Liquids

The flash point temperature is the primary flammability parameter used to characterize the fire and explosion hazard of liquids.

Several different experimental methods are used to determine flash points, each of which produces a somewhat different value. The two most commonly used methods are open cup and closed cup, depending on the physical configuration of the experimental equipment. The open-cup flash point is typically a few degrees higher than the closed-cup flash point.

One method to determine the flash point temperature is by an open-cup apparatus, like that shown in Figure 6-3. The liquid to be tested is placed in the open cup. The liquid temperature is measured with a thermometer while a Bunsen burner is used to heat the liquid. A small flame is established on the end of a movable wand. During heating, the wand is slowly moved back and forth over the open liquid pool. Eventually a temperature is reached at which the liquid is volatile enough to produce a flammable vapor, and a momentary flashing flame occurs in the open cup. The temperature at which this first occurs is called the flash point temperature. Note that at the flash point temperature, only a momentary flame is expected. A higher temperature, called the fire point temperature, is required to produce a continuous flame.

The problem with the open-cup flash point apparatus is that air movements over the open cup may change the vapor concentrations and increase the experimentally determined flash point. To prevent this interference, most modern flash point methods employ a closed-cup procedure. In this apparatus, a small, manually opened shutter is provided at the top of the cup. The liquid is placed in a preheated cup and allowed to sit for a fixed time period. The shutter is then opened and the liquid is exposed to the flame. Closed-cup methods typically result in lower flash points.

The open-cup method shown in Figure 6-3 is frequently used to obtain an initial estimate of the flash point temperature since the temperature can be increased continuously in one experiment until a flash is obtained. Then, a closed-cup method is used to obtain a more precise value, since multiple trial-and-error runs must be done.

Satyanarayana and Rao showed that the flash point temperatures for pure materials correlate well with the boiling point of the liquid.² They were able to fit the flash point for more than 1200 compounds with an error of less than 1% of the absolute temperature using the equation

²K. Satyanarayana and P. G. Rao. “Improved Equation to Estimate Flash Points of Organic Compounds.” Journal of Hazardous Materials 32 (1992): 81–85.

Tf=a+b(c/Tb)2e−c/Tb(1−e−c/Tb)2(6-1)

where

T_f is the flash point temperature (K),

a, b, and c are constants provided in Table 6-1 (K), and

Table 6-1 Constants Used in Equation 6-1 for Predicting the Flash Point

Source: K. Satyanarayana and P. G. Rao. “Improved Equation to Estimate Flash Points of Organic Compounds.” Journal of Hazardous Materials 32 (1992): 81–85.

T_b is the boiling point temperature of the material (K).

Table 6-1 provides constants for Equation 6-1.

Flash points can be estimated for multicomponent mixtures if only one component is flammable and if the flash point temperature of the pure flammable component is known. In this case, the flash point temperature is estimated by determining the temperature at which the vapor pressure of the flammable component in the mixture is equal to the pure component vapor pressure at its flash point. Experimentally determined flash points are recommended for multicomponent mixtures with more than one flammable component.

Example 6-1

Methanol has a flash point of 54°F, and its vapor pressure at this temperature is 62 mm Hg. What is the flash point of a solution containing 75% methanol and 25% water by weight?

Solution

The mole fractions of each component are needed to apply Raoult’s law. Assuming a basis of 100 kg of solution, we obtain the following:

	Kilograms	Molecular weight	Kg-moles	Mole fraction
Water	25	18	1.39	0.37
Methanol	75	32	2.34	0.63
			3.73	1.00

Raoult’s law is used to compute the partial vapor pressure, P, of the methanol in the vapor, based on the saturation vapor pressure, P^sat:

P=xPsatPsat=p/x=62/0.63=98.4mmHg

Using a graph of the vapor pressure versus temperature, shown in Figure 6-4, the flash point of the solution is 20.5°C (68.9°F).

Gas and Vapor Mixtures

LFLs and UFLs for gas and vapor mixtures are often needed. These mixture limits are computed using Le Châtelier’s equation:³

³H. Le Châtelier. “Estimation of Firedamp by Flammability Limits.” Annals of Mines 8, no. 19 (1891): 388–395.

LFLmix=1Σt−1nyiLFLi(6-2)

where

LFLi is the lower flammable limit for component i (in volume percent) of component i in fuel and air,

y_i is the mole fraction of component i on a combustible basis, and

n is the number of combustible species.

Similarly, for the upper flammability limit,

UFLmix=1Σt−1nyiUFLi(6-3)

where UFLi is the upper flammable limit for component i (in volume percent) of component i in fuel and air.

Le Châtelier’s equation is empirically derived and is not universally applicable. Mashuga and Crowl derived Le Châtelier’s equation using thermodynamics.⁴ The derivation shows that the following assumptions are inherent in this equation:

⁴C. V. Mashuga and D. A. Crowl. “Derivation of Le Châtelier’s Mixing Rule for Flammable Limits.” Process Safety Progress 19, no. 2 (2000): 112–117.

• The product heat capacities are constant.

• The number of moles of gas is constant.

• The combustion kinetics of the pure species is independent and unchanged by the presence of other combustible species.

• The adiabatic temperature rise at the flammability limit is the same for all species.

These assumptions were found to be reasonably valid at the LFL and less so at the UFL.

Proper usage of Le Châtelier’s rule requires flammability limit data at the same temperature and pressure. Also, the flammability data reported in the literature may be from different sources, with wide variability in the data. Combining data from these different sources may cause unsatisfactory results, which may not be obvious to the user.

Flammability Limit Dependence on Temperature

In general, the flammability range increases with temperature.⁵ The following empirically derived equations are available for vapors:

⁵M. G. Zabetakis, S. Lambiris, and G. S. Scott. “Flame Temperatures of Limit Mixtures.” In Seventh Symposium on Combustion (London, UK: Butterworths, 1959), p. 484.

LFLT=LFL25−0.75ΔHc(T−25)(6-4)

LFLT=UFL25+0.75ΔHc(T−25)(6-5)

where

∆H_c is the net positive heat of combustion (kcal/mol), and

T is the temperature (°C).

Equations 6-4 and 6-5 are very approximate and work for only a very limited number of hydrocarbons over a limited temperature range. The 0.75 is equal to 100 C_p, with the heat capacity dominated by nitrogen.

Flammability Limit Dependence on Pressure

Pressure has little effect on the LFL except at very low pressures (less than 50 mm Hg absolute), where flames do not propagate.

The UFL increases significantly as the pressure is increased, broadening the flammability range. An empirical expression for the UFL for vapors as a function of pressure is available:⁶

UFLp=UFL+20.6(logP+1)(6-6)

⁶M. G. Zabetakis. “Fire and Explosion Hazards at Temperature and Pressure Extremes.” AICHE Symp., Vol. 2, Bureau of Mines, Pittsburgh, PA (1965).

where

P is the pressure (megapascals absolute) and

UFL is the upper flammable limit (volume percent fuel plus air at 1 atm).

Estimating Flammability Limits

For some situations, it may be necessary to estimate the flammability limits without experimental data. Flammability limits are easily measured; experimental determination is always recommended.

Jones found that for many hydrocarbon vapors the LFL and the UFL are a function of the stoichiometric concentration (C_st) of fuel:⁷

⁷G. W. Jones. “Inflammation Limits and Their Practical Application in Hazardous Industrial Operations.” Chemical Reviews 22, no. 1 (1938): 1–26.

LFL=0.55Cst(6-7)

UFL=3.50Cst(6-8)

where C_st is volume percent fuel in fuel plus air.

The stoichiometric concentration for most organic compounds is determined using the general combustion reaction

CmHxOy+z O2→mCO2+x2H2O(6-9)

It follows from the stoichiometry that

z=m+x4−y2

where z has units of moles O₂/mole fuel.

Additional stoichiometric and unit changes are required to determine C_st as a function of z:

Cst=moles fuelmoles fuel + moles air×100=1001+(moles airmoles fuel)=1001+(10.21)(moles O2moles fuel)=1001+(z0.21)

Substituting z and applying Equations 6-7 and 6-8 yields

LFL=0.55(100)4.76m+1.19x−2.38y+1(6-10)

UFL=3.50(100)4.76m+1.19x−2.38y+1(6-11)

Another method correlates the flammability limits as a function of the heat of combustion of the fuel.⁸,⁹ A good fit was obtained for 123 organic materials containing carbon, hydrogen, oxygen, nitrogen, and sulfur. The resulting correlations are

⁸T. Suzuki. “Empirical Relationship between Lower Flammability Limits and Standard Enthalpies of Combustion of Organic Compounds.” Fire and Materials 18 (1994): 333–336.

⁹T. Suzuki and K. Koide. “Correlation between Upper Flammability Limits and Thermochemical Properties of Organic Compounds.” Fire and Materials 18 (1994): 393–397.

LFL=−−3.42ΔHc+0.569ΔHc+0.0538ΔHc2+1.80(6-12)

UFL=6.30ΔHc+0.567ΔHc2+23.5(6-13)

where

LFL and UFL are the lower and upper flammable limits (volume percent fuel in air), respectively, and

∆H_c is the positive heat of combustion for the fuel (in 10³ kJ/mol).

Equation 6-13 is applicable only over the UFL range of 4.9–23%. If the heat of combustion is provided in kcal/mol, it can be converted to kJ/mol by multiplying by 4.184.

The prediction capability of Equations 6-6 through 6-13 is only modest at best. For hydrogen, the predictions are poor. For methane and the higher hydrocarbons, the results are improved. Thus, these methods should be used only for a quick initial estimate and should not replace actual experimental data.

Flammability limits, in general, are defined in air. As you will see later, flammable limits in pure oxygen are frequently useful for designing systems to prevent fires and explosions. Combustion in pure oxygen also exhibits a lower oxygen limit (LOL) and an upper oxygen limit (UOL), just like the LFL and UFL in air. These flammability limits have units of percent fuel in oxygen. Table 6-2 presents flammability data for a variety of fuels in pure oxygen. In general, for most common hydrocarbons, the LOL is close to the LFL.

Table 6-2 Flammability Limits in Pure Oxygen

^aThe limits are insensitive to P_H2o above a few mm Hg.

Source: Data from B. Lewis and G. von Elbe. Combustion, Flames, and Explosions of Gases (New York, NY: Harcourt Brace Jovanovich, 1987).

Hansen and Crowl derived an empirical equation for the UOL based on drawing lines along the flammable boundaries.¹⁰ They found that a good estimate of the UOL can be found from

UOL=UFL[100−CUOL(100−UFL0)]UFL0+UFL(1−CUOL)(6-14)

¹⁰Travis J. Hansen and Daniel A. Crowl. “Estimation of the Flammable Zone Boundaries for Flammable Gases.” Process Safety Progress 29 (June 2010): 3.

where

UOL is the upper oxygen limit (volume percent fuel in oxygen),

UFL is the upper flammable limit (volume percent fuel in air),

UFL₀ is the oxygen concentration at the upper flammable limit (volume percent oxygen in air), and

C_UOL is a fitting constant.

This equation requires only UFL data. Hansen and Crowl found a good fit to experimental data with Equation 6-14 for a number of fuels using C_UOL = −1.87.

Limiting Oxygen Concentration (LOC) and Inerting

The LFL is based on fuel in air. However, oxygen is the key oxidizing ingredient and there is a minimum oxygen concentration required to propagate a flame. This is an especially useful result, because explosions and fires can be prevented by reducing the oxygen concentration regardless of the concentration of the fuel. This concept is the basis for a common procedure called inerting (see Chapter 7).

Below the limiting oxygen concentration (LOC), the reaction cannot generate enough energy to heat the entire mixture of gases (including the inert gases) to the extent required for the self-propagation of the flame. The LOC has also been called the minimum oxygen concentration (MOC) and the maximum safe oxygen concentration (MSOC), among other names.

Table 6-3 contains LOC values for a number of materials. The LOC depends on the inert gas species. It has units of percentage of moles of oxygen in total moles. If experimental data are not available, the LOC is estimated using the stoichiometry of the combustion reaction and the LFL. This procedure works for many hydrocarbons.

Table 6-3 Limiting Oxygen Concentrations (LOCs)

Note: LOC is the volume percent oxygen concentration above which combustion can occur.

Source: Data from National Fire Protection Association. NFPA 69, Standard on Explosion Prevention (Quincy, MA: National Fire Protection Association, 2014).

Example 6-6 shows that the LOC can be estimated using the equation

LOC=z(LFL)(6-15)

Equation 6-15 does not produce very good results.

Hansen and Crowl¹¹ found that a better estimate of the LOC is given by

LOC=(LFL−CLOCUFL1−CLOC)(UFL0UFL)(6-16)

¹¹Travis J. Hansen and Daniel A. Crowl. “Estimation of the Flammable Zone Boundaries.” Process Safety Progress 29 (June 2010): 3.

where

LOC is the limiting oxygen concentration (percent oxygen),

LFL is the lower flammable limit (percent fuel in air),

UFL is the upper flammable limit (percent fuel in air),

UFL₀ is the oxygen concentration at the upper flammable limit (volume percent oxygen in air), and

C_LOC is a fitting constant.

Data analysis of numerous experimental values found that C_LOC = –1.11 gave a good fit for many hydrocarbons.

Flammability Diagram

A general way to represent the flammability of a gas or vapor is by the triangle diagram shown in Figure 6-5. Concentrations of fuel, oxygen, and inert material (in volume or mole percent) are plotted on the three axes. Each apex of the triangle represents either 100% fuel, oxygen, or nitrogen. The tick marks on the scales show the direction in which the scale moves across the figure. Thus, point A represents a mixture composed of 60% methane, 20% oxygen, and 20% nitrogen. The zone enclosed by the dashed line represents all mixtures that are flammable. Because point A lies outside the flammable zone, a mixture of this composition is not flammable.

The air line represents all possible combinations of fuel plus air. It extends from the point where fuel is 0%, oxygen is 21%, and nitrogen is 79% to the point where fuel is 100%, oxygen is 0%, and nitrogen is 0%. The equation for this line is

Fuel%=−(10079)×nitrogen%+100(6-17)

The stoichiometric line represents all stoichiometric combinations of fuel plus oxygen. The combustion reaction can be written in the form

Fuel+zO2→combustionproducts(6-18)

where z is the stoichiometric coefficient for oxygen. The intersection of the stoichiometric line with the oxygen axis (in volume percent oxygen) is given by

100(z1+z)(6-19)

Equation 6-19 is derived by realizing that on the oxygen axis, no nitrogen is present. Thus the moles present equals fuel (1 mole) plus oxygen (z moles). The total moles is thus 1 + z, and the mole or volume percent of oxygen is given by Equation 6-15.

The stoichiometric line extends from a point where the fuel is 100/(1 + z), oxygen is 100z/(1 + z), and nitrogen is 0%, to a point where fuel is 0%, oxygen is 0%, and nitrogen is 100%. The equation for the stoichiometric line is

Fuel%=100−Nitrogen%(1+z)(6-20)

The LOC is also shown in Figure 6-5. Clearly, any gas mixture containing oxygen below the LOC is not flammable since the flammability zone does not extend below the LOC.

The shape and size of the flammability zone on a flammability diagram changes with a number of parameters, including fuel type, temperature, pressure, and inert species. Thus, the flammability limits and the LOC also change with these parameters.

Several rules and equations can be developed for working with flammability diagrams. More details on the development of these rules can be found on the website for this textbook. These rules are as follows:

1. If two gas mixtures R and S are combined, the resulting mixture composition lies on a line connecting the points R and S on the flammability diagram. The location of the final mixture on the straight line depends on the relative moles in the mixtures combined: If mixture S has more moles, the final mixture point will lie closer to point S. This is identical to the lever rule used for phase diagrams.

   Figure 6-6 shows this rule and the following equation results:

   xAM−xARxAS−xAM=xCM−xCRxCS−xCM(6-21)

   

2. If a mixture R is continuously diluted with mixture S, the mixture composition follows along the straight line between points R and S on the flammability diagram. As the dilution continues, the mixture composition moves closer and closer to point S. Eventually, at infinite dilution the mixture composition is at point S.

3. For systems having composition points that fall on a straight line passing through an apex corresponding to one pure component, the other two components are present in a fixed ratio along the entire line length.

   Figure 6-7 shows this rule and the following equation results:

   xAxB=x100−x(6-22)

   

4. The LOC can be estimated by reading the oxygen concentration at the intersection of the stoichiometric line and a horizontal line drawn through the LFL. This is equivalent to the equation

LOC=z(LFL)(6−15)

The following equations are used to transform triangle diagram coordinates (t_A, t_c) to rectangular coordinates (x, y):

y=tCsin(60π180)x=1−tA−ycot(60π180)(6-23)

where the sin and cot values in the parentheses are in degrees. These transformations are useful for drawing a triangle diagram using a spreadsheet.

Another interesting feature with triangle diagrams is that the three triangle legs can be any length and the rules still apply. In this case, Equation 6-23 must be modified accordingly.

These rules are useful for tracking the gas composition during a process operation to determine whether a flammable mixture exists during the procedure. For example, consider a storage vessel containing pure methane whose inside walls must be inspected as part of its periodic maintenance procedure. For this operation, the methane must be removed from the vessel and replaced by air for the inspection workers to breathe. The first step in the procedure is to depressurize the vessel to atmospheric pressure. At this point the vessel contains 100% methane, represented by point A in Figure 6-8. If the vessel is opened and air is allowed to enter and mix with the fuel, the composition of gas within the vessel will follow the air line in Figure 6-8 until the vessel gas composition eventually reaches point B, pure air. During this operation, the gas composition passes through the flammability zone. If an ignition source of sufficient strength were present, then a fire or explosion would result.

The procedure is reversed for placing the vessel back into service. In this case, the procedure begins at point B in Figure 6-8, with the vessel containing air. If the vessel is closed and methane is introduced and mixes with the air, then the gas composition inside the vessel will follow the air line and finish at point A. Again, the mixture is flammable as the gas composition moves through the flammability zone.

An inerting procedure can be used to avoid the flammability zone for both cases. This is discussed in more detail in Chapter 7.

The determination of a complete flammability diagram requires several hundred tests using a specific testing apparatus (see Figure 6-15 later in this chapter). Diagrams with experimental data for methane, ethylene, and hydrogen are shown in Figures 6-9, 6-10, and 6-11, respectively. Data in the center region of the flammability zone are not available because the maximum pressure exceeds the pressure rating of the test vessel. For these data, a mixture is considered flammable if the pressure increase after ignition is greater than 7% of the original ambient pressure, in accordance with ASTM E918.¹² Note that many more data points are shown than are required to define the flammability limits. This was done to obtain a more complete understanding of the pressure versus time behavior of the combustion over a wide range of mixtures. This information is important for mitigation of an explosion.

¹²ASTM E918-83, Standard Practice for Determining Limits of Flammability of Chemicals at Elevated Temperature and Pressure (W. Conshocken, PA: ASTM, 2011).

Figure 6-11 is a different geometry from Figures 6-9 and 6-10 but still conveys the same information. Note that the hydrogen axis is diagonal, while the nitrogen and oxygen axes are rectangular. The LFL (about 4% fuel) is still shown as the lower intersection of the flammability zone with the air line, and the UFL (about 75% fuel) is the upper intersection of the flammability zone with the air line. The LOC is the oxygen line that just touches the flammability zone—in this case about 5% oxygen. Some people prefer this form of the triangle diagram since it is easier to plot—the nitrogen and oxygen are the x and y axes, respectively.

A number of important features are shown in Figures 6-9 to 6-11. First, the size of the flammability zone increases from methane to ethylene to hydrogen—the UFL is correspondingly higher. Second, the combustion of the methane and ethylene produces copious amounts of soot in the upper fuel-rich parts of the flammability zone. There is no soot with hydrogen because there is no carbon. Finally, the lower boundary of the flammability zone is mostly horizontal, and the LOL can be approximated by the LFL.

For most flammable materials, detailed experimental data of the type shown in Figures 6-9 to 6-11 are unavailable. Several methods have been developed to approximate the flammability zone:

Method 1 (Figure 6-12): Given the flammability limits in air, the LOC, and flammability limits in pure oxygen, the procedure is as follows:

1. Draw flammability limits in air as points on the air line.

2. Draw flammability limits in pure oxygen as points on the oxygen scale.

3. Use Equation 6-19 to locate the stoichiometric point on the oxygen axis, and draw the stoichiometric line from this point to the 100% nitrogen apex.

4. Locate the LOC on the oxygen axis, and draw a line parallel to the fuel axis until it intersects with the stoichiometric line. Draw a point at this intersection.

5. Connect all the points shown.

The flammability zone derived from this approach is only an approximation of the actual zone. Note that the lines defining the zone limits in Figures 6-9 to 6-11 are not exactly straight. This method also requires flammability limits in pure oxygen—data that are not readily available. Flammability limits in pure oxygen for a number of common hydrocarbons are provided in Table 6-2.

Method 2 (Figure 6-13): Given the flammability limits in air and the LOC, the procedure is as follows: Use steps 1, 3, and 4 from method 1. In this case, only the points at the nose of the flammability zone can be connected. The flammability zone from the air line to the oxygen axis cannot be detailed without additional data, although it extends all the way to the oxygen axis and typically expands in size. The lower boundary can also be approximated by the LFL.

Method 3 (Figure 6-14): Given the flammability limits in air, the procedure is as follows: Use steps 1 and 3 from method 1. Estimate the LOC using Equation 6-15 or 6-16. This is only an estimate, and usually (but not always) provides a conservative LOC.

Autoignition

The autoignition temperature (AIT) of a vapor, sometimes called the spontaneous ignition temperature (SIT), is the temperature at which the vapor ignites spontaneously. The autoignition temperature is a function of the concentration of vapor, volume of vapor, pressure of the system, presence of catalytic material, and flow conditions. It is essential to experimentally determine AITs at conditions as close as possible to process conditions.

Composition affects the AIT; rich or lean mixtures have higher AITs. Larger system volumes, increases in pressure, and increases in oxygen concentration all decrease AITs. This strong dependence on conditions illustrates the importance of exercising caution when using AIT data.

AIT data are provided in Appendix B.

Auto-oxidation

Auto-oxidation is the process of slow oxidation with accompanying evolution of heat, sometimes leading to autoignition if the energy is not removed from the system. Liquids with relatively low volatility are particularly susceptible to this problem. Liquids with high volatility are less susceptible to autoignition because they self-cool as a result of evaporation.

Many fires are initiated as a result of auto-oxidation, which is also referred to as spontaneous combustion. Some examples of auto-oxidation with a potential for spontaneous combustion include oil on a rag in a warm storage area, insulation on a steam pipe saturated with certain polymers, and filter aid saturated with certain polymers. In fact, cases have been recorded where 10-year-old filter aid residues were ignited when the land-filled material was bulldozed and exposed to air, allowing auto-oxidation and eventual autoignition. These examples illustrate why special precautions must be taken to prevent fires that can result from auto-oxidation and autoignition.

Adiabatic Compression

An additional means of ignition is adiabatic compression. For example, gasoline and air in an automobile cylinder will ignite if the vapors are compressed to an adiabatic temperature that exceeds the autoignition temperature. This is the cause of preignition knock in engines that are running too hot and too lean.

Several large accidents have been caused by flammable vapors being sucked into the intake of air compressors, with their subsequent compression resulting in autoignition. A compressor is particularly susceptible to autoignition if it has a fouled after-cooler. Safeguards must be included in the process design to prevent undesirable fires that can result from adiabatic compression.

The adiabatic temperature increase for an ideal gas is computed from the thermodynamic adiabatic compression equation:

Tf=Ti(PfPi)(γ−1)/γ(6-24)

where

T_f is the final absolute temperature,

T_i is the initial absolute temperature,

P_f is the final absolute pressure,

P_i is the initial absolute pressure, and

γ is the heat capacity ratio given by C_p / C_v.

The potential consequences of adiabatic temperature increases within a chemical plant are illustrated in the following two examples.

These examples illustrate the importance of careful design, careful monitoring of conditions, and periodic preventive maintenance programs when working with flammable gases and compressors. This is especially important today, because high-pressure process conditions are becoming more common in modern chemical plants.

Gases/Vapors

The apparatus used to characterize the explosive behavior of gases and vapors is shown in Figure 6-15. This apparatus consists of a spherical pressure vessel with an adequate pressure rating to withstand 252the maximum pressure of the explosion. A vessel volume of 10 to 20 liters is typically used. A high-precision pressure gauge is used to measure the pressure during the gas mixing as well as during the explosion. A temperature gauge measures the temperature since the results are dependent on the temperature. The mixing bar is used to mix the gases. A fuse wire is typically used to ignite the gas, consisting of a 1-cm 40-gauge wire. In most cases, a computer is used to operate the experiment and collect the data.

The experimental procedure is as follows. The apparatus is initially evacuated. Gases are then metered into the vessel through the gas manifold, with the concentrations being controlled by measuring the partial pressure from the pressure gauge. The mixing bar is active during the gas addition. The mixer is then turned off. After a short time delay to let the gas reach equilibrium, the igniter is triggered and the explosion is initiated. The results are highly dependent on gas composition, so it is important to use ultra-high-purity gas sources.

Since a deflagration occurs, the pressure in the vessel is uniform across the volume during the explosion. Measurement of the combustion pressure on the sphere surface provides information on the progress of the explosion.

Two parameters are used to characterize the behavior of gas/vapor explosions: the maximum pressure and the maximum pressure rate. The maximum pressure is indicative of the combustion equilibrium, while the maximum pressure rate is indicative of the flame front’s propagation speed and is representative of the robustness of the explosion. Clearly, higher values for these parameters indicate an increased explosion hazard.

Figure 6-16 shows how these two parameters are determined experimentally from pressure–time data for a single experiment run at a specific concentration. After ignition of the gas/vapor at t = 0, the pressure increases rapidly to a peak value; it then decreases at a much slower rate due to quenching and cooling from the vessel surface. The maximum pressure is easily determined from the peak pressure. The maximum pressure rate is determined from the maximum slope of the pressure time curve. In this case, the maximum pressure is 8.5 bar and the maximum pressure rate is 316 bar/s.

The experiment is repeated at different concentrations, with the maximum pressure and maximum pressure rates being determined at each concentration. The highest maximum pressure and pressure rates do not necessarily occur at the same concentration.

The flammable limits for this fuel are determined from the maximum pressure versus concentration plot shown in Figure 6-17. Usually a criterion of a 7% pressure increase is used to define these limits. For the data shown, the lower flammable limit is 4.9% and the upper limit is 16.2%.

A plot of the logarithm of the maximum pressure slope versus the logarithm of the vessel volume frequently produces a straight line of slope −1/3, as shown in Figure 6-18. This relationship is called the cubic law and is represented by the following equations:

For gases: (dPdt)maxV1/3=constant=KG(6-25)

For dusts: (dPdt)maxV1/3=KSt(6-26)

where K_G and K_St are the deflagration indexes for gas and dust, respectively. The subscript “St” for the dust deflagration index comes from the German word Staub, meaning “dust.”

Figure 6-19 shows how the deflagration index, K_G, varies with composition for methane.

As the robustness of an explosion increases, the deflagration indexes K_G and K_St increase. The cubic law states that the pressure front takes longer to propagate through a larger vessel. P_max and K_G data for vapors are shown in Table 6-6. Table 6-6 shows that good agreement is found between different investigators for the maximum pressure but that only limited agreement is found for the K_G values. K_G values are sensitive to experimental configuration and conditions.

Table 6-6 Maximum Pressures and Deflagration Indexes for a Number of Gases and Vapors

Data sources:

NFPA 68, Venting of Deflagrations (Quincy, MA: National Fire Protection Association, 1997).

NFPA 68, Standard on Explosion Protection (Quincy, MA: National Fire Protection Association, 2018).

W. Bartknecht. Explosions-Schutz: Grundlagen und Anwendung (New York, NY: Springer-Verlag, 1993).

J. A. Senecal and P. A. Beaulieu. “K_G: Data and Analysis.” In 31st Loss Prevention Symposium (New York, NY: American Institute of Chemical Engineers, 1997).

Dusts

The experimental apparatus used to characterize the explosive nature of dusts is shown in Figure 6-20. This device is similar to the vapor explosion apparatus, with the exception of a larger volume—typically 20 L or larger—and the addition of a sample container and a dust distribution ring. The distribution ring ensures proper distribution and mixing of the dust before ignition.

The experimental procedure is as follows. The dust sample is placed in the sample container. The computer system opens the solenoid valve, and the dust is driven by air pressure from the sample container through the distribution ring and into the dust sphere. After a delay of several milliseconds to ensure proper mixing and distribution of the dust, the ignitor is discharged. The computer measures the pressure as a function of time using high- and low-speed pressure transducers. The air used to drive the dust into the sphere is carefully metered to ensure a pressure of 1 atm (1.013 bar) within the sphere at ignition time. A typical pressure versus time plot from the dust explosion apparatus is shown in Figure 6-21.

The data are collected and analyzed in the same fashion as for the vapor explosion apparatus. The maximum pressure and the maximum rate of pressure increase are determined, as well as the flammability limits.

Table 6-7 shows experimental data for dusts. This includes the maximum pressure during combustion, P_max and the deflagration index, K_St, using Equation 6-26. Notice at the top of Table 6-7 that dusts are also classified into four St-classes depending on the value of the deflagration index. The higher the deflagration index, the higher the St-class.

Table 6-7 St-Classes for Dusts and Combustion Data for Dust Clouds

Source: Data selected from R. K. Eckoff. Dust Explosions in the Process Industries (Oxford, UK: Butterworth-Heinemann, 1997). A 2003 edition is also available.

Application of Flammability Data of Gases/Vapors and Dusts

Characterization of the explosive behavior of gases, vapors, and dusts is highly dependent on the apparatus and procedure. The results are not fundamentally based, unlike the case for heat capacity or density. Thus, experimental flammability data should always be obtained at conditions as close as possible to the actual process conditions and those data should be applied using proper engineering judgment.

The explosion characteristics determined using the vapor and dust explosion apparatus are used to operate the process safely, as shown below. Note that these experimental parameters are not an absolute boundary between safe and unsafe operation so suitable safety margins must be applied.

1. The flammable limits are used to determine the safe concentrations for operation or the quantity of inert material required to control the concentration within safe regions.

2. The maximum rate of pressure increase indicates the robustness of an explosion. Thus, the explosive behavior of different materials can be compared on a relative basis. The maximum rate is also used to design a vent for relieving a vessel during an explosion before the pressure ruptures the vessel or to establish the time interval for adding an explosion suppressant (water, carbon dioxide, or other) to stop the combustion process.

Detonation and Deflagration

The damage from an explosion largely depends on whether the explosion results from a detonation or a deflagration. The difference between the two reflects whether the reaction front propagates above or below the speed of sound in the unreacted gases. For ideal gases, the speed of sound or sonic velocity is a function of temperature only and has a value of 344 m/s (1129 ft/s) at 20°C. Fundamentally, the sonic velocity is the speed at which information is transmitted through a gas.

In some combustion reactions, the reaction front is propagated by a strong pressure wave, which compresses the unreacted mixture in front of the reaction front above its autoignition temperature. This compression occurs rapidly, resulting in an abrupt pressure change or shock in front of the reaction front. Such an event is classified as a detonation, and it results in a reaction front and leading shock wave that propagates into the unreacted mixture at or above the sonic velocity of the unreacted gas.

For a deflagration, the energy from the reaction is transferred to the unreacted mixture by heat conduction and molecular diffusion. These processes are relatively slow, causing the reaction front to propagate at a speed less than the sonic velocity in the unreacted gas.

Figure 6-22 shows the physical differences between a detonation and a deflagration for a combustion reaction that occurs in the gas phase in the open. For a detonation, the reaction front moves at a speed greater than the speed of sound. A shock front is found a short distance in front of the reaction front. The reaction front provides the energy for the shock front and continues to drive it at sonic or higher speeds.

For a deflagration, the reaction front propagates at a speed less than the speed of sound. However, the pressure front moves at the speed of sound in the unreacted gas and moves away from the reaction front. One way to conceptualize the resulting pressure front is to consider the reaction front as producing a series of individual pressure fronts. These pressure fronts move away from the reaction front at the speed of sound and accumulate to form the main pressure front. The main pressure front will continue to grow in size as additional energy and pressure fronts are produced by the reaction front.

The pressure fronts produced by detonations and deflagrations are markedly different. A detonation produces a shock front, with an abrupt pressure rise, a maximum pressure of greater than 10 atm, and total duration that is typically less than 1 ms. The pressure front resulting from a deflagration is characteristically wide (many milliseconds in duration), flat (without an abrupt shock front), and with a maximum pressure much lower than the maximum pressure for a detonation (typically 6 to 10 times the initial pressure).

The behaviors of the reaction and pressure fronts differ from those shown in Figure 6-22 depending on the local geometry constraining the fronts. Different behavior occurs if the fronts propagate in a closed vessel, in a pipeline, or through a congested process unit. The gas dynamic behavior for complex geometries is beyond the scope of this text.

A deflagration can also evolve into a detonation—a phenomenon called a deflagration to detonation transition (DDT). This transition is particularly common in pipes but is unlikely to occur in vessels or open spaces. In a piping system, energy from a deflagration can feed forward to the pressure wave, resulting in an increase in the adiabatic pressure rise. The pressure then builds and eventually results in a full detonation.

Confined Explosions

A confined explosion occurs in a confined space, such as a vessel or a building. The two most common confined explosion scenarios involve explosive vapors and explosive dusts. Empirical studies have shown that the nature of the explosion is a function of several experimentally determined characteristics, which depend on the explosive material used. These characteristics include flammability or explosive limits, the rate of pressure rise after the flammable mixture is ignited, and the maximum pressure after ignition. They are determined using two similar laboratory devices, shown in Figures 6-15 and 6-20.

Blast Damage Resulting from Overpressure

The explosion of a dust or gas (either as a deflagration or a detonation) results in a reaction front moving outward from the ignition source preceded by a shock wave or pressure front. After the combustible material is consumed, the reaction front terminates, but the pressure wave continues its outward movement. A blast wave, which is composed of the pressure wave and subsequent wind, causes most of the damage in such an explosion.

Figure 6-23 shows the variation in pressure with time for a typical shock wave at a fixed location some distance from the explosion site. The explosion occurs at time t₀. There exists a small but finite time t₁ before the shock front travels from its explosive origin to the affected location. This time, t₁, is called the arrival time. At t₁, the shock front has arrived and a peak overpressure is observed, immediately followed by a strong transient wind. The pressure quickly decreases to ambient pressure at time t₂, but the wind continues in the same direction for a short time. The time period t₁ to t₂ is called the shock duration. The shock duration is the period of greatest destruction to free-standing structures, so its value is important for estimating damage. The decreasing pressure continues to drop below ambient pressure to a maximum underpressure at time t₃. For most of the underpressure period from t₂ to t₄, the blast wind reverses direction and flows toward the explosive origin. Although the underpressure period is associated with some damage, it is much less than the damage associated with the overpressure period because the maximum underpressure is only a few psi for typical explosions. The underpressure for large explosions and nuclear explosions, however, can be quite large, resulting in considerable damage. After attaining the maximum underpressure at time t₃, the pressure will approach ambient pressure at time t₄. At this time, the blast wind has moved beyond the reference point.

An important consideration is how the pressure is measured as the blast wave passes. If the pressure transducer is at right angles to the blast wave, the overpressure measured is called the side-on overpressure (sometimes called the free-field overpressure). At a fixed location, shown in Figure 6-23, the side-on overpressure increases abruptly to its maximum value (peak side-on overpressure) and then drops off as the blast wave passes. If the pressure transducer is placed facing toward the oncoming shock wave, then the measured pressure is the reflected overpressure. The reflected overpressure includes the side-on overpressure and the stagnation pressure. The stagnation pressure is caused by deceleration of the moving gas as it impacts the pressure transducer. The reflected pressure for low side-on overpressures is about twice the side-on overpressure and can reach as high as eight or more times the side-on overpressure for strong shocks. The reflected overpressure reaches its maximum when the blast wave arrives normal to the wall or object of concern, but decreases as the angle changes from normal. Many references report overpressure data without clearly stating how the overpressure is measured. In general, overpressure implies the side-on overpressure and frequently the peak side-on overpressure.

Blast damage is based on the determination of the peak side-on overpressure resulting from the pressure wave impacting a structure. In general, the damage is also a function of the rate of pressure increase and the duration of the blast wave. Good estimates of blast damage, however, are obtained using just the peak side-on overpressure.

Damage estimates based on overpressures are given in Table 6-9. As illustrated, significant damage is expected for even small overpressures.

Table 6-9 Damage Estimates for Common Structures Based on Overpressure

Note: These values are approximations.

Source: V. J. Clancey. “Diagnostic Features of Explosion Damage,” paper presented at the Sixth International Meeting of Forensic Sciences, Edinburgh, UK, 1972.

Experiments with explosives have demonstrated that the overpressure can be estimated using an equivalent mass of TNT, denoted as m_TNT, and the distance from the ground-zero point of the explosion, denoted as r.²⁰ The empirically derived scaling law is

²⁰W. E. Baker. Explosions in Air (Austin: University of Texas Press, 1973); S. Glasstone. The Effects of Nuclear Weapons (Washington, DC: U.S. Atomic Energy Commission, 1962).

ze=rmTNT1/3(6-27)

The equivalent energy of TNT is 1120 cal/g.

Figure 6-24 provides a correlation for the scaled overpressure p_s versus scaled distance z_e with units of m/kg^1/3. To convert ft/lb^1/3 to m/kg^1/3, multiply by 0.3967. The scaled overpressure p_s is given by

ps=p0pa(6-28)

where

p_s is the scaled overpressure (unitless),

p₀ is the peak side-on overpressure (gauge), and

p_a is the ambient pressure (absolute).

The data in Figure 6-24 are valid only for TNT explosions occurring on a flat surface. For explosions occurring in the open air, well above the ground, the resulting overpressures from Figure 6-24 are multiplied by 0.5. Most explosions occurring in chemical plants are considered to originate on the ground.

The data in Figure 6-24 are represented by the empirical equation

p0pa=1616[1+(ze4.5)2]1+(ze0.048)21+(ze0.32)21+(ze1.35)2(6-29)

The procedure for estimating the overpressure at any distance r resulting from the explosion of a mass of TNT is as follows: (1) use the scaling law and the correlations of Figure 6-24 to estimate the overpressure, and (2) use Table 6-9 to estimate the damage.

TNT Equivalency

TNT equivalency is a simple method for equating a known energy of a combustible fuel to an equivalent mass of TNT. The approach is based on the assumption that an exploding fuel mass behaves like exploding TNT on an equivalent energy basis. The equivalent mass of TNT is estimated using the following equation:

mTNT=ηmΔHcETNT(6-30)

where

m_TNT is the equivalent mass of TNT (mass),

η is the empirical explosion efficiency (unitless),

m is the mass of hydrocarbon (mass),

ΔH_c is the lower heat of combustion of the flammable gas (see Appendix B [energy/mass]), and

E_TNT is the energy of explosion of TNT (energy/mass).

A typical value for the energy of explosion of TNT is 1120 cal/g = 4686 kJ/kg = 2016 Btu/lb

The explosion efficiency is one of the major problems in the equivalency method. The explosion efficiency is used to adjust the estimate for a number of factors, including incomplete mixing with air of the combustible material and incomplete conversion of the thermal energy to mechanical energy. The explosion efficiency is empirical, with most flammable cloud estimates varying between 1% and 10%, as reported by a number of sources. Explosion efficiencies can also be defined for solid materials, such as ammonium nitrate. A frequently used value in such cases is 2%.

The TNT equivalency method also uses an overpressure curve that applies to point-source detonations of TNT. Vapor cloud explosions (VCEs) are explosions that occur because of the release of flammable vapor over a large volume and are most commonly deflagrations. Because the TNT equivalency method is unable to consider the effects of flame speed acceleration resulting from confinement or congestion from process equipment, the overpressure curve for TNT tends to overpredict the overpressure near the VCE and to underpredict it at distances away from the VCE.

A key advantage of the TNT equivalency method is that it is easy to apply because the calculations are simple. The procedure to estimate the damage associated with an explosion using this method is as follows:

1. Determine the total quantity of flammable material involved in the explosion.

2. Estimate the explosion efficiency and calculate the equivalent mass of TNT using Equation 6-30.

3. Use the scaling law given by Equation 6-27 and Figure 6-24 (or Equation 6-29) to estimate the peak side-on overpressure.

4. Use Table 6-9 to estimate the damage for common structures and process equipment.

This procedure can be applied in reverse to estimate the quantity of material involved based on damage estimates.

TNO Multi-Energy Method

The TNO method identifies the confined volumes in a process, assigns a relative degree of confinement or congestion, and then determines the contribution to the overpressure from this confined volume (TNO is an acronym for the Netherlands Organization for Applied Scientific Research). Semi-empirical curves are used to determine the overpressure. The basis for this model is that the energy of explosion depends highly on the level of congestion and depends less on the fuel in the cloud.

The procedure for using the multienergy model for a VCE is as follows:²¹

1. Use a dispersion model to determine the extent of the cloud. In general, this is done by assuming that equipment and buildings are not present, because of the limitations of dispersion modeling in congested areas.

2. Conduct a field inspection to identify the congested areas. In most cases, heavy vapors tend to move downhill.

3. Identify potential sources of strong blasts within the area covered by the flammable cloud. Potential sources of strong blasts include congested areas and buildings, such as process equipment in chemical plants or refineries, stacks of crates or pallets, and pipe racks; spaces between extended parallel planes (e.g., those beneath closely parked cars in parking lots, as well as open buildings such as multistory parking garages); spaces within tube-like structures (e.g., tunnels, bridges, corridors, sewage systems, and culverts); and an intensely turbulent fuel–air mixture in a jet resulting from release at high pressure. The remaining fuel–air mixture in the flammable cloud is assumed to produce a blast of minor strength.

4. Estimate the energy of equivalent fuel–air charges by (a) considering each blast source separately; (b) assuming that the full quantities of fuel–air mixture present within the partially confined/obstructed areas and jets, identified as blast sources in the cloud, contribute to the blasts; (c) estimating the volumes of fuel–air mixture present in the individual areas identified as blast sources (this estimate can be based on the overall dimensions of the areas and jets; note that the flammable mixture may not fill an entire blast source volume and that the volume of equipment should be considered where it represents an appreciable proportion of the whole volume); and (d) calculating the combustion energy E (in joules) for each blast by multiplying the individual volumes of the mixture by 3.5 × 10⁶ J/m³ (this value is typical for the heat of combustion of an average stoichiometric hydrocarbon–air mixture).

5. Assign a number representative of the blast strength for each individual blast. Some companies have defined procedures for this; however, many risk analysts use their own judgment.

   A safe and most conservative estimate of the strength of the sources of a strong blast can be made if a maximum strength of 10—representative of a detonation—is assumed. However, a source strength of 7 seems to more accurately represent actual experience. Furthermore, for side-on overpressures less than approximately 0.5 bar, no differences appear for source strengths ranging from 7 to 10.

   The blast resulting from the remaining unconfined and unobstructed parts of a cloud can be modeled by assuming a low initial strength. For extended and quiescent parts, assume a minimum strength of 1. For more nonquiescent parts, which are in low-intensity turbulent motion (for instance, because of the momentum of a fuel release), assume a strength of 3.

6. Once the energy quantities E and the initial blast strengths of the individual equivalent fuel–air charges are estimated, the Sachs-scaled blast side-on overpressure and positive-phase duration at some distance R from a blast source is read from the blast charts in Figure 6-25 after calculation of the Sachs-scaled distance:

R¯=R(E/Po)1/3(6-31)

²¹Guidelines for Evaluating the Characteristics of Vapor Cloud Explosions, Flash Fires, and BLEVEs (New York, NY: American Institute of Chemical Engineers, 1994).

where

R¯ is the Sachs-scaled distance from the charge (dimensionless),

R is the distance from the charge (m),

E is the charge combustion energy (J), and

P_o is the ambient pressure (Pa).

The blast peak side-on overpressure and positive-phase duration are calculated from the Sachs-scaled overpressure and the Sachs-scaled positive-phase duration. The overpressure is given by

p0=ΔP¯s•pa(6-32)

and the positive-phase duration is given by

td=t¯d[(E/Pa)1/3co](6-33)

where

Po is the side-on blast overpressure (Pa),

ΔP¯s is the Sachs-scaled side-on blast overpressure (dimensionless),

p_a is the ambient pressure (Pa),

t_d is the positive-phase duration (s),

t¯d is the Sachs-scaled positive-phase duration (dimensionless),

E is the charge combustion energy (J), and

c_o is the ambient speed of sound (m/s).

If separate blast sources are located close to one another, they may be initiated almost simultaneously, and the respective blasts should be added together. The most conservative approach to this issue is to assume a maximum initial blast strength of 10 and to sum the combustion energy from each source in question. Further definition of this important issue (for instance, the determination of a minimum distance between potential blast sources so that their individual blasts can be considered separately) is a factor in present research.

The major problem with the application of the TNO multienergy method is that the user must decide on the selection of a severity factor, based on the degree of confinement or congestion. Little guidance is available for partial confinement geometries. Furthermore, it is not clear how the results from each blast strength should be combined.

Another popular method to estimate overpressures is the Baker–Strehlow–Tang method. This method is based on a flame speed, which is selected depending on three factors: (1) the reactivity of the released material, (2) the flame expansion characteristics of the process unit (which relates to confinement and spatial configuration), and (3) the obstacle density within the process unit. A set of semi-empirical curves is used to determine the overpressure. A complete description of the procedure is provided by Baker et al.²²

²²Q. A. Baker, C. M. Doolittle, G. A. Fitzgerald, and M. J. Tang. “Recent Developments in the Baker– Strehlow VCE Analysis Methodology.” Process Safety Progress 17, no. 4 (1998): 297.

The TNO multienergy and Baker–Strehlow–Tang methods are essentially equivalent, although the TNO method tends to predict a higher pressure in the near field and the Baker–Strehlow method tends to predict a higher pressure in the far field. The confinement and congestion are better defined in the Baker–Strehlow–Tang method than in the TNO method. Both methods require more information and detailed calculations than the TNT equivalency method. In particular, both require identifying regions of high confinement or congestion in the process area.

Energy of Chemical Explosions

The blast wave resulting from a chemical explosion is generated by the rapid expansion of gases at the explosion site. This expansion can be caused by two mechanisms: (1) thermal heating of the reaction products and (2) the change in the total number of moles by reaction.

For most hydrocarbon combustion explosions in air, the change in the number of moles is small. For example, consider the combustion of propane in air. The stoichiometric equation is

C3H8+5O2+18.8N2→3CO2+4H2O+18.8N2

The initial number of moles on the left-hand side is 24.8, and the number of moles on the right-hand side is 25.8. In this case. only a small pressure increase is expected as a result of the change in the number of moles, and almost all the blast energy is due to thermal energy release.

The energy released during an explosion is computed using standard thermodynamics. Typically, the heat of combustion is used, but the reaction energy can be easily computed using standard heats of formation. Heat of combustion data are provided in Appendix B. In most cases, the lower heat of combustion is used, where the water product is in the vapor phase, not liquid. Since an explosion occurs within a few milliseconds, the explosive energy is released long before the water vapor can condense into liquid.

The released explosion energy is equal to the work required to expand the gases. Crowl reasoned that this expansion work is a form of mechanical energy.²³ The thermodynamic availability is a state function used to determine the maximum mechanical energy extractable from a material as it moves into equilibrium with its surroundings. Sussman showed that the thermodynamic availability for a reacting system can be computed using the standard Gibbs energy of formation.²⁴ Crowl then concluded that the energy of explosion for a material exploding at room temperature and pressure is equal to the standard Gibbs energy of formation. Crowl also showed how the energy of explosion could be determined for materials exploding at different gas compositions and nonambient temperatures and pressures. However, these adjustments are normally small.

²³D. A. Crowl. “Calculating the Energy of Explosion Using Thermodynamic Availability.” Journal of Loss Prevention in the Process Industries 5, no. 2 (1992): 109–118.

²⁴M. V. Sussman. Availability (Exergy) Analysis (Lexington, MA: Mulliken House, 1981).

Example 6-12

Consider the explosion of a propane–air vapor cloud confined beneath a storage tank. The tank is supported 1 m off the ground by concrete piles. The concentration of vapor in the cloud is assumed to be at stoichiometric concentrations. Assume a cloud volume of 2094 m³, confined below the tank, representing the volume underneath the tank. Determine the overpressure from this vapor cloud explosion at a distance of 100 m from the blast using the TNO multienergy method.

Solution

The heat of combustion of a stoichiometric hydrocarbon–air mixture is approximately 3.5 MJ/m³, and by multiplying by the confined volume, the resulting total energy is (2094 m³)(3.5 MJ/m³) = 7329 MJ. To apply the TNO multienergy method, a blast strength of 7 is chosen. The Sachs-scaled energy is determined using Equation 6-26. The result is

R¯=R(E/Po)1/3=100 m[(7329×106 J)/(101,325 Pa)]1/3=2.4

The curve labeled 7 in Figure 6-26 is used to determine the scaled overpressure value of about 0.13. The resulting side-on overpressure is determined from Equation 6-30:

p0=ΔP¯s⋅pa=(0.13)(101.3 kPa) =13.2 kPa=1.9 psi.

From Table 6-9, it appears that this explosion will result in distortion of steel frame buildings and is almost strong enough to result in partial collapse of walls and roofs of houses.

Energy of Mechanical Explosions

For mechanical explosions, a reaction does not occur and the energy is obtained from the energy content of the contained substance. If this energy is released rapidly, an explosion may result. Examples of this type of explosion are the sudden failure of a tire full of compressed air and the sudden catastrophic rupture of a compressed gas tank.

Four methods are used to estimate the energy of explosion for a pressurized gas: Brode’s equation, isentropic expansion, isothermal expansion, and thermodynamic availability. Brode’s method²⁵ is perhaps the simplest approach. It determines the energy required to raise the pressure of the gas at constant volume from atmospheric pressure to the gas pressure in the vessel. The resulting expression is

²⁵H. L. Brode. “Blast Waves from a Spherical Charge.” Physics of Fluids 2 (1959): 17.

E =(P2−P1)Vγ−1(6-34)

where

E is the energy of explosion (energy),

P₁ is the ambient pressure (force/area),

P₂ is the burst pressure of the vessel (force/area),

V is the volume of expanding gas in the vessel (volume), and

γ is the heat capacity ratio for the gas (unitless).

Because P₂ > P₁, the energy calculated from Equation 6-34 is positive, indicating that the energy is released to the surroundings during the vessel rupture.

The isentropic expansion method assumes that the gas expands isentropically from its initial to final state. The following equation represents this case:

E=(P2Vγ−1)[1−(P1P2)(γ−1)/γ](6-35)

The isothermal expansion case assumes that the gas expands isothermally. This is represented by the following equation:

E=nRgT1ln(P2P1)= P2Vln(P2P1)(6-36)

where

n is the number of moles of gas (moles),

R_g is the ideal gas constant, and

T₁ is the ambient temperature (degrees).

The final method uses thermodynamic availability to estimate the energy of explosion. Thermodynamic availability represents the maximum mechanical energy extractable from a material as it comes into equilibrium with the environment. The resulting overpressure from an explosion is a form of mechanical energy. Thus, thermodynamic availability predicts a maximum upper bound to the mechanical energy available to produce an overpressure.

An analysis by Crowl using batch thermodynamic availability resulted in the following expression to predict the maximum explosion energy of a gas contained within a vessel:²⁶

²⁶D. A. Crowl. “Calculating the Energy of Explosion Using Thermodynamic Availability.” Journal of Loss Prevention in the Process Industries 5, no. 2 (1992): 109–118.

E=P2V[ln(P2P1)−(1−P1P2)](6-37)

Note that Equation 6-37 is nearly the same as Equation 6-36 for an isothermal expansion, with the addition of a correction term. This correction term accounts for the energy lost as a result of the second law of thermodynamics.

The question arises as to which method to use. Figure 6-26 presents the energy of explosion using all four methods as a function of initial gas burst pressure of the vessel. The calculation assumes an inert gas initially at 298 K with γ=1.4. The gas expands into ambient air at 1 atm pressure. The isentropic method produces a low value for the energy of explosion. The isentropic expansion results in a gas at a very low temperature; the expansion of an ideal gas from 200 psia to 14.7 psia results in a final temperature of 254°R, or -254^°F This is thermodynamically inconsistent because the final temperature is ambient. The isothermal expansion method predicts a large value for the energy of explosion because it assumes that all the energy of compression is available to perform work. In reality, some of the energy must be expelled as waste heat, according to the second law of thermodynamics. The thermodynamic availability method accounts for this loss through the correction term in Equation 6-37. All four methods continue to be used to estimate the energy of explosion for compressed gases.

It is thought that Brode’s equation more closely predicts the potential explosion energy close to the explosion source (near field), and that the isentropic expansion method predicts better the effects at a greater distance (far field). However, it is unclear where this transition occurs. Also, a portion of the potential explosion energy of vessel burst is converted into kinetic energy of the vessel pieces and other inefficiencies (such as strain energy in the form of heat in the vessel fragments).

Missile Damage

An explosion occurring in a confined vessel or structure can rupture the vessel or structure, resulting in the projection of debris over a wide area. This debris (also called missiles) can cause appreciable injury to people and damage to structures and process equipment. Moreover, such missiles can be projected to large distances from the explosion, causing additional remote damage.

Missiles are frequently a means by which an accident propagates throughout a plant facility. For example, a localized explosion in one part of the plant may project debris throughout the plant. This debris strikes storage tanks, process equipment, and pipelines, resulting in secondary fires or explosions. This chain of damage is called the “domino effect” for explosions.

Clancey developed an empirical relationship between the mass of explosive and the maximum horizontal range of the fragments,²⁷ as illustrated in Figure 6-27. This relationship is useful during accident investigations for calculating the energy level required to project fragments over an observed distance.

²⁷V. J. Clancey. “Diagnostic Features of Explosion Damage,” paper presented at the Sixth International Meeting of Forensic Sciences, Edinburgh, UK, 1972.

Blast Damage to People

People can be injured by explosions from direct blast effects (including overpressure and thermal radiation) or indirect blast effects (mostly missile damage). Blast damage effects are estimated using probit analysis, as discussed in Section 2-6.

Vapor Cloud Explosions (VCE)

The most dangerous and destructive explosions in the chemical process industries are VCEs. These explosions occur as the following sequence of events:

1. Sudden release of a large quantity of flammable vapor (typically this occurs when a vessel, containing a superheated and pressurized liquid, ruptures)

2. Dispersion of the vapor throughout the plant site while mixing with air

3. Ignition of the resulting vapor cloud

The accident at Flixborough, England, is a classic example of a VCE. The sudden failure of a 20-inch cyclohexane line between reactors led to almost instantaneous vaporization of an estimated 30 tons of cyclohexane. The vapor cloud dispersed throughout the plant site, mixed with air, and was ignited by an unknown source 45 seconds after the release. The entire plant site was leveled and 28 people were killed.

A summary of 29 international VCEs over the period 1974–1986 shows property losses for each event of between $5,000,000 and $100,000,000 and 140 fatalities (an average of almost 13 per year).²⁸ Any process containing quantities of liquefied gases, volatile superheated liquid, or high-pressure gases is considered a good candidate for a VCE.

²⁸Richard W. Prugh. “Evaluation of Unconfined Vapor Cloud Explosion Hazards.” In International Conference on Vapor Cloud Modeling (New York, NY: American Institute of Chemical Engineers, 1987), p. 713.

VCEs are difficult to characterize, primarily because of the large number of parameters needed to describe an event. Some of the parameters that affect VCE behavior are quantity of material released, fraction of material vaporized, probability of ignition of the cloud, distance traveled by the cloud before ignition, time delay before ignition of cloud, probability of explosion rather than fire, existence of a threshold quantity of material, efficiency of explosion, and location of ignition source with respect to release.²⁹ Accidents occur under uncontrolled circumstances, and data collected from real events are difficult to quantify and compare.

²⁹Sam Mannan, ed. Lees’ Loss Prevention in the Process Industries, 3rd ed. (Amsterdam, Netherlands: Elsevier, 2005), p. 17/134.

Qualitative studies³⁰ have shown that (1) the ignition probability increases as the size of the vapor cloud increases; (2) vapor cloud fires are more common than explosions; (3) the explosion efficiency is usually small (approximately 2% of the combustion energy is converted into a blast wave); and (4) turbulent mixing of vapor and air and ignition of the cloud at a point remote from the release increases the impact of the explosion.³¹ Congestion due to process equipment or confinement is also an important issue.

³⁰Sam Mannan, ed. Lees’ Loss Prevention in the Process Industries, 3rd ed. (Amsterdam, Netherlands: Elsevier, 2005), p. 17/140.

³¹Richard W. Prugh. “Evaluation of Unconfined Vapor Cloud Explosion Hazards.” In International Conference on Vapor Cloud Modeling (New York, NY: American Institute of Chemical Engineers, 1987), p. 714.

From a safety standpoint, the best approach is to prevent the release of material. A large cloud of combustible material is hazardous and almost impossible to control, despite any safety systems installed to prevent ignition. Methods that are used to prevent VCEs include keeping low inventories of volatile and flammable materials, using process conditions that minimize flashing if a vessel or pipeline is ruptured, using analyzers to detect leaks at low concentrations, and installing automated block valves to shut systems down while the spill or release is in the incipient stage of development.

Boiling-Liquid Expanding-Vapor Explosions³²

³²Sam Mannan, ed. Lees’ Loss Prevention in the Process Industries, 3rd ed. (Amsterdam, Netherlands: Elsevier, 2005), p. 17/167; Frank Bodurtha. Industrial Explosion Prevention and Protection (New York, NY: McGraw- Hill, 1980), p. 99.

A boiling-liquid expanding-vapor explosion (BLEVE, pronounced ble’-vee) is a special type of accident that can explosively release large quantities of materials. It occurs when a tank containing a liquid held above its atmospheric pressure boiling point ruptures, resulting in the explosive vaporization of a large fraction of the tank contents. If the materials are flammable, a VCE might result; if they are toxic, a large area might be subjected to toxic materials. In either situation, the energy released by the BLEVE process itself can result in considerable damage.

BLEVEs are caused by the sudden failure of the container as a result of any cause. The most common type of BLEVE is caused by external fire. The steps resulting in this type of event are as follows:

1. A fire develops external and adjacent to a tank containing a liquid.

2. The fire heats the walls of the tank.

3. The tank walls below liquid level are cooled by the liquid, increasing the liquid temperature and the pressure in the tank.

4. If the flames reach the tank walls or roof where there is only vapor and no liquid to remove the heat, the tank metal temperature rises until the tank loses it structural strength.

5. The tank ruptures, explosively vaporizing its contents.

It is likely that the vessel will fail at a pressure below the design pressure of the vessel due to the weakening of the vessel walls due to the thermal heating. It is also likely that the vessel will fail below the set pressure of any pressure protection systems on the vessel.

If the liquid is flammable and a fire is the cause of the BLEVE, the liquid will ignite as the tank ruptures. Often, the boiling and burning liquid behaves as a rocket fuel, propelling vessel parts for great distances. When a BLEVE occurs in a vessel, only a fraction of the liquid vaporizes; the amount depends on the physical and thermodynamic conditions of the vessel contents. The fraction vaporized is estimated using the methods discussed in Section 4-7.