Theory and Experiment

Transcription

1 Previous Page for a vertical surface was used. The "hazard range to severe burns" proposed by Lihou and Maund (1982) would be 600 m for this fireball. Table 6.9 tabulates distances at which the thermal effects described by CCPS (1989) occur. There is reasonable agreement between these values and those given by Pietersen. Leaf-browning at 1200 m agrees with the threshold value of 1050 m for wood combustion. The fact that glass is broken and cloth is ignited at a distance of 600 m is, in a broad sense, in reasonable agreement with the threshold value for equipment damage. Nevertheless, it is difficult to comment on the validity of models because available damage information is limited, even though the San Juanico accident is presently one of the best-described BLEVE accidents BLAST EFFECTS OF BLEVEs AND PRESSURE-VESSEL BURSTS This section addresses the effects of BLEVE blasts and pressure vessel bursts. Actually, the blast effect of a BLEVE results not only from rapid evaporation (flashing) of liquid, but also from the expansion of vapor in the vessel's vapor (head) space. In many accidents, head-space vapor expansion probably produces most of the blast effects. Rapid expansion of vapor produces a blast identical to that of other pressure vessel ruptures, and so does flashing liquid. Therefore, it is necessary to calculate blast from pressure vessel rupture in order to calculate a BLEVE blast effect. This section first presents literature review on pressure vessel bursts and BLEVEs. Evaluation of energy from BLEVE explosions and pressure vessel bursts is emphasized because this value is the most important parameter in determining blast strength. Next, practical methods for estimating blast strength and duration are presented, followed by a discussion of the accuracy of each method. Example calculations are given in Chapter Theory and Experiment The rapid expansion of a vessel's contents after it bursts may produce a blast wave. This expansion causes the first shock wave, which is a strong compression wave TABLE 6.9. Calculated Distances from Radiation Flux Given by CCPS (1989) for a BLEVE at San Juanico Radiation Intensity Distance Effect (kw/m 2 ) (m) Level of minor discomfort Threshold of pain Combustion of wood threshold Hazardous for equipment level

2 in the surrounding air traveling from the explosion center at a velocity greater than the speed of sound. The fluid expands spherically and does not mix immediately with the surrounding air, so a sort of fluid "bubble" is formed which has an interface with surrounding air. The released fluid's momentum causes it to overexpand, and the pressure within the bubble then drops below ambient pressure. After the fluid bubble reaches its maximum diameter, it collapses again, thus producing a phase of negative pressure and reversed wind direction in the surrounding air. The bubble rebounds upon reaching its minimum diameter, thus producing a second shock. The bubble will continue to oscillate before coming to rest, producing ever-smaller pressure waves. The most important blast-wave parameters are peak overpressure p s and positive impulse i s, as shown in Figure The deep negative phase and second shock are clearly visible in this figure. The strength and shape of a blast wave produced by a sudden release of fluid depends on many factors, including type of fluid released, energy it can produce in expansion, rate of energy release, shape of the vessel, type of rupture, and character of surroundings (i.e., the presence of wave-reflecting surfaces and ambient air pressure). The type of fluid is very important. It can be a gas, a superheated liquid, a liquid, or some combination of these. Unsuperheated liquid cannot produce a blast, so the volume of unsuperheated liquid in a vessel need not be considered. In the following subsections, a selection of the theoretical and experimental work on pressure vessel bursts and BLEVEs will be reviewed. Attention will first be focused on an idealized situation: a spherical, massless vessel filled with ideal pressure (psi) time (sec) Figure Pressure-time history of a blast wave from a pressure vessel burst (Esparza and Baker 1977a).

3 gas and located high above the ground. Increasingly realistic situations will be discussed in subsequent subsections Free-Air Bursts of Gas-Filled, Massless, Spherical Pressure Vessels The pressure vessel under consideration in this subsection is spherical and is located far from surfaces that might reflect the shock wave. Furthermore, it is assumed that the vessel will fracture into many massless fragments, that the energy required to rupture the vessel is negligible, and that the gas inside the vessel behaves as an ideal gas. The first consequence of these assumptions is that the blast wave is perfectly spherical, thus permitting the use of one-dimensional calculations. Second, all energy stored in the compressed gas is available to drive the blast wave. Certain equations can then be derived in combination with the assumption of ideal gas behavior. Experimental Work. Few experiments measuring the blast from exploding, gasfilled pressure vessels have been reported in the open literature. One was performed by Boyer et al. (1958). They measured the overpressure produced by the burst of a small, glass sphere which was pressurized with gas. Pittman (1972) performed five experiments with titanium-alloy pressure vessels which were pressurized with nitrogen until they burst. Two cylindrical tanks burst at approximately 4 MPa, and three spherical tanks burst at approximately 55 MPa. The volume of the tanks ranged from m 3 to m 3. A few years later, Pittman (1976) reported on seven experiments with m 3 steel spheres that were pressurized to extremely high pressures with argon until they burst. Nominal burst pressures ranged from 100 MPa to 345 MPa. Experiments were performed just above ground surface. Finally, Esparza and Baker (1977a) conducted twenty small-scale tests in a manner similar to that of Boyer et al. (1958). They used glass spheres of 51 mm and 102 mm diameter, pressurized with either air or argon, to overpressures ranging from 1.22 MPa to 5.35 MPa. They recorded overpressures at various places and filmed the fragments. From these experiments, it was learned that, compared to the shock wave produced by a high explosive, shock waves produced by bursting gasfilled vessels have lower initial overpressures, longer positive-phase durations, much larger negative phases, and strong second shocks. Figure 6.11 depicts such a shock. Pittman (1976) also found that the blast can be highly directional, and that real gas effects must be dealt with at high pressures. Numerical Work. The results of experiments described above can be better understood when compared to the results of numerical and analytical studies. Numerical studies, in particular, provide real insight into the shock formation process. Chushkin and Shurshalov (1982) and Adamczyk (1976) provide comprehensive reviews of the many studies in this field. The majority of these studies were performed for military purposes and dealt with blast from nuclear explosions, high explosives, or

4 fuel-air explosions (FAEs: detonations of unconfined vapor clouds). However, many investigators studied (as a limiting case of these detonations) blast from volumes of high-pressure gas as well. Only the most important contributions will be reviewed here. Many numerical methods have been proposed for this problem, most of them finite-difference methods. Using a finite-difference technique, Erode (1955) analyzed the expansion of hot and cold air spheres with pressures of 2000 bar and 1210 bar. The detailed results allowed Erode to describe precisely the shock formation process and to explain the occurrence of a second shock. The process starts with expansion from the initial volume. This creates a shock wave in the surrounding air, called the main shock, which travels faster than the contact surface of gases originally present in the bursting vessel and ambient air. At the same time, a rarefaction wave is created which depressurizes the gas in the vessel. Behind this wave, an inwardly moving shock forms. It does not acquire a net inward velocity until the rarefaction wave has reached the center, but after that, it moves inward and reflects at the origin. This reflected shock moves outward toward the contact surface. At the time it strikes the contact surface, the gases at the contact surface are more dense and much cooler than surrounding air. Consequently, the shock is partially reflected on the contact surface. The portion that is transmitted is called the second shock; it may eventually overtake the main shock. Baker et al. (1975) used a finite-difference method with artificial viscosity to obtain blast parameters of spherical pressure vessel explosions. They calculated twenty-one cases, varying pressure ratio between vessel contents (gas) and surrounding atmosphere, temperature ratio, and ratio of the specific heats of the gases. They used ideal-gas equations of state. Their research was aimed at deriving a practical method to calculate blast parameters of bursting pressure vessels, so they synthesized the results into graphs presenting shock overpressure and impulse as a function of energy-scaled distance (Figures 6.21 and 6.23, pages 207 and 210). The method of Baker et al. is the best practical method for calculating the blast parameters of pressure vessel bursts. It will be described in detail in Section Baker et al. assume, as the standard model for this method, a free-air burst of a spherical vessel. Baker et al. provide the following guidelines for adapting this method to surface bursts of nonspherical vessels: Multiply the energy of the explosion by 2 to conservatively account for the earth's reflection of the shock wave, and multiply by distance-dependent multiplication factors to account for the nonsymmetrical shock wave. The latter multiplication factors were determined experimentally for high explosives. In Section , instead of a free-air burst, a surface burst of a spherical vessel is assumed as the standard model, and the procedure is rearranged. Otherwise, no modifications were made to the Baker et al. method. A comparison of numerical results contained in Figures 6.21 and 6.23 with the experimental results of Esparza and Baker (1977) indicates that values in Figure 6.21 overstate slightly the shock overpressure, even after taking into account the kinetic energy absorbed by fragments. Impulses compare well.

5 Adamczyk (1976) noted that this work shows that equivalence with high explosives is usually attained only in the far field for high bursting-pressure ratios and temperature ratios. When low bursting-pressure ratios or temperature ratios are used, overpressure curves do not coalesce in the far field; hence, equivalence with high explosives may not be attained. He noted that many of the curves that do not coalesce are those with gases whose sound speeds are relatively low speeds. Such curves represent situations in which the potential energy within the sphere is not converted efficiently to kinetic energy of the medium. Such conversion depends on propagation of the rarefaction wave into surrounding gas. However, since this wave propagates at sonic velocity, a considerable time lapses before it releases the energy stored in the high-pressure gas. This analysis suggests that the rate of conversion of potential energy to the surrounding gas can be an important parameter in blastphenomena considerations. Guirao and Bach (1979) used the flux-corrected transport method (a finitedifference method) to calculate blast from fuel-air explosions (see also Chapter 4). Three of their calculations were of a volumetric explosion, that is, an explosion in which the unburned fuel-air mixture is instantaneously transformed into combustion gases. By this route, they obtained spheres whose pressure ratios (identical with temperature ratios) were 8.3 to 17.2, and whose ratios of specific heats were to Their calculations of shock overpressure compare well with those of Baker et al. (1975). In addition, they calculated the work done by the expanding contact surface between combustion products and their surroundings. They found that only 27% to 37% of the combustion energy was translated into work. Analytical Work. Analytical work performed on pressure vessel explosions can be divided into two main categories. The first attempts to describe shock, and the second is concerned with the thermodynamic process. The peak overpressure developed immediately after a burst is an important parameter for evaluating pressure vessel explosions. At that instant, waves are generated at the edge of the sphere. The wave system consists of a shock, a contact surface, and rarefaction waves. As this wave system is established, pressure at the contact surface drops from the pressure within the sphere to a pressure within the shock wave. Initial shock-wave overpressure can be determined from a one-dimensional technique. It consists of using conservation equations for discontinuities through the shock and isentropic flow equations through the rarefaction waves, then matching pressure and flow velocity at the contact surface. This procedure is outlined in Liepmann and Roshko (1967) for the case of a bursting membrane contained in a shock tube. From this analysis, the initial overpressure at the shock front can be calculated with Eq. (6.3.22). This pressure is not only coupled to the pressure in the sphere, but is also related to the speed of sound and the ratio of specific heats. The explosion process can also be described in thermodynamic terms. In this approach, the states of the gases before the beginning and after the completion of

6 the explosion process are compared. Explosion energy can thus be calculated. This energy is a very important parameter because, of all the variables, it has the greatest influence on blast parameters and thus on the destructive potential of an explosion. The thermodynamic method has limitations. Since the method ignores the intermediate stages, it cannot be used to determine shock-wave parameters. Furthermore, a shock wave is an irreversible thermodynamic process; this fact complicates matters if these energy losses are to be fully included in the analysis. Nevertheless, the thermodynamic approach is a very attractive way to obtain an estimate of explosion energy because it is very easy and can be applied to a wide range of explosions. Therefore, this method has been applied by practically every worker in the field. Unfortunately, there is no consensus on the measure for defining the energy of an explosion of a pressure vessel. Erode (1959) proposed to define the explosion energy simply as the energy, e x,br» that must be employed to pressurize the initial volume from ambient pressure to the initial pressure, that is, the increase in internal energy between the two states. The internal energy U of a system is the sum of the kinetic, potential, and intramolecular energies of all the molecules in the system. For an ideal gas it is where U = internal energy (J) p = absolute pressure (Pa) V = volume (m 3 ) 7 = ratio of specific heats of gas in system (-) Therefore C x,br * s (6.3.1) (6.3.2) where the subscript 1 refers to initial state and the subscript O refers to ambient conditions. Other investigators use the work done by the expanding surface between the gases originally in the vessel and the surroundings as the energy of the explosion, /s ex wo. The system expands from state 1 (the initial state) to state 2, with p 2 equal to the ambient pressure p Q. After expansion, it has a residual internal energy U 2. The work which the system can perform is the difference between its initial and residual internal energies. ex,wo ^U 1 -U 2 (6.3.3) where C x,wo * s ^16 wor k performed in expansion from state 1 to state 2.

7 Thus, for an ideal gas, the work is (6.3.4) For an ideal gas, pv 1 is constant for isentropic expansion (that is, without energy addition or energy loss). Therefore, V 2 * s: This gives, for the work: (6.3.5) (6.3.6) It is illustrative to compare work ex>wo with added energy E txbr. The ratio e x,w</ E cx Br can be written as f^ = J- [(I - P 1 ) - (1 + P 1 )I 1^i (6.3.7) ^ex,br PI where P 1 is the nondimensional overpressure in the initial state (P 1 Tp 0 ) - 1- This function is depicted in Figure Investigators of vapor cloud explosions (Chapter 4) often use the combustion energy as a measure for the energy of the explosion. This energy heats, and thereby pressurizes, the initial volume. Combustion energy is equal to the change in internal energy from the unburned state to the burned state (without expansion). Thus, combustion energy is similar to Brode's definition of explosion energy. However, during combustion, the ratio of specific heats changes, thus creating a difference of a few percent. Adamczyk (1976) is one of the few who tried to incorporate energy losses from the irreversible shock process into the calculation. He proposes to use the work done by gas volume in a process illustrated in Figure 6.12 and described below. At the instant a pressure vessel ruptures, pressure at the contact surface is given by Eq. (6.3.22). The further development of pressure at the contact surface can only be evaluated numerically. However, the actual p- V process can be adequately approximated by the dashed curve in Figure In this process, the constantpressure segment represents irreversible expansion against an equilibrium counterpressure p 3 until the gas reaches a volume V 3. This is followed by an isentropic expansion to the end-state pressure p Q. For this process, the point (p 3, V 3 ) is not on the isentrope which emanates from point (p l9 V 1 ), since the first phase of the expansion process is irreversible. Adamczyk calculates point (p 3, V 3 ) from the conservation of energy law and finds (6.3.8)

8 Figure p-v diagram showing actual and assumed path process for a bursting sphere (Adamczyk 1976). If a new variable, = PsJLA> (6<3.9) Pi ~ Po is defined, E ex)m /E exer for the entire process can be expressed as a function of, P 1, and Tf 1. ](6.3.10) The first term is due to the irreversible expansion from V 1 to V 3, and the second term to the isentropic expansion from V 3 to V 2. Adamczyk does not actually say how p 3 should be chosen. A reasonable choice for p 3 seems to be the initial-peak shock overpressure, as calculated from Eq. (6.3.22). The equation presented above can be compared to the results of Guirao et al. (1979). They numerically evaluated the work done by the expanding contact surface. When the difference between

9 combustion energy and Brode's energy is taken into account, their results are about 10% lower than those resulting from Eq. (6.3.10). This small difference indicates that Eq. (6.3.10) is reasonably accurate. Aslanov and Golinskii (1989) give yet another definition of explosion energy. They say that use of the work done by gas expansion underestimates the energy. The alternative they propose is derived from a rigorous thermodynamic analysis. Imagine an arbitrary control surface enclosing a volume V c. (The pressure vessel is somewhere inside the control volume.) Before the vessel bursts, the internal energy inside the control volume is (for an ideal gas) (6.3.11) where ^0 is the ratio of specific heats of ambient air. After the explosion, the pressure eventually equals the ambient pressure, and the internal energy becomes Therefore, the energy E cxag that has crossed the control surface is (6.3.12) (6.3.13) The difference between this equation and the equation for ex, W o is that the internal energy of the air that is displaced by the expanded gases is taken into account. Note that, when ^1 is equal to ^0, Eq. (6.3.13) is equivalent to Eq. (6.3.2). Aslanov and Golinskii advocate the use of the energy E exag as the energy of the explosion. They claim that this gives a better correlation with numerical calculations and with experiments. In Figures 6.13, 6.14, and 6.15, the proposed measures for the explosion energy are compared. Figure 6.13 gives the ratio E exwo /E eker for three values of the ratio of specific heats of the pressurized gas, and Figure 6.14 does the same for e x,ag^ex,br Figure 6.15 gives an impression of the ratio E GxM /E^BT for Adamczyk's definition of the explosion energy. This ratio is different for every type of gas. In this figure, the pressurized gas was air of 300, 3000, and 30,000 K. The ambient air was at a pressure of 1 bar and a temperture of 300 K. Analysis of Figures makes it clear that the four definitions give widely varying results. They all approach Brode's equation for high initial overpressures, but for initial pressures of practical interest, the results vary by a factor of 4. Thus, there is no consensus on the definition of the most important variable of an explosion, its energy. All experimental and most numerical results given in the literature use Brode's definition. However, when the fluid is a nonideal gas or a liquid, almost everyone uses the work done in expansion as the explosion energy (see Section ). The available prediction methods for blast parameters are based on these two, conflicting, definitions.

10 Pressure (P 1 Xp 0 -D r=1.66 y=1.4 r=1.2 Figure Comparison between energy definitions: E exiwo /^ex,bf Pressure (P 1 Xp 0 -D Figure Comparison between energy definitions: E wag /E ektbr.

11 Pressure (P 1 Xp 0 -D E w A J 1 XT 0 O T/TO + T/T 0 y= OO Figure Comparison between energy definitions: exiad / exibr Surface Bursts of Gas-Filled, Massless, Spherical Pressure Vessels In the previous subsection, an idealized configuration was studied. In this and following subsections, the influences of the neglected factors will be discussed. When an explosion takes place at the surface of the earth or slightly above it, the shock wave produced by the explosion will reflect on the earth's surface. The reflected wave overtakes the first wave and increases its strength. The resulting shock wave is similar to a shock wave which would be produced in free air by the original explosion together with its mirror image. This subject has received little attention in the context of pressure vessel bursts. Pittman (1976) studied it using a two-dimensional numerical code. However, his results are inconclusive, because the number of cases he studied was small and because the grid he used was coarse. Baker et al. (1975) recommend, on the basis of experimental results with high explosives, the use of a method described in detail in Section That is, multiply the volume of the explosion by 2, read the overpressure and impulse from graphs for free-air bursts, and multiply them by a factor depending on the range Nonspherical Bursts of Gas-Filled, Massless Pressure Vessels When a pressure vessel is not a sphere, or if the vessel does not fracture evenly, the resulting blast wave will be nonspherical. This, of course, is the case in almost every actual pressure vessel burst. Loss of symmetry means that detailed calculations

12 lead wave cloud interface Figure Positions of interface and lead shock versus time for a spheroid burst (Raju and Strehlow 1984). and experimental measurements become much more complicated, because the calculations and measurements must be made in two or three dimensions instead of one. Numerical calculations of bursts of pressurized-spheroid gas clouds were made by Raju and Strehlow (1984) and by Chushkin and Shurshalov (1982). Raju and Strehlow (1984) compute the expansion of a gas cloud corresponding to a constant volume combustion of a methane-air mixture (P 1 Tp 0 = 8.9, ^1 = 1.2). In Figure 6.16, the region originally occupied by the gas cloud is shaded, and the position and shape of the shock wave and the contact surface at different times following the explosion are shown as solid and dashed curves. The shape of the shock wave is almost elliptical, with ellipticity decaying to sphericity as the shock gradually degenerates into an acoustic wave. Scaled peak overpressure and positive impulse as a function of scaled distance are given in Figures 6.17 and The scaling method is explained in Section 3.4. Figures 6.17 and 6.18 show that the shock wave along the axis of the vessel is initially approximately 50% weaker than the wave normal to its axis. Since strong shock waves travel faster than weak ones, it is logical that the shape of the shock wave approaches spherical in the far field. Shurshalov (Chushkin and Shurshalov

13 1982) performed a similar calculation; results confirmed those of Raju and Strehlow (1984). Shurshalov also found that the shock wave approaches a spherical shape more rapidly when the explosion is stronger. Even greater differences in shock pressure can be found when the pressure vessel does not burst evenly, but ruptures into two or three pieces. In that case, a jet emanates from the rupture, and the shock wave becomes highly directional. Pittman (1976) found experimental overpressures along the line of the jet to be greater, by a factor of four or more, than pressures along a line in the opposite direction from the jet. Baker et al. (1978b) tried to analyze, with a two-dimensional numerical code, the case of a spherical vessel bursting into two equal parts. They may have used a massless vessel in their calculations, but their vessel probably had a mass typical of normal storage vessels. This is not clear from their description. Baker et al. analyzed only six cases, including three different overpressures and three ratios of specific heat, each at ambient temperature. In addition, they had to use a large cell size because of limitations in computer power. They found that overpressures along the line of the jet could be predicted by a method similar to the one they presented for spherical bursts, which is described in Section The main difference is that the starting point must be chosen at a lower overpressure, PHl=O 2-- = = 90 BAKER'S PENTOLITE 5--BURSTING SPHERE MAX OVERPRESSURE Pe 2> DISTANCE (ENERGY SCALED) R Figure P 8 versus R generated by a spheroid burst (Raju and Strehlow 1984). fl = '(Po/W 3. / 3 S = Ps/Po ~ L

14 1--PHI=O 2--PHI=45 3--PHI = BAKER 1 S PENTOLITE 5--BURSTlNG SPHERE IMPULSE (ENERGY SCALED) j c o DISTANCE(ENERGYSCALED) R Figure / versus R generated by a spheroid burst (Raju and Strehlow 1984). R = '(PO/W 3 ; / = (/Sa0K(Po 2^ W 3 ) P s0 instead of P s0. Therefore, this method gives overpressures for the jet of a pressure vessel rupture that are lower than the overpressures of a spherical burst. It is logical that a jet's overpressures are lower because, since overpressures outside a jet are lower than inside, the jet will spread out, thus lowering its overpressure. However, the limitations of their analysis, coupled with uncertainty as to whether the vessel was massless or not, cast doubts on the accuracy of their method Bursts of Heavy, Gas-Filled Pressure Vessels In previous sections, it has been assumed that all energy within a pressure vessel is available to drive the blast wave. In fact, energy must be spetot to rupture the vessel and propel its fragments. In some cases, the vessel expands before bursting, thus absorbing additional energy. Should a vessel also contain liquid or solids, a fraction of the available energy may be spent in its propulsion. Vessel Expansion. In most cases, vessels rupture without significant expansion. In most cases in which a vessel is exposed to external fire, the vessel wall temperature distribution is very uneven. Then, typically, only a small bulge is produced before

15 the vessel bursts. If a vessel fails as a result of mechanical attack, there is no expansion. Vessel expansion can be a significant factor if rupture results from an internal pressure build-up, but that topic is outside the scope of this volume. For these reasons, expansion of the vessel may be safely neglected. Vessel Rupture. The energy needed to rupture a vessel is very low, and can be neglected in calculation of explosion energy. For a typical steel vessel, rupture energy is on the order of 1 to 10 kj, that is, less than 1% of the energy of a small explosion. Fragments. As will be explained in Section 6.4, between 20% and 50% of available explosion energy may be transformed into kinetic energy of fragments and liquid or solid contents Blast from BLEVEs A vessel filled with a pressurized, superheated liquid can produce blasts upon bursting in three ways. First, the vapor that is usually present above the liquid can generate a blast, as from a gas-filled vessel. Second, the liquid will boil upon depressurization, and, if rapid boiling occurs, a blast will result. Third, if the fluid is combustible and the BLEVE is not fire induced, a vapor cloud explosion may occur (see Section ). In this subsection, only the first and second types of blast will be investigated. Experimental Work. Although a great many investigators studied the release of superheated liquids (that is, liquids that would boil if they were at ambient pressure), only a few have measured the blast effects that may result from release. Baker et al. (1978a) reports on a study done by Esparza and Baker (1977b) in which liquid CFC-12 was released from frangible glass spheres in the same manner as in their study of blast from gas-filled spheres. The CFC was below its superheat limit temperature. No significant blast was produced. Investigators at BASF (Maurer et al. 1977; Giesbrecht et al. 1980) conducted many small-scale experiments on bursting cylindrical vessels filled with propylene. The vessels were completely filled with liquid propylene at a temperature of around 340 K (which is higher than the superheat limit temperature J sl ) and a pressure of around 60 bar. Vessel volumes ranged from x 10~ 3 m 3 to 1.00 m 3. The vessels were ruptured with small explosive charges, and after each release, the resulting cloud was ignited. While the experiments focused on explosively dispersed vapor clouds and their subsequent deflagration, the pressure wave developed from the flashing liquid was measured. The investigators found that overpressures from the evaporating liquid compared well with those resulting from gaseous detonations of the same energy.

16 (Energy here means the work which can be done by the fluid in expansion, ex>wo.) This means that energy release during flashing must have been very rapid. As described in Section , British Gas performed full-scale tests with LPG BLEVEs similar to those conducted by BASF. The experimenters measured very low overpressures from the evaporating liquid, followed by a shock that was probably the so-called "second shock," and by the pressure wave from the vapor cloud explosion (see Figure 6.6). The pressure wave from the vapor cloud explosion probably resulted from experimental procedures involving ignition of the release. The liquid was below the superheat limit temperature at time of burst. Theoretical Work. Theoretical work on the blast from superheated liquid addresses two questions: 1. How, and under what circumstances, does the liquid flash explosively? 2. How much energy is liberated in the process? Reid (1976 and 1980) proposed the most likely explanation to the first question. His theory is described in detail in Section 6.1. (BLEVE theory). In short, Reid's theory is as follows: Before the vessel ruptures, its liquid is in equilibrium with its saturated vapor. Upon rupture, vapor blows off and liquid pressure drops rapidly. Equilibrium is lost, and liquid vaporizes vigorously at the liquid-vapor and the liquid solid interfaces. Such vaporization, however, may be insufficient to maintain pressure. If the liquid is below its superheat limit temperature, it may not boil throughout the bulk of the liquid, because forces between its molecules are stronger there than at the liquid-vapor and liquid-solid interfaces. However, if the liquid is above its superheat limit temperature when the pressure drops, further microscopic bubbles begin to form and grow. Because this phenomenon occurs almost instantaneously throughout the bulk of the liquid, a large fraction of liquid can be transformed into vapor within milliseconds. The precise timing is governed by the time it takes for the decompression wave to pass through the liquid. Instantaneous boiling takes place only if the temperature of a liquid is higher than its superheat-limit temperature T sl (also called the homogeneous-nucleation temperature), in which case, boiling occurs throughout the bulk of the liquid. This temperature is only weakly dependent on the initial pressure of the liquid and the pressure to which it depressurizes. As stated in Section 6.1., T sl has a value of about 0.89r c, where T c is the (absolute) critical temperature of the fluid. Thus, the BLEVE theory predicts that, when the temperature of a superheated liquid is below 7 sl, liquid flashing cannot give rise to a blast wave. This theory is based on the solid foundations of kinetic gas theory and experimental observations of homogeneous nucleation boiling. It is also supported by the experiments of BASF and British Gas. However, because no systematic study has been conducted, there is no proof that the process described actually governs the type of flashing that causes strong blast waves. Furthermore, rapid vaporization of a superheated liquid below its superheat limit temperature can also produce a blast wave, albeit a weak

17 one. Also, present work (Venert 1990) suggests that certain operations can cause a fluid to become pre-nucleated, which enables the fluid to flash explosively upon depressurizing. Analysis of an incident (Van Wees 1989) involving a carbon dioxide storage vessel suggests that carbon dioxide can evaporate explosively even when its temperature is below r sl. This may occur because carbon dioxide crystallizes at ambient pressure, thus presenting enough nucleation sites for liquid to flash. The theory explains why a succession of shocks may occur in BLEVEs. A first shock is produced by the escape of vapor, a second by evaporating liquid, a third by the "second shock" of the oscillating fluid bubble, and possible additional shocks produced by combustion of released fluid. It is also possible for these shocks to overlap each other, especially at greater distances from the explosion. Determination of the energy released by flashing liquid is a problem addressed by many investigators, including Baker et al. (1978b) and Giesbrecht et al. (1980). They all define explosion energy as the work done by the fluid on surrounding air as it expands isentropically. In this case, the change in internal energy must be calculated from experimentally obtained thermodynamic data for the fluid. In Section , a method is given for calculating overpressure and impulse, given energy and distance. This method produces results which are in reasonable agreement with experimental results from BASF studies. The procedure is presented in more detail by Baker et al. (1978b). Wiedermann (1986b) presents an alternative method for calculating work done by a fluid. The method uses the "lambda model" to describe isentropic expansion, and permits work to be expressed as a function of initial conditions and only one fluid parameter, lambda. Unfortunately, this parameter is known for very few fluids. TNT Equivalence. Explosion strength is often expressed as "equivalent mass of TNT' in order to permit estimates of possible explosion damage. For BLEVEs and pressure vessel bursts, using this equivalence is unnecessary because the methods mentioned above give explosion blast parameters which relate directly to the amount of possible damage potential. However, the concept of TNT equivalence is still useful because it appeals to those who seldom deal with blast parameters. For reasons explained in Section 4.3.1, BLEVEs or pressure vessel bursts cannot readily be compared to explosions of TNT (or other high explosives). Only the main points are repeated here. TNT explosions have a very high shock pressure close to the blast source. Because a shock wave is a non-isentropic process, energy is dissipated as the wave travels from the source, thus causing rapid decay of overpressures present at close range. Blast waves close to the source of pressure vessel bursts differ greatly from those from TNT blasts. The impulse at close range from a pressure vessel burst is greater than a TNT explosion with the same overpressure. Therefore, it is conservative to use

18 damage relationships which are based on nuclear explosions, such as those in Table 6.9, since the positive-phase duration of a nuclear explosion is very long. A complicating factor is that there is disagreement over the amount of energy in TNT. For these reasons, the concept of TNT equivalency appears to have little application to near-field estimates. In the method which will be presented in Section , the blast parameters of pressure vessel bursts are read from curves of pentolite, a high explosive, for nondimensional distance R above two. For these ranges, using TNT equivalence makes sense. Pentolite has a specific heat of detonation of 5.11 MJ/kg, versus 4.52 MJ/kg for TNT (Baker et al. 1983). The equivalent mass of TNT can be calculated as follows for a ground burst of a pressure vessel: where WTNT = ^ < 6 ' 3 ' 14 ) WTNT = equivalent mass of TNT (kg) /ITNT = heat of detonation of TNT (4.52 MJ/kg) E 6x = energy of explosion (J) (Calculated from procedures described in Section ) Table 6.10 presents some damage effects. It may give the impression that damage is related only to a blast wave's peak overpressure, but this is not the case. For certain types of structures, impulse and dynamic pressure (wind force), rather than overpressure, determine the extent of damage. Table 6.10 was prepared for blast waves of nuclear explosions, and generally provides conservative predictions for other types of explosions. More information on the damage caused by blast waves can be found in Appendix B Practical Methods for Calculating Blast Effects In this section, three methods for calculating the blast parameters of pressure vessel bursts and BLEVEs will be presented. All methods are related; that is, one basic method and two variations are presented. The choice of method depends upon phase of the vessel's contents and distance to the blast wave's "target," as illustrated in Figure The application of information in Figure 6.19 requires some explanation. The decision as to which calculation method to choose should be based upon the phase of the vessel's contents, its boiling point at ambient pressure T b, its critical temperature J c, and its actual temperature T. For the purpose of selecting a calculation method, three different phases can be distinguished: liquid, vapor or nonideal gas, and ideal gas. Should more than be performed separately for each phase, and the

19 TABLE Conditions of Failure of Side-on Overpressure-Sensitive Elements (Glasstone, 1957) Structural Element Glass windows Corrugated asbestos siding Corrugated steel or aluminum Wood siding panels standard house construction Concrete or cinder-block wall panels 8 or 12 inch thick (not reinforced) Self-framing steel panel building Oil storage tank Wooden utility poles Loaded rail cars Brick wall panel 8 or 1 2 inch thick (not reinforced) Failure Usually shattering, occasional frame failure Shattering Connection failure followed by buckling Failure, usually at main connections, allowing a whole panel to be blown in Shattering of wall Collapse Rupture Snapping failure Overturned Shearing, flexure failure Approx. Side-on Overpressure (bar) (psi) blast-parameter calculation should be based upon the total amount of energy released. Temperature determines whether or not the liquid in a vessel will boil when depressurized. The liquid will not boil if its temperature is below the boiling point at ambient pressure. If the liquid's temperature is above the superheat-limit temperature 7 sl (r sl = 0.89r c ), it will boil explosively (BLEVE) when depressurized. Between these temperatures, the liquid will boil violently, but probably not rapidly enough to generate significant blast waves. However, this is not certain, so it is conservative to assume that explosive boiling will occur (see Section 6.3.2). A good estimate of the range, or distance from the vessel to the "target," can only be made after initial steps of the basic method have been completed. Therefore, this point will be explained in Section along with a description of the basic method Calculation of Blast Parameters of Gas Vessel Bursts Baker et al. (1975) developed a method, presented below, for predicting blast effects from the rupture of gas-filled pressure vessels. They include a method for calculating the overpressure and impulse of blast waves from the rupture of spherical or cylindri-

20 start collect data liquid,2 ^ ideal gas phase contents) temperature calc. energy with basic method explosive flashing assume explosive flashing vapor, non-ideal gas far field range near field refined method no blast effects calc. energy with explosive flashing method calc. enen explosive flashing method end continue with basic method Figure Selection of blast-calculation method. cal vessels located at ground level. The relationship of overpressure to distance for a rupturing pressure vessel depends strongly upon the pressure, temperature, and ratio of specific heats of the contained gas. When pressures and temperatures are high, blast waves in the far field are very similar to those generated by high explosive-detonation. This similarity forms the basis for the basic method, in which the compressed gas's stored energy is first calculated, then overpressure and impulse are read from charts which relate detonation-blast parameters to charges of high explosive with the same energy. The general procedure of the basic method is shown in Figure This method is suitable for calculations of bursts of spherical and cylindrical pressure vessels which are filled with an ideal gas, placed on a flat surface, and distant from other obstacles which might interfere with the blast wave.

21 start collect data calculate energy 3 calculated R of 'target 1 step 7 of explosive flashing method check R refined method determine P 8 determine I adjust P 8 and I calc. PS and i s check P 8 end Figure Basic method.

22 Step 1: Collect data. Collect the following data: the vessel's internal pressure (absolute), p the ambient pressure, p Q the vessel's volume of gas-filled space, V 1 the ratio of specific heats of the gas, ^1 the distance from the center of the vessel to the "target," r, the shape of the vessel: spherical or cylindrical. Step 2: Calculation compressed-gas energy. The energy ex of a compressed gas is calculated as follows: where E ex = energy of compressed gas (J) P 1 = absolute pressure of gas (N/m 2 ) P 0 = absolute pressure of ambient air (N/m 2 ) V 1 = volume of gas-filled space of vessel (m 3 ) ^y 1 = ratio of specific heats of gas in system (-) (6.3.15) This energy measure is equal to Erode's definition of the energy, multiplied by a factor 2. The reason for the multiplication is that the Erode definition applies to free-air burst, while Eq. (6.3.15) is for a surface burst. In a free-air burst, explosion energy is spread over twice the volume of air. Step 3: Calculate R of the 'target. 99 Calculate the nondimensional distance of the "target," /?, with: (6.3.16) where r is the distance in meters at which blast parameters are to be determined. This scaling method is explained in Section 3.4. Step 4: Check R. For R < 2, the basic method gives too high a value for blast overpressure. In such cases, use the refined method, described in Section , to obtain a more accurate pressure estimate. Step 5: Determine P 8. To determine the nondimensional side-on overpressure P 8, read P 8 from Figure 6.21 or 6.22 for the appropriate R. Use the curve labelled "high explosive" if Figure 6.21 is used.

23 high e cplosive Figure 6.21._NondimensionaU>verpressure versus nondimensional distance for overpressure calculations R = r(po/ e x) 1/3, P 5 = Ps/Po - 1 (Baker et al. 1975).

24 Figure P 8 versus R for pentolite. R = /WE 6x ) 1 * ^s = Ps/Po - 1 (Baker et al. 1975).

25 Step 6: Determine /. To determine the nondimensional side-on impulse /, read / from Figure 6.23 or 6.24 for the appropriate R. Use the curve labeled "vessel burst." For R in the range of 0.1 to 1.0, the 7 versus R curve of Figure 6.24 is more convenient. Step 7: Adjust P s and 7 for geometry effects. The above procedure produces blast parameters applicable to a completely symmetrical blast wave, such as would result from the explosion of a hemispherical vessel placed directly on the ground. In practice, vessels are either spherical or cylindrical, and placed at some height above the ground. This influences blast parameters. To adjust for these geometry effects, P s and 7 are multiplied by some adjustment factors derived from experiments with high-explosive charges of various shapes. Tables 6.1 Ia and 6.1 Ib gives multipliers for adjusting scaled values for cylindrical vessels of various R and for spheres elevated slightly above the ground, respectively. The blast wave from a cylindrical vessel is weakest along its axis. (See Figures 6.17 and 6.18.) Thus, the blast field is asymmetrical for a vessel placed horizontally. The method will only provide maximum values for a horizontal tank's parameters. Step 8: Calculate p s9 i s. Use the following equation to calculate side-on peak overpressure p s p Q and sideon impulse i s from nondimensional side-on peak overpressure P 8 and nondimensional side-on impulse 7: (6.3.17) (6.3.18) where a Q is speed of sound in ambient air in meters per second. For sea-level average conditions, p 0 is approximately kpa and a 0 is 340 m/s. Step 9: Check p s. This method has only a limited accuracy, especially in the near field (see Section ). Under some circumstances, the calculated p s might be higher than the initial pressure in the vessel P 1, which is physically impossible. If this should happen, take P 1 as the peak pressure instead of the calculated p s Refinement for the Near Field The method presented above is based on the similarity of the blast waves of pressure vessel bursts and high explosives. This similarity holds only at some distance from the explosion. In the near field, the peak overpressure and impulse from a pressure

26 Figure / versus R for pentollte and gas vessel bursts. R = r (Po/E ex ) 1/3. / = QiPoV(Po 213 E W 1/3 ) (Baker et al. 1975). vessel burst differ greatly from those of a detonation of a high explosive, except when the pressure vessel is filled with a very hot high-pressure gas. Baker et al. (1978a) developed a method which can predict blast pressures in the near field. This method is based on results of numerical simulations (see Section ) and replaces Step 5 of the basic method (Figure 6.20). The refined method's procedure is shown in Figure 6.25.

27 vessel burst Figure / versus R for gas vessel bursts. R = r(po/e ex ) 1/3, / = (' s ao)/(po 2/3 ex 1/3 ) ( Bak r * al. 1975).

28 TABLE 6.11 a. Adjustment Factors for P 8 and / for Cylindrical Vessels of Various R (Baker et al. 1975) Multiplier for R PS 1 < *0.3^ >1.6^ > Step 1: Collect additional data. In addition to the data collected in Step 1 of the basic method, the following data are needed: the ratio of the speed of sound in the compressed gas to its speed in ambient air, Ct 1 Ja 0 the ratio of specific heats of the ambient air, ^0 = 1.40 For an ideal gas (aja^2 is (6.3.19) where T 0 = absolute temperature of ambient air (K) T 1 = absolute temperature of compressed gas (K) M 1 = molar mass of compressed gas (kg/kmol) Af 0 = molar mass of ambient air (29.0 kg/kmol) y Q and ^1 are specific heat ratios (-) Step 2: Calculate the initial distance. This refinement assumes that an explosion's blast wave will be completely symmetrical. Such a shape would result from the explosion of a hemispherical vessel placed TABLE 6.11 b. Adjustment Factors for Spherical Vessels Slightly Elevated above Ground (Baker et al. 1975) Multiplier for R PS / < >

29 start from step 4 of basic method collect additional data 2 calculate starting distance calculate P 8, 4 locate starting point on Fig determine P 8 'continue with step 6 of basic method Figure Refined method to determine P 8. directly on the ground. Therefore, a hemispherical vessel is used instead of the actual vessel for calculation purposes. Calculate the hemispherical vessel's radius r 0 from the volume of the actual vessel V 1 : (6.3.20) This is the starting distance on the overpressure versus distance curve. It must be transformed into the nondimensional starting distance, /? 0, with: (6.3.21)

30 Step 3: Calculate the initial peak overpressure P 80. The peak shock pressure directly after the burst, /? so, is much lower than the initial gas pressure in the vessel P 1. As the shock wave travels away from the vessel, the peak shock pressure decreases. The nondimensional peak-shock overpressure directly after the burst P 80 is defined as (p so /p 0 ) ~~ 1 - It is given by the following expression (see Section ): where (6.3.22) P 1 = initial absolute pressure of compressed gas (Pa) P 0 = ambient pressure (Pa) P 80 = nondimensional peak shock overpressure directly after burst: (-) PSO = (PjPo) ~ 1 P 80 = peak shock overpressure directly after burst (Pa) 7 0 = ratio of specific heats of ambient air (-) 7j = ratio of specific heats of compressed gas (-) a Q = speed of sound in ambient air (m/s) ^1 = speed of sound in compressed gas (m/s) This is an implicit equation which can only be solved by iteration. One might use a spreadsheet or a programmable calculator to solve for P 80 from this equation. An alternative is to read P 80 from Figure 6.26 or P1/PO Figure Gas temperature versus pressure for constant P 30 for ^y 1 = 1.4 (Baker et al. 1975).

31 P1/PO Figure Gas temperature versus pressure for constant P 80 for ^1 = 1.66 (Baker et al. 1975). Step 4: Locate the starting point on Figure In Steps 2 and 3, the vessel's nondimensional radius and the blast wave's nondimensional peak pressure at that radius were calculated. As a blast wave travels outward, its pressure decreases rapidly. The relationship between the peak pressure P 8 and the distance R depends upon initial conditions. Accordingly, Figure 6.21 contains several curves. Locate the correct curve by plotting (R, P 80 ) in the figure, as illustrated in Figure Step 5: Determine P 8. To determine the nondimensional side-on overpressure P 8, read P 8 from Figure 6.21 for the appropriate R (calculated in Step 3 of the basic method). Use the curve which goes through the starting point, or else draw a curve through the starting point parallel to the nearest curve. Continue with Step 6 of the basic method in Section Method for Explosively Flashing Liquids and Pressure Vessel Bursts with Vapor or Nonideal Gas In the preceding subsections, bursting vessels were assumed to be filled with ideal gases. In fact, most pressure vessels are filled with fluids whose behavior cannot be described, or even approximated, by the ideal-gas law. Furthermore, many vessels are filled with superheated liquids which may vaporize rapidly, or even explosively, when depressurized.

32 Figure Location of starting point on graph of P 3 versus R (Baker et al. 1975). (Compare Figure 6.21.) Equation (6.3.15) is not accurate for the calculation of explosion energy of vessels filled with real gases or superheated liquids. A better measure in these cases is the work that can be performed on surrounding air by the expanding fluid, as calculated from thermodynamic data for the fluid. In this section, a method will be described for calculating this energy, which can then be applied to the basic method in order to determine the blast parameters. In many cases, both liquid and vapor are present in a vessel. Experiments indicate that the blast wave from expanding vapor is often separate from that generated by flashing liquid. However, it is conservative to assume that the blast waves from each phase present are combined. This method is given in Figure Step 1: Collect the following data: Internal pressure/?! (absolute) at failure. (A typical BLEVE is caused by a fire whose heat raises vessel pressure and reduces its wall strength. Safety-valve design allows actual pressure to rise to a value 1.21 times the safety valveopening pressure.) Ambient pressure p 0. Quantity of the fluid (volume V 1 or mass).

33 start collect data check the fluid determine U 1 determine u, 5 calculate specific work calculate energy calculate R continue with step 5 of basic method Figure Calculation of energy of flashing liquids and pressure vessel bursts filled with vapor or nonideal gas.

34 Distance from center of vessel to "target" r. Shape of vessel: spherical or cylindrical. Note that the recommended value for P 1 is not always conservative. In some cases, heat input may be so high that the safety valve cannot vent all the generated vapor. In such cases, the internal pressure will rise until the bursting overpressure is reached, which may be much higher than the vessel's design pressure. For example, Droste and Schoen (1988) describe an experiment in which an LPG tank failed at 39 bar, or 2.5 times the opening pressure of its safety valve. Note also that this method assumes that the fluid is in thermodynamic equilibrium; yet, in practice, stratification of liquid and vapor will occur (Moodie et al. 1988). If the fluid is not listed in Table 6.12 or Figure 6.30, thermodynamic data for the fluid at its initial and final (expanded to ambient pressure) states are needed as well. These data include the properties of the fluid: specific enthalpy h specific entropy s specific volume v. Thermodynamic data on fluids can be found in Perry and Green (1984) or Edmister and Lee (1984), among others. The method or determining the thermodynamic data will be explained in detail in Step 3. Step 2: Determine if the fluid is given in Table 6.12 or Figure The work performed by a fluid as it expands has been calculated for seven common fluids, namely: ammonia carbon dioxide ethane isobutane nitrogen oxygen propane. If the fluid of interest is listed, skip to Step 5. Step 3: Determine internal energy in initial state, H 1. The work done by an expanding fluid is defined as the difference in internal energy between the fluid's initial and final states. Most thermodynamic tables and graphs do not present W 1, but only h, p 9 v, T (the absolute temperature), and s (the specific entropy). Therefore, u must be calculated with the following equation: h = u + pv (6.3.23)

35 TABLE Expansion Work of NH 3, CO 2, N 2, O 2 Liquid Vapor Pi e ex e ex /v f e ex e ex/v f Fluid T 1 (K) (10 5 Pa) (kj/kg) (MJ/m 3 ) (kj/kg) (MJ/m 3 ) Ammonia, 7 S, = K Carbon dioxide, 7 S = K Nitrogen, T 8, = K Oxygen, 7 sl = K Expansion work. kj/kg Expansion work, Btu/lbm Temperature, K I saturated A saturated saturated ethane propane i so butane Figure Expansion work per unit mass of ethane, propane, and isobutane.

36 where h = specific enthalpy (enthalpy per unit mass) (J/kg) u = specific internal energy (J/kg) p = absolute pressure (N/m 2 ) v = specific volume (m 3 /kg) To use a thermodynamic graph, locate the fluid's initial state on the graph. (For a saturated fluid, this point lies either on the saturated liquid or on the saturated vapor curve, at a pressure P 1.) Read the enthalpy A 1, volume V 1, and entropy S 1 from the graph. If thermodynamic tables are used, interpolate these values from the tables. Calculate the specific internal energy in the initial state M 1 with Eq. (6.3.23). The thermodynamic properties of mixtures of fluids are usually not known. A crude estimate of a mixture's internal energy can be made by summing the internal energy of each component. Step 4: Determine internal energy in expanded state, U 1. The specific internal energy of the fluid in the expanded state M 2 can be determined as follows: If a thermodynamic graph is used, assume an isentropic expansion (entropy s is constant) to atmospheric pressure p Q. Therefore, follow the constantentropy line from the initial state to p Q. Read A 2 and V 2 at this point, and calculate the specific internal energy M 2. When thermodynamic tables are used, read the enthalpy A f, volume v f, and entropy s f of the saturated liquid at ambient pressure, /? 0, interpolating if necessary. In the same way, read these values (A g, v g,,y g ) for the saturated vapor state at ambient pressure. Then use the following equation to calculate the specific internal energy M 2 : where M 2 = (1 - X) h f + XA g - (1 - X)p 0 v f - X Po v g (6.3.24) X = vapor ratio (S 1 s f )/(s g s f ) s = specific entropy Subscript 1 refers to initial state. Subscript f refers to state of saturated liquid at ambient pressure. Subscript g refers to state of saturated vapor at ambient pressure. Equation (6.3.24) is only valid when X is between O and 1. Step 5: Calculate the specific work. The specific work done by an expanding fluid is defined as. *ex = U 1 - U 2 (6.3.25) where e ex is specific work. (See Section ) The results of these calculations are given for seven common gases in Table 6.12 and Figures 6.30 and The fluid temperature at the moment of burst must be known. If only pressure is known,

37 Temperature. F Expansion work, MJ/m 3 Expansion work, Btu/ft 3 Temperature, K I saturated * saturated e saturated ethane propane iso-butane Figure Expansion work per unit volume of ethane, propane, and isobutane. use thermodynamic tables to find this temperature. The table gives superheat limit temperature T sl, initial conditions, and specific work done in expansion based upon isentropic expansion of either saturated liquid or saturated vapor until atmospheric pressure is reached. Figures 6.30 and 6.31 present the same information for saturated hydrocarbons. In Figure 6.30, the saturated liquid state is on the lower part of the curve and in Figure 6.31 it is on the upper part of the curve. Below T sl, the line width changes, indicating that the liquid probably does not flash below that level. Note that a line has been drawn only to show the relationship between the points; a curve reflecting an actual event would be smooth. Note that a liquid has much more energy per unit of volume than a vapor, especially carbon dioxide. Note: It is likely that carbon dioxide can flash explosively at a temperature below the superheat limit temperature. This may result from the fact that carbon dioxide crystallizes at ambient pressure and thus provides the required number of nucleation sites to permit explosive vaporization. Step 6: Calculate expansion energy. To calculate expansion energy, multiply the specific expansion work by the mass of fluid released or else, if energy per unit volume is used, multiply by the volume

38 of fluid released. Multiply the result by 2 to account for reflection of the shock wave on the ground, as follows: E n = 2^m 1 (6.3.26) where Tn 1 is the mass of released fluid. Repeat Steps 3 to 6 for each component present in the vessel, and add the energies to find the total energy E ex of the explosion. Step 7: Calculate, using Eq. (6.3.16), the nondimensional range R of the "target" as follows: r i "te] where r is the distance in meters at which blast parameters are to be determined. Continue with Step 5 of the basic method. Note that the refinement for the near field cannot be made for nonideal gases, because Eq. (6.3.22) applies only to ideal gases. Therefore, blast pressure is conservatively estimated by determining the blast pressure resulting from detonation of a high-explosive charge having the same energy Blast Parameters of Free-Air BLEVEs or Pressure-Vessel Bursts For BLEVEs or pressure vessel bursts that take place far from reflecting surfaces, the above method may be used if a few modifications are made. The blast wave does not reflect on the ground. Thus, the available energy E 6x is spread over twice the volume of air. Therefore, instead of using Eq. (6.3.15), calculate the energy with Qr else, instead of using Eq. (6.3.26), use ^l^tt (6-3.27) ex = ejn v (6.3.28) Further in Step 7 of the basic method, do not multiply overpressure or impulse by vessel-height compensation factors Accuracy The methods presented above give upper estimates of blast parameters. Since the measured blast parameters of actual pressure-vessel bursts vary widely, even under well-controlled conditions, and since these methods are based on a highly schematized model, the blast parameters of actual bursts may be much lower. The main sources of deviation lie in estimates of energy and in release-process details. It is unclear whether the energy equations given in preceding sections are good estimates of explosion energy. In addition, energy translated into kinetic

39 energy of fragments and ejected liquid is not subtracted from blast energy. This may produce an error of up to 50%, which translates into an overstatement of overpressure by 25%. (See Section ) In practice, vapor release will not be spherical, as is assumed in the method. A release from a cylinder burst may produce overpressures along the vessel's axis, which are 50% lower than pressures along a line normal to its axis. If a vessel ruptures from ductile, rather than brittle, fracture, a highly directional shock wave is produced. Overpressure in the other direction may be one-fourth as great. The influences of release direction are not noticeable at great distances. Uncertainties for a BLEVE are even higher because of the fact that its overpressure is limited by initial peak-shock overpressure is not taken into account. The above methods assume that all superheated liquids can flash explosively, yet this may perhaps be the case only for liquids above their superheat-limit temperatures or for pre-nucleated fluids. Furthermore, the energies of evaporating liquid and expanding vapor are taken together, while in practice, they may produce separate blasts. Finally, in practice, there are usually structures in the vicinity of an explosion which will reflect blast or provide wind shelter, thereby influencing the blast parameters. In practice, overpressures in one case might very well be only one-fifth of those predicted by the method and close to the predicted value in another case. This inherent inaccuracy limits the value of this method in postaccident analysis. Even when overpressures can be accurately estimated from blast damage, released energy can only be estimated within an order of magnitude FRAGMENTS A BLEVE can produce fragments that fly away rapidly from the explosion source. These primary fragments, which are part of the original vessel wall, are hazardous and may result in damage to structures and injuries to people. Primary missile effects are determined by the number, shape, velocity, and trajectory of fragments. When a high explosive detonates, a large number of small fragments with high velocity and chunky shape result. In contrast, a BLEVE produces only a few fragments, varying in size (small, large), shape (chunky, disk-shaped), and initial velocities. Fragments can travel long distances, because large, half-vessel fragments can "rocket" and disk-shaped fragments can "frisbee." The results of an experimental investigation described by Schulz-Forberg et al. (1984) illustrate BLEVE-induced vessel fragmentation. All parameters of interest with respect to fragmentation will be discussed. The extent of damage or injury caused by these fragments is, however, not covered in this volume. (Parameters of the terminal phase include first, fragment density and velocity at impact, and second, resistance of people and structures to fragments.) Figure 6.32 illustrates results of three fragmentation tests of 4.85-m 3 vessels 50% full of liquid propane. The vessels were constructed of steel (StE 36; unalloyed Next Page