ASHRAE Journal - July 2023 - 53

TECHNICAL FEATURE
by recent literature.4 The present work, by means of
mass and concentration balance of airfl ows in HVAC
systems, calculates the pathogen concentration, the
resultant infection probability and the number of
potentially infected individuals for different space
layouts of segregated rooms served by the same HVAC
system. Airfl ows and the number of people in the
room are presumed steady state, while virus concentration
is time dependent.
The main purpose of this work is to help build a
conscious risk assessment plan for HVAC systems
for designers, manufacturers, building owners and
building managers.
Model and Input Data
According to the Wells-Riley model,4 the probability
for a susceptible individual to contract a disease via
aerosol infection follows a Poisson probability function
given by Equation 1:
−
Pe 0
=−
1
p Ct dt
T
¥∫ ()
I
¥∫
pC t dt
T
I ()
(1)
where
P = probability of infection of any exposed susceptible
individual, a real number in the interval [0, 1]
= number of infectious quanta
inhaled by a susceptible individual
during the exposure time T, quanta
p = pulmonary inhalation rate of a susceptible individual,
m3/h
T = total time of exposure, h
CI(t) = instantaneous volume concentration at time
t of infectious quanta in the environment (considered
well mixed), quanta/m3
Gammaitoni and Nucci derive an expression for calculating
the viral concentration CI given the following
simplifying assumptions: the quanta emission rate q is
considered constant over time, the latent period of the
disease is longer than the time scale of the model and
the droplets are distributed instantaneously and uniformly
in the room.5 This equation, which considers all
vectors of viral load removal in the room volume (inactivation,
deposition and ventilation), is as follows:
C
I = +−  * e
N*
q*Iq*

VN*


n0
V
I
V


(2)
−Nt*
where
q = infectious quanta emission rate by one
asymptomatic infected individual, quanta h−1
I = number of asymptomatic infected individuals
N = total virus removal rate in space, N = λ + k + rn, h−1
λ = viral inactivation rate in space, h−1
k = viral particle deposition (gravitational settling)
rate in space, h−1
rn = air renewal (outdoor air exchange) rate, h−1
V = room volume, m3
n0 = initial level (at t = 0) of infectious quanta present
in volume V, quanta
t = time, h
For n0 = 0, Equations 1 and 2 yield Equation 3 for the
probability of infection P:
P 1


=−exp 
qI p
V
**
 −−

1

*
2
NT e
N
−NT*




(3)
 
This paper applies this model (with all connected
assumptions, particularly well-mixed environments)
in simulating some HVAC layouts of offi ce buildings.
The level of activity of all involved individuals is
assumed to be in the category " speaking during light
activity. "
Please see online materials and I-P versions of the
equations and related nomenclature for this article at
tinyurl.com/JournalExtras.
Quanta Emission Rate Input Data
Among all the input parameters required for the
application of th e above model (Equations 1 through 3),
the infectious quanta emission rate q of an asymptomatic
infected individual related to the SARS-CoV-2
virus is unquestionably the most uncertain and controversial
one, with a huge range.
At present, the only available data specifi cally
related to the original SARS-CoV-2 virus come from
a single group of authors, Buonanno et al.4,6 These
authors propose " a forward emission approach to
estimate the quanta emission rate of an infected
individual on the basis of viral load in the sputum
and the concentration of droplets expired during
different activities. " 4 They analyze the worst-case
scenario in the presence of an asymptomatic SARSCoV-2-infected
individual in several microenvironments:
a pharmacy, a supermarket, a restaurant, a
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53
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ASHRAE Journal - July 2023

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