Valérie Guillard
email: guillard@um2.fr

Patrice Buche
email: patrice.buche@supagro.inra.fr

Sébastien Destercke
email: sebastien.destercke@hts.utc.fr

Nouredine Tamani
email: tamani@lirmm.fr

Madalina Croitoru
email: croitoru@lirmm.fr

Luc Menut
email: luc.menut@supagro.inra.fr

Carole Guillaume
email: guillaume@um2.fr

Nathalie Gontard
email: gontard@um2.fr

A Decision Support System to design modified atmosphere packaging for fresh produce based on a bipolar flexible querying approach

Keywords: MAP modeling, multi-criteria querying, decision support system, knowledge engineering, respiring product

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

Introduction

Despite targeted campaigns and programs for promoting their health benefits, consumption of fresh fruits and vegetable is still limited by their short shelf life, which is not easily compatible with current modes of distribution and purchase (once a week) in medium-to high-income countries.

Beyond respect of the chill chain and initial food quality, Modified Atmosphere Packaging (MAP) was proved to be an efficient way to delay senescence and spoilage, without using controversial preservative compounds, and so to extend shelf life of fresh produce [START_REF] Floros | Introduction to modified atmosphere packaging[END_REF], Guillaume et al., 2008, Zagory and Kader, 1988]. MAP relies on the establishment of an optimal /recommended atmosphere for the produce and can be achieved by matching the gas (O 2 and CO 2 ) permeation rate of the film with the respiration rate of the produce. If a wealth of information has been published on MAP (more than 400 occurrences for "modified atmosphere packaging and fruit and vegetable" in ISI Web of Knowledge), there is a lack of systematic treatment of the data using knowledge management system in order to provide a full (complete) Decision Support System (DSS).

By providing suitable information, such numerical tools could help designers and users to select film properties that best fit particular purposes and targets. This approach is especially important when developing packaging made from biodegradable materials, which becomes a new trend, as their limited barrier properties, possibly optimized using smart and/or composite multilayer material [START_REF] Guillaume | Biobased packaging for improving preservation of fresh common mushrooms (Agaricus bisporus L.)[END_REF], can turn out to be an asset to extend shelf life of respiring foods [START_REF] Cagnon | Nano and micro-structuring of materials from a single agropolymer for sustainable MAP preservation of fresh food[END_REF], Guilbert et al., 2011, Guillaume et al., 2008]. To facilitate MAP design, mathematical models, socalled virtual MAP, have been developed by researchers working in this field to design passive [Mahajan et al., 2007, Souza-Gallagher andMahajan, 2013] or active MAP [START_REF] Cagnon | Nano and micro-structuring of materials from a single agropolymer for sustainable MAP preservation of fresh food[END_REF], Charles et al., 2003, Charles et al., 2005] for fresh and fresh-cut fruits and vegetable. Online applications are today available for free (www.tailorpack.com) or charged access (www.packinmap.com).

Such numerical tools simplify the package design steps by predicting the gas permeability values that permit to reach recommended atmosphere for the target product and therefore to extend shelf life while maintaining quality and safety of the packed food.

Up to now, all the aforementioned tools only considered the gas permeabilities of the packaging material as a basis for packaging design. The design of food packaging is not only driven by maximizing shelf life of the food, and numerous other requirements may interplay for final decision, re-lated to processing, marketing, commercial, or distribution concerns (as cost, process ability of constituents, industrial feasibility, environmental impact, safety and stability of the packaging material all over the food life cycle, waste management, etc.). Then, aside the constraint of food shelf life and quality, correlated to gas permeation rates of the material, it also relies on user's preferences, naturally expressed as wishes (e.g. transparent material would be preferred) or constraints (e.g. cost of raw material must be less than 3e/kg). Some constraints and/or wishes are also related to the fact that consumers may reject the use of some additives or of nano-technology in the packaging material because of the unknown consequences on their health, or more simply they may prefer transparent rather than opaque packaging.

To help stakeholders of the food chain in the choice of a packaging material that would suit all the requirements of a given fresh fruit or vegetable, development of decision aid tools is foreseen. The European project EcoBioCap (www.ecobiocap.eu) aims at designing the next generation of packaging material using advanced composite structures based on constituents derived from the food industry (cf figure 1).

In the framework of this project, we aim at developing a Decision Support System (DSS) to help parties involved in the packaging design to make rational decisions based on knowledge expressed by the experts of the domain.

The Decision Support System developed in this context aims at solving the dilemma of multi-criteria demands in the design of packaging for fresh produce. This DSS relies on the development of a querying system (i) able to store and maintain data in dedicated databases (which could be incomplete or imprecise) about packaging material characteristics (e.g. gas permeabilities, cost, transparency, mechanical properties, etc.) and fresh food parameters (e.g. respiration parameters, optimal storage conditions), (ii) allowing stakeholders to express their needs and requirements as queries addressed to the system databases, and (iii) retrieving the packaging materials ranked from the most to the least satisfactory according to the expressed requirements.

The original contribution of this paper is to detail the design and the implementation of the proposed Flexible and Bipolar Multi-criteria Querying system, part of the DSS for the EcoBioCap project:

• Functional description of the system based on the approach described in [START_REF] Destercke | A flexible bipolar querying approach with imprecise data and guaranteed results[END_REF],

• Databases development and filling with food and packaging characteristics,

• Open source implementation with Java 1 , R for numerical processing 2 , and MySQL 3 relational database management system.

Functional specifications of the bipolar flexible querying system are introduced in Section 2. Its corresponding software architecture is detailed in Section 3. Implementation aspects and some tests are displayed in Section 4. Section 5 concludes the paper.

1 www.java.com 2 http://www.r-project.org 3 www.mysql.com

7

We detail here the main functions that the bipolar flexible querying system has to provide to the users. Prospective users of the EcoBioCap DSS have been identified in the Stakeholder Advisory Board of the EcoBioCap FP7 project.

Functional requirements implemented in the EcoBioCap DSS are the following:

1. Collecting and managing data available about the packaging material characteristics, 2. Collecting and managing data available about the respiration parameters of fresh produce, 3. Managing users' preferences expressed over packaging material targeted characteristics as constraints or wishes, 4. Dealing with missing data, since in real cases some required packaging characteristics could be unknown, so stakeholders of the food chain may face the problem of missing data, 5. Managing imprecise data, since characteristics associated with packaging materials (eg. O 2 permeability values) and food products (eg. maximal respiration rates) may be imprecise, 6. Retrieving the ranked list of all relevant packaging with their main characteristics, 7. Guaranteeing the retrieval of packagings which are the closest to the requirements (called guaranteed solutions) in case of empty set of solutions, 3 Architecture of the flexible querying system

Databases

The flexible querying system defines and implements two databases: (i) fresh food database containing the respiration parameters of the fresh produce used in the virtual MAP simulation (maximal respiration rate, Mickaëlis-Menten constant, energy of activation, optimal gas concentration required for the fresh produce optimal conservation, respiratory quotient), and (ii) packaging materials database storing all the data related to the packaging material:

O 2 and CO 2 permeabilities, temperature at which the permeability measurement was done, film thickness, mechanical properties, indication about the cost, the renew-ability or not of the raw material used for producing the packaging film, the biodegradability, the transparency, etc. Both databases contain informations collected from the literature in the field and they are maintained within MySQL (www.mysql.com) RDBMS (Relational DataBase Management System).

Whenever available, each datum is stored with its confidence interval to allow uncertainty propagation during simulations.

The virtual MAP module

The virtual MAP simulation module computes the optimal permeance which guaranties the best shelf life for the packed food, by combining data from the fresh food database and parameters given by the user. Inputs extracted from the fresh food database are:

• parameters of the Mickaëlis-Menten type equations: maximal respiration rate Rmax, respiratory quotient RQ, Mickaëlis-Menten constant Km, etc.

• optimal O 2 and CO 2 content targeted in the packaging headspace when running simulation.

Parameters given by the user include the targeted shelf life, the food mass to pack, the storage temperature, and the geometric dimensions of the packaging (surface and volume). By using mass transfer mathematical equations (based on Fick's law) coupled with Mickaëlis-Menten equation for respiration, the virtual MAP returns the optimal O 2 and CO 2 permeances and permeabilities for the preservation of the food.

The virtual MAP module has been implemented using the R software for numerical computing (http://www.r-project.org).

The multi-criteria flexible querying module

To build such a querying system, methodologies based on Flexible Multi-Criteria Querying process were used. The needs and requirements are modeled as user preferences, approach widely studied in the field of flexible querying of databases and information retrieval systems. Flexible querying systems allow users expressing preferences in their queries. These queries are run on regular relational databases and deliver a set of discriminated answers, which are ranked from the most to the least preferred. Preferences are usually expressed as ordinary and binary sets. But they may lead to empty set of answers and enlarged intervals of preferences relaxing the constraints could be more expressive than a single value. In this context, fuzzy sets theory [Zadeh, 1965] provides a general model for the interpretation of queries in-volving preferences. The querying system [START_REF] Destercke | A flexible bipolar querying approach with imprecise data and guaranteed results[END_REF] can also cope with lack of data or imprecise data in the database corresponding to the characteristics related to the packagings like the optimal permeance, the dimension of the packaging, its shape, etc.

Besides, expressed user preferences have different levels of importance or priority. The shelf life and sanitary criteria ensuring a good preservation of the packed product are intuitively more important than the color or the transparency of the packaging. Therefore, some preferences are modeled as constraints that the satisfaction is mandatory, and some others are wishes that satisfaction is optional. Any packaging material which does not satisfy the constraints is definitely discarded and the more packaging satisfies the wishes the more preferred it is. It is natural then to make use in this context of a bipolar approach for the querying process since it permits to handle compound preferences made of mandatory conditions and optional conditions. Bipolarity refers to the human reasoning which combines pro and con information to take decisions, to make choices or judgments. It has been widely studied during the last years in the field of preference modeling for flexible querying. Several approaches have been introduced for the expression and the evaluation of fuzzy bipolar conditions [START_REF] Bordogna | A fuzzy query language with a linguistic hierarchical aggregator[END_REF], Dubois and Prade, 2002b, Dubois and Prade, 2002a, de Tré et al., 2009], [START_REF] Zadrozny | Bipolar queries using various interpretations of logical connectives[END_REF], Zadrozny and Kacprzyk, 2009, Liétard et al., 2011, Tamani et al., 2013]. In this paper, we consider fuzzy bipolar conditions as a particular case of fuzzy conditions, and we rely on the interpretation intro-duced by Dubois and Prade [Dubois and Prade, 2002b, Dubois and Prade, 2002a, Dubois and Prade, 2008], in which a bipolar condition is made of constraints that are a mandatory condition (which refer to the negative pole or con information) and wishes that are optional conditions (which refer to the positive pole or pro information), and globally expressing "constraints, and if possible wishes".

Moreover, the main difference of our flexible querying approach in comparison with the aforementioned ones is that in our case we take into consideration the fact that some values associated with packaging materials attributes can be imprecise or uncertain, since they were obtained from experimental data returned from repetitions corresponding to an interval instead of a single value. Therefore, as for query preferences, values in the database are also considered as fuzzy sets, but with a semantic adapted to imprecise data instead of preferences, as defined in [START_REF] Dubois | The three semantics of fuzzy sets[END_REF], Haemmerlé et al., 2007, Buche et al., 2011].

Predicted optimal gas permeances, computed by the virtual MAP module become two input parameters corresponding to one criterion (considered by default as constraints since related to food quality, but could be also switched to wishes in the GUI 4 ) in the multi-criteria flexible querying module.

The multi-criteria flexible querying module combines these inputs to form a bipolar query addressed to the packaging database. The returned list of packagings is ranked from the most to the least relevant one with regard to 4 Graphical User Interface 14 the expressed preferences. The user can finally specify whether the ranking has to take into account unknown values for the mandatory criteria. If the ranking must consider unknown values for the mandatory criteria, then each delivered packaging is annotated with the percentage of known values over which the ranking was carried out. In the opposite case, if the ranking must only consider known values for the mandatory criteria and if no packaging in the database has the required characteristics, (leading to empty set answer), then the system activates the guaranteed result function which computes the most similar packagings or the closest packagings to the ideal one.

As previously stated, the flexible querying system relies on a bipolar approach handling fuzzy conditions to model user preferences expressing pro and con informations.

Fuzzy sets theory:

The fuzzy sets theory 5 is introduced by Zadeh [Zadeh, 1965] to express the gradual membership of an element to a set. A fuzzy set generalizes a crisp set in which membership grades are in {0, 1}. If a fuzzy set is a discrete set then it is denoted F = {(x 1 , µ F (x 1 )), ..., (x n , µ F (x n ))}, otherwise it is characterized by its membership function, generally a trapezoidal function. For instance, Figure 3 illustrates the membership (trapezoidal) function µ P eO 2 5 Formally, a fuzzy set F is defined on a referential U by a membership function µ F : U → [0, 1], such that µ F (x) denotes the membership grade of x in F . In particular, µ F (x) = 1 denotes the full membership of x in F , µ F (x) = 0 expresses the absolute nonmembership and when 0 < µ F (x) < 1, it reflects a partial membership (the closer to 1 µ F (x), the more x belongs to F ).

corresponding to an O 2 permeance preference. The union ∪ and the intersection ∩ operators are defined with a couple of (t-norm, t-conorm) such as (min, max). Let F , G be two fuzzy sets,

µ F ∪G (x) = max(µ F (x), µ G (x)), µ F ∩G (x) = min(µ F (x), µ G (x)), and the com- plement of F , denoted F c , is defined by µ F c (x) = 1 -µ F (x).
The logical counterparts of ∩, ∪ and the complement are respectively ∧ (AND operator), ∨ (OR operator) and ¬ (negation operator).

The flexible bipolar querying method:

The flexible bipolar querying method implemented in the DSS corresponds to a 'pros and cons' approach. Criteria chosen by the user (wishes and/or constraints) are multiple and also sorted by importance.

More formally, a bipolar query is pair of a sorted combination of contraints and wishes of the form Q = (C, W ), where C = {C (1) , ..., C (n) } and W = {W (1) , ..., W (m) }; each C i,i=1,...,n (resp. W j,j=1,...,m ) is a subset of contraints (resp. wishes) of the same importance or priority expressed on the attributes of packaging material such that:

• ∀i, i ∈ {1, ..., n}, if i < i then contraints in C (i) take priority over C (i )

• ∀j, j ∈ {1, ..., m} if j < j , wishes in W (j) take priority over W (j )

An example of such a query with two constraints and one wish is represented as a sorted combination of fuzzy sets displayed in Handling imprecise and uncertain values. Considering the food packaging application, enlarged intervals for the values could be taken into account (e.g. uncertainties due to biological variability [START_REF] Destercke | A flexible bipolar querying approach with imprecise data and guaranteed results[END_REF] or tolerance threshold expressed by the user). In the flexible querying system, as for query preferences, values in the database are also considered as fuzzy sets, but with a semantic adapted to imprecise data instead of preferences, as defined in [START_REF] Dubois | The three semantics of fuzzy sets[END_REF].

Thanks to the homogeneous representation of preferences and uncertain values, the comparison between a fuzzy set having a semantic of preference with a fuzzy set having a semantic of imprecision can be defined using two classical measures of possibility theory: a possibility degree of matching (denoted Π) and a necessity degree of matching (denoted N ) [START_REF] Dubois | Possibility theory-An approach to computerized processing of uncertainty[END_REF] defined as follows:

• the possibility degree of matching between two fuzzy sets v and v defined on a referential domain Dom, denoted

Π(v, v ), is Π(v, v ) = Sup x∈Dom (min(µ v (x), µ v (x))),
• the necessity degree of matching between v and v denoted N (v, v ), is 5 for a graphical representation). Intuitively, the possibility degree of matching is an optimistic comparison, as it corresponds to the maximum degree that satisfies simultaneously the membership function of the two fuzzy sets (representing preferences and uncertainty, respectively). The necessity degree may be considered as a pessimistic comparison, as it corresponds to the inverse of the degree of inclusion of the fuzzy set associated with the uncertainty interpretation (i.e., our knowledge stored in the database) with the one associated with the preferences.

N (v, v ) = Inf x∈Dom (max(µ v (x), 1 -µ v (x))) (see Figure
When two criteria C 1 and C 2 of the query are of equal priority, the re-

spective couples of comparison degrees [N C 1 , Π C 1 ] and [N C 2 , Π C 2 ],
for a given material stored in the database, are aggregated to provide a unique couple

of comparison degrees [N C 1 ∩C 2 , Π C 1 ∩C 2 ] where N C 1 ∩C 2 = min(N C 1 , N C 2 ) and Π C 1 ∩C 2 = min(Π C 1 , Π C 2 ).
At the end, the algorithm provides a ranking of equivalent classes: the first one contains the best materials that are of similar quality and the last one contains those materials that are the less satisfactory while still fulfilling the constraints. For further details about the ranking process, the reader is referred to [START_REF] Destercke | A flexible bipolar querying approach with imprecise data and guaranteed results[END_REF].

Handling missing data. It's worth noticing that those comparison degrees may be evaluated even if, for a given material stored in the database, some data are missing. For any fuzzy sets of preferences, comparison degrees with packaging materials for which data are missing in the database will be equal to

[N = 0, Π = 1].
That means that, when a material stored in the database is associated with a missing datum, the DSS will consider that this material could potentially match the food requirement related to this criteria (Π = 1) and, simultaneously, that the degree of necessity that this material match the food requirement is equal to 0 (N = 0).

Handling empty set as answer. In the case where every packaging material has a possibility degree of matching of 0 for at least one constraint (no material is candidate), the DSS warns the user and searches the materials which are the closest, according to some distance, to satisfy the constraints.

That is, for each material M in the database, the system computes a distance d(M, C) between the material and the constraints C, and orders the materials according to this distance. This distance can be seen as the minimal modification the constraints C would have to undergo so that material M satisfies it (see [START_REF] Destercke | A flexible bipolar querying approach with imprecise data and guaranteed results[END_REF] for more details). Finally, the user is informed that the specified constraints are probably too restrictive but still receives a list of materials that almost satisfy his/her needs.

Validation of the flexible querying system

The validation of the results delivered by the DSS has been done twofold.

Firstly, it relied on the validation of the virtual MAP model which has been done in the past on endives and tomatoes [START_REF] Charles | Active modified atmosphere packaging of fresh fruits and vegetables: Modeling with tomatoes and oxygen absorber[END_REF], Charles et al., 2005, Cagnon et al., 2012, Cagnon et al., 2013]. Secondly, it has been done using a classical use-cases testing procedure of the functionalities associated with the flexible bipolar querying system presented in section 3.3. This validation has been done by involving stakeholders of the food chain participating to the EcoBioCap project. Some collective testing sessions have been organized in 2012 and 2013 in order to validate by the potential users the functionalities of the DSS. Following these testing sessions, the users have requested the implementation of two possible behaviors of the database flexible querying concerning missing data handling. The first request corresponds to the one described in section 3.3 in which, to inform the user, a percentage of known values corresponding to the querying criteria has been added to each answer.

The second request corresponds to the desire of having a more restrictive querying mode forbidding the ranking of packagings with unknown values.

Consequently, now, both modes of querying are available in the DSS.

Implementation

The flexible querying system was implemented as a web application accessible on http://pfl.grignon.inra.fr/EcoBioCapQuerying/. A short demonstration video is available for download on http://umr-iate.cirad.fr/axes-de-recherche/ingenierie-des-connaissances/themesde-recherche/ecobiocap-dss.

The interface of the application is made of 3 parts:

• the upper part, shown on Figure 6, is dedicated to the permeance simulation and allows the setting of the fresh food and packaging parameters. It is connected to the fresh food database to retrieve the characteristics associated with the selected fresh food. Figure 6 displays in the upper part the optimal permeance properties for the apricot Bergeron, computed by the DSS, for a shelf life of 7 days in ambient temperature (20 • C), mass food of 0.5 kg, volume of 1 l and surface of 756 cm 2 .

• the middle part allows the user expressing his/her preferences. In this version, the user can only specify his/her preferences about the O2/CO2 permeances, the storage temperature, the biodegradability and the transparency of the packaging material. The text of the multicriteria querying shown on Figure 6 would be : "I want a packaging material that suits to my product, apricot (eg. its O2 and CO2 permeances match the apricot requirement) for the range of temperature between 14 and 26 • C". It must be noticed that the optimal permeances computed by the DSS are automatically replicated in the middle part with a predefined deviation for the min-max and enlarge min-max intervals. Those values correspond to the fuzzy preferences associated with permeances as presented in Figure 3. They may be modified by the user before launching the querying of the packaging database. Further details (commercial packaging or not, available reference of the scientific publication from where the information has been extracted, etc.) about delivered packaging materials can also be displayed as illustrated in Figure 7 for the same case of Apricot.

The DSS considers not only mandatory criteria such as packaging permeabilities but also wishes of the user. For instance the user may have the following query: "I want a packaging material that permits to preserve the shelf life of my product (Apricot) in the range of temperature 14-26 • C and if possible biodegradable". This query corresponds to three constraints: O2 and CO2 permeabilities and temperature and one wish. Figure 8 illustrates this query. We notice that the wish permits to break tie between packagings having the same ranking with regard to constraints. In the present case study (Apricot), the two materials with number 1 in Figure 7 where polyolefins, oil-based materials, which are not biodegradable. Therefore the segregation between them shown in Figure 8 is not made on their biodegradability characteristics but on the fact that in one case, this criterion is filled in the database (case of lupolen, become rank 2 in the new classification) and in the case of polyethylene (rank 1), this value is not filled and thus considered as potentially reachable (cf section 3.3, paragraph Handling missing data). The user is informed about lacking data thanks to the column % known values. By example, for the case of polyethylene, it is 50 % as only two values are known (see Figure 8): the O2 permeance and the temperature. Finally, Figure 9 illustrates the guaranteed result function of the DSS which delivers the closest packaging materials according to a distance calculated between the query constraints and the actual value of those materials. The guaranteed result function is launched when there are not actually any packaging having all the criteria values fulfilled in the packaging database and satisfying the query constraints. In the query corresponding to the case study of Figure 9, the criteria biodegradability is not a wish but a constraint. As no packaging material of the database fully satisfies this query, the guaranteed result function is computed. A warning is sent to the user through a pop-up window (see Figure 9) in which is indicated, for each mandatory criterion, the percentage of packagings which do not fulfill the constraint or have an unknown value. The ranking of packaging materials proposed to the user is made with the packagings which are the closest to the targeted ones (constraints in the query). In the present case study, as biodegradability became mandatory, the first ranked material is a biodegradable one "wheat gluten" even if its O2/CO2 permeabilities are further from the target than those of polyehylene, the material selected in the first query (Figure 7). This last query well illustrates how the DSS could always guarantee some results.

Conclusion and prospect

In this paper, we proposed a Decision Support System (DSS) for selecting packaging material for fresh fruits and vegetables which relies on an interdisciplinary approach, coupling process engineering with knowledge engineering and computer science. Mass transfer models aiming at realizing virtual MAP simulations are gathered with packaging and fresh produce databases in a web-application. A bipolar querying module was developed in order to allow the user querying the packaging database starting from food requirements such as mass transfer properties and other criteria like transparency, biodegradability, cost, etc. If several packaging materials are in the same equivalent class after having satisfied the constraints, a refined ranking is proposed on the wishes. In the querying process, the imprecision associated with the data stored in the database is taken into account thanks to the use of comparison degrees between user preferences and data. If none packaging material satisfies the query, the DSS gives a ranking of the less distant packaging material from the target constraints.

Compared to the current stakeholder decision-making practices, this DSS is a significant breakthrough in the field of food packaging, especially that of fresh respiring produce. As aforementioned, due to their intense respiring metabolism, fresh produce necessitate, for their packaging material, specific values of O2/CO2 permeabilites, belonging to a narrow and specific range of values, that depends on the nature of the product. In practice, the choice of this packaging material is based on the specifications defined by the food manufacturer. To define the specifications of O2/CO2 permeabilities, experimental trials on various materials with a large panel of gas permeabilites are carried out until the packaging suitable to preserve the food is found. This "pack-and-pray" approach is fully empirical and remains qualitative without any formalization of the link between packaging properties and needs of the food. We can easily imagine the added value that the use of a numerical tool like this DSS would bring to food manufacturers by helping them to choose the right packaging material. In addition to the main criterion associated with food shelf life, the DSS proposed in this paper answers to multi-criteria queries including other food packaging characteristics. Therefore, in addition to the permeabilities criteria, it permits to analyze several other criteria that could be constraints or wishes related to the food manufacturer constraints, acceptances and needs: biodegradability, transparency etc. This type of tool was never attempted previously in that field. Among the list of possible packaging retrieved by the DSS, the user has to choose one (usually the one ranked in first) and then to test it in real condition of use. Compared to the empirical approach that requires numerous experimental trials, using the DSS the user will have only one trial to perform (validation step). For the reasons aforementioned, the DSS proposed in this paper definitively assists decision-making in the field of food packaging for fresh produce. This work has highlighted the importance of storage databases and of their content. Data associated with new packaging materials developed dur-of the project, the DSS will be used to benchmark the new packagings developed for different case studies (respiring cheese, strawberries and mushrooms) (to be further presented). More generally, it is crucial to fill in databases and especially the packaging database with a maximum of data in order to have a panel of materials representative of the different possibilities available on the market and in R&D. As the manual entering of data in databases is a time consuming task, methodologies coming from the computer science field allowing the semi-automatic "feeding" of databases from documents founds on the Web should be developed and is a perspective of this work.

Figure 1 :

 1 Figure 1: The EcoBioCap project.

Figure 2 Figure 2 :

 22 Figure2details the components of the developed flexible querying system implementing the required functionalities. Namely, (i) two databases (for fresh foods and packaging materials), (ii) the virtual MAP simulation and (iii) the multi-criteria flexible querying system.

Figure 3 :

 3 Figure 3: Example of a fuzzy set corresponding to O 2 permeance preference.

  Figure 4. It corresponds to the following query: Q(C = {{P ref O2P ermeance , P ref CO2P ermeance }, {P ref P rice }}, W = {{P ref T ransparency }}).

Figure 4 :

 4 Figure 4: Example of a bipolar query.

Figure 5 :

 5 Figure 5: Example of overlapping and inclusion measures.

Figure 6 :

 6 Figure 6: Permeance values obtained in the case of Apricot.

Figure 7 :

 7 Figure 7: Ranked list of suitable packaging in the case of Apricot (only constraints are considered). Details are displayed for the first packaging.

Figure 8 :

 8 Figure 8: Ranked list of suitable packagings in the case of Apricot (a wish is also considered).

Figure 9 :

 9 Figure 9: List of the closest packagings to the ideal one in the case of Apricot.

Stakeholders,,Requirements+about+Fresh+product:+ Packaging+Geometry,+ Shelf+life,+mass,+temperature+++


Bouillot Baptiste

Le Quang Du

L E Quang Duyen

Herri Jean-Michel

Thermodynamic study of clathrates hydrates from hydrocarbon gas mixtures Consequences for capture CO 2 and flow assurance

Keywords: Thermodynamics, Clathrates hydrates, CO 2 capture, Flow assurance

This work is a contribution to the global understanding of the coupling between kinetics and thermodynamics to explain the composition of the clathrate hydrates during their crystallization from an aqueous liquid and a hydrocarbon gas phase. In this work, we face new experimental facts that open questioning after comparing the classical modeling of clathrate hydrates following the approach of [1] with our experimental data following a new procedure allowing determining the hydrate composition during crystallization and at equilibrium. In this paper, we present details on the experimental procedure to measure the composition of the hydrate that crystallizes from a hydrocarbon gas mixture. We show that the results are time dependent and tend to thermodynamic equilibrium as time tends to infinity.

An immediate consequence concerns two major domains of applications, CO 2 capture from power plants, as well as flow assurance in the oil and gas industry. In fact, in both the cases, the crystallization is under non equilibrium conditions, and we conclude here that it necessarily leads to the formation of hydrates with a composition which is not predicted by classical modeling.

Introduction

Context

The offshore extraction of petroleum in deeper conditions increases day after day and favors the conditions of hydrate formation (low temperature and high pressure).

Hydrates are ice-like structures; formed by a process of crystallization, due to the union of water molecules around a "guest molecule", in our case a gas molecule. When they form in the pipeline, they often lead to large pressure drops and in some cases to an impermeable plug, representing a great concern in flow assurance.

There are some methods used to deal with the hydrate formation. The most common among them is the use of thermodynamic hydrate inhibitors (THIs), which act on the hydrate equilibrium conditions, shifting it to higher pressure and lower temperature. The proportion of THIs injected is designed from the necessary shift to prevent hydrate formation, and the quantities of THI can be too much important and in consequence costly. Therefore, the researchers are urged to find other ways to handle the problem. Thus the focus changed from preventing the hydrate formation, and moved to avoiding the pipeline blockage, by the use of low dosage hydrate inhibitors (LDHIs) including kinetic hydrate inhibitors (KHIs) and anti-agglomerates (AAs). The first acts by delaying or slowing the first steps of the crystallization (nucleation and growth), and the second works by preventing agglomeration then acting as dispersant.

As an oil/gas field matures, the fraction of water increases. Another parameter comes into play, since the cost of THIs injection is increased and the benefit of LDHIs is not well known. The development of new hydrate management strategies is limited by the understanding of hydrate plug formation mechanism. Also, the system, where the oil is the dispersed phase (oil-in-water emulsion), is poorly studied. Therefore, exploring the hydrate formation at high water cut shows a real interest, both at the level of the description of the crystallization itself as well as of the population level, but also at the crystal size level to describe its composition. We need first to describe the population level to understand the different mechanism of nucleation, growth and agglomeration under flowing (Figure 1) in order to design the type of additive to inject [START_REF] Leba | Chord length distributions measurements during crystallisation and agglomeration of gas hydrate in a waterin-oil emulsion: Simulation and experimentation[END_REF][START_REF] Cameirao | Chord length distributions interpretation using a polydispersed population: Modeling and experiments[END_REF]. After choosing the type of additive to delay or to prevent the crystallization, one needs to evaluate the quantity of additive to inject, and this quantity is dependent on the maximum quantity of hydrate that can be formed. The quantity of hydrates that can be formed can be estimated from a mass balance and depends on the estimation of the hydrate composition. In this work we focus on the fact that the hydrate composition could not be estimated directly from flash calculation implementing thermodynamic equilibrium calculation. In fact, in this work, we show that crystallization occurs under non equilibrium conditions giving hydrate with a composition different from equilibrium.

Figure 1: conceptual picture for hydrate formation in water-in-oil (W/O) emulsions

There are two critical interrelated steps in the formation of a plug: hydrate (shell) growth and hydrate agglomeration. Upon nucleation, a hydrate film rapidly forms around the water droplets. After the film has formed completely, the growth rate transition from a heat transfer limited process to a process limited by mass transfer. Hydrate forming gas molecules (guest) initially dissolved inside the water droplet can migrate to the hydrate film. At longer timescales the hydrate formation rate is limited by the mass transfer of the water or guest molecule through the hydrate film [START_REF] Turner | PhD Thesis "Clathrate Hydrate Formation in Water-in-Oil Dispersions[END_REF]. Once formed, it is assumed that the hydrate particles remain in the oil phase.

Another consequence of the non-equilibrium crystallization concerns a domain of application relative to gas separation and especially CO 2 capture [START_REF] Herri | How to explain the hydrate composition from CO2-C1-C2-C3-C4 gas mixtures: toward a kinetic understanding versus thermodynamic and consequences on the evaluation of the kihara parameters[END_REF]. In the capture process considered here, CO 2 is physically adsorbed in solid gas hydrate crystals, rather than chemically bonded to a solvent such as in the amine process. Since the two main constituents of power station flue gasses, N 2 and CO 2 are both known to form gas hydrates with water at low temperatures and high pressures, a mixed hydrate containing H 2 O, N 2 and CO 2 is expected to form. From our experimental data, we observed pure CO 2 can form. The selectivity towards CO 2 in the mixed hydrate is dramatically enhanced in a way which cannot be explained by thermodynamic, but only from kinetic [START_REF] Herri | Derivation of a Langmuir type of model to describe the intrinsic growth rate of gas hydrates during crystallisation from gas mixtures[END_REF].

Clathrate hydrates

Gas clathrate hydrates, hereafter named gas hydrates, are ice like, solid inclusion bodies of hydrogen bonded water and small guest molecules. Hydrogen bonded water clusters may form cavities, where small guest molecules are encapsulated. The three most commonly occurring hydrate crystal structures are; structure I (sI), structure II (sII) and structure H (sH). The three structures are formed by a total of five different water cavities, the 5 12 , 5 12 6 2 , 5 12 6 4 , 5 12 6 8 and the 4 3 5 6 6 3 [START_REF] Sloan | Clathrate hydrates of natural gases[END_REF][START_REF] Sloan | Clathrate hydrates of natural gases[END_REF]. A schematic of these cavities may be found in (Figure 2). The physical properties of the hydrate cavities and unit cells are provided in (Table 1). In its pure form, the unit cell of the sI hydrate contains two small 5 12 and six large 5 12 6 2 cavities while a unit cell of the sII hydrate contains sixteen small 5 12 and eight large 5 12 6 4 cavities. Both of these unit cell lattice structures belong to the cubic type. The sH hydrate structure is more complex and contains three 5 12 , two 4 3 5 6 6 3 and one 5 12 A given hydrate structure is typically determined by the size and shape of the guest molecule. Each cavity may encapsulate one or in rare cases more guest molecules of proper sizes. It is the presence of the guest molecule that stabilizes the crystalline water structure at temperatures well above the normal freezing point.

Thermodynamic modelling: state of the art

In the case of hydrates, the thermodynamic equilibrium is the equality of chemical potentials of water in the liquid phase and in the hydrate phase. This relationship can be rewritten by introducing reference states. For the hydrate, the reference state used in the van der Waals and Platteeuw model is a hypothetical phase β which corresponds to the empty cavities hydrate. The equilibrium equation is then

Where In Eq [START_REF] Leba | Chord length distributions measurements during crystallisation and agglomeration of gas hydrate in a waterin-oil emulsion: Simulation and experimentation[END_REF]. ν i is the number of cavities of type i per mole of water (see Table 1) and i j  is the

Modeling of

    L w ∑ ( ∑ ) (2)
occupancy factor ( ] 1 , 0 [  i j 
) of the cavities of type i by the gas molecule j. This last parameter is very important to define the thermodynamic equilibrium and to determine the hydrate properties.

Figure 3 : Schematic of the equilibrium between the clathrate hydrate phase and the liquid phase using a reference state.

Modeling of

     w
The chemical potential of water in the aqueous phase is calculated by means of the Gibbs-Duhem equation of classical thermodynamics which expresses the variation of the free enthalpy with temperature, pressure and composition. The reference conditions are the temperature T 0 = 273.15 K and the pressure P 0 = 1 bar. The difference of the chemical potential of water between the reference phase (liquid in our case, but it could be ice or vapour phase) and the (hypothetical) empty hydrate phase β,

   
 w , can be written as follows:

| ∫ | ∫ | | (3)
The activity of water in the liquid phase, L w a , is given as the product of the mole fraction of water in the liquid phase, w x , and the activity coefficient of water, L w

 , hence L w w L w  x a 
. In a good approximation, the aqueous phase (this work) can be regarded as ideal and the activity coefficient therefore can be set to unity, resulting in w L w

x a  . However, in the presence of polar molecules, or salts, the system usually shows strong deviations from ideality and L w  needs an appropriate description, for example using eNTRL model [START_REF] Kwaterski | Modelling of gas clathrate hydrate equilibria using the electrolyte non-random two-liquid (eNRTL) model[END_REF].

The value of

T v    L
w is a first order parameter. It has been measured with high accuracy by [START_REF] Von Stackelberg | On the structure of gas hydrates[END_REF] from X ray diffraction. Since that data is believed to be very reliable, the parameter

| | ( ) (5)
The model becomes first order dependent on (hereafter referred to as

0 , L w     ) The values of 00 L w , TP     (here after called 0 , L w     ), 0 , L w   h , T v    L w , 0 , L w ,    p c and   L w , p b
have been detailed by [START_REF] Sloan | Clathrate hydrates of natural gases[END_REF]. A special attention has been given by us to the values of [START_REF] Sloan | Clathrate hydrates of natural gases[END_REF] has reported different values from different authors, and he retained the data from [START_REF] Dharmawandhana | The measurement of the thermodynamic parameters of the hydrate structure and application of them in the prediction of natural gas hydrates[END_REF]. From our work [START_REF] Herri | Gas hydrate equilibria for CO2-N2 and CO2-CH4 gas mixtures-Experimental studies and thermodynamic modelling[END_REF], from fitting from experimental data about the CO 2 -N 2 -CH 4 hydrate equilibrium, we prefer now to work with the values from [START_REF] Handa | Thermodynamic properties of empty lattices of structure I and structure II clathrate hydrates[END_REF], given in [START_REF] Herri | Gas hydrate equilibria for CO2-N2 and CO2-CH4 gas mixtures-Experimental studies and thermodynamic modelling[END_REF].

0 , L w     and 0 , L w   h

Experimental procedure and set-up

Experimental set-up

The apparatus used for this study is presented in Figure 4. This experimental set-up is mainly composed of an instrumented batch reactor (Autoclave, 2.36 L). This reactor was fed with pure gas, or prepared gas mixture. A HPLC pump (JASCO-PU-1587) allowed the liquid injection (water + LiNO 3 as tracers for determining by mass balance the amount of aqueous phase in the cell at each step). A cryostat (HUBERT CC-505) allowed the temperature control with 0.02°C accuracy, and two sapphire windows (12cm x 2cm) are placed on each sides of the reactor to survey the inside. The reactor was stirred on both upper side (vapor phase) and lower side (liquid/hydrate phase). The pressure, and the temperature on both upper/lower side, were monitored online by a pressure sensor (0.1 bar accuracy) and a temperature sensor (Pt 100, 0.02 0 C accuracy), with the help of a data acquisition system. To be able to determine the composition of each phase at the equilibrium, the gas phase composition was monitored online using a gas chromatograph (VARIAN model CP-3800 GC with a 50m PORA BOND Q column). A ROLSI injector was used for the sampling (a few µm3 each sample), and Helium was used a carrier gas. The liquid phase could be analyzed offline by ionic chromatography (DIONEX ionic exchange chromatograph). A valve allowed the sampling of the liquid phase (water + LiNO3) with the help of the inner pressure of the reactor.

Figure 4 : Experimental set-up

Experimental procedure at high crystallization rate

The first experimental procedure was the same as in our previous studies on gas hydrates equilibrium [START_REF] Herri | Gas hydrate equilibria for CO2-N2 and CO2-CH4 gas mixtures-Experimental studies and thermodynamic modelling[END_REF]. In this procedure, the crystallization occurred at a "high rate" (or at a high supersaturation). At first, the reactor was cleaned and vacuum is made (for 40÷50 minutes). Then, the cell was filled with the desired composition either by direct injection of the various components or from a bottle where the mixture has been prepared.

The pressure was measured, and the temperature was set to 1°C (internal regulation of the cryostat). The gas composition in the cell is checked with GC analysis before any measurement.

A 10 mg/L water mixture of LiNO 3 was prepared and injected (about 800÷1000g) into the reactor thanks to the HPLC pump (n°13). The used water was ultrapure water (first category, 18.2 MΩ.cm).

A rise in the pressure, due to the added volume of liquid, was observed. Then, the reactor was stirred at the rate of 450 rpm, on both upper side, and lower side. The gas was charged into the liquid phase, and after some time (induction time), the crystallization begins. Due to the exothermicity of the reaction, a brief rise in temperature was observed. At this point, we waited for the equilibrium to be reached (no more temperature/pressure evolution). This took about 2 to 4 days depending on the mixture and initial pressure. When the equilibrium was reached, a sample of the gas phase was taken and injected into the gas chromatograph to determine the molar composition. A liquid sample was also taken to be analyzed offline by ionic chromatography (about 4.5÷5.5mg).

Then, the dissociation of the hydrate was started. The temperature was increased by about 1.5°C. When the new equilibrium was reached (24h), new samples of the fluid phases are taken. Then, the process was repeated until there was no longer a hydrate phase in the reactor. The whole procedure is summarized on Figure 5 and6.

Experimental procedure at low crystallization rate

In this second procedure, the objective is to focus on thermodynamic equilibrium avoiding as much as possible any kinetic effect. In this procedure, the crystallization rate should be closer to the hydrate formation process in pipelines at steady state (constant evolution of the pressure and of the temperature along the pipes). The objective is to stay as close as possible to the thermodynamic equilibrium curve, in order to decrease the kinetic effect on crystallization.

The pressure/temperature evolution as function of the time for the only experiment with this procedure is shown on Figure 3. Instead of decreasing very quickly the temperature to the final point (between 0 and 2°C), the crystallization occurred close to the initial point in the hydrate free area. Then, the temperature was decreased very slowly (about 0.1 ÷ 0.3 °C per day). Every a decreased of 1°C samples of the gas and liquid phases were taken and analyzed. This procedure concerns only the gas mixture n°12.

In the next section, it is explained which the studied mixtures are, and how they have been prepared.

Mass balance calculation

At given values of the state variables, a gaseous, a liquid and a solid hydrate phases are present in the system the initial quantity of the gases in the reactor is distributed between these three phases. Thus, in equilibrium, the quantity of gas in the hydrate phase can be determined from a mass balance according to:

Where is the mole number of the gases injected into reactor, and are the mole numbers of the gaseous component i (i: CO 2 , N 2 , hydrocarbon) in the hydrate, the liquid and the gas phase, respectively. The amount of substance of the gases dissolved in the liquid phase is then estimated by means of corresponding gas solubility data, whereas the mole number of the gases present in the gas phase is calculated by using an equation of state approach as outlined in the next sections.

Calculation of compressibility index

The compressibility factor in the gas phase in any equilibrium state can be calculated by means of the classical Eq.( 7) combined with means of a suitable equation of state (EOS), e.g., a classical cubic EOS. For the data evaluation in this study, the Soave-Redlich and Kwong (SRK) and (EOS) equation has been used parameters from [START_REF] Danesh | PVT and Phase Behaviour of Petroleum Reservoir fluids[END_REF].

( ⃗) (7)
With respectively G n n  (at each situation) and in Eq. ( 7), T, P, and V are the temperature, pressure and total volume, respectively, while ) , , ( 1

N y y y   
, n and R represent the vector of the mole fractions of the components in the mixture, the total mole number in the gas mixture, and the universal gas constant.

Composition of the gases initial inside reactor

Before injecting water inside reactor, at homogeneous and stability gases mixtures, the mole fraction of each gas in the gas phase x j (j is CO 2 , N 2 , hydrocarbon) is determined by using gas chromatography analysis (*).

We recall here that the reactor of total inner volume V R = 2.44 (liter) is initially filled with the gaseous components at the initial temperature 0 T and under the initial total pressure 0 P .

( ) (8)
Utilizing the results from (*) means that the system consists of a gas phase only, being composed of the gases components j, each of which having the initial mole fractions x j (j is CO 2 , N 2 , hydrocarbon). Combine with the measurements of temperature, pressure, and the compressibility factor in the gas phase, the initial total mole number in the gas phase G 0 n is derived from Eq. ( 8).

Then, we obtain mole number of each gas in initial situation.

Composition of the gases solubility in liquid phase a) The volume of the aqueous phase:

As mentioned above, the liquid phase contains LiNO 3 as a tracer. Initially the concentration of lithium 0 ] Li [  and the initial volume of liquid L 0 V are known. During the crystallization and dissociation steps, the concentration of lithium is measured by ion-exchange chromatography after sampling. So, we can calculate the volume of liquid water from a mass balance for the Li + ions: [START_REF] Sum | [END_REF] Where L

V and [Li + ] are the volume of the liquid aqueous phase and the molar concentration of lithium in this phase, i.e., in the sample, corresponding to a given step of the crystallization or dissociation. [START_REF] Thiam | Etude des conditions thermodynamiques et cinetiques du procede de captage de CO2 par formation d'hydrates de gaz : application au melange CO2-CH4[END_REF] The solubility of a gas in a liquid is determined by the equations of phase equilibrium. If a gaseous phase and a liquid phase are in equilibrium, then for any component i the fugacity in both phases must be the same: [START_REF] Herri | Gas hydrate equilibria for CO2-N2 and CO2-CH4 gas mixtures-Experimental studies and thermodynamic modelling[END_REF] The mole number of gas in the liquid phase Eq. ( 10) is calculated in a good approximation by using solubility data of the gas in water [START_REF] John | [END_REF] under the assumption that LiNO 3 , due to its low concentration (10 ppm), does not affect this solubility.

b) The mole fraction of gases dissolved in liquid phase

For the solving equilibrium, there are two different approaches:

The classical or unsymmetrical approach, called -, which consists of choosing an equation of state (EOS) for the gas phase and a solution model for the liquid phase [START_REF] Kwaterski | Modelling of gas clathrate hydrate equilibria using the electrolyte non-random two-liquid (eNRTL) model[END_REF] The fugacity of the pure liquid components The symmetric approach, called( ), consists in describing the gas phase and the liquid phase in terms of equations of state (EOS) along with appropriate mixing rules [START_REF] Dharmawandhana | The measurement of the thermodynamic parameters of the hydrate structure and application of them in the prediction of natural gas hydrates[END_REF] For treating the gas solubility, the unsymmetrical approach is combined with the unsymmetrical convention, which corresponds to infinite dilution reference (i.e. the activity coefficients of the gas molecules into the water equal to unity). The equilibrium condition reads: [START_REF] Handa | Thermodynamic properties of empty lattices of structure I and structure II clathrate hydrates[END_REF] where H i is Henry's law constant. It is expressed by means of the relation

( ( ) ) (15)
The so-called solubility models enable the calculation of Henry's law constant. It has to be reminded that the Henry's law constant is determined at the saturated vapour pressure of the pure solvent ( Psat i H , ).Thus, the Poynting factor corrects for the pressure difference between P sat of the pure solvent (here is the water) and the system pressure P. The partial molar volume of the gas i at infinite dilution (  i  ) can be calculated from a correlation proposed by [START_REF] Vidal | Thermodynamic: "Méthodes appliquées au raffinage et au génie chimique[END_REF]. However, it is fixed here to 32 cm 3 .mol -1 for the majority of the components.

[17] Proposed the following correlation for Henry's constant with temperature

( ) (16)
The coefficients A and B are compiled in Table 2. The temperature is expressed in Kelvins and Henry's constant is given in atmospheres.

Table 2: Constants for calculating Henry's constant [START_REF] John | [END_REF] c) The mole number of gases in the liquid phase:

The mole number of a gas in a liquid is determined by the Eq. ( 17) and the mole number of liquid ( ) is known.

Because, the very good approximations i n and j n << L O H n 2 , and L w L V V  . Therefore, in this case, we can be considered the values i n = 0 during the time calculate j n and vice versa.

Composition of the gases in gas phase

Eq. ( 7) has also been used to determine the total amount of the gas phase in a state corresponding to the three phase hydrate-liquid-vapor equilibrium. In the latter case, the initial values of the variables are to be replaced by the corresponding values measured in that equilibrium state, i.e, 0 T , 0 P , 0 , j y and G 0 n are to be substituted for T, P, j y and G n . The volume of the reactor V R has been replaced by the actual value of the gas phase G V , which for any given equilibrium state has been approximated by: ( )

Utilizing the results from the gas chromatographic analysis we have mole fraction of each gas in composition ( eq i x ). Combine

Results

Discussion

The experimental results of CO 2 and N 2 gases mixtures (Table 3) can be regarded as a good case study at thermodynamic equilibrium. The equilibrium pressure is simulated with a precision of 3,1% and the composition of gas in the hydrate phase is simulated with a precision of 1,04 % for CO 2, and of 24,7% for N 2 respectively.

In a way, this result is surprising when compared to other results presented in Tables 4÷6, because the experimental procedure was used here at high crystallization rate, and we can suspect a non-equilibrium formation regime.

In fact, having a look to Table 4, which gives results from an experiment at high crystallization rate also, but for a different gas mixture CO 2 -CH 4 -C 2 H 6 , we observe that neither the hydrate composition nor the pressure are at equilibrium (in accordance with simulated results).

So, it can be said that the crystallization performed at high driving force can or cannot form hydrate at equilibrium. It depends on the gas molecules.

To be sure that hydrates are formed at equilibrium, we show on Table 5 that it is necessary to use the experimental procedure at low driving force. In that case, the crystallization from the gas mixture CO 2 -CH 4 -C 2 H 6 gives a hydrate composition near from equilibrium, at a pressure which is very well predicted by simulation also. The only exception is that the composition of C 2 H 6 which deviates from modeling is very high whatever the crystallization regime. In our understanding, we consider that bigger molecules such as ethane have a lower mobility in the liquid, and a lower solubility. It can give an enclathratation rate which is not high enough to compete with the smallest molecules and/or the high soluble molecules enclathration rates.

In the last table (Table 7) gives the experimental results concerning the CH 4 -C 3 H 8 gas mixture. The data are not compared to modeling because we did not retrieve the Kihara parameters of propane up to now, which are necessary to model the occupancy of cavities in the classical Van der Waals & Platteeuw model (1959) [START_REF] Van Der Waals | Clathrate solutions[END_REF].

The determination of Kihara parameters is explained in detailed in [START_REF] Herri | Carbon dioxide, argon, nitrogen and methane clathrate hydrates: Thermodynamic modelling, investigation of their stability in Martian at mospheric conditions and variability of methane trapping[END_REF] and [START_REF] Chassefière | The evolution of Venus: Present state of knowledge and future exploration[END_REF]. It implies to extract from experimental data base a single gas equilibrium curve which covers a large enough temperature range. It is the case for N 2 , CO 2 , CH 4 , and C 2 H 6 , but not C 3 H 8 .

For propane, the determination of Kihara parameters implies to extract from experimental data base, the gas mixture equilibrium data, for gases components (except propane) which the Kihara parameters are well known.

But, we need to be sure that the experimental data are really at equilibrium, and we open here a doubt about the difficulty to form a hydrate truly at equilibrium, even by waiting very long time during crystallization as we did for CO 2 -CH 4 -C 2 H 6 mixture without forming a hydrate for which C 2 H 6 composition is at equilibrium. So, for us, at the moment, we are in a main difficulty to be sure to give experimental data in presence of propane at equilibrium. So we cannot propose a simulation in Table 6.

Conclusion

Gas hydrate equilibrium experiments of hydrocarbon gas mixtures (N 2 -CO 2 -CH 4 -C 2 H 6 -C 3 H 8 ) were performed in an instrumented batch reactor. In this study, both classic pressure/temperature equilibrium data but also molar compositions (gas phase and hydrate phase) are given.

 The two procedures used (high and low crystallization rates) highlight the kinetic effect on hydrate formation. For example, the enclathration of the bigger molecule (ethane) is more important at low crystallization rate.

 In the end this work, a modeling part was not added since it is the subject of another work.

In this other work, based on a kinetic consideration [START_REF] Herri | Derivation of a Langmuir type of model to describe the intrinsic growth rate of gas hydrates during crystallisation from gas mixtures[END_REF] there is a questioning about the validity of these measurements as thermodynamic measurements (but as kinetic measurements). This is why the present data were analyzed using a thermodynamic model in an in-house software to discuss the possibility to crystallize gas hydrate at thermodynamic equilibrium at a high crystallization rate [START_REF] Herri | How to explain the hydrate composition from CO2-C1-C2-C3-C4 gas mixtures: toward a kinetic understanding versus thermodynamic and consequences on the evaluation of the kihara parameters[END_REF].

List of symbols

  6 8 cavities[START_REF] Sum | [END_REF]. This hydrate structure forms a hexagonal unit cell.

Figure. 2 :

 2 Figure. 2: Water molecules forming cages corresponding to hydrate structures, sI, sII and sH.

  Clathrate hydrate structures[START_REF] Herri | Gas hydrate equilibria for CO2-N2 and CO2-CH4 gas mixtures-Experimental studies and thermodynamic modelling[END_REF]

  of the chemical potentials between water in hydrate or liquid phase and water in the reference state, respectively.

  order parameter as well. A refinement of the model is given by[START_REF] Sloan | Clathrate hydrates of natural gases[END_REF][START_REF] Sloan | Clathrate hydrates of natural gases[END_REF] that takes into account the temperature dependence of

Figure 5 :

 5 Figure 5: Pressure -Temperature evolution during equilibria experiments at high crystallization rate.

Figure 6 :

 6 Figure 6: Pressure -Temperature evolution during equilibria experiments at high crystallization rate.

Figure 8 :Figure 7 .

 87 Figure 8 : Pressure -Temperature evolution during equilibria experiments at low crystallization rate

v

  is the molar volume of the pure liquid component i (i = solvent) at saturation. The exponential term is called Poynting correction factor. It represents the deviation between the saturated vapor pressure of component i and the equilibrium pressure.

A 1 [v

 1 Coefficient in correlating equation for Henry's law constant, and in Parrish and Prausnitz' equation, respectively B Coefficient in correlating equation for Henry's law constant [K -1 ], and in the Parrish and Prausnitz relation, respectively  Chemical potential of a species or component, Fraction of sites occupied (by a particular species and for a specific type of cavity as indicated by additional subscripts, dimensionless x Mole fraction of a chemical species, dimensionless; L iThe molar volume of the pure liquid component i iThe partial molar volume of the gas i at infinite dilutionCoefficient of fugacityActivity coefficient[-]

Table 3 :

 3 CO 2 -N 2 Clathrate Hydrate equilibrium data. The simulation curve is obtained with the GasHyDyn simulator and compared with the Experimental Equilibrium Data (High crystallization

	rate)
		Experimental Equilibrium Data			GASHYDYN Prediction
	T	P	Gas composition	Hydrate composition	Structure	P	Hydrate composition
	(°C)	(MPa) xCO 2	xN 2	xCO 2	xN 2		(MPa)	CO 2	N 2
	2.3	2.46	0.667 0.333 0.971 0.029	SI	2.53	0.955	0.045
	3.1	2.6	0.689 0.311 0.979 0.021	SI	2.69	0.958	0.042
	3.3	2.66	0.699 0.301 0.978 0.022	SI	2.73	0.960	0.040
	4.3	2.87	0.723 0.277 0.975 0.025	SI	2.99	0.962	0.038
	5.2	3.13	0.747 0.253 0.974 0.026	SI	3.22	0.966	0.034
	6.0	3.38	0.768 0.232 0.971 0.029	SI	3.48	0.968	0.032
			Mean Deviation (%)			%D=3.1 %D=1.04 %D=24.7

Table 4 :

 4 CO 2 -CH 4 -C 2 H 6 Clathrate Hydrate equilibrium data. The simulation curve is obtained with the GasHyDyn simulator and compared with the Experimental Equilibrium Data (High

	crystallization rate)
	Experimental Equilibrium Data		GASHYDYN Prediction
	T	P	Hydrate composition Structure	P	Hydrate composition
	(°C) (MPa) CO 2 CH 4 C 2 H 6		(MPa)	CO 2	CH 4	C 2 H 6
	2.75 3.54 0.144 0.769 0.087	SI	2.72	0.097	0.739	0.164
	3.65 3.81 0.144 0.769 0.087	SI	2.90	0.103	0.717	0.180
	5.15 4.23 0.141 0.774 0.085	SI	3.22	0.106	0.683	0.210
	6.55 4.56 0.141 0.777 0.082	SI	3.64	0.107	0.669	0.224
	7.80 5.12 0.135 0.777 0.089	SI	4.11	0.112	0.662	0.226
	9.25 5.99 0.049 0.804 0.148	SI	4.83	0.127	0.661	0.211
			Mean Deviation (%)		%D=21.7 %D=48.18 %D=11.4 %D=119.2

Table 5 :

 5 CO 2 -CH 4 -C 2 H 6 Clathrate Hydrate equilibrium data. The simulation curve is obtained with

	the GasHyDyn simulator and compared with the Experimental Equilibrium Data (Low
	crystallization rate, 0.1 ÷ 0.3 °C/day)
	Experimental Equilibrium Data		GASHYDYN Prediction
	T	P	Hydrate composition Structure	P	Hydrate composition
	(°C) (MPa) CO 2	CH 4 C 2 H 6		(MPa)	CO 2	CH 4	C 2 H 6
	-	3.775 0.066 0.851 0.083	SI	3.641	0.062	0.843	0.095
	-	3.56 0.085 0.892 0.023	SI	3.512	0.061	0.846	0.093

Table 6 :

 6 CH 4 -C 3 H 8 Clathrate Hydrate equilibrium data. The simulation curve is obtained with the GasHyDyn simulator and compared with the Experimental Equilibrium Data (Low crystallization

	rate, 0.1 ÷ 0.3 °C/day)
		Experimental Equilibrium Data		GASHYDYN Prediction
	T	P	Gas composition	Hydrate composition	Structure	P	Hydrate composition
	(°C)	(MPa)	xCH 4	xC 3 H 8	xCH 4	xC 3 H 8		(MPa)	xCH 4	xC 3 H 8
	5,9	1,08	0,902	0,098	0,809	0,191	SI	-	-	-
	4,8	0,94	0,905	0,095	0,815	0,185	SI	-	-	-
	3,7	0,83	0,910	0,090	0,818	0,182	SI	-	-	-
	2,6	0,72	0,912	0,088	0,823	0,177	SI	-	-	-
	1,8	0,66	0,912	0,088	0,825	0,175	SI	-	-	-
	0,9	0,59	0,914	0,086	0,827	0,173	SI	-	-	-
			Mean Deviation (%)			%D= -%D= -%D= -

Acknowledgements

This work has been supported by the projects: iCap, SECOHYA, ACCACIA and TOTAL-Archimede.

Furthermore, the authors are grateful to all members of the GasHyDyn team for their constant support and to the technical staff members: Fabien Chauvy and Alain Lallemand.