Models for nearly every occasion: Part I - One box models

ABSTRACT

The standard “well mixed room,” “one box” model cannot be used to predict occupational exposures whenever the scenario involves the use of local controls. New “constant emission” one box models are proposed that permit either local exhaust or local exhaust with filtered return, coupled with general room ventilation or the recirculation of a portion of the general room exhaust. New “two box” models are presented in Part II of this series.

Both steady state and transient models were developed. The steady state equation for each model, including the standard one box steady state model, is augmented with an additional factor reflecting the fraction of time the substance was generated during each task. This addition allows the easy calculation of the average exposure for cyclic and irregular emission patterns, provided the starting and ending concentrations are zero or near zero, or the cumulative time across all tasks is long (e.g., several tasks to a full shift).

The new models introduce additional variables, such as the efficiency of the local exhaust to immediately capture freshly generated contaminant and the filtration efficiency whenever filtered exhaust is returned to the workspace. Many of the model variables are knowable (e.g., room volume and ventilation rate). A structured procedure for calibrating a model to a work scenario is introduced that can be applied to both continuous and cyclic processes. The “calibration” procedure generates estimates of the generation rate and all of remaining unknown model variables.

KEYWORDS:

• Exposure assessment
• modeling
• one box model
• well-mixed room model

Acknowledgments

This work was not funded by any organization. However, the authors thank Perry Logan (3M), Michael Murphy (3M), and Ron Pearson (Environmental Health & Safety, Inc.) for the discussions that led to the recognition that new one box and 2Box models might be a useful addition to our collective modeling toolbox.

Notes

¹In this article, the phrase “filtered exhaust” simply implies that the contaminant—gas, vapor, mist, fume, or particulate—is removed from the air stream by some process. The filtration or removal efficiency is generally not constant, varying with the type of removal process and the maintenance of the equipment and filters or capture media.

2 Given the uncertainties in the input values, model predictions should not be expected to have more than two significant figures.