4.3. VAPOR CLOUD EXPLOSION BLAST MODELING

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1 F* = turbulence transport coefficient Rto = Ape/k,F(Wfu) = combustion rate c v = specific heat (constant volume) T = temperature H c = heat of combustion Previous Page The major mechanism of a vapor cloud explosion, the feedback in the interaction of combustion, flow, and turbulence, can be readily found in this mathematical model. The combustion rate, which is primarily determined by the turbulence properties, is a source term in the conservation equation for the fuel-mass fraction. The attendant energy release results in a distribution of internal energy which is described by the equation for conservation of energy. This internal energy distribution is translated into a pressure field which drives the flow field through momentum equations. The flow field acts as source term in the turbulence model, which results in a turbulent-flow structure. Finally, the turbulence properties, together with the composition, determine the rate of combustion. This completes the circle, the feedback in the process of turbulent, premixed combustion in gas explosions. The set of equations has been solved with various numerical methods: e.g., SIMPLE (Patankar 1980); SOLA-ICE (Cloutman et al. 1976). Over the years, this concept was refined in several ways. A scale dependency was modeled by the introduction of scale-dependent quenching of combustion. The first stage of the process was simulated by quasi-laminar flame propagation. In addition, three-dimensional versions of the code were developed (Hjertager 1985; Bakke 1986; Bakke and Hjertager 1987). Satisfactory agreement with experimental data was obtained. Appendix F is a case study by Hjertager et al. illustrating the above method. Such numerical methods will become more widely used in the long term. These techniques will probably remain research tools, rather than routine evaluation methods, until such time as available computing power and algorithm efficiency greatly increase. The concept of numerical simulation of turbulent premixed combustion in gas explosion has also been adopted by others: Kjaldman and Huhtanen (1985) arrived at a similar concept on the basis of the multipurpose PHOENICS code. the REAGAS code (Van den Berg et al and Van den Berg 1989) VAPOR CLOUD EXPLOSION BLAST MODELING The long list of vapor cloud explosion incidents indicates that the presence of a quantity of fuel constitutes a potential explosion hazard. If a quantity of flammable material is released, it will mix with air, and a flammable vapor cloud may result. If

2 the flammable mixture finds an ignition source, it will be consumed by a combustion process which, under appropriate (boundary) conditions, may develop an explosive intensity and blast. It is highly desirable that vapor cloud explosion hazards be reduced by appropriate risk management measures. If possible, separation between large storage or manufacturing areas and residential areas should be sufficient to eliminate the risk of blast damage. This may not be an option for those working at a chemical plant or refinery. Designers should consider the possibility of a vapor cloud explosion in the siting and design of process plant buildings. For these and other purposes, blast-modeling methods are needed in order to quantify the potential explosive power of the fuel present in a particular setting. The potential explosive power of a vapor cloud can be expressed as an equivalent explosive charge whose blast characteristics, that is, the distribution of the blastwave properties in the environment of the charge, are known Methods Based on TNT Blast For many years, the military has investigated the destructive potential of high explosives (e.g., Robinson 1944, Schardin 1954, Glasstone and Dolan 1977, and Jarrett 1968). Therefore, relating the explosive power of an accidental explosion to an equivalent TNT charge is an understandable approach. Thus, damage patterns observed in many major vapor cloud explosion incidents have been related to equivalent TNT-charge weights. Because the need to quantify the potential explosive power of fuels arose long before the mechanisms of blast generation in vapor cloud explosions were fully understood, the TNT-equivalency concept was also utilized to make predictive estimates, i.e., to assess the potential damage effects from a given amount of fuel. The use of TNT-equivalency methods for blast-prediction purposes is quite simple. The available combustion energy in a vapor cloud is converted into an equivalent charge weight of TNT with the following formula: where W f = the weight of fuel involved (kg) WTNT = equivalent weight of TNT or yield (kg) H f = heat of combustion of the fuel in question (J/kg) #TNT = TNT blast energy (J/kg) a e = TNT equivalency based on energy (-) a m = TNT equivalency based on mass (-) (4.37) The literature is inconsistent on definitions. TNT equivalency is also called equivalency factor, yield factor, efficiency, or efficiency factor.

3 If the equivalent weight of TNT is known, the blast characteristics, in terms of the peak side-on overpressure of the blast wave, can be derived for varying distances from the explosion. This is done using a chart containing a scaled, graphical representation of experimental data. Various data sets are available that may differ substantially. In Figure 4.17, for instance, two blast curves (peak side-on overpressure versus scaled distance) are presented. They are different because they result from substantial differences in experimental setup, a surface burst of TNT (on the left) and a free-air burst of TNT (on the right). TNT-equivalency methods are the simplest means of modeling vapor cloud explosions. TNT equivalency can be regarded as a conversion factor by which the available heat of combustion can be converted into blast energy. In one sense, TNT equivalency expresses the efficiency of the conversion process of chemical energy (heat of combustion) into mechanical energy (blast). In a numerical exercise described in section 4.2.2, it was shown that, for a stoichiometric, hydrocarbon-air detonation, the theoretical maximum efficiency of conversion of heat of combustion into blast is equal to approximately 40%. If the blast energy of TNT is equal to the energy brought into the air as blast by a TNT detonation, a TNT equivalency of approximately 40% would be the theoretical upper limit for a gas explosion process under atmospheric conditions. However, the initial stages in the process of shock propagation in the immediate vicinity of Overpressure (Psi) Peak overpressure (Psi) (a) Ground range (ft./lbs. 1/3 ) (b) Distance from burst (feet) Figure Side-on blast peak overpressure due to (a) a TNT surface burst. (Kingery and Panill 1964) and (b) a free-air burst of TNT (Glasstone and Dolan 1977).

4 a detonating TNT charge are characterized by a high dissipation rate of energy. If this loss of energy is taken into account, the TNT equivalency for a gas detonation at lower blast overpressure levels is expected to be substantially higher than 40%. Furthermore, accidental vapor cloud explosions are anything but detonations of the full amount of available fuel. Therefore, practical values for TNT equivalencies of vapor cloud explosions are much lower than the theoretical upper limit. Reported values for TNT equivalency, deduced from the damage observed in many vapor cloud explosion incidents, range from a fraction of one percent up to some tens of percent (Gugan 1978 and Pritchard 1989). For most major vapor cloud explosion incidents, however, TNT equivalencies have been deduced to range from 1% to 10%, based on the heat of combustion of the full quantity of fuel released. Apparently, only a small part of the total available combustion energy is generally involved in actual explosive combustion. Methods for vapor cloud explosion blast prediction based on TNT equivalency are widely used. Over the years, many authors, companies, and authorities have developed their own procedures and recommendations with respect to issues surrounding such predictions. Some of the differences in these procedures include the following: The portion of fuel that should be included in the calculation: The total amount released; the amount flashed; the amount flashed times an atomization factor; or the flammable portion of the cloud after accounting for dispersion over time. The value of TNT equivalency: A value based on an average deduced from observations in major incidents; or a safe and conservative value (whether or not dependent on the presence of partial confinement/obstruction and nature of the fuel). The TNT blast data used: A substantial scatter in the experimental data on highexplosive blast can be observed which is due to differences in experimental setup. Although often referenced differently, most recommendations can be tracked back to ground burst data developed by Kingery and Pannill (1964). The energy of explosion of TNT: Values currently in use range from 1800 to 2000 Btu/lb, which correspond to 4.19 to 4.65 MJ/kg. Below are examples of some of the many different approaches used. Their proponents' recommendations are quoted as literally as possible. Some of them are demonstrated in detail in chapter 7. Dow Chemical Co. (Brasie and Simpson 1968) Brasie and Simpson (1968) use the Kingery and Pannill (1964) TNT blast data to represent blast parameter distributions, and the US Atomic Energy Commission's recommendations (Glasstone 1962) for the attendant structural damage. Brasie and Simpson (1968) base their recommendation for the TNT equivalency of vapor clouds on the damage observed in three chemical-plant explosion incidents. Analyzing the

5 damage in these incidents, they deduced a TNT yield which is highly dependent on the distance to the explosion center. Although values for TNT equivalency ranging from 0.3% to 4% have been observed, Brasie and Simpson recommend, for predictive purposes, conservative values for TNT equivalency as follows: 2% for near-field, and 5% for far-field effects (based on energy), applied to the full quantity of fuel released. In a later paper, Brasie (1976) gives more concrete recommendations for determining the quantity of fuel released. A leak potential can be based on the flashing potential of the full amount of liquid (gas) stored or in process. For a continuous release, a cloud size can be determined by estimating the leak rate. For a combined liquid-vapor flow through holes of very short nozzles, the leak rate (mass flow per leak orifice area) is approximately related to the operating overpressure according to: W h = 2343P 0-7 (4.38) where W h is leak mass flux in kilograms per second per square meter and P is operating overpressure in bars. This estimation formula seems to give reasonable answers up to about 2 to 70 bars operating overpressure. It is not valid beyond the thermodynamic critical pressure. The leak rate may be factored for the actual flash fraction. The flow rate of release, W 9 can be found as the product of the mass flux and the cross sectional area of the leak orifice. The weight of flammable fuel in the cloud can be estimated by multiplying the rate of release by the time span needed to attain the lower flammability limit in the drifting plume. In a conservative approach, for stable atmospheric conditions (characterized by an ambient wind speed of 2.23 m/s), the time span can be approximated by (4.39) where t f = time span (s) W = rate of release (kg/s) M = molecular weight (kg/kmol) / = lowerflammabilitylimit (vol%) TNT equivalency should be applied to the quantity of fuel calculated with the above equations. For planning purposes, Brasie (1976) recommends the use of TNT equivalencies of 2%, 5%, and 10% (based on energy) in calculations to determine the sensitivity of geometry to the yield. UT Research (Eichler and Napadensky 1977) In their research to determine safe stand-off distances between transportation routes and nuclear power plants, Eichler and Napadensky (1977) recognized that the

6 blast effects produced by vapor cloud explosions are highly dependent on mode of combustion. They recognized the possibility that rapid deflagration or detonation of all combustibles involved might result in much higher TNT equivalencies than those recommended by Brasie and Simpson (1968) and others. In addition, they recognized that blast effects from vapor cloud explosions are often highly directional. Therefore, they determined an upper limit of TNT equivalency for vapor cloud explosions by analyzing the blast produced in experiments in which spherical fuel-air charges of varying compositions were detonated (Kogarko et al. 1966; Balcerzak et al. 1966; Woolfolk and Ablow 1973). They concluded that the blast from a detonating fuel-air charge can be reasonably well represented by TNT blast data. Because a distance-dependent TNT equivalency was anticipated, they determined TNT equivalency for stoichiometric fuel-air charges only for the level of 1 psi (0.069 bar) peak side-on overpressure. They found a value of about 20%, based on energy. In addition, Eichler and Napadensky derived TNT equivalencies from the damage observed in some major vapor cloud explosion incidents of the 1970s: The Flixborough explosion was analyzed on the basis of damage figures presented by Munday and Cave (1975). Assuming a 60,000 kg cyclohexane release, they found a TNT equivalency of 7.8% on the basis of energy, which corresponds with a mass equivalency of 81.7%. These equivalences were calculated on the basis of the full quantity of material released. For the Port Hudson vapor cloud explosion, they found TNT equivalencies of 8.7% and 96%, based on energy and mass basis, respectively. These equivalencies were calculated from damage data presented by Burgess and Zabetakis (1973), and are based on the full quantity of fuel (31,750 gallons, 70,000 kg) of propane released. Although the blast effects of the East St. Louis tank-car accident (NTSB 1973) were found to be highly asymmetric, average TNT equivalencies of 10% on an energy basis and 109% on a mass basis were found. These equivalencies were calculated based on the assumption of a full tank-car inventory (55,000 kg) of a mixture of propylene and propane. Another tank car was punctured at Decatur (NTSB report 1975). TNT equivalencies of % and % were calculated on energy and mass bases, respectively. These equivalencies were calculated based upon a full tank car inventory (152,375 Ib, 68,000 kg) of isobutane. Taking into account the possibility of highly directional blast effects, Eichler and Napadensky (1977) recommend the use of a safe and conservative value for TNT equivalency, namely, between 20% and 40%, for the determination of safe standoff distances between transportation routes and nuclear power plants. This value is based on energy; it should be applied to the total amount of hydrocarbon in the largest single, pressurized storage tank being transported.

7 HSE (1979 and 1986) Although it recognized that much higher values have been occasionally observed in vapor cloud explosion incidents, the U.K. Health & Safety Executive (HSE) states that surveys by Brasie and Simpson (1968), Davenport (1977, 1983), and Kletz (1977) show that most major vapor cloud explosions have developed between 1% and 3% of available energy. It therefore recommends that a value of 3% of TNT equivalency be used for predictive purposes, calculated from the theoretical combustion energy present in the cloud. To allow for spray- and aerosol-formation, the mass of fuel in the cloud is assumed to be twice the theoretical flash of the amount of material released, so long as this quantity does not exceed the total amount of fuel available. Blast effects are modeled by means of TNT blast data according to Marshall (1976), while 1 bar is considered to be upper limit for the in-cloud overpressure (Figure 4.18). Because experience indicates that vapor clouds which are most likely to explode "side-on" overpressure, bar,,, -,^- * actual distance, m "scaled distance" = -g mkg~ 1M \/WTNT Figure Peak side-on overpressure due to a surface TNT explosion according to Marshall (1976). (TNT in kilograms.)

8 are those which have formed rapidly, the HSE recommends ignoring the effect of cloud drift. Given a certain release of a given fuel, the procedure of vapor cloud explosion blast modeling according to HSE can be subdivided into a number of successive steps: Determine the flash fraction on the basis of actual thermodynamic data. The cloud inventory is equal to the flash fraction times the amount of fuel released. To allow for spray and aerosol formation, the cloud inventory should be multiplied by 2. This number may not, of course, exceed the total amount of fuel released. The equivalent weight of TNT can now be calculated according to: W / / W^1n = 0.03 ^ (4.40) "TNT where WTNT = equivalent weight of TNT or yield (kg) W^ = the weight of fuel in the cloud (kg) //TNT = TNT blast energy (J/kg) H f = heat of combustion of fuel in question (J/kg) Once the equivalent charge weight of TNT is estimated, the blast peak overpressures in the field can be found by applying this charge weight to the scaled distance in the blast chart (Figure 4.18). The positive-phase duration of the blast wave from a vapor cloud explosion is in the range of 100 and 300 ms. Exxon (unpublished) To estimate the total quantity of material in the vapor cloud, Exxon suggests that the following guidelines be used: If a gas is released, the quantity of material in the cloud (to be used in the calculation) is the lesser of (a) the total inventory of material or (b) the product of the rate of release times the time required to stop the leak. If a liquid is released, the quantity of material in the cloud (to be used in the calculation) is the product of the liquid's evaporation rate and the time required for the cloud to reach a likely ignition source, as limited by the quantity spilled. The quantity spilled is the lesser of (a) the total inventory of material or (b) the product of the rate of release and the time required to stop the leak. If the material released is either in two phases or flashing, the quantity of material in the cloud (to be used in the calculation) is the lesser of (a) the product of twice the fraction vaporized and the total inventory of material or (b) the product of twice the fraction vaporized, the rate of release, and the time required to stop the leak.

9 Exxon recognizes that blast effects by vapor cloud explosions are influenced by the presence of partial confinement and/or obstruction in the cloud. Therefore, in order to determine an equivalent TNT yield for vapor clouds, Exxon recommends use of the following values for TNT equivalency on an energy basis: 3% if the vapor cloud covers an open terrain; 10% if the vapor cloud is partially confined or obstructed. The open-terrain factor should be used if the release occurs in flat terrain and few structures are nearby, for example, in an isolated tank farm consisting of one or two well-spaced tanks. Otherwise, the partial-confinement yield factor should be used to give reasonably conservative damage estimates. These figures were developed on the basis of the gross quantities of material released in accidents. They may underpredict blast if used in conjunction with the amount of flammable mixture in the cloud developed from dispersion calculations. If the amount of fuel based on dispersion calculations is to be used, higher TNT equivalencies would be justified. The upper limit on yield factor in such instances would be 80%. These guidelines are recommended for application in combination with the Kingery and Panill (1964) TNT surface (ground range) burst data (Figure 4.17). Industrial Risk Insurers (1990) As a tool for estimating the loss of property potential of vapor cloud explosion incidents at chemical plants or refineries, the possibility of two credible incidents is considered. A credible spill for Probable Maximum Loss Potential. The minimum spill source is the largest process vessel. The maximum spill size is the combined contents of the largest process vessel, or train of process vessels connected together if not readily isolated. Between these extremes, a credible spill may be estimated after taking into account the presence of remotely operated shutoff valves adequate for an emergency, and automatic dump or flare systems. A credible spill for Catastrophic Loss Potential. For a catastrophic loss potential, the spill size should be based on the contents of vessels or connected vessel train. The existence of shutoff valves between vessels should not be considered. In addition, the catastrophic failure of major storage tanks should be considered. Leaks in pipelines carrying materials of concern from large-capacity, off-site, remote storage facilities must be considered. For this purpose, it must be assumed that the pipeline is completely severed and that the spill will run for 30 minutes. Industrial Risk Insurers (1990) states that the TNT equivalency of actual chemical plant vapor cloud explosions is in the range of 1% to 5%. A value of 2% based on

10 OI/SMETER OF OVERPRESSURE CIRCLES - FEET YIELD - TONS OF TNT Figure Diameters of side-on overpressure circles for various explosive yields (1 ton = 2000 Ib) (based on free-air bursts). available energy is recommended for use in estimating probable maximum and catastrophic losses. This TNT equivalency should be used in combination with airburst TNT-blast data according to Glasston and Dolan (1977), represented in Figure Figure 4.19 presents blast data so as to permit the diameters of overpressure circles to be read as a function of charge weight for various side-on overpressures. Factory Mutual Research Corporation (FMRC) (1990) According to FMRC (1990), a credible spill scenario at a chemical plant or refinery consists of a 10-minute release from the largest vessel or train of vessels through the connection that will allow the greatest discharge; a 10-minute release from an atmospheric or pressurized tank based on gravity and storage pressure as the driving force (the operation of internal excess flow valves, if present, may be considered in mitigating the amount discharged); a 10-minute release from above-ground pipelines carrying material from a largecapacity, remote source; loss of the entire contents of the tank for mobile tanks, such as rail and truck transportation vessels.

11 The quantity of fuel in a cloud is calculated by use of release and (flash) vaporization models that have been extensively described by Hanna and Drivas (1987). To account for aerosol formation during vaporization, the flash fraction should be doubled up to, but not exceeding, a value of unity. Pool vaporization is also considered. The equivalent charge weight of TNT is calculated on the basis of the entire cloud content. FMRC recommends that a material-dependent yield factor be applied. Three types of material are distinguished: Class I (relatively nonreactive materials such as propane, butane, and ordinary flammable liquids); Class II (moderately reactive materials such as ethylene, diethyl ether, and acrolein); and Class III (highly reactive materials such as acetylene). These classes were developed based on the work of Lewis (1980). Energy-based TNT equivalencies assigned to these classes are as follows: Class TNT Equivalency I 5% II 10% III 15% TNT-blast data for hemispherical surface bursts are used to determine the blast effects due to the equivalent charge. These blast data are based on the Army, Navy, and Air Force Manual (1990). Hazard Reduction Engineering Inc. (Prugh 1987) One of the complicating factors in the use of a TNT-blast model for vapor cloud explosion blast modeling is the effect of distance on the TNT equivalency observed in actual incidents. Properly speaking, TNT blast characteristics do not correspond with gas explosion blast. That is, far-field gas explosion blast effects must be represented by much heavier TNT charges than intermediate distances. To some extent, Prugh (1987) remedied this problem by introducing the concept of virtual distance. On the basis of literature data, Prugh determined a virtual distance, dependent on the weight of fuel involved in the vapor cloud explosion, expressed in an empirical relation. If virtual distance is added to real distance in estimating blast effects, then these effects can be approximated from a single equivalent TNT charge covering the entire field. In fact, this is the approximate yield observed for far-field blast effects. To express the maximum potential explosive power of a fuel, a safe and conservative value for TNT equivalencies of vapor cloud explosions was estimated from literature data on major incidents, after correction for virtual distance. Prugh (1987) concluded that the maximum energy-based TNT equivalency is highly depen-

12 dent on the quantity of fuel present in the cloud, and ranges from 2% for 100 kg up to 70% for 10 million kg of fuel. These TNT equivalencies should be used in combination with high-explosive blast data by Baker (1973). Instead of graphical representation, Prugh (1987) recommends the use of simple equations which relate basic blast parameters to distance from the explosion center. These expressions can be readily implemented in a spreadsheet on a personal computer. British Gas (Harris and Wickens 1989) On the basis of an extended experimental program described in Section 4.1.3, Harris and Wickens (1989) concluded that overpressure effects produced by vapor cloud explosions are largely determined by the combustion which develops only in the congested/obstructed areas in the cloud. For natural gas, these conclusions were used to develop an improved TNT-equivalency method for the prediction of vapor cloud explosion blast. This approach is no longer based on the entire mass of flammable material released, but on the mass of material that can be contained in stoichiometric proportions in any severely congested region of the cloud. An equivalent TNT charge, expressing the explosive potential of a congested/ obstructed region, should be calculated based on a 20% TNT equivalency of available energy. This TNT equivalency should be applied in combination with TNTblast data developed by Marshall (1976) (Figure 4.18). Harris and Wickens (1989) argue that, for releases of gases considered more reactive than natural gas, this approach might be inappropriate because, under specific circumstances, transition to detonation engulfing any portion of the cloud may occur. The Harris and Wickens (1989) approach appears to be very similar to the multienergy method (Van den Berg 1985), whose background is described in more detail in Section In addition, the nature of partially confined, obstructed, and congested areas is described in more detail there Methods Based on Fuel-Air Charge Blast Vapor cloud explosion blast models presented so far have not addressed a major feature of gas explosions, namely, variability in blast strength. Furthermore, TNT blast characteristics do not correspond well to those of gas-explosion blasts, as evidenced by the influence of distance on TNT equivalency observed in vapor cloud explosion blasts. The Baker-Strehlow Method An extensive numerical study was performed by Strehlow et al. (1979) to analyze the structure of blast waves generated by constant velocity and accelerating flames propagating in a spherical geometry. This study resulted in the generation of plots

13 of dimensionless overpressure and positive impulse as a function of energy-scaled distance from the cloud center. The study examined flamed speeds ranging from low velocity deflagrations to detonations. The time period covered by numerical calculations was extended well after the flame had extinguished and yielded blast parameters out to considerable distances from the source region. Thus, the pressure and impulse curves encompass regions both inside and outside the combustion zone. Baker and his colleagues (1983) compared the Strehlow et al. (1979) curves to experimental data, then applied them in research programs, accident investigations, and predictive studies. They developed the methods for use of Strehlow's curves. Application of the Baker-Strehlow method for evaluating blast effects from a vapor cloud explosion involves defining the energy of the explosion, calculating the scaled distance (R) 9 then graphically reading the dimensionless peak pressure (P 5 ) and dimensionless specific impulse (I 5 ). Equations (4.41) and (4.42) provide the means to calculate incident pressure and impulse based on the dimensionless terms. where where R = scaled distance (-) r = distance from target to center of vapor cloud (m) P 0 = atmospheric pressure (Pa) E = energy (J) ^V^o = dimensionless overpressure (Figure 4.20) (-) / 5 = scaled impulse (-) i = incident impulse (Pa-s) A 0 = speed of sound in air (m/s) PQ = atmospheric pressure (Pa) E = energy. (J) (4.41) (4.42) Graphical solution of Figures 4.20 and 4.21 requires selection of the proper curve based on the maximum flame speed attained. Strehlow et al. (1979) studies showed that a constant speed flame and an accelerating flame with the same maximum speed generated equivalent blast waves. Thus, flame speed data from experimental studies and accident investigations can be used objectively to select the proper curve. Each curve is labeled with two flame speeds: M w and M su. The flame speed M w is relative to a fixed coordinate system (i.e., on the ground), whereas M su represents the flame speed relative to the gases moving ahead of the flame front. Both M w and M su Mach numbers are calculated relative to the ambient speed of

14 Pentolite Bursting Sphere Figure Dimensionless blast side-on overpressure for vapor cloud explosions (Strehlow etal. 1979). sound. While M w is the appropriate parameter for comparison to most experimental data, the user should not assume that all experimental data are reported on this basis. Flame speed is a function of confinement, obstacle density, fuel reactivity, and ignition intensity. Confinement and obstacles have a coupled effect, so flame speed cannot be inferred from experiments that model only one of the user's parameters correctly. Fuel reactivity is a qualitative parameter that is generally used to categorize a fuel's propensity to accelerate to high flame speeds. It is generally accepted that hydrogen, acetylene, ethylene oxide, and propylene oxide have high reactivity; methane and carbon monoxide have low reactivity; and all other hydrocarbons have average reactivity. Ignition sources may be either soft or hard. Open flame, spark, or hot surfaces are examples of soft ignition sources, while jet and high explosives are categorized as hard ignition sources. Ignition intensity has almost no influence on flame speed for soft ignition sources; confinement, obstacles, and fuel reactivity are most important here. By contrast, ignition intensity is the most important variable if a hard ignition source is present.

15 Literature provides the basis for a user to objectively determine the maximum flame speed that will be achieved with a particular combination of confinement, obstacles, fuel reactivity, and ignition source. _ The energy term E must be defined to calculate energy-scaled standoff/?. The energy term represents the sensible heat that is released by that portion of the cloud contributing to the blast wave. Any of the accepted methods of calculating vapor cloud explosive energy are applicable to the Baker-Strehlow method. These methods include: Estimating the volume within each congested region, calculating the fuel mass for a stoichiometric mixture, multiplying the fuel mass by the heat of combus- BURSTING SPHERE a BAKER ( PENTOLITE ) A MACH 8-0 ADDITION MACH 5-2 ADDITION (CJ) MACH 4.0 ADDITION MACH 2.0 ADDITION MACH 1.0 ADDITION (M 8* ) MACH 0.5 ADDITION (M^ O.O662) MACH 0.25 ADDITION (M $«0.034) r KERNEL ADDITION TAU w KERNEL ADDITION TAU- 20 IMPULSE ( ENERGY SCALED ),. RADIUS ( ENERGY SCALED ), R Figure Dimensionless blast side-on specific impulse for vapor cloud explosions (Strehlow etal. 1979).

16 tion, and treating each congested volume within the flammable portion of the cloud as a separate blast source (see Multienergy Method). Estimating the total release of flammable material within a reasonable amount of time (generally 2 to 5 minutes) and multiplying this by the heat of combustion of the material times an efficiency factor (generally in the range of 1% to 5% for ordinary hydrocarbons). Estimating the amount of material withinflammablelimits (usually by dispersion modeling) and multiplying this by the heat of combustion times an efficiency factor (usually higher than the one applied above, generally 5% to 20%). Once the energy has been calculated, it must be multiplied by a ground reflection factor (i.e., hemispherical expansion factor), because Figures 4.20 and 4.21 are based on spherical expansion parameters. The ground reflection factor is generally 2 for vapor clouds that are in contact with the ground. If a vapor release is elevated and does not disperse to ground level, a factor between 1 and 2 must be selected. Because blast waves are generated in confined regions of vapor clouds, most vapor cloud explosions will be relatively close to the ground, and a factor of 1.7 to 2.0 is appropriate. Yellow Book, Committee for the Prevention of Disasters (1979) Wiekema (1980) used, as a model for vapor cloud explosion blast, the gas dynamics induced by a spherical expanding piston (Yellow Book 1979). A piston-blast model offers the possibility to introduce a variable initial strength of the blast. The piston blast was generated by computation, and is graphically represented in Figure The figure shows the peak side-on overpressure and the positive-phase duration of the blast wave dependent on the distance from the blast center for three arbitrarily chosen piston velocities. The graph is completed with experimental data from detonation of fuel-air mixtures developed by Kogarko (1966). Data are reproduced in a Sachs-scaled representation. This approach makes it possible to model a vapor cloud explosion blast by consideration of the two major characteristics of such a blast. These are, first, its scale, as determined by the amount of combustion energy involved and, second, its initial strength, as determined by combustion rate in the explosion process. Blast scale was determined by use of dispersion calculations to estimate fuel quantity within flammability limits present in the cloud. Initial blast strength was determined by factors which have been found to be major factors affecting the process of turbulent, premixed combustion, for example, the fuel's nature and the existence within the cloud of partial confinement or obstacles. The most common fuels were divided into three groups according to reactivity. The low-reactivity group included ammonia, methane, and natural gas; hydrogen, acetylene, and ethylene oxide were classified as highly reactive. Those within these extremes, for example, ethane, ethylene, propane, propylene, butane, and isobutane, were classified as medium-reactivity fuels.

17 before combustion after combustion low reactivity medium reactivity Figure The piston-blast model. Subsequently, it was assumed that blast strength is primarily determined by the fuel's reactivity (Figure 4.22), and that partial confinement, congestion, and obstruction in the cloud were only secondary influences. These assumptions are, however, highly questionable. The Multienergy Method (Van den Berg 1985) A comprehensive collection of estimates of TNT equivalencies was deduced from damage patterns observed in major accidental vapor cloud explosions (Gugan 1978). From these estimates, it can be concluded that there is little, if any, correlation between the quantity of combustion energy involved in a vapor cloud explosion

18 and the equivalent-charge weight of TNT required to model its blast effects. Some of these discrepancies are due to differences in the definition of the amount of material contained in the cloud. Evaluation of experimental data from work covered in Section 4.1 tends to confirm this concludion. These data indicate that, for quiescent clouds, both the scale and strength of a blast are unrelated to fuel quantity present in a cloud. These parameters are, in fact, determined primarily by the size and nature of partially confined and obstructed regions within the cloud. The factor of reactivity of the fuel-air mixture is of only secondary influence. These principles are recognized in the multienergy method for vapor cloud explosion blast modeling (Van den Berg 1985; Van den Berg et al. 1987). Considerations underlying the multienergy method for vapor cloud explosion blast modeling follow. There is increasing acceptance of the proposition that a fuel-air cloud originating from an open air, accidental release is very unlikely to detonate. The nonhomogeneity of the cloud's fuel-air mixture, inherent in atmospheric turbulent dispersion (Section 3.1), generally prevents the propagation of a detonation (Van den Berg 1987). The severe explosion on December 7, 1970, at Port Hudson, Missouri, where nearly all of a large, unconfined vapor cloud detonated, is attributable to several exceptional coincidences. Those included the location, which was a shallow valley, the calm atmospheric conditions, and the exceptionally long ignition delay all of which provided the opportunity for molecular diffusion to mix the dense propane cloud sufficiently with air (NTSB report 1972 and Burgess and Zabetakis 1973). The subsequent detonation is unprecedented among documented incidents. Therefore, in the vast majority of cases, the assumption of deflagrative combustion is a sufficiently safe approach to vapor cloud explosion hazard assessment. Experimental research during the last decade (Section 4.1) has shown clearly that deflagrative combustion generates blast only in those portions of a quiescent vapor cloud which are sufficiently obstructured and/or partially confined (Zeeuwen et al. 1983; Harrison and Eyre 1987; Harris and Wickens 1989; Van Wingerden 1989a). The conclusion that a partially confined and/or obstructed environment is conducive to deflagrative explosive combustion has now found wide acceptance (Tweeddale 1989). Moreover, those cloud portions already in turbulent motion when ignition occurs may develop explosive, blast-generative combustion. Consequently, high-velocity, intensely turbulent jets within a flammable-vapor cloud (Section 4.1.2), such as those resulting from fuel releases from high-pressure sources, should be viewed as possible blast sources. The remaining portions of a cloud containing a flammable vapor-air mixture burn out slowly without contributing significantly to blast. This model is called the Multi-Energy concept. Contrary to other modeling methods, in which a vapor cloud explosion is regarded as an entity, the Multi- Energy concept defines a vapor cloud explosion as a number of sub-explosions corresponding to the various sources of blast in the cloud.

19 Figure Vapor cloud containing two blast-generative objects. Figure 4.23 illustrates two common blast-generators: chemical plants and railcar switching yards (Baker et al. 1983), each blanketed in a large vapor cloud. The blast effects from each should be considered separately. Blast effects can be represented by a number of blast models. Generally, blast effects from vapor cloud explosions are directional. Such effects, however, cannot be modeled without conducting detailed numerical simulations of phenomena. If simplifying assumptions are made, that is, the idealized, symmetrical representation of blast effects, the computational burden is eased. An idealized gas-explosion blast model was generated by computation; results are represented in Figure Steady flame-speed gas explosions were numerically simulated with the BLAST-code (Van den Berg 1980), and their blast effects were calculated. Figure 4.24 represents the blast characteristics of a hemispherical fuel-air charge of radius R 0 on the earth's surface, derived for a fuel-air mixture with a heat of combustion of 3.5 X 10 6 J/m 3. The charts represent only the most significant blast-wave parameters: side-on peak overpressure (AP 8 ) and the positive-phase blastwave duration (7*) as a function of distance from the blast center (R). The data are fully nondimensionalized, with charge combustion energy (E) and parameters characterizing the state of the ambient atmosphere: pressure (P 0 ) and speed of sound (CQ). This way of scaling (Sachs scaling) takes into account the influence of atmospheric conditions. Moreover, Sachs scaling allows the blast parameters to be read in any consistent set of units. Initial blast strength in Figure 4.24 is represented by a number ranging from 1 (very low strength) up to 10 (detonative strength). The initial blast strength number is indicated in the charts at the location of the charge radius. In addition, Figure 4.24 gives a rough indication of the blast-wave shape, which corresponds to the characteristic behavior of a gas-explosion blast. Pressure waves, produced by fuel-air charges of low strength, show an acoustic overpressure decay behavior and a constant positive-phase duration. On the other hand, shock waves in the vicinity of a charge of high initial strength exhibit a more rapid overpressure decay and a substantial increase in positive-phase duration. Eventually,

20 combustion energy-scaled distance (R) combustion energy-scaled distance (R) p o = atmospheric pressure C 0 = atmospheric sound speed E = amount of combustion energy R 0 = charge radius Figure Fuel-air charge blast model.

21 the high-strength blast develops a behavior approximating acoustic decay in the far field. Another significant feature is that, at a distance larger than about 10 charge radii from the center, a fuel-air charge blast is more-or-less independent of initial strength for values of 6 (strong deflagration) and above. In the application of the multienergy concept, a particular vapor cloud explosion hazard is not determined primarily by the fuel-air mixture itself but rather by the environment into which it disperses. The environment constitutes the boundary conditions for the combustion process. If a release of fuel is anticipated somewhere, the explosion hazard assessment can be limited to an investigation of the environment's potential for generating blast. The procedure for employing the multienergy concept to model vapor cloud explosion blast can be divided into the following steps: Assume that blast modeling on the basis of deflagrative combustion is a sufficiently safe and conservative approach. (The basis for this assumption is that an unconfined vapor cloud detonation is extremely unlikely; only a single event has been observed.) Identify potential sources of strong blast present within the area covered by the flammable cloud. Potential sources of strong blast include extended spatial configuration of objects such as process equipment in chemical plants or refineries and stacks of crates or pallets; spaces between extended parallel planes, for example, those beneath closely parked cars in parking lots, and open buildings, for example, multistory parking garages; spaces within tubelike structures, for example, tunnels, bridges, corridors, sewage systems, culverts; an intensely turbulent fuel-air mixture in a jet resulting from release at high pressure. The remaining fuel-air mixture in the cloud is assumed to produce a blast of minor strength. Estimate the energy of equivalent fuel-air charges. Consider each blast source separately. Assume that the full quantities of fuel-air mixture present within the partially confined/obstructed areas and jets, identified as blast sources in the cloud, contribute to the blasts. Estimate the volumes of fuel-air mixture present in the individual areas identified as blast sources. This estimate can be based on the overall dimensions of the areas and jets. Note that the flammable mixture may not fill an entire blast-source volume and that the volume of equipment should be considered where it represents an appreciable proportion of the whole volume. Calculate the combustion energy E [J] for each blast by multiplication of the individual volumes of mixture by 3.5 X 10 6 J/m 3. This value (3.5 x

22 10 6 J/m 3 ) is a typical one for the heat of combustion of an average stoichiometric hydrocarbon-air mixture (Harris 1983). Estimate strengths of individual blasts. A safe and most conservative estimate of the strength of the sources of strong blast can be made if a maximum strength of 10 is assumed. However, a source strength of 7 seems to more accurately represent actual experience. Furthermore, for side-on overpressures below about 0.5 bar, no differences appear for source strengths ranging from 7 to 10. The blast resulting from the remaining unconfined and unobstructed parts of a cloud can be modeled by assuming a low initial strength. For extended and quiescent parts, assume minimum strength of 1. For more nonquiescent parts, which are in low-intensity turbulent motion, for instance, because of the momentum of a fuel release, assume a strength of 3. If such an approach results in unacceptably high overpressures, a more accurate estimate of initial blast strength may be determined from the growing body of experimental data on gas explosions (reviewed in Section 4.1), or by performing an experiment tailored to the situation in question. Another very promising possibility is the application of numerical simulation by use of advanced computational fluid dynamic codes, such as FLAGS (Hjertager 1982, 1989), EXSIM (Hjertager 1991), PHOENICS (Kjaldman and Huhtanen 1985) or REAGAS (Van den Berg 1989), outlined in Section Van den Berg et al. (1991) demonstrated one way to use such codes for vapor cloud explosion blast modeling. An example of the use of these advanced codes is shown in Appendix F. Further definition of initial blast strength is, however, a major research need that is so far unmet. Once the energy quantities E and the initial blast strengths of the individual equivalent fuel-air charges are estimated, the Sachs-scaled blast side-on overpressure and positive-phase duration at some distance R from a blast source can be read from the blast charts in Figure 4.24 after calculation of the Sachsscaled distance: where R = Sachs-scale distance from charge (-) R = real distance from charge (m) E = charge combustion energy (J) P 0 = ambient pressure (Pa) (4.43) The real blast side-on overpressure and positive-phase duration can be calculated from the Sachs-scaled quantities: P 8 = A/> s - P 0 (4.44)

23 and where PS^ = side-on blast overpressure (Pa) AP 8 = Sachs-scaled side-on blast overpressure (-) P 0 = ambient pressure (Pa) t + = positive-phase duration (s) t + = Sachs-scaled positive-phase duration (-) E = charge combustion energy (J) C 0 = ambient speed of sound (m/s) (4.45) If separate blast sources are located close to one another, they may be initiated almost simultaneously. Coincidence of their blasts in the far field cannot be ruled out, and their respective blasts should be superposed. The safe and most conservative approach to this issue is to assume a maximum initial blast strength of 10 and to sum the combustion energy from each source in question. Further definition of this important issue, for instance the determination of a minimum distance between potential blast sources so that their individual blasts may be considered separately, is a factor in present research. If environmental and atmospheric conditions are such that vapor cloud dispersion can be expected to be very slow, the possibility of unconfined vapor cloud detonation should be considered if, in addition, a long ignition delay is likely. In that case, the full quantity of fuel mixed within detonable limits should be assumed for a fuel-air charge whose initial strength is maximum Special Methods In the overview of experimental research, it was shown that explosive, blastgenerating combustion in gas explosions is caused by intense turbulence which enhances combustion rate. On one hand, turbulence may be generated during a gas explosion by an uncontrolled feedback mechanism. A turbulence-generative environment, in the form of partially confining or obstructing structures, must be present for this mechanism to be triggered. On the other hand, turbulence may also be generated by external sources. For example, fuels are often stored in vessels under pressure. In the event of a total vessel failure, the liquid will flash to vapor, expanding rapidly and producing fast, turbulent mixing. Should a small leak occur, fuel will be released as a high-velocity, turbulent jet in which the fuel is rapidly mixed with air. If such an intensely turbulent fuel-air mixture is ignited, explosive combustion and blast can result.

24 Special methods tailored to these phenomena have been developed for modeling such effects. These methods consist of a collection of experimental data framed in graphs or semiempirical expressions. Explosively Dispersed Vapor Cloud Explosions (Giesbrecht et al. 1981). The Giesbrecht et al. (1981) model is based on a series of small-scale experiments in which vessels of various sizes ( ) containing propylene were ruptured. (See Section 4.1.2, especially Figure 4.5.) Flame speed, maximum overpressure, and positive-phase duration observed in explosively dispersed clouds are represented as a function of fuel mass. The solid lines in Figure 4.5 represent extrapolations of experimental data to full-scale vessel bursts on the basis of dimensional arguments. Attendant overpressures were computed by the similarity solution for the gas dynamics generated by steady flames according to Kuhl et al. (1973). Overpressure effects in the environment were determined assuming acoustic decay. The dimensional arguments used to scale up the turbulent flame speed, based on an expression by Damkohler (1940), are, however, questionable. Exploding Jets (Stock et al. 1989). Stock et al. (1989) collected experimental data obtained in two different programs on exploding jets: a program on natural gas and hydrogen jets by Seifert and Giesbrecht (1986), and a program on propane jets by Stock (1987). These tests have been described in Section 4.1.2; a summary of general conclusions follows. Overpressure within a vapor cloud is dependent upon outflow velocity, orifice diameter, and laminar flame speed expressed in the following semi-empirical relation: where ^max = in-cloud overpressure (Pa) M 1 = laminar flame speed (m/s) M 0 = outflow velocity (m/s) J 0 = orifice diameter (m) P max = (constant)^ 8X^0) 09 (4.46) The semiempirical theory underlying this equation can be extended to describe blast overpressure decay. If acoustic behavior is assumed, results can be framed in the following expression for blast overpressure as a function of distance from the blast center. where for natural gas: a = 840, b = 23 for hydrogen: a = 3728, b = 55 P = (au Q 9 d l b)/r (4.47)

25 P overpressure at distance r r = distance from blast center (Pa) (m) 4.4. SUMMARY AND DISCUSSION The great attractiveness of TNT equivalency methods is the very direct, empirical relation between a charge weight of TNT and resulting strucural damage. Therefore, TNT equivalency is a useful tool for calculating the property-damage potential of vapor clouds. The various methods reviewed, however, cover a large range of values for TNT equivalency which all are, in some sense, applicable. TNT equivalencies given by the sources identified below are based upon averages deduced from damage observed in a limited number of major vapor cloud explosion incidents: Brasie and Simpson: 2%-5% of the heat of combustion of the quantity of fuel spilled. The UK Health & Safety Executive: 3% of the heat of combustion of the quantity of fuel present in the cloud. Exxon: 3%-10% of the heat of combustion of the quantity of fuel present in the cloud. Industrial Risk Insurers: 2% of the heat of combustion of the quantity of fuel spilled. Factory Mutual Research Corporation: 5%, 10%, and 15% of the heat of combustion of the quantity of fuel present in the cloud. These figures can be used for predictive purposes to extrapolate "average major incident conditions" to situations under study, provided the actual conditions under study correspond reasonably well with "average major incident conditions." Such a condition may be broadly described as a spill of some tens of tons of a hydrocarbon in an environment with local concentrations of obstructions and/or partial confinement, for example, the site of an "average" refinery or chemical plant with dense process equipment or the site of a railroad marshaling yard with a large number of closely parked rail cars. It must be emphasized that the TNT equivalencies listed above should not be used in situations in which "average major incident conditions" do not apply. A more deterministic estimate of a vapor cloud's blast-damage potential is possible only if the actual conditions within the cloud are considered. This is the starting point in the multienergy concept for vapor cloud explosion blast modeling (Van den Berg 1985). Harris and Wickens (1989) make use of this concept by suggesting that blast effects be modeled by applying a 20% TNT equivalency only to that portion of the vapor cloud which is partially confined and/or obstructed.

26 TNT blast is, however, a poor model for a gas explosion blast. In particular, the shape and positive-phase duration of blast waves induced by gas explosions are poorly represented by TNT blast. Nevertheless, TNT-equivalency methods are satisfactory, so long as far-field damage potential is the major concern. If, on the other hand, a vapor cloud's explosive potential is the starting point for, say, advanced design of blast-resistant structures, TNT blast may be a less than satisfactory model. In such cases, the blast wave's shape and positive-phase duration must be considered important parameters, so the use of a more realistic blast model may be required. A fuel-air charge blast model developed through the multienergy concept, as suggested by Van den Berg (1985), results in a more realistic representation of a vapor cloud explosion blast. Because it is usually very difficult to evaluate beforehand the conditions which may induce an initial blast, a conservative approach is to apply an initial blast strength of 10 to the fuel-air charge blast model. This model, however, offers possibilities for future development. The multienergy approach allows experimental data and advanced computational methods to be incorporated in blast modeling procedures. A database containing a complete overview of data on vapor cloud explosion incidents and gas explosion experiments should be developed for this purpose. Such a database could be used to easily and inexpensively determine more appropriate values for initial blast strength. A database cannot, however, possibly cover all situations that may arise in practice. These voids could be filled by computed values. Therefore, the design and development of computer codes, such as FLAGS (Hjertager 1982 and 1989) and REAGAS (Van den Berg 1989), are of paramount importance. Although the model of spherical fuel-air charge blast is the most realistic available, it is nevertheless a highly idealized concept that, at best, applies only to the far field. Near-field blast effects are mostly directional as a consequence of a preferential direction in the combustion process induced by partial confinement. In addition, structural blast loading is influenced largely by neighboring objects. Such effects can only be studied and quantified by simulation with multidimensional numerical methods such as BLAST (Van den Berg 1980). Codes such as REAGAS and BLAST could be utilized in vapor cloud explosion hazard analysis, as described by Van den Berg et al. (1991). REFERENCES Army, Navy, and Air Force Manual "Structures to resist the effects of accidental explosions." TM , NAVFAC P-397, AFR Revision 1. Auton, T. R., and J. H. Pickles. 1978, "The calculation of blast waves from the explosion of pancake-shaped vapor clouds." Central Electricity Research Laboratories note No. RD/L/N 210/78. Auton, T. R., and J. H. Pickles Deflagration in heavy flammable vapors. Inst. Math. Appl. Bull. 16:

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