis equipment may be attractive. Also, F and Sc have completely different chemical reaction mechanisms which plays a key role in the preparation of different radiopharmaceuticals.

The 44g Sc radioisotope has other properties making it more versatile than the classic 18 F. Firstly, it decays in large proportion via an excited state at 1157 keV. The gamma line following the 99% positron emission feeding this state was suggested as an ideal coincidence partner to the two 511 keV annihilation quanta in the so-called three-photon PET technique [START_REF] Mausner | Radionuclide development at BNL for nuclear medicine therapy[END_REF][START_REF] Grignon | Nuclear medical imaging using β+ γ coincidence from 44 Sc radio-nuclide with liquid xenon as detection medium[END_REF][START_REF] Thirlof | Perspectives for Highly-Sensitive PET-Based Medical Imaging Using β+γ Coincidences[END_REF] which is expected to improve substantially the energy resolution originating from the finite range of the annihilating positrons. A decrease in the patient dose is also expected employing this technique [START_REF] Lang | Sub-millimeter nuclear medical imaging with reduced dose application in positron emission tomography using β γ coincidences[END_REF]. 44 Sc is also particularly interesting due to an isomeric state, 271 keV above its ground state, decaying via an E4 transition to the ground state with a half-life of 2.4 d. The exploitation of this decay cascade was recently proposed [START_REF] Huclier-Markai | Optimization of reaction conditions for the radiolabeling of DOTA and DOTA-peptide with 44m/44 Sc and experimental evidence of the feasibility of an in vivo PET generator[END_REF]Alliot et al., 2015aAlliot et al., , 2015b;;[START_REF] Duchemin | Production of scandium-44m and scandium-44g with deuterons on calcium-44: cross-section measurements and production yield calculations[END_REF] to form an in vivo 44m Sc/ 44g Sc generator providing an internal positron source for many hours of the 44m Sc half-life. The 44 Ca(d,2n) 44m,g Sc reaction was used in this series of experiments. The deuteron reaction on 43 CaCO 3 was also recently reported [START_REF] Bilewicz | Cyclotron production of theranostic pair 43 Sc-47 Sc on calcium targets[END_REF] as leading to the 43 Sc diagnostic radioisotope.

Besides the Sc positron emitters, prospective imaging radioisotopes-, the β - decaying 47 Sc radioisotope (T 1/2 = 3.35 d) is a candidate for employment as a low energy electron emitting therapeutic agent, constituting with one of the lighter Sc positron emitters an ideal theranostic pair. Its suggested fast or slow neutron production routes were investigated in a number of references [START_REF] Kolsky | Radiochemical purification of no-carrier-added scandium-47 for radioimmunotherapy[END_REF][START_REF] Mausner | Radionuclide development at BNL for nuclear medicine therapy[END_REF][START_REF] Majkowska-Pilip | Macrocyclic complexes of scandium radionuclides as precursors for diagnostic and therapeutic radiopharmaceuticals[END_REF][START_REF] Bartoś | New separation method of no-carrier-added 47 Sc from titanium targets[END_REF][START_REF] Połosak | Stability of 47 Sccomplexes with acyclic polyamino-polycarboxylate ligands[END_REF][START_REF] Müller | Promising Prospects for 44 Sc-/ 47 Sc-Based Theragnostics: Application of 47 Sc for Radionuclide Tumor Therapy in Mice[END_REF]Domnanich et al., 2017) together with (γ,p) reactions (Habs and Koester, 2011;[START_REF] Mamtimin | Sc-47 production from titanium targets using electron linacs[END_REF][START_REF] Rotsch | Electron linear accelerator production and purification of scandium-47from titanium dioxide target[END_REF]. Research into a production method and radiopharmaceutical preparations based on this radioisotope was recently proposed within the IAEA Coordinated Research Project (CRP) [START_REF] Iaea | Call for Coordinated Research Project[END_REF]. Its accelerator production was discussed in this research project and also recently announced [START_REF] Bilewicz | Cyclotron production of theranostic pair 43 Sc-47 Sc on calcium targets[END_REF][START_REF] Bilewicz | New Cyclotron Method for 47 Sc Production and Conjugation of 47 Sc to Monoclonal Antibodies[END_REF]. Quite recently it was also studied by some of us [START_REF] Misiak | 47 Sc production development by cyclotron irradiation of 48 Ca[END_REF] using the 60 MeV proton cyclotron in Kraków with a natural CaCO 3 target. In the present, independent investigation the 28 MeV proton beam from the cyclotron at NCNR, Świerk was used to irradiate natural as well as isotopically enriched 48 CaCO 3 targets and a 48 TiO 2 target. Finally, for verification purposes natural CaCO 3 and natural TiO 2 targets were irradiated with the lowest (33 MeV) available energy energy from the Arronax cyclotron.

After the publication of the alpha particle routes for the formation of the two lightest Sc radioisotopes, in the present paper we investigate their production efficiency using proton and deuteron beams. However, we demonstrate that in order to achieve the best efficiency or isotopic purity the necessary energy of these projectiles in some cases should be above the energies available from most popular medical accelerators. In the case of the therapeutic 47 Sc we also compare the production efficiency and radioisotopic purity of this isotope formed via the proton and alpha particle routes.

The experimental data gathered using proton and deuteron beams are compared with the evaporation code EMPIRE and the TENDL library, based on TALYS evaporation model calculations.

Our experimental determinations of the Thick Target Yield [START_REF] Krasnov | Thick target yield[END_REF] of 43 Sc and 44g Sc are also compared with the values calculated using the experimental cross-section data from two very recently published papers dealing with the determination of the cross-section for the production of positron emitting Sc radioisotopes by proton induced reactions on Ca targets [START_REF] Carzaniga | Measurement of 43 Sc and 44 Sc production cross-section with an 18 MeV medical PET cyclotron[END_REF][START_REF] Alabyad | Experimental measurement and theoretical calculations for proton, deuteron and α-particle induced nuclear reactions on calcium: special relevance to the production of 43,44[END_REF].

Finally, a review paper dealing, among others, with the status of the production routes and theranostic applications of medical Sc radioisotopes appeared very recently [START_REF] Müller | Scandium and terbium radionuclides for radiotheranostics: current state of development towards clinical application[END_REF]. Some questions, raised in this review are answered in the present publication.

MATERIALS AND METHODS

The accelerators employed

The target irradiations with protons were performed using three cyclotrons: a GE PETtrace p/d machine with a nominal energy of 16.5 MeV (p) and 8.4 MeV (d), a homemade C30 proton cyclotron (Sura et al., 1981;Marti ed. 2001) and for some control measurements the ARRONAX machine [START_REF] Poirier | The C70 Arronax and beam lines status[END_REF]. The first cyclotron is operated at the Radiopharmaceuticals Production and Research Centre put into operation by the Heavy Ion Laboratory, University of Warsaw a few years ago [START_REF] Choiński | The Radiopharmaceuticals Production and Research Centre established by the Heavy Ion Laboratory of the University of Warsaw[END_REF]. This cyclotron was recently equipped with an external beam line for solid sample irradiations, also allowing a good cooling conditions for these samples [START_REF] Choiński | Accelerator production of 99m Tc-an external, well cooled, target holder for the PETtrace cyclotron[END_REF]. During the experiments described here the maximum proton energy impinging on the irradiated samples was determined by calculating the beam current as a function of the beam energy for a few monitor reactions, the cross-sections of which were taken from the most recent IAEA compilation (IAEA, 2017). The proton energy was assumed to correspond to the minimum value of the standard deviation between the calculated beam currents. The upper part of Fig. 1 presents an example of such a beam energy determination. The cyclotron energy can also be determined from the saturation activity ratio of the monitor reactions, as proposed by the Jülich group [START_REF] Piel | Excitation Functions of (p,xn)-Reactions on natNi and Highly Enriched 62Ni: Possibility of Production of Medically Important Radioisotope 62Cu at a Small Cyclotron[END_REF][START_REF] Spellerberg | Target development for diversified irradiations at a medical cyclotron[END_REF]. This is presented in the lower part of Fig. 1, taking into account all the sensitive saturation activity ratios of radioisotopes produced in the monitor foils employed. The adopted beam energy irradiating the investigated CaCO 3 samples in the PETtrace external beam line was assessed as 15.2±0.1MeV (15.3 MeV-½ the energy degradation in the monitor foils). The maximum deuteron energy was correspondingly assumed to be 6.8 MeV. The maximum C30 proton energy was determined using the TOF method as equal to 28.0±0.5 MeV and the ARRONAX machine proton energy was 33.0±0.5 MeV as given by the producer and confirmed by the saturation activity ratio determination.

Calcium and Titanium targets for proton and/or deuteron irradiation

The majority of the studies on the production of Sc radioisotopes have been performed using calcium carbonate as target material. The ARRONAX group (Alliot et al., 2015b) used a thick target of 96.9% enriched 44 CaCO 3 for production of 44m Sc/ 44g Sc in vivo positron generator with a deuteron beam. Similar studies of the production (with protons) and investigation of the 44g Sc radioisotope employed a thin enriched 44 CaCO 3 target [START_REF] Bartoś | New separation method of no-carrier-added 47 Sc from titanium targets[END_REF][START_REF] Krajewski | Cyclotron production of 44 Sc for clinical application[END_REF][START_REF] Müller | Promising Prospects for 44 Sc-/ 47 Sc-Based Theragnostics: Application of 47 Sc for Radionuclide Tumor Therapy in Mice[END_REF][START_REF] Van Der Meulen | Cyclotron production of 44 Sc: From bench to bedside[END_REF]. Quite recently the PSI group (Domnanich et al., 2016) employed a thick target composed of the enriched Ca or Ti material backed by graphite to produce 43 Sc. Pure metallic targets (natural thick target -Wisconsin-Madison group [START_REF] Severin | Cyclotron Produced 44g Sc from Natural Calcium[END_REF][START_REF] Hernandez | 44 Sc: An Attractive Isotope for Peptide-Based PET Imaging[END_REF][START_REF] Valdovinos | Separation of cyclotron-produced 44 Sc from a natural calcium target using a dipentylpentylphosphonate functionalized extraction resin[END_REF] or water target (water solution of natural calcium nitrate -Vancouver group [START_REF] Hoehr | 44g Sc production using a water target on a 13 MeV cyclotron[END_REF] have also been used for the production of 44g Sc.

In the present studies of the reaction characteristics -as a function of projectile energy we used pellet targets designed as a homogenous mixture of the enriched target material, CaCO 3 or TiO 2, with graphite [START_REF] Stolarz | Targets for production of the medical radioisotopes with alpha and proton or deuteron beams[END_REF]. The content of the enriched material in the mixture varied from 10 to 25% for CaCO 3 and for TiO 2 it was 20%.

This method allows the production of thin as well as thick targets with low content of enriched material, while preserving the thickness of the target, ensuring the required decrease in the projectile energy. In a number of irradiations, determining the reaction yield natural CaCO 3 targets, prepared in a similar way were also used.

Thin foils beam monitors made of nat. Cu, Ni or Ti were added to each target. The thicknesses of the target and aluminium foil acting as energy degrader corresponded to the desired reaction cross-section range in the target material.

Data acquisition and evaluations

The data acquisition systems and evaluations methods were identical to those previously described for alpha particle induced reactions [START_REF] Szkliniarz | Production of medical Sc radioisotopes with an alpha particle beam[END_REF]. For the sake of completeness, they are briefly summarized below.The gamma ray spectra of the irradiated samples were collected using two HPGe counters (EG&G ORTEC, model: GEM, HPGe 70.1 mm x 69.8 mm, 60% efficiency and CANBERRA, model: BE2825, thickness: 25.5 mm, active area: 2800 mm 2 , with 0.6 mm thick Carbon Epoxy window). Shortly after irradiation the samples were placed at approximately 1 m distance from the detector. Later they were placed inside 10 cm thick Pb shielding (selected for its low background). A supplementary Sn-Cu inner shielding (2.5 mm thickness of Sn and 0.5 mm thickness of Cu) eliminated a large part (around 97%) of the Pb fluorescence X-ray peaks caused by the sample radiation. Data were collected using the TUKAN8k/National Centre for Nuclear Research system. The gammaray spectra were analyzed using the TUKAN8k/National Centre for Nuclear Research software. The samples irradiated using the C30 cyclotron in Świerk were first measured using a HPGe EG&G ORTEC vertical detector, model: GMX-25190-p, 56.8 mm x 70.0 mm with a 0.5 mm thick Be window and analyzed using Gamma Acquisition & Analysis V1.4, Copyright 1999 By Canberra Industries. They were transported to the HIL counting system later in the day of irradiation and their subsequent decay was also followed. The samples irradiated using the ARRONAX cyclotron were measured using a HPGe CANBERRA detector with efficiency 20% at 1.33 MeV and analyzed using FitzPeaks software.

Typical detector dead time during the measurements was below 10%. The energy calibrations and absolute efficiencies of the HPGe detectors were determined using calibrated 133 Ba, 137 Cs, 152 Eu and 241 Am sources (with an uncertainty in their activity below 3%).

After the series of gamma-ray spectra measurements for each sample the half-lives of the observed lines were determined and compared with data from the literature. Using their observed activities A(T) at measuring time T the radioisotope activity produced at the End of Bombardment (A EOB ) was calculated. Similarly, following the prescription of Ref. [START_REF] Krasnov | Thick target yield[END_REF] the experimental Thick Target Yields (in MBq/µAh) were calculated from the formula:

TTY exp = λ A exp(λT)/{I (1-exp(-λt))},
where λ is the decay constant of the product and t is the irradiation time. These values were compared with the theoretical Thick Target Yields, TTY σ, from the formula (1) of Ref. [START_REF] Szkliniarz | Production of medical Sc radioisotopes with an alpha particle beam[END_REF] using the calculated cross-section values. The cross-sections of the studied reactions were obtained using the EMPIRE [START_REF] Herman | EMPIRE: Nuclear Reaction Model Code System for Data Evaluation[END_REF] evaporation code and the TENDL cross-section library [START_REF] Koning | Modern Nuclear Data Evaluation with The TALYS Code System[END_REF]. The default option was used for the model parameters. In Fig. 2 the calculated cross-sections of the proton and deuteron induced reactions on 42,43,44 Ca isotopes as obtained with the EMPIRE code are shown. (The TENDL library gives very similar results with the exception of the deuteron induced reactions on a 42 Ca target, see below). Fig. 3 shows the crosssections of the Sc isotopes produced on the 48 Ca target calculated with the same code: the (p,2n) reaction leading to 47 Sc and (p,n) and (p,3n) to the produced impurities. Finally, in Fig. 4 the cross-sections of the proton induced reactions on a 48 Ti target are shown. The theoretical TTY th are calculated using the crosssections for incident energies from the particle bombarding energy impinging on the target down to the point when the cross-section becomes zero. Target Yield, TY are used, instead of the Thick Target Yield for cases when the target thickness is smaller than the projectile range with non-zero reaction cross-section. The experimental A EOB , Thick Target Yields (TTY) or Target Yields (TY), as determined for the investigated radioisotopes are presented in Tables 3, 4 and 6.

RESULTS AND DISCUSSION

Production of 43 Sc radioisotope

The production of 43 Sc using protons at energies available from medical accelerators was most recently investigated by the Bern-PSI group (Domnanich et al., 2016a(Domnanich et al., , 2017)). The 43 Ca(p,n) 43 Sc and 46 Ti(p,α) 43 Sc reactions were used.

In the present work two ways of producing 43 Sc were investigated: following our previous communication [START_REF] Bilewicz | Cyclotron production of theranostic pair 43 Sc-47 Sc on calcium targets[END_REF] the (d,n) reaction on a 42 CaCO 3 target and the (p,n) reaction on a 43 CaCO 3 target. The Thick Target Yields for various proton bombarding energies are presented in Table 3 and for deuterons in Table 4. The EOB activities and produced impurities for 15.2-2.2 MeV proton energy and 6.8-0 MeV deuteron energy are given in Table 5. The Thick Target Yield data of both reactions are compared to the theoretical values in Fig. 5.

From Figs. 2 and 5 it is evident that deuterons with energies of around 7 MeV produce only half of the possible 43 Sc activity in this reaction. A deuteron energy of 15 MeV, only available from cyclotrons with 30 MeV proton beams would double the 43 Sc production yield. The (p,n) reaction on presently available 43 CaCO 3 targets (enriched to 90% with 4.4% 44 Ca content) gives a much higher TTY value but with about 11% 44 Sc impurity.

We have previously shown [START_REF] Szkliniarz | Production of medical Sc radioisotopes with an alpha particle beam[END_REF]) that if an alpha particle beam of energy around and above 20 MeV is available, the formation of very pure 43 Sc radioisotope using an extremely cheap natural CaCO 3 target may well be the most preferred production method, even avoiding the target recovery process.

Production of 44g Sc and 44m Sc radioisotopes

The production and medical applications of the two 44 Sc isomers were previously investigated in a number of works indicated above. In our irradiations both natural as well as 94.8% isotopically enriched 44 CaCO 3 were used.

Besides 40 Ca the most abundant calcium isotope in the natural material is 44 Ca (2.086%). Therefore as the irradiation of 40 Ca by protons produces only short lived products, the natural target can be used for the preliminary, research production of 44 Sc. A number of such targets in CaCO 3 form were irradiated with the PETtrace proton beam for research on preclinical application of Sc radioisotopes by teams collaborating in the realization of a Polish Funding Agency NCBiR grant (Bilewicz et al., 2018;Mikołajczak et al., 2018;Kilian et al., 2018). For the 15.2 MeV proton energy, the TTY value obtained for 44 Sc was 17.2(6) MBq/µAh, with 3% of the largest impurity of 43 Sc. This value would be increased to about 47 MBq/µAh if metallic targets were used.

The Thick Target Yields of 44g Sc and 44m Sc determined for various proton energies are shown in Table 3. The EOB activities and relative activities of contaminating radioisotopes produced in these samples for 15.2-2.2 MeV proton energy are given in Table 5. In Fig. 6 the determined TTY values of 44g,m Sc are compared with the calculated ones and in Fig. 7 the evolution with time of the relative intensities of Sc isotopes. In Fig. 6 the data of Refs. [START_REF] Severin | Cyclotron Produced 44g Sc from Natural Calcium[END_REF][START_REF] Valdovinos | Separation of cyclotron-produced 44 Sc from a natural calcium target using a dipentylpentylphosphonate functionalized extraction resin[END_REF] are also shown. In these references, natural Ca metallic targets were irradiated. Therefore, the absolute values of TTY from these references were converted to CaCO 3 target equivalents, multiplying them by 0.36 to reflect the difference in target atomic mass and stopping power. After such a conversion, the metallic target data are about 40% lower than those obtained in our experiment and also as calculated using the evaporation model cross-section values. This discrepancy is due to the proton beam being wider than the hole in the aluminium ring on which the calcium was pressed in the Wisconsin experiments with the metallic targets (Valdovinos, 2017).

In Refs. [START_REF] Huclier-Markai | Optimization of reaction conditions for the radiolabeling of DOTA and DOTA-peptide with 44m/44 Sc and experimental evidence of the feasibility of an in vivo PET generator[END_REF]Alliot et al., 2015aAlliot et al., , 2015b;;[START_REF] Duchemin | Production of scandium-44m and scandium-44g with deuterons on calcium-44: cross-section measurements and production yield calculations[END_REF] the feasibility of the formation of an in vivo 44m Sc/ 44g Sc generator based on a high spin 44m Sc isomer with a 2.4 days half-life, decaying to the 3.97 h 44g Sc by a 271 keV (E4) transition was investigated. Irradiation of 44 Ca by a 16 MeV deuteron beam was proposed. The use of this reaction was motivated by the higher 44m Sc/ 44g Sc cross-section ratio in comparison with proton induced reactions on the same target. Similarly, in our recent paper [START_REF] Szkliniarz | Production of medical Sc radioisotopes with an alpha particle beam[END_REF] we discussed the production of this isomeric state using a 29 MeV alpha-particle beam and we demonstrated that for this projectile the measured ratio of the Thick Target Yield, TTY 44m Sc/ 44gd Sc is about 20 times larger than for 16 MeV proton induced reactions and almost 5 times larger than for 15 MeV deuteron induced reactions. Therefore, the production of 44m Sc using this irradiation route may be of interest. However, the much lower 44m Sc production cross-section for protons is compensated for by the substantially larger projectile range in a thicker target (smaller stopping power for this projectile). As a result, as demonstrated in our above mentioned reference, the Thick Target Yield and the EOB activity of 44m Sc is similar for protons as for deuterons and alpha particles, only with a much longer cooling time necessary for lighter projectiles. This is shown in Fig. 8 comparing the activity evolution of 44m,g Sc produced using beams of protons, deuterons and alpha-particles of the same intensity impinging on 100% enriched, thick CaCO 3 targets. However, in considering the in vivo 44m Sc/ 44g Sc generator production two other aspects should be taken into account. Namely, the enriched 42 Ca target for the alpha-particle irradiations is about 4 times more expensive than the 44 Ca for deuteron and proton induced reactions. On the other hand, to generate the same 44m Sc thick target activity a much thicker target is necessary for deuterons and protons which compensates for the price difference but leads to a lower specific activity of samples prepared by deuteron bombardment and much lower by the proton route. All these aspects should be considered for large scale in vivo scandium generator production.

Production of 47 Sc radioisotope

In the above mentioned first report of the Coordinated Research Project a number of possible nuclear reactions to produce 47 Sc with a 3.35 d half-life are listed. We have previously investigated [START_REF] Szkliniarz | Cyclotron production and research of radioisotopes for diagnostic and medical therapy[END_REF] 47 Sc production via the (α,n) reaction on a nat CaCO 3 target. Independently, shortly before our investigation 47 Sc production by an alpha particle beam was studied in a paper by a Japanese group [START_REF] Minegishi | Production of scandium-43 and -47 from a powdery calcium oxide target via the nat/44 Ca(α,x)-channel[END_REF] We have calculated using the natural target data measured at 20 MeV alpha particle bombarding energy a TTY value of 47 Sc equal to 1.0(1) MBq/µAh for a highly enriched 44 CaCO 3 target with a strong contamination of relatively short lived 43 Sc (about 28%) and the dangerous long lived 46 Sc (1.3% at EOB after 12 h irradiation). Using the EMPIRE evaporation code, we estimated that rather pure 47 Sc can be formed at a bombarding energy of 16 MeV. At this energy, however, the calculated 47 Sc TTY value for 95% enrichment of 44 CaCO 3 is only about 0.5 MBq/µAh, much below the possibilities for practical use of this production route with presently available alpha-particle beam intensities at the currently operating accelerators.

The proton route 48 Ca(p,2n) 47 Sc was recently investigated by some of us using the Kraków cyclotron, delivering a 60 MeV proton beam [START_REF] Misiak | 47 Sc production development by cyclotron irradiation of 48 Ca[END_REF] irradiating a natural CaCO 3 target. In the present, independent investigation the C30 cyclotron at Świerk and the Arronax machine were used, irradiating a 62.9% enriched 48 CaCO 3 target and natural CaCO 3 targets as well as a titanium dioxide target.

From Fig. 3 it is clear that only a small energy region may be available for this reaction without important production of impurities: the (p,n) reaction leads to the slightly shorter lived 44 h 48 Sc whereas the (p,3n) reaction produces the much longer lived 84 d 46 Sc. Both these impurities emit a number of high energy gamma lines and should be minimized or eliminated from the produced 47 Sc.

In Fig. 9 the determined Thick Target Yield of 47 Sc by the (p,2n) reaction on a 97.1% 48 CaCO 3 target for different energies is shown and compared with TENDL library and EMPIRE evaporation code predictions. The presented data are deduced from experiments with proton energies of 15.2 -2.2 MeV, MeV. The analysis of the measured spectra indicates that only the 22.8-17.1 MeV proton energy range may be considered as appropriate. In Fig. 12 the evolution with time of Sc and Ca isotopes produced in a 97.1% 48 Ca sample after a 8 h proton bombardment is presented. Although for this energy range the EOB activity of the long lived 46 Sc impurity is not observed the 48 Sc activity represents about 26% of the 47 Sc activity (Table 5). Assuming that 380 h cooling time is applied to the 48 Ca sample irradiated with a 1 µA proton beam the observed gamma ray spectrum does not indicate other strong contaminant activities. At this time after EOB the 47 Sc activity is 26 MBq. Therefore, with a 100 µA beam intensity the 48 Ca target should be irradiated for 10 h in order to obtain 3 GBq of 47 Sc at 380 h after EOB with 1% of 48 Sc contamination. Assuming that there is no biological excretion i.e. that this 1% 48 Sc activity remains in the patient till complete decay, the received supplementary dose coming from 48 Sc activity would be about 54 mSv (IAEA, 2011). Similarly, a cooling time of 120 h leads to 21 GBq of 47 Sc with 10% of 48 Sc. A fraction of 2 GBq of 47 Sc extracted from it comes with a 48 Sc impurity that leads to 340 mSv supplementary dose.

It is worth mentioning here that in Ref. [START_REF] Misiak | 47 Sc production development by cyclotron irradiation of 48 Ca[END_REF] for an energy range very similar to ours of 24.1 -16.9 MeV the contribution of 48 Sc was found to be more than a factor 1.4 lower than determined in the present work. The reason for this discrepancy, illustrated in Fig. 10, is unknown. The similar comparison for 47 Ca production is showed on Fig. 11.

A relatively cheap 48 Ti target was used for the investigation of a second route suggested in the IAEA Report (IAEA, 2016) namely the 48 Ti(p,2p) 47 Sc reaction. The calculated cross-sections for this reaction are presented in Fig. 4, together with the cross-sections of the generated impurities. The irradiation experiment was performed using the C30 cyclotron at Świerk, with 15 nA of 27.7 MeV protons impinging on a thick 48 TiO 2 target during about 5 h and verified by the irradiation of a natural TiO 2 target with 28.0-18.3 MeV protons during 20 min at the ARRONAX facility.

Table 6 shows the Thick Target Yield of 47 Sc, the 47 Sc activity after 8 h of irradiation with a current of 1 µA of a 48 Ti target. At EOB, the strongest impurity activity belongs to 44g Sc, produced in seven reaction paths [START_REF] Soppera | JANIS Book of proton-induced cross-sections[END_REF]. It can be calculated that 40 h after EOB the 44g,m Sc activities each represent about 70% of the 47 Sc activity and could perhaps be used (after a slightly longer cooling time) within the same sample irradiation as diagnostic partners of 47 Sc. However at this time the produced activity with a 100 µA proton beam would be only 2 GBq, with 0.03% contamination of the dangerous 46 Sc radioisotope.

SUMMARY AND CONCLUSIONS

The 43 Sc and 44 Sc medical radioisotopes previously investigated using alpha particle beams were produced in the present work with proton beams and 43 Sc also by deuteron beams. A third Sc isotope produced by protons was added to this investigation, namely the therapeutic 47 Sc, a theranostic partner of the 43 Sc or 44 Sc positron emitters. The Thick Target Yield and the isotopic purity of the produced positron emitters were determined and compared with evaporation model predictions.

It was deduced that the most appealing route for the production of the 43 Sc radioisotope would be irradiation of natural CaCO 3 or metallic Ca targets with an alpha-particle beam of energy around and above 20 MeV. Reasonable sample intensities and acceptable isotopic purity would be obtained in 15 MeV deuteron induced reactions on isotopically enriched 42 CaCO 3 . The proton irradiation of 43 CaCO 3 , although with substantially higher efficiency than the deuteron route, leads to samples with about 10% of 44 Sc impurity with the presently available enrichments.

Substantial quantities of relatively pure (impurities equal to or below 3%) 44g Sc can be produced using a 15 MeV proton beam impinging on natural CaCO 3 or metallic Ca targets. At this proton energy using an enriched 44 CaCO 3 target the very high Thick Target Yield of about 800 MBq/μAh was determined for the ground state of 44 Sc. Although at this bombarding energy the TTY of 44m Sc is about 200 times lower, it was estimated that about 1 GBq of this isomer without directly produced ground state activity can be obtained during 12 hours irradiation of a 100% enriched sample with 25 μA proton beam current followed by 40 h cooling time.

There is growing interest in the accelerator production of the therapeutic 47 Sc radioisotope which may be considered as a theranostic partner of the above discussed Sc positron emitters. Although fast and slow neutron induced reactions were mainly used to date to produce substantial quantities of 47 Sc, the cyclotron routes were also advocated in the ongoing Common Research Project (CRP) of the IAEA (IAEA, 2016). We have previously produced this radioisotope with an alpha-particle beam [START_REF] Szkliniarz | Cyclotron production and research of radioisotopes for diagnostic and medical therapy[END_REF] but the determined TTY was too low to have practical applications with the presently available beam intensities. Two other reactions were investigated in the present work: 48 Ca(p,2n) 47 Sc and 48 Ti(p,2p) 47 Sc. As is evident from the calculated cross section values, these reactions can only be used to obtain relatively pure 47 Sc over a small energy range. Selecting this range for the first reaction from 23 to 17 MeV one obtains about 50 MBq/μAh for the Target Yield. However, at EOB these irradiation conditions give a contaminating activity of 48 Sc of about 26% of the 47 Sc. The yield is even lower for the second reaction investigated which also produces important impurities.

The experimental data obtained were compared with the evaporation code EMPIRE and the TENDL library, based on TALYS evaporation model calculations. The agreement between theoretical predictions and experimental data is with a few exceptions, rather good. (experimental data are recalculated for 95.9% target enrichment for deuterons and 90% for protons). TENDL data are taken from [START_REF] Koning | Modern Nuclear Data Evaluation with The TALYS Code System[END_REF] while EMPIRE from [START_REF] Herman | EMPIRE: Nuclear Reaction Model Code System for Data Evaluation[END_REF]. [START_REF] Severin | Cyclotron Produced 44g Sc from Natural Calcium[END_REF] and [START_REF] Valdovinos | Separation of cyclotron-produced 44 Sc from a natural calcium target using a dipentylpentylphosphonate functionalized extraction resin[END_REF] measured with a metallic target and converted to the 44 CaCO 3 equivalents are also shown. Additional TTY curves are calculated from cross-section data measured by (Carzianga et al., 2017) and [START_REF] Alabyad | Experimental measurement and theoretical calculations for proton, deuteron and α-particle induced nuclear reactions on calcium: special relevance to the production of 43,44[END_REF].

TABLES

FIGURESFig. 1 .

 1 FIGURES

Fig. 2 .

 2 Fig. 2. Calculated cross-sections for the production of 43 Sc and 44 Sc radioisotopes with proton and deuteron projectiles. The EMPIRE (Herman et al., 2007) evaporation code was employed.

Fig. 3 .

 3 Fig. 3. Calculated cross-sections for proton induced reactions with the emission of 1, 2 and 3 neutrons on a 48 Ca target. The EMPIRE (Herman et al., 2007) evaporation code was employed.

Fig. 4 .

 4 Fig. 4. Calculated cross-sections for the production of 47 Sc, 46 Sc and 44 Sc radioisotopes with proton beams on 48 Ti target. The EMPIRE (Herman et al., 2007) evaporation code was employed. The symbol * indicates other reaction channels considered: (p,α+n) + (p,d+t) + (p,n+p+t) + (p,2n+ 3 He) + (p,n+2d) + (p,2n+p+d) + (p,3n+2p).

Fig. 5 .

 5 Fig. 5. Comparison of the experimentally determined 43 Sc Thick Target Yield with the theoretical estimates for a deuteron beam impinging on an isotopically enriched 42 CaCO 3 target and protons impinging on enriched 43 CaCO 3 (experimental data are recalculated for 95.9% target enrichment for deuterons and

Fig. 6 .

 6 Fig. 6. Measured Thick Target Yields of 44g Sc and 44m Sc radioisotopes produced in the 44 Ca(p,n) reaction compared with the theoretical predictions based on TENDL cross-section and EMPIRE evaporation code calculations. The data from Refs.[START_REF] Severin | Cyclotron Produced 44g Sc from Natural Calcium[END_REF] and[START_REF] Valdovinos | Separation of cyclotron-produced 44 Sc from a natural calcium target using a dipentylpentylphosphonate functionalized extraction resin[END_REF] measured with a metallic target and converted to the 44 CaCO 3 equivalents are also shown. Additional TTY curves are calculated from cross-section data measured by(Carzianga et al., 2017) and[START_REF] Alabyad | Experimental measurement and theoretical calculations for proton, deuteron and α-particle induced nuclear reactions on calcium: special relevance to the production of 43,44[END_REF].

Fig. 7 .

 7 Fig. 7. Evolution with time of the relative intensities of Sc radioisotopes produced during a 4 h irradiation of a 44 CaCO 3 (94.8%) target with a 15.2-2.2 MeV proton beam.

Fig. 8 .

 8 Fig. 8. Activity of produced samples of 44m,g Sc after 12 h irradiation time of a thick target with proton, deuteron and alpha particle beams of 25 μA intensity.

Fig. 9 .Fig. 10 .

 910 Fig.9. Measured Thick Target Yield of 47 Sc obtained using the 48 Ca(p,2n) reaction with theoretical predictions based on EMPIRE[START_REF] Herman | EMPIRE: Nuclear Reaction Model Code System for Data Evaluation[END_REF] evaporation code calculations and TENDL[START_REF] Koning | Modern Nuclear Data Evaluation with The TALYS Code System[END_REF] predictions. The experimental data are converted to 97.1% 48 CaCO 3 target enrichment. The data of Ref.[START_REF] Misiak | 47 Sc production development by cyclotron irradiation of 48 Ca[END_REF] are obtained from their partial yields in the measured energy intervals adding the interpolated, not measured values.

Fig. 11 .

 11 Fig. 11. The same as Fig. 8 but for the 48 Ca(p,x) 47 Ca reaction.

Fig. 12 .

 12 Fig. 12. Evolution with time of the relative intensities of radioisotopes produced on Ca during an 8 h irradiation of a 48 CaCO 3 target with a 22.8-17.1 MeV proton beam. The experimental data are converted to 97.1% 48 CaCO 3 target enrichment.

Table 1

 1 Isotopic composition of calcium carbonate targets made of natural and isotopically enriched materials. (The isotopes with the quoted enrichment values are available from ISOFLEX, USA).

	40 Ca[%

] 42 Ca[%] 43 Ca[%] 44 Ca[%] 46 Ca[%] 48 Ca[%]

	nat Ca*	96.94	0.647	0.135	2.086	0.004	0.187
	42 Ca*	29.9	68	0.4	1.5	<0.01	0.2
	42 Ca	3.24	95.9	0.13	0.7	<0.01	0.03
	43 Ca*	23.8	1.0	62.2	12.8	<0.01	0.2
	43 Ca	5.3	0.18	90	4.44	<0.01	0.08
	44 Ca*	5.03	0.1	<0.01	94.8	<0.01	<0.05
	48 Ca*	27.9	0.3	0.1	2.2	<0.1	69.2
	48 Ca	2.72	0.02	0.01	0.15	<0.01	97.1
	*Used in the experiments.

Table 2

 2 Isotopic composition of the titanium dioxide target made of isotopically enriched material.

46 Ti [%] 47 Ti[%] 48 Ti[%] 49 Ti[%] 50 Ti[%]

	48 Ti	0.09	0.1	99.63(10)	0.12	0.06

Table 3

 3 Comparison of the measured Thick Target Yield [MBq/µAh] of the medical Sc radioisotopes for the different CaCO 3 targets irradiated with proton beams with various energies.

	Isotope:	43 Sc	44gd Sc	44m Sc	47 Sc
	Target and enrichment:	43 CaCO 3 (90%)	nat CaCO 3	44 CaCO 3 (94.8%)	44 CaCO 3 (94.8%)	48 CaCO 3 (97.1%)
	p energy [MeV]		Thick target yield [MBq/µAh]
	7.6	61(6)	2.6(4)	120(20)	0.13(5)
	9.7	109(11)	6.1(4)	280(20)	0.40(4)	0.47(5)
	10.7	180(20)	8.2(9)	370(40)	0.84(5)	2.1(2)
	11.3		8.7(9)	400(40)	1.5(1)
	11.9	200(20)	11(1)	500(50)	1.3(2)	6.8(8)
	12.8	210(20)	11(1)	490(50)	2.0(2)	10(1)
	14.3	260(30)	16(1)	730(50)	2.7(3)	21(2)
	15.2	317(14)	17.2(6)	780(30)	3.6(1)	31(2)
	17.5	410(40)
	21.8		23(1)	1030(50)	5.9(3)	94(6)
	22.0		22(2)	980(100)	7.5(8)
	22.4					98(5)
	22.8		21(1)	940(40)	7.0(2)	105(6)
	28.2					136(8)
	28.5		23(1)	1020(50)	8.0(4)	139(16)

Table 4 .

 4 Comparison of the measured Thick Target Yield [MBq/µAh] of the medical 43 Sc radioisotope irradiated with deuteron beams in two energy ranges.

	Isotope:	43 Sc
	Target and	42 CaCO 3
	enrichment:	(95.9%)
	d energy	TTY
	[MeV]	[MBq/µAh]
	4.7-0	5.6(8)
	6.8-0	45(4)

Table 5

 5 Examples of the deduced End of Beam intensities and relative impurities in medical Sc samples, produced with the available, most enriched (see Table2) CaCO 3 targets using proton and deuteron beams.

			43 Sc	44 Sc	47 Sc
	irradiation time	4 h	4 h	8 h
			proton beam (1 µA)
	energy [MeV]	15.2 -2.2	15.2 -2.2	15.2 -2.2	22.8 -17.1
	target		43 CaCO 3 (90%)	nat CaCO 3	44 CaCO 3 (94.8%)	48 CaCO 3 (97.1%)
	EOB [MBq]	910(40)	50(2)	2240(80)	420(40)
		43 Sc 100	3.0(2)	0.0049(6)	0.25(4)
		44 Sc 12.0(1.5)	100	100	0.106(13)
	relative	44m Sc 0.95(12)	0.62(3)	0.62(3)	0.0077(9)
	intensity	47 Sc 0.0131(17)	0.56(7)	0.0033(4)	100
	at EOB	48 Sc 0.025(3)	1.1(1)	0.0063(8)	26(3)
		47 Ca 0.00033(5)	0.014(2)	8.4(12)E-5	13.0(1.6)
		43 K				0.0096(13)
			deuteron beam (1 µA)
	energy [MeV]	6.8-0
	target		42 CaCO 3 (95.9%)
	EOB [MBq]	129(11)
		43 Sc 100
	relative	44 Sc 0.25(16)
	intensity	44m Sc 0.0054(19)
	at EOB	47 Sc 0.0019(2)
		48 Sc 0.06(2)

Table 6 47

 6 Sc production results extrapolated for 8 h irradiation time with 1 µA of proton beam and a 48 TiO 2 (99.63%) target for proton energy 28.0-18.3 MeV.

	projectile energy	28.0-18.3 MeV
	47 Sc TY [MBq/µAh]		2.6(5)
	measuring time	at EOB	40 h post-EOB
	activity 47 Sc [MBq]	20(4)	14(3)
		47 Sc	100	100
		43 Sc	4.3(1.2)	0.0048(14)
	relative	44g Sc	170(40)	71(19)
	isotopic	44m Sc	80(20)	66(18)
	activities	46 Sc	0.033(9)	0.046(12)
		48 Sc	0.08(2)	0.058(15)
		48 V	190(50)	250(60)

ACKNOWLEDGEMENTS

The authors warmly thank the PETtrace operation team for running a number of the beam hours necessary for the research described in this paper. Discussions with Krzysztof Ciupek , Nick Keeley and Ulli Koester, are appreciated. Part of this work was performed within the framework of the EU Horizon 2020 project RIA-ENSAR2 (654 002). This research was also partly supported by the Polish Funding Agency NCBiR grant No. DZP/PBS3/2319/2014.


"Production of innovative radionuclides for therapy or diagnostic: nuclear data measurements and comparison with TALYS code"

Nuclear medicine Many useful / potentially useful isotopes identified for applications in nuclear medicine Cyclotrons and accelerators being used in an increasing number of countries along with reactors -Diagnosis (γ, β + ) -Therapy (β -, α, e Auger ) Nuclear data -Accurate and reliable sets of data -Well defined production routes and decay properties -Optimum production of specific radionuclides, minimization / elimination of impurities, realistic dose calculations Nuclear data needs addressed by successive: -Experimental physicist generations -IAEA Coordinated Research Projects initiated in the 90's, European FPs, national programs

Nuclear codes

Provide a large set of nuclear data in terms of targets, projectiles and energy range to constrain and develop predictive simulation tools of nuclear reactions 13/06

-Target/monitor/degrader pattern -Thin foils:

E loss small and constant -One cross section value per foil Activity and cross section:

σ = Act . A χ. Φ . 𝒩𝒩 A . ρ . e . (1 -e -λ.t ) σ = σ ′ . 𝜒𝜒 ′ .

Use of a Faraday cup:

-Beam dump placed at the end of the stack to control the intensity during the irradiation To achieve:

-optimum production of specific radionuclides -minimization or elimination of impurities -realistic dose calculations

Comparisons have been performed systematically with the TALYS 1.9 code -state of the art models included -possibility to combine models to better describe data -a set of models have been found to allow a good description of all our collected data

  of radioisotopes with very different characteristics is suitable: -Radiation type for the different applications -Half-life to match the bio-distribution time -Chemical properties to attach to the vector molecule -Production yields to get the purest product -Prod. capacities to envisaged large scale use The nuclear physicist could have crucial contribution: -Identify production route and define production process (spallation, fission or activation) -Identify and quantify contaminants -Define waste management process -Discuss with physicians to promote its use Over the last years, several radionuclides have emerged: -β + : Cu-64, Ga-68, Zr-89 … -γ: Sn-117m … -β -: Ho-166, Lu-177 … -α: At-211, Bi-212, Bi-213, Ra-223, Ac-225 ... -Theranostic: Sc-44/Sc-47, Cu-64/Cu-67, Ga-68/Lu-177 … -Auger: Sn-117m, Tb-155 (at the research level for the moment) Terbium quadruplet: Tb-149, 152, 155, 161To do so, we possess facility (will possess) available for irradiations equipped

-A

  HPGe coaxial detector γ spectra recorded on 8192 channels -Dead time: < 10% (sum peak) -FWHM:1.04 keV at 122 keV ( 57 Co) -Activity values: FitzPeaks 1.97 keV at 1332 keV ( 60 Co) -T 1/2 , E γ , I γ : Lund/LBNL, NNDC -Energy and efficiency calibrations: Co and Eu γ rays used to extract production cross section of 230,232,233 Pa Target and monitor:  counted twice  during > 24 hrs  2 large set of data have been collected using the stacked-foil technique at ARRONAX -with different type of projectiles (proton, deuteron and alpha particles) -for materials all over the mass range -for diagnosis and therapy purposes in nuclear medicine

Capsule and foils Irradiation station and beam line IAEA recommended cross sections:

	-11 reactions available for protons
	27 Al (2), nat Ni, nat Ti (2), nat Cu (5), nat Mo
	-11 reactions available for deuterons
	27 Al (2),

Act . A . ρ′ . e′ . (1 -e -λ ′ .t ) 𝜒𝜒. Act′ . A′ . ρ . e . (1 -e -λ.t )

Use of a monitor foil:

 error on e, e': ≤ 1%  error on t: negligible nat Fe, nat Ni(3), nat Cu (5), nat Ti(2) -6 reactions available for alpha-particles 27 Al (2), nat Ti and nat Cu (3)

TALYS

Code for the simulation of nuclear reactions Many state-of-the-art nuclear models

Provide a complete description of all reactions channels and observables

Nuclear reactions

Projectiles : n, p, d, t, He-3, α particles TALYS code version 1.9 the combination of models that best describes the whole set of available data for all projectiles, targets and incident energies defined by the TALYS authors TALYS 1.9 Default One combination of models that best describes our whole set of data for proton, deuteron, alpha particles as projectile (and also some literature data) has been defined by A. Guertin et al. TALYS 1.9 Adj.

Models


Salaheddine Chabab

Alain Valtz

Snaide Ahamada

Christophe Coquelet
email: christophe.coquelet@mines-paristech.fr

Hydrate Stability of carbon dioxide + oxygen binary mixture (CO 2 + O 2 ) in pure water: Measurements and modeling

Knowledge of the dissociation conditions of mixed-gas hydrate systems is of great importance for scientific understanding (e.g. Clathrate hydrates in the outer solar system) and engineering applications (e.g. flow assurance, refrigeration and separation processes). In this work, CO 2 +O 2 hydrate dissociation points were measured at different O 2 mole fractions (11%, 32% and 50%) using isochoric pressure search method. The consistency of these new data was verified using the Clausius-Clapeyron relationship. The measurements performed for pressures up to 19 MPa overcome the lack of data for this system, and also allows to evaluate the model predictions from pure CO 2 hydrate to pure O 2 hydrate. To predict gas hydrate stability curves, in this work, the well-established hydrate theory of van der Waals and Platteeuw (vdWP) is combined with an electrolyte CPA-type Equation of State (e-PR-CPA EoS) which has been successfully used to represent with high accuracy the fluid phase equilibria (including gas solubility and water content) of complex systems containing gas, water and salt. The resulting model (e-PR-CPA + vdWP) was applied to the O 2 +H 2 O and CO 2 +H 2 O+(NaCl) systems by comparing with literature data. In the studied temperature range (>270K), the model predicts as expected a hydrate structure of type I for O 2 , CO 2 and their mixtures. An excellent reproduction of the measured data by this complete model was obtained without any additional adjustable parameters.

Introduction

The growing integration of renewable energies, mainly intermittent (with issues of overcapacity and redundancy) in the short term (energy transition) and the total replacement of fossil hydrocarbons use in the long term, requires a flexible solution for large-scale energy storage. In the framework of the ANR (Agence Nationale de la Recherche) FLUIDSTORY project, a combination of Power-to-Gas (PtG) and Gas-to-Power (GtP) technologies with temporary underground gas storage is proposed as a solution for storing intermittent surplus renewable electricity while recovering and keeping CO 2 in a closed loop. To manage the temporal differences between the gas production from PtG and the gas consumption (GtP), this concept called EMO (Electrolysis-Methanation-Oxycombustion) involves the underground storage of these different energy carriers (O 2 , H 2 , CH 4 , CO 2 ) in salt caverns built in very tight salt layers, with very large volumes, and which can withstand very high pressures (that can exceed 200 bars depending on the depth of the reservoir). Under certain temperature and pressure conditions (especially at temperatures below the critical temperature of CO 2 and at high pressure), CO 2 can be stable in the liquid state, which is not desired in underground storage because of the thermal effects on the rock (the salt layer) due to the phase transitions that the gas undergoes. The proposed solution is the storage of CO 2 and O 2 in the same cavern. The mixing of the two gases reduces the critical temperature of the mixture (CO 2 +O 2 ) and keeps the gas in a supercritical state under the operating conditions of the storage.

However, for the design and simulation of storage facilities and also for the evaluation of possible risks, it is necessary to study the thermophysical properties of this mixture.

In some cases, the temperature in the storage reservoir may be low enough to form hydrates in the wellhead or in surface facilities (pipes, compressors, etc.) [START_REF] Habibi | An investigation into design concepts, design methods and stability criteria of salt caverns[END_REF][START_REF] Merey | Prediction of pressure and temperature changes in the salt caverns of Tuz Golu underground natural gas storage site while withdrawing or injecting natural gas by numerical simulations[END_REF] . The large temperature difference between the bottom of the reservoir and the wellhead is due to the thermal gradient that depends on the depth and nature of the geological formation and also due to the Joule-Thomson effect resulting from the rapid expansion (high flow rate) of the extracted gas. Kleinitz and Boehling 3 presented temperatures of some underground storage facilities showing the necessity of injecting hydrate inhibitors in the reservoir to avoid blockage of the flow path and possibly the stoppage of production for maintenance purposes. To limit these flow assurance issues, it is crucial to know the temperature and pressure conditions under which gas hydrates are stable. In addition, important properties to be studied for such storage applications include the gas density and viscosity, its solubility in brine, as well as gas hydrate stability curves. In our recent work, we have studied the density of the CO 2 +O 2 mixture [START_REF] Ahamada | Experimental density data of three carbon dioxide and oxygen binary mixtures at temperatures from 276 to 416 K and at pressures up to 20 MPa[END_REF] and the solubility of CO 2 5, 6 , O 2 [START_REF] Chabab | Measurements and modeling of high-pressure O2 and CO2 solubility in brine (H2O+NaCl)[END_REF] and H 2 [START_REF] Chabab | Measurements and predictive models of high-pressure H2 solubility in brine (H2O+ NaCl) for underground hydrogen storage application[END_REF] in brine under underground storage conditions. Herein, in the continuity of the previous work, we are interested in the study of the dissociation points of the hydrates of CO 2 , O 2 and their mixtures under the transport and storage conditions.

Generally thermodynamic models are parameterized only on binary systems by optimizing binary interaction parameters, and therefore thanks to mixing rules, phase equilibria (fluidfluid and hydrate-fluid) of multi-component (more than two compounds) systems can be predicted. This reduces the number of experiments required. However, a minimum of measurements must be performed to validate model predictions.

Several studies have reported dissociation point data for CO 2 and O 2 hydrates. However, to date there are no published data on the hydrates of the mixture of these two gases (CO 2 +O 2 ).

Chapoy et al. [START_REF] Chapoy | Effect of impurities on thermophysical properties and phase behaviour of a CO2-rich system in CCS[END_REF] measured and modelled a representative CO 2 -rich flue gas system in the presence of impurities (O 2 , Ar and N 2 ). This study and other ones [START_REF] Løvseth | CO2Mix Project: Experimental determination of thermo-physical properties of CO2-rich mixtures[END_REF][START_REF] Westman | Vapor-liquid equilibrium data for the carbon dioxide and oxygen (CO2+ O2) system at the temperatures 218, 233, 253, 273, 288 and 298 K and pressures up to 14 MPa[END_REF] showed that even in small concentrations, the presence of these impurities changes the phase diagram of the system. In a Joint Industry Project (JIP) report on the impact of impurities on the CCS chain, containing streams can also be used for other applications, for instance: 1) hydrate separation processes, in particular CO 2 capture from oxy-combustion flue gas [START_REF] Kang | Hydrate phase equilibria of the guest mixtures containing CO2, N2 and tetrahydrofuran[END_REF] which mainly contain CO 2 , O 2 and H 2 O by gas hydrates formation since CO 2 hydrates are more stable than other gas hydrates (flue gas impurities) [START_REF] He | A literature research on the performance evaluation of hydrate-based CO2 capture and separation process[END_REF] ; 2) the study of mixed gas hydrates in the outer solar system 14

; 3) and finally allowing the evaluation of predictive models.

In this work, CO 2 +O 2 hydrate dissociation points were measured at different O 2 mole fractions (11%, 32% and 50%) using isochoric pressure search method. In the second section of this paper, the experimental apparatus is described and the measured data are presented and checked. To predict the stability conditions of single-gas and mixed-gas hydrate systems, in the third section, a complete model for calculating hydrate-fluid and fluid-fluid phase equilibria is presented. It consists of a combination of the well-established hydrate theory of van der Waals and Platteeuw (vdWP) 15 with the e-PR-CPA Equation of State (EoS) 5 .

Experimental

Materials

In Table The principle of the experimental apparatus used to measure dissociation points of gas hydrates of the CO 2 +O 2 mixture is based on the isochoric pressure search method. The experimental device is illustrated in Figure 1 and is the same one used in the previous work at Armines -Mines ParisTech [START_REF] Hajiw | Impact of aromatics on acid gas injection[END_REF][START_REF] Tzirakis | Hydrate equilibrium data for the CO2+ N2 system with the use of tetra-n-butylammonium bromide (TBAB), cyclopentane (CP) and their mixture[END_REF][START_REF] Hajiw | Hydrate mitigation in sour and acid gases[END_REF] . It consists of a cylindrical constant volume (128 cm 3 ) equilibrium cell equipped with a Stirring Device (SD), two pressure transducers (LPT and HPT) to be more precise in each specific pressure range, a platinum resistance thermometer (PP) at the bottom of the cell (in aqueous phase) and introduced in a thermostatically controlled bath (LB) to maintain a constant temperature (TR). The evolution of temperature The measurement procedure summarized in Figure 2 consists of looking for the pressure at which the hydrates are completely dissociated. A gas mixture of a certain quantity and composition is introduced in the equilibrium cell which is previously evacuated and filled with a known quantity of water. The mixture is then strongly agitated (800 RPM). The temperature is decreased until the hydrate phase is formed (sudden pressure drop). The temperature is then increased stepwise by 1K until the dissociation pressure of the hydrate phase is reached. For each step of temperature increase, equilibrium conditions are reached by allowing enough time at each step (8h/step). The hydrate dissociation point is determined by the intersection of the thermal expansion curve of the fluid and the equilibrium heating cycle curve. Once the hydrate dissociation point (P, T) is determined, more gas is added to the equilibrium cell to measure another point, and so on until enough experimental points are obtained. Finally, the equilibrium cell is emptied, cleaned and evacuated.

Experimental results

The expanded uncertainties (with a coverage factor ) are between 0.1 and 0.6 K for temperature ( ) and between 0.04 and 0.25 MPa for pressure ( ). The measured data are listed in Table 3 and presented in Figure 3a. The aqueous fraction (AqFr, see Equation 2), which is the ratio between the number of moles of water and the total number of moles in the system (water and gas ), was determined for each measured point.

(2) 3) [START_REF] Sloan | Hydrate dissociation enthalpy and guest size[END_REF] , the evolution of the enthalpy of dissociation of the hydrate as a function of temperature is examined. Given the small temperature range, we can consider that the compressibility factor does not vary significantly, and since the enthalpy of dissociation does not vary rapidly [START_REF] Sloan | Hydrate dissociation enthalpy and guest size[END_REF] , this equation can be used in a small dissociation temperature range to check the linearity of the measured data in terms of as a function of 1/T.

(

) 3
where P and T are respectively the hydrate dissociation pressure and temperature (in equilibrium with the vapor (or liquid) and aqueous phases), R the ideal gas constant, Z the compressibility factor and the apparent enthalpy of dissociation of the hydrate phase.

The results of the consistency tests on the measured data are shown in Figure 3 (b, c andd).

Overall the measured data are consistent. . When a breakpoint is present, it means that we have gas hydrate when there is a phase split in the gas-rich phase (CO 2 +O 2 ) including a vapor phase and a CO 2 -rich liquid phase (other than the aqueous phase). In the modeling part (next section), the phase behavior (single-phase and two-phase) of the gas mixture in equilibrium with the aqueous phase and the hydrate phase is highlighted for the different CO 2 +O 2 mixture compositions. For the calculation of fluid phase equilibria with an equation of state, it is necessary to know the overall composition (or feed composition) of the system. However, generally, mixed-gas hydrate data are provided in terms of "water-free" gas composition ( ) and aqueous fraction AqFr ( ) (see Equation 2) in order to study hydrates with a fixed global gas mixture composition. In order to be able to model mixed-gas hydrate systems, we provide below the equations used to convert these "apparent" quantity (

) into "real" mole fractions ( , -).

Using Equation 2, the mole number of water is:

(4)
Considering a total mole number of 1 for the gas mixture ( and ),

the Equation 4becomes:

(5)

Finally, the real mole fractions are calculated by:

Applying Equation 6to water and a gas i, we obtain:

(7) (8)
The aqueous fraction has no effect on single-gas hydrate systems, since in two-phase thermodynamic equilibrium (which is always the case for gas-water systems), the calculation of the compositions in each phase of a binary system is independent of the global composition (using Gibbs' phase rules, the degree of freedom is two in this case, for example, in a liquidvapor PT-flash calculation, the same results of liquid x and vapor y compositions are obtained for any global composition z stable in the liquid-vapor state). However, for mixed-gas hydrate systems, the degree of freedom is higher than two, hence calculations of the hydrate dissociation conditions are sensitive to the aqueous fraction, and the composition of the gas-rich phase can vary significantly from the overall composition if one of the gases is more absorbed than the other in the hydrate.

At thermodynamic equilibrium, one can write the equality of the chemical potential of water in the liquid phase and in the hydrate phase. As illustrated in the schematic of Figure 4, the e-PR-CPA model calculates gas fugacities and the osmotic coefficient of water which is then transformed into water activity (Equation 10), in order to calculate the chemical potential of water in the liquid and hydrate phases. A multiphase flash [START_REF] Michelsen | The isothermal flash problem. Part I. Stability[END_REF][START_REF] Michelsen | The isothermal flash problem. Part II. Phase-split calculation[END_REF] is calculated at each step until the Hydrate-Liquid-Vapor (HLV) or Hydrate-Liquid-Liquid (HLL) equilibrium is reached.

Newton's method was applied to find the dissociation pressure at fixed temperature and the dissociation temperature at fixed pressure. The different terms of the vdWP model (Figure 4)

were calculated by the Munck et al. [START_REF] Munck | Computations of the formation of gas hydrates[END_REF] method.

The vdWP model derived from statistical thermodynamics is an established theory for the study of phase equilibria involving hydrates following the implementation proposed by Parrish and Prausnitz 23 . Since then, several studies have been published using this approach, therefore the vdWP model is very well described in the literature. The equations proposed by Munck et al. [START_REF] Munck | Computations of the formation of gas hydrates[END_REF] have been used in this work for the calculation of the chemical potential of water in the liquid and hydrate phase. However, since we use a different equation of state, a reparameterization of the parameters used in the calculation of the Langmuir constant is necessary.

A. e-PR-CPA EoS

A detailed description of the e-PR-CPA EoS equations and parameterization is given in our previous work [START_REF] Chabab | Thermodynamic study of the CO2-H2O-NaCl system: Measurements of CO2 solubility and modeling of phase equilibria using Soreide and Whitson, electrolyte CPA and SIT models[END_REF] . However, we recall here the main terms and definitions of the parameters.

For the modeling of complex systems including gas, water and ions, the e-PR-CPA EoS (expressed in terms of reduced residual Helmholtz free energy in Equation 9)

combines several terms to represent the different types of interactions in these systems. For molecular interactions, the selection concerns the well-known cubic term of Peng-Robinson (PR) [START_REF] Peng | A new two-constant equation of state[END_REF] to describe attractive and repulsive forces between species, and the Wertheim's association theory [START_REF] Wertheim | Fluids with highly directional attractive forces. I. Statistical thermodynamics[END_REF] used in SAFT and CPA -type EoS to describe association phenomena (self-association between identical molecules and cross-association between different molecules). For electrolyte interactions, the MSA theory (Mean Spherical Approximation) [START_REF] Blum | Mean spherical model for asymmetric electrolytes: I. Method of solution[END_REF] and the Born term [START_REF] Born | Volumen und hydratationswärme der ionen[END_REF] were chosen to represent ion/ion and ion/solvent (solvation) interactions, respectively.

Like most thermodynamic models, the parameterization of the e-PR-CPA EoS on pure and binary systems will allow to predict multicomponent (ternary, quaternary, etc.) systems.

However, comparison with some experimental data is necessary to verify if the model is well adapted to the studied systems. Concerning fluid phase equilibria modeling, the e-PR-CPA EoS counts for pure compounds:

 Five parameters for the solvent (water): three parameters ( , , ) to determine the energy parameter and the co-volume in the PR cubic term, and two parameters (association energy and bonding volume ) to calculate the Wertheim association term.

 Three parameters for each ion: three parameters ( , and ion diameter ) for the calculation of the energy parameter and the co-volume in the PR cubic term.

 No parameters for the gas (only the critical temperature and pressure and the acentric factor must be known, which is the case for all gases).

Halite is the main and almost "the only pure" mineral in salt layers where storage caverns are built, hence the water+NaCl mixture was chosen as a representative brine mixture. Before modeling phase equilibria involving fluid and hydrate phases, the osmotic coefficient of the aqueous electrolyte water+NaCl and the two-phase equilibria calculated by the e-PR-CPA must be verified. In Figure 5, the calculations at different salinities (in terms of NaCl molality: m=[mol/kg w ]) of the vapor pressure and the osmotic coefficient of the water+NaCl system by the e-PR-CPA EoS were compared with experimental literature data. As shown in the figure, the model accurately correlates these two properties and estimates their variation as a function of temperature and NaCl molality. The water activity used to calculate the chemical potential of water in the liquid phase (see Figure 4) is easily obtained from the osmotic coefficient by the following relationship (Equation 10):

where is the molar mass of water and is the molality of each ion (Na+ and Cl-in our case).

Concerning binary systems, generally a Binary Interaction Parameter (BIP or in the cubic term) is to be determined in particular for binaries whose species are not associative.

However, for mixtures of associative compounds, when solvation is possible, the crossassociation volume can be considered as a second adjustable parameter in order to improve the calculations [START_REF] Kontogeorgis | Solvation Phenomena in Association Theories with Applications to Oil & Gas and Chemical Industries[END_REF] . Since the e-PR-CPA EoS is reduced to the PR EoS in the case of systems that do not contain associative compounds and electrolytes (e.g. gas mixtures), it is possible to use parameters already available in the literature to represent this type of system.

In Table 4, the different parameters of the e-PR-CPA model as well as the thermophysical properties used for their determination (by optimization) are presented.

The parameters of the pure compounds as well as the interaction parameters of the CO 2 +H 2 O+NaCl and O 2 +H 2 O+NaCl systems used in this work are from our previous work [START_REF] Chabab | Thermodynamic study of the CO2-H2O-NaCl system: Measurements of CO2 solubility and modeling of phase equilibria using Soreide and Whitson, electrolyte CPA and SIT models[END_REF][START_REF] Chabab | Measurements and modeling of high-pressure O2 and CO2 solubility in brine (H2O+NaCl)[END_REF] . The binary interaction parameter ( ) used to represent Vapor Liquid Equilibria (VLE) of the CO 2 -O 2 binary system was taken from the work of Lasala et al. [START_REF] Lasala | VLE properties of CO2-Based binary systems containing N2, O2 and Ar: Experimental measurements and modelling results with advanced cubic equations of state[END_REF] .

In Figures 6 and7, the predictions of the VLE of the CO 2 +H 2 O+NaCl, O 2 +H 2 O+NaCl and CO 2 +O 2 systems by the e-PR-CPA EoS are compared to the experimental data. As shown in the figures, the e-PR-CPA EoS accurately estimates gas solubility in water and brine (Figures 6a and6b) and water content in gas-rich phases (Figure 7a) and captures very well the saltingout effect of gas due to the presence of NaCl under different thermodynamic conditions. The complete study of these systems as well as precise solubility data tables are provided in our previous work [START_REF] Chabab | Measurements and modeling of high-pressure O2 and CO2 solubility in brine (H2O+NaCl)[END_REF] . The VLE of the CO 2 +O 2 gas mixture calculated by the same model which is reduced to the PR EoS (since there are no electrolytes or associative compounds) are quite good, however this representation can be improved especially in the region of the critical points of the mixture by using other mixing rules (see Lasala et al. [START_REF] Lasala | VLE properties of CO2-Based binary systems containing N2, O2 and Ar: Experimental measurements and modelling results with advanced cubic equations of state[END_REF] and Ahamada et al. [START_REF] Ahamada | Experimental density data of three carbon dioxide and oxygen binary mixtures at temperatures from 276 to 416 K and at pressures up to 20 MPa[END_REF] ), multiparametric EoS (e.g. EoS-CG), or adding a crossover treatment (see Dicko and Coquelet [START_REF] Dicko | Application of a new crossover treatment to a generalized cubic equation of state[END_REF] and Janecek et al. [START_REF] Janeček | A generalized Kiselev crossover approach applied to Soave-Redlich-Kwong equation of state[END_REF] ). All these options add additional parameters, which is not necessary for our study, as demonstrated by the prediction results obtained for multicomponent systems (see section 3.3).

The water activity and fluid phase equilibria are known, to model gas hydrate systems following the approach described earlier, it remains to determine the Langmuir constants of each gas in a cavity of type (two types of cavities exist for hydrates: small and large cavities).

B. Langmuir constant

The Langmuir constants quantify the interactions between guest (gas) and host (water) molecules in hydrate cavities. Generally, the formula (Equation 11) proposed by van der

where is Boltzmann's constant, is the temperature and is the cell radius.

In order to avoid the numerical calculation of the integral in Equation 11, Parrish and Prausnitz [START_REF] Parrish | Dissociation pressures of gas hydrates formed by gas mixtures[END_REF] proposed a simplified empirical expression (Equation 12) of the Langmuir constant which was then used and refined in subsequent studies (e.g. the notable work by Munck et al. [START_REF] Munck | Computations of the formation of gas hydrates[END_REF] ).

(12)

In Equation 12, the and coefficients are specific to gas and cavity types (small or large) and are optimized on experimental gas hydrate data. In this work we have used similar empirical relationships inferred from the shape of the Langmuir constants (for each gas and Structures I and II are the most common forms of gas hydrates [START_REF] Koh | Fundamentals and applications of gas hydrates[END_REF] . From a modeling point of view, the most stable hydrate structure is the one with the lowest dissociation pressure. Pure CO 2 is well known to form hydrate of structure I. The (e-PR-CPA + vdWP) model predicts a type I hydrate structure for CO 2 hydrate and this is also the case for O 2 . The latter is a subject of discussion, basically it has been considered in the past that O 2 forms type I hydrate (like any other small molecule) but later experimental studies [START_REF] Davidson | Crystallographic studies of clathrate hydrates[END_REF][START_REF] Tse | Structure of oxygen clathrate hydrate by neutron powder diffraction[END_REF] have shown that it rather forms type II hydrates. However, according to different studies carried out at different temperature ranges, it is found that O 2 at low temperatures (<270 K) forms type II hydrates and forms type I hydrates at higher temperatures [START_REF] Mohammadi | Equilibrium data and thermodynamic modeling of nitrogen, oxygen, and air clathrate hydrates[END_REF] which is the case in our study. decreases the critical point of the mixed-gas and shifts its phase envelope to lower temperatures, and it seems that the 50% O 2 mixture or even less the 32% O 2 mixture are preferred to ensure that there is no phase change (especially phase split to liquid-vapor equilibrium) in the gas stored in the cavern.

For an overview, in Figure 10, the hydrate stability results of the ternary CO 2 +O 2 +H 2 O system are plotted from pure CO 2 hydrate to pure O 2 hydrate, showing the effect of oxygen on the stability of the CO 2 -rich mixed-gas hydrate. This Figure shows that at high pressure (>20 MPa) the hydrate dissociation temperature of the mixed gas CO 2 +O 2 becomes higher than that of pure CO 2 , therefore precautions must be taken to avoid hydrate formation at the wellhead or in the pipelines during the transport of this gas stream which is assumed to be saturated with water vapor after its withdrawal from the cavity. However, in reality the stored gas is in equilibrium with almost "pure" NaCl-brine and not pure water, which led us to study in the following section the effect of NaCl on this mixed-gas system. The study of this system involves several variables including the composition of the mixedgas, the aqueous fraction and the salinity (NaCl molality). Taking the example of the FluidSTORY project on the combination of the Power-to-Gas (PtG) and Underground Gas Storage (UGS) technologies discussed earlier in the introduction, the quantity of O 2 in the EMO unit is relatively less than CO 2 [START_REF] Kezibri | Conceptual design and modelling of an industrial scale power to gas-oxy-combustion power plant[END_REF] , that is why we choose to study the mixture with 32% O 2 . The aqueous fraction was kept the same (AqFr=0.7) as that of the mixed-gas system (without salt, see Figure 9a) with 32% O 2 , as well as two salinities were studied (1m and 4m), one was limited to 4m since the O 2 solubility data in NaCl brine on which the e-PR-CPA EoS was adjusted are limited to this salinity (4m, see Chabab et al. [START_REF] Chabab | Measurements and modeling of high-pressure O2 and CO2 solubility in brine (H2O+NaCl)[END_REF] ). The modeling results obtained are shown in Figure 11. As expected, NaCl significantly decreases the hydrate dissociation temperature of this gas mixture. The shape of the curve remains the same with a shift to the left by adding the salt. The model also detects when there are several phases in equilibrium especially at 4m when the hydrate dissociation curve crosses the phase envelope of the gas mixture. According to the trend of the dissociation points calculated by the model in this region, we notice from the slight change in the curve that there is a phase split and that at a pressure higher than the bubble line and at the left of the gas hydrate dissociation curve, the hydrate is rather in equilibrium with a gas-rich liquid phase and not with a vapor phase.

Conclusions

In this work the phase behavior of systems containing CO 2 , O 2 , H 2 O and possibly NaCl, and in particular the gas hydrate stability conditions of CO 2 , O 2 and their mixtures were studied.

The isochoric pressure search method was used to overcome the lack of data for the CO 2 +O 2 +H 2 O system by measuring new hydrate dissociation points of the CO 2 +O 2 gas mixture at different global compositions. The consistency of the measured data was verified using the Clausius-Clapeyron relationship. In addition to the fact that these data were measured for a promising massive energy storage application (combination of PtG with UGS using the EMO process), these data will serve for the evaluation of predictive models, and also to help to avoid problems related to flow assurance by taking the necessary precautions when transporting gas streams composed of CO 2 , O 2 and water, for instance, oxycombustion flue gas.

To predict the dissociation conditions of gas hydrates, in this work, the established hydrate The model allowed a complete study of phase equilibria (hydrate-fluids and fluid-fluids) of gas/water systems and also to accurately predict the effect of the presence of salt on the stability of gas hydrates. The excellent results obtained using this model for single-gas and mixed-gas hydrate systems without adding additional parameters for the latter are the result of an advanced equation of state (e-PR-CPA) and a theoretically solid solution for gas hydrates (vdWP).

Figure 1 :

 1 Figure 1: Schematic representation of the used apparatus. DW: degassed water; DAU: data acquisition unit; EC: equilibrium cell; GC: Gas cylinder; LPT: low pressure transducer; HPT: high pressure transducer; LB: liquid bath; PP: platinum probe; SD:

  and pressure is monitored by means of a Data Acquisition Unit (DAU) connected to a DAU software to manage the stepwise variation of temperature and record the acquired data. The temperature probe (100 Ω) is calibrated against a 25-Ohm platinum resistance thermometer (model 5628, Fluke Hart Scientific) which is calibrated by LNE (Laboratoire National de Métrologie et d'Essais). The LPT and HPT pressure transducers were calibrated against pressure automated calibration equipment (PACE 5000, GE Sensing and Inspection Technologies) and a dead weight pressure balance (Desgranges & Huot 5202S, CP 0.3-40MPa, Aubervilliers, France), respectively.

Figure 2 :

 2 Figure 2: Measurement principle of gas hydrate dissociation points by isochoric pressure search method.

Figure 3 :

 3 Figure 3: Hydrate dissociation points of the CO 2 +O 2 gas mixture: measured data (a) and consistency tests (b, c and d). The red symbols (graph c) represent measurements where the gas mixture was in liquid-vapor equilibrium (see Figure9b).

Figure 4 : 3 . 1 .

 431 Figure 4: Schematic diagram of the approach used to calculate gas hydrate equilibria with the e-PR-CPA model combined with the Van der Waals and Platteeuw model.

Waals and Platteeuw 15

 15 developed using the Lennard-Jones-Devonshire cell theory (considering a spherically symmetrical cell) is used to determine the Langmuir constants. For this, the Kihara potential 32 (McKoy and Sinanoğlu 33 ) whose parameters are adjusted on experimental hydrate stability data is used to calculate the spherically symmetrical cell potential .

Figure 5 :

 5 Figure 5: Saturation vapor pressure (a) and osmotic coefficient (b) of H 2 O + NaCl system. Comparison of literature data (symbols) 34-40 with predictions (solid lines) by e-PR-CPA EoS.

Figure 6 :

 6 Figure 6: Comparison of experimental data (symbols) 6, 41-49 with predicted CO 2 (a) and O 2 (b) solubilities in NaCl-brine at 323 K for different salt molalities using the e-PR-CPA EoS (solid lines).

Figure 7 :

 7 Figure 7: Water content in CO 2 +H 2 O and O 2 +H 2 O systems (a) and VLE of the CO 2 +O 2 mixture (b) at different temperatures: Comparison of experimental data (symbols, (a): 47, 48, 50-54 ; (b): 29 ) with predictions (solid lines) using e-PR-CPA model (a) and PR EoS (b).

  The modeling results of the stability conditions of O 2 hydrate in pure water and CO 2 hydrate in pure water and NaCl-brine are shown in Figure8. By comparing with experimental literature data, the developed model (e-PR-CPA + vdWP) correlates accurately the gas hydrate data in pure water and also predicts well the inhibitory effect of NaCl on the stability of CO 2 hydrate at different concentrations (in terms of salt molality) which tends to destabilize the hydrate proportionally to its concentration. Model calculations are reliable over a wide range of temperature and pressure (up to 100 MPa) for gas hydrates in pure water. The high quality predictions of the effect of salt (NaCl) on CO 2 hydrates is due to the accurate representation of the salting-out effect by the e-PRCPA EoS and also to the excellent vdWP hydrate theory. In addition, it should be noted that the model has been successfully applied to other single-gas and mixed-gas hydrate systems (CH 4 +H 2 O, CH 4 +H 2 O+NaCl and CH 4 +CO 2 +H 2 O etc.).

Figure 8 :Figure 9 :

 89 Figure 8: Hydrate dissociation conditions of the O 2 +H 2 O (a) and CO 2 +H 2 O+(NaCl) (b) mixtures: Comparison of literature experimental data with predictions using the (e-PR-CPA + vdWP) model.

  of the coupling of the e-PR-CPA EoS with the vdWP theory. As shown in Figure9, by plotting the gas hydrate dissociation curve and the phase envelope of the gas mixture obtained by the e-PR-CPA model, we can accurately identify the different types of coexisting phases (liquid, aqueous, vapor and gaseous) at each temperature and pressure condition, which is very useful. As shown in plots a, b, c and d of Figure9, the addition of O 2 effectively

Figure 10 :

 10 Figure 10: Hydrate dissociation conditions of the CO 2 +O 2 +H 2 O ternary system from pure O 2 hydrate to pure CO 2 hydrate. Comparison of literature and measured data with predictions using the (e-PR-CPA + vdWP) model (solid lines).

Figure 11 :

 11 Figure 11: Hydrate dissociation conditions of the CO 2 +O 2 +H 2 O+(NaCl) quaternary system: Prediction of the effect of NaCl concentration (from salt-free to 4m) on the mixed-gas hydrate system (32% O 2 , at fixed aqueous fraction AqFr=0.7) using the (e-PR-CPA + vdWP) model. The bubble and dew lines are determined by the PR EoS.

  theory of van derWaals and Platteeuw (vdWP) is combined with the e-PR-CPA EoS which has shown in this and previous work excellent capabilities to determine water activity in brine, gas solubility in water and brine and to predict the water content in gas-rich phase. The resulting model (e-PR-CPA + vdWP) was successfully applied to the O 2 +H 2 O and CO 2 +H 2 O+NaCl systems by comparing with literature data as well as to the CO 2 +O 2 +H 2 O mixed-gas hydrate system by comparing predictions with the new reported measurements.

Table 1 : Chemical samples used for experimental work (CAS Registry Number, mole fraction purity and suppliers of chemicals).

 1 1, the suppliers of Carbon dioxide (CO 2 , CAS Number: 124-38-9) and Oxygen (O 2 ,

	CAS Number: 7782-44-7) and the given purities are listed. Water (H 2 O, CAS Number: 7732-
	18-5) was deionized and degassed.
	Chemicals	CAS Reg. No.	Supplier	Purity (mol %) Analysis method a
	Carbon dioxide	124-38-9	Air Liquide	99.995	GC
	Oxygen	7782-44-7	Air Liquide	99.999	GC
	Water (ultrapure) 7732-18-5	MilliporeTM ( direct-Q5)	18.2 MΩ•cm
	(Perichrom, France) is used for peaks integration and their analysis. The calibration of the GC
	detector is obtained after introduction of several known pure component volumes.
	Appropriate syringes are considered. A PORAPAK R (80/100 mesh, 1.2 m X 1/8" Silcosteel)
	packed column is used. A calibration curve between moles number introduced and GC peak
	surface is determined and accuracies are determined. The resulting relative accuracies
	concerning the mole numbers are 0.7 % for CO 2 and 0.8 % for O 2 . The uncertainty of molar
	fractions (x 1 ) is determined by Equation 1:

a GC: Gas Chromatography Three mixtures of CO 2 +O 2 were considered in this study, their compositions are listed in Table

2

. The mixtures were prepared in a gas reservoir considering the difference of total pressure. First, the gas reservoir is put under vacuum. CO 2 was first introduced into the gas reservoir and the pressure was recorded (P1). Afterwards, O 2 is introduced and pressure is recorded (P2). The temperature of the gas reservoir is selected in order to have a monophasic phase inside. Approximate composition is estimated using x O2 =(P2-P1)/P2. In order to have the accurate value of the gas mixture composition, a Gas Chromatograph (Varian, model CP 3800), equipped with a thermal conductivity detector (TCD) is used. WINILAB III software

Table 2 : Compositions of the studied CO 2 +O 2 mixtures: Expected composition and real composition mole fractions

 2

	Mixture	Expected composition mole fractions	Real composition mole fractions (x)	Standard uncertainties
		O 2	CO 2	O 2	CO 2	u(xCO 2 )
	MIX1	0.3	0.7	0.3238	0.6762	0.0016
	MIX2	0.1	0.9	0.1104	0.8896	0.0006
	MIX3	0.5	0.5	0.4984	0.5016	0.0015
	2

.2. Apparatus and method

Table 3 : Measured data of hydrate dissociation conditions of the CO 2 +O 2 gas mixture and expanded uncertainties (k=2): 0.10≤U(T)≤0.60 K and 0.040≤U(p)≤0.251 MPa.

 3

	Mixture	Loaded water (mole)	(cm 3 )	AqFr (mole fraction) Temperature [K]	Pressure [MPa]
		1.16050	20.97	0.902 ± 0.017	274.17	2.178
		1.16050	20.97	0.886 ± 0.018	277.00	3.017
		1.16050	20.97	0.836 ± 0.015	279.75	4.233
		1.16050	20.97	0.761 ± 0.013	282.17	6.054
	MIX1	1.16050	20.97	0.671 ± 0.010	283.88	8.353
		1.16050	20.97	0.550 ± 0.007	284.96	11.194
		2.04400	36.94	0.838 ± 0.009	283.26	7.227
		2.04400	36.94	0.681 ± 0.006	285.38	13.245
		2.80600	50.71	0.583 ± 0.006	286.07	18.741

A consistency test was applied to the measured data. Using the Clausius-Clapeyron relation (Equation

Table 4 : e-PR-CPA EoS configuration: model parameters and properties used in the fitting.

 4

	Adjusted on:

Hydrate stability of the O 2 +H 2 O and CO 2 +H 2 O+(NaCl) mixtures

	3.2.
	(a)	1				(b)
						CO 2 +O 2 system
	fraction	0.1
	mole	0.01
	O / yH 2	0.001		yH2O in CO2+H2O system / 423 K yH2O in CO2+H2O system / 373 K yH2O in CO2+H2O system / 323 K yH2O in O2+H2O system / 348 K
				yH2O in O2+H2O system / 323 K	VLE (xO2) exp data / 273 K	VLE (xO2) exp data / 293 K
				yH2O in O2+H2O system / 298 K	VLE (yO2) exp data / 273 K	VLE (yO2) exp data / 293 K
				e-PR-CPA model	PR EoS (kij=0.114)
	0.0001
		0	10	20	30	40
				Pressure / MPa

Table 3 ) and literature 11 (d) experimental data with predictions using the (e-PR-CPA + vdWP) model (solid lines). The bubble and dew lines of the different gas mixtures are determined by the PR EoS.

 3

		25									12
			MIX1 (32%O2+68%CO2)		bubble line / PR EoS (kij=0.114)			MIX2 (11%O2+89%CO2)		bubble line / PR EoS (kij=0.114)
		20	(e-PR-CPA + vdWP) model / AqFr=0.7	dew line / PR EoS (kij=0.114)			10	(e-PR-CPA + vdWP) model / AqFr=0.965	dew line / PR EoS (kij=0.114)
												Liquid + Hydrate
											8
	MPa	15								MPa
	/									/
	Pressure	10	Vapor + Liquid + Hydrate					Pressure	6	Vapor + Liquid + Hydrate
											4
												Vapor + Hydrate
		5									2
								CO 2 +O 2 +H 2 O system							CO 2 +O 2 +H 2 O system
		0									0
		272	274	276	278	280	282	284	286	288	272	274	276	278	280	282	284	286
					Temperature / K								Temperature / K

Hydrate stability of the CO 2 +O 2 +H 2 O mixture

  Concerning the mixed-gas hydrate system (CO 2 +O 2 ), the (e-PR-CPA + vdWP) model also predicts a hydrate structure of type I. In Figure9, the predictions of the hydrate stability conditions of this system are compared with the measured data (from this work, see Table3) at different O 2 compositions (11%, 32% and 50% water-free mole fraction) and also with those of Chapoy et al.[START_REF] Chapoy | Final Report JIP (confidential) : Impact of Common Impurities on CO2 Capture, Transport and Storage 2011 -2014 PROGRAMME[END_REF] at 5% O 2 . Remarkable accuracy in the predictions of this system at different gas mixture compositions from 5 to 50% O 2 is obtained. The calculations were performed at different fixed aqueous fractions AqFr in a very representative way of the experimental aqueous fractions listed in Table3which are not fixed (decreases with each increase in pressure by adding more gas mixture). It should be noted that no further adjustments were made, i.e. only the good representation of the single-gas hydrate systems and the VLE of the systems (gas-gas and gas-water) allowed the accurate prediction of the multi-component system (CO 2 +O 2 +H 2 O), and this is thanks to the good theoretical basis

3.4. Hydrate stability of the CO 2 +O 2 +H 2 O+NaCl mixture

  Since all the necessary parameters are already available, in particular theinteraction parameters CO 2 +O 2 , O 2 -Na+, O 2 -Cl-, O 2 -H 2 O, CO 2 -Na+, CO 2 -Cl-and CO 2 -H 2 O,we can model the quaternary system CO 2 +O 2 +H 2 O+NaCl with a high degree of confidence.

The developed model (e-PR-CPA + vdWP) has shown its predictive capabilities, in particular the transition from simple binary systems to multi-component systems and mixed-gas+water).

CO 2 +O 2 +H 2 O+NaCl system Vapor + Liquid + Hydrate Vapor + Hydrate Liquid + Hydrate

	(32% O2 + 68% CO2) Hydrate
	(e-PR-CPA + vdWP) model / AqFR=0.7 / salt-free
	(e-PR-CPA + vdWP) model / AqFR=0.7 / 1m NaCl
	(e-PR-CPA + vdWP) model / AqFR=0.7 / 4m NaCl
	bubble line / PR EoS (kij=0.114)
	dew line / PR EoS (kij=0.114)

Acknowledgments

We thank Dr. Martha Hajiw for the various useful discussions. Financial support from Agence Nationale de la Recherche (ANR) through the project FluidSTORY (n° 7747, ID ANR-15-CE06-0015) is gratefully acknowledged.

Supporting Information (SI)

Tables of CO 2 and O 2 hydrate dissociation data in water and NaCl brine in a wide range of pressure and temperature.