Using a spreadsheet to compute contaminant exposure concentrations given a variable emission rate.

Two key elements of mathematical exposure models are the contaminant's emission rate and pattern of dispersion in room air. Assuming that the mass emission rate is constant and room air is perfectly mixed affords relative mathematical simplicity. However, treating a highly variable emission rate as constant underestimates peak exposure intensity, which may be toxicologically important, and assuming a well-mixed condition underestimates exposure intensity near the source. In the past decade multizone models and turbulent diffusion models have been used to account for spatial variability in airborne concentrations, and variable emission rate functions have been described for different processes. Due to the greater complexity of these models, closed-form equations for concentration as a function of time may not be available. This article presents a numerical method that combines a variable contaminant emission rate function with the three dispersion constructs most commonly used by industrial hygienists-the well-mixed room, the near field/far field, and hemispherical turbulent eddy diffusion. The article describes how the numerical method is implemented by a computer spreadsheet program, and illustrates the method using a sinusoidal contaminant emission rate function.