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!