# Investigating overpressure BLEVE effects on 100% liquid full vessel

El Mehdi Laamarti, A.M. Birk, Clément Chanut, Frederic Heymes

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El Mehdi Laamarti, A.M. Birk, Clément Chanut, Frederic Heymes. Investigating overpressure BLEVE effects on 100% liquid full vessel. Process Safety and Environmental Protection, 2025, 199, pp.107191. 10.1016/j.psep.2025.107191. hal-05068763

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# Investigating overpressure BLEVE effects on 100 % liquid full vessel

E.M. Laamarti<sup>a,b</sup>, A.M. Birk<sup>a</sup>, C. Chanut<sup>b</sup>, F. Heymes<sup>b,*</sup>

## ARTICLE INFO

Keywords:

Overfilling

Boiling liquid expanding vapor explosion
(BLEVE)

Shock wave overpressure

Hydrostatic failure

Compressed liquid

Impulse

## ABSTRACT

Despite extensive research done over several decades, BLEVE accidents persist and yet the complexity of this particular type of explosion poses ongoing challenges in the industry. Existing literature underscores the need to investigate BLEVE hazards to mitigate substantial threats to property and life, especially in populated areas. While previous studies have provided definitions and models for BLEVE, primarily concentrating on free field overpressure, the respective contributions of vapor and liquid phases in hazard formation remain unclear among various authors. This paper delves into the dynamics of a BLEVE emphasizing the critical role of liquid fill level in the overpressure hazard. This research is based on recent BLEVE experimental campaigns conducted in 2022 and 2024 on small-scale cylindrical aluminum vessels filled with pure propane. Cutting-edge scientific tools, including low and high-speed measurement instruments were employed to capture detailed data to extend the current understanding of a BLEVE. Particular attention was given to the fully liquid cases (100 %) as they represent a special case of a BLEVE. Valuable findings were obtained from experimental results regarding the relative contributions of vapor and liquid phases, addressing a critical gap in BLEVE comprehension. Key findings from experimental data indicate that the full liquid cases are characterized by two distinct types of failure pressures: the failure pressure and the saturation pressure at failing temperature. Additionally, it was observed that the full liquid cases exhibited the lowest peak overpressure and the longest lead overpressure duration relative to the failure pressure. A distinct trend line was identified in the full liquid experiments. If validated at large scale, the results of this investigation could serve as useful knowledge for industry and engineering by assisting in estimating the risks and consequences associated with BLEVE accidents, thus contributing to enhanced safety practices in industrial settings.

## 1. Introduction

The boiling liquid expanding vapor explosion (BLEVE) corresponds to a particular type of physical explosion very common to the industrial sector. The potential hazards capable of unleashing catastrophic consequences have been a subject of investigation by many researchers over the past decades. Regrettably, to date, BLEVE accidents persist and yet a complete understanding of the phenomenon remains elusive. For this paper, we define the BLEVE as the sudden release of thermo-mechanical energy due to the catastrophic failure of a pressure vessel containing a pressure liquefied gas such as propane or heated water (Chen et al., 2007; Heymes et al., 2019; Heymes et al., 2020). The contained liquid is well above its normal atmospheric pressure boiling point temperature at the moment of failure. The loss of containment results in a rapidly expanding vapor and flashing liquid. Such processes hold true for flammable and non-flammable substances. One common mode of failure

of a pressure vessel is when the vessel wall is accidentally heated and reaches a state beyond its design limits. This lead to an increase in internal pressure. The high wall temperature weakens the vessel walls and causes failure.

The understanding of the BLEVE mechanism has been elaborated through the years, based on observations from experiments and real-life cases for various fluids, scales, and vessel shapes. Walls (1978) was among the first to come up with a definition stating that the BLEVE corresponds to the “ Failure of a major container into two or more pieces, occurring at a moment when the contained liquid is at a temperature above its boiling point at normal atmospheric pressure.”. While most BLEVE accidents resulted in projectile hazards, experiments have shown that projectiles are not systematically produced.

A clear definition of BLEVE has been then developed by witnessing and studying the tragic BLEVE accidents, including several documented by Abbasi and Abbasi (2007). Indeed, the BLEVE accidents commonly

<footnote><sup>a</sup> Queen's University Department of Mechanical and Materials Engineering, Kingston, ON K7L 3N6, Canada</footnote>

<footnote><sup>b</sup> Laboratoire des Sciences des Risques, IMT Mines Ales, Ales, France</footnote>

<footnote>* Corresponding author.</footnote>

<footnote>E-mail address: frederic.heymes@mines-ales.fr (F. Heymes).</footnote>
resulted in projectiles, fireballs, flashfires, vapor cloud explosions, shock wave overpressure, and domino effect and yet more recently in Bologna, Italy in August 2018, a traffic accident triggered a BLEVE that caused partial bridge collapse in the highway. This called for the importance of studying the ground load hazard.

Most of the publications focused on estimating the lead blast over-
pressure from a BLEVE using the thermo-mechanical expansion energy
in the vessel at the moment of failure. Starting from Brode (1959) with
the constant volume energy addition, Smith and Van Ness (1996) with
the isothermal expansion to more recent methods considering real gas
behavior; for instance, adiabatic irreversible vapor expansion with a
flash fraction of the liquid proposed by Planas-Cuchi et al. (2004), Casal
and Salla (2006) where part of the energy released was used to rupture
the vessel and eject the projectiles, and Hemmatian et al. (2017) that
proposed a new method based on a quasi-linear relationship between
mechanical energy, explosion temperature and filling degree.

Nevertheless, these models mainly focus on the far-field effect while the most damage tends to happen at the near-field. Some authors, for instance Laboureur et al. (2015) and Eyssette (2018) performed several propane BLEVE experiments at a small-scale and focused on the near-field overpressure. Birk et al. (2018) propose to study the near-field effect of the blast using the Friedman Whitham relation for spherical shock waves from Friedman, (1960) giving a satisfactory overprediction of the subsequent higher overpressure. Moreover, Laamarti et al. (2024) extends the study by developing a mathematical correlation to estimate the duration of lead peak overpressure and the subsequent impulse based on operating conditions from small-scale experiments. Indeed, limited interest has been given to the duration of the strongest lead peak overpressure, and, consequently, the impulse. The destructive potential of the BLEVE does not solely stem from the highest peak overpressure but, rather, is primarily influenced by the highest impulse (Dunjó et al. 2016). Nevertheless, all the models available in the literature are contradictory on whether the lead shock overpressure results from solely vapor phase or a flash fraction of the liquid is also implicated.

According to Birk et al. (2019), the ground load in a BLEVE is attributed mostly to the liquid phase. The low delayed phase change of the liquid is too slow to contribute to the lead shock overpressure formation. This aligns with the conclusions of Baker et al. (1983). Consequently, in the case of overfilling, it is anticipated to have the highest ground load, compared to lower liquid fill levels, and no shock formation.

The most catastrophic instance of BLEVE resulting from overfilling, as documented by Abbasi and Abbasi (2007), occurred in 1978 in San Carlos, Spain. This tragic accident involved a propylene BLEVE and resulted in a staggering total of 211 fatalities due to the fires and possible vapor cloud explosion. But was it really a 100 % liquid full BLEVE? Consequently, there arises a need to investigate experimental BLEVE scenarios to have a more in-depth understanding on the respective contribution of vapor and liquid phase.

The small-scale experiments are introduced as a crucial tool for
investigating BLEVE dynamics, allowing for a controlled and repeatable
environment to study the complex interactions leading to vessel rupture.
Despite their reduced size, these experiments effectively capture
fundamental thermodynamic, fluid dynamic, and structural failure
mechanisms that also govern large-scale BLEVE events. Additionally,
they allow for a further analysis of processes such as rapid depressur-
ization, flash boiling, shock wave formation and ground loading effects
while maintaining safety and cost efficiency. Moreover, small-scale ex-
periments serve as a foundation for the development of numerical
models (Laamarti et al., 2024) that can be extrapolated if validated at
large-scale.

This paper delves into the dynamics of the BLEVE and the critical
importance of liquid fill level on the overpressure hazard. This investi-
gation relies on a new dataset comprising 70 small-scale experiments
conducted during the recent propane BLEVE experimental campaigns in
2022 and 2024, complemented by 20 more experiments from Eyssette

(2018). Advanced scientific instrumentation was employed to perform
low and high-speed measurements. The experimental results extend the
existing data for a larger range of controlled variables including burst
pressure, liquid fill level, and weakened length.

2. Theoretical background

2.1. Contribution of liquid and vapor phase

The contribution of the liquid and the vapor phases in the BLEVE
event is crucial to understand the dynamics and potential consequences.
However, the precise impact of each phase on the hazards associated
with BLEVE accidents remains unclear and disputable between authors.
This ambiguity can be attributed to the dynamic nature of BLEVE events.
BLEVEs are transient events involving the intricate opening of the vessel
and the release of the vessel contents. This involves rapid and complex
phase transitions. The transition from the liquid to vapor phase, referred
to as flashing, occurs rapidly due to the abrupt and substantial pressure
drop, making it challenging to precisely quantify the individual contri-
bution of each phase. Modeling such multiphase complex flows accu-
rately requires sophisticated computational methods, and the inherent
uncertainties in these models contribute to the challenge of determining
phase-specific contributions.

Based on experimental observations from Baker et al. (1983), Birk and Cunningham (1996), Balke (1999) and Birk et al. (2007) the lead shock overpressures are governed by the vapor phase expansion only. The supersonic shock propagation outpaces the ability of the liquid to be directly involved. As a result, the contribution of the liquid boiling repressurization of the vessel can only occur during the third wave overpressure. The second shock overpressure is also produced by only the vapor phase from the low pressure conditions created beneath the first shock overpressure and the high pressure released from the vessel. Advancements in experimental techniques, as demonstrated by Birk et al. (2019) through high-speed imaging, confirm the validity of these assumptions. Indeed, observations indicate that the liquid fill level has a major contribution to the steepness of the overpressure. Furthermore, Eyssette (2018) through shadowgraph images and pressure signals, observed that two experiments under similar operating conditions but varying liquid fill levels exhibited distinctly different overpressure trends. The scenario with a higher vapor content displayed a more pronounced initial pressure shock and the highest shock overpressure magnitude, in contrast to the case with a higher liquid fill level. The vapor space produces a lead shock followed by an underpressure followed by a second shock overpressure. The liquid produces a third-wave dynamic overpressure but it is not a shock. This suggests that in situations where the vessel contains 100 % liquid fill level, having a shock is not expected.

Giesbrecht et al. (1981) conducted medium-scale BLEVE experi-
ments using spherical glass pressure vessels (0.226–1 m³) 100 % full of
liquid propylene. They concluded that the overpressures obtained could
only be attributed to “the spontaneous evaporation process of the flash
fraction of the liquid which can vaporize at isentropic expansion”. The
process of evaporation of superheated liquid, sometimes referred to as
explosive boiling, relies on ideal assumptions and is contingent upon
achieving homogeneous nucleation temperature (atmospheric super-
heat limit temperature), as outlined by Reid (1976), (1979). Indeed, this
form of nucleation requires special conditions, including the absence of
preferred nucleation sites, perfect surface roughness, no impurities, no
bubbles, homogeneous temperature stratification. This is far from being
achieved in real-world pressure vessels. Data on the steepness of the
resulting overpressure and pressure signals could aid in determining
whether the observed overpressures were shocks or just strong dynamic
overpressures. This approach of explosive evaporation is supported by
authors like Prugh (1991), Planas-Cuchi et al. (2004), Van den Berg et al.
(2004), and Casal and Salla (2006).

Current literature reveals a wide range of studies and models put
<figure><img src="image_4.png" /><figcaption>Fig. 1. [Left] Pressure-volume (P-V) and [Right] Pressure-temperature (P-T) chart.</figcaption></figure>

<figure><img src="image_5.png" /><figcaption>Fig. 2. Apparatus from BLEVE 2022/2024 experimental campaigns.</figcaption></figure>

forth to predict the overpressure associated with BLEVE. Wang et al. (2022) reviewed BLEVE overpressure prediction methods, highlighting challenges in near-field and far-field studies, including the need for more comprehensive experiments on factors like crack geometry, environmental interactions, and liquid types. Indeed, the models adopt diverse approaches regarding liquid and vapor contributions and do not account for the complexity of the opening dynamics, while most hazards are associated with the shape of vessel failure (Laamarti et al. 2024) and the groove shape length as studied by Li et al. (2018, 2020) on CO2 BLEVEs.

The current experimental data available in the literature lacks near-field controlled measurements, primarily because of safety concerns and technical considerations which limits the complete understanding of the underlying physics. To address this gap, controlled small-scale propane BLEVE experiments were conducted with detailed instrumentation. The objective was to investigate the validity of these assumptions and examine scenarios involving fully liquid-filled vessels.

## 2.2. Theory of compressed liquid

In a typical BLEVE scenario, the liquid and vapor inside the vessel remain in a thermodynamic equilibrium along the saturation line and the vessel fails under saturation conditions. Before vessel failure and during the heating process, the liquid undergoes thermal expansion due to heating, reducing therefore the available vapor phase volume. For a compressed liquid case, the liquid fill level rises, eventually reaching the top walls of the vessel, exerting therefore an increasing pressure on the

vessel structure under hydrostatic conditions. The static pressure and temperature leaves the saturation line and follow the path of a steep pressure rise, (see Fig. 1 [Right]) defined by factors such as the vessel's stiffness and the thermal expansion of the liquid. We consider this scenario as a particular case of a BLEVE, where the failure occurs under compressed liquid conditions rather than at typical saturation conditions.

The pressure-volume chart shown in Fig. 1 illustrates a typical process of initial depressurization for a compressed liquid. Following vessel failure, the compressed liquid initially at point A undergoes an isothermal drop in pressure until reaching point B. Throughout this phase, the liquid maintains its state without undergoing any phase change. However, upon reaching point B, the liquid enters a metastable superheated state. If the process continues to C, the superheat becomes unstable, and homogeneous nucleation takes place. However, as mentioned earlier this probably does not happen in real-life pressure vessel accidents, as flashing typically begins before reaching point C. Flashing will lead to a drop in temperature in the liquid.

Thus, once reaching point B, the experimental test exhibits a behavior typical of a BLEVE. Indeed, in actual BLEVEs the pressure drop is non-isothermal (point B') however the process is commonly regarded as isothermal due to the minimal variations in properties of compressed liquid with pressure, unlike superheated vapor (see appendix). Consequently, it is generally accepted to approximate the behavior of compressed liquid as that of saturated liquid at the given failure temperature. An improvement could potentially be achieved by applying a correction factor. However, this term is too small within the
<figure><img src="image_6.png" /><figcaption>Fig. 3. Blast gauges positions.</figcaption></figure>

<figure><img src="image_7.png" /><figcaption>Fig. 4. Summary of pressure-temperature (P-T) from Eyssette (2018), BLEVE 2022 and BLEVE 2024 experimental datasets. [Bara stands for Bar absolute].</figcaption></figure>

scope of the analysis and can therefore be negligible.

# 3. Small-scale BLEVE experiments

## 3.1. Apparatus

Experimental investigations were conducted to replicate real-life BLEVE scenarios on a small-scale (Length to diameter L/D = 6). The tubes involved are cylindrical, made of aluminum 6061 T6 annealed to T0 temper to reduce material tensile strength. The respective dimensions are 305 ± 5 mm long, 50.8 ± 0.8 mm in diameter and, 1.65 ± 0.05 mm thickness. To control the burst location, machining was performed using a milling machine along a specific length on the top of the tube, reducing the wall thickness and introducing a local weakening of the vessel. Keeping the thickness of the thinned area constant, an increase in the weakened length correlates with a decrease in failure pressure. Additionally, reducing the wall thickness significantly decreases the burst pressure. The controlled (independent) variables were the failure pressure, liquid fill level, and the weakened length. The dependant variables were the overpressure magnitude, duration and impulse. The experimental tubes were filled with propane (purity

99.5 %) for the desired liquid fill levels, weakened lengths, and failure pressures.

Various instruments were employed to capture details of the BLEVE, including:

* Four high-speed cameras strategically positioned to encompass a wide array of viewpoints from the experiment:

* Phantom TMX 7510 (76,0000 fps (frames per second) / 1280 × 800 pixels / exposure time: 3 µs) (Front side)

* Phantom V2512 (88,000 fps (frames per second) / 384x512 pixels / exposure time: 3 µs) (Top view to observe crack dynamics)

* Phantom V711 (7500 fps / 800x1280 / exposure time: 20 µs) (Window side)

* Photron FASTCAM SA5 (20,000 fps / 448x776 / exposure time: 125 µs). (End side)

* Thirteen pencil blast gauges with a total of eighteen sensors across different locations to measure the overpressure. Four vertical blast sensors above the tube are PCB137B28 [1 µs response time/ 14.5 mV kPa⁻¹ sensitivity / 0.2 % uncertainty] and the other gauges around the tube are PCB 137A23 [4 µs response time/ 14.5 mV.kPa⁻¹ sensitivity / 0.2 % uncertainty]. The acquisition sample rate is 200kS/s.

* Thermocouples type K at the middle of the tube in both liquid/vapor phases [Range from -270-1260 °C and uncertainty ± 2.2 °C]

* Static pressure in the vessel end: 1 mm diameter (TC-direct 716-072). [Range from 0 to 40 Bar, 0.5 s response time, uncertainty ± 0.3 %]

* Regular and high-speed pressure transducers at the tube end fitting, one piezoelectric pressure sensor PCB M101A02 transducer. [Range up to 34.5 Bar and uncertainty of 138 mBar]

* Four piezoelectric load cells PCB M202B each capable of measuring up to 44.5 kN of force. [uncertainty of 0.01 kN]

120 VAC electric heater (125 watts) to heat the propane liquid from below.

* Electric valves for purging/venting, propane weight scale, a tube cradle, Swagelok end fittings with Dk-Lok ferrules, an infrared camera FLIR GF320 GASFIND to detect leaks.

* LTM Cinepar 575 W HMI projector and MultiLed MX 550 W (50 000 Lumen) used for lightening.

The setup used to measure the near-field overpressure involved thirteen PCB 137A23 blast gauges strategically positioned at various angles (horizontal, vertical, 45-degree tilt) across different locations. Along these blast gauges, eighteen sensors are placed to measure the intensity of the blast. This arrangement enabled precise control of the overpressure concerning time, orientation, directionality, and distance. Each sensor's position is denoted with coordinates (x,y,z).

These blast gauges are specifically designed with a pointed shape to minimize their interference with airflow and pressure waves associated with BLEVE, ensuring a more accurate and representative measurement of actual overpressure. Fig. 3 illustrates the location and orientation of the sensors relative to the tube, where the left side denotes the filling side, and the right side represents the window side. We define the near-field overpressure being 3-10 times the tube diameter.

## 3.2. Experiment Overview

A summary of the thermodynamic conditions at failure from the experimental campaigns conducted in 2018 (20 experiments), 2022, and 2024 (70 experiments) is illustrated on a pressure-temperature (P-T) diagram in Fig. 4. Numerous experiments were performed at varying failure pressures, progressively complementing the dataset.
<figure><img src="image_8.png" /><figcaption>Fig. 5. [Left] Static Pressure [Right] Static Temperature from Experiment 1 - 2022.</figcaption></figure>

<table><caption>**Table 1**
Summary of Liquid full cases.</caption><thead><tr><th>Experimental campaign</th><th>Experiment number</th><th>L<sub>c</sub> (mm)</th><th>P<sub>f</sub> (Barg)</th><th>P<sub>sat at T<sub>fail</sub></sub> (Bara)</th><th>Degree of compressed liquid (P<sub>f</sub>-P<sub>sat at T<sub>fail</sub></sub>) in (Barg)</th></tr></thead><tbody><tr><td rowspan="5">2024</td><td>29</td><td>150</td><td>34.4</td><td>27.5</td><td>7.9</td></tr><tr><td>30</td><td>150</td><td>33.5</td><td>28.3</td><td>6.2</td></tr><tr><td>31</td><td>75</td><td>30.4</td><td>26.2</td><td>5.2</td></tr><tr><td>32</td><td>75</td><td>20.5</td><td>12.7</td><td>8.8</td></tr><tr><td>33</td><td>75</td><td>27.0</td><td>22.9</td><td>5.1</td></tr><tr><td rowspan="4">2022</td><td>1</td><td>150</td><td>19.8</td><td>17.0</td><td>3.8</td></tr><tr><td>12</td><td>150</td><td>24.9</td><td>15.0</td><td>10.9</td></tr><tr><td>13</td><td>150</td><td>27.7</td><td>19.1</td><td>9.6</td></tr><tr><td>32</td><td>75</td><td>22.9</td><td>19.2</td><td>4.7</td></tr><tr><td>Eyssette (2018)</td><td>17</td><td>150</td><td>19.8</td><td>10.4</td><td>10.4</td></tr></tbody></table>

Upon closer examination in Fig. 4, three distinct behaviors can be identified, primarily influenced by the liquid fill level. In most cases, the failure pressure is aligned with the saturation line, and the vessel has vapor and liquid in saturated equilibrium. When the liquid fill level (expressed as volume fraction) at failure falls greater than 0 or less than 100 % the liquid and vapor inside the vessel are saturated equilibrium, thus following the saturation line. If there is no liquid inside the vessel then we have only vapor or superheated vapor and a BLEVE is not possible and the pressure deviates from the saturation curve (similar to Air in Fig. 4). Similarly, if there is no vapor remaining, the pressure also leaves the saturation line and sharply increases under compressed liquid conditions. Ultimately, vessel failure occurs under hydrostatic rather than thermodynamic saturation conditions with 100 % liquid full. (ref: corresponding to the ten data points visible above the saturation line in Fig. 4)

The spinodal line delineates the theoretical limit between metastable and unstable liquid superheat. Beyond this limit, nucleation occurs at the molecular level, leading to homogeneous nucleation. For practical pressure vessels, the nucleation starts before the spinodal is reached. For a sudden pressure drop to ambient pressure, the highest degree of metastable superheat is achieved at the atmospheric superheat limit ($T_{SL}$ = 53.45 °C for propane).

Some authors, such as Reid (1979), propose that a BLEVE only occurs with homogeneous nucleation. If this holds true, real-world pressure vessels have probably not experienced a BLEVE due to the requirement of perfect smooth surface roughness, no impurities, no pre-existing bubbles, a large degree of superheat and homogeneous temperature stratification.

In the small-scale BLEVE experiments, verification of homogeneous nucleation was not possible with our apparatus. This requires sophisticated non-intrusive experimental techniques capable of detecting rapid changes in local pressures, and temperatures.

While the most severe BLEVEs typically occur when the liquid temperature at failure surpasses or equals the temperature of the superheat limit, it is noteworthy that a BLEVE can still happen when the vessel fails at a pressure below this limit. This can be observed in Fig. 4, where several experiments were conducted below this limit. However, the resultant consequences and hazards are typically less severe in such instances.

This limit delineates the terminology of “Cold BLEVE” and “Hot BLEVE” (Birk et al., 1993). Hot BLEVEs are considered more powerful as they can theoretically attain higher degrees of metastable superheat by approaching closer to the spinodal line.

### 3.3. Compressed Liquid

One of the objectives during the 2022 and 2024 experimental campaigns was to study BLEVEs resulting from 100 % liquid full scenarios. The main point was to gain a deeper understanding of the behavior and the underlying dynamics of BLEVEs occurring under compressed liquid conditions often referred to as subcooled liquid. In this state, the substance exists as a liquid but is subjected to pressure greater than its saturation pressure at the given temperature.

Fig. 5 illustrates the static pressure and temperature during the heating/filling process in a compressed liquid scenario. Initially, the tube is filled to a specific liquid fill level, ensuring it reaches full liquid capacity at the desired burst pressure as propane expands with rising temperature. As heating progresses, pressure and temperature inside the vessel increase along the saturation line. Once the vessel reaches full liquid capacity, a rapid pressure rise occurs, with the slope of pressure determined by the vessel's stiffness and the thermal expansion of the liquid.

As an example, in experiment 1 - 2022 the failure pressure and temperature are respectively 19.8 Barg and 49.7 °C [g stands for gauge
<figure><img src="image_9.png" /></figure>

<figure><img src="image_10.png" /><figcaption>Fig. 6. Lead overpressure for Experiment 5–2024 and 28 – 2024 at (Left) TOP1 gauge [15 cm vertically] (Right) TOP4 gauge [40 cm vertically].</figcaption></figure>

<figure><img src="image_11.png" /></figure>

<figure><img src="image_12.png" /><figcaption>Fig. 7. Lead overpressure for Experiment 29 – 2024 and 8 – 2024 at (Left) TOP1 gauge [15 cm vertically] (Right) TOP4 gauge [40 cm vertically].</figcaption></figure>

(relative) pressure]. Therefore, based on this saturation temperature, the corresponding saturation pressure is 17 Barg. Hence, the operating conditions of the experiments are presented as follows:

* The failure pressure $P_f$ [Barg or Bara]: g and a stand for gauge (relative) and absolute pressure

* The saturation pressure at failure temperature $P_{sat at Tfail}$ [Barg]

* The liquid fill level (volume fraction) $\varphi$ [%]

* The weakened length $L_c$ [m]: reduced wall thickness through machining.

The full liquid cases obtained from the experimental campaigns are presented in the following Table 1.

# 4. Experimental results

## 4.1. BLEVE overpressure

### 4.1.1. Influence of Liquid fill level

After obtaining the near-field overpressure data, the objective is to better understand the influence of the liquid fill level. Consequently, experimental tests conducted during the BLEVE 2024, under similar weakened lengths but varying liquid fills, were compared at two different sensors positions TOP1 and TOP4:

$$ \text{— \underline{Experiment 5–2024: } } L_c = 150 \text{ mm } | P_f = P_{sat at Tfail} = 23.3 \text{ Barg } | \varphi = 50 \% $$

$$ \text{— \underline{Experiment 28–2024: } } L_c = 150 \text{ mm } | P_f = P_{sat at Tfail} = 23.2 \text{ Barg } | \varphi = 99 \% $$

The overpressure fully forms between 3 and 4 times the diameter of the tube, approximately 15–20 cm above the tube for this apparatus, thus it is very interesting to compare the experiments at TOP1 gauge positioned at 15 cm above the tube. Fig. 6 distinctly illustrates what will later be referred to as the peak overpressure and the duration of the overpressure. Fig. 6 shows that in both experiments, the overpressure reaches TOP1 gauge simultaneously because they were both initiated with identical time intervals prior to the measurement. The lead overpressure observed in the 50 % liquid fill case displays a steeper rise compared to that in the 99 % case. This difference in steepness implies qualitatively that the lead overpressure in the 50 % liquid fill case may constitute a shock overpressure. Indeed, a shock overpressure is characterized by a sudden and sharp increase in pressure followed by a rapid decrease within a relatively short time, and that can be seen in Fig. 6. Moreover, in Fig. 6 (Left) it is apparent that the second wave speed forms later in experiment 28 – 2024 compared to experiment 5 – 2024.

### 4.1.2. Influence of Liquid fill level under similar $P_{sat at Tfail}$ [Compressed Liquid]

In Fig. 7, the following experiments are compared:

$$ \text{— \underline{Experiment 8–2024: } } L_c = 150 \text{ mm } | P_f = P_{sat at Tfail} = 26.2 \text{ Barg } | \varphi = 54 \% $$

$$ \text{— \underline{Experiment 29–2024: } } L_c = 150 \text{ mm } | P_f = 34.4 \text{ Barg; } P_{sat at Tfail} = 26.5 \text{ Barg } | \varphi = 100 \% $$
<figure><img src="image_13.png" /></figure>

<figure><img src="image_14.png" /><figcaption>Fig. 8. Lead overpressure for Experiment 30 – 2024 and 29 – 2024 at (Left) TOP1 gauge [15 cm vertically] (Right) TOP4 gauge [40 cm vertically].</figcaption></figure>

<figure><img src="image_15.png" /></figure>

<figure><img src="image_16.png" /><figcaption>Fig. 9. Lead overpressure for Experiment 17 – 2018 and 18 – 2018 at (Left) TOP1 gauge [15 cm vertically] (Right) TOP4 gauge [40 cm vertically].</figcaption></figure>

Fig. 7 compares the behavior of compressed liquid to ascertain if it differs from the high liquid fill level cases. The leak peak overpressure magnitude is nearly 1.5 as high for the 54 % liquid fill level compared to the 100 % liquid fill level, indicating a substantial contribution of the vapor phase in overpressure formation being primarily governed by the failure pressure. The graph shows a similar pattern at low liquid fill levels, where the overpressure starts with a steep pressure rise followed by an abrupt pressure decrease over a short duration. This overpressure behavior may suggest a shock formation for the 54 % liquid fill level case.

It is challenging to quantify the speed of the shock with the current instrumentation. The belief is that the liquid has a delayed phase change and does not contribute to shock formation. Despite the liquid fill level affecting the overpressure impulse, other factors such as the opening dynamics, the crack start position (middle or side), and consequently the crack speed come into play. Similar to Fig. 6 (Right), Fig. 7 (Right) shows that in Experiment 8 – 2024, the overpressure reaches the TOP4 gauge (positioned 40 cm vertically) faster than in Experiment 25 – 2024. Additionally, it’s noteworthy that the overpressure exhibits a longer decay time for scenarios involving compressed liquid. Moreover, it’s important to mention that the highest overpressure magnitudes observed in the three BLEVE campaigns were consistently obtained with low liquid fill levels, typically around 20 %.

### 4.1.3. Influence of $P_f$ and $P_{sat at Tfail}$ [Compressed Liquid]

In Fig. 8, the following experiments are compared:

$$ \text{— Experiment 29 – 2024: } L_c = 150 \text{ mm } |P_f = 34.4 \text{ Barg; } P_{sat at Tfail} = 26.5 \text{ Barg } | \varphi = 100 \% $$

$$ \text{— Experiment 30 – 2024: } L_c = 150 \text{ mm } |P_f = 33.5 \text{ Barg; } P_{sat at Tfail} = 27.3 \text{ Barg } | \varphi = 100 \% $$

Experiment 29 – 2024 and 30 – 2024 were analyzed under compressed liquid conditions, focusing on differences in the actual failure pressure $P_f$ and $P_{sat at Tfail}$. Experiment 29 – 2024 exhibited a higher $P_f$, whereas experiment 30 – 2024 demonstrated a higher $P_{sat at Tfail}$. Despite experiment 30 – 2024 having higher $P_{sat at Tfail}$, the slightly higher overpressure from TOP1 observed in experiment 29 – 2024 suggests that $P_f$ may play a role in governing the overall overpressure. However, these findings are inconclusive due to potential uncertainties in the experimental conditions and measurements. Further experiments under similar conditions are required to better understand and draw a clearer conclusion on the contributions of $P_f$ and $P_{sat at Tfail}$ to the resulting overpressure.

### 4.1.4. Influence of liquid fill level under similar $P_f$ [Compressed Liquid]

In Fig. 9, for instance, two experiments, respectively Experiment 17 – 2018 and 18 – 2018 conducted by Eyssette (2018) were compared failing both under a quasi similar $P_f$ but different $P_{sat at Tfail}$ and liquid fill levels. The operating conditions for these experiments are:

$$ \text{— Experiment 17 – 2018: } L_c = 150 \text{ mm } |P_f = 19.8 \text{ Barg; } P_{sat at Tfail} = 9.4 \text{ Barg } | \varphi = 100 \% $$

$$ \text{— Experiment 18 – 2018: } L_c = 150 \text{ mm } |P_f = 17.5 \text{ Barg; } P_{sat at Tfail} = 17.5 \text{ Barg } | \varphi = 61 \% $$
<figure><img src="image_17.png" /><figcaption>Fig. 10. Lead overpressure for Experiment 29 – 2024 and 31 – 2024 at (Left) TOP1 gauge [15 cm vertically] (Right) TOP4 gauge [40 cm vertically].</figcaption></figure>

<figure><img src="image_18.png" /></figure>

<figure><img src="image_19.png" /><figcaption>Fig. 11. Lead overpressure for Experiment 2 – 2024 and 15 – 2024 at (Left) TOP1 gauge [15 cm vertically] (Right) TOP4 gauge [40 cm vertically].</figcaption></figure>

<figure><img src="image_20.png" /></figure>

<figure><img src="image_21.png" /><figcaption>Fig. 12. Crack propagation from High-speed Video V25 for Experiment 2 – 2024 and 15 – 2024.</figcaption></figure>

This case demonstrates an important comparison between two scenarios with quasi-similar failure pressures $P_f$ and weakened lengths but different $P_{sat \ at \ Tfail}$. One scenario involves a system that is 100 % liquid-filled, where the liquid remains compressed at the point of failure. In

contrast, the other scenario includes a vapor space, which leads to the formation of a shock wave. Notably, in the fully liquid filled case, no shock wave is observed. Additionally, the spike in pressure recorded at 15 ms is attributed to signal noise rather than actual physical
<figure><img src="image_22.png" /><figcaption>Fig. 13. Lead peak overpressure from TOP 1 gauge [15 cm vertically] for high liquid fill levels cases [90–100 %] across different experimental campaigns at different weakened lengths [Black T#:150 mm; Orange T#: 125 mm; Blue T#: 100 mm; Red T#: 75 mm] with respect to $P_{sat at Tfail}$(The dashed black line identifies the peak vs saturation pressure at failure temperature for 100 % liquid fill level).</figcaption></figure>

<figure><img src="image_23.png" /><figcaption>Fig. 14. Lead peak overpressure from TOP 1 gauge [15 cm vertically] for high liquid fill levels cases [90–100 %] across different experimental campaigns at different weakened lengths [Black T#:150 mm; Orange T#: 125 mm; Blue T#: 100 mm; Red T#: 75 mm] with respect to $P_f$ (The dashed black line identifies the peak vs Failure pressure for 100 % liquid fill level).</figcaption></figure>

phenomena. The comparison highlights the critical role of saturation pressure in shock wave formation when vapor space is present. The saturated vapor contributes to the formation of the shock wave.

### 4.1.5. Influence of weakened length [Compressed Liquid]

In Fig. 10, the following experiments are compared:

- **Experiment 29 – 2024:** $L_c = 150$ mm $|P_f = 34.4$ Barg; $P_{sat at Tfail} = 26.5$ Barg $| \varphi = 100 \%$

- **Experiment 31 – 2024:** $L_c = 75$ mm $|P_f = 30.4$ Barg; $P_{sat at Tfail} = 25.2$ Barg $| \varphi = 100 \%$

When both experiments have a 100 % liquid fill and similar $P_f$ equal

<figure><img src="image_24.png" /><figcaption>Fig. 15. Lead peak overpressure from TOP 1 gauge [15 cm vertically] for all liquid fill cases across different experimental campaigns at different weakened lengths with respect to $P_{sat at Tfail}$.</figcaption></figure>

<figure><img src="image_25.png" /><figcaption>Fig. 16. Lead peak overpressure from TOP 1 gauge [15 cm vertically] for all liquid fill cases across different experimental campaigns at different weakened lengths with respect to $P_f$.</figcaption></figure>

to $P_{sat at Tfail}$, the scenario with the shorter weakened length exhibits a lower and slower rise in overpressure. In this case, the vessel does not fully open, which reduces the formation of a strong overpressure.

### 4.1.6. Influence of opening dynamics

To better understand the influence of the opening dynamics on the resulting overpressure, Fig. 11 compared the following experiments conducted under similar operating conditions. This comparison highlights how variations in the vessel’s rupture behavior can impact the overpressure profiles, even when all other parameters are kept constant. These experiments are:

- **Experiment 2 – 2024:** $L_c = 150$ mm $|P_f = 29.4$ Barg; $P_{sat at Tfail} = 29.4$ Barg $| \varphi = 17 \%$

- **Experiment 15 – 2024:** $L_c = 150$ mm $|P_f = 29$ Barg; $P_{sat at Tfail} = 29$ Barg $| \varphi = 16 \%$

Fig. 11 demonstrates the repeatability of the measured overpressures, albeit with some variability. For instance, two experiments
<figure><img src="image_26.png" /><figcaption>**Fig. 17.** Duration of lead overpressure from TOP 1 gauge [15 cm vertically] for all liquid fill levels cases across different experimental campaigns at different weakened lengths with respect to $P_{sat at Tfail}$.</figcaption></figure>

<figure><img src="image_27.png" /><figcaption>**Fig. 18.** Duration of lead overpressure from TOP 1 gauge [15 cm vertically] for all liquid fill levels cases across different experimental campaigns at different weakened lengths with respect to $P_f$.</figcaption></figure>

conducted under nearly identical conditions showed a 30 % different in peak overpressure. This discrepancy is likely attributable to subtle variations in the exact manner in which the vessel unfolds during each experiment, emphasizing the sensitivity of the overpressure dynamics of the vessel's rupture behavior. The variation in rupture behavior is primarily attributed to the crack propagation speed along the weakened length. A faster crack speed results in a more rapid expansion of the contents, leading to a stronger overpressure.

Fig. 12 further shows the difference in the rupture behavior for these two cases. The opening area of the crack is higher for Experiment 15 - 2024 compared to Experiment 2 - 2024 at 113 µs allowing for faster expansion of the contents and thus leading to a stronger shock as in Fig. 11. The shock wave is not visible as it requires shadowgraph imaging; however, the formation of the white cloud following the shock wave can be observed. Initially, the white cloud appears smaller in Experiment 2 - 2024 compared to Experiment 15 - 2024. The initial white cloud results from the vapor phase and is later followed by a two-phase cloud formed due to liquid flashing.

<figure><img src="image_28.png" /><figcaption>**Fig. 19.** Impulse per unit area of lead overpressure from TOP 1 gauge [15 cm vertically] for all liquid fill levels cases across different experimental campaigns, at different weakened lengths with respect to $P_{sat at Tfail}$.</figcaption></figure>

<figure><img src="image_29.png" /><figcaption>**Fig. 20.** Impulse per unit area of lead overpressure from TOP 1 gauge [15 cm vertically] for all liquid fill levels cases across different experimental campaigns, at different weakened lengths with respect to $P_f$.</figcaption></figure>

## 4.2. Lead peak overpressure magnitude

To depict the general pattern of lead peak overpressure obtained from the TOP1 gauge positioned at 15 cm above the tube, the high liquid fill levels ranging from 90 % to 100 % were represented relative to the actual failure pressure $P_f$ (Fig. 13) and saturation pressure at failure temperature $P_{sat at Tfail}$ (Fig. 14). The findings are organized by varying weakened lengths represented with different text color for clarity (Black T#:150 mm; Orange T#: 125 mm; Blue T#: 100 mm; Red T#: 75 mm) and are further sorted by the year of the campaign.

Figs. 13 and 14 show T34 (experimental test 34) from the BLEVE 2024 campaign, where a partial failure resulted in a jet release rather than a BLEVE. Indeed, the release mechanism involved a rapid expansion of the contents through a small opening.

The choice to represent the lead peak overpressures as a function of $P_f$ or $P_{sat at Tfail}$ relies on two distinct approaches:

* Opting for $P_f$ suggests that once the vessel opens, the overpressure forms instantly with the actual conditions experienced by the vessel
<table><caption>**Table 2**
Non-isothermal failure saturation temperature.</caption><thead><tr><th>Campaign</th><th>T#</th><th>L<sub>c</sub> (mm)</th><th>P<sub>f</sub> (Barg)</th><th>T<sub>fail</sub> (°C)</th><th>P<sub>sat at Tfail</sub> (Bara)</th><th>P<sub>sat non-isothermal</sub> (Bara)</th></tr></thead><tbody><tr><td rowspan="6">2024</td><td>29</td><td>150</td><td>34.4</td><td>73.2</td><td>27.5</td><td>26.9</td></tr><tr><td>30</td><td>150</td><td>33.5</td><td>74.7</td><td>28.3</td><td>27.8</td></tr><tr><td>31</td><td>75</td><td>30.4</td><td>70.7</td><td>26.2</td><td>25.9</td></tr><tr><td>32</td><td>75</td><td>20.5</td><td>36.6</td><td>12.7</td><td>12.5</td></tr><tr><td>33</td><td>75</td><td>27.0</td><td>63.9</td><td>22.9</td><td>22.7</td></tr><tr><td>1</td><td>150</td><td>19.8</td><td>49.7</td><td>17.0</td><td>16.9</td></tr><tr><td rowspan="4">2022</td><td>12</td><td>150</td><td>24.9</td><td>44.0</td><td>15.0</td><td>14.8</td></tr><tr><td>13</td><td>150</td><td>27.7</td><td>55.1</td><td>19.1</td><td>18.7</td></tr><tr><td>32</td><td>75</td><td>22.9</td><td>55.4</td><td>19.2</td><td>18.7</td></tr><tr><td>17</td><td>150</td><td>19.8</td><td>28.3</td><td>10.4</td><td>10.3</td></tr><tr><td>Eyssette (2018)</td><td></td><td></td><td></td><td></td><td></td><td></td></tr></tbody></table>

Consequently, this suggests that the overpressure is much faster for the saturation pressure at failing temperature to be directly involved. $P_f$ governs the velocity at which the vessel cracks, thus directly influencing the overpressure. Given the rapidity of the overpressure buildup, $P_{sat at Tfail}$ intervenes later in time, as the vessel's content typically transitions to saturation conditions before reaching a metastable superheated state but after the vessel is open. However, this argument is not yet proven and will require to position an internal transient pressure sensor close to the vessel burst position in concordance with the high-speed camera.

* Using $P_{sat at Tfail}$ indicates a stronger dependence on temperature rather than pressure for defining compressed liquid properties. This reflects a thermodynamic approach.

The trend observed in the experiments for the 100 % liquid full cases, represented by circles, reveals significant insights. Firstly, it highlights that these cases generally exhibit the lowest overpressure magnitudes relative to the failure pressure. This observation underscores the influential role of the liquid fill level in determining overpressure magnitude, indicating that the vapor phase tends to generate stronger overpressure magnitudes.

Consequently, cases involving compressed liquid may produce weaker pressure waves in the near-field overpressure. However, in Fig. 13, where the lead peak overpressure is plotted against the $P_{sat at Tfail}$, two experiments, specifically T31 (BLEVE 2022) and T4 (BLEVE 2024) (not liquid full cases; $\varphi < 100 \%$), fall below the curve for the 100 % liquid fill cases if the dotted line was extended. Thus, for these two specific cases, where the liquid fill level is near 100 %, specifically around 98–99 %, the lead peak overpressure is lower than those from the 100 % liquid fill and the following may be attributed to the influence of $P_f$.

Indeed, higher $P_f$ (and higher stresses in the vessel) may result in a faster initial opening of the vessel and this gives a higher lead shock overpressure. Thus, the lead peak overpressure has been represented as a function of $P_f$ in Fig. 14. This depiction clearly defines the minimum peak overpressures achievable when considering the maximum liquid fill with respect to the failure pressure $P_f$.

Furthermore, the behavior of the 100 % full liquid cases is particularly noteworthy. There is a distinct pattern where, initially, there exists a plateau of low failure pressures (dotted black line on Figs. 13 and 14) with low lead overpressures. This observation suggests a transition point where vessels cease to fail partially, and instead, the overpressure dynamics become directly influence by the actual failure pressure.

During this phase, the vessels undergo partial failure, without producing substantial overpressure. However, beyond a certain threshold (around 18 Barg $P_{sat at Tfail}$ and 25 Barg for $P_f$), the overpressure rises rapidly with increasing pressure. For propane, the atmospheric superheat limit temperature $T_{SL}$ of 53.5 °C has a saturation pressure of 17.5 Barg. It is possible that for 100 % liquid fill cases the $T_{SL}$ does play a role, but this requires further validation.

Upon examining $P_{sat at Tfail}$ in Fig. 13, the onset of low overpressures

and partial failures initiates close to the temperature corresponding to the atmospheric superheat limit temperature proposed by Reid (1979). But this is only true for liquid fill cases very close to 100 %. Indeed, he stated that the BLEVE occurs when the liquid is equal to or above its superheat limit temperature at vessel failure. The transition from a plateau to a steep incline, as well as the shift from partial to complete opening failure in liquid-filled vessels, may be linked to the superheat limit temperature. To determine the precise pressure at which the vessel undergoes complete rupture, further experiments are required to investigate the $P_{sat at Tfail}$ within the range of 15–23 Barg. Moreover, the energy and pressure are important. For cases lower than 100 % liquid fill, there is energy in the vapor phase that is immediately available to do work on the vessel walls. Liquid must flash to vapor to do work on the vessel walls.

To provide a clearer insight into the impact of the liquid fill levels on overpressure, Fig. 15 and Fig. 16 illustrate the peak overpressure data obtained from the TOP1 gauge across three distinct experimental campaigns (2018, 2022 and 2024). The plot delineates variations in peak overpressure concerning different liquid fill levels and corresponding failure pressures. The cases with 100 % liquid fill are represented with squares and also with an asterisk as they represent cases with liquid fill levels exceeding 80 %.

Fig. 15 and Fig. 16 effectively categorize various liquid fills based on their impact on lead peak overpressure. Notably, the lowest overpressure readings are observed in scenarios involving compressed liquid, with overpressure increasing as liquid fill decreases. The highest overpressure values are recorded in cases with a 20 % liquid fill. However, as liquid fill decreases, the disparity in overpressure between each liquid fill group reduces.

Furthermore, while compressed liquid cases can generate significant overpressure, it was observed in Section 4.1 that the overpressure rise is not steep or rapid enough to classify as a shock. Fig. 14 underscores once more the influence of liquid fill on overpressure and hints at a nuanced relationship between overpressure, liquid fill, and failure pressure. Fig. 14 strongly demonstrates the influence of $P_f$ for 100 % liquid full cases which is believed to be linked to the opening dynamics, crack speed, the opened area defined by the weakened length, and the non-uniform thickness of the tube. Additionally, we believe that other variables, such as the way the tubes were tightened, may also exert influence. Certainly, the mechanical behavior varies depending on how stress is distributed within the structure and factors such as material properties and geometry.

### 4.3. Duration of lead overpressure

The duration of lead overpressure holds significant importance in evaluating safety risks and gauging the potential impact of overpressure events. By understanding how long an overpressure lasts, we gain insights into its potential effects on structures, equipment, and nearby populations. A prolonged overpressure can subject structures to sustained stress, increasing the risk of fatigue-induced failure over time. Knowing this duration is instrumental in planning emergency responses.
It allows for the appropriate measures, such as reinforcing structures or adopting protective interventions, to ensure compliance with regulatory standards and enhance overall safety protocols.

Emphasis was placed on analyzing the lead peak overpressure at TOP1, situated 15 cm vertically, where overpressure reaches its peak intensity. Fig. 17 and Fig. 18 provide a comprehensive overview of the findings regarding the duration of lead overpressure.

Fig. 17 and Fig. 18 demonstrate a distinct trend based on the liquid fill level, particularly for the compressed liquid cases denoted by squares. These cases show a sharp decline in the duration of lead overpressure relative to failure pressure, followed by a potential plateau around $P_f = 34$ Barg. As the liquid fill level decreases, the influence of the liquid fill level on lead overpressure duration from TOP1 gauge reduces. However, the graph indicates a significant decrease in duration with decreasing liquid fill level and increasing relative failure pressure. Liquid full cases present the highest duration values, especially the compressed liquid cases, serving as reference points for estimating worst-case scenarios of the longest duration.

### 4.4. Impulse per unit area of lead overpressure

The impulse per unit area of lead overpressure has been represented in Fig. 19 and Fig. 20. The impulse per unit area is determined by multiplying the duration of lead overpressure, as depicted in Figs. 17 and 18, by the peak overpressure from Fig. 15 and Fig. 16, and then dividing by 2. The impulse captures the change in momentum over a defined period, offering insight into system dynamics. It is valuable in assessing the force generated by the BLEVE, aiding in determining the most powerful BLEVE. Understanding impulse enables engineers and safety specialists to gauge the potential impact of explosions on surrounding structures and materials. A high incident impulse can indeed cause significant damage to buildings (Marx and Werts 2013). Hence, the importance of impulse becomes evident.

Figs. 19 and 20 show that the impulse generated from the 100 % liquid fill cases remains consistently low compared to other experiments and represents the lower bound of impulse values. As the liquid fill level decreases, there is a tendency for the impulse to increase relative to $P_f$; This suggests that the strongest impulse per unit area, is expected to originate from the lowest liquid fills. While a “V” trend is apparent in the 100 % liquid fill cases in Fig. 20, drawing a conclusive trend would necessitate further testing.

Fig. 19 presents similar results, but with 100 % liquid fill cases depicted as a function of the saturation pressure at the temperature of failure $P_{sat at Tfail}$. Consistent with previous observations, the impulse exhibits a significant increase immediately following the $T_{sl}$ corresponding to the $P_{sat at Tfail}$. In contrast in Fig. 20, the 100 % cases merge with lower liquid fill level cases while maintaining a low impulse per unit area.

## 5. Conclusion

The paper delves into the contribution of liquid fill levels in the generation of lead peak overpressure hazards during a BLEVE (Boiling Liquid Expanding Vapor Explosion). The study draws upon results derived from three small-scale experimental campaigns involving a total of 90 experiments filled with pure propane. It primarily focuses on scenarios where the vessel is filled to 100 % capacity with liquid, leading to hydrostatic failure, and underscores the distinctive dynamics compared to conventional BLEVE occurrences.

The results are represented in relation to $P_{sat at Tfail}$ and $P_f$ to elucidate the differences and their impact on overpressure. From this study, the $P_f$ under compressed liquid condition enables a faster crack opening, allowing the overpressure to expand more effectively based on the energy supplied by $P_{sat at Tfail}$. Consequently, when comparing compressed liquid experiments to those with slightly lower liquid fill

levels (98–99 %), the overpressure is higher for compressed liquid experiments to those with slightly lower liquid fill levels when expressed as a function of $P_{sat at Tfail}$. However, at very low liquid fill levels, this trend no longer holds, as the liquid fill level plays a more significant role in determining the overpressure magnitude and impulse. Regarding the weakened length, a shorter weakened length restricts the rapid expansion of the contents, resulting in a weaker and longer overpressure. Nevertheless, determining which failure pressure to consider necessitates a further and closer examination of the mechanical and thermodynamics processes occurring at the rupture location in accordance with high-speed cameras, given the rapid occurrence of such events. This analysis will help determine whether $P_f$ influences the overpressure from the BLEVE prior to reaching $P_{sat at Tfail}$.

The paper highlights the significant contribution of the vapor phase in generating the lead shock overpressure and its subsequent duration, particularly evident in cases with high and full liquid fills, where the overpressure is strong but not a shock. Experiments with high liquid fill show a longer duration of lead overpressure and a smaller peak compared to those with similar conditions (such as failure pressure and weakened length) but lower liquid fills. Moreover for high liquid fill levels, the magnitude of the lead overpressure increases with higher failure pressures, while the duration decreases. The weakened length plays a role in dictating how the vessel will open; it requires more energy for a complete opening at a smaller weakened length compared to a larger one. Consequently, a shorter weakened length at relatively low failure pressure results in partial failure, leading to a reduced overpressure magnitude and a longer duration. Furthermore, an analysis of the impulse per unit area, describing the momentum produced by a failing vessel and its relation to overpressure magnitude and duration, reveals that the 20–40 % liquid fill cases at relatively low failure pressures exhibit higher impulse energy. This suggests that even at low failure pressures, these cases have sufficient impulse energy to cause significant damage.

In scenarios where the vessel was entirely filled with liquid, a distinct behavior emerged concerning peak overpressure. For instances with low failure pressures, partial openings BLEVE occurred, resulting in a plateau in overpressure values regardless of weakened length. However, at a specific failure pressure, the overpressure magnitude, although relatively low compared to the other liquid-filled cases, began to increase strongly relative to the failure pressure. Further experiments are needed to determine if such change of slope and the transition from partial opening to complete opening is either related to the higher pressure and energy or to the superheat limit temperature. Additionally, the duration of the leading overpressure was significantly longer compared to other liquid fill levels and followed a consistent trend line. Despite the longer duration observed for 100 % liquid fills, the subsequent impulse remained relatively low, representing the lower boundary of the dataset. Hence, while the liquid full cases fail differently compared to other cases they experience the same steps as a BLEVE once $P_f$ reaches the $P_{sat at Tfail}$.

While the 100 % liquid fill cases yielded the weakest overpressure relative to failure pressure, exploring the ground load for such scenarios will be interesting. Existing literature indicates that the liquid phase primarily contributes to high ground loads. However, given the unique characteristics of 100 % liquid fill cases, it prompts the question of whether we should anticipate a distinct trend in ground load behavior.

## Declaration of Competing Interest

The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: El Mehdi Laamarti reports financial support was provided by Queen's University. El Mehdi Laamarti reports financial support was provided by IMT mines Ales. If there are other authors, they declare that they have no known competing financial interests or personal relationships that could
have appeared to influence the work reported in this paper.

Queen's University, Kingston, Canada and IMT mines Ales, Ales, France

## Acknowledgements

The authors gratefully acknowledge the financial contribution from

## Appendix

### Thermodynamic analysis of compressed liquid

In the analysis of a compressed liquid BLEVE experiencing failure with a pressure drop from point A to B, as described in Section 2.2, a key simplification is made: the change in volume is considered negligible due to the low compressibility of the liquid. This assumption streamlines the calculations, as the volume variations are small enough to be considered almost constant. Nevertheless, in reality, the volume and the temperature of the liquid can indeed change, even if the magnitude of this change is typically minor.

To understand this in more detail, let's consider a scenario involving a pressure vessel containing a compressed liquid, which is examined at different time instants (see Figure A1):

* At time $t_R$ (liquid full state): The vessel is at a state when filling reaches 100% liquid full.

* At time $t_0$ (pre-rupture state): The liquid has almost reached burst pressure and the liquid is compressed.

* At time $t_f$ (post-rupture state): The vessel has burst and liquid did undergo a pressure drop (whether isothermal or non-isothermal)

<figure><img src="image_30.png" /><figcaption>Fig. A1. Pressure vessel before and after rupture under compressed liquid conditions</figcaption></figure>

The energy change of the compressed liquid when pressure drops due to tank failure can be described by the first law of thermodynamics, taking into account the internal energy variations, work done, and any heat transfer.

$$dU = \delta Q + \delta W \qquad (1)$$

The process is considered adiabatic, there is no heat exchange meaning that $\delta Q = 0$. During that depressurization the work done on the vessel walls is not considered. We do only consider work done by the system due to the liquid volume change.

$$dU = 0 - P_{atm}dV = - P_{atm}dV \qquad (2)$$

The third equation X corresponds to the state function that correlates state variables of the system, such as temperature (T), pressure (P), volume (V) and others:

$$X = f(T, P, V, \dots) \qquad (3)$$

The actual non-isothermal saturation temperature $T_{sat non-isothermal}$ can then be determined using the EES software (Engineering Equation Solver) with propane properties (Miyamoto and Watanabe, 2000).

The results obtained for all compressed liquid experiments are presented in Table 2.

The non-isothermal pressure was obtained when the program converged with a tolerance of $10^{-6}$. This difference between the non-isothermal or isothermal pressure is small, especially when considering the inherent uncertainties in measurement instruments and the assumption that no work is done on the vessel walls. Consequently, the minor temperature variation can be disregarded for practical purposes and the isothermal $P_{sat at T_{fail}}$ is considered.
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