HAF-IFE TIME FOR VOC EMISSION AND SORPTION OF POROUS BUIDING MATERIAS C.-S. ee is Ph.D. Candidate, Departent of Building, Civil, and Environental Engineering; F. Haghighat is Professor, Departent of Building, Civil, and Environental Engineering; W. S. Ghaly is Associate Professor, Departent of Mechanical and Industrial Engineering, Concordia University, Montreal, Quebec, Canada ABSTRACT Most labeling or regulating systes for VOC eissions fro building aterials and furnishings adopts the axiu eission rate or concentration as a criterion. This criterion alone, however, ay not be sufficient for solid (dry) building aterials of which eissions are often characterized by low eission rates with slow decay rates. Half-life tie, which is often adopted for decaying probles, can be a good suppleent. For aterial eissions, half-life tie can be defined as the tie required eitting 50% of the initially contained VOC ass in the aterial. For sink effect, it is defined as the tie to absorb 50% of the axiu VOC ass that the aterial can absorb for a given indoor air VOC concentration. This study theoretically calculates the half-life tie for VOC eission and sorption of porous building aterials. The analytical odel considers the internal diffusion and physical adsorption in the porous solid, and the convection over the upper surface of the aterial. The effects of air velocity (expressed as Reynolds nuber) and aterial properties on the half-life tie were investigated. The theoretically calculated half-life tie were copared with experientally easured half-life tie available in literature. INTRODUCTION Building aterials are ajor sources of indoor air pollutants like volatile organic copounds (VOC). In order to control and reduce the VOC eissions fro the building aterials, several labeling or regulating systes have been introduced [Kukkonen et al., 00;DSIC, 000; Oppl, 999]. The coonly adopted criterion is the axiu eission rate or concentration of TVOC and soe carcinogenic copounds considering only the priary eission. For wet surface coating aterials like paint and wood stain, the eissions are characterized by the initially high VOC eission rates with fast decay rates; hence, regulating only the axiu eission rate or concentration can be sufficient. This criterion alone, however, ay not be an effective easure for solid (dry) building aterials. Solid aterials show relatively low eission rates with slow decay rates. In ters of the priary eission source, solid aterials are less significant than wet aterials; however, porous solid aterials also act as secondary eission sources through sorption processes, resulting in lower chaber air concentration but prolonged eissions. Therefore, VOC eissions fro solid aterials needs to be assessed in ters of tie as well as the axiu eission rates. The labeling syste used in Denark and Norway (000) adopted a tie criterion, i.e., indoor-relevant tie-value, which is defined as the tie required to reach the acceptable concentration (50% of the iniu value between odour and irritation thresholds) of indoor cliate under standard conditions. The indoor-relevant tie-value is liited for priary eission only. Half-life tie is generally applied for decaying probles, e.g., decay of radioactive substances. In this study half-life tie is adopted as a easure to characterize the VOC source (eission) and sink (sorption) effects of porous solid building aterials. This study theoretically calculates the half-life tie using an analytical odel that considers the internal diffusion and physical adsorption/desorption within the porous aterial, and the boundary layer resistance due to convection over the aterial. A paraetric study was carried out to investigate the dependence of half-life tie on the aterial properties (diffusion coefficient, porosity, sorption property, thickness and length) and the air velocity (expressed as Reynolds nuber).
Meininghaus et al. (000) easured aterial properties like diffusion coefficient and sorption properties of various building aterials through twin chaber tests using the CIMPAQ type chabers, and also reported half-life tie obtained fro the desorption-phase data. These data were copared with the theoretically calculated a half-life tie. ANAYTICA MODE DEVEOPMENT Figure shows the scheatic diagra of the VOC source and sink proble considered. A porous solid aterial of length, and thickness b, has a constant gas-phase effective diffusion coefficient D e,g, effective adsorbed-phase or surface diffusion coefficient D e,ad, sorption property K, porosity ε, and initial concentration C o. There is no ass transfer along the edges of the solid. The boundary layer exists due to lainar or turbulent convection over the solid and the VOC concentration in the abient air (C ) can be a function of tie. The convection ass transfer coefficient (h D ) can be obtained fro Sherwood nuber correlations. The governing equation of one-diensional gas-phase and surface diffusions within the porous aterial including physical adsorption/desorption is given by, C Cad C Cad ε = De, g D e, ad () where, ε = porosity [diensionless]; C = the gas-phase VOC concentration [g voc / 3 air]; C ad = physically adsorbed-phase VOC concentration [g voc / 3 aterial]; D e,g = effective diffusion coefficient for gas-phase diffusion [ /s]; D e, ad = effective diffusion coefficient for adsorbed-phase or surface diffusion [ /s]; y = space coordinate []; t = tie [s] An adsorption isother relates the adsorbed-phase concentration (C ad ) with the gas-phase concentration (C). In this odel, Henry (linear) isother was used considering relatively low VOC concentration levels copared to the saturation VOC concentration, C ad where, K = sorption partition coefficient [ 3 air/ 3 aterial] Substituting this into Equation () gives, = K C () C C ( ε K) = ( De, g K De, ad ) (3) et us define the overall effective diffusion coefficient of the porous aterial (D s ) as follows, D s = De, g K De, ad (4) Applying Equation (4), Equation (3) becoes, C C = ( ε K) (5) The third boundary condition was used to describe the convection ass transfer. This is iposed at the upper surface of the solid as follows,
C = hd ( Cw C () t ) at y = 0 (6) where, h D = the convection ass transfer coefficient [/s]; C w = VOC concentration at the aterial-air interface [g/ 3 ]; C = VOC concentration in the abient air [g/ 3 ] Since only one solid aterial is considered, there is no ass flux at the botto surface of the solid. C = 0 at y = -b (7) Initially (at t=0) the solid aterial is assued to have a unifor VOC concentration (C o ). C = C Ο at t = 0, -b y 0 (8) The governing equation, Equation (5), can be nondiensionalized as follows, θ θ = (9) ( ε K) and the nondiensional variables are taken as C C θ = ; Co C t t t = = = Fo ; (0) t b D y = d y b ; The initial and the boundary conditions in Equations (6) to (8) becoe, θ Bi θ θ = 0 = 0 where, Bi is the Biot nuber (Bi = h D b/d s ). s at y = 0 () at y = -b () θ =.0 at t = 0, -b y 0 (3) The governing equation for θ(y,t ), Equation (9), together with the boundary conditions given in Equations () and (), and the initial condition given in Equation(3) is of the so-called diffusion type (parabolic in tie and elliptic in space) and can be solved analytically using the integral transfor ethod [Özisik, 980]. The nondiensionalized VOC concentration, θ(y,t ) in the solid is given as
( Β ) Β Β t Bi sin ε K θ ( y, t ) = cos{ Β ( y ) } e (4) = Β Β Bi Bi where, Β s are the eigenvalues, which are the positive roots of the following equation, Β tan Β = (5) ( ) Bi THEORETICA INVESTIGATION ON HAF-IFE TIME In the nondiensional analytical odel, the independent paraeters are (εk) and Biot nuber (Bi). Since Bi is the ratio of the diffusion to convection resistance of ass transfer, it is coprised of aterial properties (b and ) and the convection property (h D ), which is a function of Reynolds nuber and Schidt nuber. The effects of these paraeters on the half-life tie was investigated N-octane at the teperature of 5 C was used as VOCs of interest. Hence, the Schidt nuber was set as.57 and the diffusion coefficient in the air (D a ) is 6.0x0-6 /s. In this study, the effect of Schidt nuber was not investigated since the Schidt nuber for various VOC varies in a relatively sall range, 0.9 3. [Sparks, et al., 996]. (εk) was varied fro 0 to 0 5. The porosity (ε) is within the range of 0 to ; however, K varies significantly. Cox et al. (00b) easured the sorption partition coefficients of various VOCs on the vinyl flooring and reported that they ay vary fro 80 to 4. 0 5. Biot nuber (Bi) is defined as (h D b)/d s, which is the ratio of the diffusion to convection resistance of ass transfer. Bi was varied fro 9. 0-3 to.9 0 5, which were deterined fro the cobination of separate ranges of D a /D s, b/, and Re. D a /D s was varied in the range of 0 to 0 5. This range was decided based on the previous study, which showed the range of easured D a /D s for gas-phase diffusion of various building aterials are fro 4.4 to.55 0 4 [Haghighat et al., 00]. The thickness to length ration (b/) was varied fro 0-4 to 0 -. The Reynolds nuber was varied fro 0 to 0 5, which is equivalent to the air velocity fro alost stagnant to 0.34 /s when the solid length = 4.5. The ass transfer coefficient (h D ) was obtained fro the Sherwood nuber relation for the lainar forced convection over a flat plate [Holan, 990], where Sh Sh = Sherwood nuber (Sh = h D /D a ) Re = Reynolds nuber (Re = u /ν) Sc = Schidt nuber (Sc=ν/D a ) = aterial length [] D a = diffusion coefficient in the air [ /s] u = air velocity in the abient air [/s] ν = kineatic viscosity [ /s] 3 = 0.664 Re Sc (6) The axiu ass of gas-phase VOC that can be eitted fro or be absorbed by a porous aterial per unit area ax is ax = Co C b (7) where, ax has the unit of [g/ ]. The half-life tie(t 0.5 ) is defined as the tie required to eit/sink 50% of ax fro/into the aterial. In other words, t 0.5 is the tie required eitting 50% of the initially contained VOC ass in the aterial for aterial eissions; and for sink effect, the tie to absorb 50% of the axiu VOC ass that the aterial can absorb for a given indoor air VOC concentration. Since the nondiensional odel was used, t 0.5 is noralized by the diffusion characteristic tie, t d, which is defined as b /D s, and denoted as t 0.5.
Figure presents the effects of (εk) and Biot nuber on t 0.5. Figure (a) shows that as Biot nuber increases, t 0.5 decreases. However, when Biot nuber is larger than 0, in other words, if the diffusion resistance is 0 ties larger than the convection resistance, t 0.5 becoes alost constant. As (εk) increases, t 0.5 increases. As shown in Figure (b), (εk) has linear ipact on t 0.5. Biot nuber is a nondiensional paraeter that gives the ratio of diffusion resistance to convection resistance, and can be rewritten as follows: hd b hd Da b Bi = = = Sh ( Da ) ( b ) (8) Da Substituting the Sherwood nuber correlation of Equation (6) into Equation (8) gives, ( D D ) ( b ) 3 Bi = 0.664 Re Sc (9) Instead of lup sued effect of Biot nuber, the effects of separate paraeters, i.e., Re, (D a /D s ) and (b/), on t 0.5 were investigated. Applying all cobinations of aterial paraeters and Reynolds nuber, the observed trends on t 0.5 are presented in Figure 3, where, t 0.5 is plotted versus (D a /D s ) (b/) and (εk) for various Re. For a given set of aterial properties, t 0.5 increases as Re decreases: when (D a /D s ) (b/) is 0.0 and (εk) is 00, t 0.5 is 45.7 for Re =0 5, while t 0.5 is 785 for Re =0. This figure also shows that as (D a /D s ) (b/) increases the effect of Re decreases. When (D a /D s ) (b/) is 0.0, t 0.5 for Re =0 is 7 ties larger than that for Re =0 5, while the sae ratio drops to.4 when (D a /D s ) (b/) is.0. The influence of Re diinishes when (D a /D s ) (b/) is larger than.0. In other words, the assuption of negligible convection is valid for values of (D a /D s ) (b/) larger than.0. In that region, t 0.5 /(εk) is alost constant. Hence, the diensional half-life tie, t 0.5, becoes, t0.5 A ( ε K ) td = A ( ε K ) ( b ) ( Da ) (0) where, A, A are constants, i.e., A = A /D a [s]. Equation (0) indicates that (b/) can have ore significant ipact on t 0.5 than that of (εk) and (D a /D s ). COMPARISON WITH EXPERIMENTA HAF-IFE TIME Meininghaus et al. (000) carried out two-flow syste sall-scale chaber tests to study diffusion and sorption of VOCs (n-octane and ethyl acetate) in various building aterials. The aterial specien was placed between two identical chabers (i.e., CIMPAQ type). Air with constant VOC concentration is introduced in one chaber, while clean air is supplied to the other chaber for sorption phase, i.e., 4 hours for n-octane and 48 hours for ethyl acetate. In desorption phase, clean air was introduced in both chabers. Fro the experiental data, they obtained the effective diffusion coefficient and sorption properties (sorption capacity and sorption partition coefficient). They also easured half-life tie, which was defined as the tie when the VOC concentration in chaber air has dropped down to one-fourth (due to two-flow syste) of initial concentration at the beginning of desorption phase. The half-life tie was reported for five building aterials: carpet, aerated concrete, solid concrete, brick wall, and gypsu board. The experientally deterined half-life tie of those five aterials was copared with the theoretically calculated one using the previously described analytical odel. The input values of independent paraeters were obtained fro the reported data of aterial properties (i.e., diffusion coefficient, sorption partition coefficient, thickness, length and density) and experiental conditions (i.e, 0.08 /s of air velocity at 0c above the aterial surface, 4±0.5 o C). Since the reported sorption partition coefficient is ass based, it was converted to volue based one using following relation. a s
K ρ = K (0) ρ a where, K = volue based sorption partition coefficient [ 3 air/ 3 aterial] K = ass based sorption partition coefficient [kg air /kg aterial ] ρ = density of the aterial [kg/ 3 ] ρ a =density of air [kg/ 3 ] Since the porosity was not reported and it varies in sall range copared to K, it was assued that (εk) K. Table suarizes those input values for n-octane case. Table. Suary of input values Material D a /D s b/ K [ 3 air/ 3 aterial] Bi t d (=b /D s ) [s] Carpet with SBR backing 8.56 8.46x0-3 94.7 4.76 06 Aerated concrete 7.89.09x0-80.9 0.8 580 Solid concrete 57.7.49x0-60.0 56.6 70 Brick wall 8.5.49x0 -.6 30. 90 Gypsu board 7.5.4x0-68.4 5.84 86 n-octane: D a =6.0x0-6 [ /s]; =.005 []; u =0.08 [/s]; ρ a =.9 [kg/ 3 ]; Re =5; Sc =.57 Figure 4 presents coparison between experientally obtained half-life tie (t 0.5 ) and theoretically calculated t 0.5. For sall Biot nuber cases like carpet and gypsu board, the theoretically calculation underestiates t 0.5, but for larger Bi, it overestiates t 0.5. The error was less than 30% for low Bi cases (Bi=0.8 or less). For brick wall, the error is 84%. The axiu difference was observed for solid concrete case, which has the largest Bi: theoretically calculated t 0.5 is three ties larger than experiental t 0.5. The errors ay be caused not only by the difference in the boundary conditions between the analytical odel and the experient, but also by the difference in the definition of half-life tie. While the theoretical calculation is based on the accuulated ass that has eitted or sorbed, the experiental half-life tie is based on the VOC concentration. Figure 5 presents the difference in half-life tie due to the discrepancy in the definition: assbased or concentration-based. t 0.5 of both cases were obtained using the analytical odel; hence, there is no difference in boundary conditions. The ass-based t 0.5 is defined as the tie required to eit/sink 50% of ax in Equation (7) fro/into the aterial, and the concentrationbased t 0.5 is defined as the tie required the nondiensioinalized wall concentration (θ w ) to reach 0.5. The error increases as Bi increases. For the cases of Bi = 9. or larger, ass-based t 0.5 becoes uch larger than concentration-based t 0.5. This ay explain the significant overestiation of t 0.5 in theoretical calculation copared to the experiental data for larger Bi cases like solid concrete. The difference between the analytical odel, and the experiental setup and procedures, can cause the additional error and be possible reasons behind the underestiation of t 0.5 in theoretical calculation for carpet and gypsu board cases. This, however, needs further investigations. CONCUSION The half-life tie for eission/sorption of porous building aterials, was theoretically investigated. In this study, half-life tie was defined as the tie required to eit or absorb 50% of axiu transferable VOC ass. The paraetric study leads to the following conclusion:
The linear effect of (εk) is observed for t 0.5. The effect of Bi, however, is nonlinear: as Bi increases, t 0.5 decreases, but for Bi larger than 0, t 0.5 becoes alost constant. When Bi is decoposed into Re and aterial properties, i.e., (D a /D s ) (b/), the paraetric study shows that the effect of Re decreases as (D a /D s ) (b/) increases, and if (D a /D s ) (b/) is larger than.0, there is little effect of Re on t 0.5. The theoretically calculated half-life tie was copared with experientally easured one by Meininghaus et al. (000) using the reported aterial properties and flow properties. For low Biot nuber cases, the error is less than 30%. The error becoes significant for larger Biot nuber cases. This ay be caused by the difference in the definition of half-life tie. Theoretical study uses ass-based half-life tie, while experiental data was obtained fro concentration-based one. It was deonstrated that as Biot nuber increases, the difference between ass-based half-life tie and concentration-based one increases. Other factors like difference in boundary conditions, geoetry, etc. can cause additional error, but this needs further investigations. ACKNOWEDGEMENT The authors would like to express their gratitude to NSERC and EJB Foundation for supporting this research. REFERENCES Cox, S.S., Zhao, D., and ittle, J.C., Measuring partition and diffusion coefficients for volatile organic copounds in vinyl flooring, Atospheric Environent, vol. 35, pp.383-3830, 00 DSIC, Danish Society of Indoor Cliate, Introduction to the Principles behind the Indoor Cliate abeling, August, 000 Haghighat, F., ee, C.S., and Ghaly, W.S., Measureent of diffusion coefficients of VOCs for building aterials: review and developent of a calculation procedure, Indoor Air, vol., pp. 8-9, 00 Holan, J.P., Heat Transfer, 7 th edition, McGraw-Hill, Inc., 990 Kukkonen, E., Saarela, K., and Neuvonen, Experiences fro the eission classification of building aterials in Finland, Proceedings of Indoor Air 00, 9 th Int. Conf. on Indoor Air Quality and Cliate, vol. 3, pp. 588-593, Monterey, USA, June 30- July 5, 00 Meininghaus, R., Gunnarsen,., and Knudsen, H.N., Diffusion and sorption of volatile organic copounds in building aterials-ipact on indoor air quality, Environental Science & Technology, vol.34, pp.30-308, 000 Oppl, R., The EMICODE labelling syste for flooring installation products, Proceedings of Indoor Air 99, 8 th Int. Conf. on Indoor Air Quality and Cliate, vol., pp. 543-548, Edinburgh, Scotland, August 8-3, 999 Özisik, M.N., Heat Conduction, John Wiley & sons, Inc., 980 Sparks,. E., Tichenor, B. A. and Guo, Z, Gas-phase ass transfer odel for predicting volatile organic copound (VOC) eission rates fro indoor pollutant sources, Indoor Air, vol. 6, pp. 3-40, 996
y C h D Boundary layer y = 0 y = -b C o, D e,g, D e,ad, ε, K b Figure. Scheatic diagra of the odel.0e07.0e06.0e05 (ek)=0 (ek)=00 (ek)=000 (ek)=0000 (ek)=00000 t0.5.0e04.0e03.0e0.0e0.0e00.0e-03.0e-0.0e0.0e03.0e05.0e07 (a) Biot no. t0.5.0e07.0e06.0e05.0e04.0e03.0e0.0e0 Bi=9.E-03 Bi=.9E05.0E00.0E0.0E0.0E03.0E04.0E05.0E06 (b) (εk) Figure. Effects of (εk) and Biot nuber on the half-life tie, t 0.5
t0.5 /(εk).0e0.0e0.0e00 Re=00000 Re=0000 Re=000 Re=00.0E-0.0E-03.0E-0.0E-0.0E00.0E0.0E0.0E03 (D a /D s )(b/) Figure 3. Effects of Reynolds nuber on the half-life tie, t 0.5 50 40 Experient [Meininghaus et al., 000] Analytical odel t0.5 30 0 0 0 carpet aerated concrete solid concrete brick wall gypsu board Figure 4. Theoretical versus experiental half-life tie.0e04.0e03 ass based concentration based.0e0 t0.5.0e0.0e00.0e-0.0e-0.0e-03 Bi=0.009 Bi=0.09 Bi=0.9 Bi=9. Bi=9 Figure 5. Mass-based half-life tie vs. concentration-based half-life tie