Benjamin Rotenberg

Water in clay nanopores

Keywords: Water, ion exchange material, simulation. MRS Bulletin

Clay minerals are layered magnesium or aluminum silicates, which are abundant in Earth's crust. Used since ancient times for the fabrication of bricks or terracotta, they now find application in the pharmaceutical and plastics industries.

They play an essential role in oil and gas recovery, in water availability, and in preventing the dissemination of pollutants. In all of these contexts, the relevant properties of clay minerals are intimately linked to their microscopic structure, which results in a rich behavior with respect to water, solutes, and other fluids.

This article provides a brief overview of the structure, dynamics, thermodynamics, and reactivity of water in clays, highlighting the role of the various types of water-mineral interfaces. Based on recent experimental and simulation studies, we discuss several features of these interfacial materials arising from their interactions with water on the molecular scale, including swelling, wetting, hydrodynamics in clay nanopores, reactivity of clay edge sites, ion exchange, and sorption.

Introduction

Clay minerals derive from the weathering of minerals formed deep in Earth's crust. They are rich in aluminum and silicon and contribute significantly to the crust mass. They are characterized by a lamellar structure and dimensions smaller than a micron, giving rise to a large specific surface area and, for some of them, to swelling and ion exchange in the presence of water. [START_REF] Bergaya | Handbook of Clay Science[END_REF] Dispersed in water, clay minerals display colloidal behavior, as they are subject to thermal motion because of their small size. The properties of clay minerals led to their use by humans, long before there was any understanding of the underlying processes, for a variety of applications including components in the fabrication of bricks, tiles, terracotta, earthenware, and porcelain; texturizing agent in paints; fillers in paper and plastics; and cat litter. They are also used as catalysts in the pharmaceutical against the transport of fluids and solutes. Several countries are therefore considering clay-rich geological formations, possibly with clays as buffer and backfill materials as well, for the disposal of high-level and long-lived radioactive waste. [START_REF] Delage | [END_REF] The breadth of applications listed above is made possible thanks to the variety of physicochemical properties of clay minerals, arising from their microscopic structure and resulting in rich behavior with respect to water, solutes, and other fluids. This article provides a brief overview of the structure, dynamics, thermodynamics, and reactivity of water in clays, highlighting the role of the various types of water-mineral interfaces in these materials. In the following sections, we first introduce the structure of clay minerals. We then discuss several features of these interfacial materials arising from the interplay between clay minerals and water, including swelling, wetting, hydrodynamics in clay nanopores, reactivity of clay edge sites, ion exchange, and sorption.

Clay structure

Clay minerals belong to the family of aluminosilicates and encompass a wide range of chemical compositions and (to a lesser extent) structures. [START_REF] Bergaya | Handbook of Clay Science[END_REF] Unlike zeolites, which form three-dimensional crystals, clay minerals have a layered structure. Each layer consists of two to four sheets of tetrahedral (T) silicon oxide and octahedral (O) aluminum or magnesium oxide (Figure 1). O-terminated layers, as in kaolinite, are covered with hydroxyl (OH) groups, whereas Tterminated layers, such as the TOT members on which we focus here, display siloxane rings with hexagonal cavities in which hydroxyl groups from the O sheet are buried. In dioctahedral clays such as pyrophyllite, two-thirds of the octahedral sites are occupied by Al 3+ ions, whereas in trioctahedral clays such as talc, all of these sites are occupied by Mg 2+ ions. The OH groups are then oriented approximately parallel and perpendicular to the sheets, respectively, in the two types of clays. In some cases, particularly in synthetic clays, the OH groups are replaced by F -ions.

The assembly of parallel layers forms stacks called clay particles (Figure 2). In most clay minerals, some cations are substituted by others with lower valency: Si 4+ by Al 3+ in the T layer; Al 3+ by Mg 2+ or Fe 2+ and Mg 2+ by Li + in the O layer. The mineral layer is then negatively charged, and this charge is compensated by counterions between layers, typically Na + , K + , or Ca 2+ under natural conditions, in the so-called interlayer porosity (Figure 2a). Depending on the charge density of the layer and the nature of the counterions, both of which are controlled by the geochemical composition during the formation of the minerals, the interlayer cations can be hydrated in the presence of water, resulting in an increase in the interlayer distance (swelling), and/or be exchanged by other cations (ion exchange).

These particles are finite, with dimensions that largely depend on the nature of the clay. Typically, the number of layers is a few tens, and the lateral extension is a few hundreds of nanometers , with specific areas on the order of 10-10 3 m 2 /g. In addition, these layers are usually not perfectly aligned, so that the concept of clay particle can be ambiguous and the small coherence length renders the resolution of their atomic structure by x-ray diffraction a challenging task.

Nevertheless, it is clear that there are, in addition to the above-mentioned interlayer porosity, some additional pores with sizes from a few nanometers to a few hundreds of nanometers, referred to as interparticle pores (Figure 2b), through which fluids can flow. The lamellar structure further results in different types of surfaces: basal surfaces along the layers and lateral surfaces presenting different chemical moieties (as they result from the termination of the mineral layers) and providing access for water and solutes into the interlayer.

Water in clay interlayers

We first consider the case of interlayer water and discuss the thermodynamics of clay swelling, which results from the entrance of water into the interlayer. The extreme confinement down to the molecular scale results in unusual structural and dynamical properties.

Swelling

The water content in clay interlayers depends on the nature of the clay and the type of counterion, as well as the thermodynamic conditions (pressure, temperature, relative humidity [RH]). 5,6 For RH ≈ 0%, the interlayer contains no or very few water molecules. With increasing RH, water uptake first proceeds stepwise, as does the interlayer distance measured by x-ray diffraction (Figure 3a-b). 7 For RH ≈ 100%, this discrete crystalline swelling regime is followed by a more continuous one (osmotic swelling).

Whereas illite, a highly charged clay with K + counterions, exhibits no swelling, smectite clays such as montmorillonite (dioctahedral) and saponite (trioctahedral) with Na + counterions can exist with no (dry), one (monolayer), two (bilayer), or even three water layers, with increases in the interlayer distance occurring in steps corresponding to the size of a water molecule. Figure 3c shows that, for a given number of water layers and a given counterion, the mass of water per unit cell and the interlayer distance depend on the surface charge density, the localization of the charge in the T (saponite) or O (hectorite) sheets, and the replacement of OH by F in the O-terminated layers. 8 The equilibrium distance is determined by the balance between the mechanical pressure exerted on the layers and the swelling pressure induced by the hydration of interlayer counterions. Under given thermodynamic conditions, several hydration states (e.g., mono-and bilayer) might be metastable and coexist in various proportions. Such metastability is also at the origin of the hysteresis observed during adsorption/desorption cycles (see Figure 3a). Significant progress in the understanding of swelling thermodynamics and the underlying microscopic mechanisms was achieved thanks to molecular simulations, [9][10][11][12][13][14][15][16][17][18] in particular, grand-canonical Monte Carlo (GCMC) simulations. These simulations not only allowed the determination of the swelling free energies 19 and mechanical properties of clays as functions of the interlayer water content 20 but also provided insights into the microscopic interlayer structure.

Structure and dynamics of interlayer water

The structure and dynamics of water in clay layers can be probed experimentally using x-ray and neutron diffraction and using quasi-elastic neutron scattering (QENS), respectively. Combined with molecular simulations, these techniques provide a detailed picture of the interlayer properties. Figure 4a illustrates the interlayer structure of Na-saponite in the bilayer state. 21 The density profiles of Na + , O, and H in the direction perpendicular to the surface obtained by classical molecular simulations clearly support the bilayer picture, with two maxima for O atoms. OH bonds are found mainly parallel to or approximately perpendicular to the surface, whereas Na + cations are found either fully solvated in the center of the pore or partially desolvated near the surface. This figure also shows the signal predicted from these density profiles for x-ray diffraction (reflecting the electronic density, i.e., mainly O atoms), as well as neutron diffraction experiments using normal and deuterated water (both mainly reflecting the positions of H atoms). The agreement is remarkable and simultaneously confirms the validity of the model used in the molecular simulations (a modified version of the most commonly used CLAYFF model 22 ) and the interpretation of the experimental data.

Figure 4b similarly shows the signal measured by QENS for the same system, in the direction perpendicular to the clay layer, and the predictions of molecular dynamics (MD) simulations-once more in good agreement. The motion of water confined in the interlayer is highly anisotropic. 23,24 In addition, the water diffusion coefficient deduced from these results is smaller than that in bulk water, to an extent that depends on the hydration state and on the nature of the counterion. For example, in Na-montmorillonite, it decreases by factors of ~5 in the bilayer state and ~10 in the monolayer state, whereas for Csmontmorillonite in the monolayer state, water diffusion is slowed by a factor of 20. 25,26 Here again, molecular simulations have allowed some clarification of the microscopic mechanisms at play. [27][28][29][30][31][32]

Water in interparticle pores

We now turn to the case of water in interparticle pores. Such pores can be sufficiently large, with dimensions ranging from a few to a few hundred nanometers, to allow for hydrodynamic flows to develop. Transport is nevertheless limited by the smallest pore throats, for which interfacial effects play an essential role. We introduce first the structure and dynamics of water on basal surfaces, before turning to the impact of this surface water on the hydrodynamic flow in interparticle nanopores. This progression brings us naturally to the wetting properties of clay surfaces, which we discuss in the particular case of neutral clays such as talc.

Water at basal surfaces

Basal surfaces of clay particles are flat over distances much larger than molecular sizes. As a result, water on basal surfaces adopts a layered structure.

Figure 5b

illustrates the density profiles obtained from molecular simulations of water and ions in a 4-nm-wide pore between Na-(Cs-) montmorillonite surfaces containing a 1 M solution of NaCl (CsCl), depicted in Figure 5a. The strong oscillations near the surface reveal the layering of water over a distance approximately 1 nm from the surface. 33 Cl -anions are repelled from the negatively charged clay surface, whereas cations can form surface complexes that depend on the nature of the cation. Figure 5c shows typical structures of innersphere complexes (ISCs) and outer-sphere complexes (OSCs). In the former case, some surface O atoms participate in the first solvation shell of the cation, thereby resulting in a shorter distance of the ion from the surface (most Cs + ions, see Figure 5b); in the latter case, the ion remains fully solvated (most Na + ions). 34,35 Molecular simulations have further allowed the detailed investigation of the structure and dynamics of surface hydrogen-bond networks. 33,36 In the first adsorbed layer, approximately half of the water molecules donate H-bonds to surface O atoms. The remaining water molecules donate one or two H-bonds to these surface-bonded molecules (see Figure 5d). The diffusion of water molecules along the surface is slowed compared to that in the bulk. Regarding the orientational order and dynamics of the water dipole, only the component normal to the clay surface is perturbed. Similar findings have been reported for other lamellar oxides and hydroxides. [37][38][39][40]

Hydrodynamics in interparticle pores

For practical applications, one generally considers the transport of fluids through a porous material such as clays within an effective medium theory, wherein the fluid flux is linked to the macroscopic pressure gradient through the permeability of the sample (Darcy's law). This macroscopic law can be recovered, from the theoretical point of view, by upscaling the classical laws of hydrodynamics (Navier-Stokes) from the pore scale to the scale of the sample, either numerically or by numerical homogenization. 41 However, these continuous descriptions might not be valid in pores with sizes comparable to the molecular size. 42 Figure 6 illustrates how nonequilibrium molecular dynamics (NEMD) simulations allow for the investigation of the flow of fluids through such nanopores, by applying a force on the fluid mimicking the effect of a pressure gradient. In this simple slit geometry, continuous hydrodynamics predicts a parabolic velocity profile (Poiseuille flow). Despite the layering of surface water, which results in a more complex flow in the vicinity of the walls, the velocity profile more than 1.5 nm away from the surface is well described by the Navier-Stokes equation, with a viscosity equal to that of bulk water. It is necessary, however, to take into account slip boundary conditions at the clay-solution interface by introducing a slip length determined from molecular simulation. 43 This length is very small (less than the size of a water molecule for Namontmorillonite), but its effects on the overall flow through the pore can be large for nanometer-sized pores. 44 Such hydrodynamic slip is related to the hydrophilic/hydrophobic balance of clay surfaces, in particular, whether they are charged or neutral. 45

Wettability of talc and related clay minerals

The wetting properties of soils and rocks play an important role in the transport, and hence the availability, of water and hydrocarbons. In charged clays, the presence of counterions favors the presence of water on basal surfaces. On the contrary, the surface of neutral TOT clays, covered with siloxane rings, is generally hydrophobic (see Figure 1). For example, the contact angle of water droplets on pyrophyllite or talc monocrystals is large (80-90°). Such hydrophobic behavior, consistent with the above-mentioned slip, is well reproduced by molecular simulations with the CLAYFF force field, 22 which predicts similar contact angles for talc, fluorotalc, and pyrophyllite (Figure 7a). 46 In the case of talc, this contrasts with the presence of highly hydrophilic sites leading to the adsorption of water vapor, with a Gibbs free energy of adsorption of ~30 kJ/mol, consistent with the formation of a H-bond with a surface hydroxyl group. Such Hbonds cannot form in the case of fluorotalc, and as a result, this mineral does not adsorb water at low RH. 47 This dual macroscopic hydrophobicity and microscopic hydrophilicity might seem surprising. In fact, by means of an analysis of the competition between water-surface and water-water interactions based on molecular simulations, 46 it was shown that there is no contradiction between these two regimes. At low RH, the adsorption free energy for an isolated water molecule displays a strong minimum for talc above the hexagonal siloxane cavities (Figure 7b), confirming the presence of a H-bond donated by the surface hydroxyl group.

The adsorption is much weaker on pyrophyllite and fluorotalc, in which these groups are parallel to the surface and absent, respectively. At low RH, the surface coverage by water results from a balance between the adsorption energy and the favorable entropy of water in the gas phase. At high RH, water molecules interact more strongly with each other (cohesion) than with the surface (adhesion), so that the adsorption sites are empty, even in the case of talc.

Water at clay edges

Finally, we discuss the last type of clay surface, namely, lateral surfaces.

As already mentioned, these surfaces provide the only access into and out of the interlayer. They are therefore essential for swelling and ion exchange. In addition, clay edges display chemical moieties different from those on the basal surfaces that can react chemically with water and provide sorption sites for cations.

Water and ion exchange via edges

One of the most important processes governing cation retention by clays is cation exchange between ions in solution and interlayer counterions, through lateral surfaces. The exchange of interlayer Na + counterions by Cs + in solution is thermodynamically favorable (negative reaction free energy, ∆ r G) and exothermic (negative reaction enthalpy, ∆ r H). The consensus of thought was that this exchange resulted from favorable interactions between the Cs + cations and the clay surface. This point of view was challenged by Teppen and Miller, 48 who used molecular simulations to compute the free energy associated with the replacement of Na + by larger alkaline cations and found that, in fact, the interactions with the clay surface contribute unfavorably to the exchange. The overall exchange is thermodynamically favorable only because of the replacement of Cs + by Na + in the aqueous phase, that is, because of the difference in hydration free energy between the two ions. This finding underlines the essential role of water in ion exchange. Similar conclusions were drawn for the reaction enthalpy, including its evolution with interlayer water content, by combining molecular simulations with microcalorimetry experiments. 49 Molecular simulations further provided the first study of the exchange process on the microscopic scale, using the system illustrated in Figure 8a. It was found that, for Na-montmorillonite in the bilayer state, water and cations can exchange via the edges with no or small activation barriers, whereas anions are excluded from the interlayer. 50 As the interlayer distance increases, the entrance of anions can become possible. 51

Acidity of edge sites

The finite extent of clay particles results in the breaking of chemical bonds, mainly Si-O and Al-O bonds. Unsaturated surface atoms then react with water molecules, resulting in new chemical moieties. For example, the (010) faces of pyrophyllite and montmorillonite display aluminol sites, AlOH and AlOH 2 , and silanol sites, SiOH (Figure 8a). These sites can (de)protonate and play an important role in the sorption of ions, in particular, multivalent cations in the context of radioactive waste disposal. One should then be able to predict the protonation states of the various sites as functions of pH. This requires knowledge of the pK a value of each site, which is related to the reaction free energy for the transfer of the surface proton to a water molecule. For example, for a silanol group, the transfer reaction is written as

-SiOH + H 2 O(aq) → -SiO -+ H 3 O(aq) + . ( 1
)
Experimentally, titration experiments provide only a global picture of the surface, not a local picture of the state of each site. 52 One must then resort to a priori or experimental information in structure-based models such as MUSIC 53 to reproduce the titration curve. 54 Water near such surface edge sites can also be investigated using ab initio molecular dynamics (AIMD) simulations based on density functional theory (DFT), which capture the possible breaking and formation of chemical bonds. Figure 8b illustrates a proton-transfer event between an AlOH 2 site and an AlOH site on the (010) face of pyrophyllite, mediated by two surface water molecules. 55 By combining AIMD with specific techniques (e.g., thermodynamic integration), it is possible to compute the free energy associated with the deprotonation reaction in Equation 1, as well as two other quantities relevant to the thermodynamics of this process: the vertical energy gap, ΔE AH , and the reorganization free energy, ΔF (Figure 8c). SiOH is slightly more acidic than AlOH 2 , with pK a values close to 7 for both sites, whereas AlOH does not deprotonate in water (pK a ≈ 22). The reorganization free energy, arising from bond-length relaxation and solvent reorganization after deprotonation, cannot be neglected. For example, the strong stabilization of SiO -after deprotonation is explained by the arrival of two water molecules donating H-bonds. 56 This further illustrates the importance of water on clay edges. The presence of substitutions inside the mineral layer also plays a role in the acidity of neighboring edge sites. 57

Conclusions and outlook

Clay minerals display various types of surfaces associated with a range of exciting properties with respect to water. Whereas swelling involves interlayer nanopores, fluid flow through clays can also proceed through interparticle pores, thereby experiencing the influence of basal and lateral surfaces. The molecular aspects discussed herein play an essential role in the thermodynamics and transport of fluids and solutes, with measurable effects on the macroscopic scale.

Important efforts are thus devoted to upscaling the relevant features from the molecular scale to the sample scale. 41 Nevertheless, there is still plenty of room for improvement even at the bottom. From the experimental point of view, characterizing the threedimensional structure on the mesoscopic scale remains a challenge and should benefit from the latest developments in imaging techniques such as x-ray microscopy. 58 On a more microscopic scale, x-ray reflectivity has already provided new results on the interface between mica (a highly charged clay mineral) and aqueous solutions, suggesting that surface relaxation of the solid might extend over a few mineral layers. 59 From the modeling point of view, it would be desirable to improve the force fields used in molecular simulations to account for water polarization and its changes at the interface, in particular, for the sorption of multivalent ions.

Finally, although the present work discusses only water and small inorganic ions at clay surfaces, it is important to mention that other solutes such as organic molecules and other fluids (e.g., CO 2 and CH 4 ) remain much less studied on the molecular scale. [60][61][62][63] Such compounds also play important roles in various contexts ranging from pollutant sorption to the possible catalytic role of clay minerals in the origin of life, and from CO 2 sequestration to shale gas extraction. In addition, the properties of water on clay surfaces could provide useful concepts for other nanoporous materials, such as zeolites and metalorganic frameworks. 1). Using AIMD simulations, it is then possible to determine the vertical energy gap ΔE AH , that is, the energy corresponding to proton transfer from the surface to the aqueous phase without reorganization of the site after deprotonation, and the reorganization energy λ, which arises from changes in bond lengths in the vicinity of the site as well as solvent reorganization after deprotonation. The reaction free energy ΔF, directly related to the pK a of the corresponding site, is the sum of these two contributions. 55

Figure 1 .

 1 Figure 1. Microscopic structures of clay minerals. (a) Side view of pyrophyllite. Each layer consists of an octahedral aluminum oxide sheet between two tetrahedral silicon oxide sheets. (b) Top views of pyrophyllite and talc, illustrating the hexagonal siloxane rings. In pyrophyllite, two-thirds of octahedral sites are occupied by Al 3+ , and the hydroxyl (OH) group is along the surface, whereas in talc, all sites are occupied by Mg 2+ , and the OH is perpendicular to the surface. In fluorotalc (not shown), the talc OH groups are replaced by F atoms.

Figure 2 .Figure 3 .

 23 Figure 2. Mesoscopic structure of clay minerals. HRTEM images of Illite du Puy (copyright Stéphane Gaboreau, BRGM). (a) Substitutions in the mineral layer result in a permanent negative charge, compensated by counterions in the interlayer porosity (<1 nm). In some cases, these cations can be hydrated, resulting in an increase in the interlayer distance (swelling), or be exchanged by other cations in solution. (b) The finite disordered stacking of layers forms socalled clay particles with an associated interparticle porosity. These particles display basal surfaces along the layers and lateral surfaces with different physicochemical properties.

Figure 4 .

 4 Figure 4. (a) Snapshot of the interlayer of Na-saponite in the bilayer state. The bilayer structure of water is evident in the density profiles from molecular simulations, which can simultaneously reproduce the patterns observed in x-ray and neutron diffraction experiments with both normal and heavy water. (b) Results of quasi-elastic neutron scattering (QENS) experiments used to probe the dynamics of interlayer water. Molecular dynamics (MD) simulations are able to reproduce the experimental signal and provide a microscopic understanding of the anisotropic dynamics of water confined down to the molecular scale.Figure 4a reproduced with permission from Reference 21. © 2011 American Chemical Society. Figure 4b reproduced with permission from Reference 24. © 2012 American Chemical Society.

Figure 5 .Figure 6 .Figure 7 .Figure 8 .

 5678 Figure 5. Water on basal surfaces (a) Model of interparticle pore between montmorillonite surfaces used in molecular simulations (blue, Na + ; pink, Cl -; gray, water). (b) The density profiles for ions (left) and water (right) reveal the layered structure of the fluid, the sorption of cations and anion exclusion from the negatively charged surface. (c) Surface complexes formed by cations on basal surfaces. (d) The network of hydrogen bonds at the surface involves bonds with the surface and between surface water molecules. Figure 5a-c reproduced from Reference 33. © 2008 PCCP Owner Societies.

  Figure 8. (a) Lateral surfaces provide access to and from the interlayer for water and ions in interparticle pores. Clay edges display sites with moieties different from basal surfaces, such as aluminol and silanol groups on the (010) face of pyrophyllite. Depending on pH, these groups can deprotonate and serve as sorption sites for cations. (b) Proton transfer between surface sites, from AlOH 2 to AlOH, by means of a chain of proton transfer through two surface water molecules, from ab initio molecular dynamics (AIMD) simulations. (c) The thermodynamics of the acid-base reaction between surface sites and water molecules can be understood within the framework of the Marcus theory of electron transfer, adapted to proton transfer (Equation1). Using AIMD simulations, it is then possible to determine the vertical energy gap ΔE AH , that is, the energy corresponding to proton transfer from the surface to the aqueous phase without reorganization of the site after deprotonation, and the reorganization energy λ, which arises from changes in bond lengths in the vicinity of the site as well as solvent reorganization after deprotonation. The reaction free energy ΔF, directly related to the pK a of the corresponding site, is the sum of these two contributions.55 Figure 8b Reproduced with permission from Reference 55. © 2007 Elsevier.

Acknowledgments

The author is grateful to the many students and colleagues who have contributed to this work over the past 10 years, in particular, Alexandru Botan, Sami Tazi, Virgnie Marry, Mathieu Salanne, and Pierre Turq, as well as overseas collaborators, in particular, Amish J. Patel and D. Chandler.


Yue Liu

Alain Valtz

Jamal El Abbadi

Guogeng He

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

Isothermal vapour-liquid equilibrium measurements for the (R1234ze(E) + ethane) system at temperatures from 272.27 to 347.52 K

In this paper, new vapour-liquid equilibrium data of the (ethane + R1234ze(E)) binary system are presented. The measurements are performed at six isotherms ranging from 272.27 to 347.52 K and for pressures up to 4.89 MPa. The experiments were conducted by means of a "static-analytic" apparatus with phase analysis via gas chromatography, with resulting uncertainties of 0.03 K for temperature, 0.4 kPa for pressure and 0.0043 for vapour and liquid mole fractions. The experimental data were correlated with Peng-Robinson equation of state using the classical van der Waals mixing rules. For the three temperatures above the critical temperature of pure ethane, the critical compositions and pressures of the binary mixtures were also calculated based on the extended asymptotic behaviour laws. The results obtained show a good agreement between experimental measurements and modelling, with a maximal deviation of 1.13% for bubble pressures and 1.23% for vapour molar fractions.

Introduction

Over the last decades, fluorinated compounds have been thought to be one of the most important contributors to global warming potential (GWP). Refrigerants whose GWP value is above 150 are strictly prohibited in the domestic air conditioners and chillers according to the NO.517/2014 regulation 1 issued in May, 2014. Besides, according to the Kigali mendment to the Montreal Protocol, about 80 to 85 % of HFCs refrigerants will be phased out by the late 2040s [START_REF] Heath | Amendment to the Montreal Protocol on Substances that Deplete the Ozone Layer (Kigali Amendment)[END_REF] . Traditional refrigerants such as R134a have been widely used in the domestic field and commercial use. However, its high GWP value, which can reach 1300 [START_REF] Stocker | Climate Change 2013: The physical science basis. contribution of working group I to the fifth assessment report of IPCC the intergovernmental panel on climate change[END_REF] , has restricted its development. Consequently, refrigerants such as hydrofluorocarbons(HFCs), especially the fluorinated compounds which have a high GWP value will be banned or their use will be significantly reduced. In recent years, finding new refrigerants to replace the traditional ones that are harmful to the ozone layer has been a hot research topic around the world. Hydrocarbons have been thought to be one of the most suitable substitutes but their GWP values are not negligible. Generally, hydrocarbons have smaller liquid densities than most of the fluorocarbons. Hence, the amount of charge decreases significantly with hydrocarbons which will help further relieve the direct emission of refrigerants. Among the hydrocarbons, ethane (R170), with a GWP value of 20, has been thought as a promising refrigerant. But, its flammability may cause concerns when applied in an application. It is believed that mixtures containing ethane can overcome these disadvantages and present a better thermal properties and a good performance as alternative refrigerants mixture. Currently, R1234ze(E) is considered to be one of the most promising new-generation refrigerant, categorized under the family of hydrofluoroolefines (HFOs). This refrigerant has a zero ozone depletion potential (ODP), a GWP of six and an extremely short atmospheric lifetime [START_REF] Nielsen | Atmospheric chemistry of CF3CFCH2: Kinetics and mechanisms of gas-phase reactions with Cl atoms, OH radicals, and O3[END_REF][START_REF] Søndergaard | Atmospheric chemistry of trans-CF 3 CH CHF: Kinetics of the gas-phase reactions with Cl atoms[END_REF] . It is an environmentally friendly refrigerant and can be widely used in the industrial house-hold areas. Many scholars have published their experimental vapour-liquid equilibrium data of ethane or R1234ze(E) with other mixtures. In 2013, Nandi et al. [START_REF] Nandi | Isothermal vapor-liquid equilibrium of R170+n-perfluorooctane at 308-338K: Measurement, equation of state modelling, and molecular simulation[END_REF] reported their experimental isothermal vapour-liquid equilibrium (VLE) data of ethane + n-perfluorooctane binary mixture with five isotherms ranging from 308.45 to 338.43 K and pressures up to 5.69 MPa. In their work, the VLE data were correlated with Peng-Robinson equation of state (PR-EoS) [START_REF] Peng | A new two-constant equation of state[END_REF] associated with Mathias-Copeman α-function [START_REF] Mathias | Extension of the Peng-Robinson equation of state to complex mixtures: evaluation of the various forms of the local composition concept[END_REF] , and with Wong-Sandler (WS) mixing rules [START_REF] Wong | A theoretically correct mixing rule for cubic equations of state[END_REF] incorporating the NRTL excess Gibbs energy model, and also with PR-EoS with the classical one-fluid mixing rules. The experimental results indicate that the thermodynamic model with the WS mixing rules produced a better correlation of the experimental data than did the classical one-fluid mixing rules. Kochenburger et al. [START_REF] Kochenburger | Vapor-liquid and vapor-liquid-liquid equilibrium measurements and correlation of the binary mixtures 2, 3, 3, 3-tetrafluoroprop-1-ene (R1234yf)+(tetrafluoromethane (R14), trifluoromethane (R23), octafluoropropane (R218), nitrogen (R728) and argon (R740)) and ethane (R170)+ trifluoromethane (R23)[END_REF] measured the VLE data of (ethane + R23) binary mixture by means of a "vapour recirculation apparatus". The results were also correlated with PR-EoS with van der Waals mixing rules, Mathias-Klotz-Prausnitz mixing rules [START_REF] Mathias | Equation-of-state mixing rules for multicomponent mixtures: the problem of invariance[END_REF] and Mathias-Copeman α-function. A positive azeotrope was found in the (ethane + R23) system. Other scholars have also done researches on R1234ze(E).

In 2016, pressure-density-temperature-composition (P -ρ-T-x) measurements for (R1234ze(E) + R134a) binary mixture along with seven isotherms from 270.35 to 300.28 K were performed by Zhang et al. [START_REF] Zhang | Investigation of pρTx properties for R1234ze (E)+ R134a mixtures in the gas phase[END_REF] . The PR-EoS with classical van der Waals one-fluid mixing rules and a truncated virial equation of state were employed to correlate the experimental data of this system. Moreover, different models were employed to correlate the experimental data, and a good agreement was found between calculated and experimental results. Dong et al. [START_REF] Dong | Measurements of isothermal (vapour+ liquid) equilibria data for {1, 1, 2, 2-Tetrafluoroethane (R134)+ trans-1, 3, 3, 3-tetrafluoropropene (R1234ze (E)[END_REF] also measured the isothermal VLE values for the system of (R1234ze(E) + R134) at four temperatures from 258.15 to 288.15 K with an apparatus based on the "static-analytic" method. The correlation of VLE results were carried out by means of PR-EoS and Huron-Vidal mixing rules [START_REF] Huron | New mixing rules in simple equations of state for representing vapour-liquid equilibria of strongly non-ideal mixtures[END_REF] involving the NRTL activity coefficient model. A good consistency is found between the experimental and calculated values through this model at each experimental point. The results show that an azeotropic behaviour is observed for this binary system. Besides, many other researchers (Di Nicola et al. [START_REF] Di Nicola | PVTx measurements of the carbon dioxide+trans-1, 3, 3, 3-tetrafluoroprop-1-ene binary system[END_REF] , Koyama et al. [START_REF] Koyama | Measurement of vapor-liquid equilibrium of HFO-1234ze (E)/HFC-32[END_REF] ) have also measured the VLE data of the mixtures containing R1234ze(E). However, and to our knowledge, no data in the open literature can be found about the VLE data of (ethane + R1234ze(E)) binary mixture. In this work, the VLE data of this system were measured at six temperatures, three below ethane critical temperature and three above it. The measured data were correlated using PR-EoS with the classical van der Waals mixing rules. The experimental results in this work will help extend the database of the new refrigerant R1234ze(E) and its mixtures. Besides, the refrigerant ethane shows good performance in cryogenic systems. The research of ethane+R1234ze(E) will help promote the application of R1234ze(E) and its mixtures into industrial use such as the cryogenic field and ultra-cryogenic field after being well researched.

Experimental section

Materials.

In Table 1 we list the suppliers of the two chemicals and the purities (given by the suppliers and verified by gas chromatography (GC) analysis). Except from a degassing at the moment of loading the products into the equilibrium cell, no further purification of the products was needed. Experimental apparatus. The measurements were conducted based on a static-analytic apparatus [START_REF] Madani | Isothermal vapor-liquid equilibrium data for the trifluoromethane (R23)+ 2, 3, 3, 3-tetrafluoroprop-1-ene (R1234yf) system at temperatures from 254 to 348[END_REF] . As it is shown in Figure 1, the key part of the apparatus is the equilibrium cell, which consists of a transparent tube held between two titanium flanges. The top flange is connected to a 100 Ω platinum resistance thermometer probe (Pt100), a pressure transducer, two inlet valves and two samplers. The bottom flange is connected to a Pt100 probe and two outlet valves. The temperature of the cell is measured by the two Pt100 probes, which measure the temperature at the top and the bottom of the cell, respectively. The temperature probes were calibrated against a standard probe (25 Ohms, TINSLEY, U.K.) which was certified by the 'Laboratoire National d'Essai' (Paris, France) based on the 1990 International Temperature Scale (ITS 90). The accuracy of the platinum probes is ±0.03 K. The cell's pressure is measured by a pressure transducer (DRUCK, Model UNIK 500). Generally, two transducers are used to verify the precision of the measurement. One transducer is used for the low pressures measurements (0-50 bar) and another one for the high pressures measurements (up to 200 bar). The pressure transducers were calibrated with respect to a pressure automated calibration equipment (PACE 5000, GE Sensing and Inspection Technologies). The accuracies of the two pressure transducers are ±0.3 kPa and ±0.4 kPa respectively. In this study, the pressure in the cell was not higher than 50 bar, so only the low pressure transducer was used during the experiments. Before the measurements, the thermometer probes and the pressure transducers were calibrated. Both the thermometers and the pressure transducer are connected to an "Agilent" data acquisition system which is linked to a PC and provides real time reading of the values of temperature and pressure. The equilibrium cell is immersed in a liquid bath to maintain the desired temperature, and the temperature of the liquid bath is controlled by a PID controller, which provides and keeps the desired temperature with ±0.01 K. A magnetic stirrer coupled with an electric motor (HELDOLPH, model RZR2020) was held between the two flanges and help accelerate the mixing of the mixture. After the mixture reaches equilibrium, two electromagnetic capillary samplers ROLSI ® are used to sample a small amount of each phase without perturbing the equilibrium conditions and send them into the GC to analyze the compositions of the vapour and liquid phases. The relative accuracies of mole numbers are ±1.2% for ethane and ±0.9 for R1234ze(E). Consequently the maximum uncertainty of mole fractions, calculated at x ethane = 0.5 is u max (x,y) = 0.0043. Experimental Procedure. First of all, the equilibrium cell and the connecting parts are evacuated and put under vacuum by means of a vacuum pump. About 5 cm 3 of the heavier component (R1234ze(E) in this study) is introduced into the cell. Thereafter, a small amount of ethane is introduced into the equilibrium cell from a thermal press (where it is stored). It is assumed to reach the equilibrium conditions when the temperatures and the pressures stay nearly constant for at least 10 min, under continuous stirring. Once the equilibrium is obtained, the liquid and vapour samples are sent to the GC for analysis. For each equilibrium point, at least six samples are taken, for the determination of the average composition and to check the measurements repeatability (less than 1%). Then a further volume of ethane is introduced into the cell and another measurement is started. This procedure is continued until the existence points can cover the whole composition range. Once one isotherm is finished, the cell is emptied, put under vacuum and the same procedure is started for another isotherm.

Data treatment and modelling

The critical temperatures (T c ) and pressures (P c ) and acentric factors ( ) for pure ethane and R1234ze(E) which are collected from the software REFPROP v9.0 18 are provided in Table 2. The experimental VLE data of (ethane + R1234ze(E)) system was correlated with a homemade software developed at the Centre of Thermodynamics of Processes (CTP) -MINES ParisTech. The data were correlated using PR-EoS 7 combined with the classical van der Waals mixing rules.

For the three isotherms higher than the critical temperature of pure ethane, the extended asymptotic behaviour laws described by Ungerer et al. [START_REF] Ungerer | Applications of molecular simulation in the oil and gas industry: Monte Carlo methods[END_REF] (Eqs. ( 1) and ( 2)) were used for the data treatment and the estimation of critical compositions and pressures.

(

(

Where x and y stand for the molar fraction of the liquid phase and vapour phase at pressure P, respectively. x c and P c represent the critical composition and critical pressure, respectively. is a characteristic universal exponent, whose value equals to 0.325. λ 1 , λ 2 and μ are adjustable coefficients regressed from a set of several isothermal coexistence data points (P, x, y) below the critical point.

Results and Discussions

The experimental VLE measurements of (ethane + R1234ze(E)) mixture were performed at six temperatures (272.27, 283.36, 298.04, 308.04, 323.18 and 347.52) K and for pressures up to 4.89 MPa. In addition, the experimental data were correlated with PR-EoS. The experimental VLE data and the calculated ones are reported in Table 3.

In Figure 2, we present the experimental data and the correlated ones with PR-EoS. From this Figure, it is obvious that PR-EoS makes a good calculation for the VLE of the studied mixture, especially for the isotherms lower than the critical temperature of pure ethane. Figure 3 indicates the composition dependency of the relative volatility for the measured temperatures.

A very good agreement between the experimental relative volatility and the calculated values using PR-EoS can be observed. The temperature dependent parameter k ij (see figure 4) were adjusted on experimental data (and listed in Table 4) considering the objective function given by Eq. ( 3). In order to quantify the goodness of the fit of PR-EoS to the experimental data, the mean relative absolute percentage deviations (MRD) and the bias on bubble pressures and vapour mole fractions were calculated. They are all listed in Table 5. The expressions of MRD and bias are defined by Eqs. ( 4) and ( 5) as follows:

(4)

where U represents P or y 1 and N is the number of data points. For the three isotherms higher than 305.32 K and three isotherms lower than 305.32 K, two curves are correlated, respectively. Based on the extended asymptotic behaviour laws (Eqs. 1 and 2), the critical pressures and critical compositions were also calculated and their values were shown in Table 6. The estimated critical points based on experimental data are presented in Figure 5. Also, using our model and the adjusted parameter of Table 4 for T>T c,ethane (given the fact that the values of the BIP are very close, we prefer to use a non-temperature dependent BIP) and based on Heidemann and Khalil method 20 , the critical line is calculated (Table 7) and presented in Figures 5 and6. Based on these results, we can conclude that the model could represent the complete phase diagram of this system with a good accuracy, either at subcritical or supercritical conditions.

Conclusion

In this paper, new VLE data of the (ethane + R1234ze(E)) binary system are presented. This system can be classified as a type I according to van Konynenburg and Scott classification [START_REF] Van Konynenburg | Critical lines and phase equilibria in binary van der Waals mixtures[END_REF] . Experimental measurements were performed at six isotherms using a "static-analytic" apparatus with phase sampling and gas chromatography analysis, with resulting uncertainties of 0.03K for temperature, 0.4 kPa for pressure and 0.0043 for vapour and liquid mole fractions. The experimental data were correlated using PR-EoS combined with the classical van der Waals mixing rules. For the three isotherms higher than the critical temperature of pure ethane, the critical pressures and critical compositions were calculated based on the extended asymptotic behaviour laws.

The results obtained indicate that the selected model reproduce accurately the experimental VLE data of (R1234ze(E) + ethane) mixture, with a maximal deviation of 1.13% for bubble pressure and 1.23% for vapour molar fraction. These new data will be very valuable in selecting new working fluids for heat pump and refrigeration applications. They will be also very useful to extend the plethora of available data and can be used to develop predictive models and fit their parameters.

Figure

  Figure 1.Schematicdiagram of the static-analytic apparatus. C1: more volatile compound; C2: less

Figure 2 .

 2 Figure 2. Phase diagrams for the (ethane (1) + R1234ze(E)(2)) system. (•) 272.27 K; (■) 283.36 K; (▲) 298.04 K; (◆) 308.04 K; (x) 323.18 K; (+) 347.52 K. Solid lines: PR-EoS.

Figure 3 .

 3 Figure 3. Relative volatility as function of molar fraction for the (ethane (1) + R1234ze(E)(2)) system. (•) 272.27 K; (■) 283.36 K; (▲) 298.04 K; (◆) 308.04 K; (x) 323.18 K; (+) 347.52 K. Solid lines: calculated using PR-EoS.

Figure 4 .

 4 Figure 4. Plot of adjusted temperature dependent parameter k ij versus temperature. Vertical dashed line: critical temperature of ethane. Horizontal dashed line: binary interaction parameter adjusted using all the data for T>T c,ethane .

Figure 5 .

 5 Figure 5. Phase diagrams for the (ethane (1) + R1234ze(E)(2)) system. (◆) 308.04 K; (x) 323.18 K; (+) 347.52 K. (Δ) Estimated critical points using experimental data. Solid lines: PR-EoS, Dashed line: critical line.

Figure 6 .

 6 Figure 6. Critical temperature and pressure as a function of composition for the binary system ethane (1) + R1234ze(E)(2).

Table 1 . Purities and suppliers of the chemicals used in this work

 1

	Chemicals	CAS Registry Number	Purity (GC)	Supplier
	Ethane	74-84-0	99.95 vol%	MESSER
	R1234ze(E)	29118-24-9	≥ 99.5 wt%	Climalife

Table 2 . Thermal properties for ethane and R1234ze(E) pure component (Source REFPROP 9.0)

 2

	Component	T c /K	P c /MPa	Acentric factor ω
	Ethane	305.32	4.8722	0.0995
	R1234ze(E)	382.52	3.6363	0.313

Table 3 . Experimental and Calculated VLE data of (ethane (1) + R1234ze(E) (2)) system a .

 3 n x , n y : number of taken samples. △P=P cal -P exp . △y=y cal -y exp ,

	Experimental data

b

Table 4 . Adjusted k ij and objective function values.

 4

	T/K	k ij	F (Eq. 4)
	272.27	0.1044	0.013
	283.36	0.1028	0.007
	298.04	0.1017	0.011
	308.04	0.1051	0.057
	323.18	0.1058	0.069
	347.52	0.1177	0.002
	T>T c,ethane	0.1052	0.053

Table 5 . MRD and Bias values for bubble pressures and vapour phase compositions.

 5

	T/K	Bias (P)/%	MRD(P)/%	Bias(y)/%	MRD(y)/%
	272.27	-0.60	-0.05	0.71	0.14
	283.36	-0.38	0.01	0.53	0.13
	298.04	0.19	0.08	0.30	0.26
	308.04	0.10	0.24	0.34	0.30
	323.18	0.66	0.78	0.69	0.78
	347.52	-0.05	0.69	0.38	1.14
	T> T c,ethane	0.69	1.13	0.78	1.23

Table 6 . Critical pressures and critical compositions of the mixture at temperatures higher than the critical temperature of pure ethane.

 6

	T/K	P c /MPa	x c,ethane	μ * 10 3	λ 1 * 10 4	λ 2 * 10 4
	308.04	4.833	0.948	6	996	-1557
	323.18	4.912	0.751	102	910	-1201
	347.52	4.848	0.478	163	241	-938

Table 7 . Values of calculated critical temperature and pressure with temperature independent BIP.

 7

		6
		5
	MPa	4
	/
	Pressure	2 3
		1
		0
		0	0.2	0.4	0.6	0.8	1
				x 1 , y 1
			x 1	T/K	P/MPa
			0.00	382.52	3.64
			0.10	376.93	3.96
			0.20	370.71	4.26
			0.30	363.78	4.53
			0.40	356.09	4.76
			0.50	347.65	4.91
			0.60	338.57	4.98
			0.70	329.11	4.96
			0.80	319.76	4.89
			0.90	311.37	4.82
			1.00	305.32	4.87

Acknowledgments

The authors are grateful to MINES ParisTech and China-EU Institute for Clean and Renewable Energy (ICARE) for allowing the opportunity to realize this internship at CTP -MINES ParisTech, and providing all the resources that led to this work.


Camille Bernard
email: camille.bernard@imag.fr

Christine Plumejeaud-Perreau
email: christine.plumejeaud-perreau@univ-lr.fr

Marlène Villanova-Oliver
email: marlene.villanova-oliver@imag.fr

Jérôme Gensel
email: jerome.gensel@imag.fr

Hy Dao
email: hy.dao@unige.ch

An Ontology-based Algorithm for Managing the Evolution of Multi-Level Territorial Partitions

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

MULTI-LEVEL CHANGE BRIDGES

A graph structure to navigate through the TSN versions + observe the propagation of a change event through the levels

3 4 ES62' ES63' ES62'' ES63'' ES64'' ES62' ES63' ES62'' ES63'' ES64''
Iterations of the algorithm

BeforeK AfterK (1) (ES63') (2) (ES63'', ES64'') (3) (ES63') (1) (2)
(3)

Identifying clusters of changes

Builds through iterations two sets of units BeforeK and AfterK. Adds successively to the sets, units that intersect ones in the other version. Stops when one set (BeforeK or AfterK) remains identical between two iterations.

4.2

Extraction

Linking changes through the levels

Matchings of territorial units

Which attributes may vary, in which proportion, before the entity loses its identity?

Solution -configurable identity test in 3 steps:

1. An expert defines which attributes hold the identity of the units ID? Name? Geom? Super Unit? 2. For each attribute: a specific Comparison Operator is defined to measure distance between the two versions:

| u'.attribute -u''.attribute|

MODIFIABLE AREAL UNIT PROBLEM (MAUP)

Modifiable Areal Unit Potential [Grasland and Madelin] Data are not comparable due to potential changes of the territorial units over time

  Two Spanish enclaves in North Africa, Ceuta and Melilla considered as one unit in NUTS 1999 ; split in two in NUTS 2003 Input Two lists V' and V'' of units u' and u'', all units being at one Level l. Output A RDF graph describing Matching and Changes on Units Change example in the EuroStat geographic nomenclature http://purl.org/net/semantic description of TSN changes: feature by feature + cluster of changes + chain of changes + 2 case studies

  = define in which proportion attributes can vary before unit loses its identity. E.g: ( u′ . geom -u′ ′ . geom ) + 1/6 * ( u′ . name -u′ ′ . name ) 1/3 * ( u′ . identifier -u′ ′ . identifier )+ where F(α 1 , identifier), (α 2 , geom), (α 3 , name) α 1 = 1/3,α 2 = 1/3,α 3 = 1/6 ✓Australia -Australian Statistical Geography Standard (ASGS) 2 versions, 4 levels, 5356 geographic units Influence of the partition on data [Openshaw & Taylor]

Visualizing geospatial changes over time. On GItHub https://github.com/blog


est destinée au dépôt

Context

The radioactivity of the spent nuclear fuel is dominated by the α-activity of the minor actinides generated during operational time and included within the UO 2 matrix. The accumulation of α-damage and radiogenic He (shown in the graph) results in a modification of the microstructure and properties of the material, which has to be known to accurately predict the long term behaviour of the stored spent fuel.

Experiment

Two compositions were chosen:

-2.5%wt Pu, for the evolution of hardness and thermal conductivity in particular -10%wt Pu, for those properties which degrade more slowly Comparison between the XRD patterns of the two batches. Lattice parameter in good agreement with the Vegard Law for solid solutions.

  Long-term storage behaviour of spent nuclear fuel simulated by accelerated radiation damage with 238Pu-doped UO2 Emanuele de Bona, Marco Cologna, Thierry Wiss, Rudy J. M. Konings, Gianguido Baldinozzi To cite this version: Emanuele de Bona, Marco Cologna, Thierry Wiss, Rudy J. M. Konings, Gianguido Baldinozzi. Longterm storage behaviour of spent nuclear fuel simulated by accelerated radiation damage with 238Pudoped UO2. MRS Spring Meeting 2018. Fundamental Materials Science to Enable the Performance and Safety of Nuclear Technologies. Symp EN17, Apr 2018, Phoenix, United States. hal-01929654



  Samples design: bibliographic research of self-irradiation saturation values, choice of suitable compositions to reach saturation within PhD timeframe  Samples preparation: powder synthesis, pressing and sintering, achievement of a PuO 2 and UO 2 solid solution  Fresh pellets characterization  Periodic characterization: 3 different storage temperatures (room T, wet storage T ~ 200 ℃, liquid N 2 T ~ -200 ℃), monitoring of the degradation of the thermophysical properties and microstructural evolution of LWR spent fuel due to self-irradiation and helium formation Samples preparation Powder synthesis: 1. Dissolution of the Pu powder using NHO 3 and HF 2. Separation in two batches and addition of the correct amount of U solution 3. Precipitation with ammonia addition 4. Filtration with paper filters 5. Pre-calcination (400 ℃) under air to burn the filters away 6. Calcination (700 ℃) under Ar-H 2 Powder pressing and sintering: Pressing: ф = 5 mm; F = 14.5 kN; resulting p = 738 Mpa Sintering: 1650 ℃, 6 h, under Ar-H 2 Periodic characterization -room T batch After annealing of defects (4h at 1250 ℃ under Ar-H 2 ), characterization started for the room T batch. Conclusions • (U,Pu)O 2 disks successfully sintered (geometrical density of 94-96%TD), composition measured by XRD in good agreement with the Vegard Law for solid solutions • Started the characterization of the room T batch (XRD, LAF, TEM, but also RAMAN, EXAFS, NMR and DSC, not shown here) Future steps • Periodic indentation and KEMS (Knudsen cell Effusion Mass Spectrometry, i.e. He thermal desorption) for room T batch • Periodic characterization of samples stored at 200 ℃ and -200 ℃ Long-term storage behaviour of spent nuclear fuel simulated by accelerated radiation damage with 238 Pu-doped UO 2 E. De Bona a,b , M. Cologna a , T. Wiss a , R.J.M. Konings a , G. Baldinozzi b , a JRC-Karlsruhe, Eggenstein-Leopoldshafen (Karlsruhe), 76344, Germany b CentraleSupélec, Gif-sur-Yvette (Paris), F-91190, France European Commission • Joint Research Centre Nuclear Safety and Security Directorate Emanuele.DE-BONA@ec.europa.eu

2Θ2ΘFirst

  XRD results: increase of the lattice parameter as function of the storage day and dpa. Shift of the first peak of the XRD pattern as the self-irradiation damage increases. diffusivity degradation, measured at 550K by Laser Flash Analysis (LAF) Right: dislocation loops observed by TEM investigation on a 10%wt doped


LGC Florent Bourgeois
email: florent.bourgeois@ensiacet.fr

Carine Julcour-Lebigue

LGC Laurent Cassayre
email: laurent.cassayre@ensiacet.fr

CNRT France Bailly
email: france.bailly@cnrt.nc

LMDC Martin Cyr
email: martin.cyr@insa-toulouse.fr

Solène Touzé
email: s.touze@brgm.fr

Guiding mineralization process development with geochemical modelling

Keywords: CO2 utilization, mineralization, geochemical modelling, attrition-leaching, Ni-slags

Mineralization is a CO 2 utilization solution that can possibly meet all the CO 2 mitigation criteria stated by the International Energy Agency, namely CO 2 emissions reduction, economic self-sufficiency and scalability. Considered as a global niche markets solution, mineralization process development is particularly challenging, as its scope is territory dependent and combines feedstock selection, mineralization technology and undisruptive product valorization through local materials supply chains. Identification of potential mineralization pathways is a definite challenge. This paper argues that geochemical modelling is an indispensable guiding tool for mineralization process development. Owing to its capacity to predict product speciation for complex mineralization systems, the paper discusses a number of issues that illustrate and confirm the value of geochemical modelling for feedstock selection, product valorization and process engineering. Supporting arguments are provided in the context of the valorization of Ni-slags from the New Caledonian metallurgical industry. It is concluded that geochemical modelling is an undisputed building block for developing and modelling any mineralization process. Moreover, the paper argues that the full potential of geochemical modelling for mineralization process design requires its merging with high-level decision-making frameworks, such as regionalized life cycle assessment.

Introduction

According to the IEA, CCUS will have to contribute 19% of the GHG emissions reductions needed up to 2060 in order to stay below the current 2°C climate change target [1]. This statement stresses that actual CCUS solutions are definitely needed, that they must be large scale solutions, and that their actual deployment must occur sooner rather than later. Deployment of large scale solutions over such a short time horizon also implies that eligible solutions must rely on proven industrial technology. Moving to the "U" component of CCUS, the IEA [1] states that worthy CO 2 utilization solutions must meet 3 criteria: (1) they must have the potential to achieve a significant emissions reduction, (2) they must generate revenue to offset their implementation costs, and (3) they must be scalable to scales commensurate with large point sources.

Amongst CO 2 utilization options [2], mineral carbonation, also referred to as mineralization, appears to be the only CO 2 utilization solution that can meet all the above criteria. For many years, the development of mineralization as a CO 2 mitigation solution has been largely hindered by the fact that it was considered from a CCS (i.e. CCUS without the "U") perspective, leading to a biased service-to-service comparison with geological storage. Conclusions were therefore misleading and mineralization was labelled a niche and uneconomic solution to CO 2 mitigation by the CCS community. Notwithstanding the fact that mineralization does not just store CO 2 as it eliminates it, recent years have brought a completely different take on mineralization. It is now righteously described as a CO 2 utilization solution [2] that can produce useful commodities (e.g. construction and specialty materials, metals) while either eliminating CO 2 and/or reducing the carbon footprint of producing commodities by other means. The early criticism of mineralization being a niche solution has now become a strength. Indeed, as it has the potential to use CO 2 to valorize a wide variety of abundant natural and anthropogenic resources (e.g. mafic ores, brines, mining waste, metallurgical slags) into useful commodities, it can potentially process different feedstocks and therefore be deployed globally while being tailored to meet local markets. In other words, it can be tailored to valorize local feedstocks and produce materials that are needed locally also. Thus, mineralization can be described as a global niche markets solution and its economic and societal viability must be evaluated as such. Clearly, regional economic and LCA analyses must be used to guide the forms it should take locally. The need for scalability of mineralization solutions is technology dependent and must be met by the proposed mineralization solutions. The approach that is recommended by the authors is to develop solutions that rely upon proven technologies used by large-scale industries. This will not only ensure the scalability of the proposed solutions, but also their industrial acceptability and hence potential for rapid deployment.

The solution developed by the authors, which is described in the next section, has the potential to meet all these criteria. It does not preclude the need to develop many other solutions. Indeed, there is no one solution that fits all. Depending on local constraints, one mineralization solution may be more cost-effective than another, and the fact that mineralization can be implemented in different ways must be seen as an actual strength of this CO 2 utilization solution. The corollary is an implicit need to standardize the way by which one may be able to compare and select mineralization solutions. The ongoing work of ISO/TC265 to provide standard guidelines for conducting LCA analysis for CO 2 utilization solutions is important in this respect.

Nomenclature

CCUS

Mineralization by attrition-leaching

The proof of concept of the mineralization process developed by the authors, which they refer to as "attritionleaching", has been established [3,4]. Its development is currently pursued through a project supported by the New Caledonian Energy Agency (project ACE No. CS17-3160-00), whose aim is to produce materials that meet the needs of the construction sector in New Caledonia through mineralization of pyrometallurgical Ni-slags. Currently, CO 2 emissions per capita are about 25 metric tons per annum and expected to rise in New Caledonia, which is high by any standard. Moreover, the Ni mining and metallurgical industry, which accounts for 20% of the territory's GDP is blamed for half of these emissions. Beyond numbers, this is a cause of concern in terms of pollution in the capital, Nouméa, and measures are being taken to reduce this issue through modernizing industrial power production systems. The Ni mining industry also produces about 3 million tons of Ni-slags per year as industrial waste. Considering the scale of the New Caledonian mining industry and its significance to the local economy, the favorable properties of Ni-slags as a mineralization feedstock, the insularity of the territory and the stunning beauty of this southwest Pacific island, this project combines many ingredients of a significant project on mineralization.

The attrition-leaching mineralization process falls in the category of hydrometallurgical processes. Moreover, it is of the direct aqueous mineral carbonation type. Indeed, it couples dissolution of the particulate feedstock in water acidified by dissolved CO 2 with precipitation of carbonates that bind cations (e.g. Mg, Fe, Ca) that are leached out of the feedstock with dissolved CO 2 species [5]. The rationale behind the attrition-leaching mineralization process is a continuous mechanical exfoliation of carbonatable feedstock particles during their leaching to offset the surface passivation that invariably plagues their leaching. It also coproduces fine particles of feedstock particles which is favorable in terms of reactive particle surface area. The authors developed this concept in a wet stirred media mill, whose technology is proven and accepted by large-scale mining operations throughout the world [6]. Tested on a number of natural Mg-bearing ores and mining waste, this mineralization solution was found to be largely insensitive to the nature of the feedstock. The extent of carbonation that has been obtained to date with this process under batch conditions can exceed 80% in 10 to 24 hours, starting with minus 100 µm feed particles.

The scope of the mineralization process, as described earlier, makes its optimization a complicated and possibly unintuitive matter. Indeed, optimization is not limited to standard process engineering, i.e. dealing with operating conditions such as CO 2 partial pressure, temperature, solid-liquid ratio and net energy consumption, as it must also account for the processing of local feedstocks to yield products that can contribute positively to the local supply chain of construction materials. This challenging objective goes beyond standard hydrometallurgical process optimization strategies used by process engineers.

Possibilities are virtually innumerable. Indeed, depending on the composition of the feedstock, nickel slags in this case, and the operating conditions used, a variety of product phases can be formed, whose value for producing addedvalue materials will depend on the local situation. Possible target materials may include hydraulic binders [7,8], fillers and pozzolanic materials, to name just a few possibilities depending on the local supply chain for construction materials.

There is a need for guiding tools to help narrow down the possibilities prior to designing the process and conducting actual experiments. One such tool is geochemical modelling [9], which is defined here as a modeling framework that predicts the evolution of the chemical composition of phases in the mineralization system, based on thermodynamic and kinetic models. Geochemical modelling can be a judge of peace for mineralization process design. Indeed, if geochemical modelling predicts that a phase of interest does not form under particular conditions, it cannot be expected to form in real life. However, geochemical modelling predicting the formation of a particular phase does not necessarily mean that it will form in real life, and experimentation is inseparable from geochemical modelling for mineralization process design.

Given the uncertainties or lack thereof of thermodynamic and kinetic data, geochemical modelling results provide trends only, hence the value of geochemical modelling as a "guiding" tool for process design and operation. In other words, geochemical modelling results should not be understood as absolute, i.e. they are no substitute for experiments for obtaining absolute process performance values. Nonetheless, the value of geochemical modelling for mineralization process design is invaluable. The next section illustrates some of the features of geochemical modelling for guiding the attrition-leaching mineralization process design.

Geochemical modelling as a guide for Ni-slags mineralization process design and operation

Geochemical model settings

The mineralization feedstocks of interest to the project are pyrometallurgical Ni-slags produced in New Caledonia. Fig. 1 positions these slags in a MgO-Fe 2 O 3 -SiO 2 composition diagram. In terms of mineralogy, Ni-slags can be regarded as ultramafic rocks, for which the attrition-leaching mineralization process has been found to work well, producing magnesite as the main mineralization product [3,4]. A typical molar composition of Ni-slags given as metal oxides and limited to the principal metals is (SiO 2 1, MgO 0.824, Fe 2 O 3 0.104, Al 2 O 3 0.022). This is the composition used in the paper. It is noted that geochemical modelling can help quantify the effect of variations in composition, including minor elements such as Mn and Ca, which are also present in Ni-slags.

Fig. 1. Position of New Caledonian Ni-slags in the MgO-Fe2O3-SiO2 composition diagram

Prediction of mineralization products is achieved with the geochemical modelling software PhreeqC [START_REF] Charlton | Modules based on the geochemical model PHREEQC for use in scripting and programming languages[END_REF]. The numerical calculations are carried out using the R interface package to PhreeqC [START_REF] Charlton | Phreeqc: R Interface to Geochemical Modeling Software[END_REF]. Running the geochemical calculations in a numerical environment such as R makes it possible to seek process conditions that meet specific targets and carry out sensitivity analysis of process performance [START_REF] Lucia Kühn | Coupling R and PHREEQC: efficient programming of geochemical models[END_REF]. One value of geochemical modelling is to permit analyzing the sensitivity of the mineralization process to various process inputs, including:

 The composition of the feedstock, which can be modified to evaluate the effect of a minor element for example.  The feedstock particle size distribution, which affects the surface-driven process kinetics.  The process operating conditions, such as temperature and CO 2 partial pressure.  The water composition, which can be varied to assess the possibility of using sea water for example.  The nature of the grinding medium, which can possibly affect the process performance. Possibilities include using inert or reactive grinding medium [9], as well as testing the option of using autogenous attrition.

Inputs to the geochemical model for the attrition-leaching mineralization of Ni-slags

Applying geochemical modelling to mineralization process design requires feedstock specific properties (elemental and mineral composition as well as the particle size distribution (PSD)) combined with appropriate thermodynamic and kinetic models.

The thermodynamic model main features are as follows:  The gas phase is an ideal mixture of CO 2 , H 2 O, CH 4 and H 2 , each compound being described by the Peng-Robinson equation of state.  The aqueous phase is described according to the LLNL aqueous model, which is a variant of the Debye-Hückel model (the so-called B-dot equation). This approach is fully justified by the low ionic concentration of the solution (ionic strength of about 10 -3 to 10 -2 ).  The solid phases are described as stoichiometric compounds, except for the (Mg,Fe)CO 3 solid solution which was modeled with a regular solution parameter of 4.44 kJ.mol -1 at 770 K [START_REF] Chai | Synthesis, characterization, and enthalpy of mixing of the (Fe,Mg)CO3 solid solution[END_REF].

All model parameters (equilibrium constants and Debye-Hückel parameters for aqueous species) come from the 2017 version of the Thermoddem database [START_REF] Blanc | Thermoddem: A geochemical database focused on low temperature water/rock interactions and waste materials[END_REF] (downloadable at http://thermoddem.brgm.fr/). Some knowledge about speciation pathways of the system is also necessary. For example, precipitation of silica as amorphous silica is favored over quartz, therefore precipitation of quartz is blocked in the geochemical simulation. The same applies to goethite, whose formation is favored over hematite and magnetite under mineralization conditions. There is no substitute for comprehensive literature review and precise experimentation to tailor the geochemical modelling hypotheses to the mineralization system of interest. Validation of geochemical hypotheses is an iterative process, whereby questions are asked about the likelihood of formation of predicted phases and corrections made to the geochemical hypotheses depending on confirmation from literature and experiments.

The dissolution kinetics of the slag particles uses the model and associated parameters proposed by Oelkers and Schott [START_REF] Oelkers | An experimental study of enstatite dissolution rates as a function of pH, temperature, and aqueous Mg and Si concentration, and the mechanism of pyroxene/pyroxenoid dissolution[END_REF] for enstatite. As seen in Fig. 1, this is a fair assumption even though it approximates the actual mineralogy of Ni-slag samples, which X-Ray diffractograms evidence the presence of forsterite (Mg 2 SiO 4 ), enstatite (MgSiO 3 ) and ferrosilite (FeSiO 3 ). The dissolution rate r is given by: 2 0.25 0.125 0 ( ) ( )

a E RT H Mg r k e a a            ( 1
)
where a (i) is the activity of aqueous compound i, E a the activation energy and R the gas constant.

To have a realistic dissolution rate model for the Ni-slag, the pre-exponential kinetic constant k 0 was adjusted against experimental measurements. This was achieved by matching the predicted CO 2 consumption of a Ni-slag sample having the PSD of Fig. 2 with that measured in a 300 mL attrition-leaching batch experiment conducted near 180°C with P CO2 = 20 atm [3]. Such an approach for kinetic model adjustment is imperfect, and yet it is deemed sufficient for exemplifying the potential of geochemical modelling as an orientation tool for attrition-leaching mineralization process design. Among its known flaws, the approach assumes that PSD changes due to dissolution only, i.e. particle attrition kinetics of the attrition-leaching process matches the particle dissolution rate exactly. It is likely that the actual particle attrition rate exceeds the dissolution rate, hence a probable overestimation of the real Ni-slag dissolution rate.

The PSD of Ni-slag particles produced by dry milling is well described by a Rosin-Rammler distribution. A typical PSD used in batch attrition-leaching mineralization tests is shown in Fig. 2 in cumulative surface percent passing, with a top size around 100 µm.

Fig. 2. Typical particle size distribution of Ni-slags for the mineralization process

The experimental PSD is specified to PhreeqC as a discretized surface PSD given the surface-driven nature of the mineralization process. Forty or more particle size classes are used in the simulation to describe the experimental particle size distribution. Each particle size class is input to the PhreeqC as a separate phase, all classes having identical chemical composition, thermodynamic and dissolution kinetic properties.

The time variation of the slag PSD is recalculated at each calculation time step, by conserving the number of particles in each size class and recalculating their size based on the mass loss during the time step. It is assumed that particle attrition kinetics matches the particle dissolution rate exactly. Future work plans to couple the geochemical dissolution model with an actual attrition model, using grinding models suitable for stirred mills. Investigation of the 6 GHGT-14 Bourgeois, Julcour-Lebigue, Cassayre, Bailly, Cyr, Touzé actual attrition and leaching rates is an important aspect of attrition-leaching mineralization process optimization which has not yet been investigated.

Geochemical modelling as a guide to selection of attrition-leaching Ni-slag mineralization pathways

The attrition-leaching mineralization process must be optimized with respect to many variables, including time, energy and water consumption. However, given the paramount objective of producing phases that can enter the construction materials supply chain, the first question concerns the phases that can be formed by the attritionleaching mineralization process of Ni-slags. To this end, CO 2 partial pressure and temperature were varied in the range [0.1-20] atm and [100-180] °C respectively in the geochemical simulations. It is noted that the authors use the conditions [20 atm; 180°C] as their base case for conducting mineralization experiments.

Across this range of conditions, geochemical modelling predicts that Ni-slags can produce numerous phases (See Table 1). Addition of minor elements such as Ca or Mn present in the Ni-slags yield additional phases. From a product valorization standpoint, 4 families of phases are identified in Table 1, namely carbonates (whose dominating form is a Fe-enriched magnesite according to Rietveld analyses on experimental products), metal (hydr)oxides, Mg-bearing silicate phases (whose formation competes with the formation of magnesite) and other silicate phases. Some of these phases offer promising perspectives from a construction materials production perspective, whereas others may be less desirable depending on the application. Moreover, with the exception of amorphous silica for which thermodynamic data is described in the Thermoddem database, it is not possible to predict whether amorphous or crystallized aluminosilicates will form during the process. Experiments are needed to shed light on this issue for product utilization, given the higher reactivity and potential value of amorphous alumina silicate admixtures positive on concrete properties [START_REF] Nagrockienė | Properties of concrete modified by amorphous alumina silicate[END_REF].

A sensitivity analysis was carried out with respect to the effect of the presence of Al in the Ni-slags. Indeed, geochemical modelling predicts the possibility of Al forming many silicate phases with Mg depending on its grade in the Ni-slags (See Table 1). With the stoichiometry used, the formation of talc and amorphous silica is predicted to occur. TEM petrographic analyses of Ni-slag mineralization product confirmed the formation of spherules and fluffy particles as talc. Geochemical modelling predicts a strong effect of Al in the slag, whose increase yields the formation of aluminosilicate phases instead of amorphous silica. This speciation has a direct bearing on possible product valorization, depending on the amorphosity of such phases.

GHGT- 14 Bourgeois,Cassayre,Bailly,Cyr,Touzé The capacity of geochemical modelling to predict the effect of specific elements on product speciation is very powerful. Indeed, the first-hand prediction of product speciation provided by geochemical modelling is relevant for both feedstock mapping and product valorization. Geochemical modelling can be used to assess the value of local feedstocks, with or without blending, in relation to local needs for construction materials. Geochemical modelling can be used as resource mapping tool, and help define the range of feedstock compositions that one should prioritize for a particular product valorization purpose, especially if the formation of a specific phase must imperatively be avoided. Alternatively, given a feedstock, geochemical phase prediction can imply that specific separation steps must be taken to control the level of specific elements in the mineralization process. Fig. 3 shows the predicted amount of leached Ni-slag as a function of temperature and CO 2 partial pressure for a 24 hour mineralization experiment with base case conditions. It is readily seen that higher temperature and CO 2 partial pressure yield a monotonic increase in the extent of reaction of Ni-slags. For process optimization, the downward slope of the iso-contours suggests that increasing CO 2 partial pressure permits reducing temperature for the same conversion of the Ni-slags. Fig. 3 however does not say anything about the composition of the mineralization products. Figs. 4 and5 show iso-contours for the predicted mass fraction of carbonates and amorphous silica in the mineralization product, both phases being of interest for product valorization as construction materials. The hand-drawn dotted lines show the locus of the most favorable (T;P CO2 ) set points for maximizing the production of both product phases as predicted by geochemical modelling. Should one want to promote the formation of these phases, geochemical simulations indicate that a temperature of 150°C is the best set point for a CO 2 partial pressure of 20 atm, for which Fig. 3 predicts a Ni-slag dissolution between 70% and 80%. The same analysis can be carried out for any potential phase of interest, providing the information needed by materials engineers to explore all possibilities for valorization of Ni-slags as construction materials.

Geochemical modelling as a guide to selection of attrition-leaching Ni-slag mineralization operating conditions

Once solutions for product valorization have been identified, geochemical modelling can then be used for process design. In the mineralization context, prediction of pH can be obtained, which is significant for process material selection. At a temperature of 150 °C and a CO 2 partial pressure of 20 atm, geochemical modelling predict a pH value of 5 using plain water. Other questions can be asked about the effect of many basic process variables, such as slurry concentration, which echoes with a lesser water consumption. Increasing solids concentration in the range 10 to 40 wt% is not expected to affect the product speciation according to the geochemical model. Nevertheless, increasing slurry concentration is critical from a process perspective, in terms of water footprint, downstream processing and conversion of products to construction materials. As the geochemical model reported here is not coupled with a grinding model, the kinetics of appearance of the product phases is not predicted to depend on concentration of solids in the slurry. This is not expected to hold true in practice as it surely affects stirred milling performance.

Prediction of process kinetics, in terms of leaching of Ni-slag and appearance of the phases of interest, is important for process design and performance. Here also, geochemical modelling can be of assistance. Fig. 6 shows the time-dependent formation of phases that are predicted to form as a function of feed particle top size. Fig. 6 confirms the significance of the feedstock particle size on the process kinetics, which is valuable information for process design and optimization. With the attrition-leaching process, the rate of change of particle size depends both on Ni-slag leaching kinetics and attrition rate, which must be optimized as a whole. Fig. 7 shows the predicted rate of change of the Ni-slag PSD as a function of time, as predicted from shrinking particle dissolution kinetics only. It exemplifies the rapid disappearance of the finer particles driven by their high specific surface area. Other more complex process parameters can be investigated by geochemical modelling, such as gas and water composition. When dealing with mineralization processes, the possibility of using flue gases, which carry low CO 2 partial pressure and possible minor elements, is important. Notwithstanding potential corrosion issues, the possibility of using sea water instead of fresh water as the aqueous medium also offers promising alternatives from an environmental standpoint. Indeed, sea water is already being used to quench molten slags in some New Caledonian pyrometallurgical plants and preservation of fresh water resources is paramount. Here also, geochemical modelling can help predict product speciation.

Final words on selection of attrition-leaching Ni-slag mineralization pathways with geochemical modelling

This paper has exemplified that geochemical modelling can provide valuable first-hand information on the effect of key variables on mineralization process design and optimization, from feedstock assessment to product valorization.

Although an invaluable guide for narrowing down possible mineralization pathways based on particular constraints, such as the formation of desirable phases for a local materials supply chain, geochemical modelling is not self-sufficient as a decision making tool. Geochemical modelling is deemed a key building block for mineralization process modelling, whose predictions can be used to feed actual decision-making tools. To harvest its full potential for mineralization process design, geochemical modelling must be coupled with supervisory frameworks that converts its predictions into environmental and economic units, using validated regionalized impact and value assessment methods. In particular, the authors see significant potential in integrating geochemical modelling into a regionalized LCA programming environment. With the scripting interface now available in openLCA version 1.7 [START_REF] Noi | References Geochemical modelling : a guiding tool for mineralization feedstock & product valorization assessment Geochemical modelling : a guiding tool for mineralization process design Mineralogy of Ni-slags Surface leaching rate model[END_REF] for example, there is a significant potential for interfacing LCA analysis with a geochemical metamodel that calls PhreeqC through R. This is the path the authors intend to pursue in order to deliver a decision-making tool for tailoring the attrition-leaching mineralization process to produce low carbon footprint construction materials to regional markets using local feedstocks.

Conclusions

Mineralization is a promising CO 2 utilisation solution. In principle, it can meet the three CO 2 mitigation criteria set by the IEA, namely CO 2 emissions reduction, economic self-sufficiency and scalability. One promising mineralization process is the attrition-leaching process that is currently being applied for valorizing the Ni-slags produced by the New Caledonian metallurgical industry.

Mineralization process development is challenging as its scope is territory dependent and combines feedstock selection, mineralization technology and non disruptive valorization of mineralization products through local materials supply chains. Identification of potential mineralization pathways is a definite challenge, which starts with the complexity and variety of mineralization systems' geochemistry.

The paper argues that geochemical modelling as an indispensable tool for design of aqueous mineralization solutions. Using New Caledonian Ni-slags as feedstock, a large-scale and local industrial waste, the paper attempts to exemplify the capacity of geochemical modelling to predict product speciation in valuable mineralization systems. It is shown that geochemical modelling provides first-hand information critical to evaluation of both feedstock and product valorization potential. From a technological standpoint, geochemical modelling can also provide insightful information about the effect of important process operating variables on process performance.

Geochemical modelling is therefore an indisputable building block for developing and modelling any mineralization process. To harvest its full potential for mineralization process design, it is believed that geochemical modelling must be embedded into a supervisory framwork that converts geochemical model predictions into environmental and economic units, such as regionalized LCA.

As a last word of caution, if the potential of geochemical modelling is indisputable for mineralization process design, its potential depends strongly on the user's expertise and critical thinking. This point must never be underestimated, and it is certainly no substitute for dedicated experiments, which are indispensable for fine tuning geochemical model settings for s specific mineralization system. In the context of mineralization of Ni-slags by attrition-leaching, additional product characterization is necessary to confirm the predicted speciation, in particular about the formation of aluminosilicate phases and their amorphosity. Also, coupling geochemical modelling with a validated attrition model is required for further process development and optimization.

Geochemical modelling

Fig. 3 .

 3 Fig. 3. Predicted Ni-slag dissolution extent as a function of temperature and PCO2

GHGT- 14 Fig. 4 .

 144 Fig. 4. Predicted mass percent of carbonates in mineralization product as a function of temperature and PCO2

GHGT- 14

 14 Bourgeois, Julcour-Lebigue, Cassayre, Bailly, Cyr, Touzé (a) Particle top size = 100 µm (b) Particle top size = 10 µm Fig. 6. Predicted mineralization product phases (T=150°C, PCO2=20 atm).

Fig. 7 .

 7 Fig. 7. Predicted rate of change of Ni-slag PSD during the mineralization process (T=150°C, PCO2=20 atm)

Table 1 .

 1 Mineral phases formation predicted by geochemical modelling for PCO2= [0.1-20] atm and T= [100-180] °C

	Phase type	Phase name	Formula
	Carbonates	Magnesite (Synthetic)*	MgCO3
		Siderite*	FeCO3
	Metal (hydr)oxides	Amorphous Silica	SiO2
		Goethite	FeO(OH)
	Magnesium silicates	Talc	Mg3Si4O10(OH)2
		Antigorite	Mg48Si34O85(OH)2
		Montmorillonite(HcMg)	Mg0.3Mg0.6Al1.4Si4O10(OH)2
		Sudoite	Mg2Al4Si3O10(OH)8
		Chlinochlore	Mg5Al(AlSi3)O10(OH)8
		Beidellite(Mg)	Mg0.17Al2.34Si3.66O10(OH)2
		Saponite(Mg)	Mg3.17Al0.34Si3.66O10(OH)2
		Saponite(FeMg)	Mg.217FeAl0.34Si3.66O10(OH)2
	Other silicates	Minnesotaite	Fe3Si4O10(OH)2
		Chamosite.Daphnite	Fe5Al(AlSi3)O10(OH)8
		Pyrophyllite	Al2Si4O10(OH)2

* The two carbonates are described as a full (Fe,Mg)CO3 solid solution

Desirable products Mineralization of CO 2

  Si 4 O 10 (OH) 2 Antigorite Mg 48 Si 34 O 85 (OH) 2 Montmorillonite(HcMg) Mg 0.3 Mg 0.6 Al 1.4 Si 4 O 10 (OH) 2 Sudoite Mg 2 Al 4 Si 3 O 10 (OH) 8 Chlinochlore Mg 5 Al(AlSi 3 )O 10 (OH) 8 Beidellite(Mg) Mg 0.17 Al 2.34 Si 3.66 O 10 (OH) 2 Saponite(Mg) Mg 3.17 Al 0.34 Si 3.66 O 10 (OH) 2 Saponite(FeMg) Mg .217 FeAl 0.34 Si 3.66 O 10 (OH) 2 Other silicates Minnesotaite Fe 3 Si 4 O 10 (OH) 2 Chamosite.Daphnite Fe 5 Al(AlSi 3 )O 10 (OH) 8 Pyrophyllite Al 2 Si 4 O 10 (OH) 2

	Phase type	Phase name	Formula
	Carbonates	Magnesite (Synthetic)*	MgCO 3
		Siderite*	FeCO 3
	Metal (hydr)oxides	Amorphous Silica	SiO 2
		Goethite	FeO(OH)
	Magnesium silicates Mg 3 Attrition-leaching Talc
	mineralization reactor

Acknowledgements

The authors acknowledge the trust and support of the New Caledonian Energy Agency (project ACE No. CS17-3160-00) for the current developments of the attrition-leaching mineralization process in the New Caledonian regional context.

First-hand prediction of mineralization system speciation

Geochemical modelling is a pivotal brick for mineralization modelling. Geochemical modelling is defined here as a modeling framework that predicts the evolution of the chemical composition of phases in the mineralization system, based on thermodynamic and kinetic models. It is ideally suited for the attrition-leaching mineralization process as this process is unimpeded by surface leached layers and hence operates at the thermodynamic and kinetic limits of the feedstock.

• Geochemical modelling provides first-hand information critical to evaluation of both feedstock and product valorization potential. From an technological standpoint, geochemical modelling also provides insightful information about the effect of many operating variables on process performance.

• To harvest its full potential for mineralization process design, geochemical modelling must be embedded into a supervisory framework that converts geochemical model predictions into environmental and economic units, using regionalized impact and value assessment methods.

• The authors see significant potential in integrating geochemical modelling using PhreeqC into an LCA programming environment such as openLCA [9]. • A word of caution. If the potential of geochemical modelling for mineralization process design is indisputable, its depends strongly on user's expertise and critical thinking. It is no substitute for dedicated experiments, which are indispensable for fine tuning geochemical model settings. In the context of mineralization of Ni-slags by attrition-leaching, additional product characterization is underway to confirm the predicted speciation, with respect to Al content in particular, and coupling geochemical modelling with a validated attrition model is required for further process development and optimization.