Chapter 5. Hazardous Material Dispersion

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Chapter 5. Hazardous Material Dispersion

The learning objectives for this chapter are to:

Understand air dispersion and the parameters required to describe it.
Perform calculations using the neutrally buoyant plume and puff models.
Understand qualitative features of dense gas dispersion.
Understand various toxic effect criteria.
Understand hazardous material release prevention and mitigation.

During an incident, process equipment can release hazardous materials quickly and in significant enough quantities to spread in hazardous clouds throughout a plant site and the local community. A few examples are explosive rupture of a process vessel as a result of excessive pressure caused by a runaway reaction, rupture of a pipeline containing toxic materials at high pressure, rupture of a tank containing toxic material stored above its atmospheric boiling point, and rupture of a train or truck transportation tank following an accident.

Hazardous material dispersion includes the release of toxic and flammable materials. However, this chapter focuses solely on toxic material dispersion. Toxic materials are typically measured in parts per million (ppm) by volume levels, whereas flammable gases are in volume percent levels. The dispersion models presented in this chapter are more suitable for the ppm levels of toxic materials.

Serious accidents (such as that in Bhopal, India) emphasize the importance of planning for emergencies and for designing plants to minimize the frequency and consequences of hazardous material releases. Hazardous material release models are routinely used to estimate the consequences of a release on the plant and community environments. This information is useful for adding preventive and mitigative safeguards to the process. Thus, it is important that engineers understand this procedure.

Hazardous material release and dispersion models are an important part of the consequence analysis procedure shown in Figure 4-1. The release model represents the first three steps in the consequence modeling procedure:

Identifying the release incident. Which process situations can lead to a release? This was described in Sections 4-9 and 4-10.
Developing a source model to describe how materials are released and the rate of release. This was presented in Chapter 4.
Estimating the downwind concentrations of the hazardous materials using the dispersion models presented in this chapter. Once the downwind concentrations are known, several criteria are available to estimate the impact or effect, as discussed in Section 5-5.

Various options are available based on the predictions of the dispersion model. This could include applying concepts of inherently safer design by reducing inventories of hazardous materials, substituting with less hazardous materials, and reducing temperatures and pressures, to name a few options. It might also entail developing an emergency response plan for the plant site and with the surrounding community. Other possibilities include developing engineering modifications to eliminate or reduce the source of the release, enclosing the potential release and adding appropriate vent scrubbers or other vapor removal equipment, and adding area monitors to detect incipient leaks and providing block valves and engineering controls to eliminate hazardous levels of spills and leaks. These options are discussed in more detail in Section 5-6 on release prevention and mitigation.

5-1 Parameters Affecting Dispersion

Dispersion models describe the airborne transport of hazardous materials away from the release point and into the plant and community. After a release, the airborne material is carried away by the wind in a characteristic plume (Figure 5-1) or a puff (Figure 5-2). The maximum concentration of material occurs at the release point (which may not be at ground level). Concentrations downwind are smaller, because of turbulent mixing and dispersion of the substance with air.

A storage vessel and plume formed by a continuous release of material are shown. A circular vessel is mounted on a surface. The continuous release of plume occurs from an exit point provided in the vessel. The plume moves toward the direction of wind and dissipates downwind by mixing with fresh air. The wind direction is denoted using a rightward arrow. — **Figure 5-1** Characteristic plume formed by a continuous release of material.

Three stages of puff formed by near instantaneous release of a material are shown. The stages of the formed puff are marked as t 0, t 1, and t 2. The puff moves in the direction of wind. t 0 and t 2 are comparatively less in size from t 1. — **Figure 5-2** Puff formed by near instantaneous release of material. After the initial release, the puff grows in size but eventually decreases in size.

A wide variety of parameters affect atmospheric dispersion of hazardous materials:

Quantity or release rate of material
Wind speed
Atmospheric stability
Ground conditions (buildings, water, trees)
Height of the release above ground level
Momentum and buoyancy of the material released

As the wind speed increases, the plume in Figure 5-1 becomes longer and narrower. This shape occurs because the released material is carried downwind faster but is diluted faster by a larger quantity of air and increased turbulence.

Atmospheric stability relates to vertical mixing of the air. During the day, the air temperature decreases rapidly with height, encouraging vertical motions. At night, the temperature decrease is less dramatic, resulting in less vertical motion.

Temperature profiles for day and night situations are shown in Figure 5-3. During the day, the sun heats the ground, causing the temperature to be higher on the ground with the temperature decreasing above the ground. During the night, the ground cools rapidly due to thermal radiation to space, resulting in the ground having a lower temperature than the immediate air above it. The presence of clouds will affect both the daytime and nighttime temperature profiles.

A graph depicts the variation in air temperature for day and night conditions. — **Figure 5-3** Air temperature as a function of altitude for day and night conditions. The temperature gradient affects the vertical air motion. (Source: Adapted from D. Bruce Turner. *Workbook of Atmospheric Dispersion Estimates* (Cincinnati, OH: U.S. Department of Health, Education, and Welfare, 1970), p. 1.)

In the graph, the horizontal axis represents temperature (measured in degrees Celsius) that ranges from negative 1 to 11. The vertical axis represents height (measured in meters) that ranges from 0 to 500. A curve drawn on the graph represents the variation of air temperature in night, at different heights. The bottom end of the curve shows negative 1 degree temperature at 0 meters. First curve follows almost linear path till 50 meters; then, it moves upward on a slightly parabolic path till 300 meters, where temperature reaches at 5; again, it follows almost linear path and temperature starts decreasing. An almost linear inclined line drawn on the graph represents the variation of air temperature in day, at different heights. At 0 meters, the temperature is 10 degrees, which is highest. As the height increases, the temperature decreases; at the top, the temperature in the night and day are very close to each other.

Sometimes an inversion occurs, in which the temperature increases with height, resulting in minimal vertical motion. This condition most often occurs at night.

Atmospheric stability is classified into three possible classes: unstable, neutral, and stable. In unstable atmospheric conditions, the sun heats the ground faster than the heat can be removed, so that the air temperature near the ground is higher than the air temperature at higher elevations, as might be observed in the early morning hours. The instability arises because air of lower density is below air of greater density. This influence of buoyancy enhances atmospheric mechanical turbulence. With neutral stability, the air above the ground warms and the wind speed increases, reducing the effect of solar energy input, or insolation. The air temperature difference does not influence atmospheric mechanical turbulence. In stable atmospheric conditions, the sun cannot heat the ground as fast as the ground cools, so the temperature near the ground is lower than the air temperature at higher elevations. This condition is stable because the air of higher density is below the air of lower density. The influence of buoyancy suppresses mechanical turbulence.

Ground conditions affect the mechanical mixing at the surface and the wind profile with height. Trees and buildings increase mixing, whereas lakes and open areas decrease it. Figure 5-4 shows the change in wind speed versus height for a variety of surface conditions.

A graph shows the variation in the wind gradient. — **Figure 5-4** Effect of ground conditions on vertical wind gradient. (Source: Adapted from D. Bruce Turner. *Workbook of Atmospheric Dispersion Estimates* (Cincinnati, OH: U.S. Department of Health, Education, and Welfare, 1970), p. 2.)

A graph shows the variation in wind gradient in three different types of ground conditions: urban, suburbs, and flat, which are marked on the horizontal axis. The vertical axis representing height (measured in meters) ranges from 0 to 500. The wind gradient in urban conditions shows that wind speed on the ground is almost 0 and it increases with the increment of height. After reaching the height of skyscrapers, it is almost stable. The graph shows that the wind speed keeps changing till 500 meters in urban conditions. The wind gradient in suburb conditions shows that wind speed on the ground is almost 0 and increases rapidly, as compared to urban conditions, after reaching the height of trees and houses; after reaching 200 meters, it is almost stable. The graph shows that the wind speed keeps changing till 400 meters in suburb conditions. The wind gradient in flat surface conditions shows that wind speed on the ground is almost 0 and start increasing rapidly from the ground, as compared to urban and suburb conditions; after reaching 200 meters, it is almost stable. The graph shows that the wind speed keeps changing approximately till 250 meters in suburb conditions.

The release height significantly affects ground-level concentrations. As the release height increases, ground-level concentrations are reduced because the plume must disperse a greater distance vertically prior to reaching the ground. This relationship is shown in Figure 5-5.

An industrial chimney releasing plume continuously is shown. The plume moves in the direction of wind, which is shown by an arrow. As release height increases, the distance between the plume releasing source and the place where plume touches the Earth surface increases. The increased distance leads to greater dispersion and a lower concentration at ground level. — **Figure 5-5** Increased release height decreases the ground concentration.

The buoyancy and momentum of the material released change the effective height of the release. Figure 5-6 demonstrates these effects. The momentum of a high-velocity jet will carry the gas higher than the point of release, resulting in a much higher effective release height. If the gas has a density less than air, the released gas will initially be positively buoyant and will lift upward. Conversely, if the gas has a density greater than air, then the released gas will initially be negatively buoyant and will slump toward the ground. The temperature and molecular weight of the released gas determine the gas density relative to that of air (with a molecular weight of 28.97). For all gases, as the gas travels downwind and is mixed with fresh air, a point will eventually be reached where the gas has been diluted adequately to be considered neutrally buoyant. At this point the dispersion is dominated by ambient turbulence.

A vessel releasing plume is shown. The first stage of the released plume, as it comes out of the source, represents initial acceleration and dilution. Then, due to dominance of internal buoyancy, the plume starts flowing downward; again, due to dominance of ambient turbulence, it starts flowing upward. The plume flows in the direction of wind, which is shown by an arrow. — **Figure 5-6** The initial acceleration and buoyancy of the released material affect the plume character. The dispersion models discussed in this chapter represent only ambient turbulence. (Source: Adapted from Steven R. Hanna and Peter J. Drivas. *Guidelines for Use of Vapor Cloud Dispersion Models* (New York, NY: American Institute of Chemical Engineers, 1987), p. 6.)

5-2 Neutrally Buoyant Dispersion Models

Neutrally buoyant dispersion models are used to estimate the concentrations downwind of a release in which the gas is mixed with fresh air to the point that the resulting mixture is neutrally buoyant. Thus, these models apply to gases at low concentrations, typically in the ppm range.

Two types of neutrally buoyant vapor cloud dispersion models are commonly used: the plume and the puff models. The plume model describes the steady-state concentration of material released from a continuous source, whereas the puff model describes the temporal concentration of material from a single release of a fixed amount of material. The distinction between the two models is shown graphically in Figures 5-1 and 5-2. For the plume model, a typical example is the continuous release of gases from a smokestack. A steady-state plume is formed downwind from the smokestack. For the puff model, a typical example is the sudden release of a fixed amount of material because of the rupture of a storage vessel. A large vapor cloud is formed that moves downwind away from the release point.

The puff model can be used to describe a plume; a plume is simply the continuous release of puffs. However, if steady-state plume information is all that is required, the plume model is recommended because it is easier to use. For studies involving dynamic plumes (for instance, the effect on a plume of a change in wind direction), the puff model must be used.

Consider the instantaneous release of a fixed mass of material, Q∗m $Q_{m}^{*}$ , into an infinite expanse of air (a ground surface will be added later). The coordinate system is fixed at the source. Assuming no reaction or molecular diffusion, the concentration C of material resulting from this release is given by the advection equation

∂C∂t+∂∂xj(ujC)=0(5-1) $\begin{matrix} \frac{\partial C}{\partial t} + \frac{\partial}{\partial x_{j}} (u_{j} C) = 0 & (5-1) \end{matrix}$

where u_j is the velocity of the air and the subscript j represents the summation over all coordinate directions x, y, and z. If the velocity u_j in Equation 5-1 is set equal to the average wind velocity and the equation is solved, we would find that the material disperses much faster than predicted. This is due to turbulence in the velocity field. If we could specify the wind velocity exactly with time and position, including the effects resulting from turbulence, Equation 5-1 would predict the correct concentration. Unfortunately, no models are currently available to adequately describe turbulence. As a result, an approximation is used. Let the velocity be represented by an average (or mean) and stochastic quantity

uj=⟨uj⟩+u′j(5-2) $\begin{matrix} u_{j} = 〈 u_{j} 〉 + {u^{'}}_{j} & (5-2) \end{matrix}$

where

〈u_j〉 is the average velocity and

u′j $u_{j}^{'}$ is the stochastic fluctuation resulting from turbulence.

It follows that the concentration C will also fluctuate as a result of the velocity field; so

C=⟨C⟩+C′(5-3) $\begin{matrix} C = 〈 C 〉 + C^{'} & (5-3) \end{matrix}$

where

〈C〉 is the mean concentration and

C^’ is the stochastic fluctuation.

Because the fluctuations in both C and u_j are around the average or mean values, it follows that the average of the fluctuations is zero. Thus,

⟨u′j⟩=0⟨C′⟩=0(5-4) $\begin{matrix} 〈 u_{j}^{'} 〉 = 0 \\ 〈 C^{'} 〉 = 0 \end{matrix} (5-4)$

Substituting Equations 5-2 and 5-3 into Equation 5-1 and averaging the result over time yields

∂⟨C⟩∂t+∂∂xj(⟨uj⟩⟨C⟩)+∂∂xj⟨u′jC′⟩=0(5-5) $\begin{matrix} \frac{\partial 〈 C 〉}{\partial t} + \frac{\partial}{\partial x_{j}} (〈 u_{j} 〉〈 C 〉) + \frac{\partial}{\partial x_{j}} 〈 {u^{'}}_{j} C^{'} 〉 = 0 & (5-5) \end{matrix}$

The terms $〈 u_{j} 〉 C'$ and ${u^{'}}_{j} 〈 C 〉$ are zero when averaged $〈〈 u_{j} 〉 C^{'} 〉 = 〈 u_{j} 〉〈 C^{'} 〉 = 0,$ but the turbulent flux $〈 {u^{'}}_{j} C^{'} 〉$ term is not necessarily zero and remains in the equation.

At this point, there are two paths forward. The first approach is to define an eddy diffusivity (with units of area/time) such that

$\begin{matrix} 〈 u_{j}^{i} C^{'} 〉 = - K_{j} \frac{\partial 〈 C 〉}{\partial x_{j}} & (5-6) \end{matrix}$

However, the eddy diffusivity changes with position, wind velocity, prevailing atmospheric conditions, and time. Also, there is no direct way to measure eddy diffusivities. While the eddy diffusivity approach is useful theoretically, it cannot be practically applied.

The second approach is to use dispersion coefficients, which are described in the next section.

5-3 Pasquill–Gifford Model

Sutton¹ proposed the following definition for a dispersion coefficient:

$\begin{matrix} σ_{x}^{2} = \frac{1}{2} {〈 C 〉}^{2} {(u t)}^{2 - n} & (5-7) \end{matrix}$

¹O. G. Sutton. Micrometeorology (New York, NY: McGraw-Hill, 1953), p. 286.

with similar expressions given for σ_y and σ_z. The parameter n is used to fit the data. The dispersion coefficients σ_x, σ_y, and σ_z represent the standard deviations of the concentration in the downwind, crosswind, and vertical (x, y, z) directions, respectively. Values for the dispersion coefficients are much easier to measure experimentally than eddy diffusivities since the dispersion coefficients can be determined by measuring the actual downwind concentrations.

The dispersion coefficients are a function of atmospheric conditions and the distance downwind from the release. The atmospheric conditions are classified according to six different stability classes, shown in Table 5-1. These stability classes depend on wind speed and quantity of sunlight. During the day, increased wind speed results in greater atmospheric stability, whereas at night the reverse is true. This is due to a change in vertical temperature profiles from day to night, as shown in Figure 5-3.

Table 5-1 Atmospheric Stability Classes for Use with the Pasquill–Gifford Dispersion Model ^a, ^b

				Nighttime conditions^d
	Daytime insolation^c			Thin overcast
Surface wind speed (m/s)	Strong	Moderate	Slight	or >4/8 Low cloud	≤3/8 Cloudiness
<2	A	A–B	B	F^e	F^e
2–3	A–B	B	C	E	F
3–4	B	B–C	C	D ^f	E
4–6	C	C–D	D ^f	D ^f	D ^f
>6	C	D ^f	D ^f	D ^f	D ^f

Stability classes:

A, extremely unstable

B, moderately unstable

C, slightly unstable

D, neutrally stable

E, slightly stable

F, moderately stable

^aF. A. Gifford. “Use of Routine Meteorological Observations for Estimating Atmospheric Dispersion.” Nuclear Safety 2, no. 4. (1961): 47.

^bF. A. Gifford. “Turbulent Diffusion-Typing Schemes: A Review.” Nuclear Safety 17, no. 1 (1976): 68.

^cStrong insolation corresponds to a sunny midday in midsummer in England. Slight insolation corresponds to similar conditions in midwinter.

^dNight refers to the period 1 hr before sunset and 1 hr after dawn.

^eThese values are filled in to complete the table.

^fThe neutral category D should be used, regardless of wind speed, for overcast conditions during day or night and for any sky conditions during the hour before or after sunset or sunrise, respectively.

The dispersion coefficients σ_y and σ_z for a continuous source are given in Figures 5-7 and 5-8, with the corresponding correlations given in Table 5-2. Values for σ_x are not provided because it is reasonable to assume that σ_x = σ_y. The dispersion coefficients σ_y and σ_z for a puff release are given in Figure 5-9 and the equations are provided in Table 5-3. The puff dispersion coefficients are based on limited data (shown in Table 5-3) and should not be considered precise.

A graph of dispersion coefficients versus distance downwind. — **Figure 5-7** Dispersion coefficients for Pasquill–Gifford plume model for rural releases.

Two graphs represent the dispersion coefficients. The horizontal axes of both graphs represent distance downwind (measured in kilometers) that range from 0.1 to 10. The vertical axes of the two graphs represent dispersion coefficients sigma y and sigma z (measured in meters) that range from 10 to the power 0 to 10 to the power 4, in multiples of 10. In the first graph, six lines (A, B, C, D, E, and F) are drawn. Line A starts from 30 meters (an approximate point between 10 squared and 10 to the power 1) and ends slightly above 10 cubed. The remaining five lines are almost parallel to A and are sequentially below each other. All lines are drawn close to each other. In the second graph, six lines (A, B, C, D, E, and F) are drawn. Line A starts from 40 meters (an approximate point between 10 squared and 10 to the power 1) and ends slightly above 10 cubed. Remaining five lines are sequentially below each other. All lines are drawn slightly spaced apart (as compared to the first graph) from each other. Line B is almost parallel to line A and the remaining four lines follow a very slightly curved path.

Table 5-2 Recommended Equations for Pasquill–Gifford Dispersion Coefficients for Plume Dispersion

Pasquill–gifford Stability class	σ_y_(m)	σ_z_(m)
Rural conditions
A	0.22x(1 + 0.0001x)^–1/2	0.20x
B	0.16x(1 + 0.0001x)^–1/2	0.12x
C	0.11x(1 + 0.0001x)^–1/2	0.08x(1 + 0.0002x)^–1/2
D	0.08x(1 + 0.0001x)^–1/2	0.06x(1 + 0.0015x)^–1/2
E	0.06x(1 + 0.0001x)^–1/2	0.03x(1 + 0.0003x)^–1
F	0.04x(1 + 0.0001x)^–1/2	0.016x(1 + 0.0003x)^–1
Urban conditions
A–B	0.32x(1 + 0.0004x)^–1/2	0.24x(1 + 0.001x)^+1/2
C	0.22x(1 + 0.0004x)^–1/2	0.20x
D	0.16x(1 + 0.0004x)^–1/2	0.14x(1 + 0.0003x)^–1/2
E–F	0.11x(1 + 0.0004x)^–1/2	0.08x(1 + 0.0015x)^–1/2

The downwind distance x has units of meters. A–F are defined in Table 5-1.

Sources: R. F. Griffiths. “Errors in the Use of the Briggs Parameterization for Atmospheric Dispersion Coefficients.” Atmospheric Environment 28, no. 17 (1994): 2861–2865; G. A. Briggs. Diffusion Estimation for Small Emissions, Report ATDL-106 (Washington, DC: Air Resources, Atmospheric Turbulence, and Diffusion Laboratory, Environmental Research Laboratories, 1974).

Table 5-3 Recommended Equations for Pasquill–Gifford Dispersion Coefficients for Puff Dispersion

Pasquill–gifford stability class	σ_y_{(m) or} σ_x (m)	σ_z_(m)
A	0.18x^0.92	0.60x^0.75
B	0.14x^0.92	0.53x^0.73
C	0.10x^0.92	0.34x^0.71
D	0.06x^0.92	0.15x^0.70
E	0.04x^0.92	0.10x^0.65
F	0.02x^0.89	0.05x^0.61

The downwind distance x has units of meters. A–F are defined in Table 5-1.

Sources: R. F. Griffiths. “Errors in the Use of the Briggs Parameterization for Atmospheric Dispersion Coefficients.” Atmospheric Environment
28, no. 17 (1994): 2861–2865; G. A. Briggs. Diffusion Estimation for Small Emissions, Report ATDL-106 (Washington, DC: Air Resources, Atmospheric Turbulence, and Diffusion Laboratory, Environmental Research Laboratories, 1974).

The equations for cases 1 through 4 that follow were derived by Pasquill² using expressions of the form of Equation 5-7. These equations along with the correlations for the dispersion coefficients are known as the Pasquill–Gifford model.

²F. Pasquill. Atmospheric Diffusion (London, UK: Van Nostrand, 1962).

The geometry for the dispersion models is shown in Figure 5-10. The immediate downwind direction is x, the crosswind direction is y and the height above ground level is z. The origin at (x, y, z) is on the ground immediately below the release point. The height of the release above ground is given by H_r.

Dispersion modeling geometry is shown. The x axis represents downwind direction, the y axis represents crosswind direction, and the z axis represents height above ground level. The origin is marked as (x, y, z) or (0, 0, 0). The release height is marked as H r. The plume moves in the direction of wind, which is shown using a rightward arrow. — **Figure 5-10** Geometry for dispersion modeling.

Case 1: Puff with Instantaneous Point Source at Ground Level, Coordinates Fixed at Release Point, Constant Wind Only in x Direction with Constant Velocity u

This case is represented by the following equation. Details of the derivation of Equation 5-8 are provided in the supplemental content on the book’s website.

$\begin{matrix} \begin{matrix} 〈 C 〉 (x, y, z, t) = \frac{Q_{m}^{*}}{\sqrt{2} π^{3/2} σ_{x} σ_{y} σ_{z}} \exp {- \frac{1}{2} [{(\frac{x - u t}{σ_{x}})}^{2} + \frac{y^{2}}{σ_{y}^{2}} + \frac{z^{2}}{σ_{z}^{2}}]} \end{matrix} & (5-8) \end{matrix}$

where Q_m is the instantaneous release mass.

The time dependence in Equation 5-8 is achieved through the dispersion coefficients because their values change as the puff moves downwind. If wind is absent, u = 0, and Equation 5-8 does not produce a valid result since the puff does not move downwind at all.

The ground-level concentration is given at z = 0:

$\begin{matrix} 〈 C 〉 (x, y, 0, t) = \frac{Q_{m}^{*}}{\sqrt{2} π^{3/2} σ_{x} σ_{y} σ_{z}} \exp {- \frac{1}{2} [{(\frac{x - u t}{σ_{x}})}^{2} + \frac{y^{2}}{σ_{y}^{2}}]} & (5-9) \end{matrix}$

The ground-level concentration directly downwind from the release along the x axis is given at y = z = 0:

$\begin{matrix} 〈 C 〉 (x, 0, 0, t) = \frac{Q_{m}^{*}}{\sqrt{2} π^{3/2} σ_{x} σ_{y} σ_{z}} \exp {- \frac{1}{2} {(\frac{x - u t}{σ_{x}})}^{2}} & (5-10) \end{matrix}$

The center of the cloud is found at coordinates (ut, 0, 0). The concentration at the center of this moving cloud is given by

$\begin{matrix} 〈 C 〉 (u t, 0, 0, t) = \frac{Q_{m}^{*}}{\sqrt{2} π^{3/2} σ_{x} σ_{y} σ_{z}} & (5-11) \end{matrix}$

The total integrated dose D_tid received by an individual standing at fixed location (x, y, z) is the time integral of the concentration:

$\begin{matrix} D_{tid} (x, y, z) = \int_{0}^{\infty} 〈 C 〉 (x, y, z, t) d t & (5-12) \end{matrix}$

The total integrated dose at ground level is found by integrating Equation 5-9 according to Equation 5-12. The result is

$\begin{matrix} D_{t i d} (x, y, 0) = \frac{Q_{m}^{*}}{π σ_{y} σ_{z} u} \exp (- \frac{1}{2} \frac{y^{2}}{σ_{y}^{2}}) & (5-13) \end{matrix}$

The total integrated dose along the x axis on the ground directly downwind from the release is

$\begin{matrix} D_{t i d} (x, 0, 0) = \frac{Q_{m}^{*}}{π σ_{y} σ_{z} u} & (5-14) \end{matrix}$

Case 2: Plume with Continuous Steady-State Source at Ground Level and Wind Moving in x Direction at Constant Velocity u

This case is represented by the following equation:

$\begin{matrix} 〈 C 〉 (x, y, z) = \frac{Q_{m}}{π σ_{y} σ_{z} u} \exp [- \frac{1}{2} (\frac{y^{2}}{σ_{y}^{2}} + \frac{z^{2}}{σ_{z}^{2}})] & (5-15) \end{matrix}$

where Q_m is the mass release rate (mass/time)

The ground-level concentration is given at z = 0:

$\begin{matrix} 〈 C 〉 (x, y, 0) = \frac{Q_{m}}{π σ_{y} σ_{z} u} \exp [- \frac{1}{2} (\frac{y^{2}}{σ_{y}^{2}})] & (5-16) \end{matrix}$

The ground concentration along the centerline of the plume directly downwind is given at y = z = 0:

$\begin{matrix} 〈 C 〉 (x, 0, 0) = \frac{Q_{m}}{π σ_{y} σ_{z} u} & (5-17) \end{matrix}$

For continuous ground-level releases, the maximum concentration occurs at the release point.

Case 3: Plume with Continuous Steady-State Source at Height H_r above Ground Level and Wind Moving in x Direction at Constant Velocity u

The solution for this case is

$\begin{matrix} \begin{matrix} 〈 C 〉 (x, y, z) & = \frac{Q_{m}}{2 π σ_{y} σ_{z} u} \exp [- \frac{1}{2} {(\frac{y}{σ_{y}})}^{2}] \\ \times {\exp [- \frac{1}{2} {(\frac{z - H_{r}}{σ_{z}})}^{2}] + \exp [- \frac{1}{2} {(\frac{z + H_{r}}{σ_{z}})}^{2}]} \end{matrix} & (5-18) \end{matrix}$

The ground-level concentration is found by setting z = 0:

$\begin{matrix} 〈 C 〉 (x, y, 0) = \frac{Q_{m}}{π σ_{y} σ_{z} u} \exp [- \frac{1}{2} {(\frac{y}{σ_{y}})}^{2} - \frac{1}{2} {(\frac{H_{r}}{σ_{z}})}^{2}] & (5-19) \end{matrix}$

The ground-level centerline concentrations are found by setting y = z = 0:

$\begin{matrix} 〈 C 〉 (x, 0, 0) = \frac{Q_{m}}{π σ_{y} σ_{z} u} \exp [- \frac{1}{2} {(\frac{H_{r}}{σ_{z}})}^{2}] & (5-20) \end{matrix}$

The maximum ground-level concentration 〈C〉_max along the x axis is found using

$\begin{matrix} {〈 C 〉}_{\max} = \frac{2 Q_{m}}{e π u H_{r}^{2}} (\frac{σ_{z}}{σ_{y}}) & (5-21) \end{matrix}$

The distance downwind at which the maximum ground-level concentration occurs is found from

$\begin{matrix} σ_{z} = \frac{H_{r}}{\sqrt{2}} & (5-22) \end{matrix}$

The procedure for finding the maximum concentration and the downwind distance is to use Equation 5-22 to determine the downwind distance, followed by using Equation 5-21 to determine the maximum concentration.

Case 4: Puff with Instantaneous Point Source at Height H_r above Ground Level and a Coordinate System on the Ground That Moves with the Puff

For this case, the center of the puff is found at x = ut. The average concentration is given by

$\begin{matrix} \begin{matrix} 〈 C 〉 (x, y, z, t) & = \frac{Q_{m}^{*}}{{(2 π)}^{3/2} σ_{x} σ_{y} σ_{z}} \exp [- \frac{1}{2} {(\frac{y}{σ_{y}})}^{2}] \\ \times {\exp [- \frac{1}{2} {(\frac{z - H_{r}}{σ_{z}})}^{2}] + \exp [- \frac{1}{2} {(\frac{z + H_{r}}{σ_{z}})}^{2}]} \end{matrix} & (5-23) \end{matrix}$

At ground level, z = 0, and the concentration is computed using

$\begin{matrix} \begin{matrix} 〈 C 〉 (x, y, 0, t) = \frac{Q_{m}^{*}}{\sqrt{2} π^{3 / 2} σ_{x} σ_{y} σ_{z}} \exp [- \frac{1}{2} {(\frac{y}{σ_{y}})}^{2} - \frac{1}{2} {(\frac{H_{r}}{σ_{z}})}^{2}] \end{matrix} & (5-24) \end{matrix}$

The concentration along the ground at the centerline is given at y = z = 0:

$\begin{matrix} \begin{matrix} 〈 C 〉 (x, 0, 0, t) = \frac{Q_{m}^{*}}{\sqrt{2} π^{3 / 2} σ_{x} σ_{y} σ_{z}} \exp [- \frac{1}{2} {(\frac{H_{r}}{σ_{z}})}^{2}] \end{matrix} & (5-25) \end{matrix}$

The total integrated dose at ground level is found by using Equation 5-25 in Equation 5-12. The result is

$\begin{matrix} \begin{matrix} D_{tid} (x, y, 0) = \frac{Q_{m}^{*}}{π σ_{y} σ_{z} u} \exp [- \frac{1}{2} {(\frac{y}{σ_{y}})}^{2} - \frac{1}{2} {(\frac{H_{r}}{σ_{z}})}^{2}] \end{matrix} & (5-26) \end{matrix}$

Case 5: Puff with Instantaneous Point Source at Height H_r above Ground Level and a Coordinate System Fixed on the Ground at the Release Point

For this case, the result is obtained using a transformation of coordinates. If the puff moves with the wind along the x axis, the equation for this case is found by replacing the existing coordinate x by a new coordinate system, x − ut, that moves with the wind velocity. The result is

$\begin{matrix} 〈 C 〉 (x, y, z, t) & = [Puff equations with moving coordinate system (Equations 5-23 through 5-25) & (5-27) \\ \times exp [- \frac{1}{2} {(\frac{x - u t}{σ_{x}})}^{2}] \end{matrix}$

where t is the time since the release of the puff.

Isopleths

Frequently the cloud boundary defined by a fixed concentration is required for either the plume or the puff. The line connecting points of equal concentration around the cloud boundary is called an isopleth. For a specified concentration 〈C〉^*, the isopleth at ground level is determined by dividing the equation for the centerline concentration (Equation 5-10 for a puff and Equation 5-16 for a plume) by the equation for the general ground-level concentration (Equation 5-9 for a puff and Equation 5-16 for a plume). This equation is solved directly for y:

$\begin{matrix} y = σ_{y} \sqrt{2 \ln (\frac{〈 C 〉 (x, 0, 0, t)}{〈 C 〉 (x, y, 0, t)})} & (5-28) \end{matrix}$

The procedure is as follows:

Specify the isopleth concentration 〈C〉^*, the wind speed u, and time t.
Determine the concentrations 〈C〉 (x, 0, 0, t) at fixed points along the x axis using Equation 5-10 for a puff and Equation 5-16 for a plume. Define the boundary of the cloud along the x axis.
Set 〈C〉 (x, y, 0, t) = 〈C〉^* in Equation 5-28 and determine the values of y at each centerline point determined in step 2.
Plot dots at each +y and –y at each centerline point x.
Connect the dots to obtain the isopleth.

The procedure is repeated for each value of t required.

Effect of Release Momentum and Buoyancy

Figure 5-5 shows that the release characteristics of a puff or plume depend on the initial release momentum and buoyancy. The initial momentum and buoyancy change the effective height of the release. A release that occurs at ground level but in an upward spouting jet of vaporizing liquid has a greater effective height than a release without a jet. Similarly, a release of vapor at a temperature higher than the ambient air temperature will rise because of buoyancy effects, increasing the effective height of the release.

Both effects are demonstrated by the traditional smokestack release shown in Figure 5-11. The material released from the smokestack contains momentum, based on its upward velocity within the stack pipe, and it is also buoyant, because its temperature is higher than the ambient temperature. As a consequence, the material continues to rise after its release from the stack. The upward rise is slowed and eventually stopped as the released material cools and the momentum is dissipated.

A source releasing hot gases continuously is shown. The formed plume moves in the direction of wind, which is shown by an arrow. The released gases cool as they mix and dilute with cool air. As plume moves away from the source, due to neutral buoyancy, it flows slightly above the releasing source. — **Figure 5-11** Smokestack plume demonstrating initial buoyant rise of hot gases.

For smokestack releases, Turner³ suggested using the empirical Holland formula to compute the additional height resulting from the buoyancy and momentum of the release:

³D. Bruce Turner. Workbook of Atmospheric Dispersion Estimates (Cincinnati, OH: U.S. Department of Health, Education, and Welfare, 1970), p. 31.

$\begin{matrix} Δ H_{r} = \frac{{\bar{u}}_{s} d}{\bar{u}} [1.5 + 2.68 \times 10^{- 3} P d (\frac{T_{s} - T_{a}}{T_{s}})] & (5-29) \end{matrix}$

where

ΔH_r is the correction to the release height H_r,

${\bar{u}}_{s}$ is the stack gas exit velocity (m/s),

d is the inside stack diameter (m),

$\bar{u}$ is the wind speed (m/s),

P is the atmospheric pressure (millibar),

T_s is the stack gas temperature (K), and

T_a is the air temperature (K).

For heavier-than-air vapors, if the material is released above ground level, then the material will initially fall toward the ground until it disperses enough to reduce the cloud density.

Worst-Case Dispersion Conditions

For a plume, the highest concentration is always found at the release point. If the release occurs above ground level, then the highest concentration on the ground is found at a point downwind from the release.

For a puff, the maximum concentration is always found at the puff center. For a release above ground level, the puff center will move parallel to the ground and the maximum concentration on the ground will occur directly below the puff center. For a puff isopleth, the isopleth is close to circular as it moves downwind. The diameter of the isopleth increases initially as the puff travels downwind, reaches a maximum, and then decreases in diameter.

If weather conditions are not known or are not specified, then certain assumptions can be made to result in a worst-case result—that is, the highest concentration is estimated. The weather conditions in the Pasquill–Gifford dispersion equations are included by means of the dispersion coefficients and the wind speed. By examining the Pasquill–Gifford equations, it is readily evident that the dispersion coefficients and wind speed are in the denominator. In turn, the maximum concentration is estimated by selecting the weather conditions and wind speed that result in the smallest values of the dispersion coefficients and the wind speed. By inspecting Figures 5-7 through 5-9, we can see that the smallest dispersion coefficients occur with F stability. Clearly, the wind speed cannot be zero, so a finite value must be selected. The EPA⁴ suggests that F stability can exist with wind speeds as low as 1.5 m/s. In contrast, other risk analysts use a wind speed of 2 m/s to be consistent with the F stability class. For daytime conditions, some risk analysts use D stability with 3 m/s wind speed. The assumptions used in the calculation must be clearly reported.

⁴U.S. Environmental Protection Agency. RMP Offsite Consequence Analysis Guidance (Washington, DC: U.S. Environmental Protection Agency, 1996).

The worst case on the ground is frequently of interest, given that this is where people are normally present. For the plume and puff cases, we can select the following:

Plume: Along the centerline downwind from the release on ground:

$\begin{matrix} 〈 C 〉 (x, 0, 0) = \frac{Q_{m}}{π σ_{y} σ_{z} u} & (5-30) \end{matrix}$

Puff: At the center of the puff with the release on the ground:

$\begin{matrix} 〈 C 〉 (x, 0, 0) = \frac{Q_{m}^{*}}{\sqrt{2} π^{3 / 2} σ_{x} σ_{y} σ_{z} u} & (5-31) \end{matrix}$

The maximum concentration is obtained by:

Specifying the release rate, Q_m and $Q_{m}^{*}$ , at the maximum value.
Specifying all the dispersion coefficients, σ, at the minimum value. This implies F stability.
Specifying the wind speed, u, at a minimum within the stability class. For F stability, this implies 2 m/s or the EPA-suggested value of 1.5 m/s. For daytime, some risk analysts use D stability with 3 m/s wind speed.

Limitations to Pasquill–Gifford Dispersion Modeling

Pasquill–Gifford or Gaussian dispersion applies only to neutrally buoyant dispersion of gases in which the turbulent mixing is the dominant feature of the dispersion. It is typically valid only for a distance of 0.1–10 km from the release point.

It is not always clear whether a plume or puff model should be selected based on the nature of the release: The two models may produce varying results. A release of less than 15 seconds is typically modeled as an instantaneous puff release, but what about a release of 30 seconds?

The concentrations predicted by the Gaussian models are time averages. Thus, it is possible for instantaneous local concentrations to exceed the average values predicted—a difference that might be important for emergency response. The models presented here assume a 10-minute time average. Actual instantaneous concentrations may vary by as much as a factor of 2 from the concentrations computed using Gaussian models.

Example 5-1

Assume that 10 kg/s of hydrogen sulfide (H₂S) gas is released 100 m above the ground. It is a clear, sunny day, 1:00 pm, with a wind speed of 3.5 m/s. Assume rural conditions. The temperature is 30°C and the pressure is 1 atm. The molecular weight of H₂S is 34.08. Determine

The concentration 1 km downwind on the ground.
The maximum concentration from this release and the distance downwind.
The maximum discharge rate, in kg/s, to result in a maximum concentration downwind of 10 ppm.

Solution

This is a plume since it is a continuous release. From Table 5-1 for a clear sunny day (strong insolation) and a wind speed of 3.5 m/s, the stability class is B. From Table 5-2 for rural releases,

$\begin{matrix} σ_{y} & = 0.16 x {(1 + 0.0001 x)}^{- 1 / 2} \\ = 0.16 (1000 m) {[1 + (0.0001) (1000 m)]}^{- 1 / 2} \\ σ_{y} & = 153 m \\ σ_{z} & = 0.12 x = 0.12 (1000 m) = 120 m \end{matrix}$

These dispersion coefficients could also be determined using Figure 5-7.

Since this is a plume, with a release above ground level, Case 3 and Equation 5-20 applies:

$〈 C 〉 (x, 0, 0) = \frac{Q_{m}}{π σ_{y} σ_{z} u} \exp [- \frac{1}{2} {(\frac{H_{r}}{σ_{z}})}^{2}]$

Substituting the numbers

$\begin{matrix} 〈 C 〉 (x, 0, 0) & = \frac{10.0 kg/s}{(3.14) (153 m)(120 m)(3.5 m/s)} \exp [- \frac{1}{2} {(\frac{100 m}{120 m})}^{2}] \\ = 3.50 \times 10^{- 5} {kg/m}^{3} = 35.0 {mg/m}^{3} \end{matrix}$

Use Equation 2-7 to convert to ppm, being careful to use the correct units:

$\begin{matrix} C_{ppm} & = 0.08205 (\frac{T}{P M}) ({mg/m}^{3}) \\ = 0.08205 [\frac{303 K}{(1 atm) (34.08 g/mol)}] (35.0 {mg/m}^{3}) \\ = 25.6 ppm \end{matrix}$
Use Equation 5-22 to determine the value of σ_z at the location of the maximum concentration.

$σ_{z} = \frac{H_{r}}{\sqrt{2}} = \frac{100 m}{1.414} = 70.7 m$

Then use the equation in Table 5-3 to determine the downwind distance.

$\begin{matrix} σ_{z} = 0.12 x \\ 70.7 m=0.12x \\ x = 589 m \end{matrix}$

Use the equation in Table 5-2 (or Figure 5-7) to determine the value of σ_y at this location,

$\begin{matrix} σ_{y} & = 0.16 x {(1 + 0.0001 x)}^{- 1 / 2} \\ = 0.16 (589 m) {[1 + (0.0001) (589 m)]}^{- 1 / 2} \\ = 91.6 m \end{matrix}$

Now use Equation 5-21 to determine the maximum concentration at this location downwind.

$\begin{matrix} {\begin{matrix} 〈 C 〉 \end{matrix}}_{max} & = \frac{2 Q_{m}}{e π u H_{r}^{2}} (\frac{σ_{z}}{σ_{y}}) \\ = \frac{(2) (100;kg/s)}{(2.718) (3.14) (3.5 m/s) {(100 m)}^{2}} (\frac{70.7 m}{91.6 m}) \\ = 5.17 \times 10^{- 4} {kg/m}^{3} = 517 {mg/m}^{3} \end{matrix}$

This is 378 ppm from Equation 2-7.
From Equation 2-7, 10 ppm = 13.7 mg/m³ =13.7×10^-6kg/m³. Substituting into Equation 5-21 and solving for Q_m,

$\begin{array}{l} {〈 C 〉}_{\max} = \frac{2 Q_{m}}{e π u H_{r}^{2}} (\frac{σ_{z}}{σ_{y}}) \\ 13.7 \times 10^{- 6} {kg/m}^{3} = \frac{2 Q_{m}}{(2.71) (3.14) (3.5 m/s) {(100 m)}^{2}} (\frac{70.7 m}{91.6 m}) \\ Q_{m} = 2.64 kg/s \end{array}$

Example 5-2

Assume that 10 kg of hydrogen sulfide (H₂S) is released instantly on the ground. The atmospheric conditions are the same as Example 5-1.

What is the maximum concentration at the fence line 100 m away?
If the wind is 3.5 m/s, how long does it take for the puff to reach the fence line?

Solution

This is a puff since the release is instantaneous. From Table 5-1, the stability class is B. From Table 5-3 for stability class B,

$\begin{array}{l} σ_{y} = σ_{x} = 0.14 x^{0.92} = (0.14) {(100 m)}^{0.92} = 9.7 m \\ σ_{z} = 0.53 x^{0.73} = (0.53) {(100 m)}^{0.73} = 15.3 m \end{array}$

The maximum concentration is found at the center of the puff on the ground. Equation 5-11 applies:

$\begin{matrix} 〈 C 〉 (u t, 0, 0, t) & = \frac{Q_{m}^{*}}{\sqrt{2} π^{3/2} σ_{x} σ_{y} σ_{z}} \\ = \frac{10 kg}{(1.41) {(3.14)}^{3 / 2} (9.7 m) (9.7 m) (15.3 m)} \\ = 8.85 \times 10^{- 4} {kg/m}^{3} = 885 {mg/m}^{3} \end{matrix}$

From Equation 2-7, this is 647 ppm.
The time is found from

$\begin{array}{l} x = u t \\ t = \frac{x}{u} = \frac{100 m}{3.5 m/s} = 28.6 s \end{array}$

This is not very much time to mount much of an emergency response.

5-4 Dense Gas Dispersion

A dense gas is defined as any gas whose density is greater than the density of the ambient air through which it is being dispersed. This result can be due to a gas with a molecular weight greater than that of air or a gas with a low temperature resulting from auto-refrigeration during release or other processes.

Following a typical puff release, a cloud having similar vertical and horizontal dimensions (near the source) may form. The dense cloud will slump toward the ground under the influence of gravity, increasing its diameter and reducing its height. Considerable initial dilution will occur because of the gravity-driven intrusion of the cloud into the ambient air. Subsequently, the cloud height will increase due to further entrainment of air across both the vertical and the horizontal interfaces. After sufficient dilution occurs, normal atmospheric turbulence predominates over gravitational forces and typical Gaussian dispersion characteristics are exhibited.

Britter and McQuaid⁵ developed a model of dense gas dispersion by performing a dimensional analysis and correlating existing data on this phenomenon. Their model is best suited for instantaneous or continuous ground-level releases of dense gases. The release is assumed to occur at ambient temperature and without aerosol or liquid droplet formation. Atmospheric stability was found to have little effect on the results and is not a part of the model. Most of the data came from dispersion tests in remote rural areas on mostly flat terrain, so the results are not applicable to areas where terrain effects are significant.

⁵R. E. Britter and J. McQuaid. Workbook on the Dispersion of Dense Gases (Sheffield, UK: Health and Safety Executive, 1988).

Dense gas dispersion is beyond the scope of this book. Readers are referred to supplemental content on this subject provided on the book’s website.

5-5 Toxic Effect Criteria

Once the dispersion calculations are completed, the question arises: What concentration is considered hazardous? Concentrations based on TLV-TWA values, discussed in Chapter 2, are overly conservative and are designed for worker exposures, not short-term exposures under emergency conditions.

One approach is to use the probit equations developed in Chapter 2. These equations are also capable of including the effects resulting from transient changes in toxic concentrations. Unfortunately, published correlations are available for only a few chemicals, and actual data show wide variations from the correlations.

One simplified approach is to specify a toxic concentration criterion above which it is assumed that individuals exposed to this value or greater will be in danger. This approach has led to many criteria promulgated by several government agencies and private associations:

Emergency response planning guidelines (ERPGs) for air contaminants issued by the American Industrial Hygiene Association (AIHA)
Immediately dangerous to life and health (IDLH) levels established by U.S. National Institute of Occupational Safety and Health (NIOSH), already presented in Chapter 2
Emergency exposure guidance levels (EEGLs) and short-term public emergency guidance levels (SPEGLs) issued by the National Academy of Sciences/National Research Council (NRC)
Acute exposure guideline levels (AEGLs) established by the U.S. Environmental Protection Agency (EPA)
Threshold limit values (TLVs) established by the American Conference of Governmental Industrial Hygienists (ACGIH), including short-term exposure limits (TLV-STELs) and ceiling concentrations (TLV-Cs), already presented in Chapter 2
Permissible exposure limits (PELs) promulgated by U.S. Occupational Safety and Health Administration (OSHA), already presented in Chapter 2
Toxic endpoints promulgated by the EPA as part of the Risk Management Plan (RMP) regulation

These criteria and methods are based on a combination of results from animal experiments, observations of long- and short-term human exposures, and expert judgment. The following subsections define these criteria and describe some of their features.

Emergency Response Planning Guidelines

ERPGs are prepared by an industry task force and are published by the AIHA. Three concentration ranges are provided as a consequence of exposure to a specific substance:

ERPG-1 is the maximum airborne concentration below which it is believed nearly all individuals could be exposed for up to 1 hour without experiencing effects other than mild transient adverse health effects or perceiving a clearly defined objectionable odor.
ERPG-2 is the maximum airborne concentration below which it is believed nearly all individuals could be exposed for up to 1 hour without experiencing or developing irreversible or other serious health effects or symptoms that could impair their abilities to take protective action.
ERPG-3 is the maximum airborne concentration below which it is believed nearly all individuals could be exposed for up to 1 hour without experiencing or developing life-threatening health effects.

ERPG data are shown in Table 5-4. To date, 47 ERPGs have been developed and are being reviewed, updated, and expanded by an AIHA peer review task force. Because of the comprehensive effort to develop acute toxicity values, ERPGs are becoming an acceptable industry/government norm.

Table 5-4 Emergency Response Planning Guidelines (ERPGs), in ppm

Chemical	ERPG-1	ERPG-2	ERPG-3
Acetaldehyde	10	200	1000
Acetic acid	5	35	250
Acetic anhydride	0.5	15	100
Acrolein	0.05	0.15	1.5
Acrylic acid	1.0	50	250
Acrylonitrile	10	35	75
Allyl chloride	3	40	300
Ammonia	25	150	750
Benzene	50	150	1000
Benzyl chloride	1	10	50
Beryllium	NA	25 μg/m³	100 μg/m³
Bromine	0.1	0.5	5
1,3-Butadiene	10	200	5000
n-Butyl acrylate	0.05	25	250
n-Butyl isocyanate	0.01	0.05	1
Carbon disulfide	1	50	500
Carbon monoxide	200	350	500
Carbon tetrachloride	20	100	750
Chlorine	1	3	20
Chlorine trifluoride	0.1	1	10
Chloroacetyl chloride	0.05	0.5	10
Chloroform	NA	50	5000
Chloropicrin	0.1	0.3	1.5
Chlorosulfonic acid	2 mg/m³	10 mg/m³	30 mg/m³
Chlorotrifluoroethylene	20	100	300
Crotonaldehyde	0.2	1	3
Diborane	NA	1	3
1,2-Dichloroethane	50	200	300
Diketene	1	5	20
Dimethylamine	0.6	100	350
Dimethyldichlorosilane	2	10	75
Dimethyl disulfide	0.01	50	250
Epichlorohydrin	5	20	100
Ethanol	1800	3300	NA
Ethyl chloroformate	ID	100	200
Ethylene oxide	NA	50	500
Fluorine	0.5	5	20
Formaldehyde	1	10	25
Formic acid	3	25	250
Gasoline	200	1000	4000
Hexachlorobutadiene	1	3	10
Hexafluoroacetone	NA	1	50
Hexafluoropropylene	10	50	500
Hydrogen chloride	3	20	150
Hydrogen cyanide	NA	10	25
Hydrogen fluoride	2	20	50
Hydrogen peroxide	10	50	100
Hydrogen sulfide	0.1	30	100
Isobutyronitrile	10	50	200
2-Isocyanatoethyl methacrylate	ID	0.1	1
Lithium hydride	25 μg/m³	100 μg/m³	500 μg/m³
Methanol	200	1000	5000
Methyl chloride	NA	400	1000
Methylene diphenyl diisocynate	0.2 mg/m³	2 mg/m³	25 mg/m³
Methyl isocyanate	0.025	0.25	1.5
Methyl mercaptan	0.005	25	100
Methyltrichlorosilane	0.5	3	15
Monomethylamine	10	100	500
Nitrogen dioxide	1	15	30
Perfluoroisobutylene	NA	0.1	0.3
Phenol	10	50	200
Phosgene	NA	0.5	1.5
Phosphorus pentoxide	1 mg/m³	10 mg/m³	50 mg/m³
Propylene oxide	50	250	750
Styrene	50	250	1000
Sulfonic acid (oleum, sulfur trioxide, and sulfuric acid)	2 mg/m³	10 mg/m³	120 mg/m³
Sulfur dioxide	0.3	3	15
Tetrafluoroethylene	200	1000	10,000
Titanium tetrachloride	5 mg/m³	20 mg/m³	100 mg/m³
Toluene	50	300	1000
Trimethylamine	0.1	100	500
Uranium hexafluoride	5 mg/m³	15 mg/m³	30 mg/m³
Vinyl acetate	5	75	500
Vinyl chloride	500	5000	20,000

Notes: NA = Not appropriate, ID = insufficient data, µg = microgram. All values are in ppm unless otherwise noted.

Source: American Industrial Hygiene Association. Emergency Response Planning Guidelines and Workplace Environmental Exposure Levels (Fairfax, VA: American Industrial Hygiene Association, 2010). www.aiha.org.

Immediately Dangerous to Life and Health

NIOSH publishes IDLH concentrations to be used as acute toxicity measures for common industrial gases. An IDLH exposure condition is defined as a condition “that poses a threat of exposure to airborne contaminants when that exposure is likely to cause death or immediate or delayed permanent adverse health effects or prevent escape from such an environment.”⁶

⁶U.S. National Institute of Occupational Safety and Health. NIOSH Pocket Guide to Chemical Hazards (Washington, DC: U.S. Department of Health and Human Services, 2005). www.cdc.gov/niosh/npg/default.html.

IDLH concentrations also take into consideration acute toxic reactions, such as severe eye irritation, that could prevent escape from the contaminated site. The IDLH concentration is considered a maximum concentration above which only a highly reliable breathing apparatus providing maximum worker protection is permitted. If IDLH concentrations are exceeded, all unprotected workers must leave the area immediately.

IDLH data are currently available for a number of chemicals (see www.cdc.gov/niosh/idlh/intridl4.html). IDLH concentrations are developed to protect healthy worker populations and are not directly suitable for the general population, which includes sensitive populations such as older, disabled, or ill individuals. For flammable vapors, the IDLH concentration is defined as one-tenth of the lower flammability limit (LFL) concentration. Note that IDLH concentrations have not been peer-reviewed and that no substantive documentation for the values exists.

Emergency Exposure Guidance Levels and Short-Term Public Emergency Guidance Levels

Since the 1940s, the NRC’s Committee on Toxicology has submitted EEGLs for chemicals of special concern to the Department of Defense. An EEGL is defined as a concentration of a gas, vapor, or aerosol that is judged acceptable and that allows exposed individuals to perform specific tasks during emergency conditions lasting from 1 to 24 hours. Exposure to concentrations at the EEGL may produce transient irritation or central nervous system effects but should not produce effects that are lasting or that would impair performance of a task.

In addition to EEGLs, the National Research Council has developed SPEGLs, defined as acceptable concentrations for exposures of members of the general public. SPEGLs are generally set at 10–50% of the EEGL and are calculated to take into account the effects of exposure on sensitive heterogeneous populations.

The advantages of using EEGLs and SPEGLs rather than IDLH concentrations are
(1) a SPEGL considers effects on sensitive populations, (2) EEGLs and SPEGLs are developed for several different exposure durations, and (3) the methods by which EEGLs and SPEGLs were developed are well documented in NRC publications. EEGL and SPEGL values are shown in Table 5-5.

Table 5-5 Emergency Exposure Guidance Levels (EEGLs) from the National Research Council, in ppm

Compound	1-hr EEGL	24-hr EEGL	Source
Acetone	8500	1000	NRC I
Acrolein	0.05	0.01	NRC I
Aluminum oxide	15 mg/m³	100	NRC IV
Ammonia	100		NRC VII
Arsine	1	0.1	NRC I
Benzene	50	2	NRC VI
Bromotrifluoromethane	25,000		NRC III
Carbon disulfide	50		NRC I
Carbon monoxide	400	50	NRC IV
Chlorine	3	0.5	NRC II
Chlorine trifluoride	1		NRC II
Chloroform	100	30	NRC I
Dichlorodifluoromethane	10,000	1000	NRC II
Dichlorofluoromethane	100	3	NRC II
Dichlorotetrafluoroethane	10,000	1000	NRC II
1,1-Dimethylhydrazine	0.24^a	0.01^a	NRC V
Ethanolamine	50	3	NRC II
Ethylene glycol	40	20	NRC IV
Ethylene oxide	20	1	NRC VI
Fluorine	7.5		NRC I
Hydrazine	0.12^a	0.005^a	NRC V
Hydrogen chloride	20/1^a	20/1^a	NRC VII
Hydrogen sulfide		10	NRC IV
Isopropyl alcohol	400	200	NRC II
Lithium bromide	15 mg/m³	7 mg/m³	NRC VII
Lithium chromate	100 μg/m³	50 μg/m³	NRC VIII
Mercury (vapor)		0.2 mg/m³	NRC I
Methane		5000	NRC I
Methanol	200	10	NRC IV
Methylhydrazine	0.24^a	0.01^a	NRC V
Nitrogen dioxide	1^a	0.04^a	NRC IV
Nitrous oxide	10,000		NRC IV
Ozone	1	0.1	NRC I
Phosgene	0.2	0.02	NRC II
Sodium hydroxide	2 mg/m³		NRC II
Sulfur dioxide	10	5	NRC II
Sulfuric acid	1 mg/m³		NRC I
Toluene	200	100	NRC VII
Trichloroethylene	200	10	NRC VIII
Trichlorofluoromethane	1500	500	NRC II
Trichlorotrifluoroethane	1500	500	NRC II
Vinylidene chloride		10	NRC II
Xylene	200	100	NRC II

Note: All values are in ppm unless otherwise noted.

^aSPEGL value.

Acute Exposure Guideline Levels

AEGLs are developed by the U.S. EPA and are used by emergency planners and responders as guidance in dealing with accidental releases of chemicals. They are expressed as specific concentrations of airborne chemicals at which health effects may occur. These guidelines are designed to protect the elderly and children and other individuals who may be susceptible to exposures.

AEGLs are determined for five relatively short exposure periods: 10 minutes, 30 minutes, 1 hour, 4 hours, and 8 hours. There are three levels—1, 2, and 3—based on the severity of the toxic effects caused by the exposure, with level 1 being the least severe and level 3 being the most severe. The three levels are further defined as follows:

Level 1: Notable discomfort, irritation, or certain asymptomatic nonsensory effects. However, the effects are not disabling and are transient and reversible upon cessation of exposure.

Level 2: Irreversible or other serious, long-lasting adverse health effects or an impaired ability to escape.

Level 3: Life-threatening health effects or death.

Airborne concentrations below the AEGL-1 levels represent exposure levels that could produce mild and progressively increasing but transient and nondisabling odor, taste, and sensory irritation or certain asymptomatic, nonsensory effects. With increasing airborne concentrations above each AEGL level, there is a progressive increase in the likelihood of occurrence and the severity of effects.

AEGL levels represent threshold levels for the general public—including susceptible populations such as infants, children, elderly individuals, persons with asthma, and those with other illnesses. However, specific individuals subject to unique responses, could experience effects below the corresponding AEGL levels. Table 5-6 provides a selected list of AEGLs.

Table 5-6 Selected Acute Exposure Guideline Levels (AEGLs) from U.S. EPA, in ppm

Chemical name	AEGL-1					AEGL-2					AEGL-3
Chemical name	10 min	30 min	1 hr	4 hr	8 hr	10 min	30 min	4 hr	1 hr	8 hr	10 min	30 min	1 hr	4 hr	8 hr
Carbon tetrachloride	NR	NR	NR	NR	NR	27	18	13	7.6	5.8	700	450	340	200	150
Aniline	48	16	8.0	2.0	1.0	72	24	12	3.0	1.5	120	40	20	5.0	2.5
Chloroform	NR	NR	NR	NR	NR	120	80	64	40	29	4000	4000	3200	2000	1600
Methyl bromide	NR	NR	NR	NR	NR	940	380	210	67	67	3300	1300	740	230	130
Methyl chloride	NR	NR	NR	NR	NR	1100	1100	910	570	380	3800	3800	3000	1900	1300
Hydrogen cyanide	2.5	2.5	2.0	1.3	1.0	17	10	7.1	3.5	2.5	27	21	15	8.6	6.6
Vinyl chloride	450	310	250	140	70	2800	1600	1200	820	820	12,000	6800	4800	3400	3400
Acetonitrile	13	13	13	13	NR	80	80	50	21	14	240	240	150	64	42
Carbon disulfide	17	17	13	8.4	6.7	200	200	160	100	50	600	600	480	300	150
Ethylene oxide	NR	NR	NR	NR	NR	80	80	45	14	7.9	360	360	200	63	35
Phosgene	NR	NR	NR	NR	NR	0.60	0.60	0.30	0.08	0.04	3.6	1.5	0.75	0.20	0.09
Propylene oxide	73	73	73	73	73	440	440	290	130	86	1300	1300	870	390	260
Methyl ethyl ketone	200	200	200	200	200	4900^a	3400^a	2700^a	1700	1700	^b	^b	4000^a	2500^a	2500^a
Epichlorohydrin	1.7	1.7	1.7	1.7	1.7	53	53	24	14	6.7	570	160	72	44	20
Acrolein	0.03	0.03	0.03	0.03	0.03	0.44	0.18	0.10	0.10	0.10	6.2	2.5	1.4	0.48	0.27
Acrylonitrile	1.5	1.5	NR	NR	NR	8.6	3.2	1.7	0.48	0.26	130	50	28	9.7	5.2
Vinyl acetate	6.7	6.7	6.7	6.7	6.7	46	46	36	23	15	230	230	180	110	75
Chlorobenzene	10	10	10	10	10	430	300	150	150	150	1100	800	400	400	400
Phenol	19	19	15	9.5	6.3	29	29	23	15	12	NR	NR	NR	NR	NR
Ethyl isocyanate	NR	NR	NR	NR	NR	0.20	0.065	0.034	0.0085	0.0040	0.60	0.20	0.10	0.025	0.013
Furan	NR	NR	NR	NR	NR	12	8.5	6.8	1.7	0.85	35	24	19	4.8	2.4
Ethyleneimine	NR	NR	NR	NR	NR	33	9.8	4.6	1.0	0.47	51	19	9.9	2.8	1.5
Hydrazine	0.1	0.1	0.1	0.1	0.1	23	16	13	3.1	1.6	64	45	35	8.9	4.4
Sulfur dioxide	0.20	0.20	0.20	0.20	0.20	0.75	0.75	0.75	0.75	0.75	30	30	30	19	9.6
Hydrogen chloride	1.8	1.8	1.8	1.8	1.8	100	43	22	11	11	620	210	100	26	26
Hydrogen fluoride	1.0	1.0	1.0	1.0	1.0	95	34	24	12	12	170	62	44	22	22
Ammonia	30	30	30	30	30	220	220	160	110	110	2700	1600	1100	550	390
Bromine	0.033	0.033	0.033	0.033	0.033	0.55	0.33	0.24	0.13	0.095	19	12	8.5	4.5	3.3
Chlorine	0.50	0.50	0.50	0.50	0.50	2.8	2.8	2.0	1.0	0.71	50	28	20	10	7.1
Hydrogen sulfide	0.75	0.60	0.51	0.36	0.33	41	32	27	20	17	76	59	50	NR	NR
Phosphine	NR	NR	NR	NR	NR	4.0	4.0	2.0	0.50	0.25	7.2	7.2	3.6	0.90	0.45
Nitrogen dioxide	0.50	0.50	0.50	0.50	0.50	20	15	12	8.2	6.7	34	25	20	14	11

Notes: NR, Not reported. Values are in parts per million (ppm).

^aGreater than 10% LFL.

^bGreater than 50% LFL.

Source: www.epa.gov/aegl/access-acute-exposure-guideline-levels-aegls-values, accessed September 6, 2018.

Threshold Limit Values

Certain ACGIH criteria may be appropriate for use as benchmarks. The ACGIH threshold limit values—TLV-STELs and TLV-Cs—are designed to protect workers from acute effects resulting from exposure to chemicals; such effects include irritation and narcosis. These criteria are discussed in Chapter 2. The TLV criteria can be used for toxic gas dispersion but typically produce a conservative result because they are designed for worker exposures during a normal 40-hour workweek.

Permissible Exposure Limits

The PELs are promulgated by OSHA and have the force of law. These levels are similar to the ACGIH criteria for TLV-TWAs because they are also based on 8-hour time-weighted average exposures. OSHA-cited “acceptable ceiling concentrations,” “excursion limits,” or “action levels” may be appropriate for use as benchmarks.

Toxic Endpoints

The EPA has promulgated a set of toxic endpoints to be used for air dispersion modeling for toxic gas releases as part of the EPA Risk Management Plan (RMP).⁷ The toxic endpoint is, in order of preference, (1) the ERPG-2 or (2) the level of concern (LOC) promulgated by the Emergency Planning and Community Right-to-Know Act. The LOC is considered “the maximum concentration of an extremely hazardous substance in air that will not cause serious irreversible health effects in the general population when exposed to the substance for relatively short duration.” Toxic endpoints are provided for 74 chemicals under the RMP rule and are shown in Table 5-7.

⁷U.S. Environmental Protection Agency. RMP Offsite Consequence Analysis Guidance (Washington, DC: U.S. Environmental Protection Agency, 1996).

Table 5-7 Toxic Endpoints Specified by the EPA Risk Management Plan

Chemical name	Toxic endpoint (mg/L)	Chemical name	Toxic endpoint (mg/L)
Gases		Bromine	0.0065
Ammonia (anhydrous)	0.14	Carbon disulfide	0.16
Arsine	0.0019	Chloroform	0.49
Boron trichloride	0.010	Chloromethyl ether	0.00025
Boron trifluoride	0.028	Chloromethyl methyl ether	0.0018
Chlorine	0.0087	Crotonaldehyde	0.029
Chlorine dioxide	0.0028	Cyclohexylamine	0.16
Cyanogen chloride	0.030	Dimethyldichlorosilane	0.026
Diborane	0.0011	1,1-Dimethylhydrazine	0.012
Ethylene oxide	0.090	Epichlorohydrin	0.076
Fluorine	0.0039	Ethylenediamine	0.49
Formaldehyde (anhydrous)	0.012	Ethyleneimine	0.018
Hydrocyanic acid	0.011	Furan	0.0012
Hydrogen chloride (anhydrous)	0.030	Hydrazine	0.011
Hydrogen fluoride (anhydrous)	0.016	Iron, pentacarbonyl	0.00044
Hydrogen selenide	0.00066	Isobutyronitrile	0.14
Hydrogen sulfide	0.042	Isopropyl chloroformate	0.10
Methyl chloride	0.82	Methacrylonitrile	0.0027
Methyl mercaptan	0.049	Methyl chloroformate	0.0019
Nitric oxide	0.031	Methyl hydrazine	0.0094
Phosgene	0.00081	Methyl isocyanate	0.0012
Phosphine	0.0035	Methyl thiocyanate	0.085
Sulfur dioxide (anhydrous)	0.0078	Methyltrichlorosilane	0.018
Sulfur tetrafluoride	0.0092	Nickel carbonyl	0.00067
Liquids		Nitric acid (100%)	0.026
Acrolein	0.0011	Peracetic acid	0.0045
Acrylonitrile	0.076	Perchloromethylmercaptan	0.0076
Acrylyl chloride	0.00090	Phosphorus oxychloride	0.0030
Allyl alcohol	0.036	Phosphorus trichloride	0.028
Allylamine	0.0032	Piperidine	0.022
Arsenuous trichloride	0.01	Propionitrile	0.0037
Boron trifluoride		Propyl chloroformate	0.010
compound with		Propyleneimine	0.12
methyl ether (1:1)	0.023	Propylene oxide	0.59
		Toluene 2,6-diisocyanate	0.0070
Sulfur trioxide	0.010	Toluene diisocyanate
Tetramethyllead	0.0040	(unspecified)	0.0070
Tetranitromethane	0.0040	Trimethylchlorosilane	0.050
Titanium tetrachloride	0.020	Vinyl acetate monomer	0.26
Toluene 2,4-diisocyanate	0.0070

Source: U.S. Environmental Protection Agency. RMP Offsite Consequence Analysis Guidance (Washington, DC: U.S. Environmental Protection Agency, 1996).

In general, the most directly relevant toxicologic criteria currently available, particularly for developing emergency response plans, are ERPGs, SPEGLs, and EEGLs. These guidelines were developed specifically to apply to general populations and to account for sensitive populations and scientific uncertainty in toxicological data. For incidents involving substances for which no SPEGLs or EEGLs are available, IDLH concentrations provide alternative criteria. However, because IDLH concentrations were not developed to account for sensitive populations and because they were based on a maximum 30-minute exposure period, the EPA suggests that the identification of an effect zone should be based on exposure levels of one-tenth the IDLH concentration. For example, the IDLH concentration for chlorine dioxide is 5 ppm. Effect zones resulting from the release of this gas are defined as any zone in which the concentration of chlorine dioxide is estimated to exceed 0.5 ppm. Of course, the approach is conservative and gives unrealistic results; a more realistic approach is to use a constant-dose assumption for releases less than 30 minutes using the IDLH concentration.

The use of TLV-STELs and ceiling limits may be appropriate if the objective is to identify effect zones in which the primary concerns include more transient effects, such as sensory irritation or odor perception. In general, persons located outside the zone that is defined based on these limits can be assumed to be unaffected by the release.

Craig et al.⁸ have provided a hierarchy of alternative concentration guidelines in the event that ERPG data are not available; this hierarchy is shown in Table 5-8. These methods may result in some inconsistencies because the different methods are based on different concepts. Good judgment should prevail.

⁸D. K. Craig, J. S. Davis, R. DeVore, D. J. Hansen, A. J. Petrocchi, and T. J. Powell. “Alternative Guideline Limits for Chemicals without Environmental Response Planning Guidelines.” AIHA Journal (1995): 56.

Table 5-8 Recommended Hierarchy of Alternative Concentration Guidelines

Primary guideline	Hierarchy of alternative guidelines	Source
ERPG-1		AIHA
	EEGL (30-min)	NRC
	IDLH	NIOSH
ERPG-2		AIHA
	EEGL (60 min)	NRC
	LOC	EPA/FEMA/DOT
	PEL-C	OSHA
	TLV-C	ACGIH
	5 × TLV-TWA	ACGIH
ERPG-3		AIHA
	PEL-STEL	OSHA
	TLV-STEL	ACGIH
	3 × TLV-TWA	ACGIH

AIHA: American Industrial Hygiene Association.

NIOSH: National Institute for Occupational Safety and Health.

NRC: National Research Council Committee on Toxicology.

EPA: Environmental Protection Agency.

FEMA: Federal Emergency Management Agency.

DOT: U.S. Department of Transportation.

OSHA: U.S. Occupational Safety and Health Administration.

ACGIH: American Conference of Governmental Industrial Hygienists.

Source: D. K. Craig, J. S. Davis, R. DeVore, D. J. Hansen, A. J. Petrocchi, and T. J. Powell. “Alternative Guideline Limits for Chemicals without Environmental Response Planning Guidelines.” AIHA Journal (1995): 56.

5-6 Release Prevention and Mitigation

The purpose of a hazardous material release model is to provide a tool for performing release mitigation. Release mitigation is defined as “lessening the risk of a release incident by acting on the source (at the point of release) either (1) in a preventive way by reducing the likelihood of an event that could generate a hazardous vapor cloud or (2) in a protective way by reducing the magnitude of the release and/or the exposure of local persons or property.”⁹

⁹Richard W. Prugh and Robert W. Johnson. Guidelines for Vapor Release Mitigation (New York, NY: American Institute of Chemical Engineers, 1988).

The release mitigation procedure is part of the consequence modeling procedure shown in Figure 4-1. After selection of a release incident, a source model is used to determine either the release rate or the total quantity released. This information is coupled to a dispersion model and subsequent models for fires or explosions. Finally, an effect model is used to estimate the impact of the release, which is a measure of the consequence.

Risk is composed of both likelihood and consequence. Thus, an estimate of the likelihood of a release provides only half of the total risk assessment. A particular release incident might potentially have high consequences, leading to extensive plant mitigation efforts to reduce the consequence. However, if the likelihood is low, such a massive effort might not be required. Both the consequence and the likelihood must be included to assess risk.

Table 5-9 identifies a number of measures to prevent or mitigate a release. The example problems presented in this chapter demonstrate that even a small release can result in significant downwind impact. In addition, this impact can occur minutes after the initial release, reducing the time available for emergency response. Clearly, it is better to prevent the release in the first place. Inherent safety, engineering design, and management should be the first issues considered in any release mitigation procedure.

Table 5-9 Release Prevention and Mitigation Approaches

Major area	Examples
Inherent safety	Inventory reduction: Less chemicals inventoried or less in process vessels Chemical substitution: Substitute a less hazardous chemical for one more hazardous Process attenuation: Use temperatures and pressures closer to ambient
Engineering design	Plant physical integrity: Use better seals or materials of construction Process integrity: Ensure proper operating conditions and material purity Process design features for emergency control: Emergency relief systems Spill containment: Dikes and spill vessels
Management	Operating policies and procedures Training for vapor-release prevention and control Audits and inspections Equipment testing Maintenance program Management of modifications and changes to prevent new hazards Security
Early vapor detection and warning	Detection by sensors Detection by personnel
Countermeasures	Water sprays Water curtains Steam curtains Air curtains Deliberate ignition of explosive cloud Dilution Foams
Emergency response	On-site communications Emergency shutdown equipment and procedures Site evacuation Safe havens Personal protective equipment Medical treatment On-site emergency plans, procedures, training, and drills

Source: Richard W. Prugh and Robert W. Johnson. Guidelines for Vapor Release Mitigation (New York, NY: American Institute of Chemical Engineers, 1988), p. 2.

Problems

5-1.

What instantaneous release on the ground, in g, of acrolein will result in a downwind concentration 1500 m immediately downwind on the ground equal to 0.05 ppm? It is a bright sunny day with a wind speed of 3.5 m/s. Assume rural conditions, a temperature of 25°C, and 1 atm pressure. Where does the maximum concentration occur on the ground for this release?
If the release is now 10-m above ground level, what is the concentration on the ground immediately downwind at 1500 m? Where does the maximum concentration occur on the ground for this case?

5-2.

What continuous release rate on the ground, in g/s, of acrolein will result in a downwind concentration equal to 0.05 ppm located 1500 m directly downwind on the ground? It is a bright sunny day with a 3.5 m/s wind speed. Assume rural conditions, a temperature of 25°C, and 1 atm pressure. Where does the maximum concentration occur on the ground?
If the release now occurs 10 m above ground level, what is the concentration 1500 m directly downwind on the ground?
Where is the maximum concentration directly downwind (in m) for part (b) and what is its value (in ppm)?

5-3. Emergency response for the rupture of a chemical pipeline is being evaluated. The chemical is estimated to discharge from the pipeline at a rate of 4.53 kg/s. The concentration of concern is 100 ppm—anyone downwind who is exposed to a concentration higher than this must be evacuated. Calculate the downwind evacuation distance. The pipeline is at ground level. The molecular weight of the released material is 17.03. The sunlight is moderate and the wind speed is 3.5 m/s. Assume 1 atm, 25°C, and rural conditions.

5-4. A backyard barbeque grill contains a 20-lb tank of propane. The propane leaves the tank through a valve and regulator and is fed through a ½-in. rubber hose to a dual-valve assembly. After the valves, the propane flows through a dual set of ejectors, where it is mixed with air. The propane–air mixture then arrives at the burner assembly, where it is burned. Describe the possible propane release incidents for this equipment.

5-5. A burning dump emits an estimated 3 g/s of oxides of nitrogen. What is the average concentration of oxides of nitrogen from this source directly downwind at a distance of 3 km on an overcast night with a wind speed of 7 m/s? Assume that this dump is a point ground-level source.

5-6. You have been appointed emergency coordinator for the community of Smallville, shown in Figure 5-12. ABC Chemical Company is shown on the map. It reports the presence of the following chemicals and amounts: 100 lb of hydrogen chloride and 100 gal of sulfuric acid. You are required to develop an emergency plan for the community.

Determine which chemical presents the greater hazard to the community.
Assuming all of the chemical is released during a 10-min period, determine the distance downwind that must be evacuated.
Identify locations that might be affected by a release incident at the plant or that might contribute to the incident because of their proximity to the plant.
Determine transportation routes that will be used to transport hazardous materials into or out of the facility. Identify any high-risk intersections where accidents might occur.
Determine the vulnerable zone along the transportation routes identified in part (d). Use a distance of 0.5 mi on either side of the route, unless a smaller distance is indicated by part (b).
Identify any special concerns (schools, nursing homes, shopping centers, and the like) that appear in the transportation route vulnerable zone.
Determine evacuation routes for the areas surrounding the plant.
Determine alternative traffic routes around the potential hazard.
Determine the resources required to support the needs of parts (g) and (h).
Identify the means required to warn the area, and describe the content of an example warning message that could be used in an emergency at the facility.

Figure 5-12 Map of Smallville.

A map of Smallville is shown. The mega shopping center, hospital, church, little railway (represented by a railway line sign), senior citizen home, ABC chemical, mega refinery, Smallville school, south road, apple road, picnic area, city hall, and muddy river are marked on the map. One horizontal line near the Church and hospital is marked as MI 52 and one inclined line, marked as US 1, passes through the map. Respective symbols for all markings are present on the map.
Estimate the potential number of people evacuated during an emergency. Determine how these people are to be moved and where they might be evacuated to.
What other concerns might be important during a chemical emergency?

5-7. A tank has ruptured and a pool of benzene has formed. The pool is approximately rectangular with dimensions of 20 ft by 30 ft. Estimate the evaporation rate and the distance affected downwind. Define the plume boundary using 10 ppm. It is an overcast day with a 9 mph wind. The temperature is 90°F.

5-8. A tank of chlorine contains 1000 kg of chlorine at 50-bar gauge. What is the maximum hole diameter (in mm) in this tank that will result in a downwind concentration equal to the ERPG-1 at a downwind distance of 300 m? Assume 1 atm, 25°C, a molecular weight of chlorine of 70.9, and that all the liquid chlorine vaporizes.

5-9. The emergency coordinator has decided that the appropriate emergency response to the immediate release of a toxic material is to alert people to stay in their homes, with doors and windows closed, until the cloud has passed. The coordinator has also indicated that homes 4000 m downwind must not be exposed to concentrations exceeding 0.10 mg/m³ of this material for any longer than 2 min. Estimate the maximum instantaneous release of material (in kg) allowed for these specifications. Be sure to clearly state any assumptions about weather conditions, wind speed, and other conditions.

5-10. A pipeline carrying benzene has developed a large leak. Fortunately, the leak occurred in a diked area and the liquid benzene is contained within the square 50 ft × 30 ft dike. The temperature is 80°F and the ambient pressure is 1 atm. It is a cloudy night with a 5 mph wind. All areas downwind with a concentration exceeding 4 times the PEL must be evacuated.

Determine the evaporation rate from the dike (in lb/s).
Determine the distance downwind (in mi) that must be evacuated.
Determine the maximum width of the plume (in ft) and the distance downwind (in mi) where it occurs.

5-11. Use a spreadsheet program to determine the location of a ground isopleth for a plume. The spreadsheet should have specific cell inputs for release rate (g/s), release height (m), spatial increment (m), wind speed (m/s), molecular weight of the released material, temperature (K), pressure (atm), and isopleth concentration (ppm).

The spreadsheet output should include, at each point downwind, both y and z dispersion coefficients (m), downwind centerline concentrations (ppm), and isopleth locations (m).

The spreadsheet should also have cells providing the downwind distance, the total area of the plume, and the maximum width of the plume, all based on the isopleth values.

Your submitted work should include a brief description of your method of solution, outputs from the spreadsheet, and plots of the isopleth locations.

Use the following two cases for computations, and assume worst-case stability conditions:

Case a: Release rate: 200 g/s

Release height: 0 m

Molecular weight: 100

Temperature: 298 K

Pressure: 1 atm

Isopleth concentration: 10 ppm

Case b: Same as above, but release height is 10 m above the ground. Compare the plume width, area, and downwind distance for cases a and b. Comment on the difference between the two cases.

5-12. Develop a spreadsheet to determine the isopleths for a puff at a specified time after the release of material. The spreadsheet should contain specific cells for user input of the following quantities: time after release (s), wind speed (2 m/s), total release (kg), release height (m), molecular weight of released gas, ambient temperature (K), ambient pressure (atm), and isopleth concentration (ppm).

The spreadsheet output should include, at each point downwind, the downwind location, both y and z dispersion coefficients, downwind centerline concentration, and isopleth distance off-center (+/–).

The spreadsheet output should also include a graph of the isopleth location.

For your spreadsheet construction, we suggest that you set up the cells to move with the puff center. Otherwise, you will need a large number of cells.

Use the spreadsheet for the following case:

Release mass: 0.5 kg

Release height: 0 m

Molecular weight of gas: 30

Ambient temperature: 298 K

Ambient pressure: 1 atm

Isopleth concentration: 1 ppm

Atmospheric stability: F

Run the spreadsheet for a number of different times, and plot the maximum puff width as a function of distance downwind from the release.

Answer the following questions:

At what distance downwind does the puff reach its maximum width?
At what distance and time does the puff dissipate?
Estimate the total area swept out by the puff from initial release to dissipation.

Your submitted work should include a description of your method of solution, a complete spreadsheet output at 2000 s after release, a plot of maximum puff width as a function of downwind distance, and the calculation of the total swept area.

5-13. A fixed mass of toxic gas has been released almost instantaneously from a process unit. You have been asked to determine the percentage of fatalities expected 2000 m downwind from the release. Prepare a spreadsheet to calculate the concentration profile around the center of the puff 2000 m downwind from the release. Use the total release quantity as a parameter. Determine the percentage of fatalities at the 2000 m downwind location as a result of the passing puff. Vary the total release quantity to result in a range of fatalities from 0 to 100%. Record the results at enough points to provide an accurate plot of the percentage of fatalities versus quantity released. The release occurs at night with calm and clear conditions.

Change the concentration exponent value to 2.00 instead of 2.75 in the probit equation, and rerun your spreadsheet for a total release amount of 5 kg. How sensitive are the results to this exponent?

Hint: Assume that the puff shape and concentration profile remain essentially fixed as the puff passes.

Supplemental information:

Molecular weight of gas: 30

Temperature: 298 K

Pressure: 1 atm

Release height: 0

Wind speed: 2 m/s

Use a probit equation for fatalities of the form

$Y = - 17.1 + 1.69 \ln (C^{2.75} T)$

where Y is the probit variable, C is the concentration in ppm, and T is the time interval in minutes.

Your submitted work must include a single output of the spreadsheet for a total release of 5 kg, including the puff concentration profile and the percent fatalities; a plot of the concentration profile for the 5 kg case versus the distance in meters from the center of the puff; a plot of the percentage of fatalities versus total quantity released; a single output of the spreadsheet for a 5 kg release with a probit exponent of 2.00; and a complete discussion of your method and your results.

Additional homework problems are available in the Pearson Instructor Resource Center.

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Table of Contents for
Chapter 5. Hazardous Material Dispersion

Chapter 5. Hazardous Material Dispersion

5-1 Parameters Affecting Dispersion

5-2 Neutrally Buoyant Dispersion Models

5-3 Pasquill–Gifford Model

Case 1: Puff with Instantaneous Point Source at Ground Level, Coordinates Fixed at Release Point, Constant Wind Only in x Direction with Constant Velocity u

Case 2: Plume with Continuous Steady-State Source at Ground Level and Wind Moving in x Direction at Constant Velocity u

Case 3: Plume with Continuous Steady-State Source at Height H_r above Ground Level and Wind Moving in x Direction at Constant Velocity u

Case 4: Puff with Instantaneous Point Source at Height H_r above Ground Level and a Coordinate System on the Ground That Moves with the Puff

Case 5: Puff with Instantaneous Point Source at Height H_r above Ground Level and a Coordinate System Fixed on the Ground at the Release Point

Isopleths

Effect of Release Momentum and Buoyancy

Worst-Case Dispersion Conditions

Limitations to Pasquill–Gifford Dispersion Modeling

5-4 Dense Gas Dispersion

5-5 Toxic Effect Criteria

Emergency Response Planning Guidelines

Immediately Dangerous to Life and Health

Emergency Exposure Guidance Levels and Short-Term Public Emergency Guidance Levels

Acute Exposure Guideline Levels

Threshold Limit Values

Permissible Exposure Limits

Toxic Endpoints

5-6 Release Prevention and Mitigation

Suggested Reading

Atmospheric Dispersion Modeling

Release Mitigation

Problems

Table of Contents for Chapter 5. Hazardous Material Dispersion

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Chapter 5. Hazardous Material Dispersion

5-1 Parameters Affecting Dispersion

5-2 Neutrally Buoyant Dispersion Models

5-3 Pasquill–Gifford Model

Case 1: Puff with Instantaneous Point Source at Ground Level, Coordinates Fixed at Release Point, Constant Wind Only in x Direction with Constant Velocity u

Case 2: Plume with Continuous Steady-State Source at Ground Level and Wind Moving in x Direction at Constant Velocity u

Case 3: Plume with Continuous Steady-State Source at Height Hr above Ground Level and Wind Moving in x Direction at Constant Velocity u

Case 4: Puff with Instantaneous Point Source at Height Hr above Ground Level and a Coordinate System on the Ground That Moves with the Puff

Case 5: Puff with Instantaneous Point Source at Height Hr above Ground Level and a Coordinate System Fixed on the Ground at the Release Point

Isopleths

Effect of Release Momentum and Buoyancy

Worst-Case Dispersion Conditions

Limitations to Pasquill–Gifford Dispersion Modeling

5-4 Dense Gas Dispersion

5-5 Toxic Effect Criteria

Emergency Response Planning Guidelines

Immediately Dangerous to Life and Health

Emergency Exposure Guidance Levels and Short-Term Public Emergency Guidance Levels

Acute Exposure Guideline Levels

Threshold Limit Values

Permissible Exposure Limits

Toxic Endpoints

5-6 Release Prevention and Mitigation

Suggested Reading

Atmospheric Dispersion Modeling

Release Mitigation

Problems

Table of Contents for
Chapter 5. Hazardous Material Dispersion

Case 3: Plume with Continuous Steady-State Source at Height H_r above Ground Level and Wind Moving in x Direction at Constant Velocity u

Case 4: Puff with Instantaneous Point Source at Height H_r above Ground Level and a Coordinate System on the Ground That Moves with the Puff

Case 5: Puff with Instantaneous Point Source at Height H_r above Ground Level and a Coordinate System Fixed on the Ground at the Release Point