F Varaine

G Rodriguez

J M Hamy

S Kubo

T Iitsuka

H Mochida

THE SIGNIFICANT COLLABORATION OF JAPAN AND FRANCE ON THE DESIGN OF ASTRID SODIUM FAST REACTOR SINCE 2014

Introduction

After 6 years of Conceptual Design phase (called AVP Phase), the ASTRID Project has entered in January 2016 in its Basic Design Phase. Since the beginning (2010), the management of ASTRID project was organized around a strong involvement of industrial partners in the reactor design [START_REF] Rouault | ASTRID the SFR GEN 4 Technology Demonstrator Project: Where we are, where do we stand for ?[END_REF].

Since 2014, a partnership with Japanese nuclear institutes and industries is effective on two main items: ASTRID reactor design studies and R&D in support of Sodium Fast Reactors (SFR) [START_REF] Rouault | Japan-France Collaboration on the ASTRID program and Sodium Fast Reactor[END_REF]. This French-Japanese collaboration on ASTRID Program and Sodium Fast Reactor has been set up in two steps: the signature of a General Arrangement between CEA and the representatives of MEXT and METI on May 5 th , 2014; in a second step, an Implementing Arrangement was signed the same year on August 7 th by CEA, AREVA NP, JAEA, MHI and MFBR. This collaboration of a significant level is foreseen to run at least up to the end of 2019. At the beginning, the collaborative work (input data, planning and deliverables) was divided in 29 Task Sheets covering ASTRID design (3 Task Sheets) and R&D (26 Tasks Sheets). Since 2016, the contribution of JAEA/MHI-MFBR to the ASTRID reactor engineering studies has increased, passing from three to twelve Design Task Sheets. Therefore the cooperation between CEA, AREVA NP, JAEA, MHI-MFBR is fruitful and it has been complemented by all parties since July 2017 by an additional contribution to enlarge Japanese involvement in a process called "Joint Evaluation" to prepare a future potential Common Design.

This paper aims at a brief overview of involvement of JAEA/MHI-MFBR in the ASTRID design studies through these Design Task Sheets, covering in particular at the early beginning the design of an active decay heat removal system and of a passive reactor shutdown system based on a Curie point electromagnet system. In addition, some Task Sheets are focusing on thermal-hydraulic and thermo-mechanical studies related to the primary vessel.

Japan's contribution to ASTRID program is very significant. Except CEA (which acts as the industrial architect of the project), JAEA-MHI-MFBR became in 2015 the 2 nd largest contributor to the ASTRID program -behind Framatome -in terms of involved staff and related financial contribution. It means that ASTRID project has to adapt its project management to integer this important partnership.

After a brief recall of the ASTRID context and the genesis of this collaboration, this paper aims at a presentation of the significant involvement of JAEA / MHI -MFBR in the ASTRID design studies through the "Design Task Sheets" and through the "Joint evaluation".

ASTRID Project partnership

As defined in the French Law of 28 June 2006 on the sustainable management of radioactive materials and waste, CEA's Nuclear Energy Division is responsible for the ASTRID project.

For the Basic Design phase, CEA has renewed the bilateral partnerships for this new step, reflecting the determination of the different partners to be involved in the ASTRID project. As shown in Fig. 1, it was settled of 14 bi-lateral partnerships connected to CEA at the beginning of the Basic Design phase. Since beginning of the project, CEA acts as the Project manager from the definition of the main functional requirements to the assembly of the 3D mock up including performance control, configuration and interface management between elementary products. Since the AVP phase, the project management is entirely based on a Product Breakdown Structure (PBS), which is in constant evolution.

Japan and France cooperation in the nuclear SFR field before ASTRID Project

Japan and France have been involved for a long time in the peaceful use of nuclear energy and dispose of many nuclear power plants to produce electricity. Each of the two countries has been developing the technology of Sodium Fast Reactors for several decades. Japan operates JOYO and MONJU and France has operated RAPSODIE, PHENIX and SUPERPHENIX. Collaborative R&D arrangements have been existing for a long time, based on a mutual interest in the respective design and related safety approach. Indeed, even if Japan chose the concept of a loop type reactor when France considers a pool type, cross-analyses have brought to light many similarities in design, technology, materials, fuel, safety approach... It has been the subject of exchange of company employees between SFR reactor and the detachment of CEA sodium specialists on MONJU site. Several common publications can illustrate these fruitful exchanges [START_REF] Devictor | Pool and Loop type Sodium-cooled Fast Reactors -Identification of cooperation possibilities -ICAPP2011[END_REF], [START_REF] Chikazawa | R&D in support of ASTRID and JSFR: cross-analysis and identification of possible areas of cooperation[END_REF], [START_REF] Rodriguez | Monju as an international asset: international assistance and cooperation[END_REF], [START_REF] Beauchamp | Cooperation on impingement wastage experiment of Mod. 9Cr-1Mo steel, using SWAT-1R sodiumwater reaction test facility[END_REF].

The ASTRID Project partnership with Japan

The history and the ruling of the ASTRID Project partnership with Japan have been extensively explained in [START_REF] Rouault | Japan-France Collaboration on the ASTRID program and Sodium Fast Reactor[END_REF]. This chapter will just recall the main milestones.

First exchanges on a possible involvement of Japan in the ASTRID project took place in 2010, but no further action was engaged because the priority for France was to structure ASTRID project which had just been launched.

In 2013, Japan and France initiated the discussion for an entry in the ASTRID project. Five working groups were created: 1/Definition of the terms of the agreement and of its principles of governance, 2/ASTRID design activity, 3/R&D on severe accidents, 4/R&D on fuel, 5/Other R&D items (Na technology, ISI&R, Instrumentation). In 2014, these discussions led to a two-level partnership:

The "General arrangement", which establishes the main principles of collaboration; the signatories are the Japanese Ministry of economy, trade and industry (METI) and Ministry of education, culture, sports, science and technology (MEXT) on Japan side, and the CEA by delegation of the French government. It was signed on May 5 th , during the visit of the Japanese Prime Minister in Paris.

The "implementing arrangement", signed by JAEA, MHI, its subsidiary Mitsubishi FBR Systems (MFBR), AREVA (now Framatome) and CEA. It specifies in detail the principles and the governance of the R&D and design activities, the intellectual property and rights of use, the transfer of information to third parties, the rights after 2019 etc. At the starting point, 29 Task Sheets were approved, three for ASTRID design and 26 for R&D. The Executive Committee is responsible for proposing the creation of new implementing arrangements, follow their progress and solve the related difficulties (face-to-face meeting every semester). The Joint Team is in charge of the day-to-day control of design and R&D work (monthly meeting). This organization is fully embedded and coherent with the organization set-up with the other partners of the ASTRID project.

Collaborative works on design studies related to ASTRID

In the design field, Japanese team first contributed directly to the ASTRID Preliminary Design phase on three topics coherently with the ASTRID Master Plan. They concerned the design of:

-An active decay heat removal system, -a control rod system with Curie point electro magnets, -and a seismic isolation system for the Reactor Building. Design activities increased sharply during the year 2016 from three Task Sheets to nine, then to ten in 2017. Up to now, the current list of design activities is as follows:

- An overview of the technical progress of these design Task Sheets can be found in [START_REF] Rodriguez | The collaboration of Japan and France on the design of ASTRID sodium fast reactor[END_REF].

Reinforcement of the collaboration: Common view of a future SFR

In the frame of the Franco-Japanese the first collaborative agreement on ASTRID signed in 2014 has been reinforced by a bilateral collaboration agreement on nuclear energy including a specific chapter dedicated to the ASTRID signed the 21 st of March 2017 (see Fig. The project organization is performed in two steps:

-It started with a series of Face-to-Face meetings performed during the first semester of 2017 to understand the fundamental specifications from each part and the technical points of convergence and those to be further discussed for a deeper exchange and explanation. -According to this first step of evaluation, Working Groups were created to be able to achieve a better common view for a SFR common design reactor.

These Working groups are presented in Fig. 5.

Fig. 5: Table of the joint Working Group items

Each of them was composed of a board of specialists coming from CEA / Framatome / JAEA / MHI-MFBR.

Each of these working groups (except WG10) had to respect the following rules:

-They have to initiate their starting time with a Workplan accepted by all parts. -They have to perform several regular meeting by visio-conference (see Fig. 6). -They have to perform regular Progress of Technical Work report to the WG10 plus a final written synthesis at the end of 2017; and the same process is reproduced for 2018.

The objective is to confirm by each working group the requirements and expectation for ASTRID project and SFR simulation program for extrapolation to future commercial SFR. Conclusions of this joint study have to be reported to the respective national government board.

Fig. 6: The efficient use of the video conference system to exchange at 10 000 km distance

Fig. 1 :

 1 Fig. 1: Set of ASTRID Partnership

Fig. 2 :

 2 Fig. 2: Preparatory meeting of the design activity at Tokyo, June 2014

Fig. 3 :

 3 Fig. 3: First face to face meeting at Lyon, September 2014

Fig. 4 :

 4 Fig. 4: Picture of Ms Ségolène Royal and Mr Hiroshige Sekō signing the 21 st of March 2017 the New Fr-Jp collaboration agreement on Nuclear Energy

ACKOWLEDGMENTS

Many people are involved in this collaboration and it was impossible to put all of them as co-authors. Nonetheless, the authors would like to thank all persons involved in the different Task Sheets, coming from ASTRID project team, Project and Engineering teams from Japan (JAEA / MHI -MFBR) and France (FRAMATOME).

NOMENCLATURE ACS:

Above Thermal Hydraulic TS:

Task Sheet WG:

Working Group 3D:

Three-Dimensional


Sonya Nassari

Mickael Orgeur

Cédrine Blavet

Sigmar Stricker

Claire Fournier- Thibault

Delphine Duprez
email: delphine.duprez@upmc.fr

In addition to being a marker for muscle connective tissue, Odd skipped-related 2 (OSR2) is expressed in differentiated muscle cells during chick development

Keywords: chick, limb, head, muscle, connective tissue, OSR2

The zinc finger transcription factor, Odd skipped-related 2 (OSR2) is a recognized marker of connective tissue in chick embryos. OSR2 gain-and loss-of-function experiments indicate a role in irregular connective tissue differentiation in chick limb undifferentiated cells. Reinvestigation of OSR2 transcript location during chick development with in situ hybridization experiments showed that OSR2 was also expressed in differentiated muscle cells in limbs and head. OSR2 expression was also observed in differentiated myotubes in chick foetal myoblast cultures. This shows that in addition to being a marker of connective tissue, OSR2 is also expressed in muscle fibres during chick development.

.

INTRODUCTION

Connective tissue (CT) is an important component of the body supporting and connecting organs. During development, reciprocal interactions between CT and myogenic cells are required to form a functional muscular system (reviewed in Nassari et al., 2017a). In limbs, CT cells and myogenic cells are intermingled in muscle masses but have different embryological origins. CT cells originate from lateral plate, while myogenic cells originate from somites [START_REF] Bourgeois | Stable and bicistronic expression of two genes in somite-and lateral platederived tissues to study chick limb development[END_REF][START_REF] Chevallier | Limb-somite relationship: origin of the limb musculature[END_REF][START_REF] Kardon | Muscle and tendon morphogenesis in the avian hind limb[END_REF]. The muscle differentiation program is under the control of the Myogenic Regulatory Factor (MRFs), including MYF5, MYOD, MRF4 and MYOG (reviewed in Tajbakhsh, 2009). The differentiation program of limb muscle CT cells is not known (reviewed in Nassari et al., 2017a). To date, three types of transcription factors have been identified to regulate muscle formation in a non cell-autonomous manner during limb development: TCF4, a member of the TCF/LEF family [START_REF] Kardon | A Tcf4-positive mesodermal population provides a prepattern for vertebrate limb muscle patterning[END_REF][START_REF] Mathew | Connective tissue fibroblasts and Tcf4 regulate myogenesis[END_REF], the T-box transcription factors, TBX4 and TBX5 [START_REF] Hasson | Tissue Are Required for Limb Muscle and Tendon Patterning[END_REF] and the zinc finger transcription factors, Odd skipped-related 1 and 2, OSR1 and OSR2 [START_REF] Stricker | Odd-Skipped Related Genes Regulate Differentiation of Embryonic Limb Mesenchyme and Bone Marrow Mesenchymal Stromal Cells[END_REF][START_REF] Vallecillo-García | Odd skipped-related 1 identifies a population of embryonic fibro-adipogenic progenitors regulating myogenesis during limb development[END_REF] The odd gene coding for the zinc finger transcription factor odd-skipped was first identified in a screen for gene mutations in Drosophila as pair-rule genes involved in body segmentation [START_REF] Coulter | Gene activities and segmental patterning in Drosophila: analysis of odd-skipped and pair-rule double mutants[END_REF][START_REF] Nüsslein-Volhard | Mutations affecting segment number and polarity in Drosophila[END_REF]. In vertebrates, two odd-skipped-related genes, Osr1 and Osr2, have been identified [START_REF] Lan | Osr2, a new mouse gene related to Drosophila odd-skipped, exhibits dynamic expression patterns during craniofacial, limb, and kidney development[END_REF][START_REF] So | Cloning and expression analysis of a mouse gene related to Drosophila odd-skipped[END_REF]. During mouse and chick embryonic development and organogenesis, Osr1 and Osr2 exhibit partially overlapping expression domains in intermediate and lateral mesoderm and at later stages in mesonephros, branchial arches, limbs, mandibular and maxillary prominences [START_REF] Lan | Osr2, a new mouse gene related to Drosophila odd-skipped, exhibits dynamic expression patterns during craniofacial, limb, and kidney development[END_REF][START_REF] So | Cloning and expression analysis of a mouse gene related to Drosophila odd-skipped[END_REF][START_REF] Stricker | Comparative expression pattern of Odd-skipped related genes Osr1 and Osr2 in chick embryonic development[END_REF]. Osr1 and Osr2 genes display functional equivalence during mouse development, indicating that the distinct functions of Osr genes rely on their expression domains [START_REF] Gao | Functional equivalence of the zinc finger transcription factors Osr1 and Osr2 in mouse development[END_REF]. Consistent with Osr expression sites, phenotypes of Osr mutant mice indicate a role for Osr1 in heart and urogenital development [START_REF] James | Odd-skipped related 1 is required for development of the metanephric kidney and regulates formation and differentiation of kidney precursor cells[END_REF][START_REF] Wang | Odd-skipped related 1 (Odd1) is an essential regulator of heart and urogenital development[END_REF] and a role for Osr2 in palate and tooth development [START_REF] Lan | Oddskipped related 2 (Osr2) encodes a key intrinsic regulator of secondary palate growth and morphogenesis[END_REF][START_REF] Zhang | Antagonistic Actions of Msx1 and Osr2 Pattern Mammalian Teeth into a Single Row[END_REF].

Osr1 and Osr2 are recognized markers for irregular CT during chick and mouse development (reviewed in Nassari et al., 2017a). During chick limb development, the expression of both genes labels CT cells and is excluded from myogenic cells, labelled with PAX3 or MYOD [START_REF] Stricker | Comparative expression pattern of Odd-skipped related genes Osr1 and Osr2 in chick embryonic development[END_REF][START_REF] Stricker | Odd-Skipped Related Genes Regulate Differentiation of Embryonic Limb Mesenchyme and Bone Marrow Mesenchymal Stromal Cells[END_REF]. However, OSR1/2-positive cells display partial overlap with tendon SCX-positive cells and CT TCF4-positive cells in limb buds of embryonic day 4, E4, (HH24) chick embryos. However, OSRs are not expressed in tendons when they are formed [START_REF] Vallecillo-García | Odd skipped-related 1 identifies a population of embryonic fibro-adipogenic progenitors regulating myogenesis during limb development[END_REF]bioRxiv posted 20 July 2017doi:10.1101/165837). Moreover, the overexpression of either OSR1 or OSR2 promotes irregular CT differentiation, while preventing cartilage, tendon and muscle differentiation in chick limb undifferentiated progenitors [START_REF] Stricker | Odd-Skipped Related Genes Regulate Differentiation of Embryonic Limb Mesenchyme and Bone Marrow Mesenchymal Stromal Cells[END_REF][START_REF] Vallecillo-García | Odd skipped-related 1 identifies a population of embryonic fibro-adipogenic progenitors regulating myogenesis during limb development[END_REF]bioRxiv posted 20 July 2017doi:10.1101/165837). Conversely, the blockade of OSR1 or OSR2 activity decreases the expression of CT markers, while promoting cartilage marker expression in chick limb undifferentiated progenitors [START_REF] Stricker | Odd-Skipped Related Genes Regulate Differentiation of Embryonic Limb Mesenchyme and Bone Marrow Mesenchymal Stromal Cells[END_REF]. Recently, Osr1 has been shown to identify a population of embryonic fibro-adipogenic progenitors that has a non cellautonomous effect on developmental myogenesis [START_REF] Vallecillo-García | Odd skipped-related 1 identifies a population of embryonic fibro-adipogenic progenitors regulating myogenesis during limb development[END_REF]. In chick limbs, when the final muscle pattern is set, OSR2 appears mainly associated with individual muscles, while OSR1 is expressed in irregular CT within and outside muscles [START_REF] Nassari | The chemokines CXCL12 and CXCL14 differentially regulate connective tissue markers during limb development[END_REF].

In this study, we re-investigated the expression pattern of OSR2 transcripts during chick development. We showed that in addition to the already known expression in muscle CT, OSR2 was expressed in myofibres in limbs and head during chick development and in myotubes in muscle cell cultures.

RESULTS AND DISCUSSION

OSR2 has been described as being expressed in muscle CT, a subpopulation of irregular CT cells during chick limb development [START_REF] Nassari | The chemokines CXCL12 and CXCL14 differentially regulate connective tissue markers during limb development[END_REF][START_REF] Stricker | Comparative expression pattern of Odd-skipped related genes Osr1 and Osr2 in chick embryonic development[END_REF][START_REF] Stricker | Odd-Skipped Related Genes Regulate Differentiation of Embryonic Limb Mesenchyme and Bone Marrow Mesenchymal Stromal Cells[END_REF]. We re-investigated OSR2 expression with in situ hybridization experiments to sections at different developmental stages. We used the chick probe of 361 kb length located between the nucleotides 127 to 487 of OSR2 gene (Figure 1). This probe has been used previously for gene expression analysis [START_REF] Stricker | Comparative expression pattern of Odd-skipped related genes Osr1 and Osr2 in chick embryonic development[END_REF][START_REF] Stricker | Odd-Skipped Related Genes Regulate Differentiation of Embryonic Limb Mesenchyme and Bone Marrow Mesenchymal Stromal Cells[END_REF]. Moreover, this OSR2 probe did not crossreact/blast with any gene in chicken genomic databases and did not harbour the zinc finger domain of the OSR2 gene. At E3, corresponding to HH20 (40 somites), OSR1 was expressed in limb mesenchyme, while no OSR2 expression was observed in chick limb buds (Figure 2A,B). OSR2 was observed in the mesonephros (Figure 2B, arrow), as previously described [START_REF] Stricker | Comparative expression pattern of Odd-skipped related genes Osr1 and Osr2 in chick embryonic development[END_REF]. Muscle progenitors migrate from the hypaxial lips of the dermomyotomes towards the forelimb buds from E2 (HH17, 30 somites) in chick embryos [START_REF] Chevallier | Limb-somite relationship: origin of the limb musculature[END_REF][START_REF] Tozer | Involvement of vessels and PDGFB in muscle splitting during chick limb development[END_REF]. Migrating muscle progenitors assessed with MYOR expression did not express OSR2 at E3/HH20 (Figure 2B,C), showing that OSR2 was not expressed in muscle progenitors at this stage. At E5 (HH26), the OSR2 expression domains were similar to that of the myogenic transcription factor MYOD in dorsal and ventral limb muscle masses (Figure 2D,E), however it was not clear whether they were expressed in the same cells. From E5 to E8, in addition to being expressed in irregular CT between cartilage elements in distal limb regions and in dermis regions, OSR2 displayed a strong expression in developing muscles [START_REF] Nassari | The chemokines CXCL12 and CXCL14 differentially regulate connective tissue markers during limb development[END_REF][START_REF] Stricker | Odd-Skipped Related Genes Regulate Differentiation of Embryonic Limb Mesenchyme and Bone Marrow Mesenchymal Stromal Cells[END_REF]. At E9, when the final muscle pattern is set, OSR2 expression was mostly expressed in muscles regions, in addition to feather buds (Figure 2F). Within muscles, OSR2 was expressed in a subset of MF20-positive muscle fibres (Figure 2G,arrowheads) and in between MF20-positive cells (Figure 2G, arrows). These results show that in addition to being expressed in irregular and muscle CT during chick limb development, OSR2 is expressed in differentiated muscle fibres.

Previous studies have highlighted a key role for OSR2 in the development of specific craniofacial regions [START_REF] Lan | Oddskipped related 2 (Osr2) encodes a key intrinsic regulator of secondary palate growth and morphogenesis[END_REF]. During craniofacial development of mouse embryos, Osr2 expression is restricted to specific mesenchymal tissues, including the mesenchyme of the developing palatal shelves and the tongue [START_REF] Lan | Osr2, a new mouse gene related to Drosophila odd-skipped, exhibits dynamic expression patterns during craniofacial, limb, and kidney development[END_REF]. In chick embryos, OSR2 has been described to be expressed in branchial arches from E3 [START_REF] Stricker | Comparative expression pattern of Odd-skipped related genes Osr1 and Osr2 in chick embryonic development[END_REF]. In order to determine whether OSR2 was also expressed in differentiated muscle cells during chick craniofacial development, we performed in situ hybridization to head sections of chick embryos at different developmental stages. At E3 (HH20), OSR1 and OSR2 were expressed in distinct regions of the first branchial arches outside the muscle regions labelled by MYOR (Figure 3A-C). At E4 (HH22), OSR2 expression was detected in mesenchymal cells of the third branchial arches and did not overlap with that of MYOR (Figure 3D-G), which labelled the core of muscle progenitor cells in branchial arches [START_REF] Grenier | Relationship between Neural Crest Cells and Cranial Mesoderm during Head Muscle Development[END_REF]. This indicated that OSR2 was restricted to neural-crest-derived mesenchymal cells in branchial arches before E4. At E7, OSR2 was strongly expressed in muscle regions in addition to displaying an expression in the head mesenchyme (Figure 3H-J). High magnifications of muscles visualised with transverse (Figure 3K-M) and longitudinal (Figure 3N-P) sections showed that OSR2 expression was observed in MF20-positive differentiated muscle cells (Figure 3K-P We also analysed OSR2 expression in vitro, in primary cell cultures of foetal myoblasts isolated from limbs of E10 chicken embryos. Chicken foetal myoblasts were cultured in differentiation culture medium for 2 days. OSR2 expression was assessed by in situ hybridization (Figure 4A-D) and muscle cell differentiation with MF20 staining (Figure 4A,B,E,F). We observed OSR2 transcripts in MF20-positive cells (Figure 4A-F, arrows), showing that OSR2 was expressed in myotubes in chick foetal myoblast cultures

In addition to being a marker of CT and to promoting CT differentiation from chick mesenchymal stem cells [START_REF] Nassari | The chemokines CXCL12 and CXCL14 differentially regulate connective tissue markers during limb development[END_REF][START_REF] Stricker | Comparative expression pattern of Odd-skipped related genes Osr1 and Osr2 in chick embryonic development[END_REF][START_REF] Stricker | Odd-Skipped Related Genes Regulate Differentiation of Embryonic Limb Mesenchyme and Bone Marrow Mesenchymal Stromal Cells[END_REF][START_REF] Vallecillo-García | Odd skipped-related 1 identifies a population of embryonic fibro-adipogenic progenitors regulating myogenesis during limb development[END_REF] bioRxiv posted 20 July 2017 doi:10.1101/165837), we identified OSR2 as being also expressed in myosin-positive differentiated muscle cells during development of chick embryos. OSR2 expression was also observed in myotubes of chick foetal myoblast cultures. This unexpected expression of OSR2 in chick differentiated muscle fibres has never been described before and could bring new insights for OSR2 function during development. It is not clear whether Osr2 displays similar muscle expression in mice. X-gal staining of forelimb sections of E13.5 and E15.5 Osr2 Lacz/-embryos did not show any obvious expression in limb muscles [START_REF] Gao | The zinc finger transcription factors Osr1 and Osr2 control synovial joint formation[END_REF]. Moreover, Osr2 IresCre mice displayed specific expression (of reporter gene) in mandibular mesenchyme and did not display any obvious expression in muscle areas in branchial arches of E12.5 mice [START_REF] Lan | A unique mouse strain expressing Cre recombinase for tissue-specific analysis of gene function in palate and kidney development[END_REF]. Since previous expression analyses rely on genetic tools, double labelling experiments are nevertheless required to exclude an Osr2 expression in myotubes during mouse development.

MATERIALS AND METHODS

Chick embryos

Fertilized chick eggs from commercial sources (JA57 strain, Institut de Sélection Animale, Lyon, France) were incubated at 38°C in a humidified incubator until appropriate stages.

Embryos were staged according to the number of days in ovo. Staging using Hamburger and Hamilton, HH [START_REF] Hamburger | A series of normal stages in the development of the chick embryo[END_REF] or somite numbers was also used for young stages.

Chick myoblast primary cultures

Primary muscle cell cultures were prepared from skeletal muscles of forelimbs of E10 chick foetuses. Muscle cells were mechanically dissociated and seeded in plastic dishes coated with 0.1% gelatine. Myoblast primary cultures were first incubated in a proliferation medium (2/3 Minimum Essential Eagle Medium (MEM), 1/3 Hanks' salts medium 199, 10% foetal calf serum, 1% penicillin streptomycin and 1% glutamine). At 80% of confluence, differentiation was induced using a differentiation medium (2/3 Minimum Essential Eagle Medium (MEM), 1/3 Hanks' salts medium 199, 2% foetal calf serum, 1% penicillin streptomycin and 1% glutamine).

In situ hybridization to embryo sections and cells

Embryos were fixed in 4% paraformaldehyde PBS solution, rinsed successively in 4% and 15% sucrose solution, embedded in a gelatine-sucrose solution (7.5% gelatine, 15% sucrose, 50% Phosphate buffer), and frozen in chilled isopentane. Cryostat sections of 10 to 14 µm were collected on Superfrost/Plus slides (CML, France). Primary muscle cell cultures were fixed in 4% paraformaldehyde PBS solution and rinsed with PBS. Sections and cell cultures were processed for in situ hybridization as previously described [START_REF] Escot | Misregulation of SDF1-CXCR4 Signaling Impairs Early Cardiac Neural Crest Cell Migration Leading to Conotruncal Defects[END_REF][START_REF] Nassari | The chemokines CXCL12 and CXCL14 differentially regulate connective tissue markers during limb development[END_REF] using digoxigenin-labelled mRNA probes for chick OSR1, chick OSR2 [START_REF] Nassari | The chemokines CXCL12 and CXCL14 differentially regulate connective tissue markers during limb development[END_REF][START_REF] Stricker | Comparative expression pattern of Odd-skipped related genes Osr1 and Osr2 in chick embryonic development[END_REF], chick MYOR and chick MYOD [START_REF] Grenier | Relationship between Neural Crest Cells and Cranial Mesoderm during Head Muscle Development[END_REF][START_REF] Von Scheven | Protein and genomic organisation of vertebrate MyoR and Capsulin genes and their expression during avian development[END_REF].

Immunohistochemistry

Differentiated muscle cells were detected on limb and head sections and chick foetal myoblast cultures after in situ hybridization using the monoclonal antibody against sarcomeric myosin heavy chain, MF20 (Developmental Hybridoma Bank, non-diluted supernatant).

Immunohistochemistry was processed after in situ hybridization, as previously described [START_REF] Grenier | Relationship between Neural Crest Cells and Cranial Mesoderm during Head Muscle Development[END_REF][START_REF] Tozer | Involvement of vessels and PDGFB in muscle splitting during chick limb development[END_REF].

Image capturing

Images of labelled sections and cultured cells were obtained using a Leica DMI6000 B microscope or a Nikon microscope equipped for epifluorescence. Images were processed using Adobe Photoshop software.

FIGURE LEGENDS

  , arrowheads) in addition to muscle CT (Figure 3K-P, arrows).

Figure 1

 1 Figure 1

Figure 2 OSR2

 2 Figure 2

Figure 3 OSR2

 3 Figure 3

Figure 4 OSR2

 4 Figure 4

FUNDING

This work was supported by the Fondation pour la Recherche Médicale (FRM) DEQ20140329500, Association Française contre les Myopathies (AFM) N•16826. S.N. and M.O. were part of the MyoGrad International Research Training Group for Myology and received financial support from the AFM (AFM 20150532272) and FRM (FDT20150532272) and from the Université Franco-Allemande (CDF1-06-11 and CT-24-16).

COMPETING INTERESTS

The authors declare no competing or financial interests.


S Bahroun
email: bahroun@lagep.univ-lyon1.fr

S Li

C Jallut

C Valentin

F De Panthou

Control and optimization of a three-phase catalytic slurry intensified continuous chemical reactor

Keywords: Lyapunov based control, Dynamic modeling, Three-phase catalytic reaction, Intensified continuous reactor, Entropy based control

Intensified continuous mini-reactors working in high pressure and temperature conditions are particularly effective at coping with mass transfer limitations during three-phase catalytic reactions. They are highly non-linear, multivariable systems and behave differently from conventional batch, fed-batch or continuous non-intensified reactors. In this paper, the optimization and control of this new process are presented using a two-layer approach consisting of a hierarchical control structure with an optimization layer which calculates the set points for an advanced controller. The latter is based on the concavity of the entropy function and the use of thermodynamic availability as a Lyapunov function. The three-phase catalytic o-cresol hydrogenation performed under high pressure and temperature in a small-scale pilot of the RAPTOR® reactor designed by the French company AETGROUP SAS, is taken as a representative test example to illustrate the strategy. The performance of the control structure is illustrated by simulation.

Introduction

Although the batch reactor remains a key tool in the field of fine chemicals and pharmaceuticals due to its high flexibility and versatility, it presents a number of technological limitations, in particular, poor transfer of the heat released by exothermic chemical reactions and the required use of solvents which creates serious problems with regard to safety [START_REF] Stoessel | What is your thermal risk?[END_REF].

For some years, an alternative to batch reactors has been developed, thanks to progress in process intensification and the development of intensified continuous mini-reactors [START_REF] Lomel | The microreactor. A systematic and efficient tool for the transition from batch to continuous process[END_REF] [START_REF] Charpentier | In the frame of globalization and sustainability, process intensification, a path to the future of chemical and process engineering (molecule into money)[END_REF]. The intensification leads to the improved control of heat and mass transfer that makes it possible to concentrate the reagent and thus limit the quantities of solvent to be treated, as well as the inventory of hazardous substances. Consequently, the intensified continuous chemical reactors seem to be inherently safer than the conventional batch reactors, but the issue of their control has been raised by some authors [START_REF] Etchells | Process intensification. Safety Pros and Cons[END_REF] as these reactors are smaller and more sensitive to disturbances and they are required to work under high pressure and temperature conditions. This paper deals with the modeling and control of an intensified continuous stirred mini-reactor, the "RAPTOR®" (French acronym for "Réacteur Agité Polyvalent à Transfert Optimisé Rectiligne" or "Polyvalent Rectilinear Stirred Reactor With Optimized Transfer"), recently developed by AETGROUP SAS Company, a French company whose main activity is chemical process industrialization and continuous process technology. This reactor is particularly good at coping with mass transfer limitations during three-phase catalytic reactions due to its highly efficient stirring system. It is also well adapted to process intensification under extreme pressure and temperature conditions (up to 300°C and 250 bar) making it possible for a complete reaction to take place with just a few minutes residence time. In terms of catalytic reactions, this reactor can handle dispersed catalyst. For reasons of confidentiality, a detailed description of the RAPTOR® cannot be given. The case of a three-phase catalytic hydrogenation reaction is taken as a representative test example. The aim of this paper is to describe control law synthesis for intensified three-phase continuous reactors that find their basis in irreversible thermodynamics. This choice has been made due to the specific energetic features of the intensified continuous mini-reactors that will be detailed below.

As far as the control of chemical reactors is concerned, many general studies concerning the control of homogeneous chemical processes have been published. Traditional control techniques using linear system analysis and design tools together with linearized models have been used [START_REF] Aris | An analysis of chemical reactor stability and control[END_REF][START_REF] Morari | Robust Process Control[END_REF][START_REF] Uppal | On the dynamic behaviour of continuous stirred tank reactors[END_REF]. A stabilization of a class of continuous stirred tank reactors (CSTR) under classical PI control with temperature feedback was proposed by Alvarez-Ramirez and Morales [START_REF] Alvarez-Ramirez | PI control of continuously stirred tank reactors: stability and performance[END_REF]. However the use of these techniques is limited since chemical processes are highly non-linear. Therefore different non-linear methods have been proposed to control homogeneous chemical processes [START_REF] Corriou | Commande des procédés[END_REF] [START_REF] Seborg | Process Dynamics and Control[END_REF]. Feedback linearization techniques have been proposed by Limqueco and Kantor in [START_REF] Limqueco | Nonlinear output feedback control of an exothermic reactor[END_REF], where a non-linear output feedback controller is built for an exothermic, first-order reaction. Input -Output linearizing control was used by Kravaris and Chung [START_REF] Kravaris | Nonlinear state feedback synthesis by global input/output linearization[END_REF] to design a control law for trajectory tracking in batch reactor. Dochain [START_REF] Dochain | Design of adaptive linearizing controllers for non-isothermal reactors[END_REF] developed an input-output linearizing adaptive controller to control the temperature in non-isothermal stirred-tank reactor.

Non-linear geometric control tools have been used in Alvarez-Ramirez [START_REF] Alvarez-Ramirez | Stability of a class of uncertain continuous stirred chemical reactors with a nonlinear feedback[END_REF] and Alvarez-Ramirez, Suarez and Femat [START_REF] Alvarez-Ramirez | Control of continuous-stirred tank reactors: Stabilization with unknown reaction rates[END_REF], to stabilize unstable steady states in CSTR. An Interconnection and Damping Assignment-Passivity Based Control (IDA-PBC) approach was proposed by Ramírez in [START_REF] Ramírez | On the control of non-linear processes: An IDA-PBC approach[END_REF] for the control of a non-minimum phase Multi-Input Multi-Output (MIMO) CSTR.

Lyapunov based control was used by Antonellia [START_REF] Antonellia | Continuous stirred tank reactors: easy to stabilise?[END_REF] to design non-linear output feedback control for the temperature stabilization of a CSTR, in the presence of input constraints and uncertainty in the kinetic parameters. Applications of sliding mode controllers to chemical processes [16] [17] have also attracted significant interest. In Chen [START_REF] Chen | Design of a sliding mode control system for chemical processes[END_REF], simulation results revealed that the proposed sliding mode control system design methodology is applicable and promising for the non-linear regulation of time-delay chemical processes. Some research has been devoted to the control of non-intensified continuous three-phase catalytic hydrogenation reactors.

Rezende et al. [START_REF] Rezende | Control and optimization of a Three Phase Industrial Hydrogenation Reactor[END_REF] and Delba Melo et al. [START_REF] Melo | Off-line optimization and control for real time integration of a three-phase hydrogenation catalytic reactor[END_REF] evaluated a two-layer approach for the control of a three-phase catalytic reactor.

It consists of an optimization layer that calculates the set points and manipulated variables to the advanced controller layer.

The controller used was a multivariable predictive controller based on the Dynamic Matrix Control approach (DMC) in [START_REF] Rezende | Control and optimization of a Three Phase Industrial Hydrogenation Reactor[END_REF] and on the Quadratic Dynamic Matrix Control approach (QDMC) in [START_REF] Melo | Off-line optimization and control for real time integration of a three-phase hydrogenation catalytic reactor[END_REF]. The problem of optimization was solved by using the Successive Quadratic Programming (SQP) algorithm in [START_REF] Rezende | Control and optimization of a Three Phase Industrial Hydrogenation Reactor[END_REF] and the Levenberg-Marquardt and SQP method as the optimization algorithm in [START_REF] Melo | Off-line optimization and control for real time integration of a three-phase hydrogenation catalytic reactor[END_REF]. Rezende et al. [START_REF] Rezende | Algorithms for real-time integrated optimization and control: one layer approach[END_REF] proposed a one-layer approach to control a three-phase catalytic reactor.

The predictive DMC was used as the process controller, the optimization problem being solved by the using the Genetic Algorithm. Delba Melo et al. [START_REF] Melo | Evaluation of control algorithms for three-phase hydrogenation catalytic reactor[END_REF] assessed the performance of different control strategies in a three-phase catalytic reactor: feedback control, feedforward control and a combination of both strategies. The feedback strategy was implemented by using the predictive QDMC. The feedforward action was calculated with the aim of minimizing a quadratic error between the calculated exit reactor temperature and the set-point for this process variable.

By analyzing these different approaches, we can see that they involve general mathematical and control tools, and do not take energy and thermodynamic considerations into account. Looking at the problem from a different angle, our goal is to synthesize entropy based control laws based on irreversible thermodynamics. The link between thermodynamics and control strategy started with Warden, Aris and Amundson [START_REF] Warden | An analysis of chemical reactor stability and control-VIII. The direct method of Lyapunov. Introduction and applications to simple reactions in stirred vessels[END_REF], who carried out stability analysis of CSTR for finite disturbances, and Dammer and Tells [START_REF] Dammers | Thermodynamic stability and entropy production in adiabatic stirred flow reactors[END_REF] who studied open reaction systems with stable and unstable steady states far from thermodynamic equilibrium. Georgakis [START_REF] Georgakis | On the use of extensive variables in process dynamics and control[END_REF] proposed a non-linear control structure that is based on extensive thermodynamic variables. In [START_REF] Favache | Thermodynamics and chemical systems stability: The CSTR case study revisited[END_REF], Favache and Dochain presented an extension of Georgakis's results [START_REF] Georgakis | On the use of extensive variables in process dynamics and control[END_REF] regarding the stability analysis of the CSTR.

They proposed different candidate Lyapunov functions related to thermodynamic and based specifically on the entropy, the entropy production and the internal energy. Alonzo and Ydstie combined thermodynamic, passivity and Lyapunov theory. The basis of this theory was established by Ydstie and Alonzo [START_REF] Alonso | Process systems, passivity and the second law of thermodynamics[END_REF] [START_REF] Ydstie | Process systems and passivity via the Clausius-Planck inequality[END_REF] in the context of passive control design and the control of distributed systems in [START_REF] Alonso | Stabilization of distributed systems using irreversible thermodynamics[END_REF], and transport reaction systems in Ruszkowski and Ydstie [START_REF] Ruszkowski | Passivity based control of transport reaction systems[END_REF]. This paper deals with the dynamic modeling and control of a significantly complex situation as it studies the case of a threephase catalytic hydrogenation reaction performed in an intensified continuous chemical reactor. Analyzing the design, control and safety of this type of reactors is important for the future of the fine chemicals industry. Such processes involve complex reactions with constraints on thermal stability and/or selectivity [START_REF] Lomel | The microreactor. A systematic and efficient tool for the transition from batch to continuous process[END_REF]. The dynamic modeling of these reactors is also more difficult since three phases are involved in the process. These three phases are mobile and exchange species and energy. Moreover, the chemical reactions that take place are highly exothermic. The resulting process is then a multivariable highly non-linear system.

In the present work, a two-layer control approach was developed for the control of the jacketed continuous intensified reactor "RAPTOR®", with the aim of rejecting disturbances whilst maintaining safety. The choice of the controlled, manipulated and measured variables was guided by conventional industrial practices. The aim was to control the conversion at the reactor outlet. As the conversion cannot be measured online or only using a very expensive sensor, the controlled variable chosen was temperature at the mini-reactor outlet, which can be easily measured online. This point is discussed in section 4. The manipulated variable is the inlet jacket temperature, as for most of the industrial applications. The measured variables are the outlet fluid temperature and the reactor body temperature, both of which can be easily measured in an industrial context.

Constraints on the highest admissible temperature for the metal body reactor, as well as the dynamic behavior of the manipulated variable must be taken into account. The resolution of an optimization problem is combined with an advanced control algorithm based on irreversible thermodynamics. This approach is based on the works of Alonso [START_REF] Alonso | Process systems, passivity and the second law of thermodynamics[END_REF], Ydstie [START_REF] Ydstie | Process systems and passivity via the Clausius-Planck inequality[END_REF],

Ruszkowski [START_REF] Ruszkowski | Passivity based control of transport reaction systems[END_REF] and Hoang [START_REF] Hoang | Thermodynamic approach for Lyapunov based control[END_REF] [START_REF] Hoang | Lyapunov based control for non isothermal continuous stirred tank reactor[END_REF]. O-cresol hydrogenation to obtain 2-methyl-cyclohexanol is taken as an example to illustrate the approach through simulations obtained from a mathematical dynamic model of the system. The finite dimension dynamic model that we propose consists of mass and energy balance equations for the catalyst particles the gas phase and the liquid bulk phase, and is based on a spatial discretization of the reactor. The transient heat transfer between the metal body of the reactor, the coolant fluid and the bulk fluid is also taken into account due to the high (reactor body mass)/(bulk mass) ratio that is a common feature of intensified reactors [START_REF] Benaissa | Dynamic behaviour of a continuous heat exchanger/reactor after flow failure[END_REF].

Dynamic behavior of the continuous mini-reactor

Model principle

Developing efficient and reliable dynamic models for three-phase catalytic slurry continuous reactors is still a difficult task because it involves many aspects including hydrodynamics, gas-liquid and liquid-solid mass transfer, heat transfer, and reaction kinetics [START_REF] Bergault | Modeling and comparison of acetophenone hydrogenation in trickle-bed and slurry airlift reactors[END_REF]. The extreme pressure and temperature conditions and the highly efficient stirring in the RAPTOR®, make it necessary to model all these aspects because the reaction is no longer limited by mass transfer. In the literature, we find studies proposing the dynamic modeling and control of catalytic three-phase reactors [26][35-39] but as far as we know, the problem of intensified continuous mini-reactors modeling has not been addressed.

The model presented here describes the dynamic behavior of the intensified continuous mini-reactor during the catalytic hydrogenation of o-cresol. In this case, hydrogen reacts with o-cresol without solvent due to the high heat and mass transfer capacities of the mini-reactor. A three-phase catalytic reactor is a system in which gas and liquid phases are brought into contact with a porous solid phase. The reaction occurs between a dissolved gas and a liquid-phase reactant in presence of a catalyst deposited on the surface of the porous solid support [START_REF] Ramachandran | Three-phase catalytic reactors[END_REF] according to the following global stoichiometric equation:

A (g) + ν B B (l) → ν C C (l) (1)
Due to the presence of the efficient stirrer and the tubular nature of the reactor, bulk flow through the mini-reactor is treated as an association of J perfectly mixed reactors (CSTR) in series with back mixing effect as is typical for chemical reactor modeling (see Fig. 1). This is a method for the spatial discretization of the flow that is an infinite dimension system at the beginning. This flow arrangement makes it possible to take into account axial mixing within the reactor and has been confirmed by RTD measurements. It is presumed to hold for the three phases. Similarly, the counter current flow through the jacket is treated as an association of J perfectly stirred tank reactors in series. This means of considering the flows in the reactor and in the jacket is highly flexible and leads to a finite dimension model [START_REF] Choulak | A generic dynamic model for simulation and control of reactive extrusion[END_REF].

1 K-1 K K+1 J 1 K-1 K K+1 J 1 K-1 K K+1 J
Fig. 1. Flow model and spatial discretization of the mini-reactor.

A specificity of an intensified continuous mini-reactor is the large size of the metal body in relation to the volume of fluid which allows it to withstand high pressure and temperature. Therefore, the influence of the reactor body itself may be significant with respect to the thermal transient behavior of the system [START_REF] Benaissa | Dynamic behaviour of a continuous heat exchanger/reactor after flow failure[END_REF]. Consequently, the body of the mini-reactor is broken down into J pieces with uniform temperatures (see Fig. 1) in order to include a description of the reactor body in the model.

Dynamic model equations

The model consists of mass and energy balance equations for the catalyst particles, the gas phase and liquid-bulk phase, and also energy balance equations for the body of the reactor and for the cooling fluid flowing through the jacket [START_REF] Bahroun | Dynamic modelling of a three-phase catalytic slurry intensified chemical reactor[END_REF].

In three-phase catalytic reactions, the reaction rate is calculated by using the Langmuir-Hinshelwood model [START_REF] Hichri | Kinetics and slurry-type reactor modelling during catalytic hydrogenation of o-cresol on Ni/SiO 2[END_REF]:

R = k K A K B C As C Bs 1 + K A C As ( ) 1 + K B C Bs ( ) (2)
where A stands for hydrogen, B for o-cresol, C for 2-methylcyclohexanol. C As and C Bs are respectively the hydrogen and ocresol concentrations within the catalyst pores that are presumed to be uniform within the catalyst pellets.

The variations of the rate constant k with temperature are given by the Arrhenius law while those of the adsorption constants K A and K B are derived from the mass action law [START_REF] Hichri | Kinetics and slurry-type reactor modelling during catalytic hydrogenation of o-cresol on Ni/SiO 2[END_REF]:

k = 5, 46.10 8 exp(-82220 / RT s ) (3) K A = 10,55.10 -3 exp(+5003/ RT s ) (4) K B = 7,54.10 -6 exp(+16325/ RT s ) (5)
where T s is the catalyst pellet temperature that is presumed to be uniform. The parameters K A and K B in equations ( 4) and ( 5)

are adsorption equilibrium constants that decrease with temperature. These parameters are involved in the Langmuir -Hinshelwood mechanism that includes adsorption elementary steps.

The following assumptions are considered to derive the model [26] [38] [42]:

• the temperature of the liquid and gaseous phases is considered to be equal;

• a global mass transfer coefficient is used to represent hydrogen transfer from the liquid surface to the bulk.

Equilibrium conditions at the gas-liquid interface are assumed;

• the pressure drop is negligible;

• the resistances to mass and heat transfer at the catalyst pellet surface and within the pores are lumped into the overall heat and mass transfer coefficients;

• the material balance in the gas phase, assumed to be pure hydrogen, is given as a steady state;

• the gaseous phase is assumed to be ideal.

Let us first consider the dynamic part of the model. The balance equations are written for each set of three elementary volumes, the bulk V k , the jacket cooling liquid V jk and the reactor metal body V mk , denoted by the k index (see Fig. 1). The bulk volume is made up of three phases: the liquid phase volume is ε l k V k , the gaseous phase volume is ε g k V k and the solid phase volume is ε s V k

( 1 = + + k g k l s ε ε ε
). The gaseous phase hold-up k g ε and therefore the gas-liquid interface specific area k a gl are assumed to vary along the reactor axis due to hydrogen consumption. Consequently, the gaseous phase volumetric flow rate varies with the k index whilst the volumetric flow rates of the liquid and solid phases q l and q s are assumed to be constant.

Mass balance of reactant

A liquid phase ( ) ( ) ( ) ( ) k Al k Al k k k As k Al ls lsA k k Al l k Al l k Al l k Al k k l C C a k V C C a k V C q C q C q dt dC V - + - - + - + + = + - * 1 1 2 1 1 gl gl α α α ε (6) solid phase ( ) ( ) ( ) ) , , ( 2 1 1 1 1 k s k Bs k As k s s A k As k Al ls lsA k k As s k As s k As s k As k s T C C R V C C a k V C q C q C q dt dC V ρ ε ν α α α ε - - + + - + + = + - (7)
The hydrogen solubility at the gas-liquid interface is calculated by using the Henry constant that is available in [START_REF] Hichri | Kinetics and slurry-type reactor modelling during catalytic hydrogenation of o-cresol on Ni/SiO 2[END_REF]:

        = = k f k *k Al RT P He P C 4990 exp 11538 (8) Mass balance of reactant B liquid phase ) ( ) 2 1 ( ) 1 ( 1 1 k Bs k Bl ls lsB k k Bl l k Bl l k Bl l k Bl k k l C C a k V C q C q C q dt dC V - - + - + + = + - α α α ε (9) solid phase ( ) ( ) ( ) ( ) k s k Bs k As k s s B k Bs k Bl ls lsB k k Bs s k Bs s k Bs s k Bs k s T C C R V C C a k V C q C q C q dt dC V , , 2 1 1 1 1 ρ ε ν α α α ε - - + + - + + = + - (10)
Energy balances fluid (gas and liquid) phases

( ) ( ) ( ) (
)

k f l k f l k f l pl l k f k g k f k g k f k g pg g k f k s ls s k k f k m k k f pl l k l pg g k g k T q T q T q C T q T q T q C T T a h V T T hS dt dT C C V ) 2 1 ( ) 1 ( ) 2 1 ( ) 1 ( ) ( 1 1 1 1 1 1 α α α ρ α α α ρ ρ ε ρ ε + - + + + + - + + + - + - = + + - + + - - (11) solid phase ( ) ( ) ( ) ( ) ( ) ( ) k s k s B k s A r s k s k s k s s k s k s s ps s k s k f ls s k k s ps s k s T C C HR V T T q T T q C T T a h V dt dT C V , , 1 , , 1 1 ∆ - - + - + - - = + - ρ ε α α ρ ρ ε ( 12
)
mini-reactor metal body

( ) ( ) k m k J j k j k m k f k k m pm m mk T T S h T T hS dt dT C V - + - = + - 1 ρ ( 13
)
cooling medium ( ) ( )

1 1 - + - - - - = k j k j j pj j k j k J m k j k j pj j jk T T q C T T S h dt dT C V ρ ρ (14)
In order to take into account gaseous phase hydrogen consumption, the steady-state hydrogen mass balance is given according to equation ( 15):

( ) ( ) ( ) Ag T k g Ag T k g k Al k Al k gl gl k Ag T k g J S J S C C a k V J S 1 1 * 1 2 1 + - + + = - + + αε ε α ε α (15)
The hydrogen consumption is assumed to only reduce the gas hold-up k g ε in equation ( 15) which means that the hydrogen flux J Ag is assumed to be constant. The number of spherical bubbles N b k , with a constant radius r b , represents the gas hold-up k g ε according to the equation ( 16).

k k g r N V π ε = ( 16
)
The gas-liquid interface surface area a gl k depends on the number of spherical bubbles N b k according to the equation ( 17).

= + + k g k l s ε ε ε (18)
To summarize, the algebro-differential finite dimension dynamic model of the elementary k th CSTR has 9 state variables:

k g k J j k m k f k s k Bs k Bl k As k Al T T T T C C C C ε , , , , , , , , 1 + -
. The 9 independent equations are the 8 dynamic balance equations ( 6), ( 7), ( 9), ( 10), ( 11), ( 12), ( 13) and ( 14), and the gas phase steady-state balance equation [START_REF] Antonellia | Continuous stirred tank reactors: easy to stabilise?[END_REF]. To solve this algebro-differential equations system, 8 constitutive equations ( 2), ( 3), ( 4), ( 5), ( 8), ( 16), ( 17) and [START_REF] Warden | An analysis of chemical reactor stability and control-VIII. The direct method of Lyapunov. Introduction and applications to simple reactions in stirred vessels[END_REF]

are used to express R,k,K A ,K B ,ε l k ,C Al *k ,N b k ,a gl k .

Open loop simulation results for consistency and sensitivity analysis

The mathematical dynamic model that we developed makes it possible to reproduce the main features of the open-loop dynamic behavior of the intensified continuous mini-reactor. The nominal operating point of a small-scale pilot of the RAPTOR® is defined as follows. A slurry made of catalyst dispersed in liquid o-cresol is fed into the reactor with hydrogen at 200 bar. The cooling medium jacket inlet temperature is T j0 . The inlet gaseous phase hold-up is 47.5%. The main parameters used for the simulation are given in table 1. In Fig. 2, the trajectory toward the steady state of the reactor as soon as the hydrogen is introduced is represented by the dynamic behavior of the reactor outlet temperature variation from initial conditions. The operating conditions lead to a reference steady-state o-cresol conversion in the liquid phase of up to 98% at the reactor outlet, which is a very good industrial target. We observe that the fluid temperature is limited and increases by 102°C.

The catalyst temperature is slightly higher than that of the reactant fluid since the reaction takes place within the catalyst pores.

We also observe that the jacket temperature remains nearly constant which is due to the high value of the cooling fluid flow rate in the jacket compared to the fluid flow rate inside the reactor which quickly removes heat from the reactor body. The temperature of the reactor body increases by only 63°C. The metal body plays the same role as the one of a solvent in the case of a batch or fed-batch reactor. This behavior has been well documented in the literature [START_REF] Benaissa | Dynamic behaviour of a continuous heat exchanger/reactor after flow failure[END_REF]. The accumulation capacity acts only during transient periods. Such transient periods are those occurring after an incident. The reactor body tends to accumulate the energy released by the reaction thanks to its high mass compared to the bulk phases inventory mass ((reactor body mass / bulk mass) > 10). We also provide some results from steady-state simulations in order to check the model's consistency, as well as the model output sensitivity analysis with respect to input and disturbances (for confidentiality reasons, only differences with respect to values obtained for the reference steady state are presented). As far as intensified continuous reactors are concerned, the reaction takes place at a very high temperature and the jacket plays a dual role in the evolution of the reaction. On the one hand, it makes it possible to obtain good outlet conversion by increasing the temperature of the bulk. On the other hand, it affects safety since the jacket fluid makes it possible to cool the temperature of the bulk in order to avoid thermal runaway. A suitable compromise must be found. Fig. 3 illustrates the steady-state characterization of outlet bulk temperature and conversion with respect to the inlet jacket temperature. From this figure, it is observed that both outlet bulk temperature and conversion are very sensitive to the inlet temperature of the jacket fluid.

Process variable

P V ∆ r H K lsA a ls K lsB a ls
We will now consider the effects of small changes that can occur in the operating conditions which are considered as disturbances. Only those leading to the widest variations in the system's steady state are presented here.

-30% -25% -20% -15% -10% -5% qg0 +5% +10% +15% +20% +25% +30% -2 Fig. 4 illustrates the steady state characterization of outlet bulk temperature and conversion with respect to inlet gas flow. This figure highlights the fact that outlet conversion is more sensitive to variations on q g0 than outlet temperature, whilst there is a variation of less than 3%.

-5% -4% -3% -2% -1% Tfo +1% +2% +3% +4% +5% -30% -25% -20% -15% -10% -5% qlo +5% +10% +15% +20% +25% +30% In Fig. 6, the steady state characterization of bulk outlet temperature and conversion with respect to inlet bulk fluid flow is highlighted. We note that both the bulk outlet temperature and conversion are highly sensitive to q l0 . In fact, a 30% decrease in the inlet bulk fluid flow rate makes it possible to obtain total conversion with improved thermal conditions. However this result leads to a lower production rate and is therefore of less interest.

According to the observations shown in Fig. 3 to Fig. 6, the conversion is very sensitive to variations in inlet gas flow rate, inlet bulk fluid flow rate and temperature, so a disturbance in these variables greatly affects the quality of the outlet product and possibly the safety conditions. As the output variables are very sensitive to the inlet jacket temperature T j0 , we can conclude that this variable may be chosen as an effective manipulated variable in accordance with industrial practice.

Having examined the open loop considerations, we will now discuss how a control structure based on irreversible thermodynamics can be synthesized. The goal is to regulate conversion whilst avoiding thermal runaways. Therefore, methods for implementing stabilizing control are of interest and involve searching for a candidate Lyapunov function related to some of the energetic features of the reactor under consideration.

Thermodynamics aspect and availability function

In this section, we briefly summarize how a Lyapunov function for thermodynamic systems, the availability function, can be built. The availability function is issued from the second law of thermodynamics. It is positive for thermodynamic systems that are assumed to remain homogeneous. Its construction is based on two fundamental concepts of thermodynamics.

On the one hand, one has to consider the way the entropy S of a homogeneous mixture can be expressed according to the Gibbs equation [START_REF] Sandler | Chemical and Engineering Thermodynamics[END_REF]:

dS = 1 T dU + P T dV - µ i T dN i i=1 I ∑ (19)
U and V are the internal energy and the volume of the system, T, P its temperature and pressure, µ i the chemical potential and N i the number of moles of component i.

On the other hand, the second law of thermodynamics makes it possible to derive some constraints that the entropy of a homogeneous phase should satisfy. As a matter of fact, the entropy balance for an isolated system is:

dS dt = σ ≥ 0 ( 20
)
The equation [START_REF] Georgakis | On the use of extensive variables in process dynamics and control[END_REF] gives phase stability conditions of an equilibrium point for an isolated system since any trajectory that would lead to a destruction of entropy is impossible according to the second law [44][47]. Conversely, a condition that should satisfy any thermodynamic model that is used to calculate S from equation [START_REF] Dammers | Thermodynamic stability and entropy production in adiabatic stirred flow reactors[END_REF] in any conditions can be derived from equation (20) if the system under consideration is assumed to remain homogeneous. This condition is that the entropy function S = S U,V ,N i ( )

is concave [START_REF] Callen | Thermodynamics and an introduction to thermostatistics[END_REF] so that an equilibrium point is stable if the entropy function lies everywhere under the tangent plane to the entropy surface at this equilibrium point. This condition is also valid for an open system that is not at equilibrium according to the so-called local equilibrium principle. Consequently, it can be applied to the steady state of a chemical process.

The way to apply this condition consists in defining a distance between the tangent plane to the entropy surface and the entropy function. For small deviations from equilibrium or steady-state points, the so-called δ 2 S<0 function has been defined to characterize the local curvature of the entropy function and used by the Brussels School of Thermodynamic [START_REF] Kondepudi | Modern thermodynamics. From heat engines to dissipative structure[END_REF], [START_REF] Glansdorff | Thermodynamic theory of structure, stability and fluctuations[END_REF]. In the case of major disturbances, a finite distance between the tangent plane and the entropy function can be considered that reduces to -δ 2 S>0 for small disturbances. Since the entropy function S = S U,V ,N i ( ) is a first order homogeneous function, that is to say the Euler theorem applies [START_REF] De Groot | Non-equilibrium thermodynamics[END_REF][54]:

∑ = - + = I i i i N T V T P U T S 1 1 µ (21)
it can be easily verified that the following expression is valid:

( ) ( ) ( ) ( ) ( ) ∑ ∑       - -         - +       - + - - - + - + = I i i i i I i i i i i i T T N T P T P V T T U N N T V V T P U U T N V U S N V U S µ µ µ 1 1 1 , , , , (22)
where the overbar stands for the steady-state point under consideration. The quantity

( ) ( ) ( ) ( ) ∑ - - - + - + I i i i i i N N T V V T P U U T N V U S µ 1 , ,
is the equation of the tangent plane to the entropy surface at the point

( ) i N V U , , since: T N S T P V S T U S i i µ ∂ ∂ ∂ ∂ ∂ ∂ - =         =       =       1 ( 23
)
from equation [START_REF] Dammers | Thermodynamic stability and entropy production in adiabatic stirred flow reactors[END_REF]. Then the condition:

0 1 1 >       - -         - +       - = ∑ I i i i i T T N T P T P V T T U A µ µ (24)
must be satisfied for the homogeneous phase to be stable. This quantity has been defined as the availability A within the context of process control by Ydstie and co-workers [START_REF] Alonso | Process systems, passivity and the second law of thermodynamics[END_REF][START_REF] Ydstie | Process systems and passivity via the Clausius-Planck inequality[END_REF][START_REF] Alonso | Stabilization of distributed systems using irreversible thermodynamics[END_REF][START_REF] Ruszkowski | Passivity based control of transport reaction systems[END_REF] and recently applied to the non-isothermal CSTR stabilization [START_REF] Hoang | Thermodynamic approach for Lyapunov based control[END_REF] [START_REF] Hoang | Lyapunov based control for non isothermal continuous stirred tank reactor[END_REF]. In order to use the availability concept according to this approach, its time derivative dA dt has to be calculated and the way the condition A = 0 is satisfied must be analyzed. As a matter of fact, S = S U,V ,N i ( ) is not strictly concave, thus the condition A = 0 is not only verified for the steady-state point under consideration but also for all the points U k ,V k , N i,k ( )

satisfying the conditions (see equation ( 24)):

T λU ,λV ,λN i ( ) = T U ,V ,N i ( ) P λU ,λV ,λN i ( ) = P U ,V ,N i ( ) µ λU , λV ,λN i ( ) = µ i U ,V ,N i ( ) (25)
since T U,V ,N i ( ), P U,V ,N i ( ) and µ i U,V , N i ( ) are zero order homogeneous functions with respect to U,V ,N i ( ). In order for the entropy to be strictly concave and the condition A = 0 to be satisfied only at the steady-state point under consideration, a constraint has to be imposed on the system, specifically on at least one extensive variable.

Proposition for a new industrially applicable control structure

Principle

The choice of the intensified continuous mini-reactor control strategy depends on operational objectives such as safe operation, high product quality, energy savings, environmental constraints or economic gain [START_REF] Etchells | Process intensification. Safety Pros and Cons[END_REF][27][50] [START_REF] Skogestad | Planwide control : the search for the self-optimizing control structure[END_REF]. The two main objectives of the controller are a high conversion rate of the reactant and safe operation. The latter is obtained if the reactor's metal body temperature does not exceed a maximum denoted T m max . Furthermore, the controller has to reject measured disturbances -i.e.the inlet gas flow q g0, the inlet bulk fluid temperature T f0 and the inlet bulk fluid flow q l0 . As the conversion cannot be measured online, or only by means of a very expensive sensor, an indirect way of controlling the outlet conversion is to control outlet bulk temperature, which can be easily measured. Such indirect control can be obtained by controlling the temperature of the metal body at the outlet i.e. -T m J (see Fig. 1) since the metal body of the reactor is very large when compared to the bulk phases inventory mass. As a matter of fact, the reactor body tends to accumulate the energy released by the reaction. This characteristic of the intensified reactors has been shown to improve their inherent safety [START_REF] Benaissa | Dynamic behaviour of a continuous heat exchanger/reactor after flow failure[END_REF]. The variable T m J is also easily measurable in an industrial context. These specific energetic features of the mini-reactor are well-suited to designing a control law based on thermodynamic concepts such as the availability used as a Lyapunov function.

The controller that we propose is based on a two-layer hierarchical approach with an upper optimization layer and an advanced control layer, as presented in Fig. 7. The proposed control law is based on measurements which can be easily obtained in industrial conditions: the outlet bulk fluid temperature T f J and the reactor body temperature J m T at the outlet axial position as well as the disturbances (the inlet gas flow q g0, the inlet bulk fluid temperature T f0 and the inlet bulk fluid flow q l0 ). Figure 3 pointed out that the choice of the inlet jacket temperature, 0 j T , as a manipulated variable, according to industrial practice, is very relevant. This hierarchical control scheme is validated by numerical simulation. Thus, the process block is composed of the dynamic model presented in section 2 (equations (2) to ( 18)). The corresponding steady-state model is used in the optimizer block that also includes the operational limitations (the materials used for the gaskets impose a constraint on the temperature of the intensified reactor's metal body at T m max ) and the objective function (desired o-cresol conversion in the outlet bulk phase,

0 0 Bl Bl Bl C C C - = η
). The controller block includes an advanced controller based on availability as a Lyapunov function.

Inner loop entropy-based controller synthesis

During each sample period, T to apply during the inner loop control horizon. The inner loop control law proposed in this paper is based on the thermodynamic availability function. In section 3, it is shown how the availability function A can be considered as a Lyapunov function. As the mass of the bulk inventory is very low when compared to the mass of the intensified reactor's metal body, one can assume that A ≈ A m where A and A m are respectively the availability of the mini-reactor and its content and that of its metal body. The metal body of the reactor is homogeneous so its availability can therefore be calculated.

Furthermore, the mass and the volume of this metal body are constant so its entropy can be considered as strictly concave. The availability of the metal body associated to the J th CSTR with respect to J m T is:

0 1 1 >         - -         - +         - = J m J m J m J m J m J m J m J m J m J m J m J m T T N V T P T P U T T A µ µ (26)
The output feedback control is designed so that 0 J m < dt dA during the control horizon

1 + k k < < t t t . Since J m
N and J m V are constant, the time derivative of A m J is given as:

dA m J dt = 1 T m J - 1 T m J       dU m J dt (27)
The energy balance for the reactor body associated to the J Th CSTR can be given as follows:

) ( ) ( 0 J m j k j J m J f k J m T T S h T T hS dt dU - + - = (28)
From equations ( 27) and ( 28), the dynamic equation for J m A is:

dA m J dt = 1 T m J - 1 T m J       hS k T f J -hS k + h j S k ( ) T m J + h j S k T j 0 ( ) (29)
Let us choose the following non-linear control law expressed as a function of measured state variables:

( )                 - - + + - = J m J m c J m k j k J f k k j j T T K T S h hS T hS S h T 1 1 1 0 (30)
with K c strictly positive, so that

0 < dt dA J m . Then: 2 1 1         - - = J m J m c J m T T K dt dA (31)
A very similar stabilizing control law has been obtained by Hoang et al. [31][55] for the non isothermal CSTR by separating the total availability of the bulk into thermal availability and material availability and by designing a control law only based on the thermal part of the bulk availability.

Optimization layer synthesis

As we have shown in section 2, the outlet o-cresol conversion of the intensified continuous mini-reactor is sensitive to input disturbances D (inlet gas flow rate, inlet fluid temperature or flow rate). The optimization layer calculates an optimal set point,

{ }        ≤       - ∈ max .. 1 2 0 , min m J k k m j T T J Bl C Bl C D T (32)
This problem is solved by a sequential quadratic programming (SQP) algorithm.

Results and discussion

Let us analyze the closed-loop (CL) behavior of the mini-reactor when the entropy-based control proposed in sections 4.2 and 4.3 is used to reject a ramp disturbance on the inlet gas flow rate. Fig. 8 shows that the control law fully compensates for this disturbance. Fig. 9 shows the evolution of the metal temperature at the outlet axial position and the corresponding set point T m J as calculated by the optimization layer. The disturbance causes a progressive change in the set-point, so that the conversion remains as close as possible to the desired conversion despite the presence of the disturbance on 0 g q . Fig. 9 also highlights the fact that the inner loop controller ensures the metal temperature remains at the set point T m J thereby allowing the system to reject the disturbance on the inlet gas flow rate. Fig. 11 shows set point evolution T m J as calculated by the optimization layer and the metal body temperature as assumed at the outlet position of the mini-reactor. The metal body temperature follows the set point with a satisfactory evolution that guarantees an industrially applicable evolution of the manipulated variable T j 0 .

As far as a ramp disturbance on the bulk fluid flow rate is concerned, Fig. 12 shows that the proposed control law fully compensates for this disturbance. Consequently, a sudden increase in ) (t A J mk occurs, followed by a smooth decrease due to the inner control loop action. This behavior is illustrated on Fig. 14 in the event of a ramp disturbance on 0 l q (see Fig. 12 and Fig. 13). The availability function decreases during a sample period k and rises sharply to a new initial value at the beginning of the next sample period k+1. As is can be seen in Figure 15, the availability function finally converges to zero when the system reaches the steady state. Except at the instants t k , the time derivatives of J m A remain strictly negative and the availability function plays the role of a Lyapunov function.

As previously mentioned, the reactor body, due to its size, plays the role of an energy absorber that is favorable to reactor stabilization. In order to illustrate this point, we have simulated the behavior of the closed loop reactor with a smaller body mass by keeping the same controller tuning, with the case of a disturbance on q l0 used as an example. Figure 16 shows the evolution of the metal temperature at the outlet axial position, the corresponding set point T m J as calculated by the optimization layer, and the manipulated variable 0 j T . This figure highlights the fact that a decrease in the reactor's body mass greatly affects the evolution of the manipulated variable 0 j T as well as that of the state variables that exhibit oscillatory behavior. This simulation confirms the influence of the size of the reactor body on the system's behavior. In conclusion, we can notice that the disturbances considered here are satisfactorily rejected by the controller ( 0 g q , f0 T and 0 l q ) with a satisfactory evolution of the manipulated variable 0 j T . Indeed, and as mentioned in Section 2, only these disturbances greatly affect the behavior of the reactor. Both reactant A and B are pure components at the reactor inlet, so their flow rates as well as their temperature are easily measurable. Note that the proposed control law does not deal with modeling error. The reactor is sensitive to certain parameters such as the inlet gas-liquid mass transfer 0 gl glA a k mass and the heat transfer coefficient h j [START_REF] Svandová | Impact of Mass Transfer Coefficient Correlations on Prediction of Reactive Distillation Column Behaviour[END_REF].

In the presence of modeling errors or unknown disturbances, the performance of the control system will generally degrade, and the stability is guaranteed only in the case of bounded input uncertainties. Thus, the use of a state estimator to reconstruct unmeasured variables would be necessary to lead to better performance of the control system. In this work, the mass and heat transfer coefficients were obtained from experimental results. However, further investigation will be undertaken into the rejection of non-measured disturbances and robustness of the approach with respect to plant-model mismatch.

Conclusions and future works

Intensified continuous mini-reactors working in high pressure and temperature conditions and with very efficient stirring systems, such as the RAPTOR® designed by the French company AETGROUP SAS, are particularly effective at coping with mass transfer limitations during three-phase catalytic reactions. In this paper, we describe a control law based on irreversible thermodynamics. This approach has been found to be well-suited to this type of reactor due to specific energetic features related to a high (reactor body mass)/(bulk mass) ratio.

The situation under consideration is that of a jacketed continuous intensified chemical mini-reactor used to perform threephase o-cresol hydrogenation. A dynamic model of this system is proposed. The control objectives are to maintain a high steady-state outlet conversion of the reactant and to operate safely, despite the presence of measured disturbances on the inlet bulk fluid flow rate, the inlet gas flow rate or the inlet fluid flow temperature. In line with industrial practice, the manipulated variable is the inlet jacket temperature. The validity of this choice is confirmed by a steady-state sensitivity study.

The control of the process is obtained by using a two-layer approach. The upper layer of the control structure is an optimization layer, using a sequential quadratic programming algorithm that calculates the set point for the lowest layer. The lowest control layer is based on the concavity of the entropy function and the use of the thermodynamic availability as a Lyapunov function. The proposed control scheme is simple and based on measurements easily available in an industrial context. Simulated scenarios show an industrially applicable evolution of the inlet jacket temperature to reject disturbances.

Nonetheless, further investigations will be undertaken to look at the rejection of non-measured disturbances and robustness of the approach with respect to plant-model mismatch. Moreover, it would be very interesting to compare this approach based on the thermodynamics of irreversible systems with other control techniques such as Model Predictive Control. Finally, the case of the batch or fed-batch reactors that are extensively used in the fine chemicals industry will also be addressed in future works since in this case, there is no steady state. In this case, a reference trajectory to be tracked has to be determined by dynamic optimization.

NOTATION

ε

  and fluid hold-up k l ε are linked by the equation(18).

1

 1

  kg -1 . K -1 20 x 10 5 W. m -3 . K -1 Table1: Parameters used for simulation

Fig. 2 .

 2 Fig. 2. Dynamic behavior of the intensified continuous mini-reactor outlet temperatures.

Fig. 3 .

 3 Fig. 3. Steady state characterization of outlet bulk temperature and conversion with respect to the inlet jacket temperature T j0 .

Fig. 4 .

 4 Fig. 4. Steady state characterization of bulk outlet temperature and conversion with respect to inlet gas flow q g0 .

Fig. 5 .

 5 Fig. 5. Steady state characterization of bulk outlet temperature and conversion with respect to inlet fluid temperature T f0 .

Fig. 6 .

 6 Fig.6. Steady state characterization of bulk outlet temperature and conversion with respect to inlet volume flow q l0 .

Fig. 7 .

 7 Fig. 7. The two-layer hierarchical control approach.

  layer calculates a constant set point J mk T of the reactor's metal body temperature at the outlet axial position (see Fig 1). J mk T is an input for the inner loop output feedback controller. This controller calculates the input , 0 j

  guarantee a fast convergence of the o-cresol conversion rate to the desired conversion rate that is expressed as desired outlet o-cresol concentration C Bl . The optimization layer is based on the steady state version of the model described in section 2, the operational limitations (maximum temperature of the intensified reactor metal body imposed by the gaskets at T m max ), the objective function (desired outlet o-cresol concentration C Bl ) and the disturbances (inlet gas flow rate, inlet fluid temperature and inlet fluid flow rate) that are easily measurable in the industrial context. The constrained optimization problem is expressed as follows:

Fig. 8 .Fig. 9 .

 89 Fig. 8. Closed loop conversion behavior after a ramp disturbance on 0 g q .

Fig. 10 .

 10 Fig. 10. Closed loop conversion behavior after a ramp disturbance on 0 f T .

Fig. 10

 10 Fig.10shows the conversion's evolution which demonstrates the performance of the control law which fully compensates for this disturbance.

Fig. 11 .

 11 Fig. 11. Metal body temperature at the outlet position and the inlet jacket temperature after a ramp disturbance on T f0 .

Fig. 12 .Fig. 13 .

 1213 Fig.[START_REF] Alvarez-Ramirez | Stability of a class of uncertain continuous stirred chemical reactors with a nonlinear feedback[END_REF]. Closed loop conversion behavior after a ramp disturbance on q l0 . Fig.13shows that the behavior of J m T and 0 j T is also applicable. The entropy-based controller has shown to perform well in

Fig. 14 .

 14 Fig. 14. Availability function evolution at sample time.

Fig. 15 .

 15 Fig. 15. Time evolution of J m A in the event of a ramp disturbance on 0 l q .

Fig. 16 .

 16 Fig.[START_REF] Chen | Robust controller design for a class of nonlinear uncertain chemical process[END_REF]. Metal body temperature at the outlet position and inlet jacket temperature behavior after a ramp disturbance on 0 l q in the case of lower reactor mass.

Acknowledgments

This project on the intensification of fine chemicals workshops has been supported by the French research agency, the ANR (Agence Nationale de la Recherche).