Exploring a Two-Zone Mass Balance Model

After you have read about and understood the single-box model as presented in the introduction to the mass balance model tutorial, you are ready to explore more complex arrangements of zones. In the real world, homes typically consist of more than just a single room.

This exercise allows you to interactively explore a two-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 zone at the flow rate that you specify. 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 both zones. The times series are displayed as overlaid area plots with Room #2 placed behind Room #1. Observe how the shapes of the two time series change as you adjust the parameters. Please note that the upper limit of the Y axis may change to accomodate the full time series.

Two-Zone Box Model, Source in Room #1 Input Parameters
Vol 1
[m3]
Vol 2
[m3]
Emissions
[μg/min]
Duration
[min]
Flow 1-2
[m3/hr]
Flow 1-0
[m3/hr]
Flow 2-0
[m3/hr]
Deposition
[1/hr]
Note: Flow 1-2 is equal to the air flow between the rooms. 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). Flow 2-0 is the air flow between Room #2 and the outdoors (balanced in both directions). The specified deposition rate is assumed to apply to both 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 two-zone box model.
  1. Under what conditions can concentrations in Room #2 exceed those in Room #1?
  2. What parameters affect the distance in time between the concentration peaks in each room?
  3. How realistic do you think this model in describing air pollutant levels in two separate rooms of a real home due to smoking or some other pollution source? What added features would make it more realistic?
When you are finished exploring the two-zone mass balance model, you may want to proceed to the tutorial for a three-zone mass balance model.

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