A MASS TRANSFER MODEL FOR SIMULATING VOC SORPTION ON BUILDING MATERIALS

Transcription

1 Yang, X., Chen, Q., Zeng, J., Zhang, J.S., and Shaw, C.Y. 00. A ass transfer odel for siulating VOC sorption on building aterials, Atospheric Environent, 35(7), A MASS TRANSFER MODEL FOR SIMULATING VOC SORPTION ON BUILDING MATERIALS X. YANG a*, Q. CHEN b, J.S. ZHANG c, Y. AN d, J. ZENG d and C.Y. SHAW d a Departent of Civil, Architectural, and Environental Engineering, University of Miai, Coral Gables, FL , USA b Building Technology Progra, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cabridge, MA 039, USA c Departent of Mechanical, Aerospace & Manufacturing Engineering, Syracuse University, 47 Link Hall, Syracuse, NY 344, USA d National Research Council of Canada, Institute for Research in Construction, Indoor Environent Progra, M-4, Montreal Road, Ottawa, Ontario KA 0R6, Canada. Abstract - The sorption of VOCs by different building aterials can significantly affect VOC concentrations in indoor environents. In this paper, a new odel has been developed for siulating VOC sorption and desorption rates of hoogeneous building aterials with constant diffusion coefficients and aterial-air partition coefficients. The odel analytically solves the VOC sorption rate at the aterial-air interface. It can be used as a wall function in cobination with ore coplex gas-phase odels that account for non-unifor ixing to predict sorption process. It can also be used in conjunction with broader indoor air quality studies to siulate VOC exposure in buildings. Key word index: Nuerical odel, indoor air quality, diffusion coefficient, partition coefficient, environental chaber, gypsu board. Noenclature C a air phase VOC concentration [g -3 ] C ad adsorbed VOC concentration on the aterial surface [g -3 ] C VOC concentration in the aterial fil [g -3 ] D a VOC diffusion coefficient in the air [ s - ] D VOC diffusion coefficient in the aterial [ s - ] g i coponent i of the gravitation vector [ s - ] K l Languir sorption coefficient [-] K a aterial-air partition coefficient [-] L thickness of the sorption aterial [] M axiu nuber of roots for sorption M w olecular weight of the copound [g ol - ] P VOC vapor pressure [Hg] P a air pressure [Pa] Pr Prandtl nuber q VOC sorption rate [g - s - ] Q VOC eission or sorption rate in the Laplace doain s Laplace operator Sc VOC Schidt nuber S φ source ter for φ T absolute teperature [K] * Corresponding author. Tel.: ; fax: E-ail address: xudongy@iai.edu

2 T 0 u j (j=,,3) x j (j=,,3) X 0 X(j) y reference teperature [K] three coponents of air velocity coordinates coefficient to calculate the sorption rate by a solid aterial syste response under the unit triangle function f(jδτ) direction of VOC sorption in the aterial Greek Sybols β theral expansion factor [K - ] τ tie [sec] μ olecular viscosity of air [Pa.s] π i μ i roots of B(s) (see equation (7)), D L ε t Δτ Γ φ Subscripts truncation error tie step [sec] effective diffusion coefficient for φ a j air phase spatial coordinate indices sorption aterial. Introduction Building aterials have been acknowledged as a ajor eission source of volatile organic copounds (VOCs) indoors. Evidence fro a variety of investigations and systeatic studies suggests that building aterials can also affect the transport and reoval of indoor VOCs by sorption and desorption. Researchers have found that re-eission of sorbed VOCs can elevate VOC concentrations in the indoor environent (Tichenor et al., 988; Bergland et al., 988). Materials capable of depositing, adsorbing, and/or accuulating pollutants can influence indoor air quality during the entire service life of a building (Nielsen, 987). Therefore, an accurate characterization of sorption of building aterials and the sorption ipact on indoor air quality is iportant. At present, the studies of the sorption effect are ainly conducted by experients using sallscale environental chabers. In a typical chaber experient, the aterial is placed in the chaber and exposed to a VOC source (a single VOC or VOC ixture) until a stable concentration of that VOC source in the test chaber is reached. The exposure is then stopped. The sorption of the aterial can be easured by onitoring the VOC concentration at the chaber outlet and coparing the results with the predicted concentration without the aterial. Although the sorption of building aterials can be detected by well-designed experients, such studies are costly, tie-consuing, and do not allow to scale-up the sorption data fro one set of

3 environental conditions (e.g., those in a sall chaber) to others (e.g., those in a building). As a practical atter, it is obvious that we need to develop atheatical odels to predict or estiate VOC sorption of building aterials. To date, researchers have developed two types of sorption odels: the equilibriu odels and the kinetic odels. The equilibriu odels assue that the sorption and desorption are confined on the aterial surface and an equilibriu is achieved between phases at the interface. The odel paraeters are obtained by fitting the odel predictions with the experiental data using nonlinear regression ethod. Axley (99) copared several equilibriu odels that have been developed. Aong those odels, the ost proising ones for exaining the indoor environent are the Languir isother odel and the linear isother odel, a siplified asyptote of the Languir odel at low VOC concentrations. The Languir isother odel represents the equilibriu VOC concentrations on the aterial surface by: C ad K C l a = () + K C l a At low gas phase concentration that is coon in indoor environents, the Languir odel can be siplified to a linear for as: C = K C () ad l a The isother odels, together with the VOC ass balance in a test chaber, have been used to describe the sorption characteristics based on the chaber data (Dunn and Tichenor, 988; Tichenor et al., 99). These odels, although siple in principle, have liitations. First, sorption on a building aterial involves several steps that transfer the VOCs fro the bulk of the fluid phase to the specific sites within the interior of the aterial, as deonstrated in Figure. The ass transfer processes include interfacial ass transfer in the gas phase, sorption at the aterial-air interface, and for a pereable aterial, diffusion inside the aterial. Equilibriu odels neglect both the interfacial ass transfer and the aterial-phase diffusion, whereas the latter could be an iportant echanis governing the sorption of certain indoor aterials (Little and Hodgson, 996). The second liitation of the equilibriu odels lies in their statistical nature: two or ore odel paraeters ust be obtained by fitting the odel prediction with the experiental data using nonlinear regression routine. It has been found that given different initial estiations of odel paraeters, the fitted paraeters ay not be unique and the results ay differ as uch as a factor of 00 (De Bortoli et al., 996; Zhang et al, 000). Finally, ost of the equilibriu odels use the sae set of experiental data to build the odel and to evaluate the accuracy of the prediction; therefore, they have not been rigorously validated. Kinetic odels, on the other hand, take the VOC diffusion echaniss into consideration. The paraeters of kinetic odels are the physical properties of aterials. These paraeters can be obtained independently fro experients rather than fro curve fitting. Representative kinetic odels are those developed by Axley (99), Dunn and Chen (993), and ore rigorously, by Little and Hodgson (996). Those odels are, however, based on the largely untested assuption that indoor air is well-ixed. The use of such odels are liited to siple cases 3

4 (e.g., a well-ixed roo with single containant source and sink). The objective of this paper is to develop a sorption odel that can be used for ore general, non-unifor ixing conditions. The odel explicitly quantifies the essential echaniss of VOC sorption, while aintaining the odel itself in an analytically solvable for to provide a readily-accessible solution. The applicability of the sorption odel is deonstrated by coparing the odel prediction with experiental data fro sorption experients.. Model developent Consider the VOC ass transfer layers in air, aterial-air interface, and the aterial (Figure ). To atheatically solve the sorption process, we ake the following assuptions: () Fick s law applies to ass diffusion in both air and the aterial. () The aterial is hoogeneous and the VOC diffusion coefficient in the aterial and the aterial-air partition coefficient are constant. Further, the VOC sorption occurs in a very thin layer of interior building aterials. Hence the diffusion inside the aterial can be assued to be -D. (3) The ass transfer rate between the air and aterial is very sall. Hence, the heat generation/release associated with the sorption is negligible. With the above assuptions, the following section presents the governing equations of VOC ass transfer in these layers... Governing equations in air, aterial-air interface, and the aterial The VOC transport in the air is deterined by diffusion through the boundary layer over the aterial-air interface. Hence, a coplete set of airflow and VOC transport equations in the air phase are needed. For siplicity, the following discussion is confined to lainar flow (e.g., flow in a conventional sall-scale chaber without a ixing fan). The general principle however applies to turbulent flow. For an incopressible, lainar, and Newtonian flow, the conservation equations for continuity, oentu (using Boussenisseq approxiation for buoyancy), energy, and VOC species can be generalized as: τ ( ρφ) + x j ( ρu φ) = j x j ( Γ φ x φ ) + j S φ (3) where φ φ φ = for ass continuity = u j (j =,, and 3) for three coponents of oentu (u,v,w) = T for teperature 4

5 φ = C a for VOC concentrations The φ, Γ φ and S φ are shown in Table. At the aterial-air interface, VOC concentration changes fro gas phase concentration in the air side, C a (0,τ) (g/ 3 ), to solid phase concentration in the aterial side, C (0,τ) (g/ 3 ). At the equilibriu, the VOCs in the two phases are related through a sorption isother. In any siple cases, it can be assued that the equilibriu follows the linear isother shown in equation (4): C (0,τ) = K a C a (0,τ) (4) where 0 eans at the aterial-air interface (y=0). K a is the diensionless aterial-air partition coefficient. Equation (4) is in consistent with the coonly used Languir isother odel for low gas concentrations. Most building aterials are pereable to VOCs. VOCs adsorbed on such aterial surface will diffuse into the aterial. For a solid aterial with hoogeneous diffusivity, the -D transient diffusion process is governed by: C (y, τ) τ = D C y (y, τ) (5) where D is the VOC diffusion coefficient in the aterial ( /s), and y is the coordinate representing the direction that the VOC diffusion in the aterial occurs (). The VOC ass transfer rate q(y, τ) (g/ s) at an arbitrary displaceent y of aterial and tie τ is given by: C (y, τ) q(y, τ ) = D (6) y If the thickness of the aterial is L, the initial and boundary conditions for the solid aterial are: C (y, τ = 0) = 0 (7) C (0, τ) Ca (0, τ) q(0, τ ) = D = Da y y (8) C (L, τ ) 0 (9) = Equation (8) represents a ass balance at the aterial-air interface and equation (9) indicates two possibilities on the other side of the aterial (y = L ). The first possibility is that the aterial is thick copared to the diffusion distance and the other side reains unaffected by the diffusion. The second is that the VOCs have already penetrated the aterial but the other side is not a perfect barrier to VOCs. In ost cases, the diffusion process in a solid aterial is very slow and the first possibility exists. It should be entioned that soe researchers had assued a nonpereable boundary condition at y = L. Such an assuption has been challenged by Fan and 5

6 Kokko (995), who found that even when a diffusion tight facing (aluinu foil) was placed on the surfaces of an n-pentane-based foa saple, the aging process of the foa was still going on, indicating that the facing could not be perfectly diffusion tight. Apparently, further studies are desirable to deterine the ost appropriate boundary condition at y = L. In general, the sorption process can be siulated by nuerically solving the above governing equations. However, due to the extreely sall agnitude of the diffusion coefficient of VOCs in aterials, direct nuerical siulation of VOC diffusion in aterials requires very fine grids to deterine the high VOC concentration gradients especially near the aterial-air interface. This can be avoided if the VOC sorption rate, q(0,τ), can be odeled based on the air phase concentration at the interface, C a (0,τ), and the physical properties of the building aterial (see Figure ). The odel can then be used as a wall function in cobination with ore coplex gas-phase odel (e.g., equation (3)) to solve the sorption process. This fors the basic idea of the sorption odel to be developed... A new sorption odel By using the Laplace transforation, equations (5) and (6) can be rewritten as follows: C (y,s) D s C (y,s) = 0 y (0) C (y,s) Q(y,s) = D y () where s is the Laplace operator, C (y,s) and Q(y,s) are the Laplace transforation of C (y, τ) and q(y, τ), respectively. The solution to equations (0) and () with the initial and boundary conditions (equations (4), (7), (8) and (9)) reads: A(s) Q(0,s) = Ca (0,s) () B(s) s s where A(s) = K a cosh( L ) and B(s) = sinh( L ) D D s D Equation () is the response of the sorption rate to the air-phase concentration at the interface in the Laplace doain. The sorption rate in the tie doain can be obtained by an inverse Laplace transforation of equation (): A(s) q(0, τ ) = L [ Ca (0,s)] (3) B(s) 6

7 Equation (3) is solvable if C a (0, τ) is a siple function, e.g., a step or rap function. However, in indoor environents, C a (0, τ) is usually a coplex function of tie. A direct solution of equation (3) is generally not available. To solve the proble, we discretize the C a (0, τ) into the su of a series of discrete functions coposed of the peak value at each sapling point ultiplied by a unit triangle function, f(jδτ) (j = 0,,,, n), where Δτ is a tie step. As shown in Figure 3, the su of such a set of overlapping triangle functions is a first order approxiation of C a (0, τ). The sorption rate at a given tie nδτ is affected by the air-phase boundary concentration at tie nδτ as well as the boundary concentrations in the previous tie, i.e., n j= 0 q (0,nΔτ) = X(j)C a [0,(n j) Δτ] (4) where X(j) is the syste response under the unit triangle function f(jδτ) (j= 0,,,, n), and C a [0,(n-j)Δτ] is the air phase boundary concentration at tie nδτ, (n-)δτ, Δτ, respectively. To calculate the syste response at different tie steps, we first obtain the syste response under a unit rap function: τ g (τ) = (5) Δτ Based on equation (3), the syste response under such a unit rap function is: A(s) G( τ) = L [ ] B(s) s Δτ (6) B(s) has an infinite nuber of real roots as follows: s i π i = μi = D, i =,,3, (7) L By using the Heaviside expansion (Beyer, 975), equation (6) can be expressed as: G( d A(s) A(s) sτ sτ τ ) = li [s e ] + e s= μ (8) s 0 i ds B(s) s Δτ i= d [B(s) s ] Δτ ds Fro equations (7) and (8), we obtain: G( τ) = K ad τ K al + L Δτ π Δτ i= e i μiτ (9) X(0) is the response of g(τ) at tie τ = Δτ: 7

8 μ Δ KaD KaL e i τ X (0) = G( Δ τ ) = + L π Δτ i (0) i= For calculating the response of f(jδτ), j=,,, n, we decopose f(jδτ) into the su of three rap functions as: f (jδ τ) = g[(j + ) Δτ] g[jδτ] + g[(j ) Δτ] () Fro equations (9) and (), the syste response at tie τ = jδτ is then: where μiδτ μi ( jδτ) X (j) = G[(j + ) Δτ] G[jΔτ] + G[(j ) Δτ] = Wie e () i= K L =. π i Δτ a iδτ Wi ( e μ ) Now we have the sorption rate at tie τ = nδτ: q(0,nδτ) = X(0)C n n μ Δτ μi ( jδτ) a [0,nΔτ] + { Wie e Ca[0,(n j) Δτ]} j= i= i (3) Let μi ( jδτ) q i (0,nΔτ) = Wie Ca[0,(n j) Δτ] be the sorption rate corresponding to the i th root, j= we have: a [0,nΔτ] + q i (0,nΔτ) i= q (0,nΔτ) = X(0)C (4) where q i (0,nΔτ) is an unknown but can be obtained progressively as follows: q i (0,nΔτ) = WiC a[0,(n ) Δτ] + e and initially, q i (0,0)=0. μ Δτ i q [0,(n ) Δτ] i (5) Equations (4) and (5) represent the new sorption odel. Because the odel links the aterial sorption rate to the VOC history in the air, it can take the VOC deposition on the aterial surface and the VOC diffusion in the aterial into account. Once the values of the D, K a, and the air phase concentration are deterined, the sorption rate can be obtained by using the above odel. Since B(s) has an infinite nuber of roots, there should be an infinite nuber of q i (0,τ) ters corresponding to each root. However, equation (5) indicates that all the roots greater than soe cut-off value have a negligible effect, because the contribution at a tie step is always reduced 8

9 μ Δ τ by a factor ( e i ) of the previous sorption rate. If the truncation error is saller than ε t, naely, e μ Δ τ i < ε t (6) The axiu nuber of roots needed is: L ln( / ε t ) M = (7) π D Δ τ Equation (7) indicates that, the saller the L and the bigger D, Δτ, and ε, the fewer roots there will be. For exaple, if L = 0.0, ε t = 0-0, Δτ = 60 s, and D = /s, which is coon for a solid aterial, the total nuber of roots will be less than Model evaluation To evaluate a odel objectively, the data used for the evaluation process should be independent of the data used to develop the odel. Coon practice of curve-fitting, which are largely used to develop the equilibriu odels, should be avoided. In the following, the new sorption odel is incorporated into a nuerical code to siulate the dynaic sorption process. The siulation will reproduce the results of the sorption experients. The siulated results are then copared with the experiental data for validation. 3.. Sorption data fro a sall-scale test chaber To validate the sorption odel, we first easured the VOC sorption on an unpainted gypsu board using an environental test chaber. The environental chaber, shown in Figure 4, is ade by stainless steel. Three VOCs, which represent alkanes, ketones, and chlorine-substituted copounds, were tested for their sorption and desorption characteristics. They are ethylbenzene, benzaldehyde, and dodecane. Table gives the olecular weight and soe physicocheical properties of the copounds used to deterine the diffusion and partition coefficients. For each test, a specien holder was used to confine the sorption to the top surface; the surface area was The edges of the aterials were sealed with wax. After waxing the edges, the specien in the holder was kept in a well-ventilated cabinet for over two weeks. As the eission of the wax diinished, the specien in the holder was placed in the test chaber and conditioned with clean air. Test started after the background VOC concentration of the chaber air fell below μg/ 3. At the start of each test, the testing VOC was injected into the inlet flow. The aterial was placed in the chaber and exposed to the VOC source. The sink strength of the aterial was indicated by the difference of VOC concentrations between the inlet and outlet (we refer to this stage as the sorption phase). Once an apparent stable concentration of that VOC in the test chaber was reached, the exposure was stopped. Again, by onitoring the VOC concentration 9

10 for a period of tie, the desorption of the VOC by the aterial was easured. During the experients, the chaber air saples were collected by adsorption tubes and analyzed by a gas chroatography with a flae ionization detector (GC/FID). The test conditions were: Teperature: 3 ± C Relative huidity: 50 ± % Air exchange rate: 0.5 ± 0.0 h - Chaber loading factor: 0.57 / 3 The aterial properties that are required by the sorption odel were obtained fro the literature. Bodalal et al. (999) experientally easured the diffusion coefficient and partition coefficient of the unpainted gypsu board and gave the following correlations for D ( /s) and K a : D = (8) 3600M 6.6 w 0.9 K a = 0600 / P (9) Fro equations (8) and (9), the D and K a for each copound can be calculated, as shown in Table 3. After obtaining these paraeters, we can siulate the sorption and copare the predicted results with the easured data. 3.. Siulation of VOC sorption on unpainted gypsu board and coparison with the data To siulate the sorption process, the sorption odel (equations (4) and (5)) was incorporated into a nuerical code to siulate the air phase concentration with the presence of the aterial (gypsu board). Since VOC sorption has a negligible ipact on airflow, the nuerical siulation of the above process was conducted in two separate steps. First, a coercial CFD (coputational fluid dynaics) progra (CHAM, 996) was used to siulate the airflow and obtain the steady-state distributions of air velocity. The flow results were then incorporated into the VOC ass-transfer equations (equation 3 with φ=c a ) for siulating the dynaic sorption process. This procedure involved the coupling between air region, the interface, and the aterial (sorption odel). Details of the procedure are given by Yang (999). The nuerical siulation revealed tie-dependent, spatial VOC distributions in the chaber. Since the easureent (sapling) point was at the chaber outlet, the following discussion is focused on the results at that particular location. Figure 5 shows the coparison of the VOC concentrations at the chaber outlet for the odel predictions and the chaber observations for ethylbenzene, benzaldehyde, and dodecane, respectively. In general, the predicted concentrations during the sorption phase (0-30 hours) and desorption phase ( hours) agree with the easured data. However, different copounds have different discrepancies. For both ethylbenzene and benzaldehyde, the odel tends to over-predict the strength of both sorption and desorption, resulting in lower chaber concentrations during the sorption phase and higher concentrations during the desorption phase. 0

11 The dodecane behaves just the opposite, and the odel tends to underestiate the strength of sorption. The discrepancies between the predicted and easured concentrations ay be due to two different reasons. First, An et al. (999) found that the chaber walls theselves also had a considerable sink effect, especially for copounds with low vapor pressure. This ay partly explain the discrepancy between the predicted and easured results for dodecane, but not for ethylbenzene and benzaldehyde. The discrepancies for the latter copounds ay be priarily due to the possible inaccurate values used for the D and K a, which actually deterine the sorption. For exaple, a uch better agreeent for benzaldehyde can be achieved by using D = 0 - /s and K a = 3000, as illustrated in Figure 6. It is clear that an accurate ethod to obtain D and K a is essential for the further validation of the sorption odel. To evaluate the strength of the aterial on sorbing or desorbing VOCs, Figure 7 gives the percentage of the total incoing VOC rate (fro the inlet air) uptaken during the sorption period. The figure also gives the aount of VOCs released (represented by the percentage of the VOC rate released to the total VOC rate fro the inlet during the sorption phase) during the desorption period. The results indicate that the gypsu board can uptake a significant portion of the VOCs. At the beginning, about 5% (for ethylbenzene) to 55% (for dodecane) of the VOCs fro the inlet air was sorbed by the aterial. At 30 hours, the percentage dropped to 3.9% for ethylbenzene and.5% for dodecane. Fro 30 hours, the supply VOCs stopped and the aterial began to release the adsorbed VOC to the air and serve as a secondary source. At the beginning of the desorption phase (τ=35 hours), the release rate was about 0% (of the VOC rate fro the inlet during the sorption phase) for ethylbenzene and 3% for dodecane. As tie passed, the release rate decreased but this would last a long period of tie. 4. Conclusions A odel has been developed for VOC sorption on hoogeneous building aterials with a constant diffusion coefficient and partition coefficient. The odel solves analytically the VOC sorption rate at the aterial-air interface as a function of the air-phase concentration. The odel carries inforation on the physical representation of the entire sorption process. The sorption odel has been incorporated into a nuerical progra to study VOC sorption on an unpainted gypsu board. Results show that the odel can siulate the general trend of the sorption curve. The new sorption odel can be used as a wall function in cobination with ore coplex gas-phase odels that account for non-unifor ixing to predict sorption process. It can also be used in conjunction with broader indoor air quality studies to siulate VOC exposure in buildings. To successfully use the sorption odel developed, research focused on the accurate easureent of the diffusion coefficient and partition coefficient is highly needed.

12 Acknowledgeents This investigation is supported by the US National Science Foundation (Grant CMS ) and National Research Council of Canada. The authors also thank two anonyous reviewers for their insightful coents. References An, Y., Zhang, J.S., Shaw, C. Y., 999. Measureents of VOC adsorption /desorption characteristics of typical interior building aterial surfaces. International Journal of HVAC&R Research (in Press). Axley, J.W., 99. Adsorption odeling for building containant dispersal analysis. Indoor Air, Berglund, B., Johansson, I., Lindvall, T., 988. Adsorption and desorption of organic copounds in indoor aterials. In Proceedings of Healthy Buildings 88 3, Beyer, W.H., 975. Handbook of Matheatical Sciences, 5 th Edition. CRC Press, Inc. Bodalal, A., Zhang, J.S., Plett, E.G., 999. Method for easuring internal diffusion and equilibriu partition coefficients of volatile organic copounds for building aterials. Building and Environent 35 (), 0-0. De Bortoli, M., Knoppel, H., Colobo, A., Kefalopoulos, S., 996. Attepting to characterize the sink effect in a sall stainless steel test chaber. Characterizing sources of indoor air pollution and related sink effects ASTM STP 87, Aerican Society of Testing and Materials, Philadelphia, Dunn, J., Tichenor, B.A., 988. Copensating for sink effects in eissions test chabers by atheatical odeling. Atospheric Environent, Dunn, J.E., Chen, T., 993. Critical evaluation of the diffusion hypothesis in the theory of porous edia VOC sources and sinks. Modeling indoor air quality and exposure, ASTM STP 05, Aerican Society of Testing and Materials, Philadelphia, Fan, Y., Kokko, E., 995. Potential iproveent of n-pentane-based foa insulation. Journal of Cellular Plastics 3, 7-6. Little, J.C., Hodgson, A.T., 996. A strategy for characterizing hoogeneous, diffusioncontrolled, indoor sources and sinks. Characterizing sources of indoor air pollution and related sink effects, ASTM STP 87, Aerican Society of Testing and Materials, Philadelphia, Nielsen, P., 987. Potential pollutants their iportance to the Sick Building Syndroe and their release echanis. In Proceedings of Indoor Air 87, Tichenor, B.A., Sparks, L.E., White, J., Jackson, M., 988. Evaluating sources of indoor air pollution. Paper presented at 8 st Annual Meeting of the Air Pollution Control Association, Dallas, TX. Tichenor, B.A., Guo, Z., Dunn, J.E., Sparks, L.E., Mason, M.A., 99. The interaction of vapor phase organic copounds with indoor sinks. Indoor Air, Yang, X., 999. Study of building aterial eissions and indoor air quality, Ph.D. Thesis, Massachusetts Institute of Technology, Cabridge, Massachusetts. Zhang, J, Zhang, J.S., Chen, Q., Yang, X., 000. A critical review on sorption odels. In Proceedings of Health Building 000 (in Press).

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14 Table Values of φ, Γ φ and S φ in equation (3). φ Γ φ S φ 0 0 u i (i=,,3) μ Pa xi T μ/pr S T C a μ/sc S c ρg β ( T T ) 0 i Table Selected copounds and their physicocheical properties. VOCs Molecular weight Boiling point ( C) Vapor pressure (Hg) Ethylbenzene Benzaldehyde Dodecane Table 3 D and K a for siulating VOC sorption on unpainted gypsu board. Copound Ethylbenzene Benzaldehyde Dodecane D ( /s) K a

15 VOC olecules VOC concentration [ML -3 ] Gas phase Interface Solid phase Figure Scheatic of the general ass transfer regions of an adsorption process. 5

16 0 air Material q(0,τ) Ca(0,τ) interface C (0,τ) L y C (L,τ) Figure : VOC sorption on a solid aterial 6

17 C a (0,τ) 0 Δτ (n-j)δτ (n-)δτ nδτ τ Δτ Δτ f(jδτ), j=,,,n Δτ f(0) Figure 3 Discretization of the C a (0,τ) with a series of unit triangle functions. 7

18 Outlet Inlet Figure 4 A sall-scale chaber for easuring VOC sorption on a solid aterial. 8

19 c (g/ 3 ) Expt. Data No-sink odel Sorption odel 0. C (g/ 3 ) Elapsed tie (h) (a) Expt. Data No-sink odel Sorption odel 0. C (g/ 3 ) Elasped tie (h) (b) Expt. Data No-sink odel Sorption odel Elapsed tie (h) (c) Figure 5 Coparison of easured and siulated sink effects of unpainted gypsu board: (a) Ethylbenzene, (b) Benzaldehyde, (c) Dodecane. 9

20 C (g/ 3 ) Elasped tie (h) Expt. Data No-sink odel D=3.93E-, K=0053 D=E-, K=3000 Figure 6 A better agreeent between the odel prediction and experient can be achieved by adjusting the aterial properties (D and K a ). The results shown here are benzaldehyde sorption on unpainted gypsu board. 0

21 Relative flux (%) Ethylbenzene Dodecane Elapsed tie (h) Figure 7 Siulated sink effect for ethylbenzene and dodecane by unpainted gypsu. Results show the percentage of the incoing VOC rate (fro the inlet air) uptaken during the sorption period (0-30 h) and the VOCs released (represented by the percentage of the VOC rate released to the total VOC rate fro the inlet during the sorption phase) during the desorption period (> 30 h).

22 Figure caption: Fig.. Scheatic of the general ass transfer regions of a sorption process. Fig.. VOC sorption on a solid aterial Fig. 3. Discretization of the C a (0,τ) with a series of unit triangle functions. Fig. 4. A sall-scale chaber for easuring VOC sorption on a solid aterial. Fig. 5. Coparison of easured and siulated sink effects of unpainted gypsu board: (a) Ethylbenzene, (b) Benzaldehyde, (c) Dodecane. Fig. 6. A better agreeent between the odel prediction and experient can be achieved by adjusting the aterial properties (D and K a ). The results shown here are benzaldehyde sorption on unpainted gypsu board. Fig. 7. Siulated sink effect for ethylbenzene and dodecane by unpainted gypsu. Results show the percentage of the incoing VOC rate (fro the inlet air) uptaken during the sorption period (0-30 h) and the VOCs released (represented by the percentage of the VOC rate released to the total VOC rate fro the inlet during the sorption phase) during the desorption period (> 30 h).