Man Ching

Esther Chan

David Clarke

Rethinking the connection between theory and methodology: a question of mutual affordances

Keywords: Classroom research, research design, research methodology, social interaction

Theory and methodology are key considerations in research design. Different ways of conceptualising their connection can characterise differences in research practice. This paper examines connections between theory and methodology and the concomitant implications for ontology and epistemology associated with conducting research in a laboratory classroom applying a multi-theoretic research design. Using the Social Unit of Learning project as a case example, we argue that the relationship between theory and methodology is not one of "prescription" in either direction, but rather of mutual "affordance," both regarding the analyses afforded by the complex data set and the extent to which each theory affords analytical consideration of specific constructs of relevance to the setting and the interactions recorded there. These constructs shape the way in which the multimodal material is reconstructed as data amenable to particular forms of analysis.

Connection between theory and methodology

Pick up any textbooks on educational research, and you will usually find the words theory and methodology. The fundamental issues of whether theory or methodology should take priority in the process of research design, or how theory and methodology should be connected in the research process, can polarise researchers, with the views on the issues being used to characterise different research paradigms or approaches (see [START_REF] Guba | Fourth generation evaluation[END_REF][START_REF] Strauss | Basics of qualitative research: Grounded theory procedures and techniques[END_REF]. In this paper, we address connections between theory and methodology and the concomitant implications for ontology and epistemology associated with conducting research in a laboratory classroom when employing a multi-theoretic research design. We argue that in our research design, and in educational research in general, the relationship between theory and methodology need not be one of "prescription" in either direction, but rather of mutual "affordance,"1 both regarding the theoretical analyses afforded by the complex data set (i.e., generated by the methodology) and the extent to which each theory affords consideration of specific constructs of relevance to the setting and the interactions recorded there (via the methodology). We first consider a few different possible relationships between theory and methodology.

Theory can be thought of as "a coherent system of logically consistent and interconnected ideas used to condense and organise knowledge" (Neuman, 2014, p. 9), while methodology can be seen as "concerned with the logic of scientific inquiry" and in particular, consideration of "the potentialities and limitations of particular techniques or procedures" (Grix, 2002, p. 179). [START_REF] Blumer | What is wrong with social theory?[END_REF], for example, believed that some social theories exist independent of research methodology, and one does not prescribe the other. Another way to think about the connection between theory and methodology in the research process is as a sequence of critical decisions beginning with the choice of research methods (i.e., research techniques or procedures), which is framed or shaped by the methodology, which, in turn, is governed by the theoretical perspective, which reflects epistemological assumptions (i.e., a theory of knowledge) (see [START_REF] Crotty | The foundations of social research: Meaning and perspective in the research process[END_REF]. [START_REF] Crotty | The foundations of social research: Meaning and perspective in the research process[END_REF] used the connection between objectivism (epistemology), positivism (theoretical perspective), survey research (methodology), and statistical analysis (methods) as an example of such a connective chain of research process. Crotty's conceptualisation of the research process is shared by [START_REF] Grix | Introducing students to the generic terminology of social research[END_REF], who argued that "it is our ontological and epistemological positions that shape the very questions we may ask in the first place, how we pose them and how we set about answering them" (p. 179). In particular, Grix asserts that "we should guard against 'method-led' research, that is, allowing ourselves to be led by a particular research method rather than 'questionled' research, whereby research questions point to the most appropriate research method" (p. 179). Grix therefore suggests that theoretical considerations should lead or govern methodology and, thereby, methods in the research process. Also emphasising the importance of theory in the research process, [START_REF] Neuman | Social research methods: Qualitative and quantitative approaches[END_REF] presented alternative sets of research procedure for quantitative and qualitative research processes. In his schematic depiction, the qualitative research process starts with acknowledging the social self and ends with informing others, with each step guided or informed by theory (see Figure 1).

The quantitative research process according to [START_REF] Neuman | Social research methods: Qualitative and quantitative approaches[END_REF] takes on the same structure as Figure 1, beginning with topic selection (Step 1) and ends with reporting (Step 7), with each step guided, shaped or informed by theory. Different from [START_REF] Grix | Introducing students to the generic terminology of social research[END_REF] who believed that "methods themselves should be seen as free from ontological and epistemological assumptions" (p. 179), Neuman's depiction of the research process is less linear than Crotty's, and has theory identified as influencing every step in what is conceived to be a cyclic research process. However, as can be seen in Figure 1, the relationship between theory and the individual research steps represented by Neuman is unidirectional where theory "radiates" outwards to influence each research step. None of the research steps appears to influence theory.

In conducting the Social Unit of Learning project, we found the connection between theory and methodology differs from the research process characterised by [START_REF] Crotty | The foundations of social research: Meaning and perspective in the research process[END_REF] or [START_REF] Neuman | Social research methods: Qualitative and quantitative approaches[END_REF]. The combined use of the laboratory classroom and the employment of a multi-theoretic research design [START_REF] Clarke | Multitheoretic approaches to understanding the science classroom[END_REF] in the Social Unit of Learning project offer a unique opportunity to reflect on the connections between theory and methodology and the concomitant implications for ontology and epistemology in the study. Further description of the project is provided below.

The Social Unit of Learning project

The University of Melbourne has set up a laboratory classroom, the Science of Learning Research Classroom (SLRC), to study classroom teaching and learning. The facility has the capability to capture classroom social interactions with a rich amount of detail using advanced video technology. With 10 built-in video cameras and up to 32 audio inputs, the comprehensive and detailed recording of every participant in the classroom offers the possibility for systematic examination of the link between the processes and products of learning activities within the classroom setting. The facility has made possible research designs that combine a good approximation to natural social settings with the retention of some degree of researcher control over the research setting, task characteristics, and possible forms of social interaction afforded or encouraged. Such designs allow conclusions to be drawn with greater confidence about connections between interactive patterns of social negotiation and associated knowledge products (learning).

Using the SLRC, the Social Unit of Learning Project aimed to investigate the social aspects of learning and, particularly, those for which "the social" represents a fundamental and useful level of explanation, modelling and instructional intervention [START_REF] Chan | Learning research in a laboratory classroom: Complementarity and commensurability in juxtaposing multiple interpretive accounts[END_REF]. The project design can be seen as more akin to design experiments [START_REF] Cobb | Design experiments in educational research[END_REF] which involve "both 'engineering' particular forms of learning and systematically studying those forms of learning within the context defined by the means of supporting them" (p. 9). The project was designed to specifically serve the purpose of theory generation and testing through the application of a multi-theoretic research design [START_REF] Clarke | Multitheoretic approaches to understanding the science classroom[END_REF], taking advantage of the rich data that can be generated by the laboratory classroom facility.

The multi-theoretic research design adopted by the project involved the construction of a complex data set composed of video records and other supplementary data. The design allows an analytical team to juxtapose different interpretive accounts arising from different theoretically-grounded analyses in order to compare and contrast the capacity of different theories to characterise different aspects of the research setting. The theory generated from the research is intended to be a direct reflection of an attempt to provide explanatory accounts in relation to a specific data set, so in its first instantiation would be most similar to what might be called a "local theory". However, an accumulation of several such analyses of different situations might reveal similarities in the emergent local theories that suggested sufficient generalisability and commonality for more general theory, which would be less specifically tied to the data of any particular project.

Data generation

Intact Year 7 classes from a secondary school in metropolitan Melbourne were recruited with their usual teacher in order to exploit established student-student and teacher-student interactive norms.

By intact, we are referring to the existing social relationships between students, and between the teacher and students, which are left intact and not interrupted by a selective process introduced by the researcher. Eleven classes of Year 7 students (12 to 13 years old; 264 students in total) participated in the project. The students in each of the classes completed problem solving tasks individually, in pairs, and in small groups (four to six students) within a 60-minute session in the laboratory classroom. The problem solving tasks used in the project were drawn from previous research (e.g., [START_REF] Sullivan | Catering to all abilities through "good" questions[END_REF] and were purposefully chosen to make the thinking and/or social processes of the problem solving activity more visible. The tasks have the characteristics of allowing students to express their thinking through multiple modes (e.g., verbal, graphical, textual, etc.) and approach the task using different strategies or prioritise different forms of knowledge or experience. For example, two classes of students were given the following three tasks:

Task 1 (individual task) provided students with a graph with no labels with the following instructions: "What might this be a graph of? Label your graph appropriately. What information is contained in your graph? Write a paragraph to describe your graph".

Task 2 (pair task) was specified as follows: "The average age of five people living in a house is 25. One of the five people is a Year 7 student. What are the ages of the other four people and how are the five people in the house related? Write a paragraph explaining your answer."

Task 3 (small group task) stated that "Fred's apartment has five rooms. The total area is 60 m 2 . Draw a plan of Fred's apartment. Label each room, and show the dimensions (length and width) of all rooms".

The resulting data collected in the project included: all written material produced by the students; instructional material used by the teacher; video footage of all of the students during the session; video footage of the teacher tracked throughout the session; transcripts of teacher and student speech; and pre-and post-session teacher interviews.

Investigating the social aspects of learning

A multi-theoretic research design [START_REF] Clarke | Multitheoretic approaches to understanding the science classroom[END_REF] was employed to examine the complex data set from the project from multiple perspectives by multiple researchers, as well as interrogate the different theoretical perspectives through answering research questions such as the following:

1. What commonalities and differences in process and product are evident during problem solving activities undertaken by learners as members of different social units (individual, pairs, small groups, and whole class groupings)?

2. Which existing theories best accommodate (that is, provide a coherent and plausible explanation for) the documented similarities and differences in process and product and in what ways do the accounts generated by parallel analyses predicated on different theories lead to differences in instructional advocacy?

An international multi-disciplinary research team (combining education, cognitive and emotive psychology, learning analytics, and neuroscience perspectives) was recruited to develop analytical frames for coding the data.

Ontological and epistemological positioning

A major consideration regarding the validity of research findings and research evidence in educational research is the issue of ontology, which is "an area of philosophy that deals with the nature of being, or what exists" (Neuman, 2014, p. 94). The issue is distinguished from epistemology, which is "concerned with the theory of knowledge, especially in regard to its methods, validation and 'the possible ways of gaining knowledge of social reality, whatever it is understood to be' (Blaikie, 2000, p. 8)" (Grix, 2002, p. 177). In the Social Unit of Learning project, we recognise the active role that the researchers play in constructing the research setting to make the social aspects of learning visible as well as in data selection and interpretation [START_REF] Chan | Video-based research in a laboratory classroom[END_REF]. Ontological considerations place limits on the authority of any claims the research team might make regarding the generalisable characteristics of classroom learning. Any such claims must acknowledge the researchers' role in shaping the research setting to optimally simulate the common features of institutionalised classroom settings. Of course, it is the researchers' intention that such generalisability of findings be afforded by the optimised setting. We consider regularities in the multiple student interactions (e.g., across many pairs of students or across different social units) to suggest generalisable characteristics of the social aspects of learning.

With regard to the epistemological position of this project, we construct knowledge by considering both the regularities and differences in the interpretive accounts generated by the research team (cf. complementary accounts, Clarke, Emanuelsson, Jablonka, & Mok, 2006), and reconstructing these regularities as propositions. In this project, knowledge about classroom learning is generated inductively through the aggregation of these propositions to create new theory.

Mutual affordances of theory and methodology

Different from the research process depicted by [START_REF] Crotty | The foundations of social research: Meaning and perspective in the research process[END_REF] and [START_REF] Neuman | Social research methods: Qualitative and quantitative approaches[END_REF], the relationship between theory and methodology we are positing for the Social Unit of Learning project resembles a symbiotic one. In as much as the chosen theory highlights particular constructs, analytical consideration of these constructs is afforded by the data set generated through the research design (methodology) which has anticipated the need for such data (see Figure 2).

We characterise this symbiotic relationship as one of mutual and reciprocal affordance, since the chosen theory frames and affords the consideration of the constructs (such as engagement) that are the focus of the research and these in turn place anticipatory constraints on the forms of data required from the methodology. This mutual affordance can be illustrated by the consideration of questions such as:

 What (theoretically-grounded) analyses are afforded by the data produced by the researcher's methodology?  What constructs are foregrounded or prioritised by the chosen theory?  How do we connect the constructs to the data? The investigation of the social aspects of learning does not necessarily prescribe a particular methodology. However, when the research is conceptualised through a particular theory with its sets of interrelated constructs, researchers need to draw selectively from existing research traditions and established methodologies with their tenets for appropriate and rigorous investigative methods.

To provide further examples, multimodal learning analytics [START_REF] Ochoa | Multimodal learning analytics[END_REF] was used in the project to extract features in the video and audio data to characterise behavioural student engagement. Learning analytics is "the measurement, collection, analysis and reporting of data about learners and their contexts, for purposes of understanding and optimising learning and the environments in which it occurs" (Conole, Gašević, Long, & Siemens, 2011, p. 3). While learning analytics generally involves analysing log-file data captured by online systems (e.g., Learning Management System), multimodal learning analytics also includes the coding of more natural activities such as gestures, gaze, speech, or writing [START_REF] Ochoa | Multimodal learning analytics[END_REF]. Applying advanced techniques, Ochoa and his research team were able to automate the coding of student gaze direction, student posture, teacher position, student talk, and teacher talk to create indicators of student engagement, student attention, and teacher attention during various task conditions (individual, pair, and small group) (Chan, Ochoa, & Clarke, in press).

Another analytical thread applied in the project was interactivity analysis. The analysis of student interactivity was drawn from the theory of Commognition developed by [START_REF] Sfard | Learning, commognition and mathematics[END_REF].

Commognition theory resolves the thinking-communication divide by equating communication with thinking. The theory is particularly powerful for conceptualising how learning occurs and has led to the development of particular analytical tools for investigating learning, specifically in the classroom context. Interactivity analysis involves fine-grained analysis of student utterances to identify patterns of interaction between the students, such as instances where one person consistently ignores or responds (reacts) to the other person's utterances or frequently initiates new topics [START_REF] Sfard | Cognition as communication: Rethinking learning-by-talking through multi-faceted analysis of students' mathematical interactions[END_REF]. The interactive patterns can be seen as indicators of student engagement (both social and cognitive) in terms of the level of interpersonal correspondence between two people in their dialogue.

The investigation of a superordinate construct such as "engagement" can stimulate the use of a set of related mediating constructs (e.g., shared attention, participation, etc.) in psychology [START_REF] Shernoff | Optimal learning environments to promote student engagement[END_REF] in the case of the multimodal learning analytics work, while also stimulating the use of another set of constructs (e.g., communication, discursive interactions, etc.) within a specific sociocognitive theory [START_REF] Sfard | Cognition as communication: Rethinking learning-by-talking through multi-faceted analysis of students' mathematical interactions[END_REF] in the interactivity analysis. These constructs shape the way in which the multimodal material is reconstructed as data amenable to particular forms of analysis. The specific analyses carried out were afforded by the complex data set available to the project, subject to the theory affording the consideration of specific constructs of relevance to the setting and the interactions recorded.

Implications

The recognition of the reciprocality between theory and methodology has significant implications for the detailed design of any research project, since it cannot be assumed that by making the decision on one (theory or methodology or methods), the consequent decisions are thereby prescribed. The relationship must be seen as progressing in both directions taking us not only from theory to methodology and then to methods but also from methods back through methodology to theory. A researcher engaged in planning the minutiae of any one of these critical decision points is reminded in our paper to take into account those decisions in both directions throughout the research process because of the mutually affording nature of all connections.

Conclusion

It is the combination of unusually rich data that can be generated by the laboratory classroom facility and a multi-theoretic research design that has highlighted for us the necessity of considering the affordances offered by each of the selected theories, the chosen methodology, the resultant data set, and the dynamic mutuality of these affordances. As argued in this paper, the research process is not simply algorithmic with each step prescribing the form to be taken in any subsequent step. The reflective researcher must instead engage in a continually recursive reflection in the nature of the connection between any key decision and those adjacent to it in their research process in either direction.

Figure 2 :

 2 Figure 2: Steps in the qualitative research process depicted by Neuman (2014, p. 21)

Figure 2 :

 2 Figure 2: Mutual affordances of theory and methodology as illustrated by the reciprocal relationship between constructs and data in the Social Unit of Learning project

The word affordance was coined by[START_REF] Gibson | The ecological approach to visual perception[END_REF] in ecological psychology to describe the possibilities that the environment offers to an animal as the animal inhabits and interacts with the environment. We use the term to refer to the investigative options made possible (and also constrained) by the choice of theory or methodology.

Acknowledgment

This research is supported under Australian Research Council's Discovery Projects funding scheme (Project number DP170102541).


Christine Chabert
email: christine.chabert@cea.fr

Anne Saturnin

Guillaume Krivtchik

G Martin

M Tiphine

G Mathonnière

S Gabriel

A Allou

E Fillastre

F X Giffard

P Sarrat

J L Girotto

H Hancok

B Carlier

G Senentz

F Laugier

Feasibility of future prospects and transition scenarios for the French fuel cycle

This paper presents the industrial feasibility analysis of scenarios involving the progressive deployment of multiple recycling of plutonium in French sodium fast reactors (SFR), in line with the French Act dated 28 June 2006 on the sustainable management of radioactive materials and waste. Four successive phases have been defined with different degrees of SFR deployment in order to understand how best to accomplish this fuel cycle transition. -Phase A corresponds to the current state of the French nuclear reactor fleet; plutonium and uranium are recycled in mixed-oxide (MOX) and enriched reprocessed uranium (ERU) fuels in pressurised water reactors (PWR). -Phase B consists in recycling spent MOX fuel from PWRs in a limited number of SFRs. The objective of this phase is to stabilise the quantities of spent MOX fuels from PWRs. It also provides an outlet for plutonium produced by the current PWR fleet. This phase does not, however, provide an outlet for plutonium contained in spent SFR fuels. -The plutonium inventory is stabilised during phase C through the deployment of a symbiotic fleet comprising UOX-PWRs, MOX-PWRs and SFRs. This phase is characterised by the industrial reprocessing of spent SFR fuels and the recycling of Pu in SFRs and MOX-PWRs . SFRs provide an outlet for Pu extracted from spent MOX fuel while enabling isotopic correction so the Pu can be recycled in MOX-PWRs. -The objective of phase D is to deploy a fleet of reactors that no longer burn natural uranium. This may involve the full deployment of SFRs (D1) or their partial deployment in a symbiotic fleet comprising breeder SFRs and MOX-PWRs (D2). The areas of research recommended under this programme for the 2016-2018 period are also discussed in this paper.

Table I summarises the characteristics of the different phases studied in relation to the fleet composition, fuel flows and characteristic spent fuel inventories. All the cases studied in this paper are based on the assumption of a nuclear reactor fleet generating about 430 TWh/y.

The quantities of materials associated with sustainable management tend to improve with each phase transition (A through to D). This is particularly true for the consumption of natural uranium, the interim storage of materials (e.g. plutonium in spent fuels), and the final quantity of waste produced.

Each phase makes it possible to improve the industrial maturity of the fast reactors, which only represent 5% of the fleet in phase B. Design issues and the complex operating configuration remain to be resolved for phase C. It may be decided to move directly from phase B to phase D if the conditions at the time allow it.

The idea behind phase C is to halt the constant increase in the Pu inventory so as to avoid stockpiling quantities of plutonium that exceed those estimated for the scenarios. This phase therefore considers the treatment of all types of spent fuel, particularly fast reactor fuels and the multiple recycling of plutonium that has been recovered. The notion of stabilising the Pu inventory implies the deployment of a significant fraction of reactors capable of burning Pu, i.e. MOX-PWRs. This strategy requires the multiple recycling of plutonium in these reactors. To do this, the isotopic composition of the plutonium must be compatible with the recycling configuration.

As the plutonium contained in spent fuel from fast reactors has a too low energetic value to be recycled directly in MOX-PWRs, its isotopic composition must first be improved by putting it through an SFR one or two more times. In phase C, SFRs not only provide an outlet for plutonium from spent MOX fuels, but are also used to correct the isotopic composition of Pu so it can be re-used in PWRs.

Being able to restore the isotopic quality of Pu so it can be recycled in MOX-PWRs is the most complex issue of phase C, which explains why many variations were considered. Two key parameters were used to define phase C:

-The breeding gain of fast reactors: as the plutonium produced in the fertile areas of fast reactor cores has excellent isotopic characteristics ( 239 Pu/Pu tot > 90%), we can expect breeder fast reactors to improve the quality of Pu much better than self-sufficient fast reactors since they offer a higher fertile surface area.

-

The management method for plutonium resulting from the treatment of fast reactor fuels: a Pu improvement process involving a series of separate stages is more effective than a system that mixes plutonium with differing isotopic qualities, though it does entail a more complex management configuration on an industrial level. The final reference phase C is based on the deployment of breeder reactors to accelerate the correction of Pu, and the mixture of different Pu qualities to simplify fuel cycle operations.

II. FUEL CYCLE TRANSITION SCENARIOS

After having characterised each phase, the transition between these phases was analysed according to various assumptions (especially time). It was possible to assess the technical, economic and industrial feasibility and realism of the different options leading to the global scenarios comprising each phase.

As a result of this process, four global scenarios were defined: 1) scenario ABCD1; 2) scenario ABD1, which is an alternative to ABCD1 where the deployment of a 100% SFR fleet is accelerated (due to the increasingly higher cost or shortage of natural uranium); 3) scenario ABCD2 where the final fleet is symbiotic and composed of SFRs and 100% MOX EPRs; 4) scenario ABD2, which is an alternative to ABCD2 where the deployment of a symbiotic fleet is accelerated.

The year 2050 was chosen as the commissioning date for the first SFR in phase B. Phase C starts with the implementation of spent SFR fuel treatment and the deployment of additional SFRs. According to our assessment, there appears to be no pressing incentive to launch phase C any earlier, which led us to choose a B-to-C transition from 2090 corresponding to the renewal of the fuel cycle plants. Nevertheless, the deployment of three additional SFRs before 2090 is considered during this transition since it does not seem to be industrially realistic to build a new series of SFRs from 2090 at a sustained pace following a 30-year period without any construction.

The transition between C and D is estimated to take about 30 years for D1 and 50 years for D2. Equilibrium is then reached around 2190-2210 depending on the option chosen for phase D. The early transition from B to D makes it possible to reach this equilibrium much faster and to overcome our dependency on natural uranium resources sooner. In this case, our independence with respect to natural uranium is gained about 60 years earlier. This early transition from phase B to D requires an increase in the treatment capacities of plants so as to recover the plutonium contained in the spent fuels, which is needed for the accelerated deployment of a 100% SFR fleet while maintaining its total power generation at a constant level.

II.A. Total plutonium inventory

The variation in the overall plutonium inventory is shown in Figure 1. Contrary to scenario A, the transition scenarios make it possible to reach the objective of stabilising the plutonium inventory. The accelerated transition scenarios (ABD1 and ABD2) stabilise the Pu inventory at a lower level due to the fact that the spent fuel stocks are used to optimise the transition, with the

II.B. Storage of spent fuels

The accelerated transitions make it possible to significant reduce the storage of spent fuels since it is necessary to recover as much plutonium as possible from these stockpiles. Figure 2 shows the variation in these stockpiles for the different scenarios.

II.C. Natural uranium requirements

The consumption of natural uranium obviously stabilises faster in the scenarios with an accelerated transition. Scenario ABD1 makes uranium savings of about 18% compared with scenario ABCD1, while scenario ABD2 makes savings of about 16% compared with scenario ABCD2. Regardless of the transition scenario, the natural uranium requirements are significantly reduced compared with a French fleet that continues to operate with the once-through recycling of Pu in EPRs (scenario A).

II.D. Transport of SFR fuel sub-assemblies

The feasibility of transporting SFR fuel subassemblies does not appear to be called into question by our preliminary studies. Based on current regulations and transport cask designs similar to those used today, however, the number of SFR sub-assemblies will have to be reduced per transport cask. This will result in an increased number of transport operations. According to our studies, the criticality risk limits the number of SFR fuel sub-assemblies that can be transported in a cask. In terms of heat releases, SFR fuel sub-assemblies in transport casks must be kept in a helium atmosphere to promote thermal conductivity and heat removal. It will also be necessary to improve the resins used in these transport casks with respect to their heat removal performance. This issue requires further research within the scope of optimising transport casks for SFR fuels.

The table below lists the number of transport operations for three transition scenarios with respect to scenario A, i.e. continuing the current strategy of oncethrough recycling of Pu in PWRs. The total has been calculated for the 2050-2210 period.

As expected, it can be seen that the differences with respect to scenario A increase with the proportion of SFRs integrated into the fleet. The faster deployment of SFRs (scenario ABD1) also logically results in a higher total number of transport operations, excepting from UOX fuels and new radial blankets.

II.E. Waste and geological disposal

The total disposal surface area required for the three transition scenarios has also been calculated on the basis of the 2005 Andra disposal concept. These results do not currently take into account the latest concept changes recently recommended by Andra which incorporate thermo-hydro-mechanical criteria. The disposal surface areas have thus been calculated on the basis of thermal criteria, which consider a limit temperature of 90°C on the walls of the hottest waste package in the disposal facility. Scenario ABD1 requires the smallest surface area but it must be stressed that the differences in surface areas are of the same order of magnitude as the uncertainties on the study assumptions. This information will be specified in greater detail in future studies, taking into account the latest results from Andra. As a comparison, scenario A requires an overall surface area of about 6.5 km² (assumption: 722 CSD-V waste packages per year for 160 years). It is important to point out that, in this case, the disposal requirements for spent fuel will continue to rise to reach more than 47,000 tons in 2210. The deep geological disposal of these spent fuels is expected to represent an additional surface area of about 21.5 km².

II.F. Economic competitiveness

The economic analyses all indicate that the economic competitiveness of SFRs is highly dependent on the additional investment cost of the reactor compared to PWR and on the price variations of natural uranium. The competitiveness of SFRs may be reached sometime between 2080 and 2110 if an additional investment cost of 30% is made in comparison with PWRs. If this extra investment cost was increased to 50%, the date of competitiveness of SFRs would be shifted by fifteen years or so. This explains why we chose an ABD-type scenario over an ABCD scenario. Once the ABCD scenario has reached equilibrium (around 2150), the ABCD1 scenario appears to be more expensive than ABCD2 owing to the greater number of SFRs in the fleet; the contribution of the reactor cost to the fleet cost is greater than the fuel cycle cost.

III. FUTURE PROSPECTS

On the basis of these promising results, these studies will continue to explore certain avenues of research and new options. Among the needs that have been identified, the following areas are being investigated:

1. Robustness of the conclusions reached in 2015 with respect to the assumptions applied 2. Industrial overview of the transition from phase A to B, particularly with respect to the industrial fuel cycle facilities and integration of the Astrid technology demonstrator into this transition. This transition is currently being assessed on the basis of the possible commissioning of the Astrid reactor in the late 2030s. The first-in-series of the 1000 MWe SFRs will start up 25 years later. The main objective of phase B for the first SFR units will be to manage the increase in spent MOX fuel quantities from PWRs. In the meantime, Astrid must be able to demonstrate that it is possible to recycle Pu from MOX fuels in a SFR on the scale of a full reactor core. Two options for the AB scenario have been developed: either this Pu will be burned by three 1000 MWe SFRs (option 1), or Astrid will be made to contribute, which means only two 1000 MWe SFRs will be built (option 2). At the end of phase B, option 2 saves building a third 1000 MWe SFR, which represents a high investment cost considering that this reactor will not benefit from a standardised "series" effect. However, this option means that the fleet objectives are partially conditioned by this demonstrator whose fuel load plan is already rather restricted. More specifically, option 2 requires a more complex reprocessing system at the end of phase B; from 2070, Astrid must be able to demonstrate its capacity to recycle plutonium multiple times, while helping to produce Pu from MOX fuels in support of the two 1000 MWe SFRs. Option 2 is currently the reference solution in our studies.

3. The results of the disposal surface area required, which are being updated to take into account the latest developments recommended by Andra, e.g. incorporation of thermo-hydro-mechanical criteria. Andra has been asked to reassess the estimations of the disposal surface areas and excavated volumes required for each of the different phases. The results are expected in October 2017.

4. Tech watch of other reactor concepts capable of recycling plutonium from spent UOX and MOX fuels and of new MOX products, including their integration into the above scenarios. For this reason, an analysis is currently underway on the basis of past studies and within the scope of the 1991 Act on the management of radioactive waste. The different concepts have been compared against the current reference fuel cycle with the once-through recycling of Pu in PWRs and with a closed fuel cycle for sustainable SFRs. These concepts include: i) recycling MOX in PWRs two or three times by dilution or isotopic zoning, ii) multiple recycling of Pu in PWRs using a uranium-enriched "MIX concept", iii) mixture of MOX and UOX fuel rods in PWR fuel assemblies (CORAIL concept), iv) plutonium on inert structures (APA concept), and v) reactors with high conversion factors. With respect to closed fuel cycle issues (recovering materials and optimising waste management), qualitative comparisons are currently focusing on spent fuel inventories, raw material (natural uranium) savings, waste production, and costs. Two fuel concepts have been highlighted by this analysis: MIX and CORAIL concepts. Without challenging the sustainability of fast reactors and their related fuel cycle, these two concepts appear to be relatively effective and capable of reaching the Pu multiple recycling objectives. Scenarios taking into account these two concepts are currently being studied.

5. The transport capacities not only for spent and new SFR and PWR fuels, but also for PWR fuels recycling Pu. These capacities are currently being analysed and refined.

6. The costs of fuel cycle facilities and reactors, and new methodologies for improved economic assessments.

The environmental impact of the different options and the life cycle analysis (LCA).

These new results will allow us to meet the different requirements governing radioactive material and waste management issued by the French government (PNGMDR plan) under the 2006 Act on radioactive waste management.

Fig. 1 .

 1 Fig. 1. Variation in the total Pu inventory for the transition scenarios.

Fig. 2 .

 2 Fig. 2. Variation on the storage of spent fuels for the transition scenarios

Fig. 3 .

 3 Fig. 3. Accumulated consumption of natural uranium for the transition scenarios.

ACKNOWLEDGMENTS

The authors are grateful to EDF and AREVA for their support to this work through the ACF (future cycle backend) research program of the CEA.

NOMENCLATURE

EPR European Pressurized Water Reactor (EPR is a registered trademark of the AREVA NP group in the USA or other countries) . ERU Enriched Reprocessed Uranium. MOX Mixed (U,Pu) Oxide. PWR Pressurized Water Reactor. SFR Sodium Fast Reactor. FR Fast Reactor. UOX Low enriched uranium oxide. HLW High Level Waste