# Towards a new standard: Procedure proposal for the determination of mist explosion characteristics

Stephanie El-Zahlanieh, Alexis Vignes, Olivier Dufaud

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Stephanie El-Zahlanieh, Alexis Vignes, Olivier Dufaud. Towards a new standard: Procedure proposal for the determination of mist explosion characteristics. Process Safety and Environmental Protection, 2025, 198, pp.107195. 10.1016/j.psep.2025.107195. hal-05065160

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# Towards a new standard: Procedure proposal for the determination of mist explosion characteristics

Stephanie El-Zahlanieh<sup>a,b D</sup>, Alexis Vignes<sup>b D</sup>, Olivier Dufaud<sup>a, *, D</sup>

## ARTICLE INFO

### Keywords:

Mist

Aerosol explosion

Explosion severity

Standard proposal

Hydrocarbons

## ABSTRACT

Despite the occurrence of numerous accidental mist explosions, standards for the determination of liquid aerosols explosivity are still not available. This is mainly due to the lack of means of characterization, available data, and scientific knowledge in such a matter. This article proposes a complete procedure allowing the evaluation of the ignition sensitivity and explosion severity of fuel mist clouds. Specific test procedures were recommended based on a classification system dividing liquids into four quadrants according to their flash point and droplet stability during secondary atomization (i.e. the Weber ratio). The dedicated test equipment is based on a 20L explosion sphere modified to generate a hydrocarbon mist with controlled characteristics (diameter, concentration, etc.). The proposed procedures were successfully applied to seven fuels (e.g. kerosene and lube oil) and could then serve as the basis for a new standard. This article also put forward the application of such procedures in industrial cases to illustrate the importance of considering scenarios involving the generation of fuel mists, particularly those with high flashpoints, and the need to assess the safety parameters of mists through experimental means for standardization. Suitable prevention, protection and mitigation measures can then be implemented in a harmonized and systematic way.

## 1. Introduction

Since the industrial revolution, hydrocarbons have been an omni-present part of our daily lives, used in nearly every existing industry. However, their use has led to numerous incidents along their value chain, i.e., during production, handling, storage, or transportation. Among these incidents, the chemical and petrochemical industries have witnessed a significant number of explosions triggered by involuntary mist releases (Santon, 2009; Lees et al., 2019). Such inadvertent releases can lead to the formation of a flammable mixture that can cause an explosion in the presence of an ignition source. Identifying the risk of formation of an explosive mist atmosphere in or around equipment dealing with flammable fluids in industrial sectors, such as production, processing, distribution, and retail sectors, therefore appears of importance to better manage fire and explosion risks. At the European level, two Directives are currently implemented to properly manage explosion risks in the workplace (Directive 1999/92/EC, 2000) and (Directive 2014/34/EU, 2014). They clearly recognize the possible threat posed by mists.

However, there is still a lack of tools to assess explosion risks related

to mists, and only a limited amount of information is available on how to estimate the degree of the threat posed by high-flashpoint fluid mists and the type of ATEX equipment to use. Furthermore, the International Electrotechnical Commission IEC 60079-10-1 (2020) clearly states that current standards and classifications do not apply to mist hazards generated at temperatures below the flashpoint. Nonetheless, it became evident that several mist explosions did actually occur at temperatures below the flashpoint of the aerosolized liquid (Eckhoff, 2005; Eichhorn, 1955; Gant et al., 2020). In such cases, paradoxically, one of the only parameters used to determine the risk associated with the presence of a flammable mist ATEX is still the flashpoint. Indeed, while the classification of flammable gases and dust is well-established (Yuan et al., 2015), that of liquid aerosols remains less so. This is mainly due to a lack of scientific data and knowledge in such a matter, highlighted by the Energy Institute (Energy Institute, 2015), which stated that "there is little knowledge on the formation of flammable mists and the appropriate extents of associated hazardous areas". These concerns were also confirmed recently by Lees et al. (2019), Johnson et al. (2020) and Yuan et al. (2021).

Qualitative guidance can be found in some standards, including the Energy Institute's model code of safe practice EI15 (Energy Institute,

<footnote><sup>a</sup> Université de Lorraine, CNRS, LRGP, Nancy, France</footnote>

<footnote><sup>b</sup> INERIS, Parc Technologique ALATA, BP 2, Verneuil-en-Halatte F-60550, France</footnote>

<footnote>* Corresponding author.
E-mail address: olivier.dufaud@univ-lorraine.fr (O. Dufaud).</footnote>
Nomenclature

<table><tr><td>B<sub>T</sub></td><td>Spalding number (-)</td></tr><tr><td>C<sub>m</sub></td><td>Mist concentration</td></tr><tr><td>d<sub>d</sub></td><td>Droplet diameter</td></tr><tr><td>We</td><td>Weber number (-)</td></tr><tr><td>σ<sub>l</sub></td><td>Surface tension</td></tr><tr><td>ΔT</td><td>Temperature increase</td></tr><tr><td>C<sub>p</sub></td><td>Heat capacity</td></tr><tr><td>d<sub>c</sub></td><td>Cloud diameter</td></tr><tr><td>ν</td><td>Velocity</td></tr><tr><td>ρ<sub>l</sub></td><td>Density</td></tr><tr><td>μ<sub>l</sub></td><td>Dynamic viscosity</td></tr><tr><td>ΔH<sub>vap</sub></td><td>Vaporization enthalpy</td></tr></table>

2015) and IEC 60079-10-1 (2020), but there exists a lack of quantitative methods permitting to assess mist explosions, i.e. to determine quantitatively safety parameters related to their ignition sensitivity and explosion severity. As Gant (2013) pointed out, the matter is more complex for mists than for gases, vapors, and dust clouds. Although heterogeneous as a dust cloud, the droplet size distribution of a mist cloud depends even more on time, turbulence level, and concentration. Mist releases are not usually uniform and stable, mostly due to eventual evaporation, droplet breakup, coalescence, or sedimentation. Droplet fragmentation can even occur during the explosion due to the shock wave (Meng et al., 2025). Moreover, with high flashpoint multi-component fuels, the presence of volatile fractions renders studying their flammability and explosivity rather challenging. Indeed, according to the IEC 60079-10-1 (2020) standard, if a mist hazard has been established, 'Zones 0, 1, or 2' cannot be used as hazardous area classifications since the types of protection used in such zones are not necessarily applicable for mist risks. Additionally, the standard mentions that, due to their complexity, mist clouds' risk assessment should preferably be supported by specific references or operating experiences so that judgements are based on pertinent data (IEC 60079-10-1, 2020). Therefore, standards are limited to qualitative methods since each release is strongly influenced by the handled liquid.

Many efforts were made in the previous decades to quantitatively study mist hazards. For instance, Burgoyne and Cohen (1954) notably studied the effects of droplet sizes on the flammability of the mist cloud. The influence of the same parameter was also described by Liu et al. (2015) who notice a significant increase of the burning rate of hexane mist between 8 and 15 µm, i.e. in the so-called called the 'transition range' (Bowen and Cameron, 1999). This type of study has been facilitated by the development of tools for generating monodisperse aerosols, such as the Wilson's cloud chamber (Cameron and Bowen, 2001). Ballal and Lefebvre (1978) conducted several studies to measure and predict the ignition energy and quenching distance of quiescent and turbulent fuel mist clouds.

In parallel, throughout the years, a considerable number of mist-related incidents have been reported. Eckhoff (2005) dedicated a chapter of his book to shed light on the explosions of liquid droplets and past related incidents. Other incident reviews were published by Santon (2009) and Lees et al. (2019) and some instances of mist related incidents are available in Fig. 1(Eckhoff, 2005; ICES, Institute of Chemical and Engineering Sciences, 2021; NIOSH, 2003; NTSB, 2022; Shepherd et al., 1997; Vervalin, 1974; Wang et al., 2019; CTIF, 2020; Santon, 2009). Analysis of data submitted to the UK Offshore Safety Directive Regulator (OSDR) showed that of the 25 occurrences of hydrocarbon mist leaks between January 2016 and July 2018, 6 were caused by mechanical stress (vibration, dynamic shock, etc.) while 4 were due to corrosion/erosion phenomena (Lees et al., 2019). Even if the same authors claimed that the causes of rupture were varied, analysis of the

ARIA database revealed 12 accidents out of 40 caused by mechanical stress, while the 18 releases of hydrocarbon mist identified by the ZEMA database involve 6 human errors and 5 corrosion phenomena. Globally, of the 83 accidents analyzed, nearly 48 % resulted in fuel ignition.

Because of the frequency of accidents involving the ignition of lubricating oil mists on ships, specific CFD simulations were recently carried out (Ivanov et al., 2024). A liquid/area classification system was also proposed by the Health and Safety Executive (HSE), dividing industrially interesting fuels into four release classes according to their volatility and their ease of atomization (Gant et al., 2016). Based on the operating pressure and the size of the emitted aerosol particles, Krishna (2003) proposed a risk matrix to rate the risks of heat transfer fluid aerosols. Yuan et al. (2021) pinpoint a limitation of this matrix, stating that the authors only took into account the general quantities (operation pressure and droplet size), which are relatively hard to know before an incident takes place, seen that the droplet size depends on the operation pressure, the size of the orifice, and many other external conditions. Yuan et al. (2021) subsequently proposed a conceptual method allowing the risk analysis of flammable liquids. The list of dedicated studies is far from being exhaustive (Ji et al., 2021; Jia et al., 2024) and will not be detailed further on as it is out of the scope of this article. However, as this work is focused on the determination of mist explosion characteristics in a closed vessel, a summary of studies using such vessels is provided in Table 1.

Many studies were dedicated to mist explosion and economic integration enabled the dissemination and harmonization of standards (Qi et al., 2012), but there is still no standard experimental test method to evaluate safety parameters for mist ignition and explosion assessment. This absence is especially highlighted in the annex G6 of 60079-10-1 (2020) standard, which states that "because the dispersion mechanisms and the criteria of flammability for mists are different than those for gases and vapors, the methodology of classification presented [in the 60079-10-1 standard] cannot be applied". In the same annex, the "thermodynamic complexity of mists" is also stressed. It is certainly because of this complexity and the particular nature of mists that, despite existing literature, gaps remain which hinder or limit the development of a reliable methodology for determining safety parameters related to mist explosion. For instance, for a given vessel, there are no relationships that can predict the evolution of droplet size distribution (DSD) as a function of injection pressure and flow rate. This further limits the repeatability of measurements, as the DSD also depends on the turbulence of the mist, and therefore on the type of nozzle used to generate it. Temperature and pressure conditions also vary the gas/liquid ratio of the mist, making it imperative to control them. Another aspect not perfectly defined in the literature, yet essential to the standardization of test procedures, is the interaction between ignition sources (permanent spark, hot surface, or chemical ignitors...) and the flammable mist. Therefore, in the absence of such data and a standardized protocol, this study's objective was to fill this gap by proposing a pre-normative test method that will enable to assess further the phenomenology in a confined environment. It will thus provide reproducible and reliable safety data for process safety engineers who need it to classify ATEX zones, assess the consequences of explosions on people and the environment, and size vents.

Several steps were taken to propose a complete test procedure, including selecting a pertinent set of fuels and a controllable and adaptable mist generation system while producing suitable droplet sizes, concentrations, and turbulence levels (El-Zahlanieh et al., 2022a, 2022b). Characterization experiments quantified such parameters before moving on to the mist ignition step. Subsequently, as existing equipment and software programs are not yet adjusted to a mist explosion test, a control and data acquisition system was developed. Some modifications were made to the explosion vessel, and a high-voltage spark ignition system was designed to evaluate the Minimum Ignition Energy (MIE) of mist clouds. Also, calibration and validation tests were performed, establishing a complete modus operandi. The latter was
<figure><img src="image_4.png" /><figcaption>**Fig. 1.** Illustrative example of mist related or allegedly related incidents throughout the years - some are adopted from Santon (2009) and Yuan et al. (2021), Vervalin (1974), Eckhoff (2005), Shepherd et al. (1997), Wang et al. (2019), CTIF (2020), NTSB (2022), Institute of Chemical and Engineering Sciences (2021).</figcaption></figure>

followed, and the ignition sensitivity (MIE, Lower Explosion Limit or LEL, and Lower Oxygen Concentration or LOC) and explosion severity of the selected fuels were measured under ambient and varying operating conditions in one apparatus (El-Zahlanieh et al., 2022a, 2022b). This article briefly describes the experimental setup developed for performing mist explosions, details the proposed standard procedures to determine their ignition sensitivity and explosion severity and illustrates their application by exploring three case studies.

## 2. Experimental setup and methods

After having considered the combustion physics of aerosols, several steps were taken in order to choose the right tools and complete protocol, to check the accessibility to the equipment and the repeatability and reproducibility, and to verify the relevance of the benchmark. While there are other experimental tools available for their evaluation, the 20 L explosion sphere was chosen for this study. It is a standardized vessel and has been subject to numerous well-documented investigations. It can be found in most process safety laboratories and is
<table><caption>**Table 1**
Summary of some aerosol explosion experimental studies performed in closed vessels.</caption><thead><tr><th>Liquid</th><th>Explosion vessel</th><th>Mist generation method</th><th>Mist cloud conditions</th><th>Ignition source & energy</th><th>Results</th><th>Reference</th></tr></thead><tbody><tr><td>Kerosene and isopropanol</td><td>5 L spherical vessel</td><td>Six holes Electromagnetic injector 10 sequential injections</td><td>SMD between 10 and 60 µm</td><td>Spark ignition – 7 J</td><td>Kerosene: P<sub>max</sub> 4.1 bar, dP/dt<sub>max</sub>= 140 bar.s<sup>-1</sup> at 250 g.m<sup>-3</sup><br>Isopropanol: P<sub>max</sub> 8 bar, dP/dt<sub>max</sub>= 1800 bar.s<sup>-1</sup> at 700 g.m<sup>-3</sup></td><td>(Toman and Adamus, 2023)</td></tr><tr><td>Isopropyl nitrate</td><td>20 L confined cylinder</td><td>Double nozzle pneumatic atomization system</td><td>-</td><td>High temperature ignition source</td><td>Double-peak-explosion 1st: P<sub>max</sub> 6.6 bar, dP/dt<sub>max</sub>= 605 bar.s<sup>-1</sup> at Φ = 2.4; 2nd P<sub>max</sub> 15.4 bar, dP/dt<sub>max</sub>= 331 bar.s<sup>-1</sup> at Φ = 1.8</td><td>(Sun and Zhang, 2021)</td></tr><tr><td>n-heptane</td><td>20 L confined cylinder</td><td>Double nozzle pneumatic atomization system</td><td>SMD between 7.07 and 7.11 µm</td><td>High temperature ignition source</td><td>Double-peak-explosion 1st: P<sub>max</sub> 6.2 bar, dP/dt<sub>max</sub>= 1253 bar.s<sup>-1</sup> at Φ = 3.6; 2nd P<sub>max</sub> 13.4 bar, dP/dt<sub>max</sub>= 160 bar.s<sup>-1</sup> at Φ = 1</td><td>(Sun and Zhang, 2021)</td></tr><tr><td>n-octane & n-dodecane</td><td>36 L dust apparatus</td><td>Solenoid fuel injector</td><td>SMD of 110 µm for n-octane and 117 µm for n-dodecane</td><td>Coil spark – 100 mJ</td><td>n-octane: P<sub>max</sub> 6.2 bar, K<sub>a</sub> = 24 bar.m.s<sup>-1</sup> at Φ = 1; n-dodecane: P<sub>max</sub> 4.7 bar, K<sub>a</sub> = 16 bar.m.s<sup>-1</sup> at Φ = 1.1</td><td>(Yuan et al., 2019)</td></tr><tr><td>JP-10</td><td>20 L confined cylinder</td><td>Double nozzle pneumatic atomization system</td><td>SMD of 20 µm and 35 µm – u<sub>rms</sub> between 3.5 and 7 m.s<sup>-1</sup></td><td>Spark ignition – 40.32 J</td><td>20 µm: P<sub>max</sub> 8.7 bar, dP/dt<sub>max</sub>= 1210 bar.s<sup>-1</sup> at 435 g.m<sup>-3</sup><br>35 µm: P<sub>max</sub> 8.4 bar, dP/dt<sub>max</sub>= 880 bar.s<sup>-1</sup> at 626 g.m<sup>-3</sup></td><td>(Liu et al., 2016)</td></tr><tr><td>Diethyl-ether</td><td>20 L spherical vessel</td><td>Double nozzle pneumatic atomization system</td><td>SMD of 12.9 and 23 µm</td><td>Spark ignition – 40.32 J</td><td>12.9 µm: P<sub>max</sub> 9.8 bar, dP/dt<sub>max</sub>= 3245 bar.s<sup>-1</sup> at 285 g.m<sup>-3</sup><br>23 µm: P<sub>max</sub> 7.8 bar, dP/dt<sub>max</sub>= 2091 bar.s<sup>-1</sup> at 278 g.m<sup>-3</sup></td><td>(Bai and Wang, 2015a)</td></tr><tr><td>RP-5 and RP-3</td><td>20 L spherical vessel</td><td>Spray nozzle</td><td>5 different injection pressures</td><td>Pyrotechnical ignitors – 2 kJ</td><td>RP-5: P<sub>max</sub> 6.5 bar, dP/dt<sub>max</sub>= 33 bar.s<sup>-1</sup> RP-3: P<sub>max</sub> 6.4 bar, dP/dt<sub>max</sub>= 35 bar.s<sup>-1</sup></td><td>(Zheng et al., 2014)</td></tr><tr><td>10 military diesel and 35 ordinary diesel</td><td>20 L spherical vessel</td><td>Spray nozzle</td><td>5 different injection pressures</td><td>Pyrotechnical ignitors – 2 kJ</td><td>10 diesel: P<sub>max</sub> 6.4 bar, dP/dt<sub>max</sub>= 34.7 bar.s<sup>-1</sup> 35 diesel: P<sub>max</sub> 5.9 bar, dP/dt<sub>max</sub>= 34.2 bar.s<sup>-1</sup></td><td>(Lei et al., 2014)</td></tr><tr><td>Hexane</td><td>5.6, 40, 150 and 1250 L chambers</td><td>Compressed liquid dispersion system</td><td>Controlled droplet diameters between 0.25 and 0.7 mm</td><td>5 J electrical spark discharge or 2 kJ ignitors</td><td>250 µm: P<sub>max</sub> > 4 bar 700 µm: P<sub>max</sub> 2 bar</td><td>(Gieras et al., 2008)</td></tr></tbody></table>

accepted by many explosion safety stakeholders.

## 2.1. Key points of liquid aerosol combustion

The two-phase liquid/gas combustion process is controlled by four successive phenomena at the level of a single droplet, but present simultaneously throughout the burning cloud: aerosolization, vaporization, oxygen/vapor mixing, oxidation reaction. Initially, mist generation by atomization is accompanied by interactions between droplets and ambient air (e.g. droplet shear), between droplets themselves (e.g. coalescence, collision) and between droplets and vessel walls. The most significant parameters of this stage can be expressed using Laplace, Weber and Ohnesorge numbers (El-Zahlanieh, 2022).

In a second step, the presence of a heat source leads to droplet heating and phase change by evaporation. This stage is regulated by the mechanisms of convection, radiation and liquid/vapor equilibrium. The vapors then mix with the air to form a reactive medium. This phase is limited by transfer phenomena, particularly diffusive ones, and the concentration of fuel often cannot be considered homogeneous throughout the cloud. The characteristic parameters of these stages are notably the Spalding, Stanton and Lewis numbers.

Finally, the presence of an ignition source initiates oxidation reactions, and exothermic combustion transfers back the heat needed to evaporate the droplets upstream. The characteristic time of this chemical reaction is much shorter than that of the drop heating and vaporization phenomenon that controls the overall process. The ratio between the characteristic flow time and characteristic combustion time can be expressed through a Damköhler number (Law, 2006).

In a well-characterized environment, studying the evaporation of an isolated drop by raising the temperature of the surrounding gases or by combustion allows researchers to obtain first-rate information, such as evaporation speed and the influence of the medium. Godsave (1953) developed a simplified droplet evaporation model, the d²-law, to

understand the standard evaporation process of a single droplet. It demonstrates that the square of the droplet diameter decreases linearly with time in a diffusion-controlled process. It is generally considered a well-established law to represent the evaporation of a spherically symmetrical droplet in a fixed environment where the interaction between droplets is considered negligible, and the temperature of the droplet is constant and uniform. Grasping the entire precise structure of spray combustion by tracking every microscopic activity connected with each droplet that interacts with its surrounding gas is hard since spray combustion involves many small liquid droplets. Consequently, from a practical standpoint, only averaged quantities are significant. The combustion of droplets can therefore adopt four distinct combustion regimes that can be apprehended through the so-called “combustion group” theory: single droplet combustion, internal group combustion, external group combustion, and external sheath combustion (Chiu and Liu, 1977). The combustion regime depends on the physico-chemical properties of the fuel, the droplet size distribution, the aerodynamics of the mist and its concentration (i.e. mean inter-droplet distance).

The parameters influencing the biphasic combustion being numerous, it is even more important to control the operating conditions of explosion tests to ensure reproducible results and enable reliable comparison between fuels.

## 2.2. The modified 20 L ignition and explosion severity test device (MIST)

This vessel is a spherical stainless-steel chamber fitted with a double jacket allowing the circulation of a heat transfer fluid which controls and maintains a constant temperature during experiments. Fig. 2 depicts the main differences between the sphere in dust configuration, as proposed by the EN 14034 series, 2004+A1 (2011), and the modified device. Both dust container and fast acting valve were removed and replaced by a mist generation system. An ignition source, placed in the center of the enclosed vessel, is then triggered after a fixed ignition delay tv. The
<figure><img src="image_5.png" /><figcaption>**Fig. 2.** The Modified 20 L Ignition and explosion Severity Test device (MIST); on the right: the parts removed from the standard configuration.</figcaption></figure>

latter is defined as the time between the start of the dust dispersion and the actuation of the ignition source. This delay can be associated with a specific degree of cloud turbulence at the ignition time. During the explosion, two piezoelectric pressure sensors are used to record the pressure-time evolution. The 20 L explosion sphere also comprises an inlet for purging air and two outlets for exhaust gases and vacuuming.

While remaining inspired by the EN 14034 series, 2004+A1 (2011), the test method was modified to adapt to the complexity of an injected mist cloud in a confined test vessel. A specific liquid is placed in a temperature-controlled metallic reservoir and then injected in the form of a mist into the sphere. A pre-determined injection time is calculated according to the wanted sample concentration and allows the determination of the initial sphere pressure. The mist cloud is ignited after a defined time of a few milliseconds after injection, and the rest of the procedure follows that of dust clouds.

Another apparatus that could be used for the same purposes is the 1 m³ sphere. Considering the lack of experience on the cubic law applied for mist explosions, the latter would undoubtedly produce data that are more representative of industrial-scale accidents due to its larger size, provided that adequate modifications of the injection system are carried out. Nonetheless, the 20 L vessel is more available in laboratories and is easier to manipulate due to its dimensions.

## 2.3. Mist generation method

The choice of the mist generation system is of significant importance as it should be versatile, easy to find/manufacture, adaptable, and controllable. Nonetheless, sufficient concentrations should be attained with suitable Droplet Size Distribution (DSD) and turbulence levels to mimic an industrial leak as much as possible while remaining adjusted and convenient to a confined, relatively small vessel. Taking into account these considerations, a twin-fluid spray nozzle was chosen for this study. Indeed, electrospray cannot be chosen because it would be necessary to control the electrical conductivity of each fluid to be tested. Condensation does not allow to reach a wide range of DSD (e.g. Wilson cloud chamber), and liquid pressurization limits the possibility of controlling the sphere's initial temperature and pressure and testing hybrid mixtures, thus justifying the choice of a spray nozzle. Such a nozzle comes in different configurations, where the liquid can be pressurized and then atomized with an air stream or can be supplied by a siphon or

gravity-fed system.

An exemplary scheme of a twin-fluid spray nozzle is portrayed in Fig. 3. This nozzle functions due to a Venturi junction. Compressed air passes through a three-way ball valve and draws the liquid, which is placed in a temperature-controlled reservoir, up through a feed line towards the nozzle. The liquid would, therefore, be atomized by the airflow. Such a setup consists of fluid cap (noted PF) topped by an air cap (noted PA) (supplied by Spraying Systems®), ensuring an internal or external mixing of the fluids to generate a fine spray pattern. Both caps come in different orifice diameters allowing the creation of hundreds of combinations. The caps should be locked together using a specific locknut to avoid vibrations. The spray flow rate, angle, pattern, and coverage can, therefore, be controlled by varying combinations. For this study, many combinations have been tested. Nevertheless, three nozzle sets were mainly used: Nozzle set N1 represented the smallest orifice diameter and slot width (references Spraying Systems®:

<figure><img src="image_6.png" /><figcaption>**Fig. 3.** Mist generation system based on a Venturi junction. Siphon height: 190 mm.</figcaption></figure>
PF1650 + PA73420 slot), while nozzle set N2 was that with the largest orifice diameter (ref. PF60100 + PA120 circular). An intermediary nozzle set N' was also chosen (ref. PF40100 + PA122435 slot) (El-Zahlanieh et al., 2022a). The nozzles are characterized by the inner diameter $d_1$ of the fluid cap (liquid inlet), the inlet diameter $d_2$ of the air cap and its external orifice dimensions (Table 2 – dimensions $d_3$ and $d_4$ in inches).

Two electronic solenoid valves were placed on the liquid and the compressed air inlets to control the injected concentration and the liquid/air ratio and prevent potential backflow due to the explosion (Fig. 2). The body of the nozzle spray was specifically designed to fit into the explosion sphere's support ring already used for dust explosion tests (for the rebound nozzle). The height of the vertical sphere's support was also modified from 16 to 27 cm to allow the mist injection system to fit underneath the explosion sphere. This system was, hence, placed at the base of the sphere, with the nozzle set mounted inside the vessel allowing upward mist injection. The setup can tolerate air injection pressures that reach about 10 bar depending on the orifice diameter. Nevertheless, to avoid significant complexities caused by spray impingement and fragmentation due to the strong wall impacts, injection pressures were limited to a range of 2–5 bar (values determined experimentally). Occasional tests with higher pressures were carried out. Evidently, imitating the pressure of an actual industrial mist release is rather difficult inside the 20 L confined explosion sphere. Almost half of the accidental releases reported by Lees et al. (2019) occurred at pressures higher than 100 bar (with more than half occurring with a release hole equivalent diameter between 0.56 and 10 mm). Local concentrations, flow rates, and spatial heterogeneity are seldom reported. However, the selected mist generation system allows full control of the DSD and the injected concentration, simultaneously or independently. For instance, according to the supplier, for an air injection pressure of 3 bar, water flow rates as low as 0.4 and as high as 4.6 g.s⁻¹ (nozzle set N2) can be reached. Therefore, for an injection duration of 8 seconds, mist concentrations ranging from about 170–1855 g.m⁻³ are attainable in the 20 L sphere.

## 2.4. Ignition sources

As a function of the parameter to be determined, two types of ignition sources were tested: chemical ignitors of energies ranging from 100 J to 10 kJ (Sobbe GmbH) and spark ignition. The spark ignition used delivers a maximum power of 225 W. Thus, a permanent spark would be generated during 444 ms to deliver an energy of 100 J. Therefore, for higher energies, in order not to generate for a long duration and cause the droplets to sediment or/and to diffuse the ignition energy to a too large volume of mist, chemical pyrotechnical ignitors were used. However, it should be kept in mind that, contrary to spark ignition, chemical igniters do not provide a local ignition (Spitzer et al., 2023).

The permanent spark was generated following a signal sent from the KSEP 320 high voltage unit (Cesana AG), which was connected to the electrodes. To control the generation time, hence the ignition energy, the unit was bypassed by a custom control system. Similarly, a low-voltage electrical signal was supplied by the bypassed KSEP 310 unit to actuate the chemical ignitors. Both ignition sources were examined at 100 J to guarantee that they both provide similar results.

<table><caption>**Table 2**

Geometric characteristics of the nozzles.</caption><thead><tr><th>References of the fluid and air caps</th><th>Nozzle set</th><th>Fluid cap d<sub>1</sub> (in)</th><th>Air cap inlet d<sub>2</sub> (in)</th><th>Air cap ext. d<sub>3</sub> (in)</th><th>Air cap ext. d<sub>4</sub> (in)</th></tr></thead><tbody><tr><td>PF1650 + PA73420</td><td>N1</td><td>0.016</td><td>0.073</td><td>0.020</td><td>0.225</td></tr><tr><td>PF40100 + PA122435</td><td>N'</td><td>0.040</td><td>0.122</td><td>0.035</td><td>0.355</td></tr><tr><td>PF60100 + PA120</td><td>N2</td><td>0.060</td><td>0.120</td><td>0.120</td><td>0.120</td></tr></tbody></table>

In addition, a high-voltage spark ignition system was specifically developed at the LRGP to test lower ignition energies starting from about 130 mJ. This system consisted of a Brandenburg 3590–1320 DC/DC converter 12 V to 10 kV voltage with a total power of 5 W and a maximum input current of 0.5 mA. The output of this converter is adjustable, allowing the variation of the delivered energy to the mist cloud. The real spark duration, as well as the continuous delivered current, is then calculated to obtain an accurate estimation of the delivered ignition energy. The spark tungsten electrodes were placed at a separating distance of 6 ± 0.1 mm on stainless-steel electrodes which were insulated from the sphere's wall using Teflon plugs.

The choice of the ignition source would depend on the type of liquid tested and the intention of the test. The ignition source, whether chemical or spark ignitors, would be placed in the center of the sphere, with a separation distance of 13.3 cm to the injection system.

## 2.5. Global approach proposed for risk assessment of mist explosion

Several steps were taken to propose a complete test procedure, including selecting a pertinent set of fuels (ethanol, isooctane, kerosene, diesel B7, biodiesel B100, light fuel oil LFO and lube oil – Mobil DTE) and a controllable and adaptable mist generation system while producing suitable droplet sizes, concentrations, and turbulence levels (El-Zahlanieh et al., 2022b). This specific aspect of simultaneous control of droplet size distribution, concentration and turbulence is both original and imperative for this type of standardized testing. Calibration tests were carried out, enabling a complete operating protocol to be proposed and validated. Subsequently, the ignition sensitivity (minimum ignition energy MIE, lower explosion limit LEL, and limiting oxygen concentration LOC) and explosion severity (maximum explosion pressure at a given concentration $P_{ex}$, maximum rate of pressure rise at a given concentration $dP/dt_{ex}$, and their maximum values $P_{max}$ and $dP/dt_{max}$) of the selected fuels were measured under ambient and varying operating conditions in a single apparatus, the Modified 20 L Ignition and explosion Severity Test device (MIST). A flow chart representing the approach used in this study is shown in Fig. 4.

Several repeatability tests were performed and showed a satisfactory agreement with regard to existing standards applicable to dust explosion. For instance, the maximum concentration error ranged from 7 to 13 g.m⁻³ as a function of the liquid tested. The repeatability of the explosion severity tests was also assessed as each was performed at least three times. The EN 14034 series, 2004+A1 (2011) standard suggests repeatability of a maximum deviation of 5 % and a reproducibility of 10 % of the $P_{max}$ of a reference dust. Current findings have not exceeded, in terms of repeatability, a 12 % of the average $P_{ex}$ value, which can be considered acceptable for a newly developed method. These variations are associated not only with the operating and environmental conditions but also with the design of the apparatus. The EN 14034-2 standard evokes a table of the maximum permissible deviations obtained per range of rates of pressure rise of a reference dust. Table 3 compares these deviations with the maximum ones obtained experimentally for mist cloud explosions.

The effects of temperature, droplet size distribution, concentration, and other parameters such as volatilization rate have been presented in previous publications (El-Zahlanieh et al., 2022b, 2023). Additionally, flame propagation tests were performed to determine the intrinsic properties of the hydrocarbon mists, but this aspect is beyond the scope of standardization and therefore of this article. The complete approach including detailed experimental results are presented in El-Zahlanieh's (2022) PhD thesis.

This study has therefore succeeded in developing a device that is able to test the ignition sensitivity and explosion severity and benchmark mist clouds in a 'potentially standardizable way', which has never been done to our knowledge.
<figure><img src="image_7.png" /><figcaption>Fig. 4. A systematic approach to study the flammability and explosivity of fuel mist cloud.</figcaption></figure>

<table><caption>**Table 3**
Maximum permissible deviations for dust clouds explosions (EN 14034) and experimental findings for mist clouds (this study).</caption><thead><tr><th>dP/dt<sub>max</sub> (bar.<br>s<sup>-1</sup>)</th><th>Relative deviation for dust<br>clouds (%)</th><th>Relative deviation for mist<br>clouds (%)</th></tr></thead><tbody><tr><td>&lt;50</td><td>±30</td><td>±18</td></tr><tr><td>50-100</td><td>±20</td><td>±27</td></tr><tr><td>100-200</td><td>±12</td><td>±7</td></tr><tr><td>&gt;200</td><td>±10</td><td>±15</td></tr></tbody></table>

## 2.6. Limits of applicability

It should be borne in mind, however, that this type of standardization approach is not without its limitations. First of all, tests were carried out using fluids stored under ambient conditions (i.e. at temperatures ranging from 18 to 25 °C, maximum). Temperature variations beyond this range can significantly alter fluid viscosity and therefore the DSD of the mist. It is therefore important to carry out tests at a constant, controlled temperature.

The tests were carried out on mists having a DSD between 5 and 100 µm. Alternative generation systems to those described in Section 2.3, which could lead to higher droplet sizes, would require shorter ignition times to avoid sedimentation/segregation of the mist.

In addition, the experimental campaigns were carried out for concentration ranges from a few g.m⁻³ to a maximum of 800 g.m⁻³. Higher concentrations inevitably accentuate coalescence and increase rain-out phenomenon at the vessel walls. By way of comparison, for high concentrations, it might be interesting to carry out identical tests in 1 m³ sphere.

Explosion severity is determined by the parameters Pmax and dP/dtmax. An equivalent of the Kg or Kst index (e.g. Km) can only be given as an indication and depends on the validity of the cube-root-law for hydrocarbon mists (i.e. on the thickness of the flame front).

It is also worth noting that these tests do not directly concern explosive liquids, such as nitroglycerin or methyl nitrate, until it is ensured that the atomization mode does not, in the absence of an

external source, generate their ignition.

Finally, as with any standardized protocol, the aim of these procedure is not to accurately reproduce the reality of every potential mist explosion on an industrial site, but to enable a reproducible and sufficiently conservative assessment of the explosion risk, as well as a consistent classification of the safety parameters associated with different aerosols.

## 3. Proposition of a standard

When predicting a fuel mist cloud's explosion severity and ignition sensitivity, it is safer to imagine a worst-case scenario. As previously observed (El-Zahlanieh, 2022), the increase of the DSD did not lead to a more sensitive mist cloud or a severer explosion. Moreover, when a plateau was reached, the influence of increasing the mist concentration weakened. As for the turbulence level, its influence varied from one fuel, or more exactly fuel class (Gant et al., 2016), to another.

Therefore, it is advised to use nozzle set N1 (Section 2.3) for the standard test method as it is sufficient to evaluate the required parameters with a DSD that does not surpass 15 µm and concentrations reaching 200 or 250 g.m⁻³ for an air injection pressure of 3 bar.

### 3.1. Fuel classification

The liquid classification proposed by the HSE was used as a foundation (Section 2.4). Nevertheless, seen that the current classification concerns testing on a laboratory-scale test bench and that the liquid exits the spray nozzle atomized, only secondary atomization should be considered to see if the droplet resists aerodynamic and internal instabilities. Following the steps proposed by Burrell and Gant (2017), the droplet Weber number was first calculated according to Eq. (1):

$$We = \frac{\rho_l v^2 d_d}{\sigma_l} \quad (1)$$

where ρl is the liquid's density, v is the relative velocity of the droplet, d_d is the diameter of the droplet, and σl is the surface tension of the liquid. The critical Weber number, which is defined as We at which the droplet
starts to break up, can be defined using the following equation:

$$We_c = 12 \cdot \left( 1 + 1.077 \cdot \left( \frac{\mu_l}{\sqrt{\rho_l d_d \sigma_l}} \right)^{1.6} \right) \quad (2)$$

Liquids were classified according to the ratio We/We<sub>c</sub>, considering a reference mean droplet diameter d<sub>50</sub> of 9 µm, as well as a velocity of 5 m.s<sup>-1</sup> (values determined at the center of the sphere from in-situ particle size distribution measurement and from PIV experiments, respectively). Calculations of the ratio We/We<sub>c</sub> are presented in Table 4 and show that, when using the nozzle set N1, the droplets generated are considered stable. It should be noted that most of the ratio range between 0.45 and 0.71, with exception of Mobil DTE lube oil. It should also be highlighted that the ageing and storing conditions of the liquids should be considered as they affect their physical properties and therefore both the ignition sensitivity and the explosion severity of the mist.

In addition to Weber number, Spalding number B<sub>T</sub> has been considered as an indicator related to the ease of droplet evaporation. This heat transfer number is usually expressed as follows:

$$B_T = \frac{C_p \cdot \Delta T}{\Delta H_{vap}} \quad (3)$$

The increase in temperature ΔT can be associated with the Minimum Ignition Energy MIE via the mist concentration C<sub>m</sub>, the heat capacity C<sub>p</sub> and the characteristic diameter d<sub>c</sub> of the cloud's volume (Ballal and Lefebvre, 1978):

$$B_T = \frac{MIE}{\Delta H_{vap} \cdot C_m \cdot d_c^3} \quad (4)$$

When plotting B<sub>T</sub> as a function of the Weber ratio, the liquids were divided into four quadrants as shown in Fig. 5 (for an arbitrary critical diameter of 1 cm and a mist concentration of 100 g.m<sup>-3</sup>). This implies that the classification presented by the HSE (Gant et al., 2016) and adapted to the current study's reference conditions is sufficient to divide liquids according to their atomization and volatility, simultaneously reflecting on their flammability and explosivity. It should be noted that both isooctane and ethanol will be considered in Quadrant I, whereas they are not considered by HSE classification as their flashpoints (FP) are below 32 °C. Even if ethanol and isooctane vaporize quickly upon release, they may still form a mist hazard, especially in confined environments. It was, therefore, of interest to add them to the current classification and to remove the lower FP boundary.

## 3.2. Choice of test procedures

In order to initiate the experimental procedure, both the Weber ratio and the Spalding number (but as it depends on the MIE, the flashpoint can be alternatively considered) should be known. Experimenters can suppose that the reference diameter remains unchanged if the tested liquids are of very similar properties to those tested for this study. Otherwise, correlations may be used (Elkotb et al., 1982; El-Zahlanieh, 2022), and the liquid class can, therefore, be identified.

This section details the steps to choose the right procedure for each liquid class (quadrants I to IV – Fig. 5). Section 3.3 will describe the three detailed procedures (I, II, and A). If it is wished to preheat the liquid and test it at ambient temperatures, it is advised to re-evaluate its physico-chemical properties at the required temperature and recalculate its Weber ratio to verify to which class it belongs.

Moreover, if possible, it is preferred that mass flow rate and pressure

increase calibration tests be performed before the experimental cycle to determine the mist concentration and the vacuum pressure accurately. If not possible, it is advised to refer to Table 5. Furthermore, performing each test at least three times for repeatability is recommended. The sphere should be thoroughly cleaned between each experiment to avoid impurities (e.g. residual soot).

### 3.2.1. Quadrant I liquid

Among the other liquids, this fuel class is relatively easy to ignite. Fig. 6 depicts a flowchart detailing a standard procedure to determine the ignition sensitivity and explosion severity of a liquid of Quadrant I.

a) If the operating temperature exceeds 27 °C, Procedure II should be followed using a 100-J spark ignition. If ignition occurs, the experimenter should obtain the LEL, the explosion severity curves, and the P<sub>max</sub> and dP/dt<sub>max</sub> at the end of the experiment. In this case, the LEL of the liquids tends to be greater than that of their vapors. According to the predetermined requirements, the experimenter can either suppose that the MIE is less than or equal to 100 J or perform Procedure A (see Section 3.3) to determine the MIE at a chosen optimal concentration. If no ignition occurs at 100 J, it is advised to perform the same procedure using 5-kJ chemical ignitors and, if it is of interest, assess the optimal concentration at 1 kJ to obtain an MIE approximation. Seen that the sphere is preheated, it is generally unnecessary to test at 10 kJ in the case of no ignition at 5 kJ.

b) If the liquid is operated at ambient temperature, Procedure I should be followed using 100 J spark ignition. The subsequent steps are similar to those mentioned above, except that testing at 10 kJ is advised if no ignition occurs at 5 kJ. This generally does not happen in the case of Quadrant I liquids.

### 3.2.2. Quadrant II liquid

None of the selected seven liquids fell into this class; therefore, no exact procedure can be given. Nonetheless, such liquids are of the same level of volatility and have more stable droplets than those of quadrant I. Therefore, it is advised to follow the recommendations given for quadrant I liquids to cover all the bases.

### 3.2.3. Quadrant III liquid

The liquid that belongs to this quadrant (here, Mobile DTE) did not exhibit any ignition under different configurations. Nevertheless, accidental releases and fires have occurred in cases involving hydraulic oils that might fall into this category (see introduction). Most of such cases occurred at high operating temperatures. It is therefore advised to perform the right half of the flowchart proposed for a Quadrant IV liquid (framed in red in Fig. 7).

### 3.2.4. Quadrant IV Liquid

Fig. 7 portrays a flowchart detailing a proposed experimental cycle to follow for liquids belonging to this quadrant. This proposal was based on the trends observed by biodiesel mist clouds. Nevertheless, additional information may be required. Starting energy of 5 kJ (if handled at ambient temperatures) is advised to test such liquids. If no ignition occurs using 5 kJ and 10 kJ ignitors, it is advised to preheat the sphere to a temperature below the flashpoint to increase the vapor content mildly. If the operating temperature is above 27 °C, a regular experimental series following procedure II and starting at 100 J is proposed.

## 3.3. Test procedures

As mentioned before, three different procedures (I, II and A) are

<table><caption>**Table 4**
Calculated Weber ratio for the selected fluids for d<sub>50</sub> = 9 µm and v = 5 m.s<sup>-1</sup>.</caption><thead><tr><th>Liquid</th><th>Ethanol</th><th>Isooctane</th><th>JetA1</th><th>Diesel B7</th><th>LFO</th><th>Biodiesel B100</th><th>Mobil DTE</th></tr></thead><tbody><tr><td>We/We<sub>c</sub></td><td>0.71</td><td>0.70</td><td>0.60</td><td>0.55</td><td>0.61</td><td>0.45</td><td>0.01</td></tr></tbody></table>
<figure><img src="image_8.png" /><figcaption>Fig. 5. Classification of the fuels as a function of their Spalding number and Weber ratio. The flashpoint, used in HSE classification, is given for comparison.</figcaption></figure>

<table><caption>**Table 5**
Maximum flow rates and pressure increase as a function of the nozzle set and air injection pressure.</caption><thead><tr><th></th><th>Injection pressure</th><th>2 bar</th><th>3 bar</th><th>4 bar</th><th>5 bar</th></tr></thead><tbody><tr><td rowspan="3">Liquid flow rate (g.s<sup>-1</sup>)</td><td>Nozzle set N1</td><td>0.28</td><td>0.24</td><td>0.24</td><td>0.23</td></tr><tr><td>Nozzle set N'</td><td>1.32</td><td>1.15</td><td>1.15</td><td>1.13</td></tr><tr><td>Nozzle set N2</td><td>1.68</td><td>1.58</td><td>1.68</td><td>1.67</td></tr><tr><td rowspan="3">P increase (mbar.s<sup>-1</sup>)</td><td>Nozzle set N1</td><td>29.3</td><td>36.9</td><td>45.0</td><td>49</td></tr><tr><td>Nozzle set N'</td><td>32.6</td><td>39.7</td><td>50.5</td><td>57.6</td></tr><tr><td>Nozzle set N2</td><td>28.4</td><td>40.3</td><td>54.4</td><td>59.5</td></tr></tbody></table>

proposed as a function of the liquid classification.

### 3.3.1. Procedure I

This procedure takes place at a controlled ambient temperature. The sphere should be equipped with an insulating system or a temperature control apparatus. Moreover, with some modifications, the experimental cycle should follow the proposed modus operandi introduced in Section 2.2. The turbulence level is set to that corresponding to a compressed air injection pressure $P_{inj}$, equal to 3 bar. To cover a complete range of concentrations it is advised to start with 1-s injections (1-s steps) with a maximum injection time $t_{inj}$ of 10 or 12 s, depending on the mass flow rate.

### 3.3.2. Procedure II

For this procedure, the operating temperature of the liquid should be known. To perform the tests at the same temperature, the 20 L sphere should be equipped with a heating system. It is advised to perform temperature calibration tests before the experimental series to ensure that the sphere's center is heated to the required temperature after a specific time $t$. A similar procedure should be followed for the experimental cycle, except for preheating the sphere to the required temperature at which the liquid operates. Between each test, it is recommended to wait at least 5 min or the predetermined required time to stabilize the temperature in the sphere.

### 3.3.3. Procedure A

An optimal mist concentration should be identified first for determining the MIE of the liquid. Explosion severity tests should therefore be conducted before. In the case of a plateau curve, the first concentration corresponding to $P_{max}$ should be considered the optimum. Once the

concentration is identified, the high-voltage spark ignition system, presented in Section 2.4, can be installed to determine the MIE. If heating is required, procedure II should be followed for a single concentration. Otherwise, procedure I should be respected. If no ignition occurs at a specific energy, it is advised to redo the same test at least ten times. If no ignition takes place for ten consecutive times, the last tested energy at which ignition occurred is considered the MIE. Attention should be paid to the distance between the two electrodes (6 mm) and the temperature rise between tests. The relative level of humidity of the atmospheric air and the quality of the pressurized air may also affect findings. The same procedure can be carried out at any other concentration if needed.

### 3.3.4. Test report

Following the procedures mentioned above should allow the experimenter to determine:

a) The explosion severity of the mist cloud, comprising the evolution of $P_{ex}$ and $dP/dt_{ex}$ as a function of the mist concentration, as well as $P_{max}$, $dP/dt_{max}$, and their corresponding concentration $C_{opt}$.

b) The LEL of the mist cloud at the operating conditions. This parameter should be determinable from the evolution of $P_{ex}$ and $dP/dt_{ex}$ as a function of the mist concentration.

c) The MIE of the mist cloud at the operating conditions.

## 4. Case studies

Application of the previous procedures for determining the explosion severity of mists enables the assessment of explosion risk and the implementation of ATEX directives/DSEAR. The three cases below comprise different ways a mist release can occur under varying conditions; they are not intended to be applied directly to industrial cases but are only used to illustrate the practical impact of this study.

a) Case 1: a rotary fuel pump filling a Jet A1 supply tank exhibited corrosion, which led to a Jet A1 mist release. The pump was functioning at 15 bar and was located indoors.

b) Case 2: an indoor high-pressure injection pipe for a diesel engine operating at 800 bar punctured.
<figure><img src="image_9.png" /><figcaption>Fig. 6. Flowchart of a standard procedure to determine the ignition sensitivity and explosion severity of a liquid of Quadrant I.</figcaption></figure>

<figure><img src="image_10.png" /><figcaption>Fig. 7. Flowchart of a standard procedure to determine the ignition sensitivity and explosion severity of a liquid of Quadrant IV or, by extension, Quadrant II.</figcaption></figure>

c) Case 3: a ruptured control valve installed in a closed pipe-work system transporting biodiesel at 10 bar in an unobstructed heated environment of 80 °C.

Table 6 presents the release and location characteristics of the three cases. A succinct hazardous area classification procedure was followed, as proposed by IEC 60079-10-1 (2020), with additional considerations concerning the presence of droplets in the flammable clouds.

The release sources were classified as secondary grade releases

because they were accidental discharges that were not expected to occur in regular operations. The LEL values of the liquids were those identified experimentally at the corresponding temperatures. The liquid release rate was determined depending on the orifice shape and size and the pressure differential. Subsequently, it was possible to determine the released jet's atomization degree by calculating the Weber ratio discussed in Section 3.1. The release class of each liquid was consequently reattributed as shown in Fig. 5. Following the findings of Gant et al. (2016), releases belonging to Quadrant I with a pressure above 1 bar can
<table><caption>**Table 6**
Release and location characteristics of the three cases. * Safety factor as defined in IEC 60079-10-1 (2020).</caption><thead><tr><th></th><th>Case 1</th><th>Case 2</th><th>Case 3</th></tr></thead><tbody><tr><td>Leaked liquid</td><td>Jet A1</td><td>Diesel B7</td><td>Biodiesel B100</td></tr><tr><td>LEL (kg.m<sup>-3</sup>)</td><td>0.06</td><td>0.08</td><td>0.1</td></tr><tr><td>Release source</td><td>secondary</td><td>secondary</td><td>secondary</td></tr><tr><td>Release rate (kg. s<sup>-1</sup>)</td><td>0.19<br>5 mm sharp orifice – discharge coefficient 0.752</td><td>1.13<br>3 mm rounded orifice – discharge coefficient 0.952</td><td>0.08<br>2.5 mm sharp orifice – discharge coefficient 0.752</td></tr><tr><td>Release class (Fig. 5)</td><td>I</td><td>I</td><td>IV</td></tr><tr><td>Minimum ventilation flow rate (m<sup>3</sup>.s<sup>-1</sup>)</td><td>6 safety factor 0.5*</td><td>28.85 safety factor 0.5*</td><td>1.9 safety factor 0.5*</td></tr><tr><td>Volume under consideration (m<sup>3</sup>)</td><td>150 naturally ventilated building</td><td>150 naturally ventilated building</td><td>- calm conditions</td></tr><tr><td>Degree of dilution</td><td>low</td><td>low</td><td>medium</td></tr><tr><td>Zone type</td><td>zone 1 or 0</td><td>zone 1 or 0</td><td>zone 2</td></tr><tr><td>Zone extent (m)</td><td>25</td><td>40</td><td>15</td></tr></tbody></table>

be considered prone to creating a hazardous zone. Depending on the grade of release and the LEL of the clouds, a characteristic ventilation flow rate was determined, supposing that the clouds are formed of fuel vapors. It can be seen that for cases 1 and 2, this characteristic flow rate is much higher than the available air flow rate in the building (0.085 m³. s⁻¹), implying that the degree of dilution is low and classifying the hazardous areas in both cases as Zone 1; while for case 3, as biodiesel belongs to Quadrant IV and the degree of dilution is medium, Zone 2 suits as a classification. However, as the clouds would consist of both liquid droplets and a vapor phase, the characteristic ventilation flow rate may not be sufficient to decrease the cloud's concentration to less than its corresponding LEL. Ventilation may also increase coalescence or induce more turbulence. Moreover, mist clouds may absorb heat from the surroundings, adding to the vapor cloud. Several scenarios can take place, but it is clear that the LEL is insufficient to classify a hazardous area for mists, and other parameters, such as the ease of ignition, should be considered.

Another practical application of these experimental protocols would be to size explosion vents directly from the values of the parameters $dP/\ dt_{max}$ (or $K_m$ if the cube-root law is considered as valid) and $P_{max}$ of the mists instead of considering the explosion severity of the corresponding vapors (i.e. $K_g$). For instance, the deflagration index of ethanol varies from 105 bar m⁻¹.s⁻¹ for vapor (Mitu and Brandes, 2017) to 188 bar. m⁻¹.s⁻¹ for mist (El-Zahlanieh, 2022). In the case of an isolated compact enclosure of 200 m³ and a reduced pressure of 0.8 bar, the geometrical vent area A would then be increased by 1.2 m² for an ethanol mist (EN 14994, 2007).

Finally, as Puttick (2008) pointed out, the determination of a reliable MIE for a flammable mist allows to decide whether precautions against incendive electrostatic discharges are necessary. For example, although the biodiesel B100 tested in this study was found to be flammable in mist form, its MIE greatly exceed 100 mJ (i.e. 5 kJ), making grounding measures unnecessary in this case.

## 5. Conclusions

Although mist explosion has been the subject of numerous investigations, there is currently no accepted standard test procedure to determine safety parameters needed by process safety engineers for DSEAR/ATEX zone classification and to quantitatively assess the potential effects of an explosion. To remedy this shortcoming, an experimental protocol has been developed based on the extensive study of seven combustible hydrocarbons, and using existing standards for gases and powders, to determine the ignition sensitivity and explosion severity

of liquid aerosols.

A liquid classification system has been proposed: this system divided liquids into four quadrants according to their flash point and droplet stability during secondary atomization (i.e. the Weber ratio). Experimenters can assume that the reference diameter remains unchanged if the liquids tested have properties very similar to those of the liquids tested for this study; otherwise, correlations can be used, and the liquid class identified. The steps to be followed for each liquid class (quadrants I to IV) and three detailed procedures (I, II and A – Figs. 6 and 7) for assessing the ignition sensitivity and explosion severity of mist clouds have been detailed.

The development of such a protocol, whose structure is based on the usual international standards, has practical implications for process safety experts. In this way, as illustrated in Section 4, the accurate determination of a LEL for a mist enables hazardous area classification. Knowledge of explosion severity parameters also enables vents to be sized more precisely than by considering the characteristics of the respective vapors. Similarly, the determination of the MIE of a mist can be used to adjust electrostatic discharge prevention measures (e.g. relevance of vessel grounding during tank cleaning with liquid jets).

However, there is certainly room for improvement and future research is required, especially in the following areas:

a) First, it is essential to know precisely the quantity of liquid injected. Even it is preferable that mass flow and pressure rise calibration tests be carried out prior to the experimental run to accurately determine mist concentration and vacuum pressure, these steps are difficult to implement experimentally. For instance, a suitable solution would be an automated system comprising a feed valve controlled by a measurement of the mass of liquid injected.

b) Second, it is also necessary to limit or at least estimate the quantity of liquid lost by sedimentation or rain-out at the sphere's walls, which is not easy to achieve, especially at very high turbulence levels. Subsequently, a more exact estimate of the maximum injection duration can be identified. In addition, an experimental approach that can cover as many scenarios as possible while remaining controllable and comprehensible is suitable. More nozzle combinations with higher injection pressures could also be tested to explore higher or lower DSDs and turbulence levels.

c) Finally, the potential presence of impurities as well as the ageing and storing conditions of hydrocarbons should be considered as they affect both the ignition sensitivity and the explosion severity of the cloud. Accelerated ageing protocols (e.g. temperature cycling) could be applied to hydrocarbons to assess the impact of ageing on explosion risk.

As it is difficult to define the limits of a mist cloud, it is also challenging to define a standard without limitations, but one has to start somewhere! This study can therefore be the starting point through which future studies can pass to establish better understandings and procedures to evaluate the flammability and explosivity of fuel mists.

## CRediT authorship contribution statement

Stephanie El-Zahlanieh: Writing – original draft, Methodology, Investigation, Data curation. Alexis Vignes: Writing – review & editing, Supervision, Resources, Project administration, Funding acquisition, Conceptualization. Olivier Dufaud: Writing – review & editing, Validation, Supervision, Methodology, Investigation, Conceptualization.

## Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
## Acknowledgements

The authors would like to thank Yann Niedergang, Charly Koenig and David Brunello from LRGP-CNRS for their technical support in adapting and controlling the explosivity test equipment.

## Appendix A. Supporting information

Supplementary data associated with this article can be found in the online version at doi:10.1016/j.psep.2025.107195.

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