P.-O Weiss

Victimization and fear of crime on French university campuses

Introduction

The recent hashtag movement #pasdevague on Twitter, reminds us of the current situation of the issue of "violence" in educational institutions, but also how emotionally charged this theme is. While it has made it possible to make the failures of the "sanctuary" school (this republican creature where "external noises do not enter", as desired by the pedagogue Alain, 1978, p. 877) publicly visible, it has also highlighted the inconsistencies of the public processing of data provided to institutions and the imperfection of the instrument for counting victims and perpetrators. Moreover, while researchers are interested in victimization in secondary education [START_REF] Debarbieux | Les enquêtes de victimation en milieu scolaire : leçons critiques et innovations méthodologiques[END_REF], we have very little evidence to discuss victimization of higher education students, although campuses are social spaces where student numbers continue to increase each year (see also [START_REF] Cacouault-Bitaud | Sociologie de l'éducation[END_REF].

In France, the public debate is fed by a single statistical source: police and gendarmerie statistics. However, researchers have developed general population surveys, a key tool in the social sciences when considering this subject. The genesis of investigations into victimization and feelings of insecurity can be found in the United States, where security concerns date back to the 1960s with the President's Commission on Law Enforcement and Administration of Justice (Katzenbach Commission). In 1965, the first statistical victimization studies, independent of the various federal administrations, were carried out. They will continue while improving their samples every five years starting in 1973. Thus, the focal length is reversed in order to position oneself from the victim's point of view and it is quickly observed that the reported victimizations are far higher than those recorded by the administrative services.

Following the momentum of North American studies, social science researchers in France are taking advantage of this method of investigation [START_REF] Zauberman | Mesurer l'implication des jeunes dans la violence[END_REF]. The victimization survey then becomes the main measurement tool based on samples to which the sampling technique is applied. The aim is to gauge "a social phenomenon that has traditionally been measured only through administrative data" (Zauberman, 2015, p. 8). The 1980s, under the influence of American research, marked a major turning point when the two conceptions on the feeling of insecurity were analysed separately. At that time, work on fears grew under the impetus of the Centre de recherches sociologiques sur le droit et les institutions pénales (CESDIP). Many studies will develop in the following decades on very varied subjects with the creation of several specialized research centres on crime. Since the mid-1980s, the State has been promoting several sectors of research on crime through the establishment of structures and bodies, such as the French Observatory for Drug Addiction (OFDT) and the National Institute for Higher Security and Justice Studies (INHESJ). This period is marked by a strong use of quantitative data in a context of public procurement "in connection with the growing importance of statistics and "expertise" in the public debate" (Mucchielli, 2004, p. 36).

Within this profusion of research on crime knowledge, victimization surveys will be implemented among the French population. Today, they are entering the field of sociology of higher education.

The studies of the Observatoire de la vie étudiante (which focus on the living conditions of students in France) provide elements that provide a better understanding of the perception of inequalities [START_REF] Ferry | À la tête de l'étudiant.e ? Les discriminations perçues dans l'enseignement supérieur[END_REF], vulnerability [START_REF] Cordazzo | Les étudiants vulnérables : entre renoncements et travail contraint[END_REF] and student isolation (Belghith, Giret, Ronzeau and Tenret, 2017), but leave out victimizations. After several decades of research on students [START_REF] Bourdieu | Les héritiers : les étudiants et la culture[END_REF][START_REF] Levy-Garboua | Les demandes des étudiants ou les contradictions de l'université de masse[END_REF][START_REF] Baudelot | Les étudiants, l'emploi, la crise[END_REF][START_REF] Lapeyronnie | Campus blues. Les étudiants face à leurs études[END_REF][START_REF] Eicher | Le financement de la vie étudiante[END_REF][START_REF] Felouzis | La condition étudiante[END_REF][START_REF] Coulon | Le métier d'étudiant : l'entrée dans la vie universitaire[END_REF][START_REF] Mcinnis | Studies of Student Life: an overview[END_REF], apart from the study of discrimination, we have no data available on the experience of victimization and fears felt on French campuses.

University campuses: object and field

In this context, we have an original field of investigation, those particular places of social life that are university campuses on which no such research has been conducted in France. Our research subject has different characteristics.

The university campus: a particular place of social life

First of all, university campuses in France are still located in urban areas, either in the heart of city centres or increasingly on the outskirts. The evolving links between territories and universities must be examined. From a general point of view, the relationship between universities and their territory ranges from divorce in the mid-1980s, when local communities cared little about it (degraded, aging campuses deserted by students as soon as classes ended), to reconciliation following the 2000 University Plan launched in the 1990s by the Jospin government. Within urban territories, universities are then seen as an economic, social and cultural asset, thus breaking out of their isolation from local society. In reality, the relationship between the city and the university alternates phases of rapprochement and empowerment according to various developments, including student numbers. At the time, Dubet and his colleagues pointed out that "from the early 1960s, the tremendous growth in student numbers would break up the university palaces of the late 19th century and call into question the inadequacy between the university network and new urbanization" (Dubet, Filatre, Merrien, Sauvage & Vince, 1994, p. 24) In addition, the campus was also a place of sociability for an increasingly numerous group of young people. Indeed, the number of students enrolling in university increased considerably between 1960 and 2015, from 310,000 to 2,910,000. This phenomenon, which peaked at the turn of the 1980s and 1990s, is confirmed for the recent period (2016 and 2017) for both the public (+4%) and private (+2.8%) sectors. As time goes by, higher education becomes more and more attractive for baccalaureate holders and this attractiveness is combined with the extension of the duration of studies. Nevertheless, over the last twenty years, the influx of foreign students has contributed to the increase in overall enrolment. The latter represented 12.1% of students in 2013 (MESRI, 2017: 29). University campuses can also be viewed through the specificity of student life and its constraints. Indeed, the relationship to studies, travel time, paid time or even relations between students are some of the characteristics of student life.

Today, almost all general baccalaureate holders and almost three-quarters of technological baccalaureate holders are enrolled in university. Considering the share of an age group that obtains a baccalaureate and the growing proportion that continues its studies in higher education, about 60% of young people study in one of the courses of higher education.

Nationally, 58% of 20-24 year olds are engaged in higher education, from all social backgrounds. This democratization concerns in particular the children of workers and employees who gradually enter university, although the gap between the most and least privileged remains: 74% of children in managerial and intermediate professions are graduates of higher education compared to 38% of children of workers or employees over the period [2013][2014][2015]. In 2016, children of managers and higher intellectual professions are overrepresented (36%) in higher education (Belghith, Giret, Ronzeau and Tenret, 2017, p. 2) compared to their proportion (18%) in the working population (INSEE, 2016). Moreover, women have made a breakthrough in higher education since they are now in the majority (55%) and completely dominate the Humanities and Social Sciences fields (70%). On the other hand, they are proportionally less numerous in scientific fields, very selective fields, and among doctoral students. In the end, the university represents 62% of the student population, which means that it is far ahead of the IUT and the Grandes Écoles. In 2015, students receiving direct financial assistance in the form of grants or loans amounted to 710,000 (€6 billion). The increase in the population has as a corollary its diversification in terms of living conditions as well as its social characteristics. The triennial study by the OVE shows an increasing sense of integration of students into the life of their institution; 39% said they were fully integrated in 2016 compared to 34% in 2013 (Belghith, Giret, Ronzeau and Tenret, 2017, p. 3). In 2016, students received their financial resources (89% of students) in three different but sometimes complementary ways: income from paid employment (33%), public assistance (31%) and family assistance (25%). In total, as in 2013, 46% of them were employed during their studies (Belghith et al.,p. 5), earning an average of €704 per month. This income has increased by 122€ over the last three years. While almost half of the students work to finance their studies, one part is involved in an activity related to the studies they are studying (15% of employees) and another is involved in an internship or work-study program (30%). Nevertheless, 36% of them have a paid activity not related to studies, most often part-time over six months (Belghith et al.,p. 6). Although there is a decrease between 2013 and 2016 (-8 points), 57% of scholarship students still say they "do not have enough money to cover their needs". There is no significant change in the way students live between 2013 and 2016: "as in 2013, one third of students [are accommodated] at their parents' home and one third of them live in rental accommodation, alone or with a partner. Among the other types of accommodation, shared accommodation and accommodation in university residence also remain stable for 11% and 12% of students respectively" (Belghith et al.,p. 8). Finally, the SEW study makes a significant contribution to the health status of students, stating that if it is considered satisfactory overall, psychological fragility increases. Indeed, although two-thirds of those surveyed in 2016 said they were satisfied with their health status, women, roommates, foreign students and students of working class origin were generally less satisfied with their health conditions. For example, 58% of students from the most vulnerable social classes say they are satisfied with their health.

Ultimately, reports of suffering for one of the symptoms increased (+6 points) (Belghith & al.,Chart 8,p. 9). Students are also more likely than the general population to deprive themselves of medical care (13% for financial reasons). The 23-25 age group is the most affected, which is explained by the gap in which this age group finds itself and acts as a double process: the family ceases to play its protective role and protection from work is not yet effective for the self-employed.

Aix-Marseille University: territorial specificities

As of January 1, 2019, the number of universities in France stood at 70. Faced with this proliferation, Aix-Marseille University (AMU), the largest university in France and the largest in the French-speaking world, constitutes a privileged field of research. AMU is divided into five campuses, four of which are located in Marseille, the fifth taking place in the city of Aix-en-Provence. This first major subdivision masks the spread of the various sites, which number 54 throughout the PACA region. We will focus here on three of the Marseille campuses.

AMU was created in 2012 following the merger of the three public universities in the region (Université de la Méditerranée, Université de Provence, Université Paul Cézanne), a process initiated by the law nᵒ 2007-1199 of 10 August 2007 on the freedoms and responsibilities of universities (the so-called LRU law or the Pécresse law). The ambition of one of the youngest French universities is evolving internationally (10,000 foreign students). It is currently the busiest in France (74,000 students enrolled) and even the largest French-speaking campus in the world for at least two reasons: number of students and budget. In the first place, it is only their embedding in the urban fabric that distinguishes the three campuses studied. First of all, the Luminy campus is located in a special geographical location within the Calanques National Park, in a southern peri-urban area, very far from the city centre and away from any major business centre. Secondly, the Saint-Charles campus is very much part of the urban space, finding a central place in the city, wedged between the SNCF station, the bus station and the Autoroute du Soleil. Third, the northern neighbourhoods, a peripheral space, impoverished and in the process of urban restructuring in recent years, are home to the Saint-Jérôme campus.

Consequently, this territorial diversity underlines the interest of the analysis that will follow.

These different aspects led us to these three campuses to measure the victimations suffered and the fears felt by the students.

Methodology

Based on American research, particularly in the context of the Crime and Safety Survey Program [START_REF] Fleury Devoe | Student Victimization in U.S. School: Results From 2009 School Crime Supplement to the Natioanal Crime Victimization Survey[END_REF][START_REF] Barrett | The Relation Between Youth Fear and Avoidance of Crime in School and Academic Experiences[END_REF][START_REF] Sloan | Assessing the Student Right-to-Know and Campus Security Act of 1990: An Analysis of the Victim Reporting Practices of College and University Students/Sloan[END_REF][START_REF] Simon | In the Place of the Parent: Risk Management and the Government of Campus Life[END_REF], and on the tradition of French surveys (Robert andZauberman, 2011, 2017), this Marseilles university context has been the subject of victimization surveys.

Within these multiple debates exacerbating the security theme, certain categories of population and certain territories particularly concentrate these discourses and representations charged with fantasies (Mucchielli, 2001). Among all urban territories, the French suburbs are the subject of the greatest stigmatization, accumulating, through the prism of security, the most negative representations. This mechanism, which stigmatizes specific territories, is also particularly intense in the city of Marseille, now the second most populated city in France with about 866,600 inhabitants where socio-spatial contrasts are striking (INSEE, 2016; see also Donzel and Bresson, 2007, p. 90). A city considered in many respects to be a bad student at the national level, sometimes described as indomitable or rebellious [START_REF] Dell'umbria | Histoire universelle de Marseille[END_REF], is often overwhelmed by both the government and the national media more than the concrete reality of delinquent or criminal acts suggests [START_REF] Mucchielli | La Provence, terre de violence : Les présupposés culturalistes à l'épreuve de l'analyse statistique[END_REF]. Marseille is subject to politicization and media coverage that embraces everything related to delinquency or crime to the point of talking about a Marseille Bashing [START_REF] Mucchielli | Marseille bashing ?" Remarques sur la stigmatisation d'une ville réputée exceptionnellement violente[END_REF]. These very negative representations are concentrated in the northern districts of the city [START_REF] Pujol | La fabrique du monstre[END_REF] where the "shit districts" contrast sharply with the "chic districts". Within the multiple social spaces, we seek to study university campuses under the aspects of victimization and insecurity by posing the hypothesis that these aspects maintain a link with their integration into the urban fabric. The campuses selected for their different socio-spatial locations on the scale of the city of Marseille allow this hypothesis to be tested. ORDCS1 was used to support this groundbreaking field survey.

General considerations

Given the size of this university, it was necessary to make a selection based on several criteria. It seemed interesting, from a comparative perspective, to focus on a single geographical area.

The concentration of 80% of the sites in the Phocaean city predestined the latter to be chosen.

Aix-en-Provence, another campus that was nevertheless important, particularly because of its size, was left out. In addition, it was appropriate to focus only on the city of Marseille in order to ensure comparability, coherence and homogenization. The simple criterion of the differentiated national reputation of these two urban nuclei is sufficient to understand the extreme heterogeneity at different levels of these two cities between which a "battle of the centres" is being fought (Peraldi, 2015, p. 95). Finally, the selection of sites was also based on the strong contrasts in the socio-spatial location of the three university campuses mentioned above.

The main objective is to highlight and compare the acts of delinquency to which students on Marseilles campuses may have been victims during an academic year, whether or not they have informed the central administrative services or the police and gendarmerie. The victimization survey has the advantage of allowing a count of victims, but also an evaluation of the feeling of insecurity. In the continuum of discussions and debates on security over the past forty years, it is necessary to distinguish between opinions, risks of victimization and feelings of insecurity.

The initial problem is to detach oneself from common sense and break with the preconceptions about the phenomenon. On this emotionally charged subject, the evidence often contains misleading representations. As such, [START_REF] Duprez | Le mal des banlieues ? Sentiment d'insécurité et crise identitaire[END_REF] qualitative research in the North highlights the dichotomy between individuals who are afraid of crime and those who are only concerned about it. In short, we must not confuse the distinct mechanisms of fear and concern, the first refers to a feeling, the one we are seeking to know, while the second expresses an opinion. Fear can be considered as "an apprehension of risk" in partial association with local delinquency [START_REF] Pottier | On ne se sent plus en sécurité". Délinquance et insécurité. Une enquête sur deux décennies[END_REF] or with reported victimizations [START_REF] Pottier | Victimation et insécurité en Île-de-France. Les résultats de la première enquête[END_REF]. The second dimension of the sense of insecurity lies in the concerns about delinquency, which are being raised to the level of an important, even a priority social problem.

The questionnaire

At the beginning of the survey, we considered the biases associated with generalized individual computerized procurement as ultimately high to introduce it. Indeed, the risk seemed too great to seize a mass of students who saw in the victimization survey a way to report observed acts or delinquency. It was necessary to lock at the source the affect and other sources of emotion that this type of study can generate. The use of a so-called on-the-fly questionnaire was also to be excluded since, once again, respondents are asked to participate on a voluntary basis.

To do this, the idea was to negotiate upstream with the department heads, then more directly with the teachers, to use a quarter of an hour of the course time -a period when the student is available -to deploy our questionnaire and thus reach masses of "captive" students, but also to reach the whole person. In other words, both victims and non-victims had to be addressed. It should be noted that we intervened in courses where attendance was mandatory in order to capture a subset of the student population with heterogeneous socio-economic and academic characteristics. In this way, we generally collected the declarations of the Bachelor's students at different times of the day by varying the days of the week (Monday to Friday). In this case, the only method of procurement was the paper questionnaire. Then, the technique of collecting the responses of the Masters (smaller promotions) is summed up in a computerized handover of an identical questionnaire in the computer room, most often in our presence in order to orally introduce the study conducted; a method that facilitated the coding of the data and reduced the time consuming aspect of our research system. The doctoral students were investigated by sending an email (2 reminders), sometimes by the doctoral schools, sometimes by research directors, and sometimes by us via lists obtained from the laboratory directors. But each time, the electronic link was sent with a text specifying our request and the framework within which it was made. Then, in general, we favoured closed-ended questions in order to avoid another potential bias. Indeed, the excess of open-ended questions in a questionnaire tends to cause respondent fatigue and increase avoidance behaviours for some questions, coupled with an approximation in the answers, making final exploitation more difficult. About ten minutes to submit to the questionnaire was the maximum appropriate time considered, a limited time that we took into account during the design work. Finally, victimization surveys ask about the past, usually the previous year or the two previous years. Consequently, the temporality was determined on the academic year preceding our study. If the respondents' statements are based on their memories, the event in question must also be perceived by the victim as a victimization and the victim must be able to verbalize it. Despite these pitfalls and the absence of a perfect instrument, victimization surveys are those that most closely approximate the reality at a given time on a specific population, while the statistics of criminal institutions largely reflect their activity, whose priorities change over time. Comparison with other available sources is a way of checking for matches or discrepancies and possibly showing trends. In short, "a film says more than a photography" (Zauberman, 2015, p. 11).

After collecting the socio-demographic characteristics of the respondents (age, sex, place of residence, year of registration, grant allocation, income level, mode of transport), a first section of the questionnaire questions the satisfaction of the study environment through 4 indicators (drugs, acts of vandalism, site cleanliness, lighting). The second section of the questionnaire focuses on the fears expressed on and around campuses during the day, at night and during the home-university journey. The declaration of a victimization takes place in a last general section.

The initial question is formulated as follows: During the previous academic year, were you a victim of any of the following incidents? There are then 7 potential victimizations (Theft or attempted theft of your car or two-wheelers; Theft or attempted theft of an object in or on your car, Voluntary act of vandalism on your car or two-wheelers, Theft or attempted theft with or without violence of personal object(s); Insults or verbal threats; Discrimination; Physical violence or attempt). Thus, students who declare themselves victims (filters) are then invited to answer one or more modules (if they declare several different victimizations) that specify the frequency, temporality and location of the victimization. Then, victims are asked for information about the perpetrators (if identified) and their behaviour after the fact (simple reporting, handrail, complaint). In the case of multivictimization on the same item, the respondent is informed that we are only interested in the last fact that he or she suffered.

The period studied is from September 2012 to June 2015. The corpus is composed of 1,250 usable questionnaires: 529 people in Luminy (6% of students), 364 in Saint-Charles (22% of students) and 357 in Saint-Jérôme (11% of students). The collection of questionnaires was large enough to allow statistical adjustment of the sample based on SEW data on the following sociodemographic variables: sex, age, year of enrolment, whether or not they were scholarship recipients, place of residence. In the study of the victimations we present, we have chosen to speak in terms of confidence intervals. Indeed, the confidence interval reflects the statistical accuracy of the result and appears in the tables below as percentages in square brackets. Thus, rather than punctually estimating the true unknown value of the parameter θ (victim rate), we looked for an interval that "most likely" covered this true value.

Conclusion

This research discussed the results of victimization surveys for students on three campuses. We have taken care to stress the importance of categorising the acts of delinquency declared by students and to dissociate ourselves from an unfortunately (!) too widespread discourse on the evolutions or the current state of "delinquency". We have established a hierarchy of victimizations. From there, we saw that the Saint-Jérôme campus, located in the northern districts of Marseille, reported a percentage of victims that exceeded what can be seen in the city centre (Saint-Charles) and in the Parc des Calanques (Luminy). From this point of view, the withdrawal of campuses from the city centre, omitting all the concerns related to the eccentricity of a place of study and residence for some -how to get there, how to do your shopping, etc.? -largely protects against local crime. Also, the capacity of a campus has no influence on the level of recorded delinquency. More than the number of students on a campus, it is the type of incivility observed that seems to make the difference. While overall victimization rates on the campuses surveyed are lower than those recorded among the Marseille population -suggesting that the campus appears at first sight to be a more secure space -students are undoubtedly first affected in their moral and psychological integrity (insults, threats, discrimination). Interpersonal violence remains the exception. With regard to the theft of students' material goods, our results show that the objects in the car are the number one target of local crime and that it is students in outlying neighbourhoods who suffer the most.

The university must reposition itself as a space of socialization and as an institution, through its teachers and administrators, that must promote equality, open to its environment, open to society. The acts of discrimination identified take place largely within the framework of interknowledge, which suggests delinquency between users of the university site. Thus, the high proportion of discriminatory acts is partly the result of a lifestyle that exposes young people more than any other age in their lives. However, there is a card to be played here in terms of gender equality in particular and social cohesion as a whole, given the silence of the victims, which is sometimes assumed to emanate from fear, sometimes from indifference or even from a lack of trust in the institutions in order to reduce this major social phenomenon. Similarly, racism also finds expression in spite of the university ethos of both tolerance and diversity, which undoubtedly preserves this place of knowledge from its greater exacerbation in the rest of society. Ultimately, only victims of object theft tend to file complaints with the authorities.

A significant discovery breaks with certain prejudices. Indeed, there is no result to suggest that the night period favours action, regardless of the victimization studied. The particularity of the downtown area is the high proportion of students who are victims of incivility around the university, suggesting scenes from everyday life where, when clashes occur, insults can be pronounced. Students on the North End campus are facing numerous attacks on property in their vehicles.

Students are statistically unequal in terms of delinquency, some categories of individuals are more exposed and affected by different types of delinquency. The statistical tools we have used provide an opportunity to highlight a series of correlations between the crime suffered and the socio-demographic characteristics of the victims. This set of correlations in turn offers the opportunity to draw a portrait of the victims. Students tend to define themselves as victims as their graduation and age increase. In general, the experience of victimization greatly increases the chances of often feeling insecure at night, but also of perceiving the study environment as degraded. Victims also report being more frightened when they travel or leave the campus at nightfall. Another correlation could be established between the victims of insults and the possession of a scholarship, suggesting a link between financial fragility and the experience of victimization. These data therefore offer us the possibility of targeting certain types of users in particular, in particular through prevention campaigns in which all education stakeholders are involved by building relationships that promote student involvement.

The predominant place of moral and psychological violence represents the other side of the coin, with sexism and racism at the top of the list. Moreover, when we talk about predation towards consumer objects, theft is mostly carried out in the absence of the victim, excluding in most cases verbal or physically violent interaction. In the end, the overall feeling of insecurity remains rather low. Fears are highly concentrated during the night, underlining the strength of the nocturnal imaginations that feed this feeling. All other things being equal, campus students in socially more favoured areas are those who most often claim to be safe both in transportation and when travelling on campus. Conversely, the reputation of the urban centre and the northern districts, conceived as a shared, temporary and localized social representation, associated with a name and resulting from more or less powerful and formalized social evaluations, has a social consistency and a character shared by a proportion of students. This way of looking at a neighbourhood has the power to create fears without the reality of delinquency necessarily being the cause. These reflections lead us to rethink the question of the university climate as others have done before us on the school climate. Indeed, the latter is at the heart of the relationship to knowledge, of didactic and pedagogical interactions (reference). The feeling of well-being as well as that of justice in the educational institution are crucial for the success of students. To think of the climate is to pose in another way the question of the relationship between socialization and learning through the question of the meaning of studies.

The questions that have been raised during this research relate largely to the question of social cohesion in these public spaces that are university campuses. The survey attempted to fill a scientific gap to improve the understanding of this student world. Future research will undoubtedly make it possible to consolidate these initial lessons concerning the nature of victimization and the feeling of fear.

The scientific research programme called the Observatory of Delinquency and Social Contexts ran from

to 2015 under the direction of sociologist Laurent Mucchielli, research director at the CNRS and specialist in deviance phenomena and security policies.


Emerence Hoummady
email: emerence.hoummady@univ-lorraine.fr

Fabrice Golfier

Michel Cathelineau

Laurent Truche

Nicolas Durupt

Jean-Jacques Blanvillain

Jérémy Neto

Eric Lefevre

Jeremy Neto

An integrated multiscale approach to heap leaching of uranium-ore agglomerates

Keywords:

come   L'archive ouverte pluridisciplinaire

Introduction

Heap leaching is an industrial method to process low grade ores, consisting of percolating an acid or alkaline leaching solution through a 4 to 10 meter high heap of crushed ore [START_REF] Ghorbani | Heap leaching technology-current state, innovations, and future directions: a review[END_REF]. This technique is used to process several ores such as uranium, copper or nickel laterites and is based on fluid-rocks interactions at the heap scale and on the percolation of the leaching solution through ore porosity to dissolve minerals of interest at the micro-scale [START_REF] Bartlett | Metal extraction from ores by heap leaching[END_REF]. In this way, the accessibility of these minerals by the leaching solution is a limiting factor [START_REF] Ghorbani | Large particle effects in chemical/biochemical heap leach processesa review[END_REF].

Due to the significant size of heaps and the long leaching time (about 1 year for a 6 to 9 m high heap), heap leaching processes may be difficult to investigate. Smaller size experimental models and numerical models are used instead. Experimentally, columns from 0.5 to 6 m high are used to reproduce leaching conditions [START_REF] Bennett | A comprehensive model for copper sulphide heap leaching[END_REF][START_REF] Robertson | Development of an integrated heap leach solution flow and mineral leaching model[END_REF]. Such tests allow analysing the influence of the different leaching parameters. However, they may contain a bias: [START_REF] Bouffard | Hydrodynamic behavior of heap leach piles: influence of testing scale and material properties[END_REF] noted that the leached ore density decreased with the decrease of column diameter. This scale reduction decreases the ore packing density, due to wall effects, which subtly alters mechanical behaviour in the case of column leaching. In addition, heterogeneities present in the heap, such as a wide particle size distribution or the presence of inert materials, may cause an overestimation of the leaching rate measured in columns compared to that measured in situ. Numerical models [START_REF] Dixon | A mathematical model for heap leaching of one or more solid reactants from porous ore pellets[END_REF][START_REF] Mellado | An analytical model approach to heap leaching[END_REF] using parameters fitted to experimental data were also developed, in order to study the impact of the different leaching parameters [START_REF] Ghorbani | Heap leaching technology-current state, innovations, and future directions: a review[END_REF] from very simplified analytical models to more complex mechanistic approaches. They classically describe fluid flow and transport of leached solution through the heap and reaction kinetics with the minerals of interest [START_REF] Dixon | Heap leach modelingthe current state of the art[END_REF][START_REF] Dixon | Comprehensive modeling study of chalcocite column and heap bioleaching[END_REF]. Depending on the operating conditions (evolution of heap packing or of the heat within the heap), additional couplings may be required [START_REF] Dixon | Analysis of heat conservation during copper sulphide heap leaching[END_REF][START_REF] Valencia | Saltpeter extraction and modelling of caliche mineral heap leaching[END_REF]. Note that several models were proposed in the literature but few are used in industrial applications [START_REF] Ghorbani | Heap leaching technology-current state, innovations, and future directions: a review[END_REF][START_REF] Robertson | Development of an integrated heap leach solution flow and mineral leaching model[END_REF]. The main difference between these models lies in the governing assumptions and the related mass balance equations used to represent dissolved species transport, leaching solution flow and the reactional model. The Richards equation in combination with the traditional Mualem-Van Genuchten model is usually chosen to model solution flow through the heap [START_REF] Robertson | Development of an integrated heap leach solution flow and mineral leaching model[END_REF] as leaching are often occurs under partially saturated conditions. However a generalised Darcy model may also be used when the gas phase is considered [START_REF] Bennett | A comprehensive model for copper sulphide heap leaching[END_REF]. Moreover, two types of leaching transport models may be distinguished depending on the level of column heterogeneity [START_REF] Golfier | Comparison of theory and experiment for solute transport in highly heterogeneous porous medium[END_REF]: (i) models considering the heap as a homogeneous medium controlled by diffusion or advection [START_REF] Bennett | A comprehensive model for copper sulphide heap leaching[END_REF] and (ii) dual porosity models, considering the heap as two distinct regions: a stagnant region and a mobile one [START_REF] Bouffard | Investigative study into the hydrodynamics of heap leaching processes[END_REF][START_REF] Dixon | Comprehensive modeling study of chalcocite column and heap bioleaching[END_REF][START_REF] Robertson | Development of an integrated heap leach solution flow and mineral leaching model[END_REF]. Such models can closely emulate heap behaviour in case of channelling [START_REF] Ogbonna | An agglomerate scale model for the heap bioleaching of chalcocite[END_REF]. At the mineral particle scale, the easiest approach is to consider a uniform reaction model ("uniform-or homogeneous-reaction model"), meaning a uniform penetration of leaching solution within particles, independently of their size. However, when diffusion is limiting [START_REF] Sheikhzadeh | Simulation of heap leaching process in a bed of porous and spherical ore particles[END_REF], most models use the shrinking core model to describe reactions between minerals and leaching solution [START_REF] Bennett | A comprehensive model for copper sulphide heap leaching[END_REF][START_REF] Robertson | Development of an integrated heap leach solution flow and mineral leaching model[END_REF]. Although the shrinking core model is easy to apply, it supposes that the particles to be leached are spherical and that minerals distribution is homogeneous, which is not the case in experimental tests [START_REF] Bennett | A comprehensive model for copper sulphide heap leaching[END_REF]. All of these models led to identify and assess parameters that influence heap leaching efficiency such as heap temperature or leaching reagent concentration which both impact the dissolution kinetics [START_REF] Bartlett | Metal extraction from ores by heap leaching[END_REF][START_REF] Petersen | Heap leaching as a key technology for recovery of values from lowgrade oresa brief overview[END_REF]. [START_REF] Ghorbani | Large particle effects in chemical/biochemical heap leach processesa review[END_REF] also point out heap permeability as a key factor of heap leaching. If percolation of leaching solution is too slow, chemical reactions between reagent and minerals cannot occur and on the other hand, if this characteristic time is too long, it might result in the flooding of the ore [START_REF] Ghorbani | Heap leaching technology-current state, innovations, and future directions: a review[END_REF]. In addition, a low porosity may enhance plugging, causing a decrease of leaching efficiency and heap collapsing. An uneven permeability is also reported to induce channelling and to prevent irrigation of some parts of the heap. Such permeability difficulties are mostly caused by the nature of the ore and especially high clay and fine particles content.

To solve this problem, the nickel, copper and uranium industries use agglomeration, consisting of increasing ore particle size distribution by binding fines and clays together into larger particles. This improves heap permeability and stability and also prevents fines migration during leaching [START_REF] Bartlett | Metal extraction from ores by heap leaching[END_REF][START_REF] Bouffard | Review of agglomeration practice and fundamentals in heap leaching[END_REF][START_REF] Yijun | Application of agglomerated acid heap leaching of clay-bearing uranium ore in China[END_REF]. Note that most studies of agglomerate heap leaching focus on copper or nickel laterite ore [START_REF] Dhawan | Crushed ore agglomeration and its control for heap leach operations[END_REF][START_REF] Kodali | Evaluation of stucco binder for agglomeration in the heap leaching of copper ore[END_REF]Nosrati et al., 2012a,b) but up to now, the behaviour of uranium-ore agglomerates remains poorly understood. The only exception is the recent study of [START_REF] Hoummady | A multi-analytical approach to the study of uranium-ore agglomerate structure and porosity during heap leaching[END_REF] who have identified changes in the structure of uranium-ore agglomerates during leaching.

Here, we focus on leaching effects at the agglomerate scale and at the Representative Elementary Volume (REV) scale (by the use of small column leaching tests). The objective of the current work is to upscale these results to the heap scale, by using both REV leaching experiments, meter scale columns leaching tests and numerical modelling. An integrative multiscale approach, illustrated in Fig. 1, is conducted for this purpose by (i) identifying the limiting processes at the smaller scale, (ii) stating the governing assumptions at the heap scale in terms of these latter processes and (iii) predicting the uranium extraction. In addition, this study also intends to characterize and understand plugging.

Materials and methods

Ore, agglomeration and leaching processes

The agglomerates used in this study were produced from clay-rich sandstone containing about 900 ppm of uranium and > 10 wt% of clay minerals (mainly kaolinites, illites, mixed layered illite-smectite phases and chlorites) provided by AREVA and originating from Somaïr, Niger. Most of the uranium in this ore is hosted by clay minerals and especially by chlorites. In addition, this ore contains a low amount of carbonate (0.4 wt%) and calcium (0.29 wt%), compared to the aluminium content (8.32 wt%). Due to this feature and to the high clay content, this ore is ideally suited for a study of the agglomeration process.

Crushed ore was agglomerated with water and sulfuric acid, at a ratio of 25 kg of acid per 1000 kg of ore for a liquid/solid ratio of 0.08 kg/kg, within a cement mixer at a speed of 32 rpm. Half of the water was first mixed with the dry ore. Sulfuric acid mixed with the rest of the water was then added to the ore and the agglomeration carried on for 3 min. Then, agglomerates were stored for curing during at least 24 h to harden the bonds between particles [START_REF] Pietsch | Agglomeration Processes: Phenomena, Technologies, Equipment[END_REF].

REV-scale leaching tests

A series of leaching tests in small columns were conducted to assess the existence of mass transfer limitations within and around the agglomerates. At the REV scale, such limitations can be due to (i) the diffusion through the fluid boundary layer surrounding the agglomerates (external transfer limitation) and (ii) the diffusion through the pores within the agglomerate (internal mass transfer limitation). In addition, the impact of acid concentration, which can be a rate-limiting step for the reaction, was also evaluated. Experimental results discussed hereafter will be used as a basis for our upscaling analysis. Note that characterizing the structure of uranium-ore agglomerates prior to and after leaching was previously discussed in [START_REF] Hoummady | A multi-analytical approach to the study of uranium-ore agglomerate structure and porosity during heap leaching[END_REF] and the impact of agglomeration conditions on heap leaching efficiency was investigated in [START_REF] Hoummady | A multi-analytical approach to the study of uranium-ore agglomerate structure and porosity during heap leaching[END_REF]. Interested readers can refer to [START_REF] Hoummady | A multi-analytical approach to the study of uranium-ore agglomerate structure and porosity during heap leaching[END_REF] for more details about the experimental setup and analytical methods.

About 120 to 150 g of agglomerates of uniform diameter were packed in a column of 10 cm high and 4 cm diameter and leached over 10 days with a diluted sulfuric acid solution at a given flowrate defined in Table 1. This volume of agglomerates, corresponding to a homogeneous porous medium, is expected to be large enough to achieve a REV of the entire heap. The first batch from Table 1 corresponds to the reference leaching conditions and is noted as RC-batch. The leach solution was sampled daily and analysed by ICP-OES after dilution by a factor 10 with 2 vol% nitric acid (results are given with a measurement uncertainty of 10%). The extraction of each element was calculated as moles contained in the leach solution to the total moles within the ore, at the initial time. The dimensionless extraction rate η was also calculated for each element as the ratio between the current extent and the final extent of extraction.

Meter-scale column leaching tests

To scale-up leaching studies, they were carried out in a 1 m tall and 10 cm diameter column randomly packed with 9 to 10 kg of variablesize agglomerates. Agglomerates were leached for 13 days with a 10 g/l sulfuric acid solution and at a flowrate of 45 ml/h (corresponding to a specific flowrate of 6 l/m 2 /h). These conditions are similar to the reference conditions (RC) defined in Table 1 for 10-cm high columns, using the same surface flow rate and the same sulfuric acid concentration. In addition, to simulate leaching conditions at different depths within the heap, a constant compressive axial load was exerted on the 1 m tall column corresponding to the vertical stress of the equivalent mass of the overlying material. Three representative depths of the heap leaching process (0-1 m, 3-4 m and 5-6 m) were considered. As for the small columns tests, the leached solution was sampled daily and analysed by ICP-OES (results are given with an uncertainty of 10%). The column weight and the saturation index of the column at different heights (0.3 m, 0.5 m, 0.7 m and 0.9 m) were measured every 5 min by means of the Balance Link software and Trime Pico64 TDR probes. Due to column settlement, causing a modification of the porosity, these probes had to be recalibrated during the tests. These data were used to calculate the column total porosity throughout leaching. Air permeability measurements before and after leaching were also done. Experiments were repeated twice to assess reproducibility of the results.

After each experiment, the columns were partially disassembled into 5 subsections of 20 cm tall for post-mortem dry mass and water content measurement. In case of plugging, plugged areas were sampled and analysed by X-ray tomography with a Nanotom Phoenix tomograph with a resolution of 50 μm. Results were then processed, using VG Studio Max 2.2 software to determine the macro-porosity of the clogged sections.

Results and discussion

Influence of leaching parameters

Three main leaching parameters were studied: (i) the sulfuric acid content of the leaching solution, (ii) the agglomerate size and (iii) the flowrate.

Two different leaching solutions were first tested. Increasing this concentration from 5 g/l to 20 g/l was found to slightly increase the uranium extraction (Fig. 2a). Such results are consistent with those of [START_REF] Hoummady | A multi-analytical approach to the study of uranium-ore agglomerate structure and porosity during heap leaching[END_REF]. Sulfuric acid causes the dissolution of illites and kaolinites. Sulfuric acid concentration above 5 g/l is enough and thus not the limiting reactant. Obviously, the small difference in uranium extraction might be economically important but the change measured is not statistically significant.

The influence of internal mass transfer on the uranium extraction rate was investigated by changing the agglomerate size (from 5, to 10 and to 20-mm diameter). The initial uranium content was found to decrease slightly and quasi-linearly with agglomerate diameter, causing an apparent decrease of the uranium extraction with increasing agglomerate size. Results in Fig. 2b were shown as a function of the η ratio, calculated as the ratio between current extraction and the final extraction. This dimensionless extraction rate was used to consistently account for the initial varying uranium content and also agglomerates porosity variations (Fig. 2b). It was found to be the same except for the smallest agglomerates, which means that the uranium leaching kinetics was not significantly limited by internal mass transfer.

Batches #1 and #6 were carried out at two different flow rates, respectively 7.2 and 3.6 ml/h, at constant acid concentration. For comparative purpose, the results in Fig. 1c-e are presented in terms of the L/S ratio calculated as the mass of leached solution injected into the column divided by the initial mass of agglomerates within the column. Considering the measurement uncertainty, no major difference between the extraction for Si, Al, Ca or K was found at the two flowrates. As an example, Al extraction for both flow rates is shown in Fig. 2c (data not shown for the other species). Yet, this did not seem to be the case for uranium (Fig. 2d). Since a change in the initial uranium content between two batches of agglomerates was suspected, the dimensionless uranium extraction extent η was also calculated, showing similar kinetics between the two flowrates tested (Fig. 2e). Due to the measurement error of 10% of the ICP OES, the differences of dimensionless uranium extraction rate between the flowrates were assumed not to be significant. There is no evidence of significant external mass transfer limitations for acid leaching in a 10 cm tall column (i.e. at the REV scale).

Meter-scale column leaching

Evolution of the column behaviour during leaching and at different depths

Leaching conditions and packed bed properties are reported in Table 2 for the three l m-tall columns. A mass balance calculation has shown consistency between measurements of solution saturations and agglomerate column weight (Fig. 3a). Fig. 3b compares the change in the total mass of solution within the column as a function of the L/S ratio for the two limiting cases of depth increment (0-1 and 5-6 m). Three steps can be highlighted: (i) a preliminary step of filling the column with solution corresponding to the time needed by the solution to percolate down to the bottom of the column (L/S ratio < 0.1 for the 0-1 m depth), then (ii) a transient drainage step of the column (0.1 < L/S ratio < 0.25 for the 0-1 m depth) and finally (iii) a steady state in which the mass fluxes of solution going in and out of the column are equal (L/S ratio > 0.25 for the 0-1 m depth). The second step can be related to the settling of the material due to the variation in porefluid pressure when drainage occurs. This is consistent with the decrease of the total porosity observed during the early hours of irrigation (Fig. 3c). The total porosity decreases logically with depth. Permeability analyses reveal a similar trend (16 Darcy for the 0-1 m column and 7 Darcy for the 5-6 m column after settling). The establishment of steady state takes a longer time (Fig. 3b). In addition, water saturation on a vertical profile (i.e. during steady state) was measured at a ratio L/ S of 0.9. Fig. 3d highlights that the water saturation remains the same across the column. At the basis of the column, this rate slightly decreases probably due to the outflow geometry.

The pH of the feed and filtrate was similar, indicating that sulfuric acid was in excess for this scale. In this way, this factor is not a limiting factor for leaching. As extraction curves during leaching were similar to those obtained at REV scale [START_REF] Hoummady | A multi-analytical approach to the study of uranium-ore agglomerate structure and porosity during heap leaching[END_REF], specific attention was paid to uranium and calcium. Fig. 4a shows that the calcium concentration exhibits a three-step trend. During the fill, the calcium concentration exceeded the gypsum solubility, which might cause precipitation. As gypsum was found to cause plugging (Agatzini-Leonardou and Zafiratos, 2004), we estimated the total volume of gypsum which may be formed if all the calcium contained within the column precipitated. This volume reaches about 0.6% of the volume of Notes: L/S = 0.1 corresponds to about 1 day after the beginning of leaching (transient state) and L/S = 0.9 corresponds to about 7 days after the beginning of leaching (steady state). the column, i.e. about 1% of the total porosity of the column. This value is too small to be the cause of plugging. Moreover, column homogeneity along its depth precludes the presence of localised precipitates due to heterogeneous calcium concentration. This finding will be confirmed by X-ray images of plugged sections in the next section.

The final uranium extraction of 75% was higher than in the 10 cm tests but this depends on the agglomerate size of interest (extraction vary between 65% and 90% for 5 mm-to 20 mm-diameter agglomerates in 10-cm columns). The uranium extraction rate η was very similar for both tests (Fig. 4c). In other words, effective reaction (column-scale) and apparent reaction (REV scale) kinetics were very similar, thus validating the use of smaller column tests to study agglomerate leaching.

Analysis of plugged areas

To go further in the analysis, let us take a closer look at the way clogging occurs. Early on the tests, the two columns representing the conditions in the middle of the heap (3-4 m of depth) and one of the columns corresponding to the bottom (5-6 m of depth) plugged. In all cases, plugging occurred in the upper 20 cm layer, i.e. where the maximal vertical stress due to initial pre-compaction applies. The plugged sections were analysed by X-ray tomography and compared to a non-plugged unleached section (Fig. 5a,b). In the latter section, agglomerates were noticeable contrary to the plugged section where no structure was observed. Agglomerates are mechanically degraded by the weight of the heap above, subsequently causing clogging. We presume that the weight of the material above and the settling during the first step of leaching deformed the agglomerates and, combined with acid solution percolation, gradually caused their degradation. This also decreased the porosity between agglomerates from 44% to 7% and permeability from 17 to 6 Darcy (Table 3). Saturation increased and also enhanced agglomerate degradation. Pore connectivity was also found to decrease when plugged, as shown in Fig. 5d, leading to solution channelling, unlike in the non-plugged section where porosity was uniform (Fig. 5c) and solution flowed homogeneously.

3.3. Numerical model of acid leaching of uranium-ore agglomerates at the 1-m column-scale

Governing assumptions of the model

At this point, we have to infer from REV experiments the governing assumptions for heap acid leaching and build a numerical model capable of predicting the uranium extraction rate. Effective reaction kinetics will be directly upscaled from REV measurements so that lowerscale information is not discarded. Model assumptions that govern flow and transport processes can be stated as follows:

(i) The acid flow is assumed to be one-dimensional (from the top to the bottom of the heap) under variably saturated conditions. (ii) Mass transfer limitations (both internal and external) do not significantly affect the observed reaction rate as shown by REV-scale tests and are also neglected at the column scale. (iii) Uranium dissolution kinetics is not influenced by the extraction rate of the other elements in solution. Uranium dissolution and mass transport down the column can therefore be uncoupled and modelled independently of other mineral species. (iv) Acid is assumed to be in large excess so that it is constant with time and all along the column. No mass balance equation is required for acid species. (v) In a first step, hydro-mechanical coupling is discarded so that changes in porosity and permeability are neglected. As a consequence, we will focus only on 0-1 m column leaching tests and the transient behaviour before bed settlement will not be explicitly simulated.

The resulting model has been built with the COMSOL Multiphysics 4.2 software, using parameters deduced from our experiments. A 1D meter-scale column, having dimensions similar to those we used, was modelled.

Flow model

Fluid flow in the variably-saturated column was modelled using the Richards equation coupled with the model of Van Genuchten and Mualem:

+ ∂ ∂ + ∂ ∂ ⎛ ⎝ - ∂ ∂ ⎞ ⎠ = * C S S h t z K θ z h ( ) ( ) 0 e c w c
(1)

where the apparent hydraulic conductivity K w ⁎ (θ) is defined by:

= = * K θ K k ρ gk μ k θ ( ) ( ) w w rw w w rw (2)
with S, the specific storage coefficient (m -1 ), S e, the effective saturation (-), C, is the specific moisture capacity (m -1 ), z, the vertical elevation (m), θ, the water volume fraction (-), t, is time (s), k, the intrinsic permeability (m 2 ), μ w the dynamic viscosity of water (Pa/s), K w, the water hydraulic conductivity (m/s), k rw, the water relative permeability (-), and h c = p w /ρ w, g the hydraulic head (m) where p w is the water pore pressure (Pa) and ρ w, the water density (kg/m 3 ). Changes in relative conductivity, soil moisture and pressure head are described by the following relationships: [START_REF] Mualem | A new model for predicting the hydraulic conductivity of unsaturated porous media[END_REF][START_REF] Genuchten | A closed-form equation for predicting the hydraulic conductivity of unsaturated soils 1[END_REF]

= ⎧ ⎨ ⎩ + - < ≥ θ θ θ θ S h θ h ( ) , 0 , 0 r s r e c s c
(3)

= ⎧ ⎨ ⎩ < ≥ + S h h , 0 1, 0 e αh c c 1 (1 | | ) c n m (4) = ⎧ ⎨ ⎩ - - < ≥ - ( ) C θ θ S S h h ( ) 1 , 0 0, 0 αm m s r e e m c c 1 m m 1 1 (5) = ⎧ ⎨ ⎩ ⎛ ⎝ - - ⎞ ⎠ < ≥ ( ) k S S h h 1 1 , 0 1, 0 rw e l e m c c 2 m 1 (6)
We denote θ s and θ r the residual and saturated water content respectively. α, m, l and n are the Mualem-Van Genuchten parameters.

Initially, the column has a uniform pressure head fixed at -0.075 m. An inward flux is imposed at the inlet as N 0 = 1.41 • 10 -3 kg/m 2 s N 0 = 1.41. 10 -3 kg/m 2 s (corresponding to a volume flow rate per unit area of 6 l/m 2 /h) and a free drainage boundary condition is imposed at the outlet. Numerical parameters fitted against experimental saturation curves are shown in Table 4. Both hydraulic conductivity and water volume fractions were extracted from data coming from meter scale column experiments (Tables 2 and3).

The average saturation curves and local profiles at different crosssections are presented in Fig. 6. The comparison reveals a very good agreement between experimental data and numerical predictions for the mean effective saturation during steady state. The TDR measurements give similar conclusions. Although the model is constrained by experimental data, this nice concordance supports the initial hypotheses on the fluid flow behaviour within the column (no channelling effect in the upper part of the heap). However, the model fails to reproduce the transient regime and especially the stage when saturation decreases. As previously explained, this mechanical process is due to the settlement of the bed. A more complex model taking into account the hydro-mechanical effects is required so that column permeability and effective compressibility can vary during leach.

Uranium transport model

Two mass balance equations were used to describe uranium extraction and transport of the dissolved mineral within the column. As previously mentioned, only uranium mass transport governing equations are considered here, since any geochemical couplings with other mineral species are neglected. We denote by c U s and c U agglo , respectively, the uranium concentration in the acid solution and in the agglomerates. The set of governing differential equations is written as follows: This effective reaction rate is directly extracted from the apparent reaction rate R REV measured at the REV-scale, as stated in the assumptions of the model so we have:

∂ ∂ + ∂ ∂ = ∂ ∂ ⎛ ⎝ ∂ ∂ ⎞ ⎠ + t θc z uc z D x c R ( ) ( ) U s U s U U s eff (7) - ∂ ∂ = - ε c t R (1 ) U agglo eff (8)
= R χ R χ ( ) ( ) eff REV (12)
Changes in the reaction rate R REV as a function of χ are calculated from REV-scale leaching experiments and plotted in Fig. 7. A polynomial function f(χ) is fitted on this experimental correlation and used instead in our simulations with COMSOL Multiphysics for the sake of simplicity.

Comparison between experimental and numerical rates of uranium global extraction is reported in Fig. 8. We observe good agreement between the two curves, especially over the long term. The discrepancy during the first one hundred hours of leaching may be attributed to the underestimation of the saturation in the flow model, as a result of the absence of mechanical coupling. Another explanation is the lack of experimental data at the VER-scale for L/S < 0.4 that induces an uncertainty on the effective reaction rate value at the very start of the heap leaching process. This satisfying prediction of uranium leaching extraction is particularly striking since reaction rates were extracted from REV-scale column experiments and apart from the axial dispersion coefficient of uranium, no fitting with the meter -scale column experiments was employed. This comparison justifies the use of smallscale column experiments (i.e. 10 cm high columns), from which reaction rate were extracted, to investigate uranium-ore agglomerate leaching at the heap scale (i.e. 1 meter scale columns and further 6 to 9 meters high heaps).

Conclusions

The present paper focuses on the column leaching behaviour of uranium-ore agglomerates at different scales, from the representative elementary volume of the heap to the meter-scale columns tests. An original experimental set-up has been used to reproduce and investigate the leaching conditions at various depths within the heap.

The effect of leaching parameters was investigated from REV-scale leaching tests. Based on these results, several physical assumptions were set forth and we derived a numerical model of a 1-meter column of agglomerates, coupling Richards and reaction-advection-diffusion equations to simulate flow within the column and uranium extraction. A good agreement has been found with the meter-scale experiments, representative at the top of the heap.

From the results obtained in this work, our primary findings and recommendations for future work on this topic can be stated as follows:

• Micro-scale (i.e. REV scale) experiments have revealed less or no evidence of mass transfer limitations during uranium-ore agglomerate leaching. This supports the assumption that the overall reaction rate is dominated by kinetics.

• The same series of experiments in 10 cm-columns has highlighted a small impact of the acid concentration in the range of values we investigated. In addition, meter-scale experiments have shown that the sulfuric acid was in excess and not the limiting reactant. Accordingly, we have neglected changes in acid concentration in the numerical model and kept this parameter as constant. However, it should be kept in mind that this assumption is questionable for a heap of 6 to 9 m high. An additional mass balance equation for the sulfuric acid would be required to extent the model at the heap scale and to describe the acid consumption with depth (and the related impact on the uranium extraction).

• The origin of the plugging problem observed at a macro-scale during heap leaching has been elucidated. First, chemical analyses of the leaching solution have confirmed the small quantity of dissolved calcium and discarded the chemical origin assumptiondue to gypsum precipitation -for this plugging. The application of the vertical stress due to the heap weight in meter-scale leaching experiments was found to cause agglomerate degradation, which in turn induces a strong decrease of permeability and porosity, leading to clogging. This clogging mechanism, being purely mechanical, has been confirmed by X-ray tomography imaging. Using stronger agglomerates may be a solution to address this issue and improve leaching efficiency. Preliminary research on the use of polyacrylamide binder with uranium-ore agglomerates and its impact on their mechanical properties have been conducted in Hoummady et al. (in submission). Further columns tests, using such improved agglomerates, would be required to assess their technical applicability at the heap scale. • Based on the physical assumptions inferred from REV experiments, we derived a numerical model of acid leaching at the meter-scale. Further improvement of model forecasting capabilities, especially at early times of leaching, will require to integrate mechanical coupling between permeability and compressibility. This 1D model should provide a first basis for application at the heap scale. However, a study of the impact of lateral heterogeneities within a heap and the related channelling effects would be needed. In addition, due to the heap height, some assumptions such as the excess of sulfuric acid or the absence of hydro-mechanical coupling (causing heap plugging) would become invalid. Additional equations will be required for fully describing these couplings and building a predictive model of leaching at the scale of 6 to 9 m heaps.

Fig. 1 .

 1 Fig. 1. Multi-scale analysis of uranium ore agglomerates leaching.

Fig. 2 .

 2 Fig. 2. Influence of acid concentration (A), agglomerate diameter (B) and leaching flowrate on aluminium (C), uranium extraction (D) and uranium η factor (E).

Fig. 3 .

 3 Fig. 3. Comparison of the solution weight inside the column calculated by the probe data and measured by the weighing instrument (A), evolution of solution weight of the columns through time (B), changes in column porosity with time (C), and vertical saturation profile at L/S = 0.9 (D). Notes: three steps are distinguished: a filling step, a drainage step and a steady step.

Fig. 4 .

 4 Fig. 4. Evolution of A) calcium concentration, B) uranium extraction and C) uranium η factor during leaching. Notes: the comparison is done with reference conditions: agglomerates of 10 mm diameter within a 10 cm scale column, 10 g/l of sulfuric acid in the leaching solution, and a flow rate of 7.2 ml/h.

Fig. 5 .

 5 Fig. 5. X-ray tomography analyses of A) unleached non-plugged section B) leached plugged section and 3D porosity volume of C) unleached non plugged section and D) leached plugged section.

Fig. 6 .

 6 Fig. 6. Comparison of effective saturation evolution during leaching between experimental results and COMSOL model for A) the entire column B) a cross section at 0.3 m depth within the column.

Fig. 7 .

 7 Fig. 7. Relation between the reaction rate and the conversion rate extracted from REV-scale leaching experiments.

Fig. 8 .

 8 Fig. 8. Changes in the global recovery rate of uranium during leaching and comparison between experimental results (0-1 m column) and COMSOL model.

Table 1

 1 Leaching parameters used in the experimental tests.

	E. Hoummady et al.		Hydrometallurgy 178 (2018) 274-282
	Batch	Agglomerates diameter	Flowrate	Sulfuric acid ratio
	#1 (RC)	10 mm	7.2 ml/h (i.e. 6 l/m 2 /h)	10 g/l
	#2	10 mm	7.2 ml/h	5 g/l
	#3	10 mm	7.2 ml/h	20 g/l
	#4	5 mm	7.2 ml/h	10 g/l
	#5	20 mm	7.2 ml/h	10 g/l
	#6	10 mm	3.6 ml/h	10 g/l

Table 2

 2 Characteristics of leaching tests.

Table 3

 3 Evolution of sections macro porosity and permeability caused by clogging.

		Macro porosity (%)	Permeability (Da)
	Unclogged section	44%	17 Da
	Clogged section	7%	6 Da

Table 4

 4 Parameters used for the flow model.

	Parameter	Value
	Hydraulic conductivity K w (m/s)	1.6 10 -4 m/s
	Water volume fraction at saturation θ s	0.58
	Residual water volume fraction θ r	0.09
	α	19.297
	n	8
	l	0.689

Acknowledgments

The authors gratefully acknowledge the financial support of AREVA Mines, Christophe Morlot and Cedric Demeurie for their help. This work has been carried out thanks to the access to the analytical capabilities of the GeoRessources Laboratory (Université de Lorraine, CNRS, CREGU), with equipment financed by CPER program (National Funds -Lorraine region -FEDER) and Labex Ressources 21 (supported by the French National Research Agency through the national program "Investissements d'avenir") with reference ANR -10 -LABX 21 -LABEX RESSOURCES 21.