ASHRAE Journal - August 2021 - 19

TECHNICAL FEATURE
FIGURE 1 The equation of ventilation shows the basic relationship between ventilation
rate and concentration. 5
Equation of ventilation:
V qc c V
dc
dt
o
=− 1() −
oG
=− pol()+ 
General solution for equation of ventilation:
c cc e
V = Volume of space (m3)
c = Concentration (% or kg/m3)
q = Ventilation rate (m3/s)
co = Supply air concentration (% or kg/m3)
dc = Change in concentration
dt = Change in time
Vpol
cG= V 
q
cI = Initial concentration at time t = 0
n = Air change rate
the outdoor air is free from contaminants, the fi ltration
effectiveness is low enough to ignore and that
there is perfect mixing in the space. If the outdoor air
is increased 150%, then the time to get to 99% removal
can be decreased to 52 minutes. These guidelines can be
used to determine fl ush times between classes or before
starting the school day. However, the assumption of perfect
mixing in the space is usually not accurate. Stagnant
areas caused by the air distribution system can increase
the removal time.
The airborne contaminant removal formula shows
that 63% of the airborne contaminants will be removed
with each air change, but a more realistic range has been
shown to be 20% to 60%.8 ASHRAE's Building Readiness
Guide recommends that spaces be fl ushed for a duration
suffi cient to reduce the concentration of airborne
infectious particles by 95% between occupancy, which
equates to about three changes of space volume using
equivalent outdoor air for a well-mixed space.9
A study by Qian, et. al., determined that in general
" increasing [the] ventilation rate can effectively reduce
the risk of long-range airborne transmission. " 4 As mentioned
above, Li, et al., also found strong evidence to
demonstrate the association between ventilation and
the spread of infectious diseases.6 The World Health
Organization (WHO) in their Natural Ventilation for Infection
Control in Health-Care Settings study found that low ventilation
rates can result in increased infection.5 While all
of these studies point to the importance of ventilation,
FIGURE 2 Airborne contaminant removal formula.7


tt
− =−
21





ln


C
C
Q
V
2
1









⋅ =−
60




ln 1−


t1 = Initial time (min)
V = Volume of space (ft3)
Q = Airfl ow rate in ft3/h
Er = Removal effi ciency
t2 = Final time (min)
C1 = Initial contaminant concentration
C2 = Final contaminant concentration
minimum clean air rates to prevent infection have not
been established.4 - 6 Also, as mentioned in previous
parts of this article, ventilation rates have little effect
on large droplet-borne transmission.4 The presence of
pathogens in the room is only one of the susceptibility
factors involved in the infection process (see Part 13),
which further complicates determining a minimum
ventilation rate for these spaces.
While the Wells-Riley equation shows that increasing
the ventilation rate will also decrease the infection risk,
this relation may not apply uniformly across a space.
A study by Memarzadeh, et al., shows the importance
of the path between the contaminant source and the
exhaust in a patient room.10 The study determined that
increasing the ventilation rate from 4 ach to 12 ach had
little impact on the infection risk in their model when
the exhaust was not located directly over the patient's
head.Other studies have also shown that increasing
A U G U S T 2 0 2 1 ashrae.org ASHRAE JOURNAL
19
Er
100
ach







⋅=0
60,wheret1
()+−−nt
nt
ceI
TABLE 1 Airborne contaminant removal in a fully mixed, empty room with no
aerosol-generating source.
ACH
2
4
6
8
10
12
15
20
50
= Pollutant generation rate in the room (m3/s or kg/m3)
pol = source concentration
TIME (MIN) REQUIRED FOR REMOVAL
(99% EFFICIENCY)
138
69
46
35
28
23
18
14
6
TIME (MIN) REQUIRED FOR REMOVAL
(99.9% EFFICIENCY)
207
104
69
52
41
35
28
21
8
Note: Data taken from CDC's " Guidelines for Environmental Infection
Control in Health-Care Facilities, " Appendix B.7
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ASHRAE Journal - August 2021

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