Modeling Evaporating Sources

Almost all volatile organic chemicals get into the air via evaporation or vaporization.   Sometimes they are literally sprayed or ejected into the air.   Prime examples of this are sprayed material (e.g.,  spray paint, hair spray) and drum filling where the empty air volume of the drum being filled is displaced into the ambient room air along with the vapors of the entering liquid.   When sprayed, aerosol particles evaporate rapidly because the surface area-to-volume ratio of the particles is relatively large.  When filling empty containers with liquids the entire volume of the container is injected into the surrounding space as the liquid displaces the air within the drum.   What is also injected are the vapors from the incoming liquid as it splashes or otherwise enters into the container.   The EPA did some tests on this many years ago and determined that this volume has between 50% and 100% saturated vapors.    Thus if you fill 10 – 55 gallon drums you will inject 550 gallons or 2.1 m³ of air with a vapor concentration of between 50 to 100% of saturation of the filling liquid VOC.

Just to review, the saturation concentration (Csat) is what happens in the headspace of a drum.    Given enough time, evaporation takes place until the air in the headspace can hold no more.   At that point as much vapor condenses back into liquid as evaporates from it and the concentration in the drum headspace is the saturation concentration Csat.   Csat is easy to calculate.  

Csat = (VP/ATM)(10⁶)     [units = ppmV]

VP = vapor pressure of the liquid

ATM = Atmospheric pressure

The concentration expressed as ppmV is readily converted to mg/m³:

mg/m³  =  (ppmV)  MW/24.45

MW = molecular weight of the vaporizing liquid in g/mole

I have found that most of the time, when VOCs  are evaporated into the air – say from a small spill - that the resulting concentration is only a small fraction of Csat.   In these situations you can ignore what I call the “backpressure effect” in your model predictions.    If however, the concentration builds to a point where it is say 50% of Csat then the evaporate rate (generation rate G) is literally half of what it was when the initial concentration was zero.   That is because the entire force driving evaporation is the diffusion of the molecules from the liquid to the gaseous state.   If there are already a lot of molecule of the same type in the air then the net evaporation rate becomes lower.     Thus, the evaporation or generation rate (G) is constantly decreasing as the concentration in the volume is increasing.   A simple equation for this is:

G  = G0 (C/Csat)

G0 = the initial or maximum generation rate when the airborne concentration is zero.

C = the concentration in the volume.

As mentioned above I view this effect as “backpressure” and wrote a paper about it some time ago.   Anyone interested in a copy of this paper just ask me at mjayjock@gmail.com

Backpressure is the reason that wet clothes to do not dry very well in humid weather.

We need to consider backpressure in our modeling algorithms when the resulting airborne concentration might be a reasonable fraction of the saturation concentration.   This usually happens when there are large spills or when the vaporizing surfaces are very large within an interior room.   Examples would be offgassing from drying paint or carpets.

IH MOD is a freeware spreadsheet modeling tool available from the American Industrial Hygiene Association.   It addresses and handles backpressure in some of its modules.   In the next blog I will talk about many if not most of the things that IH MOD can do.