ME425/525: Advanced Topics in Building Science
Indoor environmental quality for sustainable buildings: Lecture 5
Dr. Elliott T. Gall, Ph.D.
Lecture 5
• Today’s objectiveso Dynamic mass balance
─ Follow-up from SS solution (ventilation, emission)
o Application of MB to tracer decay─ Solve for λ and E knowing C(t)
o Parameterizations for three sources + sinks─ Air-cleaning
─ Chemical reactionsi. Heterogeneous
ii. Homogeneous
• Questions?
Building air exchange rate
• Determination of Lambda
• We solved for C(t) under scenario of o Infiltration (Q×Co)
o Exfiltration (Q×C)
o Emission (E)
Q Q
CoC
E
𝐶𝑡 = 𝐶𝑡=0𝑒−𝜆𝑡 + 𝐶𝑜 +
𝐸
𝜆𝑉1 − 𝑒−𝜆𝑡
What’s initially present and decaying
What’s entering due to outdoor air, emissions
Determination of λ
• We’ve seen the importance of λo High AER, outdoor air more important
o Low AER, indoor processes more important
• How do we determine λ?
Q/V Q/V
CoC
E
Tracer decay procedure
1. Monitor C (tracer conc.) at regular intervalo Measurement rate should be much higher than rate
of process you’re measuring
2. Inject non-reactive tracer into well-mixed spaceo May operate mixing fans to ensure
3. Allow tracer to mix over some time periodo usually several hours
4. Stop injection
5. Measure decay from some well-mixed value at some initial time that you declare.
Tracer decay procedure
• Data should look something like this
𝐶𝑡 = 𝐶𝑡=0𝑒−𝜆𝑡 + 𝐶𝑜 +
𝐸
𝜆𝑉1 − 𝑒−𝜆𝑡
This equation can apply to both “gas injection” and “measurement period”, by changing the value of which term?
Tracer decay solution
• For decay period, E = 0
𝐶𝑡 = 𝐶𝑡=0𝑒−𝜆𝑡 + 𝐶𝑜 +
𝐸
𝜆𝑉1 − 𝑒−𝜆𝑡
𝐶𝑡 = 𝐶𝑡=0𝑒−𝜆𝑡 + 𝐶𝑜 1 − 𝑒−𝜆𝑡
𝐶𝑡 = 𝐶𝑡=0𝑒−𝜆𝑡 − 𝐶𝑜𝑒
−𝜆𝑡 + 𝐶𝑜
𝐶𝑡 − 𝐶𝑜 = 𝐶𝑡=0 − 𝐶𝑜 𝑒−𝜆𝑡
𝐶𝑡 − 𝐶𝑜𝐶𝑡=0 − 𝐶𝑜
= 𝑒−𝜆𝑡
Multiply:
Re-arrange:
Re-arrange:
Isolate λt: −𝑙𝑛𝐶𝑡−𝐶𝑜
𝐶𝑡=0−𝐶𝑜= 𝜆𝑡
Tracer decay solution
• Solution takes the familiar form y = mx
−𝑙𝑛𝐶𝑡−𝐶𝑜
𝐶𝑡=0−𝐶𝑜= 𝜆𝑡
• A practical example: o CO2 is often used for tracer decay tests
─ Pros:i. It’s cheapii. It’s relatively harmlessiii. Occupants emit CO2, can get some idea of AER form this
─ Cons: i. Occupants emit CO2, may affect your experimentii. Outdoor levels, adjacent spaces may be time-variantiii. Heavier than air, perfect mixing may be a challenge
• Other tracers are typically perfluorocarbons (e.g., SF6)oPro: Negligible outdoor and indoor sources/concentrationsoCon: Expensive, heavier than air, strong climate warming gases
Tracer decay test
• Real data from my apartment in Singapore:
How can we use this data to extract the best-fit air exchange rate?
Casa Clementi, built in 2011 in Singapore
Tracer decay in bedroom
Time Cin Cout ln[(Ct-Co)/(Ct=0-Co)]
11/13/2014 7:35 0 3157 400.00 0.00
11/13/2014 7:40 0.083333 3064 400 0.03
11/13/2014 7:45 0.166667 2972 400 0.07
11/13/2014 7:50 0.25 2927 400 0.09
11/13/2014 7:55 0.333333 2893 400 0.10
11/13/2014 8:00 0.416667 2871 400 0.11
11/13/2014 8:05 0.5 2837 400 0.12
11/13/2014 8:10 0.583333 2771 400 0.15
11/13/2014 8:15 0.666667 2737 400 0.17
11/13/2014 8:20 0.75 2667 400 0.20
11/13/2014 8:25 0.833333 2604 400 0.22
11/13/2014 8:30 0.916667 2536 400 0.26
11/13/2014 8:35 1 2489 400 0.28
11/13/2014 8:40 1.083333 2419 400 0.31
(h) (ppb) (ppb)
Tracer decay solution
• Regress the ln transform against time
• The slope is the best-fit air exchange rateo Linear regression
y = 0.2738xR² = 0.9815
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0 0.2 0.4 0.6 0.8 1 1.2
-ln
(C
-Co
)/(C
t=0-C
o)
Time after injection (h)
• What is the air-exchange rate of this building?
• How does it compare to the typical value of a U.S. residence?
• What is the average “age” of a parcel of air in this indoor space?
Characterization of sources
• Knowing the AER, what else can we determine?
𝐶𝑡 = 𝐶𝑡=0𝑒−𝜆𝑡 + 𝐶𝑜 +
𝐸
𝜆𝑉1 − 𝑒−𝜆𝑡
If we know λ, then we can apply to
injection period to determine E!
A second example
• Building science is often conducted in researchers own homeso for a variety of reasons
─ Institutional review board
─ Cost
─ Access
• Does home-brewing affect CO2 decay test?
Emission and decay
400
450
500
550
600
650
700
750
800
850
900
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0
CO
2 le
vel (
pp
m)
Time (h)
CO2 levels in room with emitting source (1 gallon batch of beer)
Source present
Source removed (human activity caused increase)
Decay test
Determine AER
• Analyze decay period first:
y = 0.2076xR² = 0.9843
0.00
0.10
0.20
0.30
0.40
0.50
0.60
0.70
0.80
0 0.5 1 1.5 2 2.5 3 3.5 4
-ln
(C
-Co
)/(C
t=0
-Co
)
Time after injection (h)
λ = 0.2076 h-1; close to previous example (same room)
Apply to emission period
• Use lambda from decay to analyze for period when E is non-zero:
300
400
500
600
700
800
900
1000
0.0 0.2 0.4 0.6 0.8 1.0 1.2
CO
2 le
vel (
pp
m)
Time (h)
CO2 levels in room with emitting source
CO2, measured (ppm)
CO2 predicted, E = 0 ppm m3/h
CO2 predicted, E = 2000 ppm m3/h
CO2 predicted, E =4000 ppm m3/h
CO2 predicted, E = 8000 ppm m3/h
𝐶𝑡 = 𝐶𝑡=0𝑒−𝜆𝑡 + 𝐶𝑜 +
𝐸
𝜆𝑉1 − 𝑒−𝜆𝑡 Solution to this equation, with E
varied as shown in Figure
Curve-fitting
• What is the best fit value of E across all possibilities?λ 0.2076 h-1
V 24 m3
E 4000 ppm×m3/h
Time Time (h)CO2, measured
(ppm)
CO2, predicted
(ppm)
11/10/2014 7:59 0.0000 594 594
11/10/2014 8:00 0.0167 594 596
11/10/2014 8:01 0.0333 595 598
11/10/2014 8:02 0.0500 600 600
11/10/2014 8:03 0.0667 601 602
11/10/2014 8:04 0.0833 607 604
11/10/2014 8:05 0.1000 607 607
11/10/2014 8:06 0.1167 607 609
11/10/2014 8:07 0.1333 613 611
11/10/2014 8:08 0.1500 613 613
11/10/2014 8:09 0.1667 612 615
11/10/2014 8:10 0.1833 615 617
11/10/2014 8:11 0.2000 617 619
11/10/2014 8:12 0.2167 619 621
11/10/2014 8:13 0.2333 623 623
11/10/2014 8:14 0.2500 623 625
Emitting source, transient mass-balance
Can set up in a spreadsheet, matlab, R, etc.• Compare measured value to
predicted value• Find value of E that minimizes
sum of squared errors
Error = [CO2,meas-CO2,pred]2
SSE = Sum of square errors (across all time steps for which you are comparing meas. and pred. values)
Curve-fitting
• What is the best fit value of E across all possibilities?
0
100000
200000
300000
400000
500000
600000
700000
0 2500 5000 7500 10000
Sum
of
squ
are
erro
r (p
pm
2)
Emission rate (ppm m3/h)
Minimum occurs around 4000• Precise value can be determined a
variety of ways1) Excel solver2) Matlab function fminbnd3) Calculus
Our more precise answer is 4064 ppm m3/h
Interpret results
• What do the units ppm m3/h mean?• Let’s convert to g/h to give this answer context• E, if C is in units of ppm, must have units as follows:
4000𝑝𝑝𝑚 𝑚3𝑎𝑖𝑟
ℎ= 4000
𝑚3 𝐶𝑂2106𝑚3𝑎𝑖𝑟
𝑚3 𝑎𝑖𝑟
ℎ= 0.004
𝑚3 𝐶𝑂2ℎ
• We want units of mass/time to compare, since we know a human emits about 35 g/h:
0.004𝑚3 𝐶𝑂2
ℎ
1 𝑎𝑡𝑚
0.0821𝐿 𝑎𝑡𝑚𝑚𝑜𝑙 𝐾
298 𝐾1000
𝐿
𝑚3
= 0.166𝑚𝑜𝑙
ℎ44
𝑔
𝑚𝑜𝑙
= 7.3𝑔 𝐶𝑂2
ℎ
About 20% that of a human, and definitely sufficient to affect AER measurements in an airtight home!
A little more interpretation…
Let’s analyze on a molar basis what was happening:
• CO2 and ethyl alcohol are in a 1:1 molar ratio• For every mole of CO2 produced, 1 mole of ethyl alcohol is
produced• Primary fermentation typically occurs for from between 3-5 days,
where about 70% of the ethyl alcohol is formed hours or so
Is our CO2 emission rate reasonable?
Cheers
0.166𝑚𝑜𝑙𝐶𝑂2
ℎ∗1 𝑚𝑜𝑙𝐶2𝐻6𝑂
1 𝑚𝑜𝑙 𝐶𝑂2∗46 𝑔𝐶2𝐻6𝑂
𝑚𝑜𝑙 𝐶2𝐻6𝑂∗
1
0.789
𝑚𝐿
𝑔
=9.7 mL C2H6O per hour!
In the gallon batch that was being made, a 5% ABV would yield 189 mL of C2H6O.
That implies that at this rate, 5% ABV would be achieved in 20 h!
This experiment was intentionally conducted when the carboy was bubbling vigorously, likely near peak C2H6O production by yeast in the carboy.
Molar relationships allow us to make relationships amongst reactants, products
Take the molar generation rate of CO2 from our calculation,convert to a volume generation rate.
So while CO2 is gas-phase, and C2H6O is in liquid phase, we can relate the two by understanding relationships on a molar basis.
Modeling air cleaners
To the board
Indoor air cleaners
A good deal of confusion and misinformation about IAQ…
http://www.consumerreports.org/cro/air-purifiers/buying-guide
• Likely a result of trying to keep things simpleo “Cleaning speed”? Not quite…o “350 is excellent and 100 is poor”… but what do those numbers mean?
─ Depends on the space…o What are the units? (typically CFM, ft3/h)o CADR reports are tested in accordance with ANSI/AHAM AC-1
─ Typically reported for particles, three sizes“Smoke” (0.09-1 μm), “Dust” (0.5-3 μm), “Pollen” (5-11 μm)
o Applicable to other indoor air pollutants
Evaluating air cleaners
An example providing better than usual information:
Notice any issues between the reported air flows and CADR…?
Modeling air cleaners
Q Q
CoC
E
http://www.deq.state.or.us/lab/aqm/rt/rtHourlyConc.aspx
Qc
Qc
Outdoor air quality data for Portland can be obtained from:
Levels from 15-April: Quite low! Annual mean from EPA NAAQS is 12 ug/m^3. Levels in highly polluted cities (Beijing, DElhi, routinely exceed several hundred ug/m^3)
𝐶 =𝐶𝑜 +
𝐸𝜆𝑉
1 +𝐶𝐴𝐷𝑅𝜆𝑉
The equation we derived on the board:
Modeling air cleaners
Cooking is a strong source of indoor aerosol:
Most of the “mass” of PM2.5 reported here will be in the 0.5-2.5 range, so let’s use that
https://indoor.lbl.gov/publications/compilation-published-pm25-emission
𝐶 =𝐶𝑜 +
𝐸𝜆𝑉
1 +𝐶𝐴𝐷𝑅𝜆𝑉
Modeling air cleaners
An example providing better than usual information:• Assume their reported CADR for dust 234 ft3/min
Q Q
CoC
E
Qc
Qc • Let’s assume a volume of 160 m3, or about a 600 square foot apartment.
• And a range of AERs (recall the median value for a US residence is ~0.5 per hour)
𝐶 =𝐶𝑜 +
𝐸𝜆𝑉
1 +𝐶𝐴𝐷𝑅𝜆𝑉
Modeling air cleaners
0.1
1
10
100
1000
0 0.5 1 1.5 2 2.5 3
Ind
oo
r P
M2
.5co
nce
ntr
atio
n (μ
g/m
3)
Air exchange rate (h-1)
E=0 E=0.64 mg/h E = 17 mg/h E = 120 mg/h
Outdoor levels
For high E, increasing ventilation decreases C
At low E, increasing ventilation increases C. Why?
Cooking with the microwave Grilling Pan frying meat
Modeling air cleaners
Compare scenario with the air-cleaner (left), to one without the air cleaner (right)
0.1
1
10
100
1000
0 1 2 3Ind
oo
r P
M2
.5co
nce
ntr
atio
n (μ
g/m
3)
Air exchange rate (h-1)
E=0 E=0.64 mg/h
E = 17 mg/h E = 120 mg/h
1
10
100
1000
10000
0 1 2 3
Ind
oo
r P
M2
.5co
nce
ntr
atio
n (μ
g/m
3)
Air exchange rate (h-1)
E=0 E=0.64 mg/hE = 17 mg/h E = 120 mg/h
What’s one important criticism of this analysis?
Modeling air cleaners
But…
Not only do CADRs not make sense, “turbo” flow rates yield 53 dB of noise. A quiet bedroom is <30 dB, ~50 is as noisy as running an air-conditioner (inside).
Take-away?...pun intended
http://newscenter.lbl.gov/2013/07/23/kitchens-can-produce-hazardous-levels-of-indoor-pollutants/
http://indoorair.lbl.gov/range-hood-roundup/
• Exposures from cooking are substantial, in developed and developing world• Use a fume hood that exhausts to the outdoors (and maybe then an air cleaner…)
Cooking exposures worldwide
In the developing world: o Biomass burning
─ Crop residues─ Dung─ Wood
o Inefficient, often not ventilated─ Large PM, PAH exposure
o 4% of global mortality (largest environmental contributor)
─ 2 million deaths/year
o 2/3 of lung cancer victims in dev. world do not smoke!
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