Models for nearly every occasion: Part II - Two box models
The “well-mixed room” two box models are often used to predict near and far field concentrations for a specific task, but are limited to scenarios where local exhaust controls are not used. In Part II of this series, new two box models are presented that permit local controls that either exhaust to the outside or return filtered air to the workspace. Additional models are presented that also allow for the recirculation of a filtered portion of the general ventilation flowrate. During the concentration increase phase the emission rate is assumed to be relatively constant. Both steady state and transient equations were developed for each scenario.
An additional factor, representing the fraction of time that the substance is being emitted during a task or set of tasks, was added to the standard and new steady state models. This simple modification permits the easy calculation of the average near and far field concentrations for cyclic and irregular emission patterns, provided the starting and ending concentrations are identical (e.g., zero or near zero) or the cumulative task time is long (e.g., two or more task cycles to a full shift, depending upon the number of room air changes per task). Additional variables are introduced with the new models, such as the efficiency of a local control 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). Others can be approximated using manufacturer specifications or published values (e.g., filtration efficiency). A structured procedure for calibrating a model to a work scenario is presented that can be applied to both continuous and cyclic processes. The “calibration” procedure generates estimates of all of the unknown model variables, including the generation rate and the effective near field flowrate (which takes into account potentially complex near field air currents as well as any thermal plumes created by a hot process).
