ASHRAE Journal - June 2021 - 13

TECHNICAL FEATURE
space and carrying a viral or bacterial payload)
within the room, quanta/m3 (quanta/ft3)
Vb
= breathing rate of a susceptible person, m3/h
(ft3/min)
tD = occupant time duration in the room, h (min)
ηf,Mi n h
= effective fi ltration effi ciency of mask during
inhalation .
In the present analysis, the infectious quanta are
assumed to be SARS-CoV-2 contained within small
aerosol droplets. We consider two breathing rates
refl ective of occupants in a classroom: an instructor at
a breathing rate of 1.38 m3/h (0.818 cfm) and students
at a breathing rate of 0.540 m3/h (0.318 cfm) based
on values reported by Jimenez.3 With the current
emphasis on individuals wearing masks indoors, we
include the reduction of inhaled quanta by a susceptible
individual wearing a mask with an effective
fi ltration effi ciency during inhalation of ηMinh. We
measured mask effective fi ltration effi ciencies and
reported those results in Part 1 of this series. The
infectious quanta dose is directly proportional to
average quanta concentration in the space, occupant
breathing rate, occupant time duration within the
space and the penetration of quanta that breach a
mask or face covering.
Assuming the room is well mixed, the average concentration
of infectious quanta within the room,nq
,
will depend on the number of infectious individuals
actively shedding virus, Nl, the rate of each individual's
quanta emission, q, room volume, VR, occupant time
duration in the room, tD, effective mask fi ltration effi -
ciency during exhalation, ηmexh, and aerosol loss rate,
λ. For the present analysis, we utilize separate quanta
emission rates for the instructor (110 quanta/h) and
student (19.1 quanta/h), based on values reported by
Jimenez.3
Conceptually, it makes sense that an instructor who
is speaking loudly and frequently would have a higher
quanta emission rate compared to a student who is
speaking infrequently and more quietly. Including the
effective fi ltration effi ciency of a mask functioning to
reduce the quantity of exhaled infectious quanta, the
net emission rate of quanta for infected individuals
actively shedding in the room, Q , becomes
Q NqlfMexh
=−
 ()1 η ,

(3)
where
Q
Nl
q
= net emission rate of quanta for infected individuals
actively shedding in the room, quanta/h
= number of infectious individuals actively shedding
virus
= quanta emission rate of each infectious individual,
quanta/h
ηf,Me x h
= effective fi ltration effi ciency of a mask during
exhalation.
Miller, et al., incorporated a fi rst order loss rate of
quanta due to various mechanisms that include dilution
ventilation, aerosol deposition onto surfaces and virus
decay into the calculation of the average concentration
of infectious quanta in the room:4

nq=− − e
λλ
Q
Vt
RD


1
1 ()
−λtD
1


(4)
where
λ = fi rst-order loss rate comprising the various mechanisms
that " remove " quanta from the room air
VR = room volume , m3 (ft3).
The fi rst-order loss rate can be expressed as the sum of
individual losses:
λλ λ λ λλ=+ + filtration + filtration portable + + k
OA
dist
,
S
(5)
where
λOA = dilution effect associated with the volumetric
fl ow rate of outdoor air,
V OA
into the room volume, VR, (VVOA / ), h-1
λfi ltration = removal of quanta due to fi ltration
ηfSAR
()×VV , h-1
/
λfi ltration, portable = removal of quanta due to inroom
portable fi ltration unit
( ηf portable

×VV/
,
ηf portable
,
portableR), h-1
= fi ltration effi ciency of in-room air purifying
fi ltration unit
ηf = central station supply air handling unit fi ltration
effi ciency
Vportable = volume fl ow rate of in-room portable fi ltration
unit, if present, m3/h (ft3/h)
VSA
= supply air volume fl ow rate, m3/h (ft3/h)
J U N E 2 0 2 1 ashrae .o rg ASHRAE JOURNAL
13
, being dispersed
R
λdist = deposition of quanta in the return air distribution
system , h-1
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ASHRAE Journal - June 2021

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