How to Characterize Inhalation Model Source Rates

Remember one of the simplest of models?  Its  C = G/Q   where, at equilibrium with a constant rate of G and Q, C is the steady-state concentration (mg/m³),  G is the source or emission rate (mg/min) and Q is the ventilation rate (m³/min)  for the volume (V) into which G is flowing.   In the last few blogs we have been concentrating Q and how to estimate it with tracer gas.   We also went over the first order decay model for use with a tracer gas.    This week I am going to talk about source (G) characterization.

But first and briefly, I just want to go over a much more simple way of estimating Q in a room that has obvious input or output streams of ventilation.   We know that every inhabitable room receives as much air as it exhausts or else the room would explode or the folks within it would die from lack of oxygen.  Thus, if you can measure the amount of air coming into or leaving the room you can determine its ventilation rate (Q).   You simply take the area of the incoming or outgoing stream and multiply it by the velocity of the air going in or coming out.   Q = air velocity x area.    If you have both output and input streams measure them both, the one with the highest calculated Q is the most accurate estimator.   

Back to sources (G).   In general we assume that sources are constant or  that they undergo first order decay of an initial mass.   These are all generalized descriptions of a source and like all models they attempt to portray reality but they are not strictly speaking, reality.    IF they describe reality reasonably well then they are useful.  If they do not then we need a better model.

A constant source means that G does not vary with time; it is constant.    Consider someone spraying an aerosol around their head in the application of hairspray.   The can of hairspray is used for 1 minute and then the spraying is stopped.   Measure the weight of the can at the beginning and at the end of this period and the difference is the rate of application G in units of mg/min.   You can determine the source rate of a certain ingredients within the can by knowing its concentration.  For example, if 10% of the stuff in the can is ethanol then 10% of the weight loss was this alcohol.

Imagine a leaking valve that would also put out a relatively constant mass of vapor per min as a constant source.   Another constant source would be an open and relatively deep container of solvent.    The evaporation would be constant given a constant vaporizing surface area in which the temperature remains relatively constant.   If the temperature remains virtually the same and the resulting airborne concentration does not approach a reasonable fraction of the saturation concentration of that vapor, then the source can be considered constant.   I will go over the details estimating evaporation rates and relevance of saturation concentration and “backpressure effect” in next week’s blog.

A first-order decaying source is completely analogous to the first order decaying concentration of a tracer gas.    Consider a spill of a volatile solvent on the floor.    If you plot the natural log of the weight of the remaining spill versus time you will,  in most cases with thin spills,  get a straight-line; that is, a good fit to the first order decay model.   Go back two blogs to see how this is done with Excel.

Another way of measuring the parameters (initial mass and half-life) of a first-order decaying source is to measure the time course of concentration decay in a volume with well mixed ventilation.   A series of C,t points should follow a first-order decay model and one can then back calculate the generation rate parameters that caused them.   If there is interest in more of the details of this technique I can go over them in a future blog.

There is a significantly more complicated source which is a combination of an increasing AND a first-order decaying source.  This may seem daunting but it is doable.  Consider someone cleaning a surface with a solvent.   The solvent goes on the first little section of the surface and starts to evaporate until there is no more of it left.   This is classical first order decay of G.   But that is not the whole story; indeed, solvent is applied continuously and somewhat constantly until the surface cleaning is complete.  This is a growing rate of generation (G) as the area gets larger.    This type of source has fortunately been described mathematically within the documentation for the EPA Model E-FAST2.     Reference:     http://www.epa.gov/opptintr/exposure/pubs/efast2man.pdf

Both constant and first order sources are presented and coded individually in many of the important models presented in IH MOD which you can get at:

http://www.aiha.org/get-involved/VolunteerGroups/Pages/Exposure-Assessment-Strategies-Committee.aspx.   Unfortunately, the combination of an increasing and first order decaying source types, as described in the above paragraph, has not been coded into IH MOD but it may be in future versions of this very valuable tool.    

I will go over exactly what the freeware IH MOD offers in a future blog.