Nothing is Perfect - Especially Models

Teaching always involves learning and I just love to hear from the folks reading this blog.   A very thoughtful reader, who has asked to be identified only as a “retired US Air Force Bioenvironmental Engineer”, read the recent blogs on using tracer gas for ventilation measurements.   He had the following comments which I am including and addressing below:

1.       These computations work for gases and vapors, not particulates.

2.       The assumption that the vapor or gas will occupy all room volume is reasonable for a small  room, but in a large room (i.e., an aircraft hangar) the assumption may not be valid, especially  since most solvents used in paints and coatings are heavier than air.

Let’s take point 1 first.   It is correct that these computations will not work for many if not most particulates.  It is especially true for particulates in which a significant portion of the particulate population has an aerodynamic diameter (AD) greater than 10 microns.  This is primarily because these larger particles settle to the ground in a time frame that is comparable to the tracer testing time.   If the particles are very small – for example, AD less than 0.1 microns (e.g., fumes and  non-aggregated nano-particles) they could work because they will settle very slowly.   

Note:  Aerodynamic diameter (AD) is based on the settling velocity of any particle.   That is a particle with an AD =10 microns will fall at the same rate as a unit density sphere with a diameter of 10 microns.    Thus regardless of the shape of the particle we can characterize its size in an aerosol. 

Regarding number 2 above I have some experience and the point about the model not working in large rooms is right to the mark.   The room has to be reasonably small or enough tracer has to be released and mixed that the concentration is pretty even throughout the entire volume.   This is extremely difficult to do in a very large room (e.g. airplane hangar, large warehouse).   In these volumes it is probably easiest  and best to measure the volume of fresh air coming into or out of the volume by measuring the air velocity (Vel)  and the areas (A) of the opening(s) and using the Q   = Vel  x A equation to figure out how much ventilation is going into and coming out of the room.  Remember the average amount going in will always equal the amount coming out in any reasonable time frame.  

The issue of heavier than air solvents is something that I have thought about quite a bit.   I will use the rest of this blog to present the argument that I believe that it is a non-issue in the vast majority of what we do as exposure assessors.  

It is quite nature to think that all “heavier-than-air” vapors sink and sink quickly.   Indeed, we have all seen “dry ice” vapors pouring or spilling out of a vessel or block of dry ice and dropping quickly downward.    Air is 21% oxygen (MW 32) and 79% nitrogen (MW 28) for an average MW of 28.8.    Carbon dioxide MW is 44 g/mole.  Also, its vapors are much colder than most ambient air and thus even more dense.   Both of these factors cause the CO₂ vapors to drop but perhaps the most important factor that causes the CO₂ vapor cloud to fall quickly is that this emitting cloud is essentially 100% CO₂  (because C0₂ is a gas at normal temperature and pressure) and a 100% CO₂ gas emission is at its maximum density and tends to displace all of the air in its path.    The relative density of CO₂ versus air (not counting temperature effect):   (44/28.8)(100%)  = 1.53  or 153%.

Now consider typical solvents in VOC-based paint used to paint cars.   These materials are liquids at normal temperature and pressure and even under saturation conditions their vapor concentrations only get to a small fraction of 100%.    Let’s look at toluene as an example, even assuming the worst case of a saturated vapor of toluene, it only comprises 5% (40mmHg Vapor Pressure/760mmHg ATM)  of the molecules in any volume at normal temperature and pressure with the rest being air.  

To get some idea of the actual  VOC concentrations around workers during spray painting, we did and published a one year study evaluating worker exposures in a small “bump and paint” auto body shop. Please send me an email (mjayjock@gmail.com) if  you want a copy of this paper.   In doing this work we estimated that the average MW of these paint solvent mixtures was 125g/mole.   I measured the breathing zone of workers spraying cars in a small booth that was turned off (because of cold weather outside) with essentially NO ventilation.   The highest total VOC measured in the worker’s breathing zone was about 1500 ppmV. 

The relative density of vapors with 1500 ppmV total VOC with average MW = 125 (versus pure air) is (125/28.8)(1500/1,000,000) =  0.0065 or less than 1%.   It is worth mentioning that the painters we monitored did not wear PPE and were visibly intoxicated by these exposures.   Getting back to the point of heavier than air vapors, even at 4 times this concentration (i.e., 6000 ppm V) the difference in density and buoyancy between pure air and air highly contaminated with VOC appear to be relatively small.  

In conclusion, I believe that it is fairly safe to say that VOC emissions from evaporating liquid pools, spraying or from evaporating aerosol particles will be en-trained into the normally moving ambient air and not have a strong tendency to sink.

All of this reminds me of the wise statement that:  “All models are wrong but some are useful. “   We simply need to keep engaging our minds and allow the models to tell us something useful.