Experimental study of Ignition of Bulk Storage by Hot Points

Keywords:

Fire and explosion risk is generated by chemical or biological oxidation of combustible materials. An experimental study of ignition risk due to hot points in the storage of bulk materials is required to ensure fire safety. Many parameters are involved in this phenomenon: nature of the material, storage volume and temperature, type and size of hot point, etc. The aim of this study is to describe an adapted experimental procedure to determine critical ignition temperatures of powders for different conditions and with several types of hot points. Material selected for this study is a powder of « Lucy coal ». Ignition is carried out in 1000 and 2700 cm 3 cubic baskets for two sizes of inert cylinders at a given temperature and for an inert sphere at a given initial temperature. The critical ignition temperature is defined as the hot point temperature in the middle of a 5°C interval of both temperatures: 1) ignition and 2) no ignition. First results demonstrate that the set-up procedure is relevant. Critical temperatures measured for both cylinders and for the sphere are in the same range. Discrepancies between the results obtained under these three test conditions have been explained by different basket sizes and hot points geometry. Data obtained need now to be compared to available theoretical modelling. These results will then allow predicting material behaviour under other storage conditions.

Introduction and overview

Fire and explosion risk is generated by chemical or biological oxidation of combustible materials. Selfignition concerns exothermic oxidation reactions and occurs when the heat produced by oxidation is greater than that dissipated in the environment by storage surfaces. Then, the temperature increase may lead to a fire, sooner or later. The self-ignition phenomenon depends essentially on three parameters: 1) material temperature, 2) ambient temperature and 3) storage size. Experimental characterization of self-ignition hazards in storage spaces is performed by thermal analysis of the material. Self-ignition tests in isothermal ovens lead to the critical storage size as a function of storage temperature, for a given shape. Test results are extrapolated to industrial scale by modelling using the Frank-Kamenetskii theory. Studies on self-heating were performed in the 1920s by Semenov. They were completed in the 1950s-1960s by Frank-Kamenetskii [START_REF] Franck-Kamenetskii | Diffusion and Heat Transfer in Chemical Kinetics[END_REF].

Semenov considered a homogenous temperature in the whole volume (fig. 1). This model involves geometrical characteristics of storage spaces such as surface area and volume. However, it is not valid for large storage spaces, since it does not take into account the inner and outer thermal gradients of the material. Frank-Kamenetskii theory is more precise. It includes the heat transfer resistance in the material. Frank-Kamenetskii considers that heat transfer is due to conduction inside the material, and is linked to an ideal convection at the outer surface. This model involves geometrical characteristics of the storage space and the thermal conductivity of the material. Frank-Kamenetskii's theory does not take into account the surface heat resistance, unlike Thomas and Bowes's -theory [START_REF] Bowes | Self Heating: Evaluating and Controlling the Hazards[END_REF]. Indeed, Thomas and Bowes consider simultaneously the heat transfer resistance into the material and the surface heat resistance. This model is the most complete and introduces the thermal conductivity of the material, the shape and finally convection and radiation parameters at the interface, using the Biot number ( ). It corresponds to the ratio of conduction and convection coefficients. In the case of heating by a hot spot, the initial heat contribution is not due to self-heating. Particularly four examples can be found in industrial situations [START_REF] Carson | Inflammation des matériaux pulvérulents par sources extérieures[END_REF]:

1. Hot spot of inert material at a given initial temperature introduced into powder storage. It can be metal particles introduced accidentally in a hot storage or mechanical sparks, 2. Hot spot of combustible material at a given initial temperature introduced into powder storage.

This can be linked to a part of the storage locally overheated because of a failure of temperature regulation of a dryer, or even a cigarette butt, 3. Hot spot of inert material maintained at a given temperature. This corresponds to a limit case of the first two points: very high heat capacity of the inert material or reaction rate of the oxidation limited by oxygen diffusion. This could correspond to the case of surfaces heated by outside: welding or an electrical equipment, 4. Hot spot of inert material that generates a constant heat flow. This can be due to electrical devices.

The major difference between the self-heating and the heating by hot spot is the presence of the heat source term, which is different from the chemical oxidation term, in the heat balance.

The objective of the experimental device is to establish the relation between the bulk material storage space size and the temperature of the hot point placed on the centre.

Experimental

The critical ignition temperature by hot spots is determined in 1000 and 2700 cm3 cubic baskets.

Tests are performed into a 125 L ventilated oven, regulated at ambient temperature. The tested material is a coal, so called "Lucy coal" (median particle size: 28 µm; humidity: 0 %). The cubic baskets are made, except their upper face, of 10 µm wire mesh. This is sufficiently fine to avoid sieving, but do not restrain the oxygen diffusion. Hot spots used are:

Cylindrical heating cartridges of 6.5 mm or 10 mm diameter heated by Joule effect and connected to a power supply A steel sphere of 30 mm diameter, preheated in a oven Each test is performed using a clean and dry cubic basket. The amount of coal introduced in the basket is weighted. Then, the coal is introduced into the basket, without compaction.

In the case of heating cylinders, they are introduced into the full basket. Then, six 1 mm Kthermocouples are placed inside the coal on the appropriate locations (fig. 2).

Figure 2: Location of temperature measurement points inside the coal -tests with heating cylinders

In the case of the heated sphere, four 1 mm K-thermocouples are placed into the basket before introduction of the coal sample and the sphere (fig. 3). This prevents the cooling of the heated sphere. The sphere is heated in a furnace regulated at 450°C. When the test temperature is reached, the sphere is then moved over in the full basket.

After the start of the test, the temperatures into the basket are measured as a function of time.

When the temperatures increase dramatically and go over the hot point for at least 50°C, it can be considered that an ignition occurs.

When the temperatures grow up and go over hot point temperature, but stabilize in a plateau at the hot point temperature, ignition does not occur.

The critical ignition temperature is the hot point temperature in the centre of a 5°C interval of the 2 temperatures: 1) ignition and 2) no ignition.

Results

Tests performed appears in tables 1 and 2.

Discussion

The aim of the experimental set-up is to determine critical ignition temperatures of powders under different conditions and with several types of hot points. The first results demonstrate that this protocol is relevant. Critical ignition temperatures obtained for both cylinders and sphere are in the same range. When ignition occurs, the higher the temperature of the hot point, the shorter the induction time, likewise for the delay between the start of the test and the moment at which the nearest thermocouple reached the temperature of the hot point. Nevertheless, the induction time is shorter for the tests with the sphere than for the tests with the cylinders. This result corresponds to the fact that the basket used with the sphere is about three times smaller than the basket used with the cylinders. The critical ignition temperature determined for the larger cylinder is lower than that obtained with the smaller one. This can be explained by the greater amount of energy transfer when the area of the hot point increases, at a given temperature. When no ignition occurs, the temperatures measured evolved as a function of time and always have the same shape. However, the closer the measurement point to the hot point is, the higher the temperature. However, the temperature of the hot point is never reached in the coal, which is believed to always be less than 100 °C. The sample weight does not decrease during these noignition tests, which indicates that no runaway phenomenon occurs.

Conclusion

The aim of this paper was to describe an adapted experimental protocol to determine critical ignition temperatures of powders under different conditions and with several types of hot points.

The first results demonstrate that this protocol is relevant. The critical ignition temperatures for "Lucy coal" powder obtained are:

Between 270 and 285 °C for inert 6.5 mm diameter cylinder at a given temperature in a 2700 cm3 cubic basket Between 265 and 270 °C for inert 10 mm diameter cylinder at a given temperature in a 2700 cm3 cubic basket: Between 270 and 280 °C for inert 30 mm diameter sphere at a given initial temperature in a 1000 cm3 cubic basket:

Discrepancies between the results obtained under these three test conditions have been explained considering basket sizes and hot points geometry. However, other test conditions should be experimented to acquire more data. For example, the ignition using an inert hot point at a given heating flow or using a combustible hot point at a given initial temperature was not tested. These different test conditions will allow the simulation of industrial situations of incident such as the presence of an appliance power supplied or an incandescent particle in a storage space like a silo. It will then be possible to compare data obtained to available theoretical modelling.

Figure 1 :

 1 Figure 1: Shape of theoretical temperatures in Semenov (a) and Frank-Kamenetskii (b) models, from [1]

Figure 3 :

 3 Figure 3: Location of temperature measurement points into the coal -tests with hot sphere

Figure 4 :Figure 5 :Figure 6 :Figure 7 :

 4567 Figure4: 2700 cm3 cubic basket, 6.5 mm cylinder heated at 270°C (TC1 to TC6: see fig.2; TC7: inside oven temperature)

Table 1 . Tests performed with heating cylinders

 1

	N°	Cylinder diameter (mm)	Cylinder temperature (°C)	Basket volume (cm3)	Oven temperature (°C)	Initial weight (g)	Final weight (g)	Loss of weight (%)	Result: ignition ?
	1	6.5	300	2700	27	2030	850	58	yes
	2	6.5	200	2700	27	2030	2030	0	no
	3	6.5	250	2700	27	2030	2030	0	no
	4	6.5	270	2700	27	2030	2030	0	no
	5	6.5	285	2700	27	2030	847	58	yes
	6	10	280	2700	27	2030	865	57	yes
	7	10	270	2700	27	2030	872	57	yes
	8	10	260	2700	27	2030	2030	0	no
	9	10	265	2700	27	2030	2030	0	no

Table 2 . Tests performed with heated sphere

 2

	N°	Sphere diameter (mm)	Initial sphere temperature (°C)	Basket volume (cm3)	Oven temperature (°C)	Initial weight (g)	Final weight (g)	Loss of weight (%)	Result: ignition ?
	10 30	Not measured	1000	27	536	192	64	yes
	11 30	290	1000	27	536	133	75	yes
	12 30	280	1000	27	536	134	75	yes
	13 30	240	1000	27	536	536	0	no
	14 30	270	1000	27	536	536	0	no


Experimental study of CH 4 /O 2 /CO 2 Mixtures Flammability

The oxy-combustion process uses CH 4 /O 2 /CO 2 /H 2 O mixtures at various concentrations, according to the different operation phases. To analyze the risks associated to this process, the safety characteristics of these explosive mixtures have to be taken into account. A literature review showed that some safety features of methane in oxygen or in air were not available. Thus, the flammability ternary diagram of CH 4 /O 2 /CO 2 mixtures was determined at room temperature and 1 bar pressure. Furthermore, the influence of oxygen content on the explosion severity (Pmax; dP/dt) was investigated. The ternary mixtures were prepared directly in a 20 L spherical test vessel. The concentrations of reactants were adjusted using the relationship between the partial pressure and the molar fraction of gas. The ignition source used was an alumel fusing wire. The flammability limits of methane in oxygen were extrapolated at 5 and 68% vol., by using the established CH 4 /O 2 /CO 2 mixtures ternary diagram. It also confirmed that when the carbon dioxide concentration increases, the flammability range decreases: no ignition was observed when carbon dioxide content exceeded 73%. A significant influence of the oxygen concentration on the explosion severity has been highlighted for CH 4 /O 2 /CO 2 mixtures containing respectively 10, 25, 45 and 65% vol. of carbon dioxide. The maximal explosion overpressure and the maximum pressure rise were both measured near the stoechiometry. Maximum values of Pmax and dP/dt measured for a 10% vol. carbon dioxide concentration were 11.2 bar rel. and 5904 bar/s respectively, while they were 3.6 bar rel. and 72 bar/s respectively in the case of a 65% vol. carbon dioxide content in the mixture.

Introduction

This study is part of a whole study intended to highlight the technological constraints and risks associated with the oxy-combustion process, to prevent incidents and accidents that could affect its technological development. This process uses CH 4 /O 2 /CO 2 mixtures for varying concentrations, depending on different operation phases. This paper aims to establish the explosion characteristics of these mixtures, since only a part of them are available in the literature [START_REF] Zabetakis | Flammability Characteristics of Combustible Gases and Vapours[END_REF] to [START_REF] Qin | Oxygen Composition Modulation Effects on flame Propagation and Nox formation in Methane/air Premixed flames[END_REF]. In this study, the flammability diagram of CH 4 /O 2 /CO 2 mixtures is determined at room temperature and 1 bar pressure, in a 20 L spherical vessel. Furthermore, the influence of oxygen concentration on explosion characteristics Pmax and (dP/dt) is investigated.

Experimental

The ternary mixture is prepared directly into the test vessel. Its composition is calculated and measured by the relationship between partial pressure and molar fraction of gas. Indeed, the mole fraction of each component can be determined by measuring the pressure in the vessel after each addition of gas. Firstly, a partial vacuum below 40 mbar is obtained in the vessel, then CO 2 , CH 4 and O 2 are successively added, up to 1 bar absolute. Before each test, the circuit and the chamber are purged with air. In addition, a control for absence of leakage is made once the partial vacuum is established in the vessel. The test vessel used is a 20 L steel spherical vessel (fig. 1). It is equipped with gas inlets for introducing inert gas, fuel, oxygen and compressed air. The ignition source used is a 0.1 mm diameter alumel fusing wire, disposed in the center of the vessel. The ignition is controlled electronically. This ignition source is consistent with that described in standard [START_REF]Determination of the maximum explosion pressure and the maximum rate of pressure rise of gases and vapours[END_REF]. Measuring equipment implemented includes a piezoresistive static pressure sensor and two piezoelectric dynamic pressure sensors.

Results

flammability ternary diagram

The results obtained at 1 bar are shown on the ternary diagram (fig. 2

flammability characteristics of O 2 enriched mixtures

The influence of oxygen concentration on the explosion severity was highlighted. The results of Pmax and (dP/dt) appear in Table 1 below. The two figures below (fig. 3 and4) represent the evolution of the overpressure and the rate of pressure rise, for the different concentrations of inert gases tested.

Discussion and conclusion

Determination of the flammability characteristics of binary CH 4 /O 2 mixtures was not performed, since the vacuum obtained is partial and a minimal amount of N 2 is always present in the vessel. However, we can estimate by extrapolation LEL and UEL of methane in oxygen to be 5% and 68% respectively. In this diagram, we also noted that when the CO 2 concentration increases, the severity decreases. No ignition was observed when carbon dioxide content exceeded 73%. The two graphs exposed highlight the significant influence of oxygen concentration on the violence of explosion. The explosion pressure and rate of pressure rise are highest near the stoechiometry. Elevated CO 2 concentration significantly reduced the explosion severity. Maximum values of Pmax and dP/dt measured for a 10% vol. carbon dioxide concentration were 11.2 bar rel. and 5904 bar/s respectively, while they were 3.6 bar rel. and 72 bar/s respectively in the case of a 65% vol. carbon dioxide content in the mixture.

Figure 1 :

 1 Figure 1: 20 L sphere

  ). On this figure, the summit represents a pure component. The sides of the triangle represent mixtures reduced to two components. Orange points label the compositions where an explosion was observed, whereas white points represent the compositions for which no explosion took place. The right straight indicates stoechiometric CH 4 /O 2 mixtures. Gradually, the yellow area was determined, which represents the compositions of flammable CO 2 /CH 4 /O 2 mixtures. The red crosses indicate the points on which the explosion characteristics of oxygen-enriched mixtures are measured.

Figure 2 :

 2 Figure 2: experimental flammability ternary diagram

Figure 3 :Figure 4 :

 34 Figure 3: Evolution of the overpressure depending on the mixture composition

Table 1 : Influence of oxygen concentration on the explosion severity

 1

		Molar Composition (%)			Results
	CO 2	CH 4	O 2	Pmax (bar rel.)	(dP/dt) (bar/s)
	63.50	9.68	26.82	3.4	44
	64.84	10.91	24.25	3.5	52
	65.31	12.01	22.67	3.6	72
	65.16	14.30	20.54	0	0
	44.90	9.80	45.30	5.8	110
	45.17	11.21	43.62	6.5	254
	45.07	13.90	41.02	7	506
	45.00	15.90	39.10	7.6	638
	44.86	17.90	37.25	7.5	754
	45.39	18.82	35.79	6.9	656
	45.02	19.90	35.08	7.2	636
	25.08	19.88	55.04	9.6	3080
	25.07	23.92	51.01	10.1	2742
	25.11	25.00	49.89	10.4	3918
	25.04	25.85	49.11	9.3	2296
	10.03	28.00	61.97	11.3	5904
	10.01	28.97	61.02	11.1	5720
	10.14	30.03	59.83	11.2	5692
	10.14	31.93	57.93	10.5	5046


Stéphane Pagnon
email: stephane.pagnon@ineris.fr

Ineris

Bony-Dandrieux Aurelia
email: aurelia.bony-dandrieux@mines-ales.fr

Tixier Jerome
email: jerome.tixier@mines-ales.fr

Sensitivity Analysis of Atmospheric Dispersion Modeling In Emergency Situation

Keywords: emergency, atmospheric, dispersion, sensitivity

Each day, accidents involving hazardous materials are managed by Emergency Services. In order to bring the best adapted operational answer, it is necessary to determine with accuracy the concentrations of the gas to which people will be exposed. The expert in charge of modeling is facing a major difficulty: few (or no) information. Therefore, for a given situation, the generation of different effect distances is possible.

A sensitivity analysis was carried out in order to determine the most influential parameters on the estimation of safety distances. The goal is to identify the parameters for which it is necessary to pay a very detailed attention.

The first step of the study was to define the system to be analyzed. The second step consisted in working out a complete model of evaluation of safety distances in emergency situation. This was done by combining an existing dispersion model (SLAB) with a specifically developed application for the calculation of input parameters. The input data are operational data which can be collected from the accident site and the output data are safety distances. The third step consisted in selecting two test cases representative of an accident situation involving hazardous chemicals (leak on a wagon of ammonia and a wagon of propane). After that, it was characterizing the range of possible values of the whole input parameters. A fourth step consisted in applying two methods of sensitivity analysis: a screening method (MORRIS's method) and a local sensitivity analysis. Finally, the application of these methods, on the same case study, made it possible to highlight the points of convergence of the methods and their advantages. Finally, the parameters for which it is useless / useful to initiate considerable efforts to recover a reliable value were highlighted.

1.

INTRODUCTION

Every day, accidents or pre-accidents involving hazardous materials or chemical processes are managed by Emergency Services. These accidents can cause air pollution. For each phase of an emergency situation (threat, accident, post-accident), in order to bring the best adapted operational answer, it is necessary to determine with accuracy the concentrations of gas to which people will be exposed.

The expert in charge of modeling is facing a major difficulty: few (or no) information to characterize the situation. Therefore, for a given situation, information transmitted (or parameters taken by default in order to complete missing information) may differ dramatically. The result is the generation for a same situation of different effect distances.

An analysis of sensitivity was carried out in order to determine the most influential parameters on the estimation of safety distances. The goal is to identify the parameters for which it is necessary to pay a very detailed attention, either in obtaining a value, or in the choice of a default value, or in its treatment.

The first step of the study was to define the system to be analyzed.

The second step consisted in working out a complete model of evaluation of safety distances in emergency situation. This was done by combining an existing dispersion model (SLAB) with a specifically developed application for the calculation of the input parameters of the dispersion model. The second objective of this model was also to automate calculations for the sensitivity analysis described in the present paper. The input data of the model are operational data which can be collected from the accident site and the output data are safety distances corresponding to effect thresholds. Keeping in mind that this model must be used in emergency situations, three principles were adapted: minimize the number of input data, select methods and models having fast computing times but describing as accurately as possible each physical phenomenon.

The third step consisted in selecting test cases representative of an accident situation involving hazardous chemicals. Two accident scenarios were studied: leak on a wagon of ammonia (toxic liquefied gas) and leak on a wagon of propane (flammable liquefied gas). After that, it was possible to characterize the range of possible or probable values of the whole input parameters needed to make calculations.

A fourth step consisted in applying to this system two methods of sensitivity analysis: a screening method (MORRIS's method) and a local sensitivity analysis.

BACKGROUND

Methods of sensitivity analysis

There are mainly three types of methods for sensitivity analysis:

• Screening methods: qualitative methods that reduce the number of input parameters of a model by identifying the most influential parameters on the output [START_REF] Bettonvil | Searching for important factors in simulation models with many factors: Sequential bifurcation[END_REF] [2] [3] [START_REF] Morris | Input screening: Finding the important model inputs on a budget Reliability Engineering & System Safety[END_REF]. They are used when the number of input parameters is significant in order to reduce the computation time. • Local sensitivity analysis: quantitative methods based on the calculation of a sensitivity index representative of the model output variations due to a small change of one input parameter [START_REF] Turányi | Local Methods[END_REF]. These methods are simple and fast, but appear insufficient to characterize the sensitivity of complex models. Indeed, local sensitivity analysis does not take into account interactions between parameters [START_REF] Saltelli | How to avoid a perfunctory sensitivity analysis Environmental Modelling & Software[END_REF]. • Global sensitivity analysis [START_REF] Saltelli | Sensitivity Analysis Wiley[END_REF] [8]: quantitative methods for determining the variables that contribute most to the variability of the model response. Unlike local sensitivity analysis, these methods can take into account the density of probability of each input variable and they treat the variation of all parameters simultaneously.

MORRIS's method

The MORRIS's method [START_REF] Morris | Factorial Sampling Plans for Preliminary Computational Experiments[END_REF] [10], better known as the elementary effects method, is the best known screening method. It gives an idea of how the model is answering to potential changes of input parameters. This method allows a rapid identification of influential parameters among a large number of input variables. The influence of each factor input is studied by an approach OAT (One at A Time), that is to say only one factor varies while the others remain fixed. MORRIS's method is useful for identifying potentially influential inputs by dividing them into three groups:

• negligible effects (1)

• linear effects (2)

• nonlinear effects and / or with interactions (3)

Figure 1 : Example of graph (a, ju)

To determine these three groups, two sensitivity parameters are provided for each factor input: ju and a where ju represents the influence of an input factor on the outcome of the model and a the nonlinear effects and/or the interactions between factors.

[Eq . r -

7 = 1
representing the elementary effect of each factor input.

Practically speaking: fi is in fact the mean value of diand cris its standard deviation.

Let k be the number of factors, each varying within [0; 1], andp the number of divisions of equal values of the interval [0, l/(p-l),...., 1-1/(p-1), 1]. For each factor, we select r values, generally between 4 and 10, which give r original points. The work of Franco et al [START_REF] Francos | Sensitivity analysis of distributed environmental simulation models: understanding the model behaviour in hydrological studies at the catchment scale Reliability Engineering & System Safety[END_REF] showed that with r = 4 a good ranking of input parameters according to their influence on the final outcome is reached. On the graph below, it can be observed that the relative hierarchy of variables based on the value of ju remains unchanged for a value of r between 4 and 8. Then, from each of these points, we construct a trajectory by varying the parameters one by one from A where A = p / [2 (p-1)] to ensure an equal probability of sampling in the input space. Each trajectory consists in(k+1) points, a factor ranging from// at each stage while all others remain fixed. This brings the number of simulations with n=r (k+1).

2.1

Local sensitivity analysis The local analysis methods are based on the calculation of a sensitivity index showing the variations of model output due to a slight variation of a parameter input. The advantages and disadvantages of these methods have been presented in the following document [START_REF] Frey | Identifcation and review of sensitivity analysis methods Risk Analysis[END_REF].

Mathematically, consider a model which is written: Y=f(X1, X2,..., Xk) where Y is the response of the model and Xi, i e [l,...,k] are the input parameters, each varying in a given interval with a nominal value Xi0. The sensitivity S i of the response to a low amplitude variation of the parameters Xi corresponds to the partial derivative S i = dY/dXj. For a complex model,fis a function for which we cannot calculate the partial derivatives. Thus, the criterion of sensitivity S i can be approximated by the expression : S i = AY/AXj, where AX t is the difference between the value of X i in the interval and its nominal value X i0 , and AY is the difference between the model response at X i , Y=f(..., Xj,...J, and the nominal response atXi0, Y0 = f(-, Xw,-X other input parameters are fixed at their nominal value. However, in order to be able to rank the input parameters according to the model's sensitivity, it is more appropriate to use a dimensionless formulation of the sensitivity criterion, such as: Si = (Xw/Yo)/(AY/AXj), which is equivalent to calculating the ratio of the relative variations [START_REF] Chokmani | Analyse de l'incertitude de quatre modèles de phytoprotection relative à l'erreur des mesures des variables agrométéorologiques d[END_REF].

IMPLEMENTATION OF THE METHOD

3.1

Step 1: define the system to be analyzed The analyzed system can be defined by the definition of its input and output variables:

• Input data: the input data for the analyzed system are operational data retrieved from the accident site.

• Output data: the output of the studied system will not be gas concentrations but effect distances corresponding to two different effects (lethal and irreversible). Step 2: selecting test cases

The principle of sensitivity analysis is to study the model response in a field of input parameters values as large as possible. However, even in this case, it is necessary to fix a number of parameters.

The first one is the chemical. In the case of a leak, two main effects are feared: toxic and explosive effects. It was therefore chosen two fluids: one explosive, the other toxic. This chemical may, under normal conditions, be either liquid or gaseous. In most cases, the mass flow rate generating the cloud is more important in the case of a leak of gas than in a case of liquid layer evaporation. It was therefore decided to study a fluid, which under normal pressure and temperature, is in a gaseous state. Finally, based on the two criteria defined above (type of risk and physical state), the chosen gases must be common enough to be statistically representative of the toxic and explosive risk. Based on these criteria, it was finally decided to study specifically accidents involving rail transport of propane and ammonia.

Step 3.a: working out a complete model of evaluation of safety distances in emergency situation

In order to assess quantitatively the variability of atmospheric dispersion simulations based on input provided by the emergency services, a complete model was built. Keeping in mind that this model should be used in emergency situation, we tried to minimize the number of input data, to select methods and models with time fast calculations. However, selected models will recreate as faithfully as possible the physical phenomena they are supposed to model.

Calculation of input data: mass flow rate

The calculation is done in 3 steps. The first step is to evaluate the mass flow directly out of the release hole (D). The second step is to determine the rate of thermal flash (X). The final step is to determine the rate of spray aerosols D.( X+K).

Evaluation of the initial mass flow rate (D) and thermal flash (X)

There is a low diversity of formulas for evaluating the initial mass flow and initial thermal flash. The initial mass flow rate (D) is evaluated using an evolution of the Bernouilli's formula [START_REF]RIVM Yellow book -Methods for the calculation of physicals effects -CPR 14E TNO[END_REF] [START_REF]UIC Emission à la brèche d'une capacité débit en phase gazeuse débit en phase liquide formation et vaporisation des flaques UIC[END_REF]. The initial thermal flash is determined thanks using a classical isenthalpic expansion formula.

Determination the rate of spray aerosols (K)

It is an uneasily quantifiable parameter. Many empirical methods are offered. These correlations are based on results from observations of experiments with different chemicals and configurations. Each formula should, in theory, be applied only to configurations similar to its development. These formulas are simple to use but very dependent on the rate of thermal flash. Moreover, these methods are mostly independent of the configuration of release (direction, height, pressure). The VTT method [START_REF] Lautkaski | Experimental correlations for the estimation of the rainout of flashing liquid releases-Revisited[END_REF] was chosen because results from recent and comprehensive testing.

Atmospheric dispersion

The atmospheric dispersion codes can be classified into three categories: Gaussian models, integral models, CFD models. In order to respond quickly with a good scientific level, integral models seem currently the most appropriate models according to emergency situation specificities.

SLAB software, available on the website of the U.S. Environmental Protection Agency, meets the requirements of this research work. SLAB is an executable code that reads a text file as input and generates an output text file. This code has no interface which facilitates the automation of calculations.

The SLAB model [START_REF] Ermak | User's Manual for SLAB: An atmospheric dispersion model for denserthan-air releases Lawrence Livermore National Laboratory[END_REF] is an atmospheric dispersion model of integral type, initially based on the concept of air entrainment in a heavy gas cloud and on the effect of subsidence due to its gravity [START_REF] Zeman | The dynamics and modeling of heavier-than-air, cold gas releases[END_REF]. Coding and computer developments have been made by Ermak and Chan [START_REF] Ermak | A survey of denser-than-air atmospheric dispersion models Lawrence Livermore National Laboratory[END_REF] [17] at the Lawrence Livermore National Laboratory, USA. SLAB can be used for point or surface sources, and for instantaneous or continuous releases. The calculation of the cloud geometrical evolution by SLAB model is shown in figure below. The SLAB model predicts, along the axis of movement, the cloud geometric characteristics (the size of the plan) and concentration fields.

Wind spud U»

Figure 4 : Calculation of the cloud evolution by the integral method

Calculation of output data: effect distances

The toxic effect distances were obtained by comparison of concentration fields with threshold values for acute toxicity (example: threshold values for acute toxicity or VSTAF in France). The selected effects are irreversible and first lethal effects (LC1%). The overpressure effect distances were obtained by application of the multi-energy method [START_REF]RIVM Yellow book -Methods for the calculation of physicals effects -CPR 14E TNO[END_REF].

3.4

Step 3.b: choosing input variables and interval of variation Based on the constructed model, a minimum list of input data sufficient to describe correctly the situation can be established: The ratio of specific heats Table 1 : List of input variables In this list, stability class and wind speed are strongly dependent. This dependence is particularly highlighted in the method of estimating the stability class determined by Turner [START_REF] Turner | Workbook of Atmospheric Dispersion Estimates EPA Office Air Prog. Rep[END_REF]. In order to avoid irrelevant meteorological conditions, we used the method described in the Yellow Book 2nd Edition [START_REF]RIVM Yellow book -Methods for the calculation of physicals effects -CPR 14E TNO[END_REF] to determine the sets of meteorological parameters grouped by period of the day and season.

3.5

Step 4: coupled sensitivity analysis

It was decided to conduct the sensitivity study using a screening method called MORRIS's method. With a minimum number of experiments, this method allows to assess the sensitivity of each variable on its entire domain.

The results obtained by the MORRIS's method are graphically analyzed. Based on the graphic (jU, a), it is not trivial to estimate quantitatively the sensitivity of a parameter. That's why the MORRIS's method is coupled with a local sensitivity analysis. This local sensitivity analysis has two objectives: confirm (or invalidate) the sensitivity level of tested parameter, analyze continuity and monotonicity (increasing or decreasing function) of the model response to the input variable tested. The research strategy defined above is illustrated in the following flow chart:

RESULTS OF THE SCREENING METHOD

Screening on all variables

In a first step, a series of tests was conducted using the MORRIS's method with all input variables. A first classification of input parameters according to their influence was established. Globally, it was found that the radius of the hole was the most influential parameter. This first result provides little information as it confirms existing literature [START_REF] Pandya | Analyse de sensibilité paramétrique d'un outil de modélisation des conséquences de scénarios d'accidents. Application à la dispersion atmosphérique de rejets avec le logiciel Phast[END_REF]. In a second step, the hole radius was excluded from the sensitivity analysis in order to allow the identification of parameters whose influence could be hidden. Two hole radius values were used: the lower bound (representative of a seal leak) and the upper bound (representing a full bore rupture). At each fixed value is corresponding an experimental sub domain. The MORRIS's method is applied to each sub domain.

4.2

Screening with fixed hole radius 4.2.1 Ammonia A total of six cases have been studied using the MORRIS's method. To each case, the variables listed in table 2 We calculated (i to classify, for the same case, the parameters into three groups according:

• Green Zone: negligible if JU < 1/3 ju max

Summary of results obtained with the method of screening

The screening method has allowed us to identify unambiguously a certain number of points:

• Height of liquid (above the hole): this parameter, in the case of liquefied gas, has no real importance, • Discharge height: this parameter, in the case of toxic liquefied gases and within the studied range (0-3 m), has no real influence on the estimate of effect distances. This result is probably due in part to the modeling assumptions. First assumption: in order to take into account the non-prior knowledge of the height of a potential receiver, the concentration of gas at a maximum of 2 m above ground, is evaluated in the axis of the plume. Therefore, within the studied interval of height of release (0 to 3 m), the inhaled concentration is always calculated in the axis of the plume. Second assumption: the empirical formula used for the determination of spray aerosol does not take into the height. In fact, physically, the height of release is influencing this rate. If the release is high, the quantity of liquid on the ground is decreasing (fall time and evaporation time are longer). • Mass initially contained in the vessel: o Flammable gas: the mass contained in the vessel (within the range studied) does not affect the distance effect. The shape of the explosive cloud is stabilizing very quickly (about one minute). Therefore, the duration of leak (and thus the mass of product) has very little influence on the dispersion calculation. o Toxic gas: the duration of complete drainage, in case of small leak, is more than an hour (in fact several hours) and, in case of a full bore rupture, is less than one hour (about 15 minutes). The maximal duration of leak is assumed to be equal to one hour (making the assumption that the emergency services can stop the leak in this time interval), the mass contained (within the range studied) is influential in the case of a rupture but not in the case of a leak. • Meteorological parameters (wind speed, cloud cover, temperature): these variables are always influential. More precisely, the meteorological variables (cloud cover and wind speed in some cases) that enable the estimation of the stability class are more influential than others (temperature and wind speed in other cases).

• Multi-energy index: in the case of a flammable gas, multi-energy index is THE most influential parameter.

Other results are equivocal: some parameters, such as roughness height, generate for close configurations very different results. These equivocal results may be due to interactions between parameters.

Beyond these equivocal results, the results, obtained with the MORRIS's method, are analyzed graphically. It is not possible, from the graphics (a, |i), to estimate quantitatively the sensitivity of a parameter. Therefore, this first analysis is completed for each influential variable with a local sensitivity analysis.

RESULTS OF THE LOCAL SENSITIVITY ANALYSIS

Construction of experimental design

Implement local sensitivity analysis requires the information of a vector of input data defining a "optimal" situation. As before, we have considered three distinct periods: summer day, winter day and night. To highlight, for a given variable, the most sensitive areas in its range of values tested, a new sensitivity index Sl is built. The X variables are standardized as follows: X* = (X-X min )/(X max -X min ). For a given parameter, this index is based on the amplitude of the response Y on the entire range tested:

Sl = |(Y(X i+1 )-Y(Xi))/(X* i+1 -X*i)).(1/(Y max (X)- Y mi n(X)))|.
The interpretation of this parameter is intuitive. Indeed, if we consider an average influence of the tested parameter on its entire range of variation, a part of interval of X with:

• a value of Sl < 1 characterizes an area less influential than average,

• a value of Sl > 1 characterizes an area more influential than average. According to figures 12 and 13, it appears that hole size has a monotonically increasing influence on the effect distances. Its influence is decreasing beyond a threshold between 10 and 15 mm. One explanation is possible: for a given initial mass, if the radius is increasing, the release rate is increasing but the duration of discharge is decreasing. The dose calculation is incurring a double contradictory influence. According to figures 14 and 15, it appears that wind speed has globally an increasing influence during the day (increasing stability) and a decreasing influence during the night (decreasing stability and increasing cloud dilution). Specifically, during the day, it appears that an increase of wind speed generates two conflicting effects: increasing the stability, which leads to increased effect distances, and increasing the dilution, which leads to decreased effect distances. For wind speeds above 6 m/s, the stability classes remaining constant (D for day and night), the influence of wind is negligible.

Ammonia

Propane

The same work was done for propane. It will be presented in detail in a future paper. Among the main results, we can mention the predominant effect of the choice of the multi-energy index.

Summary of results obtained with local sensitivity analysis

Local sensitivity analysis has enabled to:

• Characterize, for a given variable, how the distance is influenced by this variable: o monotonic / non-monotonic function (example : roughness for ammonia), o continuous / non-continuous function (example: cloud cover), o constant influence (example: temperature) / non-constant (example: multienergy index). • Evaluate, in an easily understandable way, the magnitude of possible changes in results due to variation of one input parameter (example: lethal effect distances with multi-energy index of 6 / lethal effect distances with multi-energy index of 3 = +00). • Confirm the existence of variables with a complex influence on the final result (example: roughness height). There are probably interactions between this variable and other input variables or with the concentration value associated with the desired effect.

DISCUSSION AND CONCLUSION

The two cases studied were an accident on wagon carrying ammonia or propane (toxic liquefied gas / flammable liquefied gas).

The sensitivity analysis has allowed the detection of certain types of influence on the final result:

• Never influential variables: o Liquid height: Logical result because the flow in the case of LPG, mainly depends on internal pressure and not on hydrostatic pressure. o Release height (above 1 m): Logical result according to the chosen computational hypothesis. Between 0 and 1 m, the sensitivity is increased probably due to an interaction of release height with the roughness height.

• Always very influential variables:

o Wind speed and cloud cover. These two parameters are always very influential. Indeed, the wind speed is an important factor in the mechanism of atmospheric dispersion. But it is also involved in determining the atmospheric stability class in combination with the cloud cover. o Multi-energy index for flammable gas.

• Always influential variables: Temperature. Temperature is always influential and has an increasing influence on effect distances. The most likely explanation is that in case of a liquefied gas, for a same hole (shape, size and location) the mass flow is mainly depending on the internal pressure. In the case of transportation of LGP, this internal pressure can be assimilated to the saturated vapor pressure which is very sensitive (globally increasing exponentially) to the fluid temperature (equal to ambient temperature in our case). • Influential but not decisive variables: Total initial mass in the vessel. For a flammable gas, the total mass of fluid in the vessel has no influence (within the range studied). This is due to the fact that the shape of gas cloud is reaching very fast its steady state. For toxic gas, if the maximal duration of leak is assumed to be equal to one hour (to take into account the response time of emergency services), the mass contained (within the range studied) is influential in the case of a full bore rupture but not in the case of a leak. • No monotonic influence variables: Roughness. It was not possible to highlight a simple behavior of the model in function of the roughness value (which however has not a negligible influence).

The sensitivity analysis has another interest: it allows the detection of implicit assumptions used by the software (example: rain-out independent of the height of release). For a model of the same family, we can assume that the classification of the input variables according to their influence would be identical to that presented in this article.

This work is allowing the development of a first operational classification of input variables:

• Variables with little or no influence for which it is possible to set a fixed value by default (example: height of liquid above the hole). • Influential variables for which : o A precise value can be obtained easily (example: wind speed, temperature). o The recovery of value can (or must) be improved (example: cloud cover). o A deterministic approach may not be satisfactory. These are the variables for which the recovery of a reliable value is very difficult (example: size of gap) or with a non monotonic influence (example: roughness). For these variables, a possible solution might be to use intervals of expected values and simulate a suitable set of cases. A final step would be to provide to the crisis manager an operational result on the basis of all modeling performed.

Finally, future developments can be proposed like, for example, an extension of the experimental field for the local sensitivity analysis. Some areas of variations could be reviewed (example: minimum temperature closer to the boiling temperature of the product).

Figure 2 :

 2 Figure 2 : Evolution of the average influence of variables based on the number of trajectory (r)

Figure 3 :

 3 Figure3: Characterization of the system to be analyzed3.2Step 2: selecting test cases

Figure 7 :

 7 Figure

Figure 8 :

 8 Figure 8 : Graph (a, jU) Irreversible effect distances

Figure 9 :

 9 Figure 9 : Graph (o, /l), case 2We calculated (i to classify, for the same case, the parameters into three groups according:• Green Zone: negligible if JU < 1/3 ju max

16 Figure 10 :Figure 11 :

 161011 Figure 10 : Graph (a, ju), case 7

  For each experimental sub-domain, ({ammonia} x {summer (day) ; winter (day) ; night} x {little leak ; rupture}), the evolution of effect distances and local sensitivity indices based on the variation of each input parameter were estimated. Examples of results obtained are given below:

Figure 12 :Figure 13 :

 1213 Figure 12 : Ammonia, radius variation, effect distances

Figure 14 :Figure 15 :

 1415 Figure 14 : Rupture, ammonia, wind speed variation, effect distances

Win*, -s Intermediate Data Rixqu £|4KB -S SYSTEM L*SviH* antes input data recovered from Output drt* ; Data for mathematical

Table 2 :

 2 Intervals of variation of input variables

Table 3 :

 3 were sampled in their appropriate intervals. These cases are listed below: List of sub-cases for ammonia Examples of graphs (jLi, o) are given below:

	Product	Period	Type of Release	Case
	Ammonia	Night	Leakage	1
			Rupture	2
		Spring-Summer	Leakage	3
			Rupture	4
		Autumn -Winter	Leakage	5
			Rupture	6

Table 4 :

 4 The results are shown in the tables below: Influence of parameters in case of leakage, NH[START_REF] Deana | Comparison of group screening strategies for factorial experiments[END_REF]

	•	not to be overlooked if 1/3 fi max < JU < 2/3 ju max
	• Red Zone: very influential if /u > 2/3 /u max

Table 5 :

 5 Influence of parameters in case of rupture, NH3

	4.2.2 Propane
	A total of six cases have been studied using the MORRIS's method. These cases are listed
	below:
	Product	Period	Type of Release	Case
	Propane	Night	Leakage	7
			Rupture	8
		Spring-Summer	Leakage	9
			Rupture	10
		Autumn -Winter	Leakage	11
			Rupture	12

Table 6 :

 6 List of sub-cases for propaneExamples of graphs (jU, 0) are given below:

not to be overlooked very influential

	Propane
	rupture
	Irrev.
	Effect
	Dist.
	AP
	(50
	mbar)
	Lethal
	Effect
	Dist.
	AP
	(140
	mbar)
	Propane	day			night
	leak	negligible		negligible	not to be overlooked	very influential
	Irrev. Effect Dist. AP (50 mbar)	Mass Liquid height Temperature Release height Roughness Wind speed Cloud cover	Multi-energy index	Mass Liquid height Roughness Cloud cover, Temperature Release height	Wind speed	Multi-energy index
	Lethal Effect Dist. AP mbar) (140	Mass Liquid height Roughness Wind speed Temperature Release height Cloud cover	Multi-energy index	Mass Liquid height Roughness Wind speed Temperature Release height Cloud cover		Multi-energy index

Table 7 negligible

 7

	: Influence of parameters in	case of leakage, propane
	day			night
	not to be overlooked	very influential	negligible	not to be overlooked	very influential
	Mass		Mass
	Liquid height		Liquid height
	Temperature Release height Cloud cover	Multi-energy index	Temperature Release height Cloud cover		Multi-energy index
	Wind speed		Wind speed
	Roughness		Roughness
	Mass		Mass
	Liquid height		Liquid height
	Temperature Release height Cloud cover	Multi-energy index	Temperature Release height Cloud cover		Multi-energy index
	Wind speed		Wind speed
	Roughness		Roughness

Table 8 :

 8 Influence of parameters in case of rupture, propane

Table 9 :

 9 Table of values used for local analysis


Chabane Mazri
email: chabane.mazri@ineris.fr

Aleksander Jovanovic

Daniel Balos

Descriptive Model of Indicators for Environment, Health and Safety Management

Management of systems requires, amongst many other things, a thorough and continuous understanding of the actual system's state and its development trends. To do so, managers need to rely on both descriptive and explicative models of the system's strengths and weaknesses. One of the means to do so are indicators. Widely developed in all areas of management (financial, economic, logistics), Environment Health and Safety (EHS), seen by management science, are also to be approached using indicators. One can find in literature multiple references and guidelines on how to develop and/or use indicators for EHS management. Without being exhaustive, OECD, IAEA, and CCPS are examples of well known international guidelines suggesting indicators for various or specific business areas regarding all or some of the EHS dimensions. In this paper, we will see that it is particularly difficult for decision makers to select the right indicators for their organization amongst dozens of various references and hundreds of indicators. We will also see that the main difficulty in this selection process is the multiple dimensions to be considered when assessing the relevance of an indicator.

As a first answer, this paper will suggest a formal descriptive model of an EHS indicator. This model will present what we consider as necessary descriptive features for every EHS indicator so to help decision makers answering a simple question: is this indicator good or not for my organization?

Introduction

Indicators can be defined as subjective mental constructions aiming to capture one or several aspects of reality considered of importance when it comes to a specific subject [START_REF] Mazri | Set of Key Performance Indicators related to emerging risks[END_REF]. In our particular case, the specific objects are the EHS performances of industrial systems already characterized in literature as complex [START_REF] Hopkins | Thinking about process safety indicators[END_REF].

In other words, one can say that we are using subjective and very partial tools to approach complex systems that may threaten huge human, environmental and economic stakes. Once we said that, the reader can easily understand that using and interpreting indicators should be handled very carefully. Consequently, managers, being in charge of defining, using and interpreting those indicators in everyday EHS management need to be supported so to avoid multiple potential misuses already well acknowledged in literature [START_REF] Wiedemann | Risk and sustainability : Mutual lessons from approaches to the use of indicators[END_REF]. In order to provide this decision support, this paper will first describe more in depth the challenges and opportunities related to the use of EHS indicators. From that, core issues to be resolved when selecting indicators will be deducted. Finally, we will suggest a descriptive model to be used by managers to fully describe an indicator, and thus, support them in selecting an adequate set of EHS indicators.

EHS indicators: challenges and opportunities

Indicators are meant to provide a synthetic and action oriented knowledge. Those potentialities offer interesting opportunities for EHS managers that can be synthesised as follows.

Improve monitoring frequency

By providing regularly an updated description of the system, indicators allow managers to refresh their system's representation. Actually, safety reports required by Seveso directive provide, or at least should, a thorough but static description of the system generating the risk. This description is a fundamental starting point to identify and correctly shape both technical and organizational devices for risk management. Nevertheless, this description can be quickly overwhelmed by multiple explicit and/or hidden evolutions of both technical and organizational dimensions of the systems. For instance, gaps between official procedures and real practices are classical deviations that can challenge hypotheses and conclusions adopted within the safety report. By implementing relevant indicators, those gaps can be detected and either the practices or the procedures be corrected.

Make better use of information already collected for other purposes

Survival of organizations rely on their ability to collect in a systematic and organized way the information and knowledge about its environment on one hand and their own performances on the other hand. Therefore, a great amount of information is usually collected by organizations for various purposes: quality management, financial management, human resources management... As stated in [START_REF] Hse | Developing process safety indicators. A step by step guide for chemical and major hazard industries[END_REF], developing relevant safety indicators helps rationalization of information management by avoiding collection of useless information and making better use of the ones already collected and considered as necessary. To materialize those opportunities and reach real improvements in EHS management, managers need to overcome some challenges that we tried to list below.

Scope effect

As stated previously, indicators reflect only limited aspects of a complex reality. Therefore, managers will naturally pay a greater attention to those aspects. With an unchanged amount of resources, other aspects of reality will mathematically be under considered. A good example of this mechanism was provided by the BP Texas city accident. Management has developed and implemented indicators dedicated to workplace safety and considered them as representative of the global safety performance of the system (Baker panel report, 2007). By basing their representation on this subset of numbers, managers were unable to draw a broader picture that includes other aspects of safety. This example shows that if wrongly used, indicators may mislead managers instead of enlighten them. For those reasons, scope effect is to be considered as an unwelcomed side effect of using indicators. Tackling this issue requires for managers to correctly understand the strengths and weaknesses of the various indicators they are using. In other words, purposes and limits of each indicator should be well acknowledged so their users know which aspects of their system are monitored and which are not. Once those strengths and limits well understood, one can think about the complementarities between different indicators. Actually, if different indicators may separately reflect different aspects of a system, together they can cover several aspects. We will talk here about a network of indicators which complementarities make it realizable to cover all dimensions of a system. To do so, managers should be offered not only a list of candidate indicators; but also a list of complementary indicators that considered together will constitute a network capable of a satisfactory description of a system.

Organizational reluctance

Managers should be aware that each management tool introduced in an organization contributes to modify it and is, in return, modified by the organization [START_REF] Hatchuel | Rational modelling in understanding and aiding human decision making. About two case studies[END_REF]. Indicators are no exceptions. Therefore, a first condition to ensure their usefulness and added value for management is to be positively perceived and accepted by the organization.

Otherwise, and in the lack of workforce commitment, there is a big risk to develop indicators that do not reflect reality. Many mechanisms can explain this lack of commitment: • An indicator may be considered as useless by those in charge of providing data; • Not enough resources to perform required tasks, especially if field observations are necessary; • Lack of reporting culture within the organization; • Distrust of the working force towards the management. Once again, the direct consequence will be for managers to have misleading indicators that do not reflect the reality of practices and system's strengths and weaknesses.

How many indicators are necessary?

Selecting a set of EHS indicators is about finding the adequate balance between representativeness in one hand and feasibility on the other. Representativeness points the ability of the set of indicators to correctly reflect the various aspects of reality related to a system. Feasibility, on the contrary, tends to limit the number of indicators so to lighten the burden they may represent for the organization. Actually, using and communicating indicators may generate important costs for organization:

• One or several persons may be required to ensure that data are collected according to a code of practice associated to the indicator. This code of practice should at least describe the frequency and procedure of data gathering; especially if those data rely on field observations. • Regularly, indicators should be questioned to check their relevance regarding system's evolutions.

• In order to ensure a continuous commitment of workforce and first line management to correctly report the required data for EHS indicators, regular information should be provided by management on the relevance and added value associated to those indicators. In this search for equilibrium, managers have to ensure on one side that they do not dismiss an important aspect of EHS management that will leave important parameters out of the management system. On the other side, they also need to minimize the number of indicators, or at least, to dimension this number according to the reporting capacities and practices of their organization. Practices amongst companies may highly vary. There is no standard of the adequate number of indicators for EHS management. This is why finding this balance should be done according to the each system specificities, making it the direct responsibility of EHS managers. According to the various challenges and opportunities described above, a list of core questions and needs, required by managers to correctly perform this difficult selection can be summarized as follows:

• Which aspects of reality are captured by the indicator and which are still unrevealed?

• Is this candidate indicator relevant when considered alone or should it be considered as part of a network of indicators? • What will be the cost of this candidate indicator for my organization?

• Do we have all the adequate skills to correctly use and interpret this candidate indicator?

As a methodological answer, a descriptive model of EHS indicators is described in the followings.

Descriptive model of EHS indicators

A descriptive model of EHS indicators aims to list the features to be systematically described to support managers in the process of defining and selecting relevant EHS indicators for their organization. As mentioned earlier, many questions are raised during such a process. By providing all the informative elements to answer those questions, EHS managers will be able to better legitimate the choice of some candidate indicators instead of others in one hand and better manage the life cycle of the chosen indicators. Once the candidate indicator selected, the way it will be organizationally and technically implemented is still to be defined. Especially, the responsibilities and resources devoted to data collection, indicator calculation, communication and interpretation have to be defined without ambiguity. Finally, the relevance of this indicator should be regularly challenged regarding the system's evolutions. For all those reasons, regular and updated information about the way the indicator is evolving within the organization need to be gathered and stored. This descriptive model offers this opportunity and can consequently be considered also as a tool to manage the set of EHS indicators during their life cycle.

Actually, according to management science, the model to be detailed below can be considered as a knowledge management model since it aims at collecting, organizing and sharing a set of action oriented information. However, it is important to remind that this model does not provide any guideline or methodology on how to identify the EHS needs in terms of indicators. 0ne can find multiple references for various types of approaches in [START_REF] Oien | Building safety indicators: Part 1-Theoretical foundation[END_REF][START_REF] Hse | Developing process safety indicators. A step by step guide for chemical and major hazard industries[END_REF]. To adequately describe an EHS indicator, it is suggested to respect the followings items.

Item 1 : General information

For a manager who already identified the EHS dimensions that he is interested in monitoring, this first item aims to answer the following question "Does this indicator match my needs?" The information to be provided here are described in the table below. In this paper, we focused our attention on Environment, Health and Safety. Nevertheless, depending on the system's needs and the management systems implemented, additional or modified dimensions can be considered. For example, Risk dimensions one can choose to explicitly distinguish workplace safety from process safety, or covered to define a Corporate Social Responsibility dimension that will include both environment and workplace safety (ISO 26000, 2010).

Dimensions definition being open, future users should nevertheless acknowledge that a unique indicator may be more or less relevant for several dimensions.

Item 2: Technical features

If according to information given in item 1, manager(s) believe an indicator as interesting, the next step is to understand its technical features. In other terms, this second step will answer the question "How does it work?" We suggest defining the technical features of an indicator through the following sections

• _ • •_ • *• _ • .. * ± * ,
performance which, in this case, will represent a target value. Minimal and maximal Describe the upper and lower limits within which the values taken by the indicator values are considered as acceptable. Out of those limits, actions are to be taken. Input data required Data required to implement the formula described above have to be listed here.

Frequency of

How often should we measure this indicator? The periodicity of monitoring will measurement influence on the level of resources required.

As stated earlier, indicators should be considered within networks so to take Related indicators profit of their complementarities. Therefore, a list of indicators that may provide additional knowledge should be suggested to the manager.

Item 3: Organizational features

Thanks to general information and technical features items, the manager knows now what the candidate indicator can describe and how to technically implement it.

The next question to be answered is: What is the cost of this candidate indicator for my organization?

The idea here is to help managers appreciating the balance between the cost of using an indicator in one hand and the benefits in terms of insights about the system's evolution on the other hand.

To summarize, two main categories of costs can be considered here. The first is related to the consumption of human resources: technical and administrative procedures, interpretation and communication of the indicator's results. The second category is related to the additional costs required to collect missing input data or to reformulate those delivered by the organization's information system. The first category of costs will be detailed within this item, the second within the next one (information technology item). Because of the natural organizational evolutions and risk profile modifications of assessment every system, the relevance of an indicator needs to be regularly questioned procedure according to a well defined procedure.

Item 4: Information technology features

This item aims to evaluate the concordance level between input data requirements in one hand and the data provided by the organization's information system. The configuration of existing information system may facilitate, or on the contrary, Adequacy with local complicate the process of input data collection. The best configuration would be information system that all input data are already treated by the information system for other purposes.

The descriptive model of an EHS indicator presented above appeals some complementary remarks:

• The identification of needs in terms of EHS monitoring should be performed before using this model. • The various items presented are to be considered according to a chronological order.

Acknowledging the scope and limits of an indicator firstly and describing its technical features secondly will help managers to assess its relevance and its operational conditions of use. • According to this assessment, one can define the best organizational configuration to assess the expected costs of using this indicator.

• By providing a common template for EHS indicators for all kind of systems, this model will enhance exchange of experiences and best practices through different industries. Managers will appreciate the possibilities of adapting proven good practices in other type of systems.

Conclusions

The management of systems appeals necessary the development of monitoring approaches. This paper tries to suggest a model describing major aspects related to the life cycle of an EHS indicator. It tries also to offer decision makers the opportunity to insert their indicators within a coherent and complementary monitoring system composed by network of indicators.

For the sake of clarity, this model has been described through four distinct items to be considered through a chronological order. Those items guide the user through an exploration process of the various dimensions of an EHS indicator.

Future users should feel free to use additional items to better fit their expectations. For instance, this model has been used in the European project Integrisk [START_REF] Mazri | Set of Key Performance Indicators related to emerging risks[END_REF] to elaborate a Key performance indicators database for emerging risks. The description of indicators in this database has been enhanced for the project purposes by adding additional items: the type of industry in which the indicator is classically used or developed, the aspects of risk governance captured (Technology, Human and organisational, communication and regulation), the products' life cycle phases in which the indicator is to be used (Design, Manufacturing, use/operation, end of life). Nevertheless, we consider that the four items presented are the minimum set of descriptive features to be used by managers within a global approach of defining an EHS monitoring policy.

Table 1 :

 1 Detailed sections of the "General information" item

	General Information
	Short Name	Codified and unique name of the indicator
	Long name	Detailed name of the indicator
	Description and	Whatever is the quality of an indicator, it rarely captures all aspects of a reality,
	purpose	What an indicator does and what it does not should thus be clearly described.
	Source	Who issued this indicator?
	References	Reference document(s) describing the indicator.

Nature

An indicator can be qualitative, semi quantitative or quantitative.

Table 2 :

 2 Detailed sections of the "Technical features" item

	Technical features
	.... Formula and unit	Qualitative or quantitative formula to calculate values taken by the indicator , , ,, , q should be provided.
	_	. .	Some indicators may monitor the ability of a system to reach a predefined
	Target value	,

Table 3

 3 Detailed sections of the "Organizational features" item.

	Organizational features
	. .. . Indicator reference ,	A reference person in the organization should be affected to each indicator. This ... ' r . , , a ,, ... ,,, , , , , , person will be in charge of ensuring the quality of the whole process from data
		collection to interpretation and communication of the results.
	^ , Data providers . ,	According to the list of input data described within the technical features, ., , , .. ., , . , . , , , . , .... , persons in capacity of delivering those data need to be clearly identified.
	Interpretation	Interpreting values taken by an indicator is a decisive phase. Persons required to
	procedure	correctly interpret and use insights provided by this indicator should be identified.
	_ Communication . .. procedure r e	Persons within and outside the organization that should be informed about the ... ... , , , ... , " ,, ., , , .. monitoring results have to be identified as well as the method and the ... , . . , , communication channels to be used.
	Relevance

Table 4

 4 Detailed sections of the "Information technology" item.

	Information technology features
	" _ Software availability ,,, a ,. , ' ... .... Managers may be interested in knowing if existing software may facilitate the use ,, , ., a ,

a ' 1 of the indicator, and hence, reduce its costs.


S Di Tommaso

P Rotureau

B Sirjean

W Benaissa
email: wassila.benaissa@ineris.frpeggy.gruez@ineris.frcarlo-adamo@chimie-paristech.fr

P Gruez

C Adamo

A mechanistic and experimental study on the diethyl ether oxidation

Keywords:

This work presents the results of the theoretical investigations on autoxidation process of diethyl ether (DEE), a chemical largely used as solvent in laboratories and considered to be responsible for various accidents. Based on Density Functional Theory (DFT) calculations, the aims of this study were the identification of all the most probable reaction paths involved in DEE oxidation (at ambient temperature and under conditions that reflect normal storage conditions) and the characterization of products and all potential hazardous intermediates, such as peroxides. Results indicate that industrial hazards could be related to hydroperoxide formation and accumulation during the chain propagation step. A detailed kinetics model of DEE oxidation in the gas phase was then developed from all energetic and kinetics parameters collected during the mechanistic study. Outputs of the kinetics model, in terms of time of evolution of product concentrations, have been then compared with the experimentally measured concentration of products (notably hydroperoxides) issued from tests on DEE oxidation conducted under accelerated conditions with autoclaves.

Introduction

A great number of organic compounds spontaneously decompose by a free-radical reaction of the carbon chain with molecular oxygen, in a self-propagating process of auto-oxidation that may generate a large variety of peroxide molecules. Many laboratory accidents can be ascribed to the presence of such peroxides in stored chemicals [1][2][3][4], often under poor conditions, for over long periods. Ethers are typical solvents showing such a behavior. Dimethyl ether (DME) is the most investigated ether of this class both experimentally [5,6] and theoretically [7], since it has a relevant role, due to its good ignition properties, in the domain of biofuels. In particular, Andersen and coworkers [7] proposed a DFT study on the process of low temperature oxidation of this ether. Experimental studies also exist on the oxidation of the other short-chains ethers suggesting oxidation products or intermediates or giving some hints on the kinetics of the process. It is the case of diethyl ether (DEE) [8][9][10][11][12], diisopropyl ether (DIPE) [11,13] or methyl tert-butyl ether (MTBE) [14]. However few investigations have been devoted to the mechanistic elucidation of their oxidation under usual storage conditions [6,[START_REF] Di Tommaso | [END_REF]. Moreover, the chemistry of the oxidation of saturated branched ethers has some similarities with the well known of alkanes [START_REF] Semenov | Chemical Kinetics and Chain Reactions[END_REF], as suggested for DME by Andersen and Carter [6]. This has also been demonstrated for diethyl ether in our latest extensive theoretical study on its low temperature and low pressure oxidation [START_REF] Di Tommaso | [END_REF]. In this scientific context, where incomplete experimental data are available and only a sketchy picture of the process emerges, the present work proposes an in-depth study of DEE oxidation carried out at both theoretical and experimental levels to better understand the process and manage the accidental risks linked to diethyl ether use and storage. In the following, starting from a brief presentation of the results of the mechanistic study (based on quantum chemistry calculations) of all the possible reactions involved in the process, the development and the validation of the kinetics model obtained for the gas phase oxidation of DEE will be discussed. At the end, the issues of kinetics model, in terms of concentrations of products and time of reactions, will be compared with experimental data obtained on DEE oxidation tests carried out in accelerated conditions.

Materials and Methods

Molecular modeling

All the Density Functional Theory (DFT) calculations have been performed using the B3LYP functional [17] and Gaussian 03 program [18]. The 6-31+G(d,p) basis set was used to optimize structures and for subsequent frequency calculations to characterize stationary points as minima or transition states. Intrinsic reaction coordinate (IRC) calculations were also performed to verify that identified products and reactants were correctly connected [19]. For radicals (open shell systems), unrestricted DFT calculations were carried out and the obtained results were checked for wave-function instability.

Rate constants calculations

Rate constants for each elementary reaction were calculated using classical transition state theory (TST) [20]. The tunneling effect was taken into account for reactions involving inter or intramolecular hydrogen transfer using the transmission coefficient in the form proposed by Wigner [21] or Skodje and Truhlar [22] or Eckart [23]. Activation enthalpies have been computed as the difference between enthalpies of formation (with respect to isolated atoms) of all reactants and related transition states. The kinetic parameters were obtained by fitting the rate constant values obtained from TST at several temperatures between 500 and 2000 K with the equation

Ea n RT k AT e
Where A, n, and Ea are the parameters of the modified Arrhenius equation and k ∞ is the highpressure-limit rate constant.

Experimental tools

Storage of chemicals is generally performed at room temperature. Under these conditions, the kinetics are slow and real time tests can take several weeks. As the kinetics are accelerated by temperature, an experimental setting has been designed in order to store DEE at high temperature. Contrary to Naito et al. [11] who used Accelerated Rate Calorimeter (ARC) bombs of 10 mL, experiments were carried out using six 50 mL autoclaves: each stainless steel vessel had previously undergone a passivating step and equipped with a temperature sensor and a pressure transducer. The six autoclaves are inserted in a heating block controlling the temperature (cf. picture 1).

Diethyl ether (99.7%) was obtained from VWR and was used without further addition of a stabilizer. Fourteen milliliters of DEE were introduced into each autoclave and pressurized by synthesized air from a gas cylinder at an absolute pressure of 10 bars. The samples were then heated to two temperatures: 80°C and 100°C. Temperatures and pressures inside the autoclaves were recorded throughout the experiment. At determined storage times, the samples were recovered in order to determine the amount of peroxide formed. Concentration of peroxide was measured using a potentiometric titrator and a solution of potassium permanganate. This method gives the global amount of peroxide function (equivalent H 2 O 2 ).

Picture 1.Experimental setting for experiments at accelerated conditions.

Results and discussions

Molecular modeling

In figure 1 is depicted a scheme summarizing the main reaction pathways of the diethyl ether (R) oxidation issued of DFT mechanistic study of the process [START_REF] Di Tommaso | [END_REF]. Analogously to the accepted alkane autoignition mechanism [START_REF] Semenov | Chemical Kinetics and Chain Reactions[END_REF][START_REF] Denisov | Oxidation and Antioxidants in Organic Chemistry and Biology[END_REF] the oxidation process starts with an initiation step in which a radical R is produced. This species can simply undergo decomposition. Alternatively, a chain propagating cycle is established if the R radical reacts with molecular oxygen to give a ROO species. This peroxy radical can then react with a new DEE molecule to produce a hydroperoxide ROOH and regenerate a R radical. Chain termination ensues when two radical intermediates couple to each other (e.g. dimerization) with loss of the radical character. By contrast, radical isomerization may occur without interrupting the chain reaction. This schematic picture is complicated by the possible decomposition of the hydroperoxides that represent the stoichiometric products of the ideal chain-propagating cycle. The experimentally observed products are also reported.

Among the various chain initiators that have been proposed in literature, OH radical is, from our calculations, the most efficient one from an energy point of view [START_REF] Di Tommaso | [END_REF]. Competition among different pathways starts with the formation of the radical R . In conditions of low (null) oxygen concentration, its decomposition, characterized by a high rate constant (k=1.29s -1 at 298 K, as reported in figure 2), leads to the formation of acetaldehyde, formaldehyde and ethanol. In presence of oxygen, the production of peroxy radicals (ROO ) becomes important and the corresponding reaction is strongly exothermic (ΔH=-31.8 kcal/mol) and barrierless. The resulting ROO radicals can evolve along three competitive reaction pathways: hydroperoxide production, isomerization and dimerization (see figure 1). Hydroperoxide production is endothermic by 12.8 kcal/mol and has an activation barrier of approximately 13.3 kcal/mol. Nonetheless, it becomes probable in the usual conditions of autoxidation, where DEE concentration is high. Indeed, this reaction channel leads to some of the major products identified experimentally (acetic acid, acetaldehyde, ethanol) [10]. On the other hand, the isomerization reaction features significant product stabilization and activation energies comparable to that of hydroperoxide production. Moreover, it could account for the formation of some of the observed products (acetaldehyde, acetic acid, peracetic acid) [10].

However the two pathways are characterized by different entropic effects, so that the final Gibbs free energies are 23.7 and 19.3 kcal/mol for the hydroperoxide production and isomerization, respectively. These different values of Gibbs free energy enthalpy lead to a very important difference in rate constant values, as reported in figure 2.

Finally, dimerization is thermodynamically favored due to significant product stabilization. However, the activation energies along the following steps of these paths are higher than in other reactions, the lowest energy barrier being 32.3 kcal/mol. Furthermore, dimerizations are bimolecular reactions, and their kinetics are therefore highly sensitive to the concentration of peroxy radicals in the reaction medium. In fact the dimerization pathway has been suggested in literature as the major reaction channel for DEE oxidation in atmospheric conditions [12]. In solution, dimerization happens if the two peroxy radicals are close, so that the reaction is limited by the diffusion of two highly reactive species: this channel could be considered as improbable.

Therefore, among all the characterized pathways, decomposition of R and isomerization could be the most relevant in solution.

Moreover, from a hazard point of view, different hydroperoxides have been identified as products or sub products of principal reaction pathways. Considering the high activation barriers for decomposition of these compounds, their accumulation during DEE oxidation could be a (major) risk source during the storage of the chemical.

Detailed chemical kinetics model

The approach used for the development of the chemical kinetics model of the process is summarized in figure 3. The first step was the automatic generation of a detailed mechanism of the oxidation process of DEE with the software EXGAS [START_REF] Warth | [END_REF]. The mechanism produced contains thermochemistry of each species involved in the process in the form of coefficients of NASA polynomial (calculated by the software THERGAS [26] based on Benson group additivity methods) and the kinetics of each reaction considered (calculated by the software KINGAS). All thermodynamic and kinetics data issued from the DFT mechanistic study [START_REF] Di Tommaso | [END_REF] were introduced in this mechanism. The final DEE oxidation model contains 158 species and 355 reactions. Simulations were performed using the SENKIN code of the CHEMKIN II [START_REF] Kee | CHEMKIN II. A Fortran Chemical Kinetics Package for the Analysis of a Gas-phase Chemical Kinetics[END_REF] program suite assuming homogeneous gas-phase reactions in an isochoric static reactor. Temperature and pressure conditions can be selected as inputs to match target experimental data. The mechanism produced was developed and validated by the comparison with experimental literature data in terms of evolution of pressure and product concentration. In particular, because of the lack of experimental data on the DEE oxidation in the liquid phase at room temperature, the model was developed for the process in the gas phase using experimental data (concentrations of products in function of time at 153°C) from experimental work of Waddington [10]. It was then validated from comparison with the Lemay and Ouellet study [9] performed at a different temperature than Waddington. Figure 4 reports the comparison between experimental data obtained by Lemay and Ouellet [9] in their study on DEE gas phase oxidation at 168°C and the curves generated from the CHEMKIN simulation (at T=172°C) in the developed kinetics model.

Some considerations can be made on the basis of this graph:

A displacement in the observation of reactivity of the mixture between experiment and simulations is observed. In particular DEE is consumed earlier (approximately 10 minutes) in the experiment at a lower temperature (168°C instead of 172°C in simulation). We have to note that experimental parameters are not accurately detailed in the studies [9,10] used as references for the development of the kinetics model. If we consider temperature, for instance, in both cases given values are referred to the temperature of the oven in which the reactor is suspended and not to the one in the reactor, and there is no reference to the adiabaticity of the reaction vessel.

After the beginning of reactivity, the trends are well reproduced by the kinetics model as well as the selectivity of the mixture of products.

In the first period of the process, the induction time, is probably characterized by heterogeneous reactions with the reactor surface, which are not taken into account in simulations. Therefore we can conclude that the model is validated for DEE oxidation in the gas phase in terms of reproduction of product concentrations. Because of ill-defined experimental conditions in the reactor and interferences of heterogeneous wall reactions, it is difficult to make firm conclusions about the difference of reactivity observed between experiments and simulations. Consequently, temperature and residence time adjustments remain acceptable.

Experimental results

The peroxide concentration vs. time profiles are given in figure 5. These results show two tendencies: initially the peroxide concentration increases to a maximum and then decreases to reach very low values. At 80°C, the maximum is around 6000 ppm after 45 hours. By increasing the temperature from 80°C to 100°C, the maximum is reached after only 5 hours and the induction time (time before peroxides are detected) is much shorter. Figure 6 gives the pressure evolution for the experiment carried out at 80°C: pressure decreases in the first period, when peroxides are formed, and increases when the peroxide concentration decreases. According to Naito et al. [11], it is assumed that the pressure decrease corresponds to the oxygen consumption by the ether, the beginning of the autoxidation chain reaction, and the pressure increase corresponds to the formation of volatile products from peroxide decomposition. It has been indeed verified that the pressure drop is approximately equal to the initial concentration of oxygen in the autoclave. In this configuration and at this temperature, less than 1 mL of DEE should be vaporized in the autoclave. Nevertheless, the DEE is in excess relative to oxygen in gas phase. Thus the reaction could then occur either in the gas phase or liquid phase.

Further experiments need to be performed to determine more precisely the kinetics and the mechanism:

Other temperatures should be tested (for instance 60°C and 110°C) in order to extrapolate the kinetics to lower temperature. Other products identified in the molecular modeling study should be quantified (ethyl acetate, ethanol, ethyl formate, methanol, acetaldehyde, methanol…). The influence of the initial volume of DEE could give some indications about the phase where the reaction occurs. Various initial oxygen concentrations should be tested to confirm the correlation between the oxygen consumption and the peroxide production.

Nonetheless, the overall objective of this work is to couple the experimental results with the results produced by molecular and kinetic modeling to obtain a kinetics model of the oxidation of DEE in storage conditions, allowing the detection of its instability at ambient temperature.

Kinetics model vs. experiments

With this aim, data generated by CHEMKIN simulations in the kinetics model developed and validated for the gas phase oxidation of diethyl ether were compared with the experimental peroxide concentration curves described in the previous paragraph. In particular, all simulation parameters (initial reactor pressure, reactor volume, reactant concentrations) were chosen to correspond to actual experimental conditions, and the concentration of hydroperoxides was recorded. The simulation was made using a temperature of 107°C and compared with the peroxide concentrations measured during the experiment at 100°C. This comparison is reported in figure 7. The results from the simulation (at 107°C) predict a peak ROOH concentration coming 12 hours after the actual time of the peak observed in the experiment (at 100°C). In figure 7, the experimental results have been shifted in time to facilitate a comparison of the ROOH concentration. However, as seen before for the validation of the gas phase model, the ROOH concentrations predicted by the simulation and observed experimentally are quite similar. These preliminary results encourage further improvement of the kinetics model using new experimental data obtained either under accelerated conditions or at ambient temperature with the goal to better reproduce the true behavior of DEE at storage conditions.

Conclusions

Two different but complementary theoretical approaches have been used to study the oxidation process of diethyl ether: an in-depth theoretical study based on quantum chemistry calculations and a kinetics study. Concerning the reaction mechanism, both approaches show that in presence of molecular oxygen, reaction pathways involving O 2 are favored with respect to unimolecular decomposition. The kinetics model has been obtained and validated for the oxidation of DEE in the gas phase from experimental data obtained from the literature: the model reproduces well the selectivity of product blend but is less efficient for reaction time. This problem in predicting the time of reaction was also observed when comparing peroxide concentrations obtained at approximately 100°C from simulation and from preliminary oxidation tests performed with autoclaves at INERIS. However, the kinetics model is able to predict suitably the concentration of peroxides produced during the oxidation process of DEE. We can expect significant improvement in the kinetics model by taking into account the results of ongoing tests to quantify other molecular species. The objective of experimental study is also to extrapolate measurements of DEE oxidation products towards conditions of normal storage. From a risk point of view, this model is expected to determine accurately both peroxide concentrations and time of maximal concentration in order to predict potential instability and better manage industrial and laboratory risks of this chemical.

Figure 1 .

 1 Figure 1.Global scheme of the proposed mechanism of DEE (R) oxidation.The experimentally observed products are also reported.

Figure 2 .

 2 Figure 2.Sketch of the principal reaction pathways identified.For each reaction the activation free Gibbs energy and the rate constant are specified.

Figure 3 .

 3 Figure 3. Scheme of the approach used for the development of the kinetics model.

Figure 4 .

 4 Figure 4.Evolution of partial pressures of oxygen, acids and peroxides at T=172°C. Experimental curves [9] have been displaced by about 10 minutes to facilitate the comparison.

Figure 5 .

 5 Figure 5.Peroxides concentration evolution at two operating temperatures.

Figure 6 .

 6 Figure 6.Peroxides concentration and pressure evolution at 80°C.

Figure 7 .

 7 Figure 7. Comparison between peroxides concentration obtained from kinetics simulation at 107°C and experiments (at 100°C). Experimental curve has been displaced by about 12 hours to facilitate the comparison.