Fires, explosions and toxic releases

When containment is lost, what happens next depends on the material, the amount, the conditions of the release, the weather and whether and when the material finds an ignition source. The same leak of propane might disperse harmlessly, burn as a jet fire at the leak, flash back through a drifting cloud or explode with enough force to destroy buildings. Process safety engineers call the study of these outcomes consequence analysis. This lesson explains the main types of fire, explosion and toxic release, introduces the simple models used to estimate their effects, and shows how the results are used to site buildings and plan emergencies. The calculations here are simplified teaching versions; real studies use validated software and expert judgment.

From leak to outcome

A release first has to get out. Liquids under pressure come out as a jet and may partly flash to vapor; gases come out at high speed; volatile liquids form a pool that evaporates. Then the material either ignites quickly, ignites later after a cloud has formed, or does not ignite at all. An event tree lays out these branches. Lesson 7 uses event trees to estimate how often each outcome occurs; here we focus on what each outcome looks like.

Fires

The effect of a fire on people and equipment depends mainly on the thermal radiation they receive, measured in kilowatts per square meter. Sunlight on a bright summer day is about 1 kW/m². The table gives approximate effects used in consequence studies.

A simple way to estimate radiation from a fire at a distance is the point source model. It treats the fire as a single point radiating a fraction of its total heat release equally in all directions. It works reasonably well at distances several times larger than the flame size.

import math
# Point source model for radiation from a pool fire (illustrative).
burn_rate = 0.06          # kg/(m2 s), typical for hydrocarbon pools
area = 50.0               # pool area, m2
dHc = 43e6                # heat of combustion, J/kg
Xr = 0.30                 # fraction of heat radiated
tau = 0.8                 # atmospheric transmissivity
Q = burn_rate * area * dHc          # total heat release, W
print(f"Total heat release: {Q / 1e6:.0f} MW")
for R in (15, 25, 40, 60, 90):
    q = tau * Xr * Q / (4 * math.pi * R**2) / 1000   # kW/m2
    print(f"distance {R:>3} m ({R * 3.281:4.0f} ft): {q:5.1f} kW/m2")

Total heat release: 129 MW
distance  15 m (  49 ft):  10.9 kW/m2
distance  25 m (  82 ft):   3.9 kW/m2
distance  40 m ( 131 ft):   1.5 kW/m2
distance  60 m ( 197 ft):   0.7 kW/m2
distance  90 m ( 295 ft):   0.3 kW/m2

The results show why radiation drops quickly with distance: doubling the distance cuts the heat flux to a quarter. At 15 m from this 50 m² pool fire the heat flux is nearly 11 kW/m², enough to cause severe burns within seconds. At 25 m it is about 4 kW/m², painful within about 20 seconds, so people must move away quickly. Beyond about 40 m it falls below 1.6 kW/m², where even long exposure causes no discomfort. Fire protection designers use results like these to set spacing between tanks and to decide where firefighting water monitors and deluge systems are needed.

Explosions

An explosion is a sudden release of energy that produces a pressure wave. Process plants face several kinds.

The damage from an explosion is described by its peak overpressure: how far the pressure in the blast wave rises above atmospheric pressure. Small overpressures break windows; larger ones collapse buildings. Many people are injured not by the blast itself but by flying glass and collapsing structures.

One simple and widely taught way to estimate overpressure from a vapor cloud explosion is the TNT equivalence method. It converts the combustion energy of the fuel in the cloud into an equivalent mass of TNT, using an explosion efficiency that is usually only a few percent, because most of the cloud burns without contributing to the blast. Distances are then scaled by the cube root of the TNT mass, a rule known as Hopkinson scaling: two explosions produce the same overpressure at the same scaled distance.

# TNT equivalence and Hopkinson scaling for a cloud explosion (VCE), illustrative.
# Overpressure from an approximate free-air TNT correlation (Mills, 1987), kPa.
def overpressure_kpa(Z):            # Z in m/kg^(1/3)
    return 1772 / Z**3 - 114 / Z**2 + 108 / Z

m = 1000          # kg of propane in the flammable cloud
dHc = 46e6        # J/kg
eta = 0.03        # explosion efficiency (3 percent)
E_tnt = 4.6e6     # J/kg
W = eta * m * dHc / E_tnt
print(f"TNT equivalent: {W:.0f} kg")
for R in (30, 50, 80, 120, 200, 300):
    Z = R / W ** (1 / 3)
    p = overpressure_kpa(Z)
    print(f"R = {R:>3} m: Z = {Z:5.1f}, overpressure about {p:5.1f} kPa ({p / 6.895:4.2f} psi)")

TNT equivalent: 300 kg
R =  30 m: Z =   4.5, overpressure about  38.1 kPa (5.53 psi)
R =  50 m: Z =   7.5, overpressure about  16.7 kPa (2.42 psi)
R =  80 m: Z =  12.0, overpressure about   9.3 kPa (1.35 psi)
R = 120 m: Z =  17.9, overpressure about   6.0 kPa (0.87 psi)
R = 200 m: Z =  29.9, overpressure about   3.6 kPa (0.52 psi)
R = 300 m: Z =  44.8, overpressure about   2.4 kPa (0.34 psi)

The TNT method is crude. It ignores the fact that vapor cloud explosions are much more severe in congested areas full of pipes and equipment, where turbulence accelerates the flame, and weaker in open areas. Modern studies use methods that account for congestion and confinement, such as the multi-energy and Baker-Strehlow-Tang methods, or computational fluid dynamics. The simple method still shows the main point: hundreds of meters around a large release can see overpressures that break windows and injure people.

Toxic releases

A toxic gas released into the air forms a plume or cloud that moves with the wind and spreads out as it travels. How far a harmful concentration reaches depends on the release rate, the wind speed, the atmospheric stability and the toxicity of the gas. Stable conditions, which usually occur on clear nights with light winds, let a cloud travel much farther before it dilutes. Gases heavier than air, such as chlorine and cold ammonia, hug the ground and flow into low areas.

A classic teaching model is the Gaussian plume, which assumes the concentration across the plume follows a bell-shaped curve that widens with distance. For a continuous release at ground level, the concentration on the plume centerline at ground level is given below. The spread parameters σy and σz grow with distance and depend on atmospheric stability; correlations published by Briggs are often used.

import math
# Ground-level centreline concentration for a continuous ground-level release
# (Gaussian plume, Briggs rural coefficients). Teaching example, not for design.
def sig(x, cls):
    if cls == "D":   # neutral
        return 0.08 * x / math.sqrt(1 + 0.0001 * x), 0.06 * x / math.sqrt(1 + 0.0015 * x)
    if cls == "F":   # very stable
        return 0.04 * x / math.sqrt(1 + 0.0001 * x), 0.016 * x / (1 + 0.0003 * x)

m_dot = 1.0                          # kg/s of chlorine
target = 3 * 70.9 / 24.45            # ERPG-2 of 3 ppm in mg/m3
for cls, u in (("D", 5.0), ("F", 2.0)):
    print(f"Stability {cls}, wind {u} m/s:")
    for x in (200, 500, 1000, 2000, 5000):
        sy, sz = sig(x, cls)
        c = m_dot * 1e6 / (math.pi * sy * sz * u)      # mg/m3
        flag = "above" if c > target else "below"
        print(f"  {x:>5} m: {c:9.1f} mg/m3 ({flag} ERPG-2 of {target:.1f} mg/m3)")

Stability D, wind 5.0 m/s:
    200 m:     381.8 mg/m3 (above ERPG-2 of 8.7 mg/m3)
    500 m:      71.9 mg/m3 (above ERPG-2 of 8.7 mg/m3)
   1000 m:      22.0 mg/m3 (above ERPG-2 of 8.7 mg/m3)
   2000 m:       7.3 mg/m3 (below ERPG-2 of 8.7 mg/m3)
   5000 m:       1.9 mg/m3 (below ERPG-2 of 8.7 mg/m3)
Stability F, wind 2.0 m/s:
    200 m:    6655.6 mg/m3 (above ERPG-2 of 8.7 mg/m3)
    500 m:    1172.2 mg/m3 (above ERPG-2 of 8.7 mg/m3)
   1000 m:     339.1 mg/m3 (above ERPG-2 of 8.7 mg/m3)
   2000 m:     109.0 mg/m3 (above ERPG-2 of 8.7 mg/m3)
   5000 m:      30.5 mg/m3 (above ERPG-2 of 8.7 mg/m3)

Even this simple model shows two important points. First, a release of 1 kg/s of chlorine exceeds ERPG-2 out to about 2 km in neutral, breezy conditions and beyond 5 km in very stable conditions. Second, stable night-time conditions with light winds give much higher concentrations at every distance than a breezy afternoon. Real planning uses dense-gas models and tools such as ALOHA, developed by the US EPA and NOAA, or commercial software, and considers the duration of exposure. Emergency plans use the results to decide shelter-in-place zones and evacuation areas.

Using consequence results

Consequence results are used to decide where buildings and people can be, how far apart equipment should be, and what the emergency plan must cover. After Texas City, the American Petroleum Institute strengthened API RP 752 on permanent buildings and introduced API RP 753 on portable buildings such as trailers, which require siting studies for buildings occupied near process units. Under the EPA Risk Management Program (40 CFR Part 68), covered facilities must perform offsite consequence analyses for worst-case and alternative release scenarios, using defined endpoints: an overpressure of 1 psi (6.9 kPa), a radiation dose equivalent to 5 kW/m² for 40 seconds, and toxic endpoints listed in the rule, which for many substances are based on ERPG-2 values.