JOURNAL OF APPLIED PHYSICS
VOLUME 93, NUMBER 2
15 JANUARY 2003
Predictive model for CO2 generation and decay in building envelopes
Heshmat A. Aglana)
Department of Mechanical Engineering, Tuskegee University, Tuskegee, Alabama 36088
共Received 6 September 2002; accepted 25 October 2002兲
Understanding carbon dioxide generation and decay patterns in buildings with high occupancy
levels is useful to identify their indoor air quality, air change rates, percent fresh air makeup,
occupancy pattern, and how a variable air volume system to off-set undesirable CO2 level can be
modulated. A mathematical model governing the generation and decay of CO2 in building envelopes
with forced ventilation due to high occupancy is developed. The model has been verified
experimentally in a newly constructed energy efficient healthy house. It was shown that the model
accurately predicts the CO2 concentration at any time during the generation and decay processes.
© 2003 American Institute of Physics. 关DOI: 10.1063/1.1529992兴
INTRODUCTION
ventilation system they used SF6 as the tracer gas.
This widespread affliction of school buildings has been
the subject of a number of investigations. To help school
administrators with evaluating the IAQ of their facilities, the
EPA has prepared a special information package, ‘‘IAQ Tools
for Schools.’’ 10 Wheeler and Abend11 studied the impact of
maintaining acceptable IAQ on the energy efficiency of the
heating, ventilation, and air conditioning 共HVAC兲 system.
They presented various design strategies for alternative
HVAC systems using the occupancy and operational data of
the Maryland public school system. CO2 sensors in the feedback loop of the ventilation system were used to evaluate the
IAQ. They have compared IAQ for ventilation rates of 10
cfm/person with ASHRAE 62-89 and consider it to be adequate. The ‘‘Exposure Guidelines for Residential Indoor Air
Quality’’ 12 consider CO2 levels as a useful indicator of the
general IAQ, but only where there are significant ‘‘metabolic’’ and ‘‘combustion’’ sources. Similarly, it cautions the
use of relative humidity as an indicator of IAQ, since in low
occupancy buildings the humidity levels may not reach levels high enough to trigger the ventilation systems and other
pollutant concentrations may, therefore, increase.
Thus, it is important to account for CO2 levels in residential and commercial buildings under high occupancy or
‘‘crush load.’’ This will aid the development of a best practice guidelines for the enhancement of IAQ in new and existing buildings. This article focuses on the development of a
constitutive model to predict the concentration of CO2 in
building envelopes at any time during high occupancy and
when the occupancy levels return to lower levels. A healthy
house designed and built at Tuskegee University was instrumented and used to experimentally verify the proposed
model. The CO2 generation from high occupancy and CO2
decay from the building were investigated using the proposed model.
Complex relationships exist between carbon dioxide
concentration and indoor air quality 共IAQ兲 in terms of occupant comfort. This includes the impact of elevated CO2 on
comfort, the association between CO2 level and other air
contaminants, and the relationship between CO2 and ventilation. Persily1 refers to various experiments,2–7 which concluded that 15 cfm 共7 L/s兲 of outdoor air per person can
make about 80% of unacclimatized visitors to the building
have no complaint about odor. The level of odor acceptability was similar when CO2 levels were about 1000 ppm. This
has prompted the American Society of Heating, Refrigeration and Air-Conditioning Engineers 共ASHRAE兲 62-89 recommendation of 15 cfm 共7 L/s兲 and a CO2 level of less than
1000 ppm in order to maintain acceptable IAQ. Persily1 has
also presented theoretical methods for evaluating ventilation
in a building using a ‘‘tracer-gas decay’’ technique with CO2
being the tracer gas.
Ventilation in schools and residential buildings, with frequent or occasional high occupancy levels, presents a problem. According to the Environmental Protection Agency
共EPA兲,8 about 22% of the U.S. population spend part of their
day in elementary and secondary schools. About 50% of
these schools have problems linked to poor IAQ. The generation of CO2 , especially from high occupancy, is one of
the major contributing factors. Other factors include low
ventilation rate, high relative humidity, high volatile organic
compound 共VOC兲 levels, dust particulates, etc. Downing and
Bayer9 have attributed the lower ventilation rates 共5 cfm/
person兲 in the earlier version 共1975兲 of the ASHRAE 62-89
standard as one of the major reasons for poor IAQ in schools.
Compliance with the current standard 共15 cfm/person兲, in
most cases requires increase in ventilation rate. This, of
course, means changes in the control of relative humidity to
within acceptable levels to minimize indoor air quality complaints due to mildew and mold. Downing and Bayer used
VOC as a quantitative measure of odor-causing bioeffluents
instead of CO2 , and to determine the air changes by the
MODEL DEVELOPMENT
A schematic representation of a building envelope with a
forced fresh air filtration system is shown in Fig. 1. The
relevant quantities describing the volume flow rates in and
a兲
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1287
© 2003 American Institute of Physics
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1288
J. Appl. Phys., Vol. 93, No. 2, 15 January 2003
Heshmat A. Aglan
K 0 ⫺K 1 C
⫽e ⫺K 1 共 t⫺t 0 兲 .
K 0 ⫺K 1 C 0
共8兲
Rearranging Eq. 共8兲 leads to
K 0 ⫺K 1 C⫽ 共 K 0 ⫺K 1 C 0 兲 e ⫺K 1 共 t⫺t 0 兲 ,
共9兲
K 1 C⫽K 0 ⫺ 共 K 0 ⫺K 1 C 0 兲 e ⫺K 1 共 t⫺t 0 兲 ,
共10兲
or
and
C⫽
FIG. 1. Mass balance representation for model development.
out, as well as CO2 concentrations, are as follows: q i , volumetric flow rate of fresh air through the filter; q 0 , volumetric
air flow rate leaked from the building; V, volume of air
inside the building; C, concentration of CO2 inside building
at time t; C 0 , concentration of CO2 inside the building at
time t 0 ; and S, generation rate of CO2 , mass per unit time
from high occupancy or other source.
The differential equation, which governs the generation
and decay of CO2 , based on mass balance considerations,
can be expressed as
⳵ 共 VC 兲
⫽q i C i ⫺q 0 C⫹S.
⳵t
共1兲
冋
册
K0 K0
⫺
⫺C 0 e ⫺K 1 共 t⫺t 0 兲 .
K1 K1
共11兲
Substituting Eq. 共4兲 into Eq. 共11兲 yields the final equation,
which describes the generation and decay of CO2 as a function of time:
C⫽
冉
冊 冉冉
S
qi
C⫹
⫺
q0 i q0
冊 冊
S
qi
C⫹
⫺C 0 e ⫺K 1 共 t⫺t 0 兲 .
q0 i q0
共12兲
When the leak from the building, q 0 , equals the fresh air
make up, q i , Eq. 共12兲 can be written as
冉
C⫽ C i ⫹
冊冉
冊
S
S
⫺ C i ⫹ ⫺C 0 e ⫺K 1 共 t⫺t 0 兲 .
q0
q0
共13兲
Equation 共13兲 will be examined later in view of experiments
conducted on CO2 generation from high occupancy and CO2
decay after the occupants leave the building.
For constant volume of air inside the building, Eq. 共1兲 can be
written as
dC
⫽ 共 q i C i ⫹S 兲 ⫺q 0 C,
dt
V
or
dC
⫽
dt
冋冉
q iC i S
⫹
V
V
For simplicity, let
K 0⫽
冋冉
q iC i S
⫹
V
V
冊册
⫺
冊册
共2兲
q0
C.
V
and
K 1⫽
共3兲
q0
.
V
共4兲
Substituting Eq. 共4兲 into Eq. 共3兲 gives
dC
⫽K 0 ⫺K 1 C.
dt
共5兲
The integration limits of Eq. 共5兲 are from C 0 to C and t 0 to
t, where C is the concentration of CO2 at time t and C 0 is the
concentration of CO2 at an initial time t 0 . Equation 共5兲 becomes
冕
dC
⫽
C 0 K 0 ⫺K 1 C
Thus,
⫺
or
C
冉
冕
t
dt.
共6兲
冊
共7兲
t0
K 0 ⫺K 1 C
1
ln
⫽ 共 t⫺t 0 兲 ,
K1
K 0 ⫺K 1 C 0
EXPERIMENTAL VERIFICATION
The CO2 level in the building envelope, the Healthy
House built on the Tuskegee University Campus, was measured at a height of 3 ft above the floor level using a Vaisala
GMW20 series CO2 sensor. This sensor has an accuracy better than ⫾1% full scale ⫹1.5% of the reading with a repeatability better than ⫾1% of full scale and temperature dependence of ⬍0.1% full scale/°C. An Agilent Technologies
model 34970 data acquisition system was used in conjunction with the sensor to capture the CO2 concentration every 5
min during the high occupancy test of 19 people in a class
room setup, and every hour then after. This unit has a storage
capacity of 50 000 scan with programmable scanning rates.
Data from the data acquisition system were periodically
downloaded via RS-232 cable to a PC for processing.
The CO2 registered a continuous increase during the
high occupancy period reaching a value of about 2420 ppm
(V) after 80 min from starting the test, as seen in Fig. 2. This
is well beyond the ASHRAE 62-89 limit, which allows only
1000 ppm, however, it is reported by the EPA 共Ref. 13兲 that
the lowest CO2 concentration at which humans and animals
are affected is 18 000 mg/m3 关10 000 ppm (V)]. The maximum concentration reached at the Tuskegee Healthy House
during the high occupancy test of 19 people did not cause
any discomfort due to the high rate of fresh air makeup supply to the house; three times the rate recommended by
ASHRAE. Persily1 stated that high CO2 levels above 1000
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J. Appl. Phys., Vol. 93, No. 2, 15 January 2003
Heshmat A. Aglan
FIG. 2. Experimental results for CO2 generation and decay for a crush load
of 19 people in the Healthy House built on the Tuskegee University Campus.
ppm (V) may contribute to odor perception of the unacclimatized visitor at the termination of the experiment. This
was not the case in the current experiment.
The reduction in CO2 after the termination of the test
provides useful information about the leakiness of the envelope and the air changes. Figure 2 shows that the CO2 level
returned to its initial value, of about 500 ppm (V) in about
240 min from the time the occupants left the house. This
defines the complete air change cycle of the building. Thus, a
building that takes a longer time for the CO2 or any trace gas
to decay is tighter than that which takes a shorter time. Tight
construction is more energy efficient as far as heating and air
conditioning is concerned. This on the other hand, negatively
affects the indoor air quality by providing slow decay of
gases like CO2 . Thus, a balance between energy efficiency
and IAQ has to be struck. An accurate account for generation
and decay of CO2 , in order to provide the adequate fresh air
makeup to maintain acceptable IAQ with optimum energy
consumption, should be a design practice. The developed
theoretical model, Eq. 共13兲, can provide the foundation for
such design practices, especially for high occupancy buildings. The results shown in Fig. 2 will be used to verify the
proposed model 关Eq. 共13兲兴 during generation and decay of
CO2 .
GENERATION PREDICTION
For CO2 generation, t 0 ⫽t i , which is the time when the
CO2 generation starts, and C 0 ⫽C i . Thus, Eq. 共13兲 becomes
C⫽C i ⫹
S
共 1⫺e ⫺K 1 共 t⫺t i 兲 兲 .
q0
共14兲
Rearranging Eq. 共14兲 gives
关 C⫺C i 兴 ⫽
冉 冊
S
关 1⫺e ⫺K 1 共 t⫺t i 兲 兴 .
q0
共15兲
Equation 共15兲 represents the generation of CO2 from high
occupancy; the rising portion of Fig. 2. If the experimental
data for generation are plotted in the form of Eq. 共15兲, the
relationship between the values in the square brackets in Eq.
1289
FIG. 3. CO2 generation data plotted in the form of Eq. 共15兲 to obtain the
slope (S/q 0 ).
共15兲 should give a straight line passing through the origin.
The slope of the straight line is (S/q 0 ). This is shown in Fig.
3, which is almost a perfect fit with the slope (S/q 0 )
⫽2537.8 ppm (V) or 4564 mg/m3. In the current experiments, the ventilation rate q 0 is 115 cfm or 0.054 m3 /s. On
this basis, the volumetric rate of CO2 generation per person,
based on CO2 density of 1970 mg/L and 19 people, should
equal 0.006 58 L/s. It is important to compare this number
obtained from the current model with the well-established
value for CO2 generation per person as described by
ASHRAE.14 This was defined based on temperature and energy factors for heat exchange between people and the
environment.15,16
The volumetric rate of CO2 generation depends on many
factors such as the volumetric rate of oxygen consumption;
Dubois body surface area;17 the metabolic heat produced by
the body, M, which is measured by the rate of oxygen consumption; and the respiration quotient, RQ, which is the ratio
of CO2 exhaled to O2 inhaled. Based on ASHRAE,18 the
volumetric rate of CO2 generation per person can be written
as
V CO2 ⫽
0.0028 A D M 共 RQ兲
.
共 0.23 RQ⫹0.77兲
共16兲
For an average size man A D ⫽1.8 m2 . 17 Metabolic rate M
depends strongly on the various types of activities19,20 and
can range between 1 and 2 for the occupants of an office
building.1 The value of RQ depends on diet, physical activity, and the physical condition of the person. For an adult of
average size engaged in light sedentary activity RQ is about
0.83.1 Using A D ⫽1.8 m2 , M ⫽1.5, and RQ⫽0.83 in Eq. 共16兲
results in V CO2 of 0.006 53 L/s. This value of CO2 generation
is almost the same as that obtained from Eq. 共15兲. This,
again, attests to the extreme accuracy of the proposed model.
In the current experiment, the value of K 1 ⫽18.72
⫻10⫺3 min⫺1 , and the initial time t 0 ⫽t i ⫽45 min, and
S/q 0 ⫽2537.8 ppm (V). Substituting these values in Eq.
共14兲, the theoretical CO2 generation can theoretically be established as a function of time. Equation 共14兲, together with
the experimental data for the period of generation, are plot-
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1290
J. Appl. Phys., Vol. 93, No. 2, 15 January 2003
Heshmat A. Aglan
various buildings for air tightness evaluation. A longer
decay time is associated with a tighter building.
• In conjunction with continuous monitoring of carbon
dioxide concentration, the model can provide the logic
for the modulation of outdoor air ventilation through
variable air volume systems.
• For a given maximum allowable carbon dioxide level,
the ventilation rate in the form of air changes per unit
time can be determined.
FIG. 4. Plot of Eq. 共18兲 together with the experimental data for CO2 generation and decay.
ted in Fig. 4. It is seen from the rising portion of the curve in
Fig. 4 that the fit is excellent and the model has a very strong
predictive power.
ACKNOWLEDGMENTS
This work was sponsored by the Department of Energy
through Oak Ridge National Laboratory. Robert Wendt,
project manager, Building Technology Center, ORNL, is acknowledged for his support and feedback.
DECAY PREDICTION
For CO2 decay, S⫽0, t 0 ⫽t g , and C 0 ⫽C g , where t g is
the time at which CO2 generation ended and C g is the concentration of CO2 at time t g . Thus, Eq. 共13兲 becomes
C⫽ 共 C i ⫹0 兲 ⫺ 共 C i ⫺C g 兲 e
⫺K 1 共 t⫺t g 兲
,
C⫽C i 关 1⫺e ⫺K 1 共 t⫺t g 兲 兴 ⫹C g e ⫺K 1 共 t⫺t g 兲 .
共17兲
共18兲
Equation 共18兲 describes the decay of CO2 with time as a
function of initial concentration C i , the air change per unit
time K 1 , and the concentration of CO2 in the building at
time t g , the end of generation.
The values of K 1 , C i , C g , and t g are known from the
current experiment, and by substituting them in Eq. 共18兲 the
relationship between CO2 concentration and time can be determined. A plot of Eq. 共18兲, together with the experimental
data for CO2 decay, are shown in Fig. 4. The solid line represents Eq. 共18兲 while the points are the experimental data. It
is apparent from Fig. 4 that the model accurately fits the
experimental data for both CO2 generation and decay.
CONCLUSIONS
A constitutive model has been developed to predict the
generation of CO2 in building envelopes resulting from high
occupancy. The model was experimentally verified in view
of experiments conducted on an affordable, energy efficient,
and healthy house. It was found that the model accurately
predicts the generation of CO2 from occupancy and the decay of CO2 after the generation ceased. The predicted volumetric flow rate of CO2 generated from occupancy compares
very well with those published in the literature. The practical
applications of the model are as follows:
• For a given initial CO2 concentration and generation
rate per person, the concentration of CO2 can be predicted at any time including the peak concentration.
• The time at which the level of CO2 reaches its initial
value after occupants leave the building can be determined. This can serve as a ranking parameter between
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