L Prat

P Guiraud
email: pascal.guiraud@ensigct.fr.

L Rigal

C Gourdon

Two phase residence time distribution in a modified twin screw extruder

Keywords: Twin-screw extruder, Biomass fractionation, Polyphasic-flow, Residence time distribution

Biomass fractionation is performed with a modified Clextral twin-screw extruder used as a thermo-mechano-chemical reactor. This new process is firstly analyzed. Visual observations, residence time distributions, and global mass balances are used to obtain information about the process phenomena and their coupling. Residence time distributions (RTD) classical models are adopted to represent the experimental plots. The influence of continuous and discrete process parameters upon the RTD of the solid and liquid phases is analyzed.

Introduction

An important application domain of twin-screw extruders (TSE) is found in the agro-industry for starch conversion and protein texturization [START_REF] Harper | Food extruders and their applications[END_REF][START_REF] Colonna | Transformations structurales de l'Amidon[END_REF]. These contactors allow the simultaneous combination of two unit operations: extrusion and cooking, thus performing both physical and chemical transformations of biopolymers in a single step. TSE can also be used as an extractor, to process essential oils [START_REF] Bouzid | Extraction des huiles essentielles par des techniques non conventionnelles[END_REF], lipids [START_REF] Isobe | A new twinscrew press design for oil extraction of dehulled sunflower seeds[END_REF], or wood pulping [START_REF] Anon | Proce ´de ´et installation de traitement en continu d'une matie `re cellulosique[END_REF][START_REF] Choudens | Les pa ˆtes chimicothermome ´caniques blanchies obtenues avec le proce ´de ´bi-vis[END_REF]. It's ability to carry out extraction and chemical reaction in a single continuous reactor makes TSE very valuable for the valorization of agroresource wastes [START_REF]Technologie d'extrusion bi-vis et fractionnement de la matie `re ve ´ge ´tale, 40 ans d'extrusion bi-vis chez CLEX-TRAL[END_REF]. TSE process economic evaluation are then under investigation [START_REF] N'diaye | Fractionnement de la matie `re ve ´ge ´tale: mise au point d'un proce ´de ´thermo-me ´cano-chimique et mode ´lisation du re ´acteur bi-vis[END_REF].

In this work, the application under consideration is the extraction of hemicelluloses from hardwood populus via alkaline solubilization. As a test case, it shall help us to enhance the knowledge of such solid/liquid contactor. The twin-screw extruder is used as a thermomechano-chemical reactor for biomass fractionation. N'Diaye et al. (1996) [START_REF] N'diaye | Fractionnement de la matie `re ve ´ge ´tale: mise au point d'un proce ´de ´thermo-me ´cano-chimique et mode ´lisation du re ´acteur bi-vis[END_REF][START_REF] N'diaye | Extraction of hemicelluloses from poplar, populus tremuloides, using an extruder-type twin screw reactor: influence of the main factors[END_REF] have demonstrated the feasi-bility of the studied process for various vegetable matters. Fig. 1 shows the process operating principle. The machine consists of a seven eight-shaped elements barrel enclosing two corotating intermeshing screws. Solid (wood) and liquid (alkaline solution) are fed into the barrel by the first transport screws and are mixed together in the transport and kneading elements. As the liquid is absorbed by the wood, reaction occurs. Further down, reversed transport screw elements (RSE) cause severe compression of the vegetable matter and allow the separation of the two phases. Liquid phase is then retrieved through a barrel filter located just upstream from the RSE.

In order to promote the TSE in the domain of agroresource valorization, the main goal is to understand its working conditions and the influence of both continuous operating parameters such as the solid and liquid feed rates, the screw speed, the temperature, NaOH percentage in the liquid, and discrete operating parameters such as the screw profile. Modeling and optimization of the functioning of such a reacting contactor, will lead to use a mass transport model in combination of a reactive extraction model. It will then allow to obtain extraction yields. Such an approach has been successfully applied to other polyphasic contactors like extraction columns for instance.

Scope and presentation of the problem

However, the current problem, in a certain way, is quite different from the one relevant to other applications of extrusion. If TSE hydrodynamics for food or polymer begins to be well known [10 -12], the two phase flow constituted by vegetable matter/liquid does not allow to adopt the mechanical approach used for other systems for now.

Complexity of the phenomena in this process first lies in the complexity of the vegetable matter itself and second in the important coupling between chemical, mechanical and physical phenomena involved.

Intrinsic physico-chemical properties classically used in chemical engineering are not easily accessible or are difficult to define for the vegetable matter. Moreover, local mass balances are complex and require drastic simplified hypothesis to be solved. Physical properties of the vegetable matter, like compressibility, are subject to thorough changes. Its internal structure is affected by the progress of the reactive extraction as NaOH breaks it, and by internal moisture occurrence. Chemically spreading, the vegetable matter is also uneasy to define. In fact, only general classes of compounds (cellulose, hemicelluloses, proteins, pectins, lipids. . .) are used. Each class contains biopolymers that can be very different in terms of molar weight, polymerization degree as well as transport properties (diffusivity), solubility, etc.

Besides, thermo-mechano-chemical processes in TSE exhibit uses and possibilities advantages which become disadvantages for their modeling. If combination of thermal, mechanical and chemical effects in a same continuous reactor allows the development of a lot of different processes, it also leads to a high phenomena interdependence. The main difficulty lies in the coupling between the particle and intraparticle physicochemistry of the vegetal matter on one hand, and the mechanical and transport phenomena on the other hand. Their links are direct via operation like crushing or compression, as well as indirect via the residence time and consequently via the reaction or the adsorption process. Furthermore, an important retroaction of the screw element geometry on the behavior within the previous elements prevails. This complex interdependence is illustrated on the Fig. 2.

This complexity lead N'Diaye et al. (1996) [START_REF] N'diaye | Extraction of hemicelluloses from poplar, populus tremuloides, using an extruder-type twin screw reactor: influence of the main factors[END_REF] to use the chemometrics approach of experimental design and response surfaces study in order to optimize at first the process. The following step, as it has been developed by many authors for polymer and food [START_REF] Janssen | Twin-screw extrusion[END_REF][START_REF] Altamore | An analysis of residence time distribution pattern in a twin-screw cooking extruder[END_REF][START_REF] Boissonat | Etude parame `trique et mode ´lisation des e ´coulements de la matie `re par analyse de la distribution des temps de se ´jour dans trois cuiseurs extrudeurs bi-vis[END_REF], is to study the matter transport via the residence time distribution (RTD) method. This approach will allow to understand the different behavior of the two phases from a global point of view and to propose explanations of the behavior of the TSE as a thermo-mecano-chemical reactor. RTD will then be considered as global responses of the system, and thus account for all internal phenomena affecting the local properties such as rheological characteristics (see Fig. 2). RTD analysis is nevertheless impeded by the incomplete filling of the TSE under standard operating conditions and by the lack of precise knowledge of the TSE filling rate.

In this work, the RTD in the TSE are obtained using a colored tracer technique. The classical reaction engineering approach is adopted to compare the RTD results with various models. In addition to continuous process parameters (i.e. screw rotational speed, feed rates and NaOH concentration), the influence of discrete parameters are also studied (screw geometry). The following part of this paper presents the matter, the material, the experimental and the numerical methods used in this work. The next part is devoted to the results and their analysis.

Matter, material, experimental and numerical methods

Feedstock

Debarked chips of populus are ground to an average size of 15×2× 2 mm using an Electra type VS1 industrial grinder. The composition of the wood chips is determined using American Standard Test and Measurement methods (ASTM D-1103, D-1106, D-1787). The wood contains 52% of cellulose, 21 -24% of lignin, 16 -19% of hemicelluloses, some pectins, proteins, aromatic compounds and aliphatic acid. The moisture content of the initial chips is about 4%. Wood chips are fed in from a bin via a feeding screw and a chute (see Fig. 1 for reactor design).

The extractive solutions are injected using a volumetric pump at a single point located 180 mm from the beginning of the screw.

Twin screw extruder

Experiments are performed using a modified clextral BC45 TSE (see Fig. 1). It is a fully intermeshing corotating twin-screw extruder. Seven sections form the 1.4 m long barrel. Four sections are heated by induction belts and cooled by water circulation. Conical holes (inlet diameter: 1mm; outlet diameter: 2 mm; eight holes per cm 2 ) in a plate form the filter element added at the end of the barrel in order to extract the liquid from the output slurry. The die consists of a 25 mm long cylindrical hole, 12 mm in diameter. Five different kinds of elements are used in the axis profile: T2F (trapezoidal two-flight screw), C2F (two-flight screw), MAL2 (bi-lobe kneading element) always positioned with a y/2 shift (i.e. in a neutral position for transport compared with conveying screw elements), MAL0 (right-handed mono-lobe kneading element) and C2FC (reversed two-flight screw element). 100 mm length elements were principally used but 50 mm length elements were also available. The usual qualitative effects of these elements are reported on Table 1 [START_REF] N'diaye | Fractionnement de la matie `re ve ´ge ´tale: mise au point d'un proce ´de ´thermo-me ´cano-chimique et mode ´lisation du re ´acteur bi-vis[END_REF][START_REF] N'diaye | Extraction of hemicelluloses from poplar, populus tremuloides, using an extruder-type twin screw reactor: influence of the main factors[END_REF][START_REF] Colonna | Flow mixing and residence time distribution of maize starch within a twinscrew extruder with a longitudinally-split barrel[END_REF][START_REF] Szydlowski | Modelling flow in an intermeshing co-rotating twin-screw extruder: flow in kneading discs[END_REF][START_REF] Tayeb | A basic model for a twin-screw extruder[END_REF][START_REF] Janssen | Twin-screw extrusion[END_REF]. The pitch of the transport screw elements varies from 66 to 25 mm. All experiments are carried out with a reverse screw element with peripheral slots grooved in the screw flight for leakage flow.

Experimental processing

The processing domain is limited by several conditions [START_REF] N'diaye | Fractionnement de la matie `re ve ´ge ´tale: mise au point d'un proce ´de ´thermo-me ´cano-chimique et mode ´lisation du re ´acteur bi-vis[END_REF]. Clogging of the reactor has to be avoided, but more important is the correct functioning of the reversed screw elements. It allows in particular the matter to form a 'plug'. This plug is necessary to press the solid in order to separate the two phases, but unfortunately, it only appears under specific conditions. Furthermore, the RSE can totally stop the transport of solid matter and, as a consequence, the TSE too. Consequently, the authorized range of parameter variation is restricted around a central functioning point defined in terms of screw rotational speed N, solid feed rate Q S , liquid feed rate Q L and NaOH concentration |. Variation ranges of these parameters are reported on Table 2. All the experiments are conducted at a fixed barrel temperature of 55°C, that is the upper limit temperature to avoid hemicelluloses chemical transformation. For the study of the profile influence, only the kneading elements and RSE are replaced in half or totality by 33 mm pitch transport elements.

For all experiments, the following parameters are measured:

the liquid and solid reactor output rates needed to perform mass balances; I, the electrical intensity used by the engine. It is related to the torque applied on the screws via a linear relation and characterizes the mechanical energy transmitted to the matter; P, the pressure exerted by the matter on the screw profile in the longitudinal axis. It is measured on the decoupler; , the solid weight percentage in the exiting solid phase. It characterizes the solid/liquid separation and appears in the mass balance. All these parameters shall be qualified as responses of the system. Steady state conditions are followed by two different experimental investigations. First, the RTD of each phases in the TSE are determined using two erythrosin tracer techniques. Then, the extruder is suddenly stopped and opened in order to observe the inside matter location.

The erythrosin tracer was chosen by N'Diaye [START_REF] N'diaye | Fractionnement de la matie `re ve ´ge ´tale: mise au point d'un proce ´de ´thermo-me ´cano-chimique et mode ´lisation du re ´acteur bi-vis[END_REF] for its neutral characteristics with respect to the process and to the good colorization of most of the vegetable matter, itself often highly colored. In the case of the liquid RTD determination, the tracer is directly incorporated in the liquid flow at the entrance of the reactor, thanks to a small derivation very close to the RSE and automatic valves. In the case of the solid RTD determination, some colored wood chips are directly put on the first screw element. The colored matter injection in both cases is small enough in mass (2 g for the liquid and 5 g for the solid) and time (<2 s), compared to the flow rates and to the mean residence times, to be considered as a Dirac pulse. Because of the reactor configuration, no experimental verification can be carry out, nor intermediary samples can be taken along the reactor. 5 ml samples of liquid every 3 s and 5 g samples of solid every 10 s are taken at the liquid and solid outlets of the apparatus. All samples are stored in a 4°C room until being analyzed.

Continuous parameters DTS identification results

System responses

I (A) N (rpm) Q L (kg h -1 ) Q S (kg h -1 ) | (%) ~L (s) Pe L ~S1 (s) ~S2 (

Experimental analysis method

Colored outlets samples are analyzed by colorimetry. Liquid phase absorption is measured but not directly on the sample because hemicelluloses present in the solution absorb at the same wave length (538 nm). Samples pH is decreased to 4 when 2 volumes of alcohol are added in order to precipitate the hemicelluloses. Then, solutions are filtered and the absorption is measured.

Each solid phase sample is ground to homogenize the color and to eliminate large size particles which disturb measurements. The absorption is then directly measured on the ground samples.

RTD models identification

The RTD data are examined through typical distribution versus time plots. RTD is defined as:

E i = C i % n i = 1 C i Dt (1)
where C i is the tracer concentration in each sample and Dt is the sampling period. Typical curves are shown on Fig. 3 for the solid and liquid RTD, respectively. All the solid RTD have the same shape: a time delay of 40 -50 s and then an increase to reach a maximum within 20 -30 s, followed by a slow decrease until zero in 500 -600 s. Liquid RTD are more symmetrical around a 40 -50 s maximum. Many authors proposed models to represent transport in TSE by a combination of tubular reactors and a cascade of continuous stirred tank reactors (for the extrusion of rice starch [START_REF] Altamore | An analysis of residence time distribution pattern in a twin-screw cooking extruder[END_REF], or for wheat starch [START_REF] Boissonat | Etude parame `trique et mode ´lisation des e ´coulements de la matie `re par analyse de la distribution des temps de se ´jour dans trois cuiseurs extrudeurs bi-vis[END_REF][START_REF] Yeh | Effects of screw speed and feed rate on residence time distribution and axial mixing of wheat flour in a twin-screw extruder[END_REF]). In this work, two different models were used: model A, an axial dispersive tubular reactor model (a two parameter model: the mean residence time ~and the Peclet number Pe) and model B, where an axial dispersive tubular reactor is associated in series with a tubular reactor (a three parameter model: the mean residence time in the tubular reactor ~1, the mean residence time in the dispersive tubular reactor ~2, and the Peclet number Pe). For both dispersive tubular reactors, closed/closed boundary conditions are used. In the axial dispersive tubular reactor, Pe and ~are defined by the following equation obtained from a mass balance on the tracer:

- L 2 Pe • ( 2 C(z,t) (z 2 + L • (C(z,t) (z +~• (C(z,t) (t = 0 (2)
where C(z,t) is the tracer concentration, (Oz) the longitudinal axis, t the time and L the reactor length. Because of the different positions of the two phases outlets, the considered length of the reactor is 1.2m for the liquid and 1.4m for the solid. RTD are numerically treated in order to identify models parameters by using a Gauss-Newton based minimization method in the Laplace domain. Fast and Inverse Fast Fourier Transformation are used to translate RTD in the real time or in the Laplace's space. It has been verified that same results were obtained with minimization in the real time domain.

Both models were tested upon the solid and liquid RTD. Model A and B give the same fitting for the liquid phase, so model A will be used for this work (the parameters will then be noted ~L and Pe L ). As shown on Fig. 3, model B gives the best fitting of the experimental data for the solid RTD, and it will then be used in this study (the parameters will be noted ~S1 , the mean residence time in the tubular reactor, ~S2 , the mean residence time in the dispersive tubular reactor and the Peclet number Pe S ). It is to be noticed that these models fit experimental RTD quite well, with a few parameters, and, as a consequence, it wasn't necessary to increase the complexity of the representation with more detailed models.

All results related to the RTD chosen model parameters identification are reported on Table 3.

Influence of the continuous parameters on the RTD responses is expressed according to the interpolation Doehlert's method (1970) [START_REF] Doehlert | Uniform shell designs[END_REF][START_REF] Khuri | Response Surfaces Designs and Analyses[END_REF] in term of polynomial functions [START_REF] Mathieu | New efficient methodology for research using optimal design (NEMROD software)[END_REF], for the mean residence times, the Pe, I, P and .

The experimental data are represented in the next paragraphs by these interpolation polynomial functions. In the case under consideration, experiments are so long and difficult to perform that this experimental method was the only one able to give sufficient data to choose a functioning point and to examine the influence of the parameters.

Results and discussion

Visual obser6ation

Stopping and opening the reactor under steady-state conditions allow to observe qualitatively the location of the solid and the local filling rate of the reactor. Notice that the reactor opening induces a loss of the liquid phase and 10-20% of the solid phase. Only a qualitative analysis of the extruder process run is then possible. Most of the solid is in the RSE, in the half part of the transport element located just before the RSE and in the two kneading elements. Overall, the reactor can be separated into two parts: before the RSE, the two phases (liquid and impregnated solid) are present, whereas only impregnated solid can be found from the RSE to the die. In this second part, the under-pressured elements (i.e. the RSE and just before the die) are totally filled with solid matter. That is not the case in the first part of the reactor. As it has been mentioned previously, the TSE is not totally full of matter under usual working conditions. Such a visual observation point out that the variations of the filling rate are significant in the kneading elements, but the occupied volume is not accessible because of the compressibility of the matter.

Global approach: continuous parameters influence

All RTD shapes being identical, the results are presented in terms of mean residence times and internal mass (product of the mean residence time by the feed rate) in the first part, and in terms of Pe and axial dispersion coefficients (D) in the second part. The last paragraph concerns some considerations about links between the axial pressure, the engine intensity and the solid weight percentage in the exiting solid phase.

Mean residence times and internal mass

Observed ~L vary from 30 to 85 s (see Table 3). The ~S1 varies from 15 to 75 s. The ~S2 varies from 120 to 300 s. Total solid residence time (~S 1 + ~S2 ) is then more important than the liquid one. This fact can be explained by the presence of the solid in the two parts of the reactor, especially in the second part where the filling rate is the more important, and, as a consequence, the residence time. there is no changes in the feed rates, the internal mass varies according to the residence times.

NaOH percentage | influence.

As displayed on Fig. 7, no influence of NaOH percentage | on the liquid or solid residence times is inferred. NaOH is used for the reaction and the extraction of hemicelluloses, and the reactive fractionation (delignification) of the matter. The alkaline solution also acts as a lubricant of solid/solid contacts (vegetable matter/barrel and vegetable matter/screw). Without NaOH, solid can not pass through the RSE and the reactor is blocked. This action on the behavior of the matter is not directly linked with the RTD but with the difficulty for the solid matter to pass through the kneading elements and particularly through the RSE, and, as a consequence, the NaOH percentage has a great influence on the energetic consumption.

4.2.1.4.

Liquid feed rate Q L influence. The mean residence time for the liquid phase ~L decreases and internal liquid mass (and then the filling rate) increases with the rising of Q L , as shown in Fig. 8 and Fig. 9. Q L does not act on the solid phase behavior, but determines the NaOH mass in the system and, consequently, its lubrication effects that helps the solid matter to pass through the kneading elements, so the energetic consumption of the TSE.

4.2.1.1.

Influence of Q S . Fig. 4 and Fig. 5 show the evolution of ~and of the internal mass respectively with the solid feed state Q S . An increase in Q S value decreases the total solid mean residence time (~S 1 + ~S2 ) (Fig. 4), but also contributes to fill the reactor with the solid phase (Fig. 5), in the kneading elements especially (see Section 3.1). The relative effect of Q S is more important on ~S2 than on ~S1 , suggesting that ~S1 , and therefore the tubular reactor model, is linked with the first part of the reactor (until the RSE) whereas t S2 , and then the dispersive tubular reactor model can be principally associated with the second part. As visual observations showed, the second part of the TSE is full of solid matter. As a consequence, an increase of Q S can only act on ~and not on the filling rate in this second part. This is not the case in the first part of the TSE, where then, the effect of ~S1 is preponderant.

These links between ~S1 and the first part and between ~S2 and the second part of the reactor are a simplified way of considering the problem though. It will only help to analyze the parameters influences on the mean residence times.

In addition, no significant influence of Q S on the transport parameters of the liquid phase could be inferred from the experiments. 4.2.1.2. Speed screw N influence. Fig. 6 shows the effect of N on ~L, ~S1 and ~S2 . As it can be expected, they all decrease with N. In the conveying screw elements, this effect of N can be explained through the matter velocity. This velocity can be related to N.p in a first approximation (where p is the pitch of the screw) and consequently, as N increases, residence times of both solid and liquid phases decrease in the conveying screw elements. In the kneading elements, it is not possible to explain easily the influence of N upon the behavior of the matter and upon the residence times. Therefore, visual observations show that the quantity of matter and then the filling rate in these elements decrease with an increase of N. As

Peclet numbers

Table 3 shows the identified Peclet numbers. As seen in Fig. 3, there is a large difference between solid and liquid RTD in terms of Pe. The Pe L vary from 15 to 100 under the examined conditions. The dispersive effect for the liquid phase comes essentially from the kneading elements in the screw profile.

The Pe S vary from 1 to 4. As seen before (see Section 3.1), the axial dispersive tubular reactor model for the solid RTD can be linked with the second part of the reactor. As a consequence, the major dispersive effects that are observed are located in the RSE and concern solely the solid phase. The reactor can be considered like an association in series of a tubular reactor and a continuous stirred vessel as far as the solid phase is concerned.

Because of the relative low sensibility of the Pe parameter during model identification, especially on Pe L , even a qualitative analysis of Pe variations can not be performed.

Intensity, pressure and solid weight percentage in the exiting solid phase

The experimental intensity I varies from 10 to 60 A, P, from 15 to 60 bar and , from 35 to 60%.

In preliminary results, it is to be noticed that I, P and are related by means of quite linear relations (Fig. 10). As I characterizes the electrical energy consumed by the engine, these linear relations suggest that the mechanical energy transmitted to the matter is mostly used for the matter compression. This compression influences also transport phenomena as it increases the solid/solid (vegetable matter/barrel and vegetable matter/screw) friction and then influences the local speed of the matter in the TSE. This hypothesis seems to be confirmed by the relation between P and which characterizes the separation of the two phases, and then the pressure exerted in the RSE.

The variations of I, P and can be linked to the solid internal mass. Fig. 11 represents an I versus solid internal mass plot. The more the reactor is filled, the more the torque applied on the screws is important. This fact can be explained by the vegetable matter/barrel and vegetable matter/screw surfaces increase with the solid internal mass, and then by the increase of the friction.

Contributions of the screw elements to the global residence times

Objecti6es, assumptions and methods

For solid/liquid extraction, the contact time duration between the two phases is of great importance. The objectives of the second part of this work is to present a first approach in the determination of the contributions of the screw elements to the global residence times. All experiments were performed at the central functioning point for the continuous parameters (Section 3.3). The screw profile was modified in order to characterize the influence of the different screw ele- ments. The kneading elements and RSE are replaced in half or totality by 33 mm pitch transport elements. Table 4 shows the experimental conditions and the corresponding results of RTD models identification. These results are then valid only for the specified continuous parameters values. So they have to be considered in a qualitative point of view, allowing to give a more physical interpretation of the previous results, and to verify the links of the RTD models with the different parts of the TSE.

In this study, two drastic simplifying hypothesis are set: (i) mean residence time in standard screw element is proportional to the pitch, (ii) the elements position does not influence their behavior. It is then possible to consider the global mean residence time as the sum of each element contribution and to identify each element mean residence times by minimizing the discrepancy between model and experimental mean residence times.

No assumptions are made on the contribution, or not, of the elements upon one or another model, or part of a model. Four contributions have to be identified: ~MAL0 , the mean residence time in a MAL0 element; ~MAL2 , the mean residence time in a MAL2 element; ~RSE , the mean residence time in a RSE element; ~S33 , the mean residence time in a conveying screw with a 33 mm pitch. The contribution of the other conveying screw element is deduced from ~S33 by multiplying ~S33 by the ratio of the pitches. The results of the identification are shown in Table 5, and Fig. 12 represents the identified mean residence times versus the experimental residence times, showing the quite good fitting of the identification.

Results

As expected, for solid or liquid phase, ~MAL0 , ~MAL2 and ~RSE are much more important than ~S33 , the mean are not equal to 0, it points out the limit in the idea that each part of the models can be linked directly to a physical area in the TSE. Even though the hypothesis are very simple, the results obtained with this contributions method confirm the usual qualitative results (see Table 1) concerning with conveying, kneading or reversed screw elements effects. It allows to use general considerations to choose the screw profile for vegetable matter extrusion and to have approximated local residence time values. Besides, it is very encouraging, as shown in Fig. 12, that this contribution method leads to satisfactory results, concerning the global residence times when changing (of course not drastically) the profile of the screw.

Conclusion

Problems generated by the complexity of the vegetable matter and by the important coupling of the phenomena in a closed reactor are numerous. However, this work shows that it is possible to ameliorate the knowledge on this kind of reactor using chemical engineering usual methods.

Through visual observation and chemical engineering analysis, this work shows that the reactor consists in two parts: one where the two phases (liquid and solid) flow co-currently, and one containing impregnated residence time in the conveying screw. There is no contribution of the RSE to ~L, or to ~S1 . RSE elements do not contribute to the liquid mean residence time ~L because solid/liquid separation occurs at the very beginning of the RSE. Moreover, for the solid mean residence times, the RSE contribute only to ~S2 . As all dispersive effects are accounted by the tubular reactor with axial dispersion model, this fact confirms the important dispersive effect of this element. The matter is submitted there to opposite flows (towards the die through the slots because of the global flow and pressure, and towards the filter because of the geometry of the reversed elements).

The contributions of the two kneading elements hide different phenomena. In these elements, there is an accumulation of solid in 'matter plugs' which implies the increase of filling rate for the liquid phase upstream these elements. The model and identification method do not allow to distinguish these effects.

The quite similar values of the contributions for ~L solid only. As far as solvent extraction is concerned, the first part is the more important because it is where the extractive reaction occurs. The second part, from the RSE to the die, is necessary for the solid/liquid separation and as a consequence for the correct functioning of the reactor. RTD study allows to point out the continuous parameters influence. This influence concerns the mean residence time and the internal mass of matter (or the filling rate of the reactor if the matter is considered incompressible in a first approximation). But, because of the high difference of the mean residence time value between the first and the second part of the reactor, an accurate analysis of the parameters influences upon the first reactor part residence time is difficult. Local RTD will have to be performed in order to obtain more precise information, but in practical, it is not yet possible. However, even if no predictions can be made through such an approach, it is possible to estimate the role played by each of the screw elements and to distinguish their actions on both liquid and solid phases. This understanding will be necessary to imagine a more physical representation, allowing the prediction of the global behavior of these new type of extractor.

Appendix

Fig. 1 .

 1 Fig. 1. Global process in a modified CLEXTRAL BC45 TSE.

Fig. 2 .

 2 Fig. 2. Interdependence between phenomena in the TSE.

Fig. 3 .

 3 Fig. 3. Experimental RTD at central functioning point for liquid (o) and solid ( ×) phase. Model A RTD for liquid (--) and solid ( • • • ) phase, model B for solid phase (-).

Fig. 5 .

 5 Fig. 5. Influence of Q S on internal mass at central functioning point.

Fig. 6 .Fig. 4 .

 64 Fig. 6. Influence of N on mean residence times at central functioning point.

Fig. 7 .

 7 Fig. 7. Influence of | on mean residence times at central functioning point.

Fig. 8 .Fig. 9 .

 89 Fig. 8. Influence of Q L on mean residence times at central functioning point.

Fig. 10 .

 10 Fig. 10. and P function of I in all observed conditions.

Fig. 11 .

 11 Fig. 11. Relationship between I and the solid internal mass in all observed conditions.

Fig. 12 .

 12 Fig. 12. Modeling versus experimental residence times for ~L (), ~S1 (X) and ~S2 ().

Table 1

 1

	Elements effects
	Element		Mixing	Shearing	Transport
	Transport screw		+	+		+++
	Kneading (mono-lobe)	+	++++	+
	Kneading (bi-lobe)	++++	+++	Neutral
	RSE		+++	+++++	-
	Table 2
	Experimental domain
		Symbol Central point	Mini-	Maxi-
					mum	mum
	Speed screw	N	175		110	250
	(rpm)
	Solid feed (kg	Q S	4.8		3.2	6.7
	h -1 )
	Liquid feed (kg	Q L	36.5		21.5	51.5
	h -1 )
	NaOH massic	|	5		3	7
	% in liquid

Table 3

 3 Experimental and RTD identification results

Table 4

 4 ~S1 suggest co-current flows for the two phases in the first part of the reactor before the RSE. Since the values of the contributions of ~MAL0 and ~MAL2 to ~S2

	RTD identification results
	Discrete parameters			DTS identification results
	MAL2 length (mm)	MAL0 length (mm)	RSE length (mm)	~L (s)	Pe L	~S1 (s)	~S2 (s)	Pe S
	50	50	100	17.82	22.56	10.88	89.13	1.07
	50	50	50	29.4	15.21	25.25	56.56	2.95
	0	50	50	18.22	21.46	22.63	56.57	2.2
	100	50	50	38.51	26.38	48.59	82.1	3.48
	50	0	50	25.4	9.857	28.59	66.9	3.15
	50	100	50	37.52	26	28.67	71.02	3.66
	50	0	100	31.42	27.56	17.33	85.51	5.43


Christine Sinoquet
email: christine.sinoquet@univ-nantes.fr

R C N R S 6241

Improvement of missing genotype imputation through bi-directional parsing of large SNP panels

Improvement of missing genotype imputation through bi-directional parsing of large SNP panels

Christine Sinoquet

Introduction

DNA strings consisting of billion of chemical bases A, T, C and G constitute the hereditary material stored in the pairs of chromosomes of eukaryotes. These genetic sequences contain information that influences physical traits, the likelihood of suffering from disease as well as response to pathogens, chemicals and other agents. Differences in individual bases are the most common type of genetic variation. These genetic differences, called single nucleotide polymorphisms (SNPs), are detected on chips analyzed through high-throughput genotyping techniques. In the domain of genetical epidemiology, associations studies attempt to link genetic variants to the risk for specific illnesses, with the objective of proposing new methods of preventing, diagnosing, and treating diseases. Case-control association studies are considered to be the simplest framework to help elucidate the genetic basis of complex diseases. Such studies deal with populations of unrelated individuals split into cohorts diagnosed with the disease of interest and cohorts of unaffected controls. The issue at stake is identifying genetic determinants -possibly combinations of determinants -, which should accumulate among cases. Amongst various difficulties likely to introduce a bias in the studies, not a least problem to cope with is the presence of undetermined SNPs, or "missing calls", in the data generated by genotyping techniques (approximately between 5% and 10%).

There are three alternatives to repeating the genotyping for the missing data, a prohibitive task both in terms of time and cost: (i) merely dismissing entire rows and columns of the SNP panel containing the missing calls is quite a drastic solution, with a strong impact on the power to detect disease-predisposing variants; (ii) inferring missing data prior to the task of interest (i.e., disease association study, genetic mapping • • • ), (iii) handling missing data while the task of interest is performed. Indeed, this third category amounts to off-line or on-line inference. A peculiar case may lead to some confusion in minds: standard genotyping techniques can not distinguish the two homologous chromosomes of an individual, therefore only the "unphased" genotype (i.e., the combination of the two homologous haplotypes) is directly observable. Thus, when the task of interest, genotype phasing, applies to data containing missing calls, two missing-data problems interfer. From now on, we will refer to genotypes as unphased genotypes.

Various computational methods have been proposed to infer -or impute -missing genotypes. Assignment of the most frequent allele identified to the missing call concerned and k-nearest neighbor voting methods (KNN) are the most simple. A review of eight methods has been more specifically dedicated to such previous methods, as well as various regression methods [START_REF] Yu | Methods to impute missing genotypes for population data[END_REF]. Other methods implement expectation maximization [START_REF] Z S Qin | Partition ligation expectation maximization algorithm for haplotype inference with single nucleotide polymorphisms[END_REF], Bayesian approaches [START_REF] Niu | Bayesian haplotype inference for multiple linked single-nucleotide polymorphisms[END_REF], Decision Forest pattern recognition [START_REF] Xie | Decision forest analysis of 61 single nucleotide polymorphisms in a case-control study of esophageal cancer; a novel method[END_REF], neural networks [START_REF] Yu | Methods to impute missing genotypes for population data[END_REF][START_REF] Sun | Imputing missing genotypic data of single-nucleotide polymorphisms using neural networks[END_REF], as well as Gibbs sampling combined with tree-based approach [1].

Other methods explicitly cope with the haplotype block structure of eukaryotic genomes. Empirical studies have confirmed that over short regions (a few kilobases in human genome), haplotypes tend to cluster into groups [START_REF] Patil | Blocks of limited haplotype diversity revealed by high-resolution scanning of human chromosome 21[END_REF]14], which entails interesting constraints for the corresponding genotypes. To inpute missing calls, this feature is exploited in various ways: entropy measure combined with dynamic programming to partition haplotypes into blocks [START_REF] Su | Inference of missing snps and information quantity measurements for haplotype blocks[END_REF], cluster membership allowed to change continuously along the chromosome according to a hidden Markov model [START_REF] Scheet | A fast and flexible statistical model for large-scale population genotype data: applications to inferring missing genotypes and haplotypic phase[END_REF]. In this line, Roberts and co-authors designed a new algorithm, NPUTE, which performs KNN imputation in the context of sliding windows modelling haplotype blocks [START_REF] Roberts | Inferring missing genotypes in large snp panels using fast nearest-neighbor searches over sliding windows[END_REF]. Their algorithm deals with SNP panels where the number of markers is much higher than the number of individuals (up to 10 4 in the case of some chromosomes). The very point central to NPUTE is efficient knowledge management from current window to next one.

Finally, among specific softwares yet also able to handle missing data, we mention for illustration methods dedicated to genotype phasing [2,[START_REF] Scheet | A fast and flexible statistical model for large-scale population genotype data: applications to inferring missing genotypes and haplotypic phase[END_REF] and detection of causal variants that have not been directly genotyped, in the framework of association studies [START_REF] Marchini | A new multipoint method for genome-wide association studies by imputation of genotypes[END_REF][START_REF] Servin | Imputation-based analysis of association studies: candidate regions and quantitative traits[END_REF].

Thoroughly examining NPUTE, we identified in dependencies between sliding windows a promising lead to infer missing calls with more confidence, therefore expecting a gain of accuracy.

Methods

Foreword

Beside gaining accuracy due to bi-directional parsing, we are also resolute to design a method which would not depend on memory availability constraints.To meet this second purpose, we implemented successive loadings of consecutive "small" SNP blocks during each parsing of the SNP panel. Thus, contrary to NPUTE, memory needs only be allocated for a SNP block rather than for the whole SNP panel. Therefore, we wish to design a variant of algorithm NPUTE, KNNWinOpti, together with a novel algorithm SNPShuttle. In the following, we will first briefly describe the original method of Roberts and co-authors. In this occasion, we will highlight the existence of calculation dependencies between blocks of the SNP panel. Moreover, these SNP block dependencies are either backward or forward dependencies, which makes the design of software also managing SNP block loading a delicate task. Then we will present KNNWinOpti. Finally, the scheme of SNPShuttle will be depicted.

The common basic concepts of NPUTE, KNNWInOpti and SNPShuttle

The input parameters for NPUTE algorithm are the SNP panel, loaded as the matrix snp[0 .. M -1][0 .. N -1] of M rows (markers) and N columns (individuals) and L, the "half-size" of any sliding window. The elements of the SNP matrix belong to {0, 1, 2}, where 0 denotes the allele with major frequency for each genetic marker, 1 is that of the least frequent allele and 2 is the label for "missing data". The key idea of NPUTE is performing fast imputation over overlapping sliding windows. In the sequel, we will respectively denote sub-matrices and rows as

snp[m .. m ′ ][n .. n ′ ] and snp[m .. m ′ ][n]. snp * [m -L .. m + L][n ..
∆(snp * [m -L .. m + L][n n ], snp * [m -L .. m + L][n]) = Σ i=m+L i=m-L,i =m ∆ m (snp[i][n], snp[i][n ′ ]
). The distance between markers, ∆ m , is merely computed as follows:

∆_m(i, j) =    0 if i = j 2 if (i, j) = (0, 1) or(i, j) = (1, 0) 1 if i = 2 or j = 2
It must be highlighted that in this algorithm, the missing calls ("2") of the context participate in the distance computation. We now denote W m the vector of the n (n -1)/2 pairwise mismatch distances between individual projections onto current window W m . Given W m , the Pairwise Mismatch Vector (PMV) related to W m , inference for any missing snp[m][n] is straightforward: considering only the N -

1 relevant entries (n, n ′ ) (n < n ′ ) and (n ′ , n) (n ′ < n) in W m , the smallest distance with individual n is identified, say, for individual n n . Provided that snp[m][n n ] is not missing itself, it is assigned to snp[m][n].
From now on, we will name P M V (m) the Pairwise Mismatch Vector with n(n -1)/2 entries such that

P M V (m)[(n, n ′ )] = ∆ m (snp[m][n], snp[m][n ′ ]), (n < n ′ ).
For tractability over large SNP panels, NPUTE fully exploits window sliding. The parsing of the SNP panel is implemented shifting the current window one range further at each step. Thus, the PMV relative to a window centered on range m is merely the PMV relative to the previous overlapping window centered on range m -1, from which the contribution of range m -L -1 must be substracted and that of range m + L must be added (see Figure 2). In addition, note that there are 2 × L + 1 non symmetric windows to be specially processed, among which 2 × L are not symmetric.

However, in the simple case of a symmetric window, W m is not merely computed as W m-1 -P M V (m -L -1) + P M V (m + L). Row m itself does not contribute to the calculation of W m , which is indeed computed as follows

W m = W m-1 + P M V (m -1) -P M V (m) -P M V (m -L -1) + P M V (m + L).(1)
Figure 1: Sliding windows. M = 14; L = 2. Depending on the row m of the SNP inferred, the sliding window is either centered on m or is non symmetric. Now all basic concepts common to NPUTE, KNNWinOpti and SNPShuttle are settled. However, even the original algorithm, NPUTE, is not so simple since special care must be taken regarding non symmetric windows. In the sequel, we will proceed gradually in the presentation of the sketch of the original algorithm, the adaptations implemented to meet the memory sparing purpose and the innovative bi-directional variant.

Sketch of the original method

The sketch for SNP panel processing is reminded in Algorithm 1. The algorithm processes apart the non symmetric window 0 (lines 1 to 3 ), then runs three loops. First loop (line 5) processes non symmetric windows 1 through L -1 and first symmetric window L. Third loop (line 18) processes only non symmetric windows M -L through M -1. General formula (1) (line 14) is adapted to the case of the L windows successively encompassing an increasing number of rows (line 7), whereas it is symmetrically tuned to the case of the L last windows (line 20).

Algorithm 1 N P U T E(M, N, SN P, L)

Input: M, the number of genetic markers; N, the number of individuals; a matrix SNP[0 .. M -1][0 .. N -1] of known markers (belonging to {0, 1}) and missing markers (2), each column corresponding to a given individual; L, half-size of a sliding window. Output: matrix SNP, where each previously missing value 2 is now replaced with either 0 or 1.

1: W

← sum_of _P MV s_f rom_to(1, L) 2: inf erence_of _missing_markers_f or_range(0) 3: previous_P MV ← compute_P MV (0) 4: 5: for m = 1 to L // LOOP I 6: (1) current_P MV ← compute_P MV (m) 7: W ← W + previous_P MV -current_P MV + compute_P MV (m + L) 8: (2) previous_P MV ← current_P MV 9: inf erence_of _missing_markers(W )

Management of backward and forward dependencies for the purpose of memory sparing

Before adapting SNP block loading to the previous algorithm, a remark is imperative. In line 14 of Algorithm 1, due to backward dependencies (compute_P M V (m -L -1)) and forward dependencies (compute_P M V (m + L)), the computation of W s is not optimized. Indeed, P M V (m + L) will be computed again as a contribution to W m+L (line 13 referring to line 6). Similarly, P M V (m -L -1) (line 14) has already been computed since it had to be dismissed from W m-L-1 as "current_P M V ". These remarks point out that the memorization should not restrain to the single last PMV vector calculated (lines 8, 15 and 21 in algorithm ), but should extend to the latest L PMVs computed instead. Moreover, similarly, forward dependencies will be accounted for through the memorization of the L PMVs relative to the highest row numbers calculated.

It now remains to combine such dependency management with the loading of successive SNP blocks of R rows (R is an input parameter). The sketch of this novel version, KNNWinOpti, is described in Algorithm 2. Since the combination of the two modifications (dependency management, SNP block loading) brings complexity in the description of the novel version, we will carefully comment it in the following.

In the original version, two PMVs are computed for row m, P M V (m + L) and P M V (m -L -1) (Algo. 1, line 14). Instead, in novel Algo. 2, P M V (m + L) is computed (line 12) and stored in the FIFO P M V _f orward (line 13) for further reuse (line 25 referring to line 11). Besides, when it is time to infer missing data in a given row, not only is the PMV relative to this row available as head of FIFO P M V _f orward (line 25 referring to line 11), its update after inference is added to FIFO P M V _backward (line 27 pointing to line 16) so that it may be reused as P M V (m ′ -L -1), the head of the previous FIFO at the time of inference for row m ′ (m ′ = m + L + 1), at line 26. Figure 3 A shows on a simple example how the two FIFO lists are synchronized. Finally, the SNP block loading manager (lines 23 and 32) ensures that row i + L was also loaded for last row i in each newly loaded block of LOOP II. The preliminary loading of a block of 2 × L + 1 rows, required by inference of row 0 and LOOP I, is crucial to the whole synchronization of the SNP block loading manager with the inferring process under way. Note that LOOP III does not refer to forward dependencies. Figure 3 B illustrates the synchronization between inference and block loading.

Depending on the number of rows involved in LOOP II, the last iteration in this loop may require the loading of less than R rows, which explains a special (trivial) treatment (lines 20 and 31 to 34).

Iterative bi-directional inference

In their method, Roberts and co-authors use a specific data structure, a mismatch accumulator array MMA, which is computed before performing inference. To be short, it plays the same role in W computation as the PMV vectors aforementioned. However, since the MMA is calculated off-line, the inference for row m will not benefit from the inference for rows of lower ranks. That is, in all cases where distance ∆ m (i, j) is approximated as 1 if i or j is equal to 2, an update would possibly lead to a refined distance 0 or 1. We took this remark into account when designing Algorithm 2, which is therefore not a simple transcription of Roberts and co-workers' method merely augmented with block loading and FIFO list management. Indeed, we are careful that any newly inferred row is added to the P M V _backward list (line 15), so that the inference might be more accurate.

Moreover, this update concern allows further optimization. It was of no consequence for Roberts et al. to scan the SNP panel from top to bottom (TB) or from bottom to top (BT) since context W m did not account of the results of previous inference for rows m -L to m -1. Nonetheless, it is attractive to confront the result of a TB scan with that of a BT scan, in order to resolve the missing SNPs with more confidence, which is implemented in our second version, SNPShuttle. Thus, any SNP inferred as the same allele identifier by successive TB and BT scans can be fixed. Any uncertain SNP will remain tagged as "missing" until a further iteration yields identical TB and BT results. The entire process is to be iterated until a minimal percentage of missing data remains uncertain or until a maximal number of iterations is reached. The SNP panel is successively cleared from its missing calls, starting with the markers easiest to guess and enriching the context of SNPs more difficult to infer. Algorithm 3 presents the scheme of SNPShuttle. At line 4, the call to top_to_bottom_scan procedure is actually a call to KNNWinOpti. Similarly, call bottom_to_top_scan is applied on the current SNP panel inverted row per row.

Conclusion

Roberts and co-authors precursory work provided a promising basis to gain accuracy with a simple algorithm. In this paper, we proposed a novel algorithm, based on iterative bi-directional parsing of SNP panels. We are currently implementing the two algorithms, KNNWinOpti and SNPShuttle. Also do we have to adapt KNNWinOpti (the core of SNPShuttle) to obtain pre-processing software dedicated to the identification of the optimized window "halfsize" L (the corresponding accuracy is computed for all non missing markers, temporarily considered as missing calls and inferred). As chip resolution increase will also rise the number of SNPs available for each chromosome, it is crucial to implement SNP block loading, as we plan to do, if the software is intended to run on on standard computer. Finally, one of our future tasks is more thoroughly examining the idea of benefitting from previously inferred missing calls, locally relying on regions of high quality.

  n ′ ] will refer to a matrix deprived of row m. Specifically, snp * [m -L .. m + L][0 .. N -1] will be named W m , for conciseness. The idea central to NPUTE is to infer the missing marker m of some individual n, snp[m][n], "copying" it from the marker m of the nearest neighbour of individual n, say individual n n , in the context W m . Such contexts roughly model the concept of haplotype block. Namely, n n is identified as the individual minimizing a distance criterion, denoted ∆, over W m . Computing the distance ∆(snp * [m -L .. m + L][n], snp * [m -L .. m + L][n ′ ]) involves comparing the projection of individuals n and n ′ onto current window W m :

12 : 1 // LOOP II 13 :

 12113 for m = L + 1 to M -Lprocess as in (1) 14: W ← +W + previous_P MV -current_P MV + compute_PMV(m + L) -compute_PMV(m -L -1) 15: process as in (2) 16: endfor 17: 18: for m = M -L to M -1 // LOOP III 19: process as in (1) 20: W ← +W + previous_P MV -current_P MV -compute_P MV (m -L -1) 21: process as in (2) 22: endfor

Figure 2 :

 2 Figure 2: A Synchronization of forward and backward FIFO lists; B Synchronization of SNP block loading manager and missing data inference; M = 14; L = 2; R = 4.

Algorithm 3

 3 SN P Shuttle(M, N, SN P, L, R, τ ) Input and Output: in addition to those of algorithm , input parameter τ specifies the minimal percentage of missing data allowed to remain uncertain 1: modif ied ← true; percentage_of _non_solved_SN P s ← 100 2: while(modif ied and (percentage_of _non_solved_SN P s > τ )) 3: modif ied ← f alse 4: T B_inf erred_SN P s ← top_to_bottom_scan(SN P ) 5: BT _inf erred_SN P s ← bottom_to_top_scan(SN P ) 6: solved_SN P s ← compare(T B_inf erred_SN P s, BT _inf erred_SN P s) 7: if (solved_SN P s is not empty) 8: updateW ith(SN P, solved_SN P s) 9: update(percentage_of _non_solved_SN P s) 10: modif ied ← true 11: endif 12: endwhile

Improvement of missing genotype imputation through bi-directional parsing of large SNP panels

Christine Sinoquet Abstract

Such difficult analyses as disease association studies, which aim at mappping genetic variants underlying complex human diseases, rely on high-throughput genotyping techniques. However, a shortcoming of these techniques is the generation of missing calls. Computational inference of missing data represents a challenging alternative to genotyping again the missing regions. In this paper, we present SNPShuttle, an algorithm designed to gain accuracy over a former method described by Roberts and co-authors [START_REF] Roberts | Inferring missing genotypes in large snp panels using fast nearest-neighbor searches over sliding windows[END_REF] (NPUTE). Given an SNP panel, NPUTE algorithm infers missing data through a single parse, relying on local similarity within sliding windows. Instead, SNPShuttle scans an SNP panel in an iterative bi-directional way, to resolve missing data with more confidence.

LINA, Université de Nantes 2, rue de la Houssinière B.P. 92208 -F-44322 NANTES CEDEX 3


Corentin Author
email: corentin.stalder@utt.fr

Stalder

Digital Twin, support for collaborative practice: application to the railway system

The digital twin is one of the promising technological concepts of the Industry 4.0. However, few research deals with the cooperative use of the digital twin. Through this PhD project, I aim to study how the digital twin of the French railway infrastructure can improve the coordination between the stakeholders of its maintenance . In order to study this, I am conducting a multisited ethnography to identify the coordination mechanisms that are involved in the work scheduling activity. I am planning to study more in depth how the digital twin can support cooperative practices by using technological probes.

This PhD takes place as part of a collaboration between SNCF Réseau and Troyes University of Technology. SNCF Réseau is the French railway infrastructure manager; it manages the maintenance, exploitation, and development of 30 000 km of railway infrastructure. As other infrastructure managers, SNCF Réseau has started to develop a national asset management strategy. This strategy seeks to coordinate the maintenance, exploitation and development of the railway infrastructure at a national scale to meet performance requirements. To do so, one of the pillars of this strategy is the digitalization of work practices.

In this context, SNCF Réseau is developing a technological concept: the railway digital twin. In the literature, the digital twin concept can be summed up as a digital replica of a physical system that is connected to it [START_REF] Grieves | Digital Twin Manufacturing Excellence through Virtual Factory Replication[END_REF]. It could also be seen as a real-time reflection of the physical asset, that interacts with the physical asset [START_REF] Tao | Digital twindriven product design, manufacturing and service with big data[END_REF].

Despite the fact that the digital twin concept has been built in order to offer a realtime, integrated and collaborative representation of the infrastructure [START_REF] Tao | Digital twindriven product design, manufacturing and service with big data[END_REF][START_REF] Tao | Digital Twin in Industry: Stateof-the-Art[END_REF], few researches address the use of digital twin whether as a means of communication, coordination, or cooperation [START_REF] Lamb | Principle-based digital twins: A scoping review[END_REF][START_REF] Tao | Digital Twin in Industry: Stateof-the-Art[END_REF] We envision the digital twin as a new technological opportunity to support coordination practices among railway infrastructure stakeholders. More precisely, we think that the digital twin can help us revisit some issues of the technological support for awareness.

Indeed, awareness has been intensively studied by CSCW scholars [START_REF] Bentley | Ethnographically-informed systems design for air traffic control[END_REF][START_REF] Heath | Collaborative Activity and Technological Design: Task Coordination in London Underground Control Rooms[END_REF] and has been characterized by a set of practice that workers have developed in order to coordinate their actions with the actions of others in a seamless way [START_REF] Schmidt | The Problem with `Awareness': Introductory Remarks on `Awareness in CSCW[END_REF]. [START_REF] Tenenberg | From I-Awareness to We-Awareness in CSCW[END_REF] proposed to revisit the concept of awareness by no longer emphasizing on how an individual perceives the activity of another but rather emphasizing on how an individual in a group perceives something, what they have called "we-awareness". This work puts forward the shared intentionality and the recursive social inference under awareness practice. Nonetheless, Tenenberg et al. did not answer the question of the technical support of we-awareness. [START_REF] Greenberg | Implications of We-Awareness to the Design of Distributed Groupware Tools[END_REF].

Research questions

In this research context, the PhD is looking at the following questions:

• How can the digital twin support a daily maintenance management practice locally while ensuring a cooperation between SNCF Réseau work entities? • Which representation of the digital twin can be appropriated by the different actors of the maintenance management? • How flexible the digital twin should be to be embedded into a local practice and at the same time ensuring cooperation with other units? • And to which extent the flexibility of the digital twin could support a standardized process?

To study those questions, a preliminary field study has been conducted. Its goal was to identify a work situation in which coordination takes place among SNCF entities. This preliminary study has allowed to identify the work scheduling activity as an interesting field to focus on regarding the research questions.

The case study: The work scheduling activity

Most of works on the railway infrastructure imply traffic interruptions. In order to minimize the impact on train traffic, these interruptions generally take place during the night, for a few hours (approximately 4 to 6 hours). The challenge when scheduling works on the infrastructure resides in maximizing the traffic while ensuring that all the works can be done and also ensuring the safety of people on the work site. For that, no train can cross the work site : elementary protection zones (ZEP in French) are put in place; ZEP are track sections that either divert trains, or turn the signals to red.

The work schedule is co-designed by three SCNF Réseau establishments:

• The infrapole, which is responsible of the maintenance of a railway sector.

• The infralog which is responsible of the renewal or development work.

• The traffic establishment, which is responsible of the traffic management on a sector.

The PhD focuses on the pre-operational work scheduling phase which starts with a coordination meeting six weeks before the works on the infrastructure take place. During this meeting, the requesters (the ones who are requesting some work to be done) (from infrapoles or infralogs) are gathered by a coordinator from a traffic establishment. During the meeting, scheduling "clashes" (e.g. two works planned at the same place at the same moment) are discussed. At the end of the meeting, a first schedule is ready. Then, this scheduling is instantiated on the train timetable in order to produce a daily work notice that is sent to the switchman of the traffic establishment the day before the works should take place. But between the coordination meeting and the daily work notice issue, the schedule may encounter some changes.

Data collection

To study the diversity of practice, we were engaged in a multi-sited ethnography [START_REF] Marcus | Ethnography in/of the World System: The Emergence of Multi-Sited Ethnography[END_REF] involving two sectors around Paris. We have combined semidirective interviews and observations on both sectors. In the sector 1, we interviewed one requester (in infrapole) and the two managers in charge of the coordination center (in a traffic establishment) and we have observed one coordination meeting. In the second sector, we observed three coordination meetings and interviewed three requesters (in infrapole). These coordination meetings took place during the COVID-19 pandemic, and therefore were conducted online. Interviews and observations were conduct by the PhD student, and discussed with supervisors. The aim of the interviews and observations was to collect the experience of work scheduling stakeholders.

First Findings

In order to describe the coordination practices that underline the work scheduling activity, we have analyzed our data through the coordinative mechanisms concept [START_REF] Schmidt | Coordination mechanisms: Towards a conceptual foundation of CSCW systems design[END_REF]. We have therefore identified the coordinative protocol, and the coordination artifacts which we have described in a manuscript submitted to the CSCW Journal.

Our analysis highlights strong differences between the two sectors. First, stakeholders of the work scheduling activity are different. Then, the schedules between them are different (e.g. in one sector, the coordination meeting deals with works that take place in six weeks, and in the other one, the coordination meeting deals with works that take place in six, three, and the following week). Finally, the artifacts used are either different or are used in a different way.

Despite those differences, we have identified three coordination mechanism that are common to the two sectors:

• The common understanding of the sector (e.g. ZEP name, tracks name …) • The construction of a common understanding of the work scheduling (what is done, when, where and by who). • The articulation around scheduling clash that is composed of an identification of clash by the coordinator, followed by a negotiation between requesters and coordinator, that can lead to arbitrage if no arrangement is found.

The digital twin to support cooperation during the work scheduling activity

To study more deeply how the digital twin can support cooperation through an representation of the infrastructure, we are willing to use technology probes [START_REF] Hutchinson | Technology Probes: Inspiring Design for and with Families[END_REF]. Through probes, we seek to learn more about how coordination takes place in the work scheduling activity, and to test different digital twin designs and features, and finally to ground the reflection on the digital twin design and how it could better support the work scheduling process.

Currently, we have designed two probes; the first one aims to plot work sites on a geographical information system and to highlight scheduling clash. The second one aims to provide an awareness of existing requests.

Expected contribution

This PhD seeks to contribute to three research communities. First, we would like to envision how the digital twin technological concept can be a new way to support cooperative practices.

Secondly, in order to address cooperative use, the digital twin concept must be designed in that way. Thus, this research aims to bring attention to cooperative use and practice-centered design to the digital twin community.

Finally, this research takes place at SCNF Réseau. Therefore, we seek to bring to SCNF Réseau a collaborative digital twin basis for the work scheduling activity and methodologies to extend this basis to other activities.


Masafumi Saitoh

Nicolas Olivier

Marion Garçon

Maud Boyet

Christophe Thomazo

Julien Alleon

Jean-François Moyen

Vincent Motto-Ros

Johanna Marin-Carbonne

wavy laminas overprinting putative microbial deposits from the 3.22 Ga Moodies Group (Barberton Greenstone Belt)"

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Reply to comment on "Metamorphic origin of anastomosing and wavy laminas overprinting putative microbial deposits from the 3.22 Ga Moodies Group (Barberton Greenstone Belt)" Masafumi Saitoh 1,* , Nicolas Olivier 2 , Marion Garçon 2 , Maud Boyet 2 , Christophe Thomazo 3,4 , Julien Alleon 5 , Jean-François Moyen 6 , Vincent Motto-Ros 7 , and Johanna Marin-Carbonne 5 Anastomosing and wavy laminae are frequently observed in the ~3.22 Ga Moodies Group in the Barberton Greenstone Belt (BGB) (e.g., [START_REF] Heubeck | An early ecosystem of Archean tidal microbial mats (Moodies Group, South Africa, ca. 3.2 Ga)[END_REF][START_REF] Homann | Morphological adaptations of 3.22 Ga-old tufted microbial mats to Archean coastal habitats (Moodies Group, Barberton Greenstone Belt, South Africa)[END_REF]. These laminae in sandstones accumulated in marine-terrestrial transitional environments have been extensively interpreted to be remnants of original microbial mats based, for instance, on lamina morphology and isotopic signals using outcrop samples from various localities in the BGB (e.g., [START_REF] Noffke | A new window into Early Archean life: Microbial mats in Earth's oldest siliciclastic tidal deposits (3.2 Ga Moodies Group, South Africa)[END_REF][START_REF] Heubeck | An early ecosystem of Archean tidal microbial mats (Moodies Group, South Africa, ca. 3.2 Ga)[END_REF][START_REF] Homann | Morphological adaptations of 3.22 Ga-old tufted microbial mats to Archean coastal habitats (Moodies Group, Barberton Greenstone Belt, South Africa)[END_REF][START_REF] Homann | Microbial life and biogeochemical cycling on land 3,220 million years ago[END_REF][START_REF] Thomazo | Carbon and nitrogen isotope biosignatures of the archean continental biosphere: A comparison with modern analogs[END_REF]. However, the influence of post-depositional processes on the lamina formation and preservation has received limited attention in previous studies. In order to bring further insights on the post-depositional history of the analyzed Moodies sandstones in light of the suggested biogenic origin of laminae, [START_REF] Saitoh | Metamorphic origin of anastomosing and wavy laminas overprinting putative microbial deposits from the 3.22 Ga Moodies Group (Barberton Greenstone Belt)[END_REF] conducted detailed petrological observation and multiple geochemical analyses on samples collected from the Saddleback Syncline in the central BGB. Based on those results, [START_REF] Saitoh | Metamorphic origin of anastomosing and wavy laminas overprinting putative microbial deposits from the 3.22 Ga Moodies Group (Barberton Greenstone Belt)[END_REF] illustrated important post-depositional processes and their substantial role in the lamina formation and modification. [START_REF] Saitoh | Metamorphic origin of anastomosing and wavy laminas overprinting putative microbial deposits from the 3.22 Ga Moodies Group (Barberton Greenstone Belt)[END_REF] emphasized that their observations did not exclude the possibility that some of the analyzed Moodies laminae were originally microbial mats. Furthermore, conclusions of this work were based solely on the analyzed sandstones collected from one outcrop from the Saddleback Syncline. Nonetheless, [START_REF] Homann | A comment on "Metamorphic origin of anastomosing and wavy laminas overprinting putative microbial deposits from the 3.22 Ga Moodies Group (Barberton Greenstone Belt)[END_REF] contested the significance of these outcomes in providing further insights into the origin of Moodies anastomosing and wavy laminae.

The origins of the Moodies laminae and of carbonaceous material (CM) within these laminae should be separated clearly to discuss their biogenicity. The comments by [START_REF] Homann | A comment on "Metamorphic origin of anastomosing and wavy laminas overprinting putative microbial deposits from the 3.22 Ga Moodies Group (Barberton Greenstone Belt)[END_REF] were based, at least in part, on misunderstanding on this point. For example, Homann and Heubeck (2021) used the term "carbonaceous laminae/laminations" repeatedly on their comments to impress their biogenicity on a reader. It is obvious that some of the Moodies laminae at other localities analyzed in previous studies are "carbonaceous" (e.g., [START_REF] Homann | Microbial life and biogeochemical cycling on land 3,220 million years ago[END_REF]. However, almost all the laminae in the Saddleback sandstones analyzed in [START_REF] Saitoh | Metamorphic origin of anastomosing and wavy laminas overprinting putative microbial deposits from the 3.22 Ga Moodies Group (Barberton Greenstone Belt)[END_REF] are not suitable to be described as "carbonaceous", because CM is only rarely observed within the laminae as clearly shown by the Raman analyses. The scarcity of CM is underpinned by both the low total organic carbon (TOC) contents measured in three samples (< 108 ppm; mean TOC = 90 +/-31 (2SD, n=3) ppm) and the low loss of ignition (LOI) measured in twenty-nine samples from all subunits (LOI < 2.5 wt.%; mean LOI = 1.1 +/-1.0 (2SD, n =29) wt.%) [START_REF] Saitoh | Metamorphic origin of anastomosing and wavy laminas overprinting putative microbial deposits from the 3.22 Ga Moodies Group (Barberton Greenstone Belt)[END_REF]. As a matter of comparison, the TOC contents of banded cherts are up to 2.2 wt.% in the older Hooggenoeg Formation and ~0.2 wt.% in the Buck Reef Chert (e.g., [START_REF] Hofmann | Carbonaceous Cherts in the Barberton Greenstone Belt and Their Significance for the Study of Early Life in the Archean Record[END_REF][START_REF] Hofmann | Cherts of the Barberton Greenstone Belt, South Africa: Petrology and trace-element geochemistry of 3.5 to 3.3 Ga old silicified volcaniclastic sediments[END_REF]. In addition to the CM scarcity observed in the Moodies sandstones [START_REF] Saitoh | Metamorphic origin of anastomosing and wavy laminas overprinting putative microbial deposits from the 3.22 Ga Moodies Group (Barberton Greenstone Belt)[END_REF], multiple lines of evidence demonstrate that substantial secondary overprints, such as sericite and Ti-oxide occurrences, are commonly observed in the laminae through the analyzed succession. Based on these observations, [START_REF] Saitoh | Metamorphic origin of anastomosing and wavy laminas overprinting putative microbial deposits from the 3.22 Ga Moodies Group (Barberton Greenstone Belt)[END_REF] concluded that the observed laminae, at the hand-specimen scale, in the analyzed rocks were features of the secondary overprints of later metamorphic processes (i.e., abiotically; also see [START_REF] Bower | Micro-Raman spectroscopic investigations of mineral assemblages in parallel to bedding laminae in 2.9 Ga sandstones of the Pongola Supergroup, South Africa[END_REF].

It is worth noting that the results in [START_REF] Saitoh | Metamorphic origin of anastomosing and wavy laminas overprinting putative microbial deposits from the 3.22 Ga Moodies Group (Barberton Greenstone Belt)[END_REF] do not exclude -but do not support either -the possibility that precursors of some of the analyzed laminae were microbial mats. Indeed, the analyzed sericite-rich laminae contain finer clastic grains compared to the underlying and overlying coarser sediments; such textures suggest that they are an original sedimentary bedding. The rare CM observed within the laminae could have been a remnant of original microbial mats, although there is no evidence to exclude other possible sources (e.g., detrital organic matter) [START_REF] Saitoh | Metamorphic origin of anastomosing and wavy laminas overprinting putative microbial deposits from the 3.22 Ga Moodies Group (Barberton Greenstone Belt)[END_REF]. In short, the petrological indices of biogenicity of the laminae are meager in the analyzed samples because they have been too modified to deliver strong, reproducible, and obvious original information. Therefore, the conclusion of Saitoh et al. ( 2021) is fully in line with recent publications aiming to illustrate and understand the complexity and potential heterogeneity of post-depositional processes on the Moodies sediments [START_REF] Reimann | Syndepositional hydrothermalism selectively preserves records of one of the earliest benthic ecosystems, Moodies Group (3.22 Ga), Barberton Greenstone Belt, South Africa[END_REF][START_REF] Janse Van Rensburg | Volcanoes in the estuaries: Insights into Earth's oldest (3.22 Ga) terrestrial microbial habitats, Moodies Group, Barberton Greenstone Belt[END_REF]. The degree of alteration in the Moodies group has been recently demonstrated to be highly heterogeneous and variable on a regional scale [START_REF] Reimann | Syndepositional hydrothermalism selectively preserves records of one of the earliest benthic ecosystems, Moodies Group (3.22 Ga), Barberton Greenstone Belt, South Africa[END_REF], particularly in association with the density of diabase dyke network in the Saddleback Syncline (Fig. 1). In that sense, [START_REF] Saitoh | Metamorphic origin of anastomosing and wavy laminas overprinting putative microbial deposits from the 3.22 Ga Moodies Group (Barberton Greenstone Belt)[END_REF] emphasized again that their conclusions were based solely on the analyzed sandstones from one outcrop of the Saddleback Syncline and should not be expanded to the entire Moodies Group.

Secondary Ti oxides and sericite cements are consistently dominant in anastomosing and wavy laminae through the analyzed succession [START_REF] Saitoh | Metamorphic origin of anastomosing and wavy laminas overprinting putative microbial deposits from the 3.22 Ga Moodies Group (Barberton Greenstone Belt)[END_REF]. Moreover, the multiple sulfur isotopic composition of sandstones is relatively homogeneous through the analyzed Saddleback succession [START_REF] Saitoh | Multiple Sulfur Isotope Records of the 3.22 Ga Moodies Group, Barberton Greenstone Belt[END_REF], and very similar to the isotopic composition of metasomatic sulfides from nearby gold mines in the central BGB [START_REF] Agangi | An atmospheric source of S in Mesoarchaean structurally-controlled gold mineralisation of the Barberton Greenstone Belt[END_REF], suggesting that the secondary addition of hydrothermal, sulfur bearing-fluids also participated in the geological history of the Moodies Group in the Saddleback Syncline. The mineralogical and geochemical homogeneity of the analyzed sandstones [START_REF] Saitoh | Multiple Sulfur Isotope Records of the 3.22 Ga Moodies Group, Barberton Greenstone Belt[END_REF][START_REF] Saitoh | Metamorphic origin of anastomosing and wavy laminas overprinting putative microbial deposits from the 3.22 Ga Moodies Group (Barberton Greenstone Belt)[END_REF] suggests that a regional post-depositional process has affected the Moodies sedimentary rocks around the studied section. Bearing this in mind, our conclusion was built on the description of rocks from the same locality -i.e., Log 9 -of [START_REF] Homann | Morphological adaptations of 3.22 Ga-old tufted microbial mats to Archean coastal habitats (Moodies Group, Barberton Greenstone Belt, South Africa)[END_REF]. Our field work was guided by a sedimentological approach and the completion of a sampling log. We were able to reproduce the facies succession described in Log 9 of [START_REF] Homann | Morphological adaptations of 3.22 Ga-old tufted microbial mats to Archean coastal habitats (Moodies Group, Barberton Greenstone Belt, South Africa)[END_REF] and the samples were collected based on this lithofacies correspondence (see Figs. 1 and2 and Table 2 of [START_REF] Saitoh | Metamorphic origin of anastomosing and wavy laminas overprinting putative microbial deposits from the 3.22 Ga Moodies Group (Barberton Greenstone Belt)[END_REF]. We disagree with Homann and Heubeck (2021)'s claim that our samples were "selectively investigated, and interpreted with scant consideration of their geological context". Our study site was selected following personal communication with M. Homann and C. Heubeck and also according to the "Geology of the Barberton Greenstone Belt: Processes on the early Earth" excursion field guide of [START_REF] Heubeck | Geology of the Barberton Greenstone Belt: Processes on the early Earth[END_REF].

Although [START_REF] Homann | Morphological adaptations of 3.22 Ga-old tufted microbial mats to Archean coastal habitats (Moodies Group, Barberton Greenstone Belt, South Africa)[END_REF] did not report precise sample positions along their logs, Fig. 1 shows that our samples are from the same locality in the Saddleback Syncline as in [START_REF] Homann | Morphological adaptations of 3.22 Ga-old tufted microbial mats to Archean coastal habitats (Moodies Group, Barberton Greenstone Belt, South Africa)[END_REF].

Similar lithology of the analyzed rocks from the same locality with the same geological context in [START_REF] Homann | Morphological adaptations of 3.22 Ga-old tufted microbial mats to Archean coastal habitats (Moodies Group, Barberton Greenstone Belt, South Africa)[END_REF] and in [START_REF] Saitoh | Metamorphic origin of anastomosing and wavy laminas overprinting putative microbial deposits from the 3.22 Ga Moodies Group (Barberton Greenstone Belt)[END_REF] indicates clearly that we did not use the least promising samples (in terms of putative biogenicity) as suggested by [START_REF] Homann | A comment on "Metamorphic origin of anastomosing and wavy laminas overprinting putative microbial deposits from the 3.22 Ga Moodies Group (Barberton Greenstone Belt)[END_REF]. Nevertheless, we also note that such "least promising" rocks should not be overlooked in general, because Archean altered rocks record complex post-depositional histories in various regional contexts and are useful to avoid leading a wrong perspective on early (and possibly extraterrestrial) life.

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  School of Geosciences and Civil Engineering, Kanazawa University, Kakuma, Kanazawa 920-1192 Japan 2. Université Clermont Auvergne, CNRS, IRD, Laboratoire Magmas et Volcans, F-63000 Clermont-Ferrand, France 3. Laboratoire Biogéosciences, Université Bourgogne Franche-Comté, Dijon, France 4. Institut Universitaire de France, 1 rue Descartes, 75231 Paris CEDEX 05, France 5. Institut des Sciences de la Terre, Faculté des géosciences et de l'environnement, Université de Lausanne, 1015 Lausanne, Switzerland 6. Univ Lyon, UJM, UCBL, ENSL, CNRS, LGL-TPE, 23 rue Dr. Paul Michelon, F-42023, Saint Etienne, France 7. Université Lyon, Université Claude Bernard Lyon 1, CNRS, Institut Lumière Matière, UMR 5306, F-69622, Villeurbanne, France *Correspondence: msaitoh@se.kanazawa-u.ac.jp; Tel.: +81-76-264-6515

Fig. 1 .

 1 Fig. 1. Locality of the studied section in Saitoh et al. (2021). (A) Map showing the distribution of "microbial laminations" and rock silicification degree along the southern limb of the Saddleback Syncline (Reimann et al., 2021). (B) Google Earth satellite image of an enlarged square in A, showing the studied section in Saitoh et al. (2021). A diabase dyke is based on Lowe et al. (2012).

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