Well mixed model vs Models that consider air concentrations close to the source

Well mixed box models are relatively easy to understand.  You start with a room (a box) and the same amount of fresh air goes into it as comes out of it.  If not it would explode or the folks inside would suffocate. You put a contaminant into the room air (emission rate G) and take it out with ventilation (Q).   Last week we saw that given a steady G and Q that the steady-state concentration (C) in the box will eventually equal G/Q.   There are other more complicated equations that determine C as it approaches steady-state but that is not important for this discussion.   In later blogs I will get into how you can determine or estimate G and Q but for now it is enough to know that this is a simple model and quite useful in many cases.  It is important to understand that the C determined by this model is the AVERAGE concentration within the room.  If the source G is relatively spread out within the room then this model works quite well.  An example of a spread out source would be paint emissions into a room with painted walls and ceiling.  If, however, the source is localized then there typically will be a much higher concentration (C) of the contaminant near the source than away from it.   An example would be someone using a volatile degreaser spray with TCE on a workbench to clean a part.  The larger the room the more the gradient or difference in concentration near the source versus the far corner of the room.  The well mixed box model does not work very well here since the average concentration in the room will be significantly lower than the breathing zone concentration of the person doing the cleaning.

Many years ago I approached this problem by assuming a virtual box within the real box of the room.  For example, I assumed that most of the contaminant would be in an area of an 8 foot cube around the source.   That is a volume of 512 ft3.   It did not matter how big the room was as long as it was larger than this virtual box.  The only thing I needed to know about the actual room was its volume (V) and its ventilation rate (Q).   Once I knew Q for the large room I would figure out the air changes per hour in that large room; that is, Q/V.   This has the units of 1/hr.   Once I had Q/V for the large room I assumed this relative exchange rate would be the same for the virtual box.   So that (Q/V)(512ft3) = Qb or ventilation rate in the virtual box in units of ft3/hr.   I'll let you do the conversion to m3/hr.  The predicted steady-state C  in this box = G/Qb.   If you want a copy of the original paper just email me (mjayjock@gmail.com) and I will send it to you.

Years later Mark Nicas came up with a much more elegant model called the 2 zone model (that considered the virtual box or NEARFIELD and the FARFIELD or rest of the room volume).  This model calculates the C in the virtual volume around the source AND the average concentration in the rest of the room.  This model and lots more are available in the freeware Excel spreadsheet IH MOD from the AIHA web site.
http://www.aiha.org/get-involved/VolunteerGroups/Pages/Exposure-Assessment-Strategies-Committee.aspx

There is another near source model known as the eddy diffusivity model which actually calculates a continuous gradient of exposure from a point source of emission (G) to any location within the volume.  To run this model one needs G and the eddy diffusivity coefficient (D).  Until recently D was hard to come by, but the very smart researchers at Stanford recently published a paper that allows one to estimate D from a room's dimensions and its ventilation rate.  Kai-Chung Cheng, et al,  Modeling Exposure Close to Air Pollution Sources in Naturally Ventilated Residences: Association of Turbulent Diffusion Coefficient with Air Change Rate.  Environ. Sci. Technol. 2011, 45, 4016-4022.  The calculation engine for the eddy diffusivity model is also available in IH MOD.

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