Three-Zone Mass Balance Model

This tutorial is the third in a series that explores the mass balance model. Here, you can explore a three-zone model. Before using this tutorial, you should read the two previous tutorials containing an introduction to the mass balance model and an exploration of a two-zone model.

For the present exercise you can explore a three-zone box model for air pollutant emissions. The pollutant mass is emitted into the first zone (Room #1), but it can travel to the second and third zones at adjustable flow rates. Pollutant mass is removed from both zones by ventilation or by deposition onto surfaces. The emissions are assumed to be instantly mixed throughout the zones.

For this exercise you can adjust the volumes of the spaces, the rate of mass emissions into the first space, the duration of the emissions, the air flow rate between the zones, the air flow rate between each of the zones and the outdoors, and the rate of pollutant deposition.

Note that you need Adobe Flash to use the control panel.

The Control Panel

Adjust the sliders on the right side to change the input parameters of the model. When you release the mouse button, the area graph on the left will be updated to reflect the new parameter value.

The graph on the left shows the minute-by-minute concentration times series of the pollutant in all three zones. Note that the plots are overlaid with Room #2 positioned behind Room #1 and Room #3 behind Room #2. Observe how the shapes of the three time series change as you adjust the parameters. Please note that the upper limit of the Y axis may change to accommodate the full time series.

Three-Zone Box Model, Source in Room #1 Input Parameters
Vol 1
[m3]
Vol 2
[m3]
Vol 3
[m3]
Emiss.
[μg/min]
Dur.
[min]
Dep.
[1/hr]
Flow 1-2
[m3/hr]
Flow 1-3
[m3/hr]
Flow 2-3
[m3/hr]
Flow 1-0
[m3/hr]
Flow 2-0
[m3/hr]
Flow 3-0
[m3/hr]
Note: Flow 1-2 is equal to the air flow between Rooms #1 and #2. Likewise for Flow 1-3 and Flow 2-3. The flow is assumed to be the same in both directions (i.e., balanced). Flow 1-0 is the air flow between Room #1 and the outdoors (balanced in both directions). Likewise for Flow 2-0 and Flow 3-0. The specified deposition rate is assumed to apply to all three rooms. The surface to volume ratios of the rooms are both assumed to be 3 m-1.

Questions

Here are some study questions that you might consider in your exploration of pollutant dynamics using the three-zone box model.
  1. What layout in a real home might be realistically represented by three zones?
  2. Adjust the volumes and air flows for the three zones to represent a layout you have in mind. How much exposure might a person in one of the adjacent rooms to a smoker receive in the layout you have chosen?

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