# Determining Infiltration Rates and Predicting Building Occupancy Using CO2 Concentration Curves

Authors: P. Parsons
Journal: Journal of Energy
 (2014)

---

## Abstract

Demand controlled ventilation (DCV) reduces energy loss by reducing the air exchange flow rate to the minimum required to maintain acceptable indoor air quality (IAQ). DCV commonly uses carbon dioxide (CO2) as a proxy for human activity and increases the ventilation rate once a preset CO2 threshold is exceeded. Significant improvements over threshold based ODV strategies are possible if the natural infiltration rate of the building is measured and the occupancy schedule determined by analysing the CO2 concentration continuously. These calculated parameters allow mathematical modeling of the ventilated space and the determination of future CO2 concentrations and allow prediction of future ventilation demands. The natural infiltration rate and the onset and duration of vacancy periods in a residential dwelling were determined by analysing CO2 concentration data. Concentration declines which fit an exponential decay curve with a correlation coefficient >0.90 identified all vacancy periods. The measured natural infiltration rate was found statistically correlated with average wind speed. A dynamic predicted occupancy map was constructed that has the potential to facilitate significant energy savings via deferred ventilation and intelligent cooling and heating strategies.


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## Body

## 1. Introduction

The energy required for heating, ventilation, and air conditioning (HVAC) of buildings can be reduced by minimizing uncontrolled air infiltration through leaks in the building envelop. The natural air infiltration rate of older North American residential structures is large enough that IAQ is seldom a problem. However, the continuous air and vapour barrier installed in new construction has necessitated the introduction of mechanical ventilation systems to remove excess moisture and maintain acceptable IAQ. This mechanical ventilation is often provided by a heat or energy recovery ventilator (HRV, ERV) which is sized based on the number and types of rooms and provides a fixed quantity of air exchanges per hour (ACH). This static approach results in excessive ventilation and energy waste during periods of low occupancy.DCV systems reduce these losses by varying the ventilation rate as needed to maintain a minimum acceptable IAQ. These systems typically use CO2 as a proxy for IAQ and trigger additional ventilation once a threshold is exceeded. Unfortunately, using a gas sensor as a demand switch wastes the opportunity to derive additional information from the continuous analysis of CO2 concentration, including the natural infiltration of the space being ventilated and its patterns of occupancy. In order to enable intelligent DCV strategies that can reduce energy waste by supplying heating and cooling only when necessary and eliminate overventilation, the characteristics of the building and its usage patterns are required. The natural infiltration rate is required to determine the current CO2 generation rate and to predict future CO2 concentrations. Decisions to defer ventilation or plan a heating and cooling schedule require a knowledge of upcoming occupancy patterns. While the occupancy schedule could be entered manually by occupants similar to programming a thermostat, the infiltration rate would require a gas diffusion study. The ideal control system would learn by analysing real-time CO2 concentration data and require minimal user setup. Currently available control systems for residential use do none of this, using simple on and off controls and a humidistat. Unfortunately, humidity is a poor proxy for human generated pollutants because it varies slowly as weather patterns change and with the seasons except for short periodic spikes driven by bathroom showers. Furthermore, natural infiltration rates are seldom known and the standard blower door tests provide leakage data at 50 Pa which far exceeds normal conditions.To confirm the assumption that an HVAC control system can learn building occupancy and calculate the natural infiltration rate from an analysis of CO2 concentration data, the author equipped a residential dwelling with a modified ventilation system and instrumentation for the continuous recording of CO2. The data was used to generate a weekly occupancy map and the natural infiltration rate was calculated every time the dwelling became vacant.This paper presents the results of analysing the CO2 concentration curves, the generated vacancy map, and the correlation between natural infiltration and wind speeds and its implication for improved HVAC control systems.


## 2.  Background

Occupant comfort is affected by temperature, humidity, odours, and CO2. The permissible exposure limit for CO2 is 5000 ppm [1] which far exceeds levels that will be encountered in a home. Yawning is not caused by CO2 even at concentrations of 30,000 ppm [2, p.384]; however, 20% of visitors are dissatisfied with body odours at CO2 concentrations of 1880 ppm [3]. CO2 generation is a function of the quantity and size of the occupants and their activity levels. CO2 also correlates proportionally with pollutants such as body odour and in a more general manner with cooking, cleaning, or smoking that produce volatile organic compounds (VOC), moisture, and particles. This makes CO2 a useful proxy for IAQ and for controlling ventilation systems.Since CO2 is nonreactive in the indoor environment and the dwelling volume is a constant, the total mass of CO2 and therefore its concentration can change only if more is added by human activity or if it is diluted via air exchange from outside. The portion of CO2 concentration change over time within the dwelling due to human activity is the CO2 generation rate divided by the total volume of the ventilated area. Assuming that the indoor air is well mixed and therefore the concentration throughout the building is a constant at any instant, the rate of concentration change due to outgoing exhaust air is the mechanical ventilation rate times the indoor concentration divided by the room volume. Similarly since the outdoor concentration is approximately a constant, the change due to incoming fresh air is the mechanical ventilation rate times the outdoor CO2 concentration divided by the room volume. This is expressed as a differential equation:
(1)
d
C
(
t
)
d
t
=
R
V
(
C
a
-
C
(
t
)
)
+
G
V
,
where C
(
t
) is indoor concentration of CO2 at time t (mass/volume), R is mechanical ventilation rate (volume/time), V is dwelling volume, C
a is ambient atmospheric CO2 concentration (mass/volume), and G is CO2 generation rate by occupants (mass/time).Separating the variables and integratingd
t from zero to t and d
C
(
t
) from C
(
0
) to C
(
t
) we obtain:
(2)
C
(
t
)
=
C
a
+
G
R
+
(
C
(
0
)
-
C
a
-
G
R
)
e
-
(
R
/
V
)
t
,
where C
(
t
) is indoor concentration of CO2 at time t (mass/volume) and C
(
0
) is initial indoor CO2 concentration (mass/volume).When all occupants vacate a dwelling, the remaining CO2 can be used as a tracer gas to measure the natural infiltration rate. When the house is vacant, G is zero and the CO2 concentration is a decaying exponential asymptotic to C
a. The beginning of the exponential decay marks the onset of vacancy and the natural infiltration rate of the dwelling is its volume divided by the time constant of the decaying exponential.The CO2 generation rate of twenty adults between 21 and 28 years of age, standing and sitting at a desk, was found to average 0.24 L/min and 0.18 L/min, respectively [4]. Assuming that household activities such as standing at a kitchen counter or watching television require similar effort, the CO2 generation rate for three adults, (3), would be 79.1 g/hr. Substituting this into (2) with large t and a natural infiltration rate of 80 m3/hr yields (4). Therefore, the maximum CO2 concentration in a well-mixed home with leakage of 80 m3/hr and three low activity adults would be 1175 ppm:
(3)
G
(
t
)
=
3
×
0.24
×
60
×
41.01
22.4
=
79.1
g
/
hr
,
(4)
C
(
∞
)
=
400
+
79.1
80
×
1.2754
×
1000
=
1175
ppm
.


## 3.  Methodology

Testing was performed on an occupied two-story, 650 m3, wood-framed home, Figure 1, built to Canadian residential standards in 2003. The air change rate with 50 Pa de-pressurization, η
50, was 2.55 air changes per hour (ACH). The maximum flow rate of the HRV was 385 m3/hr with fresh air ducts into bedrooms and living areas and return ducts in bathrooms and kitchen. The kitchen and bathrooms were equipped with dedicated exhaust fans and operable windows.Figure 1
Canadian home built in 2003.The HRV unit was modified for computer control of recirculation and fan speed. A Figaro K30 nondispersive infrared (NDIR) CO2 sensor was installed in a central sampling device for differential measurements between the indoor and outdoor air streams. Figure 2 shows the HRV unit with the access door open. The translucent box to the left of the HRV is the air source selector which also contains the NDIR sensor.Figure 2
HRV and air sampler.The CO2 concentration was measured at the return duct every 180 seconds while the HRV recirculated air at 153 m3/hr. Every 2.5 hours recirculation was disabled and fresh air was pumped into the building at 385 m3/hr. Once the fresh air readings stabilized the CO2 concentration was recorded and the system reverted to recirculation at 153 m3/hr. All measurements were logged into a database.A moving window of 200 CO2 concentration values, corresponding to 8.3 hours, was curve-fit to a theoretical decay by subtracting the background CO2 concentration from each datum and then taking its natural logarithm. The linearised data were then fit to a straight line using the least squares method. The window was advanced one data point at a time until the correlation coefficient R
2, calculated as per (5), peaked at a value ≥0.90 marking the beginning of a vacancy period. The window was further advanced sequentially until R
2 dropped below 0.50, marking the end of the vacancy period. Each exponential decay meeting the criteria R
2
>
0.90 was then mapped into one-hour time slots to produce an occupancy map. The map was then compared with personal notes from the occupants for verification:
(5)
slope
=
∑
‍
x
y
-
∑
‍
x
∑
‍
y
∑
‍
x
2
-
∑
‍
x
∑
‍
x
,
intercept
=
∑
‍
y
n
-
s
∑
‍
x
n
,
correlation
=
1
-
∑
‍
(
y
-
i
-
x
s
)
2
∑
‍
(
y
-
∑
‍
y
/
n
)
2
,
where x is seconds elapsed from start of window, y is natural log of CO2 concentration, and n is number of measurements in window period.A Davis Vantage Pro 2 weather station positioned 4 m above ground level and 5 m from the home was used to record local meteorological data.


## 4.  Results

Sequences of exponential CO2 decline were identified and the curves they were fit to, shown as red segments in Figure 3, were superimposed on a graph of actual indoor and outdoor CO2 concentrations. These overlays were generated using the equation calculated when the correlation coefficient was maximal and used to visually verify the fit.Figure 3
Estimated vacancy periods overlaid on actual data.Table1 lists the start and end of potential vacancy periods, correlation with a pure exponential decay, decay time constant, lowest CO2, and whether the identification of vacancy was correct.Table 1
Vacancy periods identified via CO2 analysis.
FitR
2
TC (h)
Start (m-d hh:mm)
End (m-d hh:mm)
Low CO2 (ppm)
Wind (kmh)
0.9811
6.0
Jan-21 07:24
Jan-21 16:43
466
15.2
0.9178
15.3
Jan-23 05:10
Jan-23 14:41
495
9.7
0.9460
7.6
Jan-24 05:46
Jan-24 13:16
479
9.0
0.9817
12.2
Jan-26 22:55
Jan-27 06:33
676
4.1
0.9614
7.8
Jan-28 04:34
Jan-28 13:52
493
9.7
0.9330
7.9
Jan-29 04:27
Jan-29 13:40
497
8.7
0.9593
9.9
Jan-30 05:00
Jan-30 14:23
531
3.0
0.9291
6.3
Jan-31 02:40
Jan-31 12:26
489
18.7
0.9586
7.0
Feb-01 06:04
Feb-01 15:29
502
15.6
0.9800
7.4
Feb-03 21:13
Feb-04 06:26
483
16.1
0.9804
7.1
Feb-05 04:58
Feb-05 13:59
470
15.9
0.9560
17.9
Feb-06 06:47
Feb-06 16:25
517
4.7
0.9473
13.6
Feb-07 05:23
Feb-07 14:27
527
3.1
0.9451
9.0
Feb-07 19:38
Feb-08 04:48
475
19.1
0.9617
3.4
Feb-11 04:21
Feb-11 13:54
432
8.5
0.9625
9.8
Feb-12 06:06
Feb-12 15:14
488
5.7
0.9341
8.6
Feb-14 05:06
Feb-14 13:43
470
12.4
0.9373
11.6
Feb-15 04:34
Feb-15 14:44
474
9.2
0.9460
06.7
Feb-18 05:48
Feb-18 15:10
452
11.6
0.9482
15.8
Feb-21 02:50
Feb-21 12:15
522
10.4
0.9631
13.2
Feb-22 04:39
Feb-22 14:29
498
4.5
0.9714
12.5
Feb-25 06:42
Feb-25 15:53
498
3.5
0.9532
09.6
Feb-26 04:42
Feb-26 13:49
471
5.5
0.9486
16.6
Mar-05 02:46
Mar-05 12:35
475
18.6
0.9795
12.7
Mar-06 07:21
Mar-06 16:24
456
5.9
0.9791
11.4
Mar-07 05:51
Mar-07 15:02
468
4.0
0.9336
31.5
Mar-09 22:52
Mar-10 09:25
568
10.1The vacancy map in Table2 shows a weekly calendar with 24 hourly time slots. Each period shows the CO2 concentration at the end of the period. Cells with multiple values represent multiple vacancies during the same time slot, over the five-week observation period.Table 2
Vacancy map forR
2
≥
0.93.
Hour
Sun.
Mon.
Tue.
Wed.
Thu.
Fri.
Sat.
1
13
0
0
0
14
0
29
2
13
0
0
0
14
0
29
3
13
0
13
0
29
0
29
4
13
0
13
0
29
0
29
5
13
25
50
0
29
29
29
6
13
38
50
13
71
29
29
7
13
50
63
25
71
43
29
8
0
63
63
38
71
43
14
9
0
63
63
38
71
43
14
10
0
63
63
38
71
43
14
11
0
63
63
38
71
43
0
12
0
63
63
38
71
43
0
13
0
63
63
38
71
43
0
14
0
63
50
38
57
43
0
15
0
38
13
38
29
43
0
16
0
38
13
25
14
14
0
17
0
13
0
25
0
0
0
18
0
0
0
0
0
0
0
19
0
0
0
0
0
0
0
20
0
0
0
0
14
0
0
21
0
0
0
0
14
0
0
22
13
0
0
0
14
0
0
23
13
0
0
0
14
0
29
24
13
0
0
0
14
0
29
The bold values indicated the periods of vacancy.


## 5.  Discussion

Setting the threshold for correlation toR
2
≥
0.90 identified all true vacancies and included three false positives.Using decays whereR
2
≥
0.95, the 95% confidence interval for the mean of the decay constant during vacancies is (8.5, 11.5) hours with a standard deviation of 2.3 and mean of 10 hours.Low wind speeds of 4 kmh yielded an infiltration rate of 650 m3/12.2 = 53 m3/hr. The mean time constant of 10 hours represents an infiltration rate of 650 m3/10 = 65 m3/hr.The infiltration rate was too low to return the indoor CO2 concentration to background levels for short vacancy periods so some vacancies would have been missed had the identification been based on absolute levels.Table3 shows a variation in infiltration rate with wind speed. The correlation between decay constants and average wind speed during the measurement period was significant with a Pearson correlation coefficient of −0.833 and a P value of 0.001. Figure 4 shows a negative correlation between the time constants and average wind speed which is expected. Wind direction is also a factor in asymmetrical houses as is turbulence [5–7]. The low end of the infiltration rate range can be used to conservatively predict CO2 and the end of a vacancy period, although if a wind sensor was installed the correlation could provide a better guess.Table 3
Wind speed versus time constant.
Wind (kmh)
TC (h)
R
2
Infiltration (m3/h)
4.1
12.2
0.982
53
9.7
7.8
0.961
84
3.0
9.9
0.959
66
15.6
7.0
0.957
92
15.8
7.5
0.979
87
15.9
7.1
0.979
91
5.7
9.8
0.963
66
4.5
13.2
0.963
49
3.5
12.5
0.971
52
5.3
9.6
0.953
68
5.9
12.7
0.979
51
4.0
11.4
0.979
57Figure 4
Correlation between wind speed and natural infiltration rate.The maximum mechanical ventilation rate of the HRV was 384 m3/hr; therefore, natural infiltration was approximately 17% of what the HRV was capable of providing. This natural leakage rate prevented interior CO2 levels from exceeding 710 ppm during the observation period with one exception during a gathering of many people where it reached 880 ppm. Three adults engaged in light activity would have been expected to ultimately produce CO2 concentrations levels of approximately 650 ppm.Periodic variation in outside CO2 concentrations, Figure 3 lower green line, was correlated with changes in indoor concentrations. The intake and exhaust vents from the HRV were installed as per building code but this resulted in mixing of the air streams that varied with atmospheric conditions. To improve the accuracy of outdoor readings, an extension duct was added to the exhaust vent which greatly reduced mixing. Random mixing made differential measurements inaccurate and resulted in missing most vacancy periods because of lower R
2 values. Since the NDIR sensor drift was negligible, the analysis was based solely on absolute indoor concentrations.During the observation period, CO2 concentrations never exceeded 710 ppm with three occupants indicating that the greatest saving from DCV would come from disabling fresh air intake most of the time.A control system which has learned the occupancy map and average infiltration rate over a period of a few weeks could be implemented as follows.If the CO2 rises above a threshold then look ahead to the next hourly time slot. If the probability of vacancy exceeds 50%, calculate the CO2 concentration at the end of the projected vacancy using the average infiltration rate. If this is less than the threshold, then do not introduce fresh air.Scenario 1.
The CO2 concentration is 800 ppm above outdoor levels at 7:30 a.m. Monday morning, and the threshold for ventilation is 600 ppm above background levels. Should mechanical ventilation be used to bring this down by 200 ppm?
The Monday 8 a.m. to 1 p.m. time slot was vacant the last five weeks without exception; the probability of vacancy is estimated at 100%. Anticipating 5 hours of vacancy and time constant of 2.6 hours, CO2 should decayed to 800
*
e
-
(
5
/
2.6
)
=
117ppm above outdoor levels. This is negligible and well below the 600 ppm threshold. Therefore, fresh air ventilation at 7:30 is not necessary and will not be required until some time after 1 p.m.Scenario 2.
Assume there will be a 1 hour vacancy, and that the probability is 75% that it will occur between 8 a.m to 9 a.m, otherwise conditions are identical to Scenario1.Since there is a greater than 50% chance of upcoming vacancy the system expects CO2 should decay to 800
*
e
-
(
1
/
2.6
)
=
544 ppm above outdoor levels. This is just below the threshold, so ventilation can be deferred.Had this been a newer home with a tighter building envelop and a time constant of 12 hours, the system would expect CO2 to decay to 800
*
e
-
(
1
/
12
)
=
736 ppm above outdoor levels. In this case, fresh air would be provided until CO2 levels returned to a concentration that could be reduced to 600 ppm by natural infiltration during the remainder of the vacancy period. Alternatively, the fan could be run at a lower speed sufficient to augment natural infiltration such that 600 ppm was reached just as occupants were expected to return.The major energy savings for such a control strategy would come from the following:(1)
automatically setting occupied and unoccupied temperatures based on the vacancy probability map;
(2)
disabling fresh air ventilation when not needed, which in this case, for a threshold of 1000 ppm, would have been all the time;
(3)
disabling fresh air ventilation before vacancy periods, which for a 9–5 work schedule might eliminate an hour of fresh air each work day depending on the initial concentrations.


## 6.  Conclusion

Periods of vacancy in residential homes were successfully detected using occupant generated CO2 as a tracer gas and following the decay in concentration. An accurate occupancy map was generated, indicating the probability and duration of future vacancies. The upper and lower limits of natural infiltration were determined from the time constant of the decay and statistically correlated with wind speed as expected.The control system for a residential DCV system could be enhanced to use these parameters to optimize energy losses by minimizing excess ventilation while maintaining IAQ. The vacancy map could also be used to automatically program heating and cool systems.



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*Source: 670236-2014-02-06.xml*