TNT equivalence

TNT equivalence is a method that expresses the blast energy of an explosion as the mass of trinitrotoluene (TNT) that would release the same energy. NUREG-1805 calls it one of the most common methods for estimating the effects of an explosion, because the blast effects of TNT have been studied extensively as a function of charge mass and distance. The method multiplies the mass of released fuel by its heat of combustion and by a yield, the fraction of the energy that drives the blast wave. It then divides the result by 4,500 kJ per kilogram of TNT. The distance to a target, divided by the cube root of the TNT mass, gives a scaled distance at which the overpressure is read from an ideal blast wave chart. The yield is the largest uncertainty, ranging from about 1 % for unconfined releases to 100 % for confined ones.

The method rests on ideal blast wave theory, which treats an explosion as an instantaneous release of energy at a single point. That suits compact condensed-phase explosives and bursting pressure vessels. For vapour clouds, however, the SFPE Handbook reports that early assessments with such correlations were not very successful, and newer methods use the flame speed or computational fluid dynamics instead. In risk studies, the resulting overpressures are related to the distances at which buildings are damaged and people are injured.

Principle

NUREG-1805 defines an explosion as a sudden and violent release of high-pressure gases into the environment, fast enough for the energy to dissipate in a shock wave. It distinguishes physical explosions, such as the failure of a tank heated from outside, from chemical explosions. Chemical explosions include gas and dust explosions as well as condensed-phase explosions of high explosives and propellants. When a firecracker or a stick of dynamite explodes, the violent reaction produces a shock or blast wave. This is a thin shell of highly compressed air and hot gases that expands rapidly in all directions. The peak overpressure in the wave is highest near the source and falls rapidly with distance.

The energy behind an explosion can take several forms. Physical energy may be pressure energy in a gas, strain energy in a metal or electrical energy, as in the burst of a vessel under high gas pressure. Chemical energy comes from a reaction, such as the combustion of a flammable gas. An explosion in a vessel tends to be uniform, while an explosion in a long pipe propagates along it. TNT equivalence applies the same yardstick to all of these, by reducing each to the energy that drives the blast wave.

Far from the source the blast wave has a characteristic shape. A shock raises the pressure suddenly to a peak, a rarefaction follows in which the pressure falls below atmospheric, and the pressure then recovers. When the recovery takes the form of a second shock, the pressure history looks like a slightly deformed letter N and is called an N wave. The impulse of the wave, its overpressure integrated over time, matters for the dynamic response of structures.

Ideal blast wave theory assumes that the energy is released instantaneously at a single point, so that the wave is described by one parameter, the blast energy. Its correlations combine theory with test data from compact condensed-phase explosives. Because the blast effects of TNT are well documented as a function of charge mass and distance, it is convenient to express other explosions as an equivalent TNT charge. As a unit of energy, the conversion table of the SFPE Handbook lists the ton (nuclear equivalent of TNT) as 4.20 × 10⁹ J.

Calculation method

NUREG-1805 sets out the method in three steps, based on the explosion protection chapter by Zalosh in the second edition (1995) of the SFPE Handbook. It applies to a flammable gas or vapour that has been released, has mixed with air within its flammable limits and has then been ignited. The first step gives the explosive energy of a flammable vapour release from its mass, its heat of combustion and the yield:

$$E=\alpha \mathrm{\Delta }{H}_{\mathrm{c}}{m}_{\mathrm{F}}$$

The yield is the fraction of the available combustion energy that takes part in generating the blast wave. It is typically about 1 % for unconfined releases and up to 100 % for confined ones. NUREG-1805 lists net heats of combustion of, for example, 46,360 kJ/kg for propane, 50,030 kJ/kg for methane and 130,800 kJ/kg for hydrogen. The second step converts the energy into an equivalent TNT mass:

$$W_{\mathrm{T}\mathrm{N}\mathrm{T}}=\frac{E}{4500}$$

Here W_TNT is in kilograms and E in kilojoules, so each kilogram of TNT stands for 4,500 kJ of blast energy. At full yield, one kilogram of propane is therefore equivalent to about 10 kg of TNT, and one kilogram of hydrogen to about 29 kg. The third step divides the distance D from the explosion by the cube root of the TNT mass to give the scaled distance:

$$D_{\mathrm{s}\mathrm{c}}=\frac{D}{W_{\mathrm{T}\mathrm{N}\mathrm{T}}^{1/3}}$$

The overpressure is then read from a chart of ideal blast wave overpressure against scaled distance, which NUREG-1805 reproduces from Zalosh in English and metric units. The chart includes the reflected shock wave and marks the ranges in which building elements fail and in which eardrum rupture, lung damage and death occur. Because the overpressure depends only on the scaled distance, a charge eight times heavier produces the same overpressure at twice the distance.

The 2002 edition of the SFPE Handbook skips the detour through TNT and scales the distance with the blast energy itself. In its dimensionless distance, R is the actual distance in metres, E the blast energy in joules and P₀ the ambient pressure in pascals. The overpressure, divided by the ambient pressure, is then read against this distance:

$$\overline{R}=R{\left(\frac{P_0}{E}\right)}^{1/3}$$

Its chart gives both the incident overpressure and the overpressure reflected head-on from a rigid wall. Neither curve includes reflection from the ground, and the usual procedure is to double the blast energy to account for it. For the burst of a pressure vessel whose gas does not ignite, the blast energy is the isentropic expansion energy of the gas, E = (P₁ − P₀)V/(γ − 1).

Symbol	Description	Unit
$E$	explosive or blast energy	kJ (NUREG-1805) or J (SFPE)
$\alpha$	yield: fraction of the combustion energy that drives the blast wave	none
$\mathrm{\Delta }{H}_{\mathrm{c}}$	theoretical net heat of combustion of the fuel	kJ/kg
$m_{\mathrm{F}}$	mass of flammable vapour released	kg
$W_{\mathrm{T}\mathrm{N}\mathrm{T}}$	equivalent mass of TNT	kg
$D$, $R$	distance from the explosion	m
$D_{\mathrm{s}\mathrm{c}}$	scaled distance	m/kg1/3
$\overline{R}$	dimensionless scaled distance	none
$P_0$	ambient pressure	Pa
$P_1$	initial pressure in a bursting vessel	Pa
$V$	vessel volume	m³
$\gamma$	ratio of specific heats of the gas	none

Blast effects and damage criteria

NUREG-1805 lists the possible effects of an explosion: blast damage, thermal effects, missile damage, ground shock, cratering and personal injury. Indirect effects add to these, such as fragments and debris set in motion by the blast, and people thrown against the ground, walls or other objects. Much of the data on these effects comes from studies of industrial and military explosives, with a growing amount from investigations of process plant explosions.

Damage thresholds are expressed as peak overpressure. In a table compiled by Clancey, typical glass failure occurs at 0.15 psig, about 1 kPa, and houses become uninhabitable through partial demolition at 1.0 psig, about 7 kPa. The walls and roofs of houses partly collapse at 2.0 psig, the lower limit of serious structural damage lies at 2.3 psig, and a building is probably destroyed completely at 10.0 psig. The extent of damage also depends strongly on nearby reflecting surfaces.

People withstand relatively high pressures. NUREG-1805 gives 35 kPa as the limit for eardrum rupture and 70 kPa as the limit for lung damage. Mortality reaches 1 % at 180 kPa, 50 % at 260 kPa and 99 % at 350 kPa. When blast waves kill, it is usually through falling objects rather than through the pressure itself. Building elements fail at far lower pressures: glass windows at 2 to 7 kPa and unrestrained brick walls at 7 to 15 kPa.

For risk studies, Barry gives a generic breakdown of damage levels. Overpressures of 2.5 to 5 psig cause heavy damage to buildings and process equipment, and about 1 % deaths from lung damage. At 1 to 2.4 psig buildings suffer repairable damage, at 0.5 to 1 psig glass breaks, and at 0.15 to 0.30 psig about 10 % of window panes break.

Worked example: a propane forklift

The examples in NUREG-1805 show how the steps work in practice. The first considers a forklift powered by liquefied petroleum gas in a nuclear power plant, whose fuel system could release 48 lb, about 21.8 kg, of propane vapour. With a yield of 100 % and the heat of combustion of propane, the first two steps give:

$$E=1.0\times 46360\times 21.8\approx 1.01\times 10^6\mathrm{k}\mathrm{J},W_{\mathrm{T}\mathrm{N}\mathrm{T}}=\frac{1.01\times 10^6}{4500}\approx 225\mathrm{k}\mathrm{g}$$

The spreadsheet in NUREG-1805 reports 1,011,491 kJ and 225 kg of TNT. A recalculation with 21.77 kg gives 224 kg, so the difference is only rounding, and the higher value is kept because it is the more severe. A smaller case is a leaking acetylene cylinder that held 40 ft³ of gas, about 2.7 lb: at full yield NUREG-1805 finds 59,179 kJ, or 13.2 kg of TNT.

The yield changes the result by two orders of magnitude. With the 1 % typical of an unconfined release, the same propane is equivalent to only about 2.25 kg of TNT. At 50 m from the release, the scaled distance is 50/225^1/3, about 8.2 m/kg^1/3, for full yield, and 50/2.25^1/3, about 38 m/kg^1/3, for 1 % yield. Any given overpressure therefore occurs 100^1/3, or about 4.6, times further away at full yield than at 1 % yield. The choice of yield thus determines the size of every hazard zone derived from the chart.

A second example in NUREG-1805 compares 10 lb of acetylene with 5 lb of hydrogen. The hydrogen has half the mass, but its heat of combustion is almost three times that of acetylene. It is therefore equivalent to 66.0 kg of TNT against 48.7 kg for the acetylene, and NUREG-1805 concludes that the hydrogen produces the larger explosive force.

Use in quantitative risk assessment

In quantitative risk assessment of chemical process plants, Barry describes a sequence of steps. The analyst defines the objectives, identifies the hazards, assesses the loss event scenarios, assesses the consequences and assesses the probabilities. Consequence assessment estimates the undesirable result of an accidental fire or explosion for a target, in terms of health and safety, property loss or business interruption.

The assessment weighs the vulnerability of the target against the intensity, distance and time of the hazardous event. Barry distinguishes two levels of vulnerability assessment. Generic tables of damage criteria, such as overpressure thresholds, give a good first-order review but are weak in terms of time relationships. Detailed heat transfer or structural impact models form a second-order assessment, used where time or the specific design, layout or emergency response warrant it.

Among the outcomes of a flammable release, Barry lists the unconfined vapour cloud explosion. A large release, usually of more than 1 ton, forms a cloud that explodes on delayed ignition and exposes the surroundings to overpressure. The exposures from such explosions can be correlated with the energy of the explosion to relate distances to levels of damage and of exposure of people. Plotted as effect zones around the point of release, the results show a fatality zone, an injury zone and a zone of partial building damage between 2 and 0.5 psig. TNT equivalence is one way to make such a correlation, because it turns the energy of a release into the distances at which chosen overpressures occur.

Vapour clouds and limitations

The weakest point of TNT equivalence is the vapour cloud explosion. Such explosions occur when a large cloud of flammable gas or vapour is ignited in a highly obstructed area, such as a chemical plant with closely spaced process equipment and storage vessels. The strength of the blast depends on the flame speed that develops and on the degree of confinement in and around the cloud. Early assessments used ideal blast wave correlations with a rough guess at the energy yield, and they were not very successful.

Zalosh gives two reasons. Most of the interest lies in the near field, close to the cloud, and even in the far field the blast from a vapour cloud decays much less rapidly than an ideal blast wave. NUREG-1805 states a related limitation: the ideal point-source correlations cannot be valid within or near the flammable vapour cloud. Current methods instead estimate the flame speed empirically and calculate a non-ideal blast wave, or they model the flame propagation with computational fluid dynamics.

Further assumptions limit the method. The fuel must be mixed with air between its flammable limits, and real mixtures may be non-uniform or stratified. The yield, which spans two orders of magnitude, has to be chosen by judgement. NUREG-1805 adds that the pressures produced are usually difficult to predict. A detonation of the released gas, inside or outside a building, would give even higher pressures, although detonations are very rare.

Damage criteria also differ between sources. Barry associates about 1 % deaths from lung damage with 2.5 to 5 psig, about 17 to 34 kPa. NUREG-1805, by contrast, gives 70 kPa as the limit for lung damage and 180 kPa for 1 % mortality. The energy assigned to TNT is not uniform either: the method uses 4,500 kJ per kilogram, while the SFPE conversion table lists 4.20 × 10⁹ J for the ton (nuclear equivalent of TNT). A TNT equivalent and the damage it implies should therefore be read with the yield and the criteria that were used to obtain it.

See also

• Deflagration
• Deflagration-to-detonation transition
• Explosion venting
• BLEVE
• Hydrogen safety

References

• Barry, T. F. (2002). Quantitative risk assessment in chemical process industries. In P. J. DiNenno, D. Drysdale, C. L. Beyler, W. D. Walton, R. L. P. Custer, J. R. Hall Jr., & J. M. Watts Jr. (Eds.), SFPE handbook of fire protection engineering (3rd ed., pp. 5-176–5-213). National Fire Protection Association; Society of Fire Protection Engineers.
• DiNenno, P. J., Drysdale, D., Beyler, C. L., Walton, W. D., Custer, R. L. P., Hall, J. R., Jr., & Watts, J. M., Jr. (Eds.). (2002). SFPE handbook of fire protection engineering (3rd ed.). National Fire Protection Association; Society of Fire Protection Engineers.
• Iqbal, N., & Salley, M. H. (2004). Fire Dynamics Tools (FDTs): Quantitative fire hazard analysis methods for the U.S. Nuclear Regulatory Commission Fire Protection Inspection Program (NUREG-1805). U.S. Nuclear Regulatory Commission, Office of Nuclear Reactor Regulation.
• Zalosh, R. (2002). Explosion protection. In P. J. DiNenno, D. Drysdale, C. L. Beyler, W. D. Walton, R. L. P. Custer, J. R. Hall Jr., & J. M. Watts Jr. (Eds.), SFPE handbook of fire protection engineering (3rd ed., pp. 3-402–3-421). National Fire Protection Association; Society of Fire Protection Engineers.