ME425/525: Advanced Topics in Building Science

Transcription

1 ME425/525: Advanced Topics in Building Science Indoor environmenal qualiy for susainable buildings: Lecure 6 Dr. Ellio T. Gall, Ph.D.

2 Lecure 6 Today s objecives o Error propagaion Apply o SS soluion (venilaion, emission, air-cleaning) o Chemical reacions Heerogeneous Homogeneous o Compeiion beween sinks Applicaion o indoor spaces, coupled mass balances o Adsorpion/desorpion processes o Quesions?

3 Compeiive phenomena Compeiion amongs sinks We solved for C() under scenario of o Infilraion (Q C o ) o Exfilraion (Q C) o Emission (E) o Air cleaning o Heerogeneous chemisry o Homogeneous chemisry C = C =0 e α + λ α C o + E αv 1 e α Where α = λ + nq c V + σ j k c C j + σ i v d,i A i V C o Q C hom. chem Q c Qc he. chem E Q

4 A realisic example We wan o rack indoor ozone dynamics o Need ime-varian mass balance Le s assume he following scenario: o A 100 m 3, well-mixed indoor space o A ceiling heigh of 2.5 m o An air exchange rae of 0.5 h -1 o No indoor ozone emissions (E = 0)

5 Air cleaning for ozone Le s assume we operae on low speed and ha ozone is removed wih an efficiency of 50% (ypical for a mid-life acivaed carbon filer). Wha is he CADR?

6 Homogeneous chemisry Wha else do we need o model our sysem? Homogeneous chemisry o Rae consan o Concenraion of second gas-phase reacan Le s assume a simple sysem, where ozone is reacing wih one oher compound, so + R hom = k c C j Wha does his C represen he concenraion of?

7 Ozone and limonene Ozone reacs rapidly wih he erpene limonene o Ubiquious indoors o Obained commercially from cirus o Presen in cleaning producs Scening agen (lemony fresh!) i. Consumer/self-care producs ii. Air fresheners Solven properies i. Cleaning producs o 45,000 ons/year produced o Iself may be an irrian o Bu, ozone + limonene yields harmful producs For now, we ll focus on jus he reacans

8 Indoor VOCs Wha are ypical indoor limonene levels? o Sudy of personal 48-h exposures in 201 individuals Mean personal limonene concenraion was found o be 32 μg/m 3 R hom = k c C j Do you hink his indoor limonene level is higher or lower han oudoors?

9 Reacion rae consan R hom = k c C j Noe unis! Rae consan is given in 1/(ppbs), while we ve have ozone, limonene levels in µg/m 3 (in his example) Many resources for hese: NIST Chemisry Webook Je Propulsion Laboraory Review aricles in he lieraure

10 Wha are ypical oudoor ozone levels? Oudoor ozone C = C =0 e λ + λ α C o + E αv 1 e α Box plos of daily 8-h maximum average ozone concenraions in six locaions across Singapore. Le s assume an average of 35 µg/m 3 of ozone. The U.S. EPA NAAQS is 70 ppb, how does our assumpion compare?

11 Heerogeneous chemisry Ozone reacs wih surfaces othree prominen surfaces Drywall (pained), Carpe, Ceiling ile i v d,i A i V

12 Heerogeneous chemisry Maerial surface imporan; T, RH less so Increase wih increase in mixing condiion, why? i v d,i A i V For 3 maerials: 1) carpe, 2) ceiling ile, 3) pained drywall

13 Heerogeneous chemisry Each v d is associaed wih an area o Assume floor is carpe Area = 5 8 = 40 m 2 o Assume walls are pained drywall Area = = 40 m 2 o Assume ceiling is ceiling ile Area = 5 8 = 40 m 2 i v d,i A i V

14 Organize he parameers lambda 0.5 h-1 air exchange rae V 100 m 3 Volume of indoor space E-ozone 0 ppb/h*m^3 ozone emission rae CADR m^3/h air cleaner clean air delivery rae kc-j 5.10E-06 1/(ppb-s) gas-phase ozone-limonene rae consan kc-j 1.84E-02 1/(ppb-h) vd,c 5.5 m/h ozone-carpe deposiion velociy vd,c 2.5 m/h ozone-ceiling ile deposiion velociy vd, pdw 0.5 m/h ozone - pained drywall deposiion velociy A, c 40 m 2 carpe area A, c 40 m 2 ceiling ile area A, pdw 65 m 2 pained drywall ara Co 35 μg/m 3 Co 17.5 ppb oudoor ozone level Clim 32 μg/m 3 Clim 5.6 ppb indoor limonene concenraion C= ppb iniial indoor ozone level C o Q C hom. chem Q c = convered parameer Qc he. chem E Q C = C =0 e λ + λ α C o + E αv 1 e α Where α = λ + nq c V + σ j k c C j + σ i v d,i A i V

15 Solving he inegraed M.B. C = C =0 e α + λ α C o + E αv 1 e α Where α = λ + nq c V + σ j k c C j + σ i v d,i A i V C o Q C hom. chem Qc he. chem E Q Q c Le s firs evaluae α wha should he unis of alpha be? α = 0.5 h m3 /h 100m 3 m ppb ppb + h 40m m h 40m m h 40m2 h 100m 3 α = 5.4 h -1

16 Indoor O3 concenraion (ppb) Simulaion resuls C-O3: AC, Hom, He C-O3: Hom, He C-O3: He Time (h) α = 4.0 h -1 α = 4.1 h -1 α = 5.4 h -1 Lower alpha resuls in higher concenraion (hink of alpha as a firs-order loss erm) Wha is he dominan removal mechanism?

17 Inerpreing resuls Compue he conribuion o he overall sink from each erm in he equaion for alpha: Conribuion o indoor sinks 3.53 h h h h -1 Air exchange Air cleaning Heerogegneous chemisry Homogeneous chemisry Surface reacions conribue mos subsanially o he removal of indoor ozone (in his example, bu also in general).

18 Indoor O 3 concenraion (ppb) Compare o α=λ C-O3: AC, Hom, He C-O3: Hom, He C-O3: He C-O3: No sinks Time (h) Wha is he implicaion of α=λ? Wha is he seady-sae concenraion in such a scenario, assuming E = 0?

19 Simplifying assumpions Wha are wo unrealisic assumpions we have made in performing his analysis? Indoor limonene is consan R hom = k c C limonene C ozone Primary ozonide Chemisry is complex, bu for every 1 mole of ozone removed, 1 mole of limonene is removed -> limonene levels will vary as well!

20 Simplifying assumpions Wha are wo unrealisic assumpions we have made in performing his analysis? Oudoor ozone is consan Island average O3 ( g/m 3 ) Ozone Temperaure Hour of day (average from 1/1/ /12/2007) Figure 1. Average O 3 and emp. in Singapore Temperaure (deg C) Oudoor ozone highly variable, diurnal rend ha is relian on solar radiaion o iniiae he chemisry (phoochemisry)

21 Implicaions of our assumpions Are we over or under-predicing loss of ozone due o limonene reacion? o Bu here are many oher compounds ozone could reac wih Assuming ozone is consan? o Could be over-predicing or under-predicing o Time-averaged soluions are common Appropriae if you ime-averaging is longer han your sysem s dynamics o approaching seadysae

22 How o resolve? We are essenially assuming limonene is a seady-sae dc lim d 0 Wha should we do? o Mass balance on limonene o Assume we have Air exchange An emission source Q Homogeneous chemisry E Q c C o C hom. chem

23 A dynamic mass balance for limonene Coupled mass balances dc lim d = λc o,lim λc lim () + E O3 V k lim O3C lim ()C O3 () A dynamic mass balance for O3 dc O3 d = λc o,o3 λc O3 () + E O3 V k lim O3C lim ()C O3 () i v d,i A i V These equaions are coupled Wih respec o limonene concenraion And ozone concenraion

24 Oudoor levels are also ime-varian A dynamic mass balance for limonene dc lim d = λc o,lim () λc lim () + E O3 V k lim O3C lim ()C O3 () A dynamic mass balance for O3 (noe no air-cleaner) dc O3 d = λc o,o3 () λc O3 () + E O3 V k lim O3C lim ()C O3 () i v d,i A i V Oudoor levels will also vary wih respec o ime

25 Numerical soluions A dynamic mass balance for limonene dc lim d = λc o,lim () λc lim () + E O3 V k lim O3C lim ()C O3 () A dynamic mass balance for O3 dc O3 d = λc o,o3 () λc O3 () + E O3 V k lim O3C lim ()C O3 () i v d,i A i V C O3 Analyical soluions for some simple scenarios may exis Numerical soluions are ofen pursued for models

26 Forward euler mehod Forward euler mehod Break derivaive ino discree erms For limonene: Where h is he ime-sep C + lim C lim = λc o,lim λc lim + E O3 V k lim O3C lim C O3 A dynamic mass balance for O3 C + O3 C O3 = λc o,o3 λc O3 + E O3 V k lim O3C lim C O3 i v d,i A i V C O3

27 Forward Euler Mehod Solve algebraically for C(+Δ) C + lim = λc o,lim λc lim + E O3 V k lim O3C lim C O3 + C lim + C O3 = λc o,o3 λc O3 + E O3 V k lim O3C lim C O3 i v d,i A i V C O3 + C O3 Upsides o Forward Euler: Simple Downsides: Unsable, requires very small ime-sep (herefore compuaion ime) Oher approaches: Modified Euler, Crank-Nicholson, Runge-Kua, ec.

28 Indoor ozone concenraion (ppb) Discreizing soluions and error Discree, Δ = 0.05 h Discree, Δ = 0.1 h Discree, Δ = h Analyical Time (h)