1. TOXIC RELEASE &
DISPERSION MODELS
LECTURE 5

2. During an accident, process equipment can release toxic materials very quickly and in significant enough quantities to spread in dangerous clouds throughout a plant site and the local community. A few examples are -
- Explosive rupture of a process vessel due to 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.
- Rupture of a train or truck transportation tank following an accident.
Serious accidents (such as Bhopal) emphasize the importance of emergency planning and for designing plants to minimize the occurrence and consequences of a toxic release. Toxic release models are routinely used to estimate the effects of a release on the plant and community environments.

3. An excellent safety program strives to identify problems before they occur. Chemical engineers must understand all aspects of toxic release to prevent the existence of release situations and to reduce the impact of a release if one occurs. This requires a toxic release model.
There are 3 steps in utilizing a toxic release model.
1. Identify the design basis. What process situations can lead to a release, and which situation is the worst?
2. Develop a source model to describe how materials are released and the rate of release.
3. Use a dispersion model to describe how materials spread throughout the adjacent rates.
The main emphasis of the toxic release model is to provide a tool useful for release mitigation. The source and dispersion models predict the area affected and the concentration of vapor throughout. The design basis is valuable for eliminating situations that could result in a release.

4. Various options are available based on the predictions of the toxic release model. To name a few, these are
1. develop an emergency response plan with the surrounding community;
2. develop engineering modifications to eliminate the source of the release;
3. enclose the potential release and add appropriate vent scrubbers or other vapor removal equipment;
4. reduce inventories of hazardous materials to reduce the quantity released; and
5. add area monitors to detect incipient leaks and provide block valves and engineering controls to eliminate hazardous levels of spills and leak.
These options are discussed in more detail on release mitigation.

5. Design Basis
The design basis describes the various scenarios leading to toxic release; it looks for what can go wrong. For any reasonably complex chemical facility, thousands of release scenarios are possible; it is not practicable to elucidate every scenario. Most toxic release studies strive to determine the largest practicable release and the largest potential release. The largest practicable release considers releases having a reasonable chance for occurrence. This includes pipe ruptures, holes in storage tanks and process vessels, ground spills, and so forth. The largest potential release is a catastrophic situation resulting in release of the largest quantity of material. This includes compete spillage of tank contents, rupture of large bore piping, explosive rupture of reactors, and so forth. Table 1 contains examples of largest practicable and largest potential releases.

6. Development of a proper design basis requires skill, experience, and considerable knowledge of the process. Hazards identification procedures are very helpful.
The completed design basis describes -
1. what went wrong,
2. the state of the toxic material released (solid, liquid, or vapor), and
3. the mechanism of release (ruptured pipe, hole in storage vessel, and so on).

7. Table 1 Examples of Largest Practicable and Largest Potential Releases

8. Example 1
Water is treated at a swimming pool using a 100-lb bottle of chlorine. The chlorine is fed from the bottle through a 1/4-in line to the water treatment facility. A relief valve on the tank prevents excessive pressure from rupturing the tank. Chlorine is stored in the bottle as a liquid under pressure and will boil when the pressure is reduced. Identify the release scenarios.

9. Solution
Scenario 1 : The bottle of chlorine ruptures, possibly from dropping the tank while unloading from a truck. The entire contents is spilled, with a fraction flashing immediately into vapor and the remaining liquid forming a boiling pool on the ground.
Scenario 2 : A hole forms in the tank either because of mechanical rupture or corrosion. A jet of flashing chlorine and a boiling pool of liquid chlorine forms.
Scenario 3 : The relief valve fails open, forming a jet and pool of boiling chlorine.
Scenario 4 : The feed line to the treatment plant fails with a jet and pool of boiling chlorine.

10. Scenario 5 : A fire develops around the chlorine tank, heating the tank until the relief valve opens.
Scenario 6 : A fire develops around the chlorine tank, but the relief valve fails closed. The tank pressure builds until it ruptures, spilling the entire tank contents explosively.
The largest practicable release could be either scenarios 2, 3, or 4, depending on the rate of material release computed using an appropriate source model. The largest potential release is scenario 6, releasing the entire tank contents almost immediately.

11. Source Models The purpose of the source model is to -
1. The form of material released, solid, liquid or vapor;
2. The total quantity of material released; and
3. The rate at which it is released.
This information is required for any quantitative dispersion model study.

12. Dispersion Models
Dispersion models describe the airborne transport of toxic materials away from the accident site and into the plant and community. After a release, the airborne toxic is carried away by the wind in a characteristic plume as shown in Figure 1 or a puff, shown in Figure 2. The maximum concentration of toxic material occurs at the release point (which may not be at ground level). Concentrations downwind are less, due to turbulent mixing and dispersion of the toxic substance with air.

13. Figure 1 Characteristic plume formed by a continuous release of material.

14. Figure 2 Puff formed by near instantaneous release of material.

15. A wide variety of parameters affect atmospheric dispersion of toxic materials -
- Wind speed
- Atmospheric stability
- Ground conditions, buildings, water, trees
- Height of the release above ground level
- Momentum and buoyancy of the initial material released
As the wind speed increases, the plume in Figure 1 becomes longer and narrower; the substance is carried downwind faster but is diluted faster by a larger quantity of air.
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, resulting in less vertical motion. Temperature profiles for day and night situations are shown in Figure 3. Sometimes an inversion will occur.

16. Figure 3 Air temperature as a function of altitude for day and night conditions. The temperature gradient affects the vertical air motion.

17. During and inversion, the temperature increases with height, resulting in minimal vertical motion. This most often occurs at night as the ground cools rapidly due to thermal radiation.
Atmospheric stability classification: unstable, neutral, stable
Ground conditions affect the mechanical mixing at the surface and the wind profile with height. Trees and buildings increase mixing while lakes and open areas decrease it. Figure 4 shows the change in wind speed versus height for a variety of surface conditions.
The release height significantly affects ground level concentrations. As the release height increases, ground level concentrations are reduced since the plume must disperse a greater distance vertically. This is shown in Figure 5.

18. Figure 4 Effect of ground conditions on vertical wind gradient.

19. Figure 5 Increased release height decreases the ground concentration.

20. The buoyancy and momentum of the material released changes the “effective” height of the release. Figure 6 demonstrates these effects. After the initial momentum and buoyancy has dissipated, ambient turbulent mixing becomes the dominant effect.
Two types of vapor cloud dispersion models are commonly used : the plume and puff models. The plume model describes the steady-state concentration of material released from a continuous source. 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 1 and 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 due to the rupture of a storage vessel. A large vapor cloud is formed that moves away from the rupture point.

21. Figure 6 The initial acceleration and buoyancy of the released material affects the plume character. The dispersion models discussed in this chapter represent only ambient turbulence.

22. The puff model can be used to describe a plume; a plume is simply the release of continuous puffs. If, however, steady-state plume information is all that is required, the plume model is recommended since it is easier to use. For studies involving dynamic plumes (for instance the effect on a plume due to a change in wind direction), the puff model must be used.
Consider the instantaneous release of a fixed mass of material, Qm*, 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 due to this release is given by the advection equation.
(1)

23. where uj is the velocity of the air and the subscript j represents the summation over all coordinate directions, x, y, and z. if the velocity, uj, in Equation 1 is set equal to the average wind velocity and the equation is solved, one would find that the material disperses much faster than predicted. This is due to turbulence in the velocity field. If one were able to specify the wind velocity exactly with time and position, including the effects due to turbulence, Equation 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;
(2)

24. where <uj> is the average velocity and uj’ is the stochastic fluctuation due to turbulence. It follows that the concentration, C, will also fluctuate as a result of the velocity field, so,
(3)
where <C> is the mean concentration and C’ is the stochastic fluctuation. Since the fluctuations in both C and uj are around the average or mean values, it follows that,
(4)
Substituting Equation 2 and 3 into Equation 1 and averaging the result over time, yields,
(5)

25. The terms <uj>C’ and uj’<C> are zero when averaged (<<uj>C’> = <uj><C’> = 0), but the turbulent flux term <uj’C’> is not necessarily zero and remains in the equation.
An additional equation is required to describe the turbulent flux. The usual approach is to define an eddy diffusivity, Kj (with units of area/time), such that
(6)
substituting Equation 6 into Equation 5 yields,
(7)

26. If the atmosphere is assumed to be incompressible,
(8)
and Equation 7 becomes
(9)
Equation 9, together with appropriate boundary and initial conditions, forms the fundamental basis for dispersion modelling. This equation will be solved for a variety of cases.
The coordinate system used for the dispersion models is shown in Figures 7 and 8. The x-axis is the centreline directly downwind from the release point and is rotated for different wind directions. The y-axis is the distance off of the centreline and the z-axis is the elevation above the release point. The point (x,y,z) = (0,0,0) is at the release point. The coordinates (x,y,0) are level with the release point, and the coordinates (x,0,0) are along the centreline, or x-axis.

27. Figure 7 Steady-state, continuous point source release with wind
Figure 7 Steady-state, continuous point source release with wind. Note coordinate system : x is downwind direction, y is off-wind direction , and z is vertical direction.

28. Figure 8 Puff with wind. After the initial, instantaneous release, the puff moves with the wind.