## Abstract

This study aims to find how fires and explosions can occur in enclosed spaces where electrical transformers are installed and to investigate the consequences of the damages to the surrounding areas caused by these accidents. This study began with the collection of a mineral oil waste sample from an indoor substation transformer in Riyadh, Saudi Arabia. This sample was analyzed to determine its composition. Results revealed that 30 components ranging from C6 to C30 were detected in the sample. The mixture flammability limits, calculated using Le Chatelier rules and found to be 0.97 and 6.56, indicated that the vapor mixture for the waste oil sample was not flammable at 25 °C and 1 atm. Consequence analysis was used to predict the outcome of fire and explosion events based on a transformer with a capacity of 1100 liters. The peak overpressure generated by an explosion was estimated to be 80.97 kPa. Moreover, the thermal radiation produced by various types of fires was estimated as a function of the distance from the accident center. The thermal flux from a boiling liquid expanding vapor explosion (BLEVE) was 99.8 kW/m2, which is greater than that from jet and pool fires. The probability of an individual suffering injury or dying as a result of exposure to fire and/or an explosion was estimated using dose-response models. The results showed that the peak overpressure produced by an explosion can cause severe damage within 20 m of the explosion center. However, the results also showed that there is a 100% probability of the thermal radiation from a BLEVE causing fatalities up to a distance of 140 m. The risk due to the fragmentation of the transformer tanks was also assessed, and a majority of fragments would land within a range of 111.2 m.

## 1 Introduction

The global consumption and demand for electrical energy have increased rapidly over the last few decades. Most countries produce electricity using fossil fuel-fired thermal plants [1], and fossil fuels (oil, gas, and coal) continue to play a major role in energy systems worldwide. The electricity needed for human activities is delivered through power lines or transformers. Dielectric fluids or insulating oils are key elements of electrical transformers, and these are mainly used to absorb the heat that is generated. For more than 130 years (since 1887), petroleum-based fluids have been used as coolants and insulating fluids in transformers. Although mineral oils have many advantages, including their low cost, wide availability, and good cooling performance [2], they are toxic and not easily biodegradable, and they also have low fire points [3].

Power transformers consists several parts and components as illustrated in Fig. 22 (Appendix  A). The mineral oil is stored in the transformer in two parts: the main one is the transformer tank and the second one is the conservator tank. The main transformer tank is completely filled with oil, while it does not matter how much the mineral oil level is in the conservator tank; the important thing is that the tank should not be empty. The transformer tank usually has a cubical shape, whereas the conservator tank usually has a cylindrical shape. Power transformers failures can occur due to various reasons [47]. However, the most common cause of transformer fires and explosions is due to the bushing failures [7,8].

Mineral oil can leak from transformers in several ways: it can result from the degradation of cork gaskets or the development of holes or cracks in the radiator or oil tank; oil can also leak through flanges, circuit breakers, valves, fastener assemblies, and so on [9,10]. Such leakage can cause a fire and/or an explosion due to direct contact with high-voltage elements [11]. Furthermore, these leaks are often slow drips, and with time, however, hundreds of liters of oil can spill out and spread onto the floor, forming a pool close to the transformers. This is highly dangerous because the oil can easily ignite in the presence of an ignition source such as flames or sparks, possibly leading to a pool fire event. In addition, the oil leakage will reduce the oil level in the tank, causing the transformer windings to overheat. This will damage the insulation in the windings and allow moisture to enter through the leak and degrade the transformer oil, causing the transformer to overheat. If the transformer overheats, the temperature of the mineral oil will increase, leading to the oil vaporizing and forming a flammable mixture. If this mixture is then released into the atmosphere, it can be ignited by any spark or nearby fire. It is also possible that the tank can rupture because of the heating of the transformer, and this will result in causing vapor cloud explosion (VCE) or boiling liquid expanding vapor explosion (BLEVE). It has been found that if mineral oils are heated to approximately 500 °C, methane, ethane, and ethylene will be liberated [12]. Furthermore, if the oil is heated to an extreme temperature (higher than 500 °C), hydrogen and acetylene will be liberated in addition to the above gases [12,13]. The sudden release of these gases into the atmosphere may lead to unexpected fires or explosions.

People have become more and more aware of fire and explosion accidents involving transformers located in power substations [14]. Although the probability of fire and explosion in electrical transformers is relatively low, the risk due to fire and explosion in transformer installations cannot be neglected. Transformer fires are often divided into two types: pool fires and jet (spray) fires. If the mineral oil inside a transformer tank is heated due to dielectric breakdown or due to an external fire engulfing the oil tank, the temperature of the transformer tank will increase, and this will eventually produce vapor that may form a flammable mixture with air. If the flammable mixture suddenly escapes under pressure to the atmosphere from an opening in the tank, a jet fire may occur. Explosions of oil-filled transformers, known as mixed mode explosions, can be happened due to electric sparks, arcs, or hot surfaces [15]. Sudden transformer failure can lead to an overcharge, which could generate enough heat and sparks causing high overpressure. This massive overpressure can cause the transformer to rupture and flashing the stored oil and possibly generate fireball. Vaporization of the mineral oil generates gas mixture, and this creates huge amount of overpressure inside the transformer tank, finally causing the tank to rupture, resulting in the release of significant amount of energy and high thermal radiation. This may cause scattered fragments, scattering burning oil, gases decomposition products, solid insulation materials, and molten winding conductors into the vicinity area [16].

When a transformer tank explodes and oil is splashes, this does not necessarily result in a fire. The likelihood of a fire depends on the successful operation of the protection system and how quickly it responds [17]. Although when a transformer tank explodes without causing a fire, there can be significant environmental pollution due to oil leakage to the site.

Transformer fire accidents are being reported every day; however, perhaps the worst accidents in history is the that occurred in a coal mine in western Turkey in 2014, which happened due to an electrical failure that resulted in an explosion and fire in the transformer. This accident left more than 200 people dead and 80 injured [18]. It can be concluded from this accident and from other accidents that when a transformer fails, the results often lead to significant property damage and major financial losses. Typical power substations comprise several transformer tanks, and each of these tanks contains a large quantity of mineral oil. The ignition of this oil can generate heat and pressure for the transformer tank, which can lead to rupture, allowing the burning oil to spill and spread around the tanker.

In electrical substations, mineral oil can be leaked from many parts of the transformers due to many reasons as stated earlier and especially if these transformers did not have good maintenance. Over the time, the discharged oil will be accumulated on the transformer parts and/or on the ground surrounded by the transformer. Furthermore, during the process of replacing the old oil with a new one, if the maintenance personnel do not follow the necessary instructions, this will lead to spills of oil on the places surrounding the device. Consequently, this study is aimed to investigate how could the fire and explosion events to initiate in a close place where transformer begins installed. Furthermore, results from the consequences modeling will be used with the probit analysis method to predict the degree of damage (probability) caused by accidents.

This study included the following experimental and theoretical assessments.

• The experimental work consisted of two stages. In the first stage, a sample of waste mineral oil was collected from an electrical substation in Riyadh, Saud Arabia. The composition of the sample was then determined using gas chromatography–mass spectrometry (GC–MS). In the second stage, on-site measurements were conducted using a portable gas detector.

• The theoretical part of the study consisted of using the results of the experimental work to draw flammability diagrams and to predict the likelihood of fire and explosion hazards due to the vaporization of mineral oil in electrical substations. In addition, consequence modeling was employed to estimate the potential impact of different accident scenarios (pool fire, jet fire, VCE, etc.) on people and the surrounding area.

## 2 Materials and Methods

### 2.1 Sample Collection and Composition Identification.

A sample of waste oil was obtained from a warehouse in Riyadh where used and waste oils are stored. Waste oil can be defined as oil that was used to fill a transformer tank and then used for 1 year while the transformer was in operation before being replaced with new oil because of the loss of its operational properties. The oil sample was kept in a well-sealed bottle and then stored in the laboratory cabinet under normal conditions. The oil sample was analyzed by GC–MS according to the method presented in our previous work [9] to identify its compositions. The mass and mole fractions in the liquid and vapor phases can be found according to the methods presented in the work of El-Harbawi and Al-Mubaddel [9] and El-Harbawi et al. [19].

### 2.2 On-Site Gas Detection.

The detection of flammable gases in an area suspected of being contaminated with flammable materials is very important because vapors emanating from materials such as mineral oil may exceed the allowed limits imposed by safety laws and regulations. In electrical substations, a vapor mixture can form for various reasons, including the spillage of mineral oil onto the floor during the replacement of used oil. Vapor mixtures can also be produced if bad transformer maintenance leads to the leakage of oil from any part of the transformer. A multigas detector (MultiRAE Lite PGM-6208 RAE Systems) manufactured by Honeywell, USA, was employed to measure the concentration of vapor in the confined space where a transformer was installed. This device can be used for measuring the concentration of combustible, flammable, or toxic gases in confined areas and in the atmosphere.

### 2.3 Accident Scenarios Development and Consequence Analysis.

The causes of accidents and associated scenarios were investigated, and consequence modeling was then employed to study the impact of accidents based on various scenarios. Figure 1 illustrates an event tree for the outcomes that follow the release of combustible or flammable gas and/or liquid from a tank or vessel into the atmosphere [2023]. If the release of a combustible or flammable material occurs without the material igniting, the liquid will rain out onto the ground and cause the formation of a pool that will evaporate into the atmosphere. If, however, the material ignites immediately, then a fire may start. Different types of fire are possible: these include jet fire (spray), flash fire, pool fire, fireball, and internal fire. A jet fire can occur because of the release of gas or high-pressure liquid from a pressurized unit such as a storage tank or vessel, followed by immediate ignition. A flash fire can occur if the material stored inside a container is heated to form a flammable vapor that is suddenly released into the open air. A pool fire can occur when combustible or flammable chemicals leak from a vessel or pipe and accumulate on the ground and then ignite [24,25]. If the material is a liquid and is stored at a temperature below its boiling point, the liquid will form a pool on the ground, and if the liquid is stored under pressure and at a temperature above its normal boiling point temperature, then a portion of the liquid will flash into a vapor. The remaining unflashed liquid will form a pool in the area surrounding the release [26]. A BLEVE (fireball) occurs because of the rupture of a vessel containing a liquid at a temperature above its atmospheric boiling point. After the flammable material is released into the atmosphere, it immediately ignites, forming a fireball. A BLEVE will also occurs if following the spill of a flammable liquid, the liquid ignites and the tank is completely engulfed by fire, resulting in the tank rupturing [27]. The absence of an immediate ignition source may lead to the formation of a large flammable cloud, whereas delayed ignition may cause a flash fire or VCE. The calculations performed in this work are based on models and data published by the Centre for Chemical Process Safety [26] and the U.S. Nuclear Regulatory Commission Fire Protection Inspection Program [28].

Fig. 1
Fig. 1
Close modal

### 2.4 Case Study.

Several types of transformers with different capacities are used by Saudi Electricity Company. One of the most popular types has an oil tank capacity of 1000 L and a conservator tank capacity of 100 L. This type of transformer is frequently used in electrical substations located in cities and villages. Thus, this study was concerned with this type of indoor transformer only. Figure 23 (Appendix  A) shows a sketch of the dimensions of the conservator tank and the main tank of the transformer used in this study.

## 3 Results and Discussion

### 3.1 Sample Analysis and Identification of Components.

The identification of the components of the waste oil sample was performed using the same method described in our previous work [9]. Figure 2 illustrates the results of the GC–MS analysis. Table 18 (Appendix  B) lists the details of the components found in the waste oil and summarizes the results for the flammability limits and limiting oxygen concentration (LOC) of the mixture. The results show that the waste oil sample contains several hydrocarbon components (CH–) varying from C6 to C30. More than 41% of these components belong to alkane groups.

Fig. 2
Fig. 2
Close modal

The mass and mole fractions of the components in the liquid and vapor phases were predicted using the same method adopted in our previous works [9,19]. The vapor mixture mole fraction was calculated to be 0.37 vol%. Thus, the air content in the mixture was 99.63 vol%, and the percentages of N2 and O2 were 78.71 and 20.92 vol%, respectively. Tables 2 to 19 (Appendix  A) presents the details of the calculations used to find the lower flammability limit (LFL), upper flammability limit (UFL), and LOC of the individual components of the waste oil sample and of the mixture that constituted the sample.

### 3.2 Calculation of the Lower Flammability Limit, Upper Flammability Limit, and Limiting Oxygen Concentration.

The flammability limits for the different components present in the sample were acquired from different sources [29,30]. Equations (A1) and (A2) were used to calculate the missing flammability limits. The values of LFLmix and UFLmix were predicted using the Le Chatelier equations Eqs. (A5) and (A6) and were found to be 0.97 and 6.56, respectively. The LOCs for the individual components and for the mixture were estimated using Eqs. (A7) and (A8), respectively. The value of LOCmix was found to be 11.19 vol%. The details of the calculations and the results for LFL, UFL, LFLmix, UFLmix, LOC, and LOCmix are presented in Table 19 (Appendix  B).

To determine whether the vapor mixture was flammable, a flammability diagram was constructed. For a detailed description of how to plot a flammability diagram, see the study by El-Harbawi et al. [19] and Ali and El-Harbawi [31]. Figure 3 shows the flammability diagrams for the waste oil vapor mixture. It can be seen that the vapor mixture composition, ymix, N2, and O2 is slightly outside the flammable zone, and thus, the vapor mixture can be considered not flammable at 25 °C and 1 atm.

Fig. 3
Fig. 3
Close modal

The low probability of a transformer catching fire may be due to the lack of oxygen inside the transformer. It is therefore usually difficult to form a flammable mixture inside a transformer. However, at a temperature equal to or higher than the flash point (i.e., ≥145 °C), mineral oil tends to vaporize and form a vapor mixture inside the transformer container. This mixture can ignite if it escapes into the atmosphere in the presence of an ignition source. Interestingly, the results obtained using the multigas detector indicated that there was a flammable mixture in the compartment where the transformer was located. The LFL level was measured to be 99 vol%, which is considerably higher than the allowable limit. This result indicates that flammable mixtures may exist in enclosed spaces perhaps as a result of poor ventilation systems or the accumulation of a large pool of spilled oil.

### 3.3 Consequence Analysis

#### 3.3.1 Material Outflow

##### 3.3.1.1 Vapor discharge.

The primary input to any discharge calculation is the size of the hole through which the discharge occurs. There is currently no general consensus as to what hole size should be used, but values of 10 and 25 mm can be found in the literature [26,32]. In this study, we selected a hole diameter of 25 mm because the larger the hole is, the worse will be the scenario that develops. The temperature of the oil inside the transformer tank was assumed to be 70 °C [33]. Consequently, using the methodology presented in Appendix  A, Gas/Vapor Outflow section, together with the input data presented in Table 1, vapor would be released through the assumed hole at a rate of 0.56 kg/s (Table 1).

Table 1

Input data and calculated results for the vapor and liquid discharges

Input data
Heat capacity ratio1.009
Hole size, mm25
Temperature, K343
Gas molecular weight490
Downstream pressure, bar abs1.01
Upstream pressure, bar abs1.73
Tank pressure above liquid, barg0.7168
Pressure outside hole, barg0
Liquid density, kg/m3880
Liquid level above hole, m0.4
Calculated results (vapor discharge)
Hole area, m24.91 × 10−4
Upstream gas density, kg/ m329.73
Expansion factor0.614
Vapor discharge rate, kg/s0.56
Calculated results (liquid discharge)
Velocity coefficient1.25
Exit velocity, m/s8.3
Fuel spill volume, Lit251
Dike area, m212.57
Liquid discharge rate, kg/s3.57
Input data
Heat capacity ratio1.009
Hole size, mm25
Temperature, K343
Gas molecular weight490
Downstream pressure, bar abs1.01
Upstream pressure, bar abs1.73
Tank pressure above liquid, barg0.7168
Pressure outside hole, barg0
Liquid density, kg/m3880
Liquid level above hole, m0.4
Calculated results (vapor discharge)
Hole area, m24.91 × 10−4
Upstream gas density, kg/ m329.73
Expansion factor0.614
Vapor discharge rate, kg/s0.56
Calculated results (liquid discharge)
Velocity coefficient1.25
Exit velocity, m/s8.3
Fuel spill volume, Lit251
Dike area, m212.57
Liquid discharge rate, kg/s3.57
##### 3.3.1.2 Liquid discharge.

A hole size of 25 mm was also used to calculate the rate of liquid discharge. Using the methodology presented in the Appendix  A, Liquid Outflow section, together with the input requirements presented in Table 1, liquid would be released through the hole at a rate of 3.57 kg/s (Table 1).

#### 3.3.2 Flashing and Evaporation

##### 3.3.2.1 Flashing.

Flashing phenomena will not occur if mineral oil is stored inside a transformer tank under normal conditions (T = 45 °C and P = 1.73 bar abs). However, if the temperature of the oil rises to above its boiling point and oil is then released, then it will flash. To be able to use Eq. (A13) to determine the liquid fraction that flashes from a release of superheated liquid, the liquid heat capacity averaged over the initial temperature of the liquid and the atmospheric boiling point of the liquid, together with the latent heat of vaporization of the liquid at the boiling point, are required. The reported boiling points of most mineral oils are in the range 310 °C–374 °C (average = 342 °C). Thus, the heat capacity at the average temperature, 183.5 °C [(25 °C + 342 °C)/2], is about 5.5 J/g°C. Most conventional mineral oils have a latent heat of vaporization of between 220 and 245 kJ/kg at the boiling point. Thus, according to Eq. (A13), mineral oil will start to flash when its temperature is above 342 °C.

##### 3.3.2.2 Evaporation or Boiling.

Mineral oils usually have high boiling points, and their evaporation rates at room temperature are usually negligible. However, the vapor pressure plays an important role in the evaporation process and increases as the temperature increases. Therefore, when assessing the hazards resulting from the release of flammable or combustible liquids, evaporation phenomena should not be neglected. For liquids with temperatures far from their boiling points, heating will lead to an increase in the evaporation rate. For liquids with boiling points close to or above ambient temperature and in cases where the area of pooled liquid is large, the vaporization rate can be determined using Eq. (A14) [34]. Assuming the liquid is contained within a diked area, the area of the pool can be assumed to be the area of dike. The application of Eq. (A14) requires the saturation vapor pressure at 25 °C to be known. Saturation vapor pressure data at standard conditions for the 33 components found in the waste oil sample were extracted from the free database on the ChemSpider website (www.chemspider.com), and these data are listed in Table 19. By applying the data given in Table 2, using Eq. (A14), the evaporation rate for the waste oil sample was found to be 0.00134 kg/s.

Table 2

Input data used in the pool evaporation calculation

 Area of pool, m2 12.57 Ambient temperature, K 298 Molecular weight of liquid 490 Saturation vapor pressure, mmHg 1.46
 Area of pool, m2 12.57 Ambient temperature, K 298 Molecular weight of liquid 490 Saturation vapor pressure, mmHg 1.46

#### 3.3.3 Fire Types.

The different types of fires include flash fires, jet fires, pool fires, and fireballs. Because flash fires have a short duration, the amount of heat radiation from flash fires is usually not significant, and thus, it is usually assumed that no deaths will result from this [35]. Hence, the impact of thermal radiation from flash fires was not considered in this study.

##### 3.3.3.1 Jet fires.

To estimate the consequences of a jet fire, the dimensions, geometry, and orientation of the fire, along with the amount of thermal radiation emitted, are required. Using the mathematical models for calculating the effects of jet fires that were presented in Jet Fires section and the input data presented in Table 3, the flame length was estimated to be 1.55 m, and the amount of radiation at a receiver (assumed to be located 50 m away from the flame) was determined to be 0.25 kW/m2 (Table 3). Figure 4 shows how the amount of radiation generated by this jet fire varies as a function of distance. It is important to note that the exit velocity of the jet is low (speed = 1.68 m/s), and therefore, the flame most likely will not blow out [26].

Fig. 4
Fig. 4
Close modal
Table 3

Input data and calculated results for the jet fire accident scenario

Input data
Distance from flame, m50
Hole diameter, mm25
Discharge coefficient for hole1
Leak height above ground, m2
Gas molecular weight490
Molecular weight of air29
Ambient pressure, Pa101,325
Ambient temperature, K298
Gas pressure, barg1.73
Relative humidity, %30
Heat of combustion for gas, kJ/kg46,000
Heat capacity ratio for gas1.009
Flame temperature, K2300
Moles of reactant per mole of product1
Fuel mole fraction at stoichiometric0.09
Fraction of total energy converted0.4
Calculated results
Area of hole, m24.91 × 10−4
Gas discharge rate, kg/s0.56
Exit velocity of the jet, m/s1.68
L/De ratio for flame62.1
Flame height, m1.55
Location of flame center above ground2.78
Point source view factor, m23.17 × 10−5
Water vapor partial pressure, Pa948
Atmospheric transmissivity0.766
Flux at receptor location, kW/m20.25
Input data
Distance from flame, m50
Hole diameter, mm25
Discharge coefficient for hole1
Leak height above ground, m2
Gas molecular weight490
Molecular weight of air29
Ambient pressure, Pa101,325
Ambient temperature, K298
Gas pressure, barg1.73
Relative humidity, %30
Heat of combustion for gas, kJ/kg46,000
Heat capacity ratio for gas1.009
Flame temperature, K2300
Moles of reactant per mole of product1
Fuel mole fraction at stoichiometric0.09
Fraction of total energy converted0.4
Calculated results
Area of hole, m24.91 × 10−4
Gas discharge rate, kg/s0.56
Exit velocity of the jet, m/s1.68
L/De ratio for flame62.1
Flame height, m1.55
Location of flame center above ground2.78
Point source view factor, m23.17 × 10−5
Water vapor partial pressure, Pa948
Atmospheric transmissivity0.766
Flux at receptor location, kW/m20.25
##### 3.3.3.2 Pool fires.

Accidental spills of liquid materials that are stored at temperatures lower than their boiling points will lead to the formation of circular or nearly circular pools. In the case of a transformer, mineral oil can spill and spread over the concrete floor of the transformer compartment. If an ignition source is present, a pool fire may then develop. A series of simplified relationships giving the diameter and area of a pool fire as well as the flame height, burning duration, heat release rate, emissivity, shape factor, atmospheric transmissivity, and received thermal flux are described in Pool Fire section. Using a liquid release rate of 3.57 kg/s (0.0041 m3/s) (as predicted by Eq. A12) and other input data from Table 4 presents the results for pool fire effects (Table 4). The pool fire diameter, flame height, area of the pool, and burning duration were estimated to be 4 m, 6.78 m, 12.57 m2, and 398.51 s, respectively.

Table 4

Input data and calculated results for the pool fire accident scenario

Input data
Hole diameter, mm25
Liquid leakage rate, kg/s3.88
Boiling point of liquid, K370
Heat of vaporization of liquid, kJ/kg210
Heat of combustion of liquid, kJ/kg46,000
Empirical constant, m−10.7
Ambient temperature, K298
Relative humidity, %30
Liquid density, kg/m3880
Constant heat capacity of liquid, kJ/kg K1.67
Dike diameter, m4
Mass burning rate of fuel per unit surface area, kg/m2 s0.039
Receptor distance from pool, m50
Radiation efficiency for point source model0.35
Calculated results
Maximum pool diameter, m5.50
Pool fire diameter, m4.001
Pool area, m212.57
Flame height, m6.78
Flame H/D1.70
Corner fire flame height, m29.55
Water vapour pressure of, Pa947.97
Point source height, m3.39
Regression rate (burning rate), m/s4.4 × 10−5
Burning duration, s398.51
Pool fire heat release rate, MW21.180
View factor, m22.72 × 10−5
Transmissivity0.76
Thermal flux at receptor, kW/m2 (based on point source model)0.16
Thermal flux at receptor, kW/m2 (based on solid flame model)0.18
Input data
Hole diameter, mm25
Liquid leakage rate, kg/s3.88
Boiling point of liquid, K370
Heat of vaporization of liquid, kJ/kg210
Heat of combustion of liquid, kJ/kg46,000
Empirical constant, m−10.7
Ambient temperature, K298
Relative humidity, %30
Liquid density, kg/m3880
Constant heat capacity of liquid, kJ/kg K1.67
Dike diameter, m4
Mass burning rate of fuel per unit surface area, kg/m2 s0.039
Receptor distance from pool, m50
Radiation efficiency for point source model0.35
Calculated results
Maximum pool diameter, m5.50
Pool fire diameter, m4.001
Pool area, m212.57
Flame height, m6.78
Flame H/D1.70
Corner fire flame height, m29.55
Water vapour pressure of, Pa947.97
Point source height, m3.39
Regression rate (burning rate), m/s4.4 × 10−5
Burning duration, s398.51
Pool fire heat release rate, MW21.180
View factor, m22.72 × 10−5
Transmissivity0.76
Thermal flux at receptor, kW/m2 (based on point source model)0.16
Thermal flux at receptor, kW/m2 (based on solid flame model)0.18

Fires spread faster at the corners of rooms than at room centers. This was demonstrated using Eq. (A47), which gave a flame height of 29.55 m for the corner of the room. However, theoretically, the flames will not extend beyond the ceiling of a room unless the fire breaks through the ceiling or spreads from the windows and/or doors. Moreover, if the wall linings are made of combustible materials, they will more quickly contribute to the release of heat. The rate of heat release for the aforementioned example of a pool fire was calculated to be 21.18 MW. The heat flux received by a target at a distance of 50 m from the center of the fire was calculated using two different models: the point source (Eq. (A22)) and solid flame (Eq. (A29)) models. These two models require information regarding the type of flammable liquid, the total amount of released material in the pool, and the fire radius. The results indicated that a receiver located 50 m away from the center of this pool fire would receive a heat flux of 0.16 kW/m2 based on the point source model and 0.18 kW/m2 based on the solid flame model. The results of the calculations for this pool fire are summarized in Table 4. It can clearly be concluded from these results that the characteristics of a pool fire depend mainly on the rate at which a material is released and on the pool diameter. Noting that different fuels burn at different speeds, faster burning fuels are likely to burn more rapidly and more likely to burn back to the source. Figure 5 presents the amount of radiation incident on a receiver as a function of distance from the pool fire.

Fig. 5
Fig. 5
Close modal
Table 5

Input data and calculated results for the BLEVE/fireball accident scenario

Input data
Volume of the tank, m31.1
The horizontal distance from fireball, m50
Heat of combustion of liquid, kJ/kg46,000
Water partial pressure in air, Pa2810
Calculated results
Initial flammable mass, kg968
Maximum fireball diameter, m57.4
Fireball combustion duration, s1.4
Centre height of fireball, m43
Initial ground level hemisphere diameter, m74.6
Surface emitted flux, kW/m21217.5
Path length, m37.3
Transmissivity0.714
Horizontal view factor0.12
Input data
Volume of the tank, m31.1
The horizontal distance from fireball, m50
Heat of combustion of liquid, kJ/kg46,000
Water partial pressure in air, Pa2810
Calculated results
Initial flammable mass, kg968
Maximum fireball diameter, m57.4
Fireball combustion duration, s1.4
Centre height of fireball, m43
Initial ground level hemisphere diameter, m74.6
Surface emitted flux, kW/m21217.5
Path length, m37.3
Transmissivity0.714
Horizontal view factor0.12
##### 3.3.3.3 BLEVEs/fireballs.

In this study, it was assumed that the mineral oil-filled transformer vessel was heated because of any of the reasons described previously and that, as the gas phase volume expanded and the pressure inside the vessel increased, the oil compartment might rupture. The thermal radiation produced by a fireball constitutes the main risk from a BLEVE. To compute the amount of thermal radiation released by a fireball, the dimensions of the fireball and its dynamics need to be determined first. The maximum size of the fireball depends mainly on the mass of the fuel that is released and then vaporizes. A BLEVE can cause vessels containing boiling materials to rupture and produce fragments that can fly several meters—sometimes up to a few kilometers—from the center of the explosion. The mathematical models used to calculate the effects of a BLEVE are described in Appendix  A, BLEVE/Fireball Section.

Diameter, Duration, and Height of a BLEVE Fireball

Empirical equations that can be used to calculate the diameter, duration, and height of a BLEVE fireball are given in Fireball Diameter, Duration, and Fireball Height section (Eqs. (A40)(A43)). A fireball usually has a spherical shape, and initially, its diameter is level with the ground. The first step in determining the geometry of a BLEVE is to find the amount of stored material. For a transformer tank containing 1100 L (1.1 m3) of mineral oil that has a density of 880 kg/m3, the mass of stored oil will be 968 kg. Assuming that all of the stored mineral oil contributes to the fireball and using the input data from Table 5, the geometry of the BLEVE/fireball was calculated, and the results are summarized in Table 5. The fireball diameter, duration, and height were found to be 57.4 m, 1.4 s, and 43 m, respectively.

The damage caused by a fireball will be obvious within the radius of the fireball. Outside this range, the main risk is to people who might be affected by radiation. As a general rule, the radius of a fireball is defined as the radius within which total destruction would occur and no one would likely survive. The radiation received by an object located at a given distance from a fireball can be calculated using the method described in Appendix  A. For the example described earlier, the thermal flux generated by a fireball was found to be 107.2 kW/m2 at a distance of 50 m from the tank for a vertical viewing factor and 124.6 kW/m2 for a horizontal viewing factor (Table 5). Figure 6 shows how the radiation incident on a receiver varies as a function of distance.

Fig. 6
Fig. 6
Close modal

#### 3.3.4 Hot Gas Layer Temperature.

Fires in enclosed spaces release energy and combustion products. These hot products will form a plume that will rise toward the ceiling because of buoyancy. When the plume reaches the ceiling, the hot gas layer will begin to spread horizontally along the ceiling [15,36]. To determine the temperatures generated by the fire in a room where the door is closed, the type of material lining inside the room and its thermal properties need to be known. The material used to line the interior of electrical substations is usually concrete. Table 6 lists the thermal properties of interior lining material and summarizes the other input data required for calculating the temperature of the hot gas layer.

Table 6

Input data and calculated results for the temperature of a hot gas layer in a room with a closed door

Input data
Compartment length, m6
Compartment height, m6
Compartment Width, m5
Interior lining thickness, cm30
Ambient air density, kg/m31.18
Ambient air temperature, °C25
Density of the interior lining, (kg/m3)2400
Thermal conductivity of the interior lining, kW/m K0.0016
Specific heat of air at constant pressure, kJ/kg K1
Thermal capacity of the interior lining, kJ/kg K0.75
Calculated results
Compartment volume, m3180
Mass of the gas in the compartment, kg213.22
Fire heat release rate, kW21,180
Time after ignition, s398.51
Total area of the compartment enclosing surface boundaries, m2192
Compartment hot gas layer temperature, °C3126
Input data
Compartment length, m6
Compartment height, m6
Compartment Width, m5
Interior lining thickness, cm30
Ambient air density, kg/m31.18
Ambient air temperature, °C25
Density of the interior lining, (kg/m3)2400
Thermal conductivity of the interior lining, kW/m K0.0016
Specific heat of air at constant pressure, kJ/kg K1
Thermal capacity of the interior lining, kJ/kg K0.75
Calculated results
Compartment volume, m3180
Mass of the gas in the compartment, kg213.22
Fire heat release rate, kW21,180
Time after ignition, s398.51
Total area of the compartment enclosing surface boundaries, m2192
Compartment hot gas layer temperature, °C3126

Consider a fire that starts inside a room where a transformer is installed and the door is closed. If the fire releases energy at a rate of 21.18 MW (as calculated in Sec. 3.3.3.2), using the methods presented in Fires section, the temperature of the hot gas layer inside the room will be 3126 °C. Table 6 summarizes the results of the calculations for the temperature of a hot gas layer produced by a fire in an enclosed space.

#### 3.3.5 Pressure Rise Due to Fire Growth in an Enclosed Space.

In a closed or semienclosed space, the heat released by the combustion process can lead to an increase in pressure due to the expansion of gases. Using Eq. (A51) and the input data provided in Table 7, the pressure rise would be 18,962 kPa, which is very large. It should be noted that in the event of a fire in a building, the rate at which the pressure rise is often small and the resulting pressure is often low because of gas leakage through walls, ventilation openings, and openings around windows and doors. Most buildings have leaks of some kind, and thus, the pressure will not rise to very high values.

Table 7

Input data and calculated results for the pressure rise due to the growth of a fire in an enclosed space

 Compartment height, m 6 Compartment length, m 6 Compartment width, m 5 Ambient air temperature, °C 25 Initial atmospheric pressure, kPa 101.35 Time after ignition, sec 398.51 Ambient air density, kg/m3 1.18 Fire heat release rate, kW 21,180 Specific heat for air in a constant volume, kJ/kg K 0.71
 Compartment height, m 6 Compartment length, m 6 Compartment width, m 5 Ambient air temperature, °C 25 Initial atmospheric pressure, kPa 101.35 Time after ignition, sec 398.51 Ambient air density, kg/m3 1.18 Fire heat release rate, kW 21,180 Specific heat for air in a constant volume, kJ/kg K 0.71

The calculated pressure rise described early indicates a very high value. However, most transformers are installed inside buildings equipped with wall or ceiling fans and windows for ventilation. In such cases, there will be definitely enough leaks to prevent extreme pressure rises.

#### 3.3.6 Explosion Modeling

##### 3.3.6.1 Estimating the pressure increase and energy release associated with explosions.

The combustion process raises the temperature of gases, and as a result, the system pressure will increase because of the expansion of these gases. The rapid release of high-pressure gases can lead to an explosion. One of the main effects of an explosion is a fast-moving shock or pressure wave [37]. This shock wave produces overpressures that can cause injuries or fatalities and building damage. Equations (A52) and (A53) can be used to calculate the pressure increase due to the expansion of gases and the blast-wave energy produced by a confined explosion, respectively. The input data and the results are summarized in Table 8.

Table 8

Input data and calculated results for the pressure increase and energy release associated with explosions

Input data
Heat of combustion, kJ/kg46,000
Yield, %100
Ambient air temperature, K298
Adiabatic flame temperature of burned gas, K2300
Initial ambient atmospheric pressure prior to ignition, kPa101.35
Mass of flammable vapor release, kg880
Calculated results
Maximum pressure at end of combustion, kPa875
Blast wave energy, MJ4.05 × 104
TNT mass equivalent, kg8996
Input data
Heat of combustion, kJ/kg46,000
Yield, %100
Ambient air temperature, K298
Adiabatic flame temperature of burned gas, K2300
Initial ambient atmospheric pressure prior to ignition, kPa101.35
Mass of flammable vapor release, kg880
Calculated results
Maximum pressure at end of combustion, kPa875
Blast wave energy, MJ4.05 × 104
TNT mass equivalent, kg8996

The peak overpressure and the positive phase duration are the main parameters of the blast wave from an explosion. Typical values of these parameters were calculated using the TNO multi-energy model, which is described in detail in Sec. TNO Multi-Energy Method section. By applying the inputs given in Table 9 to the TNO multi-energy model, from the curves labeled “7” (for a typical blast) in Fig. 24, the peak side-on overpressure at a distance of 50 m from the explosion was found to be 80.97 kPa. The positive phase duration was estimated using Eq. (A57) and found to be 56.44 ms. The details of these results are presented in Table 9. Figure 7 shows the peak overpressure calculated using TNO multi-energy model as a function of distance.

Fig. 7
Fig. 7
Close modal
Table 9

Input data and calculated results for overpressure using the TNO multi-energy model

Input data
The total combustion of a stoichiometric hydrocarbon/air mixture, MJ/m33.5
Standoff distance, m50
Ambient pressure, Pa101,325
Explosion energy, MJ40,480
Speed of sound at ambient, m/s5
Calculated results
Cloud volume, m311,566
Scaled distance0.68
Scaled overpressure0.80
Peak overpressure, kPa80.97
Scaled duration0.264
Duration, ms56.44
Input data
The total combustion of a stoichiometric hydrocarbon/air mixture, MJ/m33.5
Standoff distance, m50
Ambient pressure, Pa101,325
Explosion energy, MJ40,480
Speed of sound at ambient, m/s5
Calculated results
Cloud volume, m311,566
Scaled distance0.68
Scaled overpressure0.80
Peak overpressure, kPa80.97
Scaled duration0.264
Duration, ms56.44
##### 3.3.6.2 Vessel fragments.

Much of the damage and many of the deaths that result from explosions are attributable to fragments. Therefore, predictions of the impact of fragments should not be disregarded. This problem can be considered in terms of the initial velocity, energy, velocity, range, and number of fragments (Blast Wave Energy in a Confined Explosion section). When fragments are projected into the air, they fly at a high speed and may collide with an object or other targets on the ground [38]. Assuming a rupture pressure of 1.3 MPa for the transformer vessel [39] and using the input data in Table 10, the velocity and distance of travel of fragments were calculated to be 117.73 m/s and 843.18 m, respectively (Table 10).

Table 10

Input data and calculated results for velocity and travel distance of fragments

Input data
Total volume of vessel, m31.11
Total mass of vessel, kg124.8
Mass of material contained in the vessel, kg,968
Assumed number of fragments2
Mass fraction of total for fragment0.25
Burst pressure of the vessel, MPa1.3
Ambient pressure, MPa0.101
Temperature of gas within vessel, K300
Heat capacity ratio of gas within vessel1.009
Molecular weight of gas within vessel490
Calculated results
Speed of sound of gas within vessel, m/s72
Actual number of fragments3
Dimensionless velocity33.77
Actual velocity of fragment, m/s117.73
Travel range, m843.18
Input data
Total volume of vessel, m31.11
Total mass of vessel, kg124.8
Mass of material contained in the vessel, kg,968
Assumed number of fragments2
Mass fraction of total for fragment0.25
Burst pressure of the vessel, MPa1.3
Ambient pressure, MPa0.101
Temperature of gas within vessel, K300
Heat capacity ratio of gas within vessel1.009
Molecular weight of gas within vessel490
Calculated results
Speed of sound of gas within vessel, m/s72
Actual number of fragments3
Dimensionless velocity33.77
Actual velocity of fragment, m/s117.73
Travel range, m843.18

### 3.4 Impact of Fires and Explosions on Humans and Structures.

Probit analysis was used to relate the magnitude of accidents involving fires and explosions to the degree of damage they cause (probability of damage). There are several simplified probit models that can be used to predict the consequences of fires and explosions. These are described in Vulnerability section.

#### 3.4.1 Impact of Fires.

When a human being is exposed to a large amount of thermal radiation, the consequences of this exposure can range from debilitating physiological effects that gradually increase over the course of several minutes or more to those where serious pathological damage may occur quite suddenly. It has been found that the type of fire, distance from the fire, and exposure time are the main factors that need to be considered in assessing the mortality and damage due to fires [40]. A detailed analysis of fatal injuries from burns, including the application of several probit equations, can be found in Vulnerability section. As indicated earlier, the mortality rate due to flash fires is often considered zero because of the small amount of thermal radiation emitted by flash fires as well as the short duration time [35]. Moreover, a flash fire is often referred to as a deflagration explosion with negligible overpressure [27,41]. However, it is usually assumed that people caught inside a flash fire will not survive, whereas those outside will not suffer much harm [42]. For jet fires, pool fires, and fireballs, the impact of thermal radiation on human beings can be more serious than that from flash fires.

##### 3.4.1.1 Impact of jet fires.

The main parameters affecting the thermal radiation emitted by a jet fire are the duration time and the mass release rate. Close to a jet fire, the risk due to heat radiation varies with the distance from the fire. For a given exposure time, the death/injury rate due to the thermal radiation produced by a jet fire can be estimated using probit equations (Eqs. (A68)(A70)). These equations require the thermal flux (in W/m2) and the exposure time (in s) as inputs. Assuming an exposure time of 60 s, the probabilities of a fatality and first- and second-degree burns occurring were calculated as a function of distance: the results of these calculations are presented in Fig. 8.

Fig. 8
Fig. 8
Close modal

It can be observed from Fig. 8 and Table 17 that a person located at distances of 14.6, 9.64, and 8.83 m from the fire center has a 50% probability of suffering from first-, second-, and third-degree burns, respectively. This means that the danger area, the area in which third-degree burns (which have a 50% mortality rate) may occur, extends to a distance of 8.83 m from the center. (A 50% mortality rate means that 50% of hospitalized patients died because of their injuries.) Table 11 summarizes the thermal radiation dose from a jet fire that has a 50% probability of causing first-, second-, and third-degree burns at different distances.

Table 11

The thermal radiation dose from a jet fire that has a 50% probability of causing first-, second-, and third-degree burns at different distances

First degree burns3.1714.6
Second degree burns7.229.64
Third degree burns (fatality)8.548.83
First degree burns3.1714.6
Second degree burns7.229.64
Third degree burns (fatality)8.548.83

Experimental data show that exposure to a 37.5 kW/m2 dose of thermal radiation for 60 s is sufficient to have a 100% probability of causing death [43,44]. In other studies, it was assumed that exposure to a 35 kW/m2 dose of thermal radiation will cause death within a very short space of time [45]. Skin that is unprotected by clothes can be expected to suffer from second-degree burns if exposed to a thermal intensity of 5.0 kW/m2 for 30 s [46]. For doses between 37.5 and 5.0 kW/m2, people indoors will be protected by the structure, but those who are outdoors and cannot reach shelter quickly may suffer from fatal burns.

It can also be observed from Fig. 8 that at a distance of 15 m, the probability of death resulting from exposure to thermal radiation will fall to approximately 0%. The probability of first-, second-, and third-degree burns will be zero at distances of 25, 16, and 15 m, respectively.

It should be noted that if the probit function is not directly used in assessing the impact of a fire, then the use of Table 17 is recommended for obtaining the severity of the effects of thermal radiation on structures and people. The effects of thermal radiation on a structure depend mainly on whether it is made of combustible materials as well as on the length of exposure [95]. Wooden materials undergo thermal degradation due to combustion, whereas steel will fail because of the reduction in yield strength, stiffness, and modulus of elasticity. Thus, wooden structures may ignite if the intensity of radiant heat exceeds the wood ignition threshold [47]. It can be concluded from Fig. 8 and Table 17 that the major impacts on structures occur within 5 m of the center of a jet fire. Thermal radiation can cause indirect effects that do not directly affect the exposed skin. These include ignition of clothing, heating of corridors and stairways, and smoke inhalation [42].

##### 3.4.1.2 Impact of pool fires.

The thermal radiation dose generated by a typical pool fire was calculated based on the methods introduced in Appendix  A. The thermal dose was converted to the probability of injury or fatality by means of probit-type relationships. The degree of injury was found to depend on the thermal dose, the exposure time, and the distance from the fire center [48]: a heat flux of 10 kW/m2 was found to be capable of causing second-degree burns after an exposure time of 10 s, whereas 10 s exposure to a flux of 5 kW/m2 will result in onset pain. It was also found that a flux of 5 kW/m2 will cause pain in around 15‒20 s and injury (at least second-degree burns) after 30 s of exposure [49]. In this study, two exposure times were selected for investigation: a time of 60 s and a time taken to be equal to the burning duration predicted using Eq. (A38), which was 398.51 s.

Figure 9 shows the probability of first- and second-degree burns occurring due to 60 s exposure to thermal radiation from a pool fire against distance. It can be concluded from this figure that the probability of first-, second-, and third-degree burns occurring is 50% at distances of 12.22, 6.93, and 6.09 m, respectively. These results are also summarized in Table 12.

Fig. 9
Fig. 9
Close modal
Table 12

The thermal radiation dose from a pool fire that has a 50% probability of causing burns of different degrees of severity for an exposure time of 60 s

First-degree burns3.1712.22
Second-degree burns7.226.93
Third-degree burns (fatality)8.546.09
First-degree burns3.1712.22
Second-degree burns7.226.93
Third-degree burns (fatality)8.546.09

The effect of thermal radiation generated by a pool fire on structures is evident over short distances (≤5 m). It can be concluded from Fig. 5 and Table 12 that thermal radiation can cause considerable damage to buildings and other structures within a radius of approximately 5 m. At greater distances, the continuous, low-level heat flux and effects may be minimal, but physiological and pathological effects may still occur as the exposure time increases [50].

Figure 10 shows the probabilities of fatality and injury for an exposure time equal to the pool fire duration (398.51 s). The distances at which there is a 50% probability of first-, second-, and third-degree burns occurring after this time are summarized in Table 13. It can be seen from this figure and table that as the length of exposure to heat radiation from a pool increases, the probability of fatalities or injuries also increases.

Fig. 10
Fig. 10
Close modal
Table 13

Thermal radiation dose from pool fire that has a 50% probability of causing burns of different degrees of severity for an exposure time equal to pool fire duration

First-degree burns0.6828.00
Second-degree burns1.7517.20
Third-degree burns (fatality)2.0715.71
First-degree burns0.6828.00
Second-degree burns1.7517.20
Third-degree burns (fatality)2.0715.71
##### 3.4.1.3 Impact of BLEVEs.

If the temperature of the mineral oil in a transformer tank reaches a temperature above its boiling point, then a BLEVE can occur because of the rapid pressure increase. The large thermal flux and blast wave produced by a BLEVE can result in serious damage to structures and severe harm to humans in the vicinity of the accident. This damage will be particularly severe within the radius of the fireball. Outside this area, the risk is mainly to people who may be affected by the thermal radiation [51]. Therefore, the radius of the fireball is considered the radius at which no one will survive and complete destruction will occur. Fireballs usually have shorter duration times than pool fires and jet fires. In this study, the fireball duration time was estimated to be 1.4 s, and the predicted impacts were based on this time. Using the probit analysis described by Eqs. (A69)(A71), the probabilities of first-, second-, and third-degree burns occurring due to a BLEVE were estimated as a function of distance. Figure 6 shows the amount of thermal radiation at different distances from the BLEVE/fireball. The probability of various types of burns caused by a BLEVE occurring in 1.1 m3 mineral oil tanks versus distance is illustrated in Fig. 11. It can be seen from this figure that there is a 100% probability of first-, second-, and third-degree burns occurring at distances of 0, 100, and 140 m, respectively. Table 14 summarizes the distances at which there is a 50% probability of a person suffering from first-, second-, and third-degree burns.

Fig. 11
Fig. 11
Close modal
Table 14

The thermal radiation doses from a BLEVE/fireball that have a 50% probability of causing first-, second-, and third-degree burns

First-degree burns2.84206.6
Second-degree burns7.22150.2
Third-degree of burns143.242
First-degree burns2.84206.6
Second-degree burns7.22150.2
Third-degree of burns143.242

It is apparent from Fig. 11 and Table 14 that in the case of a BLEVE/fireball, the danger area extends to a distance of 42 m, which causes third-degree burns (50% fatal).

For a BLEVE/fireball occurring in a 1.1 m3 mineral oil tank, exposure to thermal radiation with an intensity of 37.5 kW/m2 would occur at a distance of about 82 m from the center of the fireball. According to Table 17, this is sufficient to demolish buildings, structures, and equipment. Tsao and Perry [52] suggested that exposure to a radiation intensity of 30 kW/m2 for 60 s has a 100% fatality rate. This study indicated that 60 s exposure to radiation from a BLEVE/fireball that has an intensity of 30 kW/m2 will have a 100% fatality rate and that this intensity will be experienced at a distance of 90 m from the center of the accident (Fig. 12). This clearly shows that even short exposure to high heat flux levels can be fatal. Hse and Osd [50] suggested that exposure to an intensity of 35 kW/m2 would lead to immediate fatalities in the vicinity of a fire. Cox [53] also indicated that people caught inside a flammable cloud at the moment of ignition would not survive, whereas those outside the flammable zone would. This means that everyone within a fireball diameter of 55.6 m will not survive. It has been documented that events such as BLEVEs and large jet fires that generate large heat fluxes usually result in severe skin burns or fatalities. The long duration time of such incidents can increase the effects even at large distances [50,54].

Fig. 12
Fig. 12
Close modal

#### 3.4.2 Impact of Explosions.

The peak overpressure resulting from an explosion was calculated using the TNO multi-energy model described in Appendix  A, TNO Multi-Energy Method section, and the results are presented in Appendix  A. These results were used in probit equations Eqs. (A71)(A74) to calculate the impact of an explosion on people and structures. The primary effects of overpressure are lung hemorrhage, eardrum rupture, injuries due to shattered windows, and structural damage. Figure 13 demonstrates the probability of these effects occurring as a function of distance from the center of an explosion. As shown in this figure, there is an approximately 95% probability of eardrum rupture for someone at the center of the explosion, whereas there is an approximately 50% probability of someone at a distance of 46.37 m suffering from an eardrum rupture. Karlos and Solomos [41] indicated that there is a 10% chance of an eardrum rupture occurring as a result of exposure to a pressure of about 0.25 bar. This indicates that as well as close to the explosion, people can suffer from a ruptured eardrum up to several kilometers away depending on the overpressure generated by the explosion. Lung hemorrhages can also result from direct exposure to excessive overpressure from an explosion. The probability of a fatality occurring as a result of a lung hemorrhage can be calculated using Eq. (A72). However, it should be noted that for an explosion in a tank with a capacity of 1.1 m3, there is almost no chance of a fatal lung hemorrhage occurring even close to the center of the explosion: as shown in Fig. 13, the maximum probability at the center of the explosion is around 1%. Karlos and Solomos [41] and Baker et al. [55] suggested that 99% of people can survive a lung hemorrhage due to shock pressures of about 2 barg. Equation (A73) is the probit equation that can be used to calculate the probability of glass shattering due to the peak overpressure. The probability of glass breaking as a function of distance is illustrated in Fig. 13. It can be concluded that there is a 100% probability of glass damage occurring at a distance of 80 m from the center of the explosion, and at 279 m from the center of the explosion, there is a 50% probability of this occurring. Table 15 summarizes the impact (50% probability of damage) due to a VCE.

Fig. 13
Fig. 13
Close modal
Table 15

Summary of the impact (50% probability of damage) of the peak overpressure on people and structures resulting from the explosion of a 1.1 m3 transformer

ImpactPeak overpressure, Po (kPa)Distance (m)
Eardrum rupture43.1546.37
Lung hemorrhage103.43 (center of the explosion)0
Glass breakage3.94279
Structures damage19,20078.07
ImpactPeak overpressure, Po (kPa)Distance (m)
Eardrum rupture43.1546.37
Lung hemorrhage103.43 (center of the explosion)0
Glass breakage3.94279
Structures damage19,20078.07

The impact of the overpressure on structures can be predicted using Eq. (A74). It is obvious from Fig. 13 that severe damage would occur within 20 m of the explosion (probability of structural damage ≈ 100%), whereas at 78 m, there is a 50% probability of structural damage.

#### 3.4.3 Effects Due to Fragments.

It is possible to study the behavior and estimate the impact of the fragments scattered by an explosion. The effect of such fragments depends on their shape, mass, number, and velocity and on the distance from the center of the explosion. In an analysis of the projectiles generated by the explosion of a 1.1 m3 tank and according to Birk and Cunningham [54], most (80–90%) of the projected fragments landed within four times the fireball radius, and some fragments traveled up to 15 times the radius. In very rare cases, fragments traveled up to 30 times the radius of the fireball. This meant that 80–90% of the fragments landed within 114.8 m of the explosion, some traveled up to 430.5 m, and a very few fragments traveled up to 861 m. In another study, Edwards et al. [56] indicated that the majority of fragments would land within 700 m. In some instances, fragments have been observed to land over 1 km from the explosion, as it occurred in Mexico City in 1985. Pettitt et al. [57] stated that the range of fragments could vary from a few meters to about 1 km, although most fragments do not travel more than 400 m. Holdern and Reeves [58] recommended that the evacuation distances for a fire involving a liquefied gas vessel should be based on the projectile range rather than the thermal hazard range because the potential projectile range exceeds the thermal radiation hazard range. Birk and Cunningham [54] suggested that, where possible, personnel should be evacuated to a distance greater than 15–30 times the fireball’s radius.

According to Eq. (A60), the velocity of the fragments would be 117.73 m/s. According to Eq. (A78), the probability of a fatal injury for someone hit by such a fragment (mass > 4.5 kg) would be 100%.

### 3.5 Risk Assessment Matrix.

A risk matrix can be used to determine the level of risk resulting from the outcomes of the previous scenarios. The risks are evaluated based on their likelihoods and impacts. As mentioned earlier, thermal radiation from flash fire is usually not significant, so the risk will be low according to Fig. 14.

Fig. 14
Fig. 14
Close modal

The scenario of a pool fire can occur in electrical substations for several reasons, as mentioned earlier. The radiant energy of the pool fire was calculated in Sec. 3.3.3.2, and according to Fig. 9, the impact was severe for the close range (<5 m) from the center of the pool fire. Therefore, according to Fig. 15, the risk will be high. Conversely, the jet fire scenario occurs less frequently than the pool fire scenario. As with the previous scenarios, the risk will be high according to Fig. 16.

Fig. 15
Fig. 15
Close modal
Fig. 16
Fig. 16
Close modal

As mentioned in Sec. 2.3, a BLEVE event can occur in electrical substations for several reasons. Since several BLEVE accidents have already been reported in substations, the probability of occurrence in Fig. 17 is chosen as possible. The blast waves and thermal radiation generated by BLEVE are usually very strong, so the risk will be extremely high.

Fig. 17
Fig. 17
Close modal

An explosion can cause various types of injuries and damage, including lung hemorrhage, eardrum rupture, glass breakage, and damage to structures. The risk assessment matrices for these four types of scenarios are illustrated by Figs. 1821 respectively.

Fig. 18
Fig. 18
Close modal
Fig. 19
Fig. 19
Close modal
Fig. 20
Fig. 20
Close modal
Fig. 21
Fig. 21
Close modal

## 4 Conclusion

In this study, the risks and consequences associated with fires and explosions in electrical substations were studied. A sample of waste oil was collected from an electrical substation in Riyadh, and the composition of the sample was analyzed using GC-MS. The flammability diagram method was employed to determine whether a flammable mixture is present during the transformer operations. The results showed that the vapor mixture is not flammable at 25 °C. The results of the consequence modeling revealed that the peak overpressure produced by an explosion could cause severe damage to structures within a radius of 50 m. Moreover, the thermal radiation emitted by a BLEVE/fireball would produce serious injuries up to a distance of 140 m.

The findings and lessons learned from this study can be summarized as follows:

• As transformers become older, fires may occur more frequently due to internal defects, malfunctions in bushings, or tap changers. Therefore, transformers must be inspected frequently.

• Transformer oil should not be allowed to discharge onto the ground in electrical substations during the replacement of old oil with new oil as oil on the ground could ignite because of direct contact with fire. In addition, in enclosed spaces, the waste oil may form a flammable mixture that can easily burn in the presence of any ignition source.

• Mineral oil is classified as a nonflammable (noncombustible) liquid. However, it can become flammable if exposed to heat. If these oils burn, the consequences are usually dire.

• Indoor substation transformers should be equipped with a good mechanical ventilation system to prevent the formation and accumulation of flammable vapor–air mixtures.

• High-temperature activities such as welding should not be performed near transformers located in enclosed spaces, especially if there is any indication of an oil leak. Oil leaking from transformers contains hydrocarbon compounds that can vaporize and form a flammable mixture, especially in enclosed spaces.

• It is recommended that a drain be constructed around the transformer to collect and drain any oil that may leak, which could result in an accumulation of mineral oil in the drainage system.

• Sufficient monitoring sensors should be installed in the compartment, where the transformer is located to detect the composition of any flammable mixtures generated.

When fires and explosions occur in electrical substations, the consequences can be severe. Therefore, engineers must consider sufficient safety distances when installing these equipment to reduce the impact on people in the vicinity.

## Conflict of Interest

There are no conflicts of interest. This article does not include research in which human participants were involved. Informed consent not applicable. This article does not include any research in which animal participants were involved.

### Appendix A

#### Transformer Type and Size Detailed Calculations

The power transformer consists of several parts and components, as shown in Fig. 22.

Fig. 22
Fig. 22
Close modal

The transformer tank accommodates the core-and-coil assembly, tap changer with connections, oil filling, bushings, and associated fittings. The oil used to fill the transformer tank is class-1 mineral oil that complies with IEC 60296 and ASTM D3487 international standards. The transformer tanks are made of 3 mm-thick mild steel and are designed to be capable of withstanding an internal pressure of up to 30 kPa without permanent deformation. The tank is provided with a pressure relief vent to prevent rupturing of the transformer. It also has a temperature indicator with a range of 0 °C‒120 °C for making readings of the oil temperature [60]. Transformers of this type are suitable for both indoor and outdoor use and are designed to comply with the following maximum temperature limits [60]:

• Top oil = 45 °C maximum

• Winding = 50 °C maximum

• Hot spot = 98 °C maximum

• Average temperature due to short circuit = 250 °C maximum.

The transformer is installed inside a compartment that has the following dimensions and properties:

• Width, wc = 4 m

• Length, Lc = 5 m

• Height, hc = 3 m

• Interior lining thickness, δ = 30 cm

• Ambient air temperature, Ta = 25 °C.

The transformer tank consists of an irregular steel box. However, in this study, it was assumed that the box was a cube holding 1000 L of oil. The conservator tank, in contrast, has a cylindrical shape (length = 153 cm; diameter = 50 m) and is only partly filled with oil (Fig. 23).

Fig. 23
Fig. 23
Close modal

The transformer tank is connected by pipework to the conservator tank. Usually the conservator tank is filled about 25–35% full, and the volume of oil in the conservator tank will then be 10–12% of the volume in the main tank [33].

The volume of the conservator tank, Vc, can be determined as follows.

Assuming that the volume of the oil in the conservator tank is 10% of the volume in the main tank, the volume of oil Vo = 0.1 × 1000 = 100 L.

This means that the total amount of oil is 1000 L (main tank) + 100 L (conservator tank) = 1100 L.

If the conservator tank is assumed to be 35% full, the capacity of the conservator tank Vc = 100/0.35 = 303 L (0.303 m3).

A fuel leak can occur anywhere in the main tank or conservator tank. Assuming the worst-case scenario, all of the stored oil will leak from the main tank and conservator tank. This means that 1100 L of oil will leak onto the floor of the transformer building.

The mass of the conservator tank, mc, can be calculated as follows:

The total volume of the shell of the conservator tank, Vcs, is expressed as follows:
$Vcs=π×L×t(d−t)$
where L is the length of the tank, cm, and t is the thickness of the tank (3 mm) [33].
Thus,
$Vcs=π×1.53×0.003(0.50−0.003)=0.007m3$
$mc=Vcs×ρSS$
where ρSS is the density of stainless steel (7800 kg/m3). Thus,
$mc=0.007×7800=54.6kg$

The mass of the main tank, mm, can be calculated as follows:

The total volume of the 3 mm shell of the main tank, Vms, is expressed as follows:
$Vms=Vm−V2=[(1+0.003)×(1+0.003)×(1+0.003)]−[1×1×1]=0.009m3→mm=0.009×7800=70.2kg$

Thus, the total mass of the two vessels = 54.6 + 70.2 = 124.8 kg.

#### Lower Flammability Limit, Upper Flammability Limit, and Limiting Oxygen Concentration

For many hydrocarbon vapors, Jones [61] found that the flammability limits are function of the stoichiometric concentration of fuel:
$LFL=0.55(100)4.76m+1.19x−2.38y+1$
(A1)
$UFL=3.50(100)4.76m+1.19x−2.38y+1$
(A2)
where LFL is lower flammable limits (vol%), UFL is the upper flammable limits (vol%), and m, x, and y can be found according to the following combustion reaction equation:
$CmHxOy+zO2→mCO2+(x2)H2O$
(A3)
Here, z is equivalent moles O2/moles fuel:
$z=m+x4−y2$
(A4)
Le Chatelier [62] suggested correlations for estimating the LFL and UFL of vapor mixtures.
$LFLmix=1∑(yi/LFLi)$
(A5)
$UFLmix=1∑(yi/UFLi)$
(A6)
where LFLi is the lower flammability limit of fuel component i (vol%), UFLi is the upper flammability limit of fuel component i (vol%), yi is the mole fraction of component i on a combustible basis, and n is combustible species number.
A simple model for predicting the LOC was proposed by Bodurtha [63]:
$LOC=z(LFL)$
(A7)
The LOC for mixtures can be determined using the following equations [64]:
$LOCmix=∑yizi∑yi/Li*=∑yizi∑yizi/LOCi$
(A8)
$Li*=LOCizi$
(A9)
where LOCmix is the LOC for the fuel mixture (vol%), zi is the stoichiometric molar ratio of oxygen to fuel mixture for compound i, and LOCi is the LOC for compound i (vol%) Eq. (A7).

#### Consequence Analysis

##### Outflow Rates

The outflow rate is affected by the physical state of the stored material and the characteristics of the failure. A release may consist of liquid, gas/vapor, or both phases [65].

###### Gas/Vapor Outflow
The majority of gas discharges from process plant leaks are initially sonic. Rate equations for sonic and subsonic discharges through an orifice were introduced by different authors [26,38,6567]. For free expansion leak (subsonic flow):
$Gv=CdAp2γMRgTγγ−1[(ppa)2/γ−(ppa)(γ+1)/γ]$
(A10)
where Gv is the gas/vapor flowrate (mass/time), Cd is the discharge coefficient (dimensionless), A is the hole cross-sectional area (length2), p is the upstream pressure (force/area), pa is the ambient pressure (force/area), γ is the heat capacity ratio (unitless), M is the gas molecular weight (kg/kg · mol), and Rg is the gas constant (pressure-volume/mole-deg).
For sonic (choked) flow,
$Gv=CdAp[γMRT(2γ+1)(γ+1)/(γ−1)]0.5$
(A11)
###### Liquid Outflow
Discharge of liquids from a hole in a vessel can be computed using the Bernoulli and Torricelli equation [26,38,6567]:
$GL=CdAρ[2(p−pa)ρ+2gh]0.5$
(A12)
where GL is the liquid flowrate (mass/time), ρ is the liquid density (mass/volume), h is the static head of the liquid (length), and g is the gravitational acceleration (length/time2).

#### Flashing and Evaporation

##### Flashing
The fraction of the liquid that flashes during a superheated liquid released to atmospheric pressure can be calculated using Eq. (A13) [67]:
$Fv=Cp(T−Tb)hfg$
(A13)
where Cp is the liquid heat capacity averaged over T to Tb (energy/mass deg), T is the liquid initial temperature (deg), Tb is the liquid atmospheric boiling point (deg), hfg is the liquid latent heat of vaporization at Tb (energy/mass), and Fv is fraction of the liquid vaporized (‒).
##### Evaporation or Boiling
The evaporation rate for liquids with boiling points close or higher than ambient temperature, and the pool area is large, can be determined using Eq. (A14) [67,68]:
$Qm=MwtKAePsatRgTL$
(A14)
where Qm is the evaporation rate (mass/time), Mwt is the pure material molecular mass (mass/mole), K is the mass transfer coefficient (length/time), Ae is the exposure area (length2), Psat is the saturation vapor pressure of the liquid (force/area), and TL is the liquid temperature (deg).
The mass transfer coefficient, K, can be calculated using Eq. (A15) [67,68]:
$K=Ko(MoMwt)1/3$
(A15)
where Ko is a reference mass transfer coefficient (length/time), Mo is a reference molecular mass (mass/mole), and Mwt is the molecular mass of species (mass/mole).

Water, which has a mass transfer coefficient of 0.83 cm/s, is usually used as the reference substance.

#### Fires

##### Jet Fires

Important calculations for jet fires are flame size and shape, flame tilt, and thermal radiation assessment [26,69].

###### Flame Shape
The model recommended by Hawthorn et al. [70] can be utilized to predict the length of the jet flame originating from a gaseous discharge:
$LDe=5.3Ct[Tad.αTv{Ct+(1−Ct)MaMf}]0.5$
(A16)
where De is the initial diameter of the jet (length), Ct is the mole ratio of fuel to reactants (‒), α is the ratio of the number of moles of reactants to moles of products (‒), Tad. is the flame temperature (deg), Tv is the initial temperature of the jet fuel (deg), Ma is the molecular mass of the air (mass/mole), and Mf is the molecular mass of the fuel (mass/mole).
Because Ct ≪ 1, α = 1, and for most actual fuels Tad./Tv it ranges between 7 and 9 [71], Eq. (A.16) can be simplified to:
$L−sDe=15Ct[MaMf]0.5$
(A17)
Andreassen et al. [69] reported that for choked releases, the exit diameter should be replaced by a hypothetical nozzle that has a diameter, Def, given by:
$DefDe=1Mef[2+(γ−1)Mef2γ+1]γ+14(γ−1)$
(A18)
where Mef is the effective Mach number, which can be calculated by:
$Mef=2γ−1[{pvpa}γ−1γ−1]$
(A19)
where $pv$ is the upstream pressure at the event orifice (force/area).
Kent [59] suggested a model to predict the lift-off distance, s:
$s=6.4πDeue4ua$
(A20)
where ue is the exit velocity (m/s), and ua is the average jet velocity (length/time) = 0.4ue.
The exit velocity can be determined by:
$ue=MefγRT/(1+γ−12Mef2)$
(A21)
where T is the upstream gas temperature (deg).
###### Heat Transfer Assessment

Thermal radiation from jet fires can be predicted using two models, namely, point source and solid flame models [26,72]. Point source model overestimates the intensity of thermal radiation at locations close to the fire because in the near field, the radiation is greatly influenced by the flame size, shape, tilt, and orientation of the observer.

The radiative heat flux to a target, Q, may be expressed as follows:
$Q=q4πx2$
(A22)
$q=fm″ΔHc−$
(A23)
where q is the energy released by radiation (kW), x is the distance from the flame center (m), f is the fraction of the heat released as radiation (–), and ΔHc is the heat of combustion of the fuel (kJ/kg).
The solid flame model is the most popular and used method, which gives the most accurate and reliable results. This model assuming the flame to have a shape as a cylinder with an equivalent diameter Deq.:
$Deq.=L2+2Ac−L$
(A24)
where Ac is the surface area of the frustum of the cone (length2), which can be calculated by:
$Ac=0.25(W12+W22)+0.5(W1+W2)L2+(W2−W12)2$
(A25)
The flame surface emissive power, Ep (energy/area), can be predicted using Eq. (A26) [69]:
$Ep=fRm.ΔHAf$
(A26)
where fR is the radiative fraction (‒).
The surface area for the jet frustum fire is given by Andreassen et al. [69]:
$Af=π4(W12+W22)+π2(W1+W2)L2+(W2−W12)2$
(A27)
Chamberlain [73] suggested the following equation to calculate fR:
$fR=0.21e−0.00323uj+0.11$
(A28)
The radiant heat flux to a target at a certain distance from the gas outlet can be estimated using Eq. (A29) [72]:
$Qj=EpFτ$
(A29)
where τ is the atmospheric transmissivity (‒), which can be calculated by Eq. (A30), and F is the view factor (‒), which can be calculated by Eq. (A32).
###### Atmospheric Transmissivity
The atmospheric transmissivity calculation is needed to determine the radiant heat flux. The simplified empirical equation is expressed as follows [26]:
$τ=2.02(Pwx)−0.09$
(A30)
where Pw is the partial pressure of water (Pascals, N/m2) and x is the length of the path from the target to the surface of the (m).
The partial pressure of water, Pw, can be calculated as follows [26]:
$Pw=101325(RH)exp(14.4114−5328Ta)$
(A31)
where RH is the relative humidity (percent).
###### View Factor
Predicting thermal radiation emitted by fire requires information on the view factor between the fire and the target [74]. The view factor depends on the shape of the flame, the distance between the flame front and the receiving target, and the position of the receiver. Equation (A32) can be used to predict the view factor [26]:
$F=14πx2$
(A32)
##### Pool Fire

The most important calculations for pool fire are as follows: pool size, flame height, burning rate, atmospheric transmissivity, flame emissive power, view factor, and thermal radiation assessment [26,38,65,66,7578].

###### Pool Size and Flame Height
The size of the pond depends on whether there are barriers located in the place where the spilled liquid collected [69]. Mudan and Croce [79] provided a correlation for the prediction of the maximum pool diameter (Eq. (A.33)):
$Dmax=2VL.πy.$
(A33)
where $VL.$ is the volumetric flowrate of the spilled liquid (volume/time), and $y.$ is the liquid burning rate (length/time).
The area of a pool fire can be calculated as follows:
$Ap=πDp24$
(A34)
where Dp is the pool diameter (length).
Thomas [80] introduced a correlation that is widely used to determine the flame length:
$HDp=42(mBρagDp)0.61$
(A35)
where H is the visible flame length (m), Dp is the equivalent pool diameter (m), mB is the mass burning rate (kg/m2 s) and this is assumed as 0.039 for mineral oil [75,81], ρa is the air density (1.23 kg/m3), and g is the gravitational acceleration (9.81 m/s2).
###### Flame Surface Emissive Power
The temperature and emissivity are usually considered the main parameters contributed to the radiation from hot gases or flames. The emissivity is the ability of a hot gas to emit heat by radiation [76]. The surface emissive power depends on the type of the fuel and the size of the fire. Mudan and Croce [82] provided the correlation to predict the emissive power:
$E=Emaxe−sDp+Es(1−e−sDp)$
(A36)
where E is the average emissive power (kW/m2), Emax is the maximum emissive power of the luminous spots (≈140 kW/m2), Es is the emissive power of smoke (≈20 kW/m2), and s is an experimental parameter (0.12 m−1).
###### Geometric View Factor

The view factor can be predicted using the same model proposed in jet fire section Eq. (A32).

The thermal flux emitted from pool fire can be calculated using the solid flame model Eq. (A29).

###### Heat Release Rate
For most organic liquids, the pool fire heat release rate is well correlated by the model of Stroup et.al. [75]:
$qr=mBΔHc(1−e−kβDp)Adike$
(A37)
where qr is the pool fire heat release rate (kW), mB is the burning rate per unit area (kg/m2 s), ΔHc is the heat of combustion of fuel (kJ/kg), Adike is the surface area of pool fire (m2), and is the empirical constant (m−1).

It has been found that liquid swimming pool fires are usually not dangerous when their diameter is smaller than about 0.2 m [76].

###### Burning Duration
The following expression can be used to calculate the burning duration of a fixed volume of fuel [76,81]:
$tb=4VπDp2ν$
(A38)
where tb is the pool fire burning rate time), V is the liquid volume (volume), Dp is the pool diameter (length), and ν is the rate of burning (regression rate), (length/time).
The following expression can be used to determine the burning rate [76,81]:
$ν=mBρ$
(A39)
where ρ is the liquid fuel density (mass/volume).
##### BLEVE/Fireball

BLEVE is an explosion caused by a sudden failure of a tank containing a liquid at a temperature well above its boiling point. This is usually occurred as a result of overheating due to an external fire such as a pool fire or jet fire [83]. Upon vessel failure, a blast wave, flying missiles, and fireball will usually be resulted [26].

###### Fireball Diameter, Duration, and Fireball Height
Many correlations for the fireball dimensions and durations have been published in different literature [26,38,65,84]. These models use the amount of the flammable liquid in the fireball to predict the diameter and duration of the fireball. Equations (A40)(A43) are used to calculate the maximum diameter, center height, and duration of the fireball [26]:
$Dmax=5.8M1/3$
(A40)
$tBLEVE=0.45M1/3forM<30,000kg$
(A41)
$tBLEVE=2.6M1/6forM>30,000kg$
(A42)
$HBLEVE=0.75Dmax$
(A43)
where $Dmax$ is the maximum fireball diameter (m), M is the initial mass of flammable liquid (kg), $tBLEVE$ is the fireball combustion duration (s), and HBLEVE is the center height of the fireball (m).
The thermal radiation release from the fireball and received by a given target might be calculated by Eq. (A29). This model requires the atmospheric transmissivity, the flame surface emissive power, and the view factors. Atmospheric transmissivity can be calculated from Eq. (A30). The bath length, x, from the target to the flame surface is given by [26]:
$x=[HBLEVE2+r2]0.5−[0.5Dmax]$
(A44)
Calculating thermal radiation also requires a prediction of the surface emitted flux, Ep [26]:
$Ep=FradMΔHcπ(Dmax)2tBELVE$
(A45)
where Frad is the radiation fraction (dimensionless). A value of 0.25–0.4 of the fuel heat of combustion can be suggested [85].
To calculate the geometric view factor of the fireball, the shape of the fireball was assumed to have a perfect sphere shape [26,86]:
$F=x(D/2)2(L2+H2)3/2$
(A46)
where D is the diameter of the fireball (m), x is the distance from a point at the ground directly below the fireball center to the observer at the ground level, and H is the center height of the fireball (m).
##### Corner Fires
Walls and corners will have major impacts on the spread and growth of fire as they will cause reduction of air entrainment available for a flame or plume. This will lengthen the flame and cause the temperature in the plume to be higher than it will be in the open [75,81]. Hasemi and Tokunaga [87,88] provided a correlation to estimate the corner fire flame height:
$Hf(corner)=0.075(qr)3/5$
(A47)
where Hf(corner) is the corner fire flame height (m) and qr is the fire heat release rate (kW).
##### Hot Gas Layer Temperature in a Close Compartment
A correlation to predict the temperature of the hot gases in a closed doors compartment is proposed by Beyler [89]:
$ΔTg=2K2K12(K1t−1+e−k1t)$
(A48)
where
$K1=2(0.4kρc)ATmcpandK2=Q.mcp$
(A49)
and ΔTg is the upper layer gas temperature rise above ambient (Tg − Ta) (K), k is the interior lining thermal conductivity (kW/m K), ρ is the interior lining density (kg/m3), c is the interior lining thermal capacity (kJ/kg K), $Q.$ is the fire heat release rate (kW), m is the gas mass in the compartment (kg), cp is the air specific heat (kJ/kg k), and t is the exposure time (s).
The interior surface area of the compartment [76,81]:
$AT=[2(wc×lc)+2(hc×wc)+2(hc×lc)]$
(A50)
where AT in the interior surface area of the compartment (m2), wc is the width of the compartment (m), lc is the length of the compartment (m), and hc is the height of the compartment (m).
##### Pressure Rise in a Closed Compartment Due to Fires
The maximum pressure difference inside a close compartment resulted from the expansion of gases is given by Eq. (A51) [90]:
$P−PaPa=tVcρacvTa$
(A51)
where P is the compartment pressure attributed to combustion (atm), Pa is the initial atmospheric pressure (atm), t is the time after ignition (s), Vc is the volume of the compartment (m3), ρa is the ambient air density (kg/m3), cv is the constant volume specific heats of air (kJ/kg K), and Ta is the ambient temperature (K).

#### Explosion Modeling

##### Pressure Rise
The pressure rise caused by the expansion of the gases can be calculated through the following equation [75]:
$Pmax=(TadTa)Pa$
(A52)
where Pmax is the maximum pressure at end of combustion (kPa), Pa is the initial ambient atmospheric pressure prior to ignition (kPa), Tad is the adiabatic flame temperature of burned gas (K), and Ta is the ambient temperature (K).
##### Blast Wave Energy in a Confined Explosion
When a large amount of evaporated flammable gas escapes from a closed vessel into the atmosphere, it mixes with air and then ignites, causing an explosion. The energy released by the rupture of a pressurized vessel can be calculated using Eq. (A53) [75,81]:
$E=∝ΔHcmf$
(A53)
where E is the blast wave energy (kJ), α = yield, ΔHc is enthalpy of combustion (kJ/kg), and mf is the mass of flammable vapor released (kg).

The yield, α, is usually in the range of 1% for unconfined mass releases, to 100% for confined vapor releases [91].

The TNT equivalent mass is calculated as follows [26]:
$mTNT=ηmΔHcETNT$
(A54)
where mTNT is the equivalent mass of TNT (kg), η is the explosion yield factor (1–10%), m is the mass of the explosive (kg), and ETNT is the heat of combustion of TNT (kJ/kg).
##### Peak Overpressure

Several models were previously published to predict the peak overpressure induced by explosions. The TNT equivalence model, the TNO multi-energy model, and the Baker–Strehlow method are the most popular and widely used methods. The TNO multi-energy model and the Baker–Strehlow method are more accurate than the TNT method, and thus, the TNO multi-energy model has been chosen to be used in the overpressure prediction in this work.

###### TNO Multi-Energy Method
TNO multi-energy method developed by Van den Berg [92] defines the peak overpressure and the positive phase duration as a function of the distance to the cloud. A combustion energy scaled distance related to the distance from the center of the explosion can be defined as follows [92]:
$R¯=r(E/pa)1/3$
(A55)
where $R¯$ is the scaled distance from the charge (dimensionless), r is the distance from the to the center of the explosion (m), and E is the explosion energy (J).

Once the scaled distance has been calculated, the scaled overpressure can be obtained from Fig. 24.

Fig. 24
Fig. 24
Close modal
The blast peak side-on overpressure is calculated from the scaled overpressure. This is given by Eq. (A56) [65,92]:
$po=Δp⋅pa$
(A56)
The positive phase duration is given by [65,92]:
$td=t¯d[(E/pa)1/3c0]$
(A57)
where $po$ is the peak overpressure (Pa), Δp is the scaled overpressure (dimensionless), td is the positive-phase duration (s), $td¯$ is the scaled positive-phase duration (dimensionless), and c0 is the ambient speed of sound (m/s) (Fig. 25).
Fig. 25
Fig. 25
Close modal
For most hydrocarbon the total combustion of a stoichiometric hydrocarbon/air mixture can be estimated as follows [93,94]:
$E=3.5Vcloud$
(A58)
where E is the energy of the explosion (mJ) and Vcloud is the volume of the vapor cloud in the congested area (m3).
Consequently, the volume of the vapor cloud in the congested area can be estimated as follows:
$Vcloud=E35$
(A59)
##### Vessel Fragments
Baker et al. [95] developed a technique for predicting initial fragment velocities for spherical or cylindrical vessels bursting into equal fragments. The dimensionless velocity (the y-axis in Fig. 26) is given by:
$νiKa0$
(A60)
where νi is the fragment velocity (length/time), a0 is the speed of sound of the initial gas in the vessel (length/time), and K is a correction factor for unequal mass fragments, as shown in Fig. 26.
Fig. 26
Fig. 26
Close modal
The scaled pressure in Fig. 27 is given by Eq. (A61) [55]:
$P¯=(P−Pa)VMca02$
(A61)
where $P¯$ is the scaled pressure (unitless), P is the bursting pressure of the vessel (force/area), V is the vessel volume (length3), and Mc is the mass of the vessel (mass).
Fig. 27
Fig. 27
Close modal
For an ideal gas, the speed of sound can be determined using Eq. (A62) [55]:
$a0=(TγRgMwt)1/2$
(A62)
where T is the absolute temperature (temperature), γ is the heat capacity ratio of the gas in the vessel (unitless), Rg is the ideal gas constant (pressure—volume/mole deg), and Mwt is the molecular mass of the gas in the vessel (mass/mole).
The data in Fig. 25 can be fitted by the following equation [55]:
$K=1.306×(massfractionofeachfragment)+0.308446$
(A63)
The following equations were proposed by Baum [95] and Birk [96] to predict the distance the projectiles reached from rupture of cylindrical tanks:
$Fortankswithcapacity<5m3:r=90×M0.33$
(A64)
$Fortankswithcapacity>5m3:r=465×M0.1$
(A65)
where M is the mass of material contained in the tank (kg) and is the distance (m).

#### Vulnerability

To estimate the effects of an accident on people and the damage it can cause, the best method is probit analysis. Probit analysis analyzes the relationship between a stimulus (dose) and the quantal response [97,98]. The relationship between the probit variable (Y) and the probability (Pr) is expressed as follows [98,99]:
$Pr=50[1+Y−5|Y−5|erf(|Y−5|2)]$
(A66)
where erf is the error function.
The probit variable, Y, can be calculated using the following expression [98,99]:
$Y=a+blnV$
(A67)
where a and b are constants that are experimentally determined from experimentation with animals, or, in some cases from information on accidents, and V is a measure of intensity of the damaging effect.

Equation (A67) is used to calculate the effects caused by accidents such as fire, explosion, and toxic emissions. Hence, the calculated effect can be converted into percentages using Eq. (A67) or Table 16.

Table 16

Transformation of probit values to percentages of mortality [98,100]

%02468
02.953.253.453.59
103.723.823.924.014.08
204.164.234.294.364.42
304.484.534.594.644.69
404.754.804.854.904.95
505.005.055.105.155.20
605.255.315.365.415.47
705.525.585.645.715.77
805.845.925.996.086.18
906.286.416.556.757.05
997.337.417.467.657.88
%02468
02.953.253.453.59
103.723.823.924.014.08
204.164.234.294.364.42
304.484.534.594.644.69
404.754.804.854.904.95
505.005.055.105.155.20
605.255.315.365.415.47
705.525.585.645.715.77
805.845.925.996.086.18
906.286.416.556.757.05
997.337.417.467.657.88
##### Damage From Fires
The heat radiation emitted by fires can cause different kinds of damage to the human body. Burns of human skin tissue are usually classified as first-, second-, and third-degree burns. Eisenberg et al. [99] developed a probit model that can be used to predict the probability of fatality due to thermal radiation Eq. (A68):
$Y=−36.38+2.56ln(Q4/3t)$
(A68)

The probit equations for nonfatal injury are expressed as follows [38]:

First-degree burns:
$Y=−39.83+3.02ln(Q4/3t)$
(A69)
Second-degree burns:
$Y=−43.14+3.02ln(Q4/3t)$
(A70)

Fire risk assessment requires a relationship between the thermal dose and the effects on people. High thermal radiation caused by fires, such as fireball, may extend a great distance above the ground, making it relatively difficult to avoid and protect against its hazard. Table 17 summarizes the effects of thermal radiation on humans and structures [38,101,102].

Table 17

Heat Flux (kW/m2)Observed effect
35–37.5Sufficient to cause damage to process equipment. Cellulosic material will pilot ignite within one minute’s exposure.
23–25Spontaneous ignition of wood after long exposure. Unprotected steel will reach thermal stress temperatures, which can cause failures. Pressure vessel needs to be relieved or failure will occur.
12.6Thin steel with insulation on the side away from the fire may reach a thermal stress level high enough to cause structural failure. Minimum energy required for piloted ignition of wood and melting of plastic tubing.
9.5Pain threshold reached after 8 s; second-degree burns after 20
4.0Sufficient to cause pain to a person if unable to reach cover within 20 s; however, blistering of the skin (second-degree burns) is likely; 0% lethality.
1.6Will cause no discomfort for long exposure.
Heat Flux (kW/m2)Observed effect
35–37.5Sufficient to cause damage to process equipment. Cellulosic material will pilot ignite within one minute’s exposure.
23–25Spontaneous ignition of wood after long exposure. Unprotected steel will reach thermal stress temperatures, which can cause failures. Pressure vessel needs to be relieved or failure will occur.
12.6Thin steel with insulation on the side away from the fire may reach a thermal stress level high enough to cause structural failure. Minimum energy required for piloted ignition of wood and melting of plastic tubing.
9.5Pain threshold reached after 8 s; second-degree burns after 20
4.0Sufficient to cause pain to a person if unable to reach cover within 20 s; however, blistering of the skin (second-degree burns) is likely; 0% lethality.
1.6Will cause no discomfort for long exposure.
##### Damage From Explosions
###### Effects of Overpressure
The main direct effects of overpressure to humans are eardrum damage, lung damage, injury due to the displacement of the whole body, and injury from shattered glasses [26,38,103]. The probit equation for eardrum rupture is given by Eq. (A71) [26,99,103]:
$Y=−15.6+1.93lnp0$
(A71)
where P0 is the overpressure.
Eisenberg et al. [99] presented a probit equation for estimating mortality due to lung hemorrhage:
$Y=−77.1+6.9lnp0$
(A72)
Fugelso et al. [103] introduced a probit relation for estimation of glass breakage due to explosion:
$Y=−18.1+2.79lnp0$
(A73)
The following probit equation has been proposed to predict the structural damage induced by explosion [26,99]:
$Y=−23.8+2.92lnp0$
(A74)
###### Effects of Fragmentation
The danger distance can be estimated using the following model [104]:
$rd=634(m)1/6$
(A75)
where rd is danger distance (m) and m is the explosive weight (kg).
Kinney and Graham [105] recommended the following formula for estimating the adequate safety distance:
$rs=120mTNT1/3$
(A76)
where rs is the safety distance for preventing missile damage to personnel (90 m minimum).
Van Den Bosch and Weterings [65] suggested two correlations to calculate the probability of fatality from missiles generated by explosion. For fragments between 0.1 kg and 4.5 kg, the probit is related to kinetic energy, such that:
$Y=−17.56+5.3lnS(forfragmentsmass0.1kgto4.5kg)$
(A77)
$Y=−13.196+10.54lnV(forfragmentsmass>4.5kg)$
(A78)
where
$S=12mfV2$
(A79)
mf is mass of the fragment (kg) and V is velocity of the fragment (m/s).

### Appendix B

Table 18

Results of the GC–MS analysis of the waste oil sample

Peak NO.Compound nameMatching (%)FormulaMWt.B.P. (°C)RT (min)Peak areaPeak area (%)HeightHeight (%)A/H
12-Methylheptane93C8H18114.2291163.0381,333,7331.6953,6691.631.4
23-Methylheptane92C8H18114.229118–1203.1021,514,2151.821,069,2281.831.42
33-Hexanone96C6H12O100.159119–1213.21,645,4261.981,670,5822.860.98
42-Hexanone95C6H12O100.159126–1273.2351,900,6782.282,033,3003.490.93
53-Hexanol95C6H14O102.175134–1363.2761,088,1951.311,211,7272.080.9
62-Hexanol96C6H14O102.175137–1383.3122,171,8162.611,917,9673.291.13
71,2-Ethanediol, monoacetate97C4H8O3104.1041823.74811,912,23114.35,429,4159.312.19
82-(2-Hydroxyethoxy)ethyl acetate96C6H12O4148.157231.0 ± 15.06.226981,7441.18701,4121.21.4
91H-Indene, octahydro-2,2,4,4,7,7-hexamethyl-, trans90C15H28208.383239.4 ± 7.08.229589,5280.71362,6000.621.63
108a-Ethyl-1,1,4a,6-tetramethyldecahydronaphthalene86C16H30222.409262.6 ± 7.08.3271,004,4181.21559,4320.961.8
222-Dodecen-1-yl(-)succinic anhydride84C16H26O3266.376348.410.9211,046,2111.26760,1951.31.38
24Heneicosane92C21H44296.574356.1 ± 5.011.1446,552,5767.885,089,5828.721.29
261-Henicosanol85C21H44O312.573366.1 ± 5.011.641,121,4721.351,332,5432.280.84
279-Tricosene, (Z)83C23H46322.611399.4 ± 9.011.723866,4861.04638,4661.091.36
281-Hexacosene83C26H52364.691405.6 ± 8.011.855730,0270.88575,8300.991.27
30Supraene94C30H50410.718458.320715.9452,179,5512.621,623,8532.781.34
Peak NO.Compound nameMatching (%)FormulaMWt.B.P. (°C)RT (min)Peak areaPeak area (%)HeightHeight (%)A/H
12-Methylheptane93C8H18114.2291163.0381,333,7331.6953,6691.631.4
23-Methylheptane92C8H18114.229118–1203.1021,514,2151.821,069,2281.831.42
33-Hexanone96C6H12O100.159119–1213.21,645,4261.981,670,5822.860.98
42-Hexanone95C6H12O100.159126–1273.2351,900,6782.282,033,3003.490.93
53-Hexanol95C6H14O102.175134–1363.2761,088,1951.311,211,7272.080.9
62-Hexanol96C6H14O102.175137–1383.3122,171,8162.611,917,9673.291.13
71,2-Ethanediol, monoacetate97C4H8O3104.1041823.74811,912,23114.35,429,4159.312.19
82-(2-Hydroxyethoxy)ethyl acetate96C6H12O4148.157231.0 ± 15.06.226981,7441.18701,4121.21.4
91H-Indene, octahydro-2,2,4,4,7,7-hexamethyl-, trans90C15H28208.383239.4 ± 7.08.229589,5280.71362,6000.621.63
108a-Ethyl-1,1,4a,6-tetramethyldecahydronaphthalene86C16H30222.409262.6 ± 7.08.3271,004,4181.21559,4320.961.8
222-Dodecen-1-yl(-)succinic anhydride84C16H26O3266.376348.410.9211,046,2111.26760,1951.31.38
24Heneicosane92C21H44296.574356.1 ± 5.011.1446,552,5767.885,089,5828.721.29
261-Henicosanol85C21H44O312.573366.1 ± 5.011.641,121,4721.351,332,5432.280.84
279-Tricosene, (Z)83C23H46322.611399.4 ± 9.011.723866,4861.04638,4661.091.36
281-Hexacosene83C26H52364.691405.6 ± 8.011.855730,0270.88575,8300.991.27
30Supraene94C30H50410.718458.320715.9452,179,5512.621,623,8532.781.34
Table 19

Details of the calculations of the LFL, UFL, and LOC of each component of the waste oil sample and of the mixture

Peak No.Compound nameAreaVap. P. (Psat) mmHg at 25 °C)Upper val. of Vap. P. (Psat) mmHg at 25 °C)Mass fr.XiXi/MWt.Mole Fr. Xi (vol%)Xi*PsatYi (vol%)YiLFL (%)UFL (%)Yi/LFLYi/UFLzLOC (vol%)[z/(1+z)] *100yi*z∑(yi*z)/LOCi
12-Methylheptane1,333,73320.5 ± 0.120.600.016030.00012.603453.62970.07060.18970.905.800.21080.032712.511.2592.592.370.2108
23-Methylheptane1,514,21519.6 ± 0.119.700.018200.00022.955758.22680.07660.20600.907.200.22890.028612.511.2592.592.580.2289
33-Hexanone1,645,42612.1 ± 0.212.300.019780.00023.663045.05460.05930.15941.307.700.12260.02078.511.0589.471.350.1226
42-Hexanone1,900,67811.011.000.022850.00024.231246.54320.06120.16471.208.000.13720.02068.510.2089.471.400.1372
53-Hexanol1,088,1953.4 ± 0.53.900.013080.00012.37479.26130.01220.03281.298.030.02540.0041911.6190.000.290.0254
62-Hexanol2,171,8162.6 ± 0.53.100.026110.00034.739414.69220.01930.05201.298.030.04030.0065911.6190.000.470.0403
71,2-Ethanediol, monoacetate11,912,2310.2 ± 0.81.000.143200.001425.513625.51360.03360.09032.4515.610.03680.00584.511.0381.820.410.0368
82-(2-Hydroxyethoxy)ethyl acetate981,7440.0 ± 1.01.000.011800.00011.47751.47750.00190.00521.6010.200.00330.0005711.2087.500.040.0033
91H-Indene, octahydro-2,2,4,4,7,7-hexamethyl-, trans589,5280.1 ± 0.21.200.007090.00000.63080.75700.00100.00270.523.310.00520.00082211.4495.650.060.0052
108a-Ethyl-1,1, 4a,6-tetramethyldecahydronaphthalene1,004,4180.0 ± 0.30.300.012070.00011.00690.30210.00040.00110.493.100.00220.000323.511.5295.920.030.0022
222-Dodecen-1-yl(-)succinic anhydride1,046,2110.0 ± 0.70.700.012580.00000.87570.61300.00080.00220.543.470.00400.00062111.3495.450.050.0040
24Heneicosane6,552,5760.0 ± 0.40.400.078770.00034.92631.97050.00260.00700.403.600.01740.00193212.8096.970.220.0174
261-Henicosanol1,121,4720.0 ± 1.81.800.013480.00000.80001.44000.00190.00510.362.320.01420.002231.511.3496.920.160.0142
279-Tricosene, (Z)-866,4860.0 ± 0.40.400.010420.00000.59890.23950.00030.00080.332.120.00260.000434.511.3997.180.030.0026
281-Hexacosene730,0270.0 ± 0.40.400.008780.00000.44630.17850.00020.00060.213.320.00300.0002398.1197.500.020.0030
30Supraene2,179,5510.0 ± 0.50.500.026200.00011.18320.59160.00080.00210.271.720.00780.001242.511.4897.700.090.0078
Total83,183,9071.000.0054100.00282.640.37191.001.03170.1524343.582833.7711.551.0317
Average11.4594.46
Peak No.Compound nameAreaVap. P. (Psat) mmHg at 25 °C)Upper val. of Vap. P. (Psat) mmHg at 25 °C)Mass fr.XiXi/MWt.Mole Fr. Xi (vol%)Xi*PsatYi (vol%)YiLFL (%)UFL (%)Yi/LFLYi/UFLzLOC (vol%)[z/(1+z)] *100yi*z∑(yi*z)/LOCi
12-Methylheptane1,333,73320.5 ± 0.120.600.016030.00012.603453.62970.07060.18970.905.800.21080.032712.511.2592.592.370.2108
23-Methylheptane1,514,21519.6 ± 0.119.700.018200.00022.955758.22680.07660.20600.907.200.22890.028612.511.2592.592.580.2289
33-Hexanone1,645,42612.1 ± 0.212.300.019780.00023.663045.05460.05930.15941.307.700.12260.02078.511.0589.471.350.1226
42-Hexanone1,900,67811.011.000.022850.00024.231246.54320.06120.16471.208.000.13720.02068.510.2089.471.400.1372
53-Hexanol1,088,1953.4 ± 0.53.900.013080.00012.37479.26130.01220.03281.298.030.02540.0041911.6190.000.290.0254
62-Hexanol2,171,8162.6 ± 0.53.100.026110.00034.739414.69220.01930.05201.298.030.04030.0065911.6190.000.470.0403
71,2-Ethanediol, monoacetate11,912,2310.2 ± 0.81.000.143200.001425.513625.51360.03360.09032.4515.610.03680.00584.511.0381.820.410.0368
82-(2-Hydroxyethoxy)ethyl acetate981,7440.0 ± 1.01.000.011800.00011.47751.47750.00190.00521.6010.200.00330.0005711.2087.500.040.0033
91H-Indene, octahydro-2,2,4,4,7,7-hexamethyl-, trans589,5280.1 ± 0.21.200.007090.00000.63080.75700.00100.00270.523.310.00520.00082211.4495.650.060.0052
108a-Ethyl-1,1, 4a,6-tetramethyldecahydronaphthalene1,004,4180.0 ± 0.30.300.012070.00011.00690.30210.00040.00110.493.100.00220.000323.511.5295.920.030.0022
222-Dodecen-1-yl(-)succinic anhydride1,046,2110.0 ± 0.70.700.012580.00000.87570.61300.00080.00220.543.470.00400.00062111.3495.450.050.0040
24Heneicosane6,552,5760.0 ± 0.40.400.078770.00034.92631.97050.00260.00700.403.600.01740.00193212.8096.970.220.0174
261-Henicosanol1,121,4720.0 ± 1.81.800.013480.00000.80001.44000.00190.00510.362.320.01420.002231.511.3496.920.160.0142
279-Tricosene, (Z)-866,4860.0 ± 0.40.400.010420.00000.59890.23950.00030.00080.332.120.00260.000434.511.3997.180.030.0026
281-Hexacosene730,0270.0 ± 0.40.400.008780.00000.44630.17850.00020.00060.213.320.00300.0002398.1197.500.020.0030
30Supraene2,179,5510.0 ± 0.50.500.026200.00011.18320.59160.00080.00210.271.720.00780.001242.511.4897.700.090.0078
Total83,183,9071.000.0054100.00282.640.37191.001.03170.1524343.582833.7711.551.0317
Average11.4594.46

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