A deflagration is the most common mode of flame propagation in accidental gas explosions. It is defined as an explosion where the combustion wave propagates at subsonic velocities relative to the unburned gas immediately ahead of the flame (which itself is set in motion by the expanding combustion products). In the deflagrative mode the flame speed ranges from a few m/s up to 500-1000 m/s. The explosion pressure will range from a few mbar to several bar, depending on the flame speed.

The flame speed and explosion pressure will strongly depend on the gas cloud and the geometrical conditions within the cloud (i.e. process equipment, piping etc.) or geometries confining the cloud (i.e. buildings etc.). To predict the flame speed and explosion pressure for a deflagration is not a simple task, even if scenario parameters such as cloud size, fuel concentration and ignition point are known. The phenomenon of flame acceleration is a mathematically stiff problem, i.e. the result is very sensitive to variation of specific parameters.

The objectives of this chapter are:

• To describe the deflagration wave and its different combustion regimes.
• To describe the importance of venting and flame acceleration due to repeated obstacles.
• To describe some important findings from CMR experiments.
• To provide the basic fundamental understanding of deflagrations, so the information in Chapters 7 to 9 is accessible.
  
  

5.1 Deflagration Waves and Explosion Pressure

We have already defined a deflagration wave as a gas explosion where the flame front propagates at subsonic speed relative to the unburned gas immediately ahead of the wave. In a gas explosion the propagating velocity can span more than three orders of magnitude. The mechanism of flame propagation will be quite different in the different velocity regimes.

When the cloud is ignited by a weak ignition source (i.e. a spark or a hot surface) the flame starts as a laminar flame. For a laminar flame the basic mechanism of propagation is molecular diffusion of heat and mass. The laminar flame structure is illustrated in Figure 5.1. This diffusion process of heat and mass into the unburned gas is relatively slow and the laminar flame will propagate with a velocity of the order of 3-4 m/s.

The propagation velocity of the laminar flame depends on the type of fuel and the fuel concentration. Figure 5.2 shows the laminar burning velocity (i.e. flame front velocity relative to the unburned mixture just ahead of the flame) for methane-, ethylene- and hydrogen-air. Methane has a maximum burning velocity of about 0.4 m/s. Maximum laminar burning velocities of 0.4-0.5 m/s are typical for hydrocarbons. Ethylene, acetylene and hydrogen have higher burning velocities due to fast chemical kinetics and high molecular diffusivity. Due to variations in apparatus and measurement techniques different sources will state different values for laminar burning velocity.

In most accidental explosions the laminar flame will accelerate and transit into a turbulent deflagration (i.e. turbulent flame), since the flow field ahead of the flame front becomes turbulent. The turbulence is caused by the interaction of the flow field with process equipment, piping, structures etc. The mechanisms generating turbulence ahead of the flame front will be discussed further in section 5.2 "Flame Acceleration in a Channel Due to Repeated Obstacles". Here we will discuss how turbulence influences the structure of the front and thereby enhances the burning rate.

One of the mechanisms causing the increased burning rate in turbulent deflagrations is the wrinkling of the flame front by large turbulent eddies. Figure 5.3 shows a wrinkled flame front. For this combustion regime the increased flame surface area is causing the burning rate to increase. This regime is characterised by the turbulent integral length scale, l_t , being significantly larger than the thickness of the flame front, d.

When the turbulent integral length scale, l_t , is of the order of the thickness of the flame front d or smaller, the flame becomes a thick turbulent flame brush. In this regime the turbulence is causing increased diffusion of heat and mass and thereby a high burning rate.

Further details about classification of combustion regimes can be found in Sand and Arntzen (1991) "Simulation of turbulent reactive flow".

When a flame propagates through a premixed gas cloud there are two mechanisms causing pressure build-up. These are:

i) fast flame propagation


ii) burning in a confined volume

In most accidental explosions a combination of these two effects causes the pressure build-up. Here we will use a flame propagating in a pipe and an explosion in a vessel as examples.

If we have a deflagration propagating in a pipe we can have situations as shown in Figure 5.4. At the location of the flame front there will be a small pressure drop. This drop in pressure is required in order to satisfy the conservation equations across the flame front.

The pressure behind the flame (in the burnt gas) will gradually decay away from the flame. This pressure decay will mainly depend on the boundary conditions on the left end of the tube (i.e. open or closed tube) and on the flame velocity.

Since the flame front is a subsonic combustion wave, the burning will influence the flow ahead of the flame. In Figure 5.4 this is illustrated by a decaying pressure and shock wave in the unburned mixture. The pressure profile ahead of the flame will depend on the flame acceleration and speed. In order to obtain a shock wave ahead of the flame, a high flame speed is required.

Figure 5.5 shows the maximum overpressure versus flame velocity in two modes of flame propagation; i) planar mode, i.e. flame propagating in a tube and ii) spherical mode, i.e. flame propagating in an unconfined cloud.

The spherical mode of flame propagation requires a higher flame velocity than the planar mode in order to obtain the same explosion pressure. This can be explained by the fact that gas can expand more freely in a spherical mode than in a planar mode.

From Figure 5.5 one sees that a flame velocity of the order of 100 m/s is required to produce pressure waves of a significant strength (~0.1 barg). The pressure in a deflagration is strongly linked to the flame velocity and burning rate. Explosion pressures for constant velocity flames have been predicted by several researchers, among them Guirao et al. (1976) and Strehlow et al. (1979). The results of such predictions are shown in Figure 5.5.

If the explosion happens inside a closed vessel, fast flame propagation is not required to obtain high pressures. A vessel as shown in Figure 5.6 will prevent the expansion of the gas when it burns and lead to pressure increase. As stated in Section 4.9, a Stoichiometric fuel-air cloud in a closed vessel will give up to 8 to 9 bar when exploding. By opening up part of the vessel wall, relief will be provided and the pressure will be reduced. The reduction will depend mainly on how fast the flame is burning in the vessel and the location and size of the vent area.

5.2 Flame Acceleration in a Channel Due to Repeated Obstacles

In a partly confined area with obstacles (i.e. process equipment, piping etc.) the flame may accelerate to several hundred meters per second during a gas explosion. The mechanisms causing the increased burning rate in turbulent deflagrations are the wrinkling of the flame front by large eddies and the turbulent transport of heat and mass at the reaction front. This turbulence is mainly caused by the interaction of the flow with structures, pipe racks, etc.

Figure 5.7 shows how turbulence is generated in the wake of obstacles in a channel. When the flame consumes the unburned gas, the products will expand. This expansion can be up to 8-9 times the initial volume. The unburned gas is therefore pushed ahead of the flame and a turbulent flow field may be generated. When the flame propagates into a turbulent flow field, the burning rate will increase dramatically. This increased burning rate will further increase the flow velocity and turbulence ahead of the flame.

In Figure 5.8 the flame speed and flow velocities are measured in a 1 m long wedge-shaped vessel. From this Figure we can see the velocities gradually increasing as the flame front propagates down the vessel. We can also see that the difference between the flame speed and the mean flow velocity, i.e. the burning velocity, also increases. The increased burning velocity will cause the explosion pressure to rise.

The mechanism of flame acceleration due to repeated obstacles constitutes a strong positive feed-back loop. This loop is shown in Figure 5.9.

The flame acceleration can to some extent be avoided by venting the hot combustion products as shown in Figure 5.10. The flow and turbulence in the unburned mixture ahead of the flame will be reduced. Venting combustion products is a very effective way of minimising the acceleration effect of repeated obstacles.

Venting of unburned gas ahead of the flame may also contribute to a lower explosion pressure, in particular when the venting directs the flow away from repeated obstacles. If venting unburned gas leads it past repeated obstacles, flame acceleration will most likely occur.

When a deflagration propagates through a region of obstacles and then ends up in an unobstructed region the flame speed will normally drop and adjust to the new environment. Figure 5.11 shows how a deflagration decelerates when it propagates from an obstructed into an unobstructed region. In this experiment, the flame speed drops from several hundred meters per second to a few tens of meters per second. The flame speed in the unobstructed region is so low that the pressure generated in this region is negligible (see Figure 5.5).

This discussion shows that for a deflagration there are two mechanisms governing the pressure build-up in partly confined gas clouds, namely:

• Flame acceleration due to enhanced burning due to turbulence generated by flow past obstacles.
• Venting providing pressure relief or reducing the effect of the feedback mechanism described previously in this chapter.
  

These mechanisms have competing effects. The flame acceleration due to turbulence will increase explosion pressure, while venting will reduce the pressure. It is the balance between these two that is governing the pressure build-up. When analysing gas explosions we have to take both of them into account. In the following section we will discuss some experiments involving both flame acceleration due to obstacles and venting.

5.3 Experiments in a 50 m³ Explosion Tube

The 50 m³ explosion tube is shown in Figure 5.12. This experimental vessel was originally located at the Raufoss test site in the Eastern part of Norway. In 1983 it was moved to CMR's Sotra test site outside Bergen. Experiments conducted in this vessel have been reported by Moen et al. (1982), Eckhoff et al. (1979), Hjertager et al.(1981, 1982, 1984, 1985) and Hjertager, (1988).

The tube is 10 m long and has a diameter of 2.5 m. The tube is closed in one end and open in the other. Inside the tube, orifice plates can be mounted. The number of rings and the inner diameter of the rings are variables. The ignition was either a matrix of electrically fired match-heads (i.e. plane ignition source) or a single match-head (i.e. point ignition source). In most of the experiments the tube was filled with a homogeneous fuel-air mixture, but in some tests the effect of nonhomogeneous fuel concentration was tested out.

Figure 5.13 shows some of the results from tests with Stoichiometric propane-air and plane ignition. The peak explosion pressure is ranging from about 1 barg to 14 barg depending on the number and size of the orifice rings inside the tube.

When the inner diameter of the orifice plate, d, is 1.74 m, the orifice plate will block 50% of the free tube area. In case of d equal to 2.25 m, the blockage ratio (i.e. B.R = 1- (d/D)² ) is 0.16 or 16%. We can see from the figure that the blockage ratio is one parameter which has a significant influence on the explosion pressure. By increasing the blockage ratio, the vent area will be reduced and the velocity flow through the open part of the orifice plate will increase. The increased velocity enhances the turbulence generation in the shear layers behind the orifice plates. The number of rings is another important parameter. Each orifice plate will generate a turbulent shear layer that will accelerate the flame up to a certain level.

From these experimental results it should be noticed that the peak explosion pressure is much higher than the pressure based on constant volume combustion of Stoichiometric propane-air at 1 atm initial pressure (i.e. ~8-9 bar). The reason for this is pre-compression of the unburned gas. Since the unburned gas may be pre-compressed by the early phase of the explosion, the explosion in its later phase will start out at a higher than ambient pressure and the explosion pressure may therefore reach local values higher than 8-9 bar.

5.4 Experiments in a Wedge-Shaped Explosion Vessel

The wedge-shaped explosion vessel is shown in Figure 5.14. The volume of the vessel is 18.5 m³. The length is 10 m and the height is 1.25 m. Inside the vessel different types (i.e. round cylinders, flat plates and boxes) and numbers of obstacles can be mounted. The top plate of the vessel can either be solid or perforated. Experiments carried out in this vessel have been reported by Bjørkhaug and Hjertager (1984a, 1984b, 1985, and 1986), Bjørkhaug (1986) and Pedersen et al. (1993 a and b).

With the wedge-shaped explosion vessel it has been possible to study the effect of various types of vent arrangements in combination with repeated obstacles. The results in Figure 5.15 show the effect of venting of gas through a perforated top plate. For 100% top confinement the top plate is solid and the only vent opening was at the end of the vessel with respect to ignition point. For the 80% top confinement case, 20% of the top plate area is open for venting.

The explosion pressure was strongly dependent on the top confinement. In the case of 50% evenly distributed top confinement, the explosion pressure was less than 0.05 bar. As the top confinement was increased from 80% to 100% the explosion pressure increased by nearly two orders of magnitude. This is typical for gas explosions. Small changes in the geometry can lead to order of magnitude changes in explosion pressure.

In the "far end venting tests" the vent area in the top plate was not evenly distributed, but located in the far end of the vessel with respect to the ignition point. In these tests, the explosion pressure was more than one bar. This shows that not only the size, but also the vent area location can be very important.

The explanation for the strong dependency of the explosion pressure on the top confinement and location of the vent area can be found in Section 5.2. Figures 5.7 and 5.10 illustrate the same situations as the experiments in the present section. When there is sufficient venting close to the ignition point, the flame speed will be low and the turbulence generated behind the obstacles will be limited. Hence, the pressure will be low. However, when the venting is less effective in the early phase of the explosion the free unburned gas will be pushed ahead of the flame and a strong turbulent flow field will be generated and the positive feed-back mechanism will accelerate the flame and cause high pressure. From this we can conclude that to vent hot combustion products at an early stage of the explosion, is a very effective means of reducing flame acceleration.

Most simple models for prediction of explosion pressure will not take the location of the vent area into account. They only use the size of the vent area as an input parameter. From the experimental results described above it is obvious that these types of simple models are inadequate and that they may in some cases generate overpressures that are wrong by orders of magnitude. The only models which can account for the combined effects of venting and equipment location on explosion overpressure are those based on solution of fluid-dynamic equations (e.g. FLACS or µFlacs, see Chapters 12 and 13).

5.5 Experiments in a Cubical Explosion Vessel

The cubical explosion vessel (Hjertager et al., 1986) is shown in Figure 5.16. The vessel consists of a corner with a length dimension of 3 m. In this corner internal obstructions were mounted. The internal obstructions tested consisted of pipes with diameter of 164 mm, 410 mm and 820 mm. Three different porosities or volume blockage ratios (VBR) where tested. The diameters, VBR's and corresponding numbers of pipes are given in Table 5.1.

For Stoichiometric propane-air mixtures the flame speed ranged from 10 m/s without obstacles to approximately 1000 m/s in the most densely packed arrangements. The pressures produced ranged from a few tens of millibar up to 4 bar. Figure 5.17 shows the peak explosion pressure for various volume blockage ratios and obstacle diameters. For the same blockage ratio the smallest obstacle diameters give the highest pressure. As expected, increased blockage ratio will increase the explosion pressure.

From these results we can conclude that not only the volume blockage ratio is of importance, but also the size (and shape) of the obstacles. In the cubical explosion vessel, the smaller obstacles allow for a larger number of repeated shear layers, and thus the positive feedback loop described in section 5.2 is traversed many times. Therefore, higher pressure is generated.

If we compare the results from the cubical vessel to similar tests (i.e. blockage ratio, number of obstacles and gas mixture) in the wedge-shaped vessel and the tube, we will find that the cubical vessel gives the lowest explosion pressure. This is shown in Figure 5.18.

In the tube, the wedge-shaped and the cubical vessels, the respective modes of flame propagation will be planar, cylindrical and spherical. As shown in Figure 5.5 a spherical mode of flame propagation requires higher flame velocity than a planar mode to generate the same explosion pressure. The pressure wave can expand more "freely" in the spherical mode and the positive feedback mechanism is not as strong as in the planar mode.

A similar experience was reported by van Wingerden et al. (1991). Experiments performed in a wedge-shaped vessel (sector) and a channel (respectively cylindrical and planar geometries) having the same length and similar obstacles showed that the terminal flame speeds were higher in the channel than in the sector. This effect decreased, however, when the degree of obstruction (blockage ratio) increased (Figure 5.19).

This understanding has practical implications. As we will discuss further in Chapter 10, it is obvious that compartments and offshore modules should not be long and narrow. In elongated compartments the planar mode of flame propagation will be dominant and may therefore cause high explosion pressure.

5.6 Experiments in a 1:5 Scale Model of an Offshore Module

The 1:5 scale model of an off-shore module is 8 m long, 2.5 m wide and 2.5 m high. The total volume is 50 m³. The internal layout in the model is interchangeable. The standard internal layouts are a compressor module (i.e. M24) or a separator module (i.e. M25). These layouts consist of equipment located on two decks, the lower deck (LD) and the upper deck / mezzanine deck (UD). Figure 5.20 shows the internal equipment in the separator module.

The module has been used for investigation of the effect of vent arrangements and ignition positions and testing of water deluge, blast panels, louver walls, relief panels etc. This work has been reported by Hjertager et al. (1987, 1988), Hjertager and Bjørkhaug (1987), Bjørkhaug (1988), and Bjerketvedt and Bjørkhaug (1991).

In this section we will focus on the effect of venting with different wall arrangements. The different layouts that were tested are summarised in Table 5.2.

Layout	Closed Areas	AV/V2/3	AV/V2/3 with louvers
	Roof, Deck	4.78
	Roof, Rear Wall, Deck	2.85	1.48
	Roof, Rear Wall, 50% of Front Wall, Deck	1.98
	Roof, Rear Wall, Front Wall, Deck	0.92	0.46

The peak pressures from the tests are given in Figure 5.21. The peak pressure is plotted versus the dimensionless parameter A_V/V^2/3 where A_V is the free vent area and V the volume of the compartment. The different vent arrangements are given in Table 5.2. Figure 5.21 also includes some data from tests in a 1:33 scale model of the same offshore module.

The results from the tests can be summarised as follows:

• The vent arrangement is extremely important for the explosion pressure. The peak pressure was about 0.01 barg when all four side-walls were open. (A_V/V^2/3 = 4.8). When the long side walls were closed and the end walls were louvered (A _V/V^2/3 = 0.46) the peak pressure was 1.9 barg. The conclusion is that explosion pressure in a compartment or building depends strongly on the vent arrangements.

• By removing the internal equipment (i.e. obstacles) the explosion pressure was reduced by a factor of 5-10. Equipment will enhance the turbulence generation during the explosion and accelerate the flame and thereby cause high pressure (see section 5.2).

• Increasing the scale from 1:33 to 1:5 increases the explosion pressure by a factor of 5 to 10. This indicates that small scale data are irrelevant for large scenarios if not properly scaled

• As a general trend propane tests gave about twice as high pressure as methane tests in a similar geometry. Explosion pressure will depend on the type of fuel.
  
  

5.7 Shape and Arrangement of Obstacles

The experiments in the tube, wedge-shaped vessel and cubical vessel demonstrated the importance of the degree of obstruction by obstacles. Area blockage ratio and volume blockage ratio are the parameters which are used to describe the degree of obstruction. Additional parameters which are important with respect to the effect of obstacles on explosion propagation are the shape of obstacles and their arrangement.

Experiments performed in a wedge-shaped vessel described by Bjørkhaug (1986) showed that the pressure development due to round obstacles was approximately half of the pressure development with similar (considering blockage ratio as a parameter) baffle-type obstacles. The main reason being the fact that the turbulence intensity in the shear layer produced by a sharp obstacle is larger than the turbulence intensity in the shear layer produced by a round obstacle.

Experiments performed by van Wingerden et al. (1991) demonstrate the effect of obstacle shape on flame speeds developed in a wedge-shape vessel (See Figure 5.22). The effect of obstacle shape seems to be more important for low degrees of obstruction than for high degrees of obstruction.

The influence of obstacle arrangement was also studied by van Wingerden et al. (1991). Figure 5.23 shows three different arrangements which were studied in a channel and the pressures that were obtained for these three arrangements.

The results of obstacle arrangements A and B demonstrate that staggering of obstacles leads to higher pressures, something that cannot be described by using a parameter such as blockage ratio only. Only CFD-computer tools such as FLACS do take obstacle arrangement into account.

5.8 Obstruction of Vent Openings

Wilkins et al. (1993) performed experiments to investigate the effect of an obstruction in front of a vent opening outside the vented structure. The experiments were performed in a 1:5 scale compressor module. A wall was placed outside the module in front of one of the vent openings at one of the short ends of the module. The distance of the wall to the vent opening was varied. Figure 5.24 shows results of the situation where ignition is effected in the centre of the module and both short ends of the module are provided with vent openings.

The results show that the effect of the wall is limited to approximately 1 m from the vent opening. This coincides with a normalised vent area (the total vent area between the module and the wall) of 2 times the original vent area. Similar results were found for other ignition/vent configurations. The results clearly show that partial obstruction of a vent opening can result in strong pressure increases. These results are important to consider when explosion venting occurs over a laydown area or when considering venting via intermodular gaps.

5.9 Jet Flames

Eckhoff et al.(1979) investigated explosions caused by jet flames emerging from a partly confined volume into another gas cloud. The test rig was the 50 m³ tube described in section 5.3. In these tests the ignition was located at the closed end of the jet-tube. Both the jet-tube and the 2.5 m diameter tube was filled with Stoichiometric propane-air. The experimental set-up is shown in Figure 5.25.

In these tests explosion pressures above 10 barg were recorded. The main conclusions from these tests were that a jet exiting from a partly confined volume acted as a very strong ignition source for the cloud inside the 2.5 diameter tube, and the explosion pressure depended on the jet flame velocity. This type of jet flame ignition have experimentally been observed to cause very violent explosions in unconfined clouds. Even transition to detonation has been reported in sensitive fuel-air mixtures (Moen et al. 1989). Experiments (Mackay et al. 1989) show that deflagration velocities of at least 500 to 700 m/s are required in order to observe transition to detonation in fuel-air.

The small scale experiments by Wilkins and Alfert (1991) indicate that "ignition" by a jetted flame in a partly confined compartment enhances the pressure build-up more when the compartment is obstructed than when it is empty.

The effect of localised explosions (jet flames) may in some situations not only cause high pressures locally but also cause high velocity flames to propagate into less confined but obstructed regions, where the high velocity of the flame may be sustained. Data published by Harris and Wickens (1989) show examples of such an effect. They showed that if a flame entered the unconfined obstacle array at a high velocity, the flame was able to stabilise at a high velocity and associated high explosion pressure. However, if the flame had a low velocity in the beginning of the array, it was not able to accelerate to high velocities and the corresponding explosion pressure was low.

All the experiments referred to in this section show that a jet flame is a stronger ignition source than a spark. In consequence analyses jet flames should be considered when explosions occur in channels, sewage systems, tunnels, motor noise shields or, more generally, when multi-compartment explosions can occur.

5.10 Type of Fuel

The consequences and the probability of occurrence of gas explosions will to a large extent depend on fuel type. Under similar experimental conditions different fuel-air mixtures will generate different explosion pressures. At the present time there are no standard procedures for classifying the explosion hazard regarding pressure generation for different fuels. However, various experiments with turbulent deflagrations (Bjørkhaug, 1988 a and b, Pedersen et al., 1993 a and b) and detonations (Bull et al. 1984) show that common fuels can be ranked, at least qualitatively.

Bjørkhaug (1988 a and b) has carried out experiments with hydrogen-air and several hydrocarbon-air mixtures (acetylene-, ethylene-, propylene-, cyclohexane-, ethane-, propane-, and methane-air) in the 1 m and 10 m wedge-shaped vessels. Some results from the 10 m wedge-shaped vessel are shown in Figure 5.27. Note that the results presented in this Figure are based on a specific experimental configuration and that the pressure levels will be different in other experimental situations. In particular higher pressures can be expected in more complex geometries, like partially confined, obstructed process areas.

Hydrogen gave the highest explosion pressure, 8 barg. Hydrogen and acetylene are the two most reactive fuels that we normally handle. Ethylene is also very reactive. Propane and ethane are somewhat less reactive and seem to form an intermediate level of explosivity. Methane is the least reactive fuel shown in Figure 5.27. Many other hydrocarbons (e.g. butane) fall into the same group as propane and ethane.

Experimental data for more complex fuels like cyclohexane and vinylchlorid monomer (i.e. VC, VCM) is limited. Bjørkhaug (1988a) performed experiments in small scale with cyclohexane which gave slightly higher pressures than methane. In larger scale cyclohexane behaved more like propane (Harris and Wickens 1989). Mackay et al (1988) showed that VC was nearly as reactive as ethylene. It is still uncertain if more complex fuels can be ranked in the same way as the common hydrocarbons.

Other substances that we normally do not regard as fuels, like ammonia (NH₃ ), can also cause explosions. Ammonia burns very slowly, but in a confined situation, it can cause serious explosions (see section 1.2 ).

For more heavy hydrocarbons such as heptane the fuel may be dispersed into the air as a mist. Experiments on mist-air mixtures are limited but experiments reported by van Wingerden et al. (1992) revealed that the reactivity of alkane mist-air mixtures is in the same order of magnitude as propane (gas)-air mixtures.

The amount of data describing turbulent explosion properties for fuel mixtures and mixtures of fuel and inert gases is limited. However, Kong and Alfert (1990) showed that by adding CO₂ to methane the explosion pressure was reduced compared with pure methane. This feature was confirmed later by Pedersen and Beuvin (1993) and Pedersen et al. (1993 a) but they also showed that relatively large quantities of CO₂ must be added before an effect can be noted.

Experiments with mixtures of various fuels have been reported by Bjørkhaug and Hjertager (1986), Kong and Alfert (1990) and Pedersen et al. (1993 a and b). Figure 5.28 shows some of the new results from the experiments in the 10 m wedge shaped vessel by Pedersen et al. (1993 b). As the Figure shows, the reactivity of natural gas is comparable to that of equivalent methane-propane mixtures.

The reactivity of heptane mist-methane mixtures and heptane mist-propane mixtures lies between that of pure methane or propane and pure heptane mist depending on the mixture composition (van Wingerden et al., 1993).

5.11 Fuel Concentration

A premixed fuel-air cloud will only burn as long as the fuel concentration is within the lower and upper flammability limits (LFL, UFL). When the fuel concentration in a cloud is near the flammability limit the burning rate will be very low. In order to obtain high pressure for near flammability limit concentrations, a confined situation is required. At the flammability limits the final pressure for constant volume combustion of fuel-air is typically 4 times the initial pressure.

For single fuels the maximum explosion pressure is normally observed at Stoichiometric or slightly rich mixtures. Figure 5.29 shows peak pressure measurements from experiments in a 1 m wedge-shaped vessel.

If we compare the results in Figure 5.29 with the data in Table 5.3 we find that the concentration leading to maximum explosion pressure is close to the Stoichiometric composition. For this geometry, the concentration range where pressure is observed, is more narrow than the flammable range. The concentration range causing significant explosion pressures is dependent on the geometry where the explosion is occurring. The more confined and obstructed the geometry, the wider the concentration range. The limits for explosion pressure as shown in Figure 5.29, must not be confused with explosion limits (or flammability limits) as defined in section 4.1 .

5.12 Inhomogeneities in the Cloud

Hjertager et al. (1985 and 1988b) have investigated the explosion propagation in methane-air clouds with concentration gradients inside a 50 m³ tube and a 1:5 scale offshore module.

In the tube the nonhomogeneous cloud was generated by a high-pressure release of methane. It was observed that the explosion pressure in a realistically generated cloud may reach values as high as in the Stoichiometric homogeneous cloud, for which care has been taken in premixing the fuel-air. However, in general the results show a strong dependency on experimental parameters such as direction of the jet, mass of methane injected, and the ignition delay time.

Gas dispersion tests in the 1:5 scale offshore module (Bjørkhaug and Bjerketvedt 1990) showed that for a high momentum release (i.e. high pressure reservoir) a relatively uniform gas cloud, the concentration of which would pass through the Stoichiometric value, was formed in large areas of the test module. This may explain why explosion pressures in real clouds may be as high as in premixed clouds. Hence it can be concluded that using a homogeneous Stoichiometric fuel-air cloud in a gas explosion analysis is a conservative, but not unrealistic assumption.

5.13 Degree of Filling by the Cloud

In an accident situation the combustible gas cloud in an obstructed and/or partly confined volume may only fill a part of the volume at the time of ignition. The filling ratio is, of course, an important parameter. But in some situations 30-50 % filling ratio may cause the same explosion pressure as a 100 % filled compartment. The reason for this is that during an explosion the gas that burns will expand and push the unburned gas ahead of the flame. Thereby air or fuel-air outside the flammable range is pushed out of the compartment. As discussed in section 4.9 the expansion of the combustible cloud on burning can be up to 8 times the initial volume. Figure 5.30 illustrates how a small cloud upon burning is pushing out air from a compartment and thereby fills the whole compartment with a combustible cloud.

Pappas (1983) made some simple calculations on the effect of having only a part of the compartment filled with a gas cloud. It was assumed that the ignition point and the gas cloud are far from the vent opening. The results are shown in Figure 5.31. The explosion pressure starts to drop at about 30% filling ratio.

An explosion in a partly filled compartment can in some instances cause the same explosion pressure as in a 100% filled compartment. It should be added that when the cloud is only filling a portion of the enclosure, the explosion pressure will be much more sensitive to the ignition location. If the ignition occurs at the edge of the smaller cloud and/or close to the vent area we can expect lower pressure for the partly filled than for the 100% filled case.

5.14 Ignition

Both the strength and the location of the ignition source can be important factors in determining the consequences of a gas explosion.

In section 5.9 it was shown that jet flame ignition of a cloud can cause very strong explosions even for unconfined situations. If a cloud is ignited by detonating a high explosive charge within the cloud the gas may detonate directly.

Even though extreme ignition scenarios exist, the most likely ignition source is a weak ignition like a hot surface or a spark. In consequence analyses it is common to choose a weak ignition source as a probable scenario.

Various experiments and FLACS simulations have shown that explosion pressures can be very sensitive to the location of the ignition point. In many scenarios the peak explosion pressure can be changed by an order of magnitude if the ignition location is moved from "worst case" to a more favourable place. In general the lowest pressure is obtained if the ignition point is :

i) close to the vent area or


ii) at the edge of the cloud

but as we will come back to in the end of this section, exceptions to this exist.

Figures 5.7 and 5.10 show how repeated obstacles generate turbulence, while venting of combustion products reduces the turbulence generation. By igniting near the vent opening the combustion products will be vented and the flow velocity and the turbulence in the unburned mixture will be low. Figure 5.32 shows how different flow regimes will be generated in the same geometry with different ignition locations. In case a) the flow velocity ahead of the flame will be low if the compartment is not too long. In case b) a high flow velocity will be generated ahead of the flame which will generate turbulence by interaction with obstacles and hence support a high burning rate and cause high explosion pressure. For simplicity obstacles have been omitted from the figure.

However, if venting combustion products is not sufficient to keep the flame speed at a low level, edge ignition may cause higher explosion pressures than central ignition. Figure 5.33 shows an example of this. In this case the flame propagation distance is a more important factor than the venting of combustion products. By increasing the length of the flame propagation, the flame will have the possibility to accelerate over a longer distance, by passing a greater number of obstacles. This effect will be most pronounced when one or more of the following apply: very reactive fuel, high density of obstructions, small vent areas or large obstructed volumes.

The practical implication of this is that one should try to locate potential ignition sources away from worst-case locations.

5.15 Scale

The knowledge of gas explosion research made a great step forward in the end of the 70's and the beginning of the 80's. Before that time the research activity was mainly focusing on laboratory tests. However, laboratory scale was not appropriate in order to understand the nature of gas explosions in an industrial environment. Large scale tests in Norway (Eckhoff et al. 1979, Moen et al., 1982 and Hjertager et al., 1988) showed that explosion venting and turbulence were important factors governing the consequences of gas explosions. Today we know that simple scaling laws do not generally apply to industrial situations (Moen et al. 1982, British Gas 1990).

Bakke and Hjertager (1983) have investigated scaling characteristics of explosions in vented obstructed channels by using an early version of the FLACS code. The channel was similar to the geometry shown in Figure 5.10. The top plate was either a solid plate or a perforated plate. The results from the simulations are shown in Figure 5.34. The legend gives the confinement of the top plate, i.e. conf. 1.0 is a solid plate and conf. 0.5 is a perforated plate with 50% blockage.

From this Figure we can see that the explosion pressure increases with increasing length scale until the pressure reaches 10 to 15 bar. The important finding in this investigation is that the venting through the top plate becomes less effective as the scale increases. For instance for a length scale equal to 2 there is nearly an order of magnitude difference between the solid plate (i.e. conf. 1.0) and 8% open top plate (i.e. conf. 0.92). For length scales of 5 to 10 this difference is 2 or less. This shows clearly the difficulties of gas explosion scaling. It is not only the venting and obstructions that are important, but also the dimensions.

5.16 Duration and Impulse

So far we have only discussed the peak pressure as the characteristic parameter for gas explosions. Actually the dynamic response of walls, decks, etc. subjected to pressure from gas explosions will depend on the pressure time curve. In addition to the peak pressure, the rise time and duration of the positive phase are important. In some cases even the negative phase of the pressure pulse can be important.

One way of characterising the pressure time curve is to use the time integral of the pressure, known as the impulse. The impulse is simpler to define than the duration of pulse and it contains more information.

The duration and the impulse depend on the size of the exploding cloud and the peak pressure. There are no simple methods of adequate accuracy for predicting the shape of pressure-time curves from gas explosions. Advanced numerical simulation tools like FLACS have to be applied.

5.17 Explosion Wind

The wind force generated by the explosion will act as a drag load on smaller equipment such as piping. The dynamic pressure (or drag, 0.5ru²) is one of the parameters characterising the explosion wind.

Figure 5.36 shows the maximum static and dynamic pressures from a FLACS simulation. We can see that the maximum pressure is 0.7-0.8 up to a normalised distance of 4, but decreases out to the vent area at 5 or 6. At the vent area the flow velocity and the dynamic pressure are high. The stagnation pressure (p + 0.5ru²) is fairly constant.

Experiments reported by Sand et al. (1992) show that measured drag forces acting on a single pipe during an explosion appear to be very close to those predicted by FLACS.

5.18 Guidelines

The main factors determining the consequences of deflagrations are:

• Type of fuel
• Fuel concentration
• Size and location of the cloud
• Location and strength/type of the ignition source
• Obstacle number and size + orientation/location
• Confinement and venting (size and position of vent area)
• Scale
  

In order to evaluate the consequences of a deflagration all of these factors have to be taken into account. Otherwise order of magnitude prediction errors can be made!

Simple scaling rules have proven to be inadequate for most industrial environments. More advanced methods such as FLACS ( Chapter 12) or µFlacs ( Chapter 13) simulations have to be applied.

The consequences of a gas explosion depend strongly on the venting arrangements and the geometrical layout (i.e. arrangement of process equipment, piping, etc.). Small changes in the geometry can change the explosion pressure significantly. It is therefore important to understand the mechanisms of flame acceleration and pressure build-up. Based on this knowledge it is often possible to suggest changes in the layout that will affect the explosion behaviour significantly and hence improve overall safety.

In design it is important to start as early as possible to consider gas explosions. It is a common mistake to start too late, when the layout has been "frozen". Start at day one (Pappas 1990). Apply the information in Chapters 9 to 11.

A deflagration in a truly unconfined cloud will propagate slowly and only produce small overpressure. Deflagrations produce high pressures when they propagate in an obstructed, partly confined area or confined volume.

When evaluating the consequences of deflagrations, not only peak pressure should be considered, but also the rise time, the duration and the impulse.