Introduction to the Mass Balance Model

On this website, we use a simple mass balance model to simulate indoor levels of SHS. The essence of the mass balance model is that the rate of change in pollutant mass in a given space at any given instant is equal to the amount coming in, minus the amount leaving. In an equation:


For this tutorial you can use a Flash animation to explore a single-zone box model, one of the most simple applications of the fundamental mass balance equation. Although the model can be applied to either air pollution or water pollution, we are interested in emissions of pollution from cigarettes and other tobacco sources.

Box Model

The pollutant mass is assumed to be emitted into a confined space, in which the emissions are instantly mixed throughout the space. The air containing the mixture of pollutants can be exchanged with the outside. The pollution in the air can also be removed from the space by active filtration and by deposition onto surfaces present in the space.

For this exercise you can adjust the following model input parameters:

  1. the volume of the space, in cubic meters
  2. the rate of pollutant mass emissions into the space, in micrograms emitted per minute
  3. the duration of the emissions, e.g., the length of a cigarette, in minutes
  4. the rate of exchange of gas or air with the outside, in room volumes exchanged per hour
  5. rate of pollutant deposition onto surfaces, in units of room volumes worth of pollutant removed per hour, and
  6. the efficiency of a filtration device, which is located in the space, with values of "0" (no pollution passing through the filter is removed) to "1" (all pollution passing through the filter is removed). The filter has a fixed recirculating flow rate of 80 m3/hour.

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 graph on the left will be updated to reflect the new parameter value.

The plot on the left shows the minute-by-minute concentration times series of the pollutant that is being emitted into the space. Observe how the peak and asymptotic values change as you adjust the parameters. Please note that the upper limit of the Y axis may change to accomodate the full time series.

[Ed. Note: If the graph below appears displaced in Internet Explorer, trying hitting your browser's "Refresh" button.]

Single Box Model, Internal Source Input Parameters


Here are some study questions that you might consider in your exploration of pollutant dynamics using the single-zone box model.
  1. What parameters control the location of the peak in time?
  2. How long does it take for pollutant to be completely removed from the space?
  3. For what parameter values does the pollutant concentration reach an asymptote (i.e., a plateau)? What physical conditions are occurring when the concentration reaches the asymptote?
  4. How does the height of the asymptote change with each parameter?
  5. How does the rate of increase in pollutant concentration depend on each parameter?
  6. How does the rate of decrease in pollutant concentration depend on each parameter?
  7. How does filtration affect the pollutant level for different room volumes? Why is this the case?
  8. Multiply the emission rate by the duration of the source. What does this number represent? What units does it have?
  9. Divide the number you got in the previous question by the volume of the space. What does this number represent? What are its units? How does it compare to the peak value observed on the plot?
When you are done with the single zone box model presented in this tutorial, you may wish to move on to explore a two-zone box model.