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Chapter 2

Process Safety

Abstract

Preventing process disasters require constant vigilance. When a plant does not experience a major mishap for a reasonable period, people tend to become complacent. They stop appreciating the importance of safety systems and control measures. This is a major reason for a disaster. The advancement of industry, science, and technology has given rise to new problems. The constant change in the industry demands a continuous change in addressing process safety concerns. Maintaining sustained process safety performance without compromising on plant production is a formidable mission. In lieu of that, the first chapter introduces the readers to the fundamentals of process safety and its common components. It then illustrates current approaches in the industry in addressing process safety problems, along with future challenges and opportunities in the field.

Keywords

Explosion; Fire; QRA; Risk; Safety regulation; Toxic

2.1. Fire

The concept of fire is one which the common person is usually familiar. One might describe a fire as “hot” or “capable of destroying buildings,” but what really is a fire? What needs to be known about fire hazards to prevent incidents? These complex questions highlight a key concept about fire safety: fire is a complicated phenomenon, but to prevent harm to workers and facilities, a fundamental understanding of fire hazards at all scales is required.

Fire, explosions, and toxic releases are considered to be the three most commonly encountered types of hazards that cause severe incidents and loss in process industries. Compared with toxic releases and explosions, fires generally cause less damage but occur more frequently (Coco and Marsh Risk, 2001). However, because a fire often precedes an explosion or toxic release, the damages and loss from fires can have dire consequences. It is, therefore, important to understand the phenomena of fire to properly address the hazards presented by it.

Fire is a specific case of oxidation reaction that involves the rapid reaction of a fuel with an oxidizer. This chemical reaction results in a net release of heat, also known as an exothermic reaction. In a fire, an ignition source supplies energy to these aforementioned combustion reactions initially, and if the excess heat from the oxidation reactions is sufficient to drive the combustion of more material, the flame becomes self-sustaining (Crowl and Louvar, 2011).

Generally speaking, the oxidizing reactions that drive the fire occur in the vapor phase. Therefore, flammable solids and liquid must first heat up and vaporize before fully combusting. For a liquid, this is as simple as heating and evaporating or, in more extreme cases, boiling. For solid flammable materials, it is more complicated and usually first involves thermal degradation, known as pyrolysis, then vaporization and combustion (Drysdale, 2011). Although general information about fires is insightful, further discussion is required to fully understand the behavior and hazards of fire at all scales.

2.1.1. The Fire Triangle

For a fire to occur, three components must be present: fuel, an oxidizer (often oxygen), and a source of ignition, as depicted in Figure 2.1. If any side of the fire triangle is removed, a fire will not form (Crowl and Louvar, 2011). If a flammable material is stored in the presence of oxygen but no ignition source is present, a fire cannot occur. Similarly, if a fuel is heated under an inert gas, a fire will not have oxygen and will not burn. Last, it is simple to see that a fire will not occur if there is no fuel. Regardless of the size of a system, without the three components of the fire triangle, a fire will not take place.

Figure 2.1 The fire triangle (American Institute of Chemical Engineers, Center for Chemical Process Safety, 2003).

While the absence of any side of the fire triangle prevents ignition, the presence of all three components of the fire triangle does not necessarily ensure that a fire will occur. Many factors relating to the three fire triangle component dictate whether a fire will occur, including the amount of each component present in the fire triangle (Crowl and Louvar, 2011). For example, a reduction in the oxygen concentration past a certain point will extinguish liquid flammable fires. The concentration of oxygen in air is an important factor in the existence of a fire.

Similarly, if the heat source used to initially begin combustion is not strong enough, a fire may fail to start. The minimum ignition energy (MIE) for a material is heavily dependent on material type, physical distribution, and the physical conditions, but most hydrocarbons have a MIE in the range of 0.01–2 mJ (Glassman and Yetter, 2008). However, increases in pressure can decrease the MIE, so it is important to account for a reduced ignition energy in pressurized systems (Glassman and Yetter, 2008). These factors play a role in estimation of ignition probability (CCPS, 2014; Moosemiller, 2011), which in turn predicts the chances of a fire as oppose to explosion or vice versa in the case of a flammable release.

The physical phase of a fuel also affects whether it can be ignited. As previously discussed, a flammable vapor mixture does not need to vaporize before catching fire, but solid and liquid must first be vaporized to burn, requiring a higher ignition energy (Crowl and Louvar, 2011). In addition, solids generally go through a thermal decomposition known as pyrolysis to produce a volatile flammable vapor (Drysdale, 2011). Consequently, the energy required to sustain a solid, liquid, or vapor fire varies.

Last, the physical geometry of the flammable fuel affects the chances that a fire will manifest. This is easily visualized when comparing the flame from a match burning top-to-bottom to one that burns from the bottom-to-top. It is clear that the fire triangle is greatly influenced by a large number of complicated factors.

2.1.2. Ignition Phenomena

Fires are initiated by an external heat source but the source can sometimes be silent and discrete. Although some fires can be started by a simple ignition source such as a spark or hot surface, protecting against ignition sources is not the only precaution that must be taken to prevent ignition. Ignition source awareness ensures that the proper precautions can be taken to control ignition sources and prevent an incident in the future.

The autoignition of a flammable mixture occurs when the temperature of the environment is high enough to provide the heat required for combustion. In studying these phenomena, it is useful to define the autoignition temperature for a vapor mixture, which is the minimal temperature at which a flammable mixture can undergo a rapid combustion process without any other ignition source (Crowl and Louvar, 2011). By maintaining a flammable mixture's temperature below its autoignition temperature, the hazard of spontaneous ignition is reduced greatly. Once above this temperature, the flammable mixture can have enough thermal energy to ignite, even without a source of heat.

Another source of ignition that is often overlooked is the auto-oxidization of a flammable liquid. This occurs when a flammable liquid has a high boiling point and is stored without temperature control. The slow oxidation of the material over time causes the temperature of the liquid to increase slowly. In volatile liquids, this heat is released by small amount of vaporization, but in low-volatility liquids, this heat can build up until it is sufficient to ignite vapor above the flammable liquid (Crowl and Louvar, 2011). Temperature controls or other precautions must be taken with similar low-volatility flammable organic liquids to avoid auto-oxidation.

2.1.3. Flammability Limits of Gases and Vapors

Flammable vapors and gases are a major fire hazard and, unlike most solids and liquids, can ignite with very little ignition energy. The ease with which flammable gas and vapor mixtures ignite warrants hazard awareness when handling these materials. However, real-world mixtures of gases and vapors are handled at a range of temperatures, pressures, and compositions, and therefore, understanding how these factors affect flammable gases and vapors is important.

The concentration of flammable vapor plays a key role in whether a fire will occur. If the concentration of a flammable vapor in air is too high, it is said to be too rich to burn. Similarly, if the vapor concentration is too low, it is said to be too lean to burn. These upper and lower concentration bounds of flammability in air are defined as the upper flammability limit (UFL) and lower flammability limit (LFL), respectively (Crowl and Louvar, 2011).

When a mixture of flammable gases is handled, the LFL and UFL of the mixture are different than the LFL and UFL of the separate components. One simple way to calculate LFL and UFL of flammable gas mixtures is to use Le Chatelier's equation, shown in Eqns (2.1) and (2.2) (Chatelier, 1891).

${LFL}_{mix} = \frac{1}{\sum_{i = 1}^{n} \frac{y_{i}}{{LFL}_{i}}}$ ${LFL}_{mix} = \frac{1}{\sum_{i = 1}^{n} \frac{y_{i}}{{LFL}_{i}}}$

(2.1)

where LFL_i is the LFL of chemical species i if it was pure, and LFL_mix is the LFL of the mixture consisting of chemical species i through n.

${UFL}_{mix} = \frac{1}{\sum_{i = 1}^{n} \frac{y_{i}}{{UFL}_{i}}}$ ${UFL}_{mix} = \frac{1}{\sum_{i = 1}^{n} \frac{y_{i}}{{UFL}_{i}}}$

(2.2)

where UFL_i is the UFL of chemical species i if it was pure, and UFL_mix is the UFL of the mixture consisting of chemical species i through n.

It should be noted the Le Chatelier's equation comes with assumptions that are reasonably valid for the LFL and less valid for the UFL. It is assumed that each chemical species has the same heat capacity as if they were pure, that there is a constant number of moles throughout combustion, that kinetics for each chemical species is independent from each other, and the each chemical species has an identical temperature rise under adiabatic conditions (Mashuga and Crowl, 2000).

The LFL and UFL are also dependent on temperature and pressure. Generally speaking, for most hydrocarbons the LFL tends to decrease with increasing temperature, while the UFL tends to increase (Zabetakis et al., 1959). One approximation for the LFL dependency is shown in Eqn (2.3), and another for the UFL in Eqn (2.4).

$LFL (T) = LFL (25 ° C) - \frac{100 C_{p}}{Δ H_{c}} (T - 25)$ $LFL (T) = LFL (25 ° C) - \frac{100 C_{p}}{Δ H_{c}} (T - 25)$

(2.3)

$UFL (T) = UFL (25 ° C) + \frac{100 C_{p}}{Δ H_{c}} (T - 25)$ $UFL (T) = UFL (25 ° C) + \frac{100 C_{p}}{Δ H_{c}} (T - 25)$

(2.4)

where C_p is the specific heat capacity at constant pressure for the flammable material in kcal/mol °C (100 C_p is often approximated at 0.75 kcal/mol °C), T is temperature in degree Celsius, and ΔH_c is the heat of combustion in kcal/mol (Zabetakis et al., 1959).

Pressure effects on the LFL and UFL should also be considered to gain a full understanding of flammability limits. For most materials, the LFL is affected little by pressure changes. The UFL, however, increases with increasing pressure. One approximation of this dependency is shown in Eqn (2.5) (Zabetakis, 1965).

$UFL (P) = UFL (P = 1 atm) + 20.6 (\log (P) + 1)$ $UFL (P) = UFL (P = 1 atm) + 20.6 (\log (P) + 1)$

(2.5)

where P is the absolute pressure measured in MPa.

Another commonly used flammability limit is similar to the LFL and UFL, except instead of measuring the flammability limits in air, the lower oxygen limit (LOL) and upper oxygen limit (UOL) measure the flammability limits of a fuel in oxygen. Similar to the LFL and the UFL, the LOL and UOL are dependent on temperature and pressure. The LOL is usually similar to the LFL of the mixture, and the UOL can be found with relatively good agreement from Eqn (2.6) (Hansen and Crowl, 2010).

$UOL = \frac{UFL [100 - C_{UOL} (100 - {UFL}_{O})]}{{UFL}_{O} + UFL (1 - C_{UOL})}$ $UOL = \frac{UFL [100 - C_{UOL} (100 - {UFL}_{O})]}{{UFL}_{O} + UFL (1 - C_{UOL})}$

(2.6)

where UFL_O is the oxygen concentration at the UFL and C_UOL is a fitting parameter (set to −1.87 by Hansen and Crowl).

One last useful flammability measurement that will be discussed is the limiting oxygen concentration (LOC). An easy way to visualize the LOC is to imagine a flammable gas mixed with air. As oxygen is removed from the flammable mixture, the fire is eventually extinguished at an oxygen concentration defined as the LOC. Similar to the other limits discussed, there are approximations to account for derivations in temperature and pressure of the system. Equation (2.7) summarizes the effects of temperature and pressure on the LOC of a flammable gas mixture (Hansen and Crowl, 2010).

$LOC = (\frac{LFL - C_{LOC} UFL}{1 - C_{LOC}}) (\frac{{UFL}_{O}}{UFL})$ $LOC = (\frac{LFL - C_{LOC} UFL}{1 - C_{LOC}}) (\frac{{UFL}_{O}}{UFL})$

(2.7)

where C_LOC is a fitting constant (experimental results shows that a value of −1.11 is appropriate for most hydrocarbons).

As the length scales of an enclosure decrease, the flammability limits of a flammable mixture are likely to change. As the volume of a flammable mixture decreases, the surface-to-volume ratio increases. As a result, heat loss in micro-scale flames is dominated by convection and conduction rather than by radiant heat (Ju and Maruta, 2011). A commonly reported flammability limit for micro-scale combustion is the quenching diameter, which measures the inner diameter of the enclosure that makes flame propagation within the container impossible. At this diameter, heat transfer to the walls by conductive and convective heat losses is so great that the combustion reactions driving the fire cannot be sustained. One simulation tested an array of flames propagating through channels and showed that a conservative estimate for the quenching diameter (overly small) in micro-channels is about 6 times the expected flame length (Daou and Matalon, 2001; Ju and Xu, 2006). In contrast, the walls of a micro-scale enclosure can also reinforce the flame rather than quench it. Since the enclosure and structures near the flame are smaller at the micro-scale, their thermal inertia is drastically reduced, allowing heat from the flame to transfer to structures as it burns, which in turn allows surrounding structures to reheat the unburned gases (Ju and Maruta, 2011). This enhances the flame and aids in combustion.

2.1.4. Types of Fires

Depending on the conditions present and the materials involved, a fire can manifest itself in many different forms, all with different behavior and specific hazards. The goal of this section is to understand common types of fire aids in identifying potential hazards and ways to mitigate them.

Fire behavior is dependent on a myriad of conditions, including operating temperature, operating pressure, and weather conditions. However, when calculating important fire hazard parameters, two main quantities prove to be the most important. These are the amount of flammable material released and the rate at which it is released. This information can be used to determine other valuable information, such as heat release rates and heat fluxes, which can directly be used when determining expected damages and loss from fires. The mechanism for the release of flammable material is highly dependent on specific process conditions, but common types of fires and the conditions in which they appear are covered in this section.

2.1.4.1. Diffusion fires

Diffusion fires are a subset of fires in which the fuel and oxidizer are physically separated with a region of rapid combustion between them. In this sense, many solid material fires are diffusional in nature with pyrolysis vapor diffusing away from a material surface where it then reacts with oxygen (Drysdale, 2011). More traditional examples of diffusion fires include jet fires, which are a release of flammable material from an orifice into ambient conditions, where it ignites and forms a fire jet.

Jet fires

Jet fires occur when a pressurized flammable material is released from an opening to a lower pressure exterior. Jet fires can be further categorized as either laminar or turbulent. The transition between these two types of fire is categorized by a dimensionless quantity called the Reynolds number, shown in Eqn (2.8).

$R e = \frac{ρ v D}{μ} = \frac{inertial effects}{viscous effects}$ $R e = \frac{ρ v D}{μ} = \frac{inertial effects}{viscous effects}$

(2.8)

where Re is the Reynolds number, ρ is the density of the fluid exiting the orifice, v is the velocity of fluid flow out of the orifice, D is the characteristic length of the orifice, and μ is the viscosity of the fluid exiting the orifice.

The dimensionless Reynolds number makes it simple and unambiguous to classify jet flames, regardless of scale. Laminar jet fires have Reynolds numbers less than 2000 at the orifice opening, while turbulent jet fires occur at substantially higher Reynolds numbers (Hottel and Hawthorne, 1949). These flammable jets have been shown experimentally to have a flame height dependency on the square root of the volumetric flow rate. However, because these fires usually occur at low Froude numbers, buoyant factors play a large role in flame behavior (Jost, 1939). Therefore, different materials have the potential to have noticeably different laminar jet flames.

At the micro-scale, most jet flames are classified as laminar because of their low Reynolds numbers. However, as the scale of jet flames decrease to the micro-scale, new complications arise. Mixing becomes increasingly poor and dominated by diffusion, which can lead to flame instabilities and complicated transient behavior (Miesse et al., 2005). Additionally, the smaller size of a jet flame means a greater surface area to volume ratio and an increased amount of heat loss, making micro jet flame behavior deviate from conventional laminar jet flames even more.

The second set of jet fire, turbulent jet fires, occurs at Reynolds numbers much greater than 2000 (Hottel and Hawthorne, 1949). As the velocity of the fuel increases, the flame begins to break up at the end (opposite of the fuel release). As the velocity increases further, this point of flame breakup gets closer and closer to the nozzle but never reaches it (Hottel and Hawthorne, 1949).

Interestingly, the efficiency of fuel burning is also increased in turbulent jet fires. High turbulence correlates to less soot formation and less heat loss in the fire overall, creating a flame that burns more completely and at higher temperatures (Delichatsios and Orloff, 1988). The flame height dependencies differ between turbulent and laminar jet fires. Instead of being related to volumetric flow rate, the height of turbulent jet fires is linearly dependent on the release orifice (Kanury, 1975).

Another important hazard parameter to calculate is the mass flow rate of flammable material during a jet fire. Since this value will affect burning rates and incident severities, determining the amount of flammable material release during a jet flame is important. Analytical and semianalytical models have been derived in the past for the release of pressurized fluids through orifices by analyzing the transport phenomena taking place. One such model is derived from a momentum balance around the orifice and relates the mass loss rate to general process conditions and material properties (American Institute of Chemical Engineers. Center for Chemical Process Safety. 2003). This model, shown in Eqn (2.9), assumes adiabatic expansion, which seems reasonable because the flammable gas is released and expands very quickly.

$M = C_{d} ρ_{a} A_{h} \sqrt{\frac{2 P_{p}}{ρ_{p}} (\frac{k}{k - 1}) [1 - {(\frac{P_{a}}{P_{p}})}^{\frac{k - 1}{k}}]}$ $M = C_{d} ρ_{a} A_{h} \sqrt{\frac{2 P_{p}}{ρ_{p}} (\frac{k}{k - 1}) [1 - {(\frac{P_{a}}{P_{p}})}^{\frac{k - 1}{k}}]}$

(2.9)

where M is the mass flow rate, C_d is the coefficient of discharge (0.85 typically for gas release), A_h is the area of the discharge opening, ρ_a is the density of the ambient air, ρ_p is the density of the process flammable fluid under pressure (the fluid that will be released), P_a is the ambient pressure, P_p is the pressure of the flammable process fluid under pressure, and k is the isentropic expansion factor defined in Eqn (2.10) as

$P v^{k} = c$ $P v^{k} = c$

(2.10)

where P is the pressure of the flammable fluid, v is the specific volume of the flammable fluid, k is the isentropic expansion factor, and c is a constant.

However, there exists a specific situation where a maximum mass release is achieved and increasing the process pressure of the fluid or reducing the ambient pressure does not increase the mass release rate further. When the maximum release rate is achieved, it is called choked flow. Finding the maximum mass flow rate with respect to downstream pressure yields the criteria for choked flow shown in Eqn (2.11).

${(\frac{P_{a}}{P_{p}})}_{choked} = {(\frac{2}{k + 1})}^{k / (k - 1)}$ ${(\frac{P_{a}}{P_{p}})}_{choked} = {(\frac{2}{k + 1})}^{k / (k - 1)}$

(2.11)

When choked flow condition is achieved, Eqn (2.9) is simplified and expressed as Eqn (2.12) and is no longer dependent on ambient conditions.

$M_{max} = C_{d} A_{h} \sqrt{P_{p} ρ_{p} k {(\frac{2}{k + 1})}^{(k + 1) / (k - 1)}}$ $M_{max} = C_{d} A_{h} \sqrt{P_{p} ρ_{p} k {(\frac{2}{k + 1})}^{(k + 1) / (k - 1)}}$

(2.12)

where M_max is the choked release rate.

After the release rate of the jet fire is established, the heat release rate is calculated simply by multiplying the mass flow rate by the heat of combustion for the flammable fluid. This heat release rate assumes complete combustion making it a conservative estimate. If the ambient air is relatively stationary and fairly laminar, the flame length can be calculated by Eqn (2.13) (Beyler, 2002).

$L = 0.2 {\dot{Q}}^{\frac{2}{5}}$ $L = 0.2 {\dot{Q}}^{\frac{2}{5}}$

(2.13)

where

\dot{Q}

$\dot{Q}$

is the heat release rate, and L is the flame length.

As ambient turbulence increases, the flame length become affected more and this model fails to provide useful results. It should also be noted that if the path of the jet flame is obstructed, it can greatly change the size and shape of the flame.

Natural fires

Natural fires are a type of diffusional flame in which natural organics make up a fuel bed and are heated to the point of pyrolysis by an external heat source. Similar to other solid flammables, these pyrolysis compounds are vaporized and transported toward the combustion region of a fire where they are burned (Drysdale, 2011). In this sense, the solid fuel is separated from the air until it burns, classifying it as a diffusional flame.

A typical natural fire has a flame height related to its diameter. Natural fires with small diameter are tall, while very large-diameter fires have significantly shorter flames and regions of material that is not on fire at all (Heskestad, 1991). A tall bonfire compared with a low, sprawling forest fire shows how this dependency works in the real world. This is explained experimentally by a reduction in the dimensionless heat release rate for increased flame diameters. For very large-diameter fires, the dimensionless heat released (introduced later in the section “Pool fires”) is significantly less than with smaller-diameter fires.

Many natural fires have three distinct regions as described originally by McCaffery (1979). The region just above the burning material where combustion occurs is termed the persistent flame. Just above the material, a rich flammable pyrolysis vapor moves into the combustion region where the fire burns with a relatively constant intensity. As the reacting combustion products move up, they enter a new region of the fire called the intermittent flame. Here, flame flickering occurs and the presence of a flame can change from moment to moment. This flickering is caused by the formation of eddies at the fire–ambient interface. The contents of the fire move up, while the surrounding air remains stationary, causing disturbances in the surface of the flame that manifest as eddies and flame flickering. As the fire eddies move up, they move through the flame and eventually past the top of the visible flame front in a process known as eddy shedding. Above the visible fire is a region termed the buoyant plume. The buoyant plume is a mixture of entrained ambient air and heated combustion products that moves up. The heated combustion products are less dense than the surrounding air so buoyant forces cause them to rise. The buoyant plume also widens out and cools as it rises and interacts with the cooler ambient conditions (Drysdale, 2011).

Pool fires

Another class of diffusional flame is the pool fire. As the name implies, a pool fire occurs when a pool of material forms and produces enough vapor to create an ignitable fuel source above the pool. Pool fires are generally a liquid, although gas and solid pool fires (such as a dense pool of gas or a solid polymer burning) also exist. Like some other types of diffusional flames, pool fires have three distinct regions: the fuel-rich core, the intermediate zone, and the downstream plume (Bouhafid et al., 1898). These three regions are similar to the regions discussed in other natural diffusion fires.

The fuel-rich core lies directly above the burning material surface and contains vaporized flammable materials. The boundaries of this region are formed by the air-entrained eddies above in the intermediate zone. This region contains a relatively small amount of combustion because the vapor is so rich (Smith and Cox, 1992). As the flammable vapor moves away from the material surface, it enters the intermediate zone where combustion is rapid. The movement of the flame up entrains cool, oxygen-rich air that fuels the fire as it moves upwards. Soot and products from incomplete combustion can be formed here as well. It is in this intermittent zone of a pool fire where the majority of heat is generated (Smith and Cox, 1992).

As the heated combustion products and vortices continue to rise, they exit the visible region of the flame and continue through to the downstream plume, which contains heated combustion products mixing with ambient air. As expected, this downstream plume broadens and cools as it rises from the fire. As the temperature drops, the kinetics of the combustion reactions slow exponentially and the formation of combustion products stops (Smith and Cox, 1992).

If the burning rate of the pool fire is assumed to be relatively constant (steady state), a simple approximation can be used to determine the steady-state diameter of the pool fire resulting from a given leak rate given in Eqn (2.14) (Spouge, 1999).

$D_{s s} = {(\frac{4 {\dot{V}}_{Leak} ρ}{π {\dot{m}}^{″}})}^{0.5}$ $D_{s s} = {(\frac{4 {\dot{V}}_{Leak} ρ}{π {\dot{m}}^{″}})}^{0.5}$

(2.14)

where D_ss is the steady-state diameter of the pool fire,

{\dot{V}}_{Leak}

${\dot{V}}_{Leak}$

is the volumetric flow rate, ρ is the density of the fuel, and

{\dot{m}}^{″}

${\dot{m}}^{″}$

is the constant mass burning rate (Spouge, 1999).

Heskestad proposed a simple model for the height for a pool fire dependent on the heat released by the fire and the diameter of the pool fire (Heskestad, 1981, 1983). However, it should be noted that this model represented in Eqn (2.15) is a simplification of pool fire phenomena and does not directly take into account many possible factors such as the vapor flow rate away from the burning material to the combustion region, effects of gravity, and time-dependent transient effects of the pool fire to name a few.

$H = 0.23 {\dot{Q}}^{2 / 5} - 1.02 D$ $H = 0.23 {\dot{Q}}^{2 / 5} - 1.02 D$

(2.15)

where D is the pool fire diameter, and the heat release rate,

\dot{Q}

$\dot{Q}$

, can be written for a simplified pool fire as Eqn (2.16).

$\dot{Q} = \dot{m} Δ H_{c} = \dot{m} ″ A Δ H_{c}$ $\dot{Q} = \dot{m} Δ H_{c} = \dot{m} ″ A Δ H_{c}$

(2.16)

where

\dot{m}

$\dot{m}$

is the mass loss rate for the pool fire,

{\dot{m}}^{″}

${\dot{m}}^{″}$

is the mass loss flux for the pool fire, and A is the area (American Institute of Chemical Engineers, Center for Chemical Process Safety, 2003). The fundamental heat, mass, and momentum transport make actual pool fire behavior very complicated, so resorting to dimensionless analysis is useful for pool fire analysis. Furthermore, the use of dimensionless variables allows fires at any scale to be comparable using the same measureable quantities. An important dimensionless parameter in the study of pool fire behavior is the dimensionless Froude number shown in Eqn (2.17).

$F r = \frac{v^{2}}{g D} = \frac{inertial effects}{bouyant effects}$ $F r = \frac{v^{2}}{g D} = \frac{inertial effects}{bouyant effects}$

(2.17)

where Fr is the Froude number, v is the fluid velocity, g is gravity, and D is the characteristic length of the pool fire (the diameter).

The Froude number is useful in establishing whether buoyant effects from the heated combustion products or the velocity of the rising gases dominate the fluid behavior of the flame.

The models derived by Orloff and Ris show that the pool fire can move laterally back and forth over the boundaries of the burning fuel, but the amount of lateral movement at the base of the fire is dependent on the Froude number. At low values of Fr, the boundary of the fire is able to move farther laterally than at higher Fr values (Orloff and Ris, 1982, 1983). With high Fr numbers, it seems the relatively high gas velocity up prevents the flame from deviating laterally compared with lower relative gas velocities associated with more rapid burning. Numerous studies have been conducted to determine the source of the pulsing behavior of diffusional flames with some progress; however, the true source of the instability of pool fires is still debated (Hertzberg, Cashdollar et al., 1978; Buckmaster and Peters, 1986; Bejan, 1991). Another dimensionless variable that appears to be useful in pulsating pool fires is the Strouhal number, shown in Eqn (2.18).

$S t = \frac{f D}{v}$ $S t = \frac{f D}{v}$

(2.18)

where St is the Strouhal number, f is the frequency of eddie shedding, D is the characteristic length, and v is the fluid velocity.

The Strouhal number contains information about the frequency of oscillations within the fluid flow. Substantial research has been done to correlate the Strouhal number and Froude number with relatively good results. Hamins showed that the relation between the Froude and Strouhal numbers as shown in Eqn (2.19) was valid for various flames (Hamins et al., 1992).

$S t \propto F r^{- 0.38}$ $S t \propto F r^{- 0.38}$

(2.19)

In addition to how a pool fire behaves, understanding the pool fires dimensions is important to fully understand the hazards they present. To first define the size of a fire, it is necessary to define the fire boundary. It is common to represent a fire as the region that emits visible light, but for turbulent flames with pulsating regions, this representation can become difficult. One way to combat this is to use a length measurement in which 50% of the flame would occur above that level and 50% of the flame would occur below that level. Using a dimensionless version of this flame length and a dimensionless heat release quantity, defined in Eqns (2.20) and (2.21), Heskestad developed a correlation for flame height as shown in Eqn (2.22) that fits experimental data closely (Heskestad, 1983; Zukoski et al., 1984).

$N = {(\frac{r C_{p} T_{0}}{H_{c}})}^{3} {\dot{Q}}_{D}^{2}$ $N = {(\frac{r C_{p} T_{0}}{H_{c}})}^{3} {\dot{Q}}_{D}^{2}$

(2.20)

where N is a dimensionless parameter, r is the mass based stoichiometric air-to-fuel ratio, C_p is the heat capacity of ambient air, T₀ is the ambient air temperature, H_c is the fuel heat of combustion, and

{\dot{Q}}_{D}

${\dot{Q}}_{D}$

is dimensionless heat released as defined in Eqn (2.21) (Heskestad, 1983).

${\dot{Q}}_{D} = \frac{\dot{Q}}{ρ_{0} C_{p} T_{0} {(g D^{5})}^{0.5}}$ ${\dot{Q}}_{D} = \frac{\dot{Q}}{ρ_{0} C_{p} T_{0} {(g D^{5})}^{0.5}}$

(2.21)

where

\dot{Q}

$\dot{Q}$

is the heat release rate of the fire, ρ₀ is the density of the ambient air, g is the acceleration due to gravity, and D is the characteristic length of the fire (Heskestad, 1983).

$\frac{Z_{f}}{D} = - 1.02 + 15.6 N^{1 / 5}$ $\frac{Z_{f}}{D} = - 1.02 + 15.6 N^{1 / 5}$

(2.22)

where Z_f is the flame height, and D is pool diameter.

Although Heskestad's correlation seems to fit the majority of data very well, acetylene (C₂H₂) data do not match Eqn (2.22) nearly as well as other mixtures (Hamins et al., 1992). Because acetylene burning forms a significant amount of soot, length scales could be redefined within the fire to more closely fit Eqn (2.22) (Delichatsios et al., 1992). Therefore, caution should be used when applying Heskestad's correlation to sooty flammable mixtures.

The key hazard from pool fires is the heat produced. Heat in a pool fire can have three ultimate destinations. First, heat can be transferred from the buoyant flame and plume to the adjacent ambient air. Second, heat can be transferred from the flame to the fuel source. Third, heat can be transferred across open spaces via radiation (Hamins et al., 1995).

The heat transferred from the buoyant plume to the surrounding ambient air is calculated through a simple energy balance and shown in Eqn (2.23).

$Q_{ambient} = v_{p} A_{p} ρ_{p} C_{p} Δ T$ $Q_{ambient} = v_{p} A_{p} ρ_{p} C_{p} Δ T$

(2.23)

where Q_ambient is the heat transferred to the ambient air, v_p is the velocity of the bouyant plume, A_p is the average area of the plume, ρ_p is the average density of the plume, C_p is the specific heat of the plume, and ΔT is the change in temperature of the plume from the hottest point of the plume to its coldest.

This equation is derived from a simple energy balance in which it is assumed that all the heat required to change in temperature of the buoyant plume is transferred to the ambient air with no energy losses or entropic considerations, so it is an approximate calculation (Hamins et al., 1995).

Aside from heating the ambient air, a fire can also radiate heat over open space to heat other objects. Radiant heating is especially hazardous because it acts in all directions, unlike conductive and convective heating that are limited in this sense. A series of studies with heptane measured the radiant heat released by using a series of radiometers to obtain vertical and radial heat flux profiles. These profiles were then used to estimate radiant heat from a fire. The results show that the fraction of heat released as radiant energy in a heptane pool fire is significant and varies depending on the diameter of the pool fire. Under 2 m, the fraction of radiant heat is relatively constant, but as the diameter grows above 2 m, the fraction of radiant heat drops. The cause for this drop at 2 m is attributed to the soot formation within the fire. Cleaner burning fuels do not exhibit a drop in radiant heat as they grow because soot particles in the flame do not block radiant heat. However, as the size of a heptane pool fire increases, a lack of available oxygen causes incomplete combustion and the formation of soot that blocks radiant heat (Hamins et al., 1995). This is similar to how standing in the shade on a hot day blocks heat from the sun. These data show that fires that form soot and carbonaceous particles are more likely to be colder than nonsooty counterparts.

A more direct way of determining the radiant heat released from a fire to an object is to use Eqn (2.24) (Shokri and Beyler, 1989). Equation (2.24) requires only two parameters to calculate the heat flux and provides a relatively straightforward method for determining radiant energies.

$q ″ = E F_{12}$ $q ″ = E F_{12}$

(2.24)

where

q ″

$q ″$

is the radiant heat flux, F₁₂ is the dimensionless view factor for the radiant energy, and E is the total emissive energy flux from the fire given in Eqn (2.25) as

$E = 58 (10^{- 0.00823 D})$ $E = 58 (10^{- 0.00823 D})$

(2.25)

where D is the diameter of the fire.

The view factor is a complicated parameter that essentially determines the fraction of radiant energy from a fire that reaches a target. Fortunately, previous algebraic analysis of these systems has yielded plots to obtain the view factor easily. Primarily, the view factor is dependent on the ratio of flame height to radius, distance from the center of the fire to the object, and the height of the target object (to be heated by a fire). A series of plots for various combinations of these parameters is found in Guidelines for Fire Protection in Chemical, Petrochemical, and Hydrocarbon Processing Facilities (American Institute of Chemical Engineers, Center for Chemical Process Safety, 2003). Once the maximum emissive heat released from the fire is calculated assuming complete combustion of all flammable material, this can be multiplied by the view factor for the specific scenario to find the heat flux on an object.

Aside from heat transfer from the plume to the ambient air and radiant heating from the fire to surrounding objects, the third destination for heat from a fire is to the fuel. When a fire burns, heat is transferred back toward the flame in a process called feedback. Feedback causes increased fuel vaporization, which in turn increases the burning rate and, thus, increases fuel vaporization further. A general expression for the heat transferred to the fuel can be written as Eqn (2.26), although it is of limited use because the heat lost

({\dot{Q}}_{lost})

$({\dot{Q}}_{lost})$

and heat associated with setting up a thermal boundary layer

({\dot{Q}}_{liquid})

$({\dot{Q}}_{liquid})$

are complex (Hamins et al., 1995).

${\dot{Q}}_{fuel} = \dot{m} H_{g} + {\dot{Q}}_{lost} + {\dot{Q}}_{liquid}$ ${\dot{Q}}_{fuel} = \dot{m} H_{g} + {\dot{Q}}_{lost} + {\dot{Q}}_{liquid}$

(2.26)

where

{\dot{Q}}_{fuel}

${\dot{Q}}_{fuel}$

is the heat transferred to the fuel,

\dot{m}

$\dot{m}$

is the mass loss rate, H_g is the heat of gasification,

{\dot{Q}}_{lost}

${\dot{Q}}_{lost}$

is the heat lost to the surroundings, and

{\dot{Q}}_{liquid}

${\dot{Q}}_{liquid}$

is the heat associated with heating the liquid in the pool fire and establishing a boundary layer.

Without further detailed knowledge of the heat transfer in the fuel, it is difficult to calculate the rate of vaporization and thus the rate of burning in a pool fire. Empirical relations from literature suggest that mass flux is directly related to the B number of the material as shown in Eqn (2.27).

$B = \frac{Δ H_{c}}{Δ H_{g}}$ $B = \frac{Δ H_{c}}{Δ H_{g}}$

(2.27)

where B is the B number, ΔH_c is the heat of combustion, and ΔH_g is the heat required to gasify a material.

The wind effects of pool fires have been empirically observed and used to develop a model for the angle of flame and the dimensionless wind velocity. When the wind impinges on a fire, the vertical axis of the flame will tilt and rotate an angle θ around the base of the fire in the direction of the wind velocity. This correlation is outlined in Eqns (2.28) through (2.30) (Society of Fire Protection Engineers, 2002):

$c o s θ = 1 for u^{*} \leq 1$ $c o s θ = 1 for u^{*} \leq 1$

(2.28)

$c o s θ = \frac{1}{\sqrt{u^{*}}} for u^{*} > 1$ $c o s θ = \frac{1}{\sqrt{u^{*}}} for u^{*} > 1$

(2.29)

where θ is the angle of the flame due to the wind, and u^∗ is the dimensionless wind velocity given in Eqn (2.30) as:

$u^{*} = \frac{u_{w}}{{(g {\dot{m}}^{″} D / ρ_{v})}^{1 / 3}}$ $u^{*} = \frac{u_{w}}{{(g {\dot{m}}^{″} D / ρ_{v})}^{1 / 3}}$

(2.30)

where D if effective fire diameter, u_w is the wind speed measured at a height of 1.6 m, g is the acceleration due to gravity,

{\dot{m}}^{″}

${\dot{m}}^{″}$

is the mass burning rate, D is the pool fire diameter, and ρ_v is the vapor density of the flammable vapor at the boiling point (Society of Fire Protection Engineers, 2002).

Fireballs

Another form of fire that is generally classified as a diffusion flame is that of a fireball. A fireball occurs when there is a sudden loss of containment, resulting in the release of a vapor of liquid that immediately ignites (American Institute of Chemical Engineers, Center for Chemical Process Safety, 2003). It is essentially a region of highly flammable material that almost instantaneously comes into contact with the surrounding air and then catches fire. A boiling liquid expanding vapor explosion (BLEVE) is a type of fireball in which a contained liquid boils, building pressure and eventually rupturing the vessel, immediately releasing all of its contents and igniting.

Studies have been done to determine the behavior of fireballs including research done by Spouge to determine correlations for fireball diameter. Equation (2.31) shows how the diameter of a fireball varies with the amount of flammable material instantaneously released (Spouge, 1999).

$D = 5.8 M^{0.333}$ $D = 5.8 M^{0.333}$

(2.31)

where D is the fireball dimension in meters, and M is the mass of flammable material in kilograms.

Furthermore, the duration of burning has also been studied. The results from this are presented as Eqns (2.32) and (2.33), which form a piecewise expression for the time of burning based on the mass of flammable material released (Spouge, 1999).

$t = 0.45 M^{0.333} for M < 37,000 kg$ $t = 0.45 M^{0.333} for M < 37,000 kg$

(2.32)

$t = 2.6 M^{0.167} for M > 37,000 kg$ $t = 2.6 M^{0.167} for M > 37,000 kg$

(2.33)

where t is amount of time a fireball will burn for in seconds, and M is the mass of released flammable material in kilogram.

A study on the fraction of radiated heat was conducted, and Eqn (2.34) shows the empirical relation that is dependent on the vapor pressure of the fuel (Roberts, 1982).

$χ_{r} = 0.27 P^{0.32}$ $χ_{r} = 0.27 P^{0.32}$

(2.34)

where χ_r is the fraction of heat released in the form of radiant energy, and P is the vapor pressure of the fluid when failure occurs in MPa absolute. Equation (2.34) was derived from empirical data below vapor pressure. In this range, the data fit the correlation well, but the validity of the results above this pressure is questionable.

2.1.4.2. Premixed fires

In addition to diffusional fires, another class of fires exists, called premixed fires. As the name suggests, a premixed fire is a fire in which a mixture of flammable vapor and air is mixed prior to being ignited. This differs from diffusion fires, which require the fuel and oxidizer to be physically separate until combined in the combustion region. Further, premixed flames can be classified as either a deflagration or a detonation, the latter being a premixed flame with a burning velocity equal to or greater than the speed of sound (Drysdale, 2011).

A common example of a premixed flame is that of a Bunsen burner. Air and flammable gas is mixed and directed toward the nozzle of the burner, where it is combusted. Before the gas burns, it is preheated in a region just before entering the combustion region where the majority of burning takes place. Last, the fuel moves past the combustion region to the post flame region where hot gases cool as they move farther from the flame front. The temperature and concentration profile of the three regions associated with the flame front are shown in Figure 2.2 and are present in all premixed flames (Lewis and von Elbe, 1987).

In the case of the Bunsen burner, the burning velocity of the fire is fixed by the flow rate at which the flammable gas mixture is fed into the combustion region. However, freely propagating premixed flames can also occur. If the effects of heat loss are ignored for the burning of a premixed flame, transport equations can easily be solved for this system to give Eqn (2.35), the burning velocity for a freely propagating premixed flame (Kanury, 1975). Equation (2.35) is an approximation and does not reflect the flammability limits experimentally seen with premixed flames due to the assumption that the energy loss from combustion is negligible.

Figure 2.2 The preheat region, combustion region, and post flame region in a premixed flame (Drysdale, 2011).

$S = {(\frac{2 k}{ρ_{0}^{2} c_{p}^{2} (T_{f} - T_{0})} {\dot{Q}}_{ave}^{'^{″}})}^{0.5}$ $S = {(\frac{2 k}{ρ_{0}^{2} c_{p}^{2} (T_{f} - T_{0})} {\dot{Q}}_{ave}^{'^{″}})}^{0.5}$

(2.35)

where S is the burning velocity, k is the ambient thermal conductivity, ρ₀ is the ambient density, c_p is the specific heat of the ambient, T_f is the final temperature of the combustion products, T₀ is the initial temperature of flammable gas, and

{\dot{Q}}_{ave}^{'^{″}}

${\dot{Q}}_{ave}^{'^{″}}$

is the average heat release rate in the reaction zone.

To make matters more complicated, the burning velocity is dependent on composition. Generally, the highest burning velocity with relation to composition occurs when the fuel concentration of a flammable mixture is marginally above the stoichiometric ratio. As the concentration deviates in either direction, the burning velocity will decrease (Lewis and von Elbe, 1987).

The burning velocity is also dependent on pressure effects and turbulent effects; however, these phenomena are not well understood and require significantly more research to understand. The scale of premixed flames can also dictate their behavior. At the micro-scale, thermal feedback is significantly more pronounced. To elaborate, because the enclosure and structures near the flame are smaller at the micro-scale, their thermal inertia is drastically reduced, allowing heat from the flame to transfer to structures as it burns, which in turn allows surrounding structures to reheat the unburned gases (Ju and Maruta, 2011). This enhances the flame and aids in combustion. In contrast, micro-scale combustion also causes a higher amount of radicals to be lost to the surrounding because a small volume of material is burning, but a relatively large surface area is available for radical loss. Similarly, this large surface area-to-volume ratio makes heat loses to conduction and convection dominant over radiant heat loses (Ju and Maruta, 2011).

Flash fires

A flash fire is a release of flammable vapor (or liquid that vaporizes) that premixes with air and expands, eventually igniting. Once ignition occurs, the burning velocity travels from the point of ignition toward the release point, potentially igniting the source as well. Since this ignites the entire volume of the vapor mixture, the volume of the flame is large and the majority of damage is due to flame impingement (American Institute of Chemical Engineers, Center for Chemical Process Safety. 2003). Large-scale flash fires are particularly dangerous as they can cover a large area and, once ignited, occur quickly and have the potentially to ignite the flammable release source. When premixed flammable mixtures are confined to smaller scales, flash fires may become more violent, and even escalate to an explosion.

2.1.5. Fire Risk Analysis

A fire risk analysis (FRA) is a tool that helps determine the overall risk for damages from fire hazards in a process. An FRA is not necessary for all processes, but for cases where there are numerous fire hazards or hazards that may be missed, an FRA can help greatly (Society of Fire Protection Engineers, 2002).

The general methodology of an FRA contains numerous steps. To truly determine the risk of fire at a plant, information about the process must first be collected. Although process information can be difficult to obtain for new or developing plants, obtaining a rough picture of process operations is needed to conduct the FRA (Society of Fire Protection Engineers, 2002). Once information on the process has been collected, hazard identification can begin. This process should be systematic and draw from the previously collected process information. Other methods for general hazard identification have already been developed and can be used for FRA, such as HAZID (hazard identification), HAZOP (hazard and operability study), checklists, and what-if scenario checklists (Society of Fire Protection Engineers, 2002).

After a list of potential fire hazards has been developed, they need to be further analyzed using another tool called a fire hazard analysis (FHA). An FHA takes previously discovered hazards and determines the severity and outcome of an incident. If the hazard was a jet flame, the FHA would calculate the outcome (property, production, injury, or loss) of the expected jet flame. This analysis does not necessarily need to be conducted for every hazard identified, and it should in fact focus more on hazards that seem to be more severe or problematic (Society of Fire Protection Engineers, 2002). After the possible outcomes of the identified fire hazards are determined, the likelihood of these incidents is found. If the outcomes from the FHA are shown to be severe enough, a likelihood analysis might not be necessary. For instance, if an expected outcome involves multiple deaths or injuries, it might be decided that no matter how low the likelihood of the event, the outcome is not acceptable. In that case, a consequence-based decision-making process would be useful (Society of Fire Protection Engineers, 2002).

If it is decided that a likelihood analysis is necessary, the frequency of each outcome from the FHA must be determined. This is done using fault trees, logic gates, and other probability-based calculations. These types of calculations require intimate knowledge about how equipment works together within the process and the modes of failure for these devices (Society of Fire Protection Engineers, 2002). This makes fault trees and logic trees very useful for the likelihood analysis of a process.

After the frequency of the expected outcomes is determined, the overall risk for the process can be found. This calculation is straightforward and shown in Eqn (2.36).

$Risk = \sum_{i = 1}^{n} f_{i} E_{i}$ $Risk = \sum_{i = 1}^{n} f_{i} E_{i}$

(2.36)

where f_i is the frequency of a specific incident, and E_i is the expected loss due to that specific incident.

Risk is defined as the overall expected outcome of incidents, taking into account all of possible incidents and their likelihoods. For each outcome found in the FHA, the expected loss (in dollars, injuries, or deaths) is multiplied by the frequency. This is done for every outcome from the FHA and then the values are summed to give the expected outcome for the process. This is the expected loss due to the process based on likelihood analysis and the outcome analysis (Society of Fire Protection Engineers, 2002).

By this point, all the information from the FRA has been condensed into a number, the total expected outcome for the process, known as the risk, but this is useless without some type of reference for risk. In some cases, this threshold risk is determined by the government and in other cases it simply depends on risk preference of the company or decision-making body involved. If the calculated risk is higher than the acceptable risk, changes must be made to reduce the severity or likelihood of incidents from occurring (Society of Fire Protection Engineers, 2002).

One common method for setting a tolerable risk level is simply called “as low as reasonably practicable” (ALARP). In this method, it must be shown that all reasonable measures to reduce risk have been taken, and doing any more is not feasible (either financially or technically). A second method is a simple cost–benefit analysis. If mitigation of hazards does not substantially help lower the risk or if reducing the risk is too expensive, it would not be necessary according to this method (Society of Fire Protection Engineers, 2002).

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Table of Contents for 2.1. Fire

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Abstract

Keywords

2.1. Fire

2.1.1. The Fire Triangle

2.1.2. Ignition Phenomena

2.1.3. Flammability Limits of Gases and Vapors

2.1.4. Types of Fires

2.1.4.1. Diffusion fires

Jet fires

Natural fires

Pool fires

Fireballs

2.1.4.2. Premixed fires

Flash fires

2.1.5. Fire Risk Analysis

Table of Contents for
2.1. Fire