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

So why is ACH used as a design parameter? The basis for this comes from the differential equations that describe concentration buildup and concentration decay. As a first step, let's examine the concentration decay due to purging. In its basic form, the concentration decay equation is of the following form:

where C(t) = Concentration at time t.

C₀ = Concentration at time 0

Q  = Ventilation rate

V  = Volume of the space

Dt  = Change in time

In the equation, the units need to be in some consistent format. For example, if the time is given in minutes, the ventilation rate needs to be given in terms of volumes per minute. At the same time, the volumetric units used in the ventilation rate must match the units used to define the space volume such as cubic feet or cubic meters. For example, if the volume of the room is given in cubic meters (m³) and the time is given in hours, the ventilation rate must be given in terms of cubic meters per hour (m³/hr). When the value of Q is given in terms of cubic feet per hour or cubic meters per hour, the value of Q/V in the exponent is the ACH.

So how does changing the ACH effect the concentration of a pollutant in a space? Figure 1 shows how the concentration of a substance declines based on different ACH. The abscissa of this graph is change in time while the ordinate is the ratio of the concentration at a given time to the initial concentration. While there were several simplifying assumptions made in the development of this graph, it shows how increasing the ACH decreases the time required to reduce a concentration of a pollutant. 

Based on this simple analysis, it can be stated that using ACH as a design parameter does have a sound basis. However, it must be recognized that it is a very simplified approach. In an upcoming post I will examine how the ventilation rate affects the concentration of a pollutant that is being emitted into a space.