Dispersion of an elevated release
Often atmospheric dispersion models are needed to determine the potential for a gas release to impact workers or the public. This is typically encountered during Fire & Gas Mapping. There are quite a few decisions that go into a well-designed dispersion model, not the least of which are related to meteorological assumptions. This can easily boggle the engineer’s mind with complex sounding terms and strange equations; so let’s not do that here. We often think of the worst-case meteorological condition to be a stable atmosphere (“F” class stability) with low wind speed. and this is indeed the worst-case for ground level releases. However, this is not necessarily true for elevated releases, such as emissions from a stack.
If the concern is potential impact to persons at ground level, a capping inversion is more likely to be the worst case. But, what is this? Let’s think about the day/night heating/cooling cycle. During sunny daytime conditions, solar heat creates a higher temperature near the ground than aloft. This is an unstable condition because a pocket of warm air below will have a lower density and want to rise up, expand, cool, and meet up with pockets of the same density. This creates rapid vertical mixing when there are low wind speed conditions (“A” class stability). During nighttime conditions, the ground cools but the air aloft has been warmed during the daytime heating cycle. The cooler air near the ground is more dense and will want to stay put. Vertical mixing nearly stops. This is a stable atmospheric condition, which we sometime describe with “F Class” stability, and it is also known as a surface inversion because the temperature profile is ‘inverted’ from the daytime situation. The profile of temperature as a function of altitude is also known as the lapse rate, and this is shown as a blue line in the figure above.
An interesting situation occurs when there is a transition between the surface inversion at night to the daytime situation. In the early- to mid-morning the ground is just starting to be heated, but the temperature profile aloft remains stable. The temperature inversion still exists but it is only found aloft, and this is what we call a capping inversion. The height of the transition between stable and unstable profiles is known as the mixing depth; in concept it is the height where below now exists a layer in which strong vertical mixing is occurring. This height steadily increases as more solar heat is pumped into the lower atmosphere. It will rise from near ground level (100 ft) to mile or more over the span of a few hours. By mid-afternoon the mixing height is ‘unlimited’ for practical purposes of dispersion modeling.
For an elevated release or emission, daytime instability promotes buoyancy, good mixing, and favorable dispersion. Nighttime surface inversions inhibit mixing which is not favorable to dispersion; however, an elevated release doesn’t want to either approach the ground or buoy up because the air is stability stratified. This inhibiting of mixing may create effects like noticeable odors at large distances downwind. As the sun heats the ground in the morning the cap above has yet to be removed — not enough heat has been pumped into the atmosphere yet; however, there is instability near ground level and at this elevation, things are being well mixed by vertical movements of air. When the top of the mixing layer is located right above the stack height, this creates the center picture below labeled “early morning”. This capping inversion creates classic fumigation plume behavior. The stack emission can’t rise up — there is a cap. The instability below stirs things up, and the plume fumigates downward toward ground. This can be the worst-case situation for impact of people located downwind of the elevated release.
Avoiding the chance of a ground level impact can be accomplished if either:
- the emission is very warm so that it wants to buoy up above the mixing depth, or
- the stack height is high enough to avoid ground level impacts because we are releasing the emission above the shallow mixing depth.
When you’re modeling dispersion or responsible for overseeing those who are, make sure you understand the range of important meteorological conditions that ought to be considered. For elevated releases, this should include a capping inversion defined by mixing depth and a very large amount of turbulence below. Unfortunately, the some of the most popular dispersion models cannot model as situation where there is not a uniform lapse rate, so this may require some expert assistance. As always, contact Kenexis for more information or if you need assistance with gas dispersion modeling.