Models for nearly every occasion: Part IV – Two-box decreasing emission models

ABSTRACT

New two-box “well-mixed room” decreasing emission (DE) models are introduced for scenarios that involve local controls, such as some form of local exhaust or local exhaust with filtered return. In addition, these models allow for the recirculation of a filtered (or cleaned) portion of the general room ventilation.

 For each control device scenario, a steady state and transient near and far field model is presented. The transient equations predict the concentration at time t after the application of the substance. The steady state equations can be use to predict the steady, unvarying “average concentration per application” whenever there are continuous applications of a substance and sufficient time has elapsed. The steady state equations can also be used to calculate the TWA for a task (or a series of tasks) whenever the beginning and end concentrations for the task (or task series) are expected to be zero (or near zero). The transient equations should be used to predict TWA exposures whenever these criteria cannot be met, or it is necessary to predict short-term exposures or peak concentrations.

 A structured calibration procedure, based on a mass balance approach, is proposed for each model. Depending upon the model, one or more calibration measurements are collected. Rearranged versions of the steady state equations are used to calculate estimates of the mass applied during each application, the near field flowrate, and (depending upon the model) the various efficiencies (e.g., local exhaust capture efficiency and the recirculation filtration efficiency). The emission rate constant must be determined using either a published approximation algorithm or experimentally.

KEYWORDS:

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

Notes

a As in Parts I and II, we are inclined to be somewhat flexible in how we use the phrase “steady state”. In Parts I and II we use it to mean a constant average concentration during each application cycle.

b The time between applications (t_a) can vary, but will be considered to be a constant in this article.

c The error will reflect any unevaporated substance (i.e., M·exp(-αT)) and the residual concentration remaining in the room (C(T)).

d A validated model is a calibrated model that has been shown, using measurements, to be reasonably predictive.