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Examining CO2 levels in school classrooms

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High CO2 levels in school classrooms continue to be a concern. As a result we reviewed the mass-balance model of ventilation. We identified several factors by fitting the model to the data. The review allowed CO2 build up, ventilation rates and exhalation rates to be examined in real (on-site) measured conditions. We discuss the theoretical model of the growth and decay of CO2 concentration in a space and how it relates to the data through the parameters of the model, providing an understanding of the drivers of CO2 concentration and some validation of the theory by the data. Results from our measurements of Australian school classrooms are similar to other parts of the world, indicating CO2 levels, ventilation rates and air temperatures do not comply with the standards.
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Topic A8: IAQ & perceived air quality
Examining CO
2
Levels in School Classrooms
Mark B LUTHER, Peter HORAN and Steven E ATKINSON
Deakin University, Victoria, Australia
Corresponding email: luther@deakin.edu.au
Keywords: Ventilation theory, Classroom ventilation, CO
2
levels, Air change rates (ACH)
SUMMARY
High CO
2
levels in school classrooms continue to be a concern. As a result we reviewed the
mass-balance model of ventilation. We identified several factors by fitting the model to the
data. The review allowed CO
2
build up, ventilation rates and exhalation rates to be examined
in real (on-site) measured conditions.
We discuss the theoretical model of the growth and decay of CO
2
concentration in a space
relates the model to the data through the parameters of the model, providing an understanding
of the drivers of CO
2
concentration and some validation of the theory by the data. Results
from our measurements of Australian school classrooms are similar to other parts of the
world, indicating CO
2
levels, ventilation rates and air temperatures do not comply with the
standards.
INTRODUCTION
This paper utilizes the results of the MABEL (Mobile Architecture and Built Environment
Laboratory) facility project, which measured several school classrooms for their CO
2
,
comfort index and temperature stratification levels (Luther and Atkinson, 2012). These
Australian results confirm what has been discovered elsewhere internationally, that school
classrooms frequently suffer poor indoor air quality, ventilation and comfort control. In an
effort to remedy these problems, as found in our evidence-based study, this paper begins first
by understanding the build up and decay of CO
2
in the provided cases.
A broad range of studies shows that ventilation rates in schools are inadequate (Mendel and
Heath, 2005). What is controversial is the number of air changes required to ventilate
classrooms to achieve acceptable levels of CO
2
and pollutants. Perhaps the causes of this are
the various units and methods of determining ventilation air change rates as well as a
misinterpretation of the standards. The ASHRAE Standard 62.1-2004 (ASHRAE 2004)
recommends a minimum of 8L/sec per person for classrooms. Depending on classroom size,
and volume this amount could typically result in between 3-5 ACH per classroom (Daisey et
al. 2003 and Becker et al. 2007).
Achieving energy efficiency stands in opposition to controlling classroom air humidity,
temperature and ventilation. Studies indicate improved student performance for elevated
ventilation rates and reduced air temperatures in classrooms in summer (Wargocki and
Wyon, 2006). These studies also observed CO
2
levels and found substantial reductions using
ventilation rates of 6.5 and 9.5L/s/person, yielding 900ppm and 780ppm respectively. Other
researchers confirm that rates of 7 – 10 L/s/person are required to reduce TVOC’s and other
pollutants (Fischer and Bayer, 2003 and Daisey, et al., 2003). Further studies confirm that air
quality symptoms increased at a ventilation rate below 10L/s/person (Seppanen et al., 1999).
Our review suggests that more accurate calculations accounting for the number of people,
their activity and the room volume as well as the air change rate, can be performed.
The above work of others and our measurement studies of several Australian school
classrooms prompted several questions. What is a reasonable respiratory (CO
2
generation)
rate for a typical student? How does the air change rate affect the CO
2
levels over time? What
influence does room volume have on the level of CO
2
for a given condition? In search of
answers to these questions we began to review the fundamental mass-balance equations.
METHODOLOGY
We present the theoretical model of CO
2
concentration in detail so as to clarify the roles of
the quantities involved. The general solution shows the relationships between the key
parameters.
Ventilation Standards and Theoretical Model
Previous work suggests that the first step in designing for ventilation is to calculate the
ventilation requirements with respect to the acceptable indoor air quality. Various national
and international standards exist, which give guidance on required fresh air design rates, but
the sources offer inconsistent advice. However, all agree that schoolrooms, due to the number
of occupants, require more dilution air than adult occupants in a similar space. The range of
values suggested in the standards is from 6.25 to 15L/s
/
person (AS 1668.2-2002 and EN
13779 2007).
In order to determine what a ventilation rate should be for a particular case the parameters
involved in causing high CO
2
levels must be understood first. We are interested in
understanding how CO
2
concentration changes in a confined space. This change occurs at
any instant at rates determined by the ventilation rate and the number of occupants in a
known volume. Given a volume, CO
2
enters it at a rate determined by the outdoor CO
2
concentration,

, and leaves it at a rate determined by the indoor CO
2
concentration at time
t, C(t). In addition, people add CO
2
to the air in the room at rates estimated from physical
measurements (Figure 1).
Figure 1. Carbon dioxide flows in a confined space
This is summarized in Equation (1) in which the rate of adding CO
2
less the rate of
exhausting CO
2
causes the concentration of CO
2
in the volume to change. This equation
expresses the mass balance, the balance of CO
2
entering and leaving the volume at some
instant, :

(
)

=


(
)
(1)
where
*
V = space volume in m
3
() = indoor CO
2
in ppm(v)

= outdoor, or ambient, CO
2
concentration in ppm(v)
t = time in s
G = indoor CO
2
generation rate in mL/s for a fixed number of occupants
Q = space ventilation rate in m
3
/s
()

= the rate of increase in the CO
2
concentration in ppm(v)/s
The rate of increase of CO
2
will be zero when + 

= (); that is, the CO
2
generated
by people balances the CO
2
introduced and removed by ventilation. If this balance is
achieved, as it will after a sufficient time,()= / + 

. This specific() is the
steady state or final value of CO
2
concentration and we label it

.
To allow for the number of people in the room, we define and in terms of as follows:

(2)
where = the number of people in the space, and = indoor CO
2
generation rate in mL/s
per person. Hence,

+



(3)
it is always true that

≥ 

. Hence,() can never fall below the ambient concentration
of CO
2
,

.
Quite often, insufficient time is available for () to reach

, and we need to know the
transient behaviour of(); that is, how() changes before settling. Furthermore, it may be
that the space is not initially in equilibrium with the environment. The solution to the above
Equation (1), satisfying initial and final values, is the exponential equation:
(
)
(

)
1

(4)
where

is the actual CO
2
concentration at  = 0.
*
Note that 1mL/m
3
= 1 ppm(v).
We ignore the unrealistic case in which, initially, CO
2
is absent from, or reduced in, the indoor air, as it
will eventually rise to the ambient concentration,

, of CO
2
.
The air change rate is in fact the quotient/ represented by the symbol ". Its reciprocal,
# = / is the time constant of Equation (4). This is the time required to change one air
volume in the space considered. It is important to understand that the concentration of CO
2
as
time passes is determined by knowing the values of three parameters, its initial
concentration,

, final concentration,

, and the air change rate, ". Of course, these values
may change in response to external or internal influences, changing the behaviour of().
Substituting " for and rearranging Equation 3,
$%
"
(


) (5)
it is clear that the three quantities determining the concentration curve that are on the right of
the equation are also related to the quantity /. This quantity is the rate at which people
add to the CO
2
concentration in the space. That is, the number of people in the room, their
average CO
2
exhalation rate and, inversely, the room volume combine to offset exfiltration
reducing CO
2
concentration to the background value.
An example of modelling various air change rates, by applying the previous equations to a
space with a constant CO
2
generation rate and fixed volume is shown in Figure 2. Note that
the time-constant, # = 1/", differs for each curve as " changes, as does the final value,

.
If the air change rate, " is small, the time-constant, #, and the final value,

, are large. The
concentration of CO
2
takes a long time to settle to a large value. On the other hand, if " is
large, the time-constant,#, and the final value,

, are small, and the concentration settles
quickly to a small value, closer to

.
Figure 2. CO
2
Concentration for Various Air Change Rates in a Classroom
Establishing a Target Value of Classroom CO
2
According to the NISTIR 6729 report by Emmerich and Persily (2001), carbon dioxide is not
generally considered to be a health problem. A limit for an 8 hour exposure and a 40 hour
work week is 5000 ppm(v) and a short 15 min exposure limit is 30,000 ppm(v).
A major driver for investigating CO
2
build up in school classrooms is discomfort, leading to
learning difficulties. Several publications by the World Health Organisation (WHO) and
ASTM D6245 (2002) recommend an upper limit value of 1000 ppm. Furthermore, studies
have been conducted to investigate the Predicted Percentage Dissatisfied (PPD) with CO
2
concentrations indicating that a 25% PPD begins at around 1000 ppm. It must be noted that
this figure is concentration above outdoor CO
2
levels, indicating that ~1,400 ppm would be
the accepted value at 25% PPD. These findings have also been confirmed in the publications
of Olesen (2004).
Estimating CO
2
Generation within a Classroom
Since we are interested in the removal of CO
2
we need to know at what rate this is being
generated. Results presented in Plowman & Smith (2007) and Emmerich & Persily (2001) for
an activity level of 1.5 met indicate a CO
2
production level of 0.0065 L/sec, or 390 mL/min.
However, it should be noted that these values are for adults and are therefore conservative.
Plowman & Smith report a tidal volume range of 6–90 L/min from which a typical tidal
volume
of 20 L/min might be assumed. The exhaled CO
2
concentration is about 4.5% or 900
mL/min. ASTM D6245 (2002)
suggests the CO
2
generation rate of a child with a physical
activity level of 1.2 met is 0.0029L/s. For an adult this this is 0.0052 L/s (320 mL/min). In
Figure 2, the CO
2
generation rate per student is assumed to be 300mL/m/person, but we
intend to investigate this parameter more closely from our measurement data.
RESULTS AND DISCUSSION
We studied 24 classrooms in four different schools during a winter period in Victoria
Australia (a cool temperate climate) with different building construction types. No classroom
had room conditioning during the measurement period. It is clear that CO
2
levels can increase
rapidly in a typical occupied non-ventilated room as shown, for example, in Error!
Reference source not found.. Furthermore, the opening of a door copes with this problem
easily during a break, indicating that a proper cross-ventilation will reduce CO
2
levels
dramatically.
Figure 3. CO
2
and Humidity Levels in a Single Classroom
We need to fit the theoretical model to the data to identify the parameters",

and

in
Equation (4) because the CO
2
concentration rarely settles to steady values. Indeed, there is no
point in Figure 3 which has reached a steady state. Given these values, we can then determine
the factor/, and hence the CO
2
exhalation rate,.
The fit of the model to seven points from 9:15 to 10:45 (left ellipse in Figure 3) is shown in
Figure 4. From Equation (5),  
= 2193 ppm/hour. Assuming a room volume of 250m
3
and that there are 22 25 people in the room, as recorded, for 25 people,  =
366mL/person/minute.
Figure 4. Door closed, room occupied
The fit of the model to the later seven points from 12:00 to 13:30 (right ellipse in Figure 3), is
shown in Error! Reference source not found.. In both cases, the room is closed and the air
change rate is 0.62 which is close to 0.60 for the earlier fit. This is a good validation of the
model. Hence,  
= 75 ppm/hour. However, the number of people recorded is 6 – 20 and
the internal partition between this and the adjacent classroom is now open, so the room
volume is now 500m
3
. This yields  = 104mL/person/minute for 6 people, a figure too low
which needs further investigation.
CONCLUSIONS
We have reviewed a number of papers which show that ventilation rates in schools are
inadequate and that the required air change rate to achieve acceptable levels is controversial.
As a result, we have gone back to the theoretical foundations of ventilation. Although this
theory is long-standing, insights from it have proved valuable.
We have explored the behaviour of CO
2
concentration in a room as a function of time, room
volume, the number of people present and their exhalation rate of CO
2
, the air change rate,
the initial concentration of CO
2
and its background concentration. As a result, we have fitted
"
0
.
62
airchanges/hour

3937
ppm
923
ppm

2193
ppm/hour
the function to the data in a number of cases, of which we have shown two fits from the same
room. This shows a consistency in the value of the air change rates required to fit the model
to the data, validating our approach. Having fit the data, we have then been able to estimate
the exhalation rate, but this is not as consistent and needs further investigation.
Having made a fit by adjusting the parameters",

and

in Equation (4) to minimize the
mean square error of the theoretical data point to the measured data point, a good estimate of
 
and therefore may be determined since and are known.
Re-examining the equations of ventilation theory and fitting measured data have provided
important insights. The causes and rates of CO
2
generation within a room are better
understood. In particular, the rate at which CO
2
is exhaled per student in a classroom under
typical user conditions can be better identified. Also, the study of air change rates and their
influence on CO
2
reduction is applicable to HVAC ventilation system design. It is important
to recall that this investigation considered non-mechanical, passive ventilation of classrooms.
These passive air-change rates could be increased through mechanical means if necessary.
Furthermore, the observation that it takes time to reach a particular CO
2
level in the real-
world classroom, where nothing remains constant for a long period of time, can mean that
active ventilation can be delayed until a threshold concentration is reached, saving energy.
Lastly, since we have a method for investigating ventilation which identifies the relevant
parameters from data, we have a model which can be used for prediction. Working in reverse,
the variation of concentration of CO
2
can be predicted as a function of time, as and the
room conditions change. This work is yet to be reported. We intend to make further findings
from our case study measurements, including advice for HVAC design and control.
Figure
5
.
Door closed, at most six people
"
0
.
60
airchanges/hour

525
ppm
1440
ppm

75
ppm/hour
REFERENCES
ASHRAE (2004) Standard 62.1-2004 Ventilation for Acceptable Indoor Air Quality,
American Society of Heating and Refrigeration and Air-conditioning Engineers, Atlanta,
Georgia, USA.
AS 1668.2 (2002) Australian Standard: The use of ventilation and airconditioning in
buildings Part 2: Ventilation design for indoor air contaminant control (excluding
requirements for the health aspects of tobacco smoke exposure) Standards Australia
International Ltd, Sydney, Australia
ASTM (2002) D6245-98 (2002 reapproved) Standard Guide for Using Indoor Carbon
Dioxide Concentrations to Evaluate Indoor Air Quality and Ventilation, ASTM
International U.S.A.
Becker R, Goldberger I, and Paciuk M (2007) Improving Energy Performance of School
Buildings while Ensuring Indoor Air Quality Ventilation, Building and Environment,
Elsevier Science Direct, vol. 42, pp. 3261–3276.
Daisey JM, Angell WJ and Apte MG (2003) Indoor Air Quality, Ventilation and Health
Symptoms in Schools: an analysis of existing information, Indoor Air Journal, Denmark,
2003, 13, 53-64
Emmerich SJ and Persily AK (2001) NISTIR 6729 Report: State-of-the-Art Review of CO
2
Demand Controlled Ventilation Technology and Application, National Institute of
Standards and Technology, Technology Administration, US Department of Commerce,
2001.
EN 13779 (2007) European Standard: Ventilation for non-residential buildings
Performance requirements for ventilation and room-conditioning systems, European
Committee for Standardisation, Brussels
Fischer JC and Bayer CW (2003) Report Card on Humidity Control, ASHRAE Journal, May
2003.
Luther MB and Atkinson SE (2012) Measurement & Solutions to Thermal Comfort, CO
2
and
Ventilation Rates in Schools, Healthy Buildings 2012, 10
th
International Conference,
Brisbane Australia, 8–12 July 2012.
Mendell MJ, & Heath GA (2005) Do Indoor Pollutants and Thermal Conditions in Schools
Influence Student Performance? A Critical Review of the Literature, Indoor Air Journal,
15, 27-32.
Olesen, BW (2004) International Standards for the Indoor Environment, Indoor Air Journal,
14 (Suppl. 7): 18-26.
Plowman S and Smith D (2007) Exercise Physiology for Health, Fitness and Performance,
Lippincott, Williams & Wilkins.
Seppanen O, Fisk WJ and Mendell MJ (1999) Association of Ventilation Rates and CO
2
Concentrations with Health and other Responses in Commercial and Institutional
Buildings, Indoor Air Journal, 9, 226–252.
Wargocki P and Wyon D (2006) HVAC and Student Performance, ASHRAE Journal,
October 2006.
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Standard 62.1-2004 Ventilation for Acceptable Indoor Air Quality, American Society of Heating and Refrigeration and Air-conditioning Engineers
ASHRAE (2004) Standard 62.1-2004 Ventilation for Acceptable Indoor Air Quality, American Society of Heating and Refrigeration and Air-conditioning Engineers, Atlanta, Georgia, USA.
NISTIR 6729 Report: State-of-the-Art Review of CO 2 Demand Controlled Ventilation Technology and Application, National Institute of Standards and Technology, Technology Administration
  • S J Emmerich
  • A K Persily
Emmerich SJ and Persily AK (2001) NISTIR 6729 Report: State-of-the-Art Review of CO 2 Demand Controlled Ventilation Technology and Application, National Institute of Standards and Technology, Technology Administration, US Department of Commerce, 2001. EN 13779 (2007) European Standard: Ventilation for non-residential buildings -Performance requirements for ventilation and room-conditioning systems, European Committee for Standardisation, Brussels