Part 2: What is the basis for using ACH as a design parameter?

In a previous post I examined how the concentration of a pollutant decreased over time as a function of different ventilation rates. This examination was limited to the case where the pollutant was at some fixed level in a space and then ventilation was introduced into that space. An example of this situation would be a pollutant leaking from a pipe into a closed room and then a valve being closed which stops the flow of the pollutant and then a fan being turned on to provide ventilation to the space. While this scenario is possible, it is probably more useful to examine the case where a pollutant is being emitted at some rate and ventilation is being supplied to attempt control the level of that pollutant. For simplicity, it will be assumed that the initial concentration of the pollutant is zero. With this simplifying assumption, this case can be modeled using a relatively simple differential equation:

where   C(t) = Concentration at time t

G = Generation rate of pollutant

Q = Ventilation rate

V = Volume of the space

Dt = Change in time

This equation comes from ACGIH's book Industrial Ventilation A Manual of Recommended Practice. As with the previous case, the units for each of the parameters must be consistent. If G is given in CFM, then the time will be minutes and the volume will need to be given in cubic feet. So what impact does changing the ACH have upon the concentration of the pollutant in a space? For this example, it is assumed that the rate of pollutant generation is 1 CFM (0.5 L/s) in a room with a volume of 10,000 cubic feet (283 cubic meters), a space roughly 29’ wide x 29’ long x 12’ tall (8.8 m x 8.8 m x 3.7 m).

As in the previous case, the ACH has a dramatic impact upon the final concentration of the pollutant in the room. At small values for ACH the concentration of a pollutant increases for quite some time until a steady state concentration is reached. For example with an ACH = 0.5 the concentration continues to increase for about 10 hours until the final concentration of 12,000 ppm (1.2% by volume) is reached. Contrast this with an ACH = 4 where the final concentration of 1,500 ppm (0.15%) is reached after an hour. As ACH increases, the final steady state concentration decreases. This chart suggests that the ventilation rate can be used to control the final concentration of pollutants in a space.

It can be reasonably concluded that using the ACH as a design parameter for a ventilation system has merit. However, it is necessary to again mention that several simplifying assumptions were made in the previous analysis which can have a dramatic effect upon the performance graphs presented here. The limitations of this method will be examined in an upcoming post.