Using mathematical models to estimate exposure to workplace air contaminants

Air sampling is traditionally used to assess exposure to airborne contaminants. However, failing to account for exposure variability by taking only a few measurements, and failing to record information on exposure determinants for the time periods monitored, substantially limit the conclusions one can draw from the data. Mathematical modeling offers a partial solution to this problem, and is a useful adjunct to exposure monitoring. The modeling approach is illustrated with two examples; the model predictions agree with limited air monitoring data. The first example is estimating short-term benzene exposure levels (specifically, 15-min time weighted averages, TWAs) among delivery truck drivers while offloading gasoline to small above-ground tanks. The benzene mass emission rate from the tank headspace is assumed to be constant and a function of the benzene content of the gasoline, temperature, and tank fill rate. Vapor is emitted from the fill hole into a surrounding near field zone which contains the driver’s breathing zone; airflow into the near field depends on the local random air speed. Monte Carlo simulation is used to examine variability in 15-min TWA exposure; a substantial proportion are predicted to exceed the 15-min TWA benzene exposure limit of 5 ppm. The second example is estimating ethylene oxide (ETO) gas levels in a well-mixed room due to use of a desktop medical sterilizer device. The variable ETO mass emission rate was modeled based on information provided in the product literature, and was used to derive a general equation for the room ETO concentration given a set of room volume and dilution ventilation values. For a poorly ventilated room, the model predicted that, the average concentration during the sterilization phase could exceed the 8-hr TWA ETO exposure limit of 1 ppm, and that during the sterilization and aeration phases the 15-min TWA ETO limit of 5 ppm could be exceeded.