Internal contaminants and decay of concentration

The impacts of the global pandemic are numerous however one in particular has been a better understanding of the importance of good ventilation in buildings. Specifically the World Health Organisation published information about the airborne transmission of COVID-19, which further emphasises the importance of good, effective ventilation.

One of the specific terms relating to air contamination and the impacts of air replacement can be referred to as decay of concentration, also referred to as half-life which describes the impact air change rates have in the dilution or decay of a contaminant contained with in air.

The decay of the concentration can be expressed by the equation:

• C = Cmax . (e -t/)
• C = [Cmax, 0] as t = [0, ∞)

Where:

• t is the time from the start of the rise or decay (s)
• τ is known as the “half-life” or air change (s)
• C is the concentration at time t (ppm)
• Cmax is the maximum concentration during rise or decay (ppm)
• τ is calculated by:

= V/Q

Where:

• V is the volume of the room (m3)
• Q is the ventilation rate (m3/s)

The initial concentration before any decay, is the maximum concentration described as Cmax. When t=τ (half-life or 1 air change), then the concentration in the room has reduced to 0.37Cmax. and when t=3τ, then the concentration C= 0.05.Cmax. This means that after 3 half-lives, the concentration in the room has been reduced by 95%.

Therefore in practice, 3 τ is considered to be the time to achieve steady state conditions, for a rise, or the time to clear the room, for a decay.

We do have to take into account the fact that the air supplied must be fresh, i.e. not recirculated and that the ventilation must be effective; fresh air must not be short circuited into the extract and it must reach everywhere in the room, to avoid areas of high contaminant concentration (stagnation).

The mechanical air change rate provided by the ventilation system is not often the same as the effective air change rate. The concept of a “mixing factor, k” can be used to describe the quality or effectiveness of the mixing process in a space. Mathematically, Q'=kQ where k = 1 for ideal mixing and k = 0.5 for poor mixing. The effect on decay levels is shown in the following equation:

Where:

• τ’ is the room’s “half-life” (s)
• V is the room’s volume (m3)
• Q is the mechanical, theoretical ventilation rate (m3/s)
• Q’ is the effective ventilation rate (m3/s)

Substituting the k value into the decay equation, the following expression is obtained:

C = Cmax . (e -t.k/)

For example, for a k factor of 0.6, when t=τ(half-life), then the concentration in the room has reduced to 0.55 Cmax, instead of the original 0.37Cmaxand when t=3τ, then the concentration is still 0.17.Cmax, compared to 0.05 for k=1.

This means that it will take longer to purge the contaminant from the room i.e. If the ACR of an isolation room is 10 ACH, for a k value of 0.6, the effective ventilation rate would be 6 ACH.

BSRIA has studied several hospital isolation rooms, with dedicated ventilation. The k factor in those rooms, which were considered well-mixed, was k= 0.8, calculated using gas tracer methodologies.

This is based on an article published on the BSRIA website as "New World Health Organisation information emphasises effective ventilation in buildings" dated June 2020.

[edit] Related articles on Designing Buildings

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• BSRIA articles on Designing Buildings Wiki.
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• HVAC balancing.
• HVAC industry defines post COVID-19 changes.
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