Examining the applicability of empirical models using short ...

Research Article

Indoor/Outdoor A

irflow

and Air Q

uality

E-mail: [email protected]

Examining the applicability of empirical models using short-term VOC emissions data from building materials to predict long-term emissions

Wei Ye1,2 (), Doyun Won3, Xu Zhang2

1. State Key Laboratory of Pollution Control and Resource Reuse, Tongji University, Shanghai, China 2. School of Mechanical Engineering, Tongji University, Shanghai, China 3. NRC Construction, National Research Council Canada, Ottawa, Ontario, Canada Abstract Chamber testing is a common method to evaluate volatile organic compound (VOC) emissions from building materials. Empirical models based on short-term testing (typically less than 28 days) are frequently used to estimate long-term emissions (up to years). However, the applicability of the empirical models for long-term prediction remains unclear in practice. Four empirical models, i.e., two constant models with and without a prerequisite (M1 and M2), a power-law model (M3), and an exponential model (M4), were used to test the applicability of predicting year-long emissions using emission data that were less than one month. The diffusion-based mass-transfer model was used to generate reference emission data with random variations involved to represent measurement errors, etc. For M1 and M2, the discrepancy ratios between the constant emissions and the characteristic average emissions are quantified. For M3 and M4, an additional measure, i.e., normalized mean square error (NMSE), was adopted to statistically study the applicability of using empirical models to predict long-term emissions. The results shown that, first, the NMSE values indicate that M3 prefers slow emissions and generally performs better than M4. However, M4 performs better for predicting year-long emissions for cases with characteristic emission time of one year. Second, both M3 and M4 predict the average life-long emissions reasonably well for most scenarios. Third, while the effects of test duration are less significant for M3 than M4, the early-stage sampling points are more important for better long-term predictions. Additionally, experimental data by National Research Council Canada (NRC) were used to validate the applicability of the empirical models in year-long emission predictions, with the results similar to those from the simulated data. This paper can be used as a reference to select appropriate empirical model(s), as well as the testing duration, to simulate long-term VOC emissions from building materials using short-term testing data.

Keywords empirical model,

theoretical model,

diffusion,

chamber testing,

emissions Article History Received: 23 February 2016

Revised: 8 May 2016

Accepted: 30 May 2016 © Tsinghua University Press and

Springer-Verlag Berlin Heidelberg

2016

1 Introduction

Volatile organic compounds (VOCs) emitted from building materials in indoor environment have been extensively studied for decades (Brown et al. 1994; Weschler 2009). A substantial amount of work has been conducted, from method development for emission testing/modeling to introduction of regulation and labeling on emissions, initially to better understand the emissions and ultimately to develop the means that can reduce exposures to indoor VOCs and improve

indoor air quality (Haghighat et al. 2002; AgBB 2012; ECA 2013; Liu et al. 2013; Zhang et al. 2016).

The VOC emissions data based on chamber tests have been used in determining whether a building product meets certain labeling criteria established by various emission standards (CDPH 2010; BIFMA 2011; AgBB 2012) and in predicting long-term concentrations in a life-cycle assessment of a building material (Chaudhary and Hellweg 2014; Park et al. 2016). VOC emissions tests are typically based on a 3- to 28-day chamber test (CDPH 2010; BIFMA 2011; AgBB

BUILD SIMUL (2016) 9: 701–715 DOI 10.1007/s12273-016-0302-7

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List of symbols

a an empirical parameter used in model M3 (μg∙sb−1)b an empirical parameter used in models M2 and M3A exposed area of the material (m2) C(x, t) material-phase compound concentration at position x and time t (μg∙m−3) C0 initial material-phase emittable concentration (μg∙m−3) D material-phase diffusion coefficient (m2∙s−1) E0 initial emission factor, that pre-determined, used in model M4 (μg∙m−2∙s−1)

0E ¢ a fitted parameter used in model M4 to replace the initial emission factor E0 (μg∙m−2∙s−1) ES average emission factor during steady state (μg∙m−2∙s−1) E emission factor (μg∙m−2∙s−1) E average emission factor calculated by an empirical model, i.e., M3 or M4 (μg∙m−2∙s−1) E characteristic emission factor (μg∙m−2∙s−1) Fom mass transfer Fourier number, Fom=Dt/L2 h a lumped constant defined by Eq. (2) (m−1) hm external convective mass transfer coefficient (m∙s−1)H(qn) a lumped variable defined by Eq. (5) (m) k an empirical parameter used in model M4 (s−1) K material/air partition coefficient L thickness of the material (m) N volumetric air change rate through the chamber (s−1) Q airflow rate through the chamber (m3∙s−1) qn eigenvalues in Eq. (4) (m−1), n = 1,2,... R0 initial emission rate (μg∙s−1) R1 the ratio of the constant emission factor at 336 h E(336h), and the characteristic emission factor ER2 the ratio of the average emission factor between

72 h and 336 h, (72h) (336h)2

E E+ , and the

characteristic emission factor E

R3 the ratio of the averaged emission factor using model M3 and the characteristic emission factor E R4 the ratio of the averaged emission factor using model M4 and the characteristic emission factor E t, t1, t2 time (s) Δti sampling time (h) u a lumped constant defined by Eq. (3) (m) V volume of the air in the chamber (m3) x distance from the bottom of the slab-shaped material (m) y gas-phase compound concentration (μg∙m−3) yexp simulated gas-phase compound concentration measurement (μg∙m−3) ymax maximum simulated errorless compound concentration (μg∙m−3) β a fraction used in Eq. (15) δi simulated random error for each simulated sampling (μg∙m−3) σ standard deviation (μg∙m−3)

Abbreviations

ACH air change rate per hour AgBB German Committee for Health-Related Evaluation of Building Products, in German: Ausschuss zur gesundheitlichen Bewertung von BauproduktenASTM American Society for Testing and Materials BIFMA Business and Institutional Furniture Manufacturers Association CDPH California Department of Public Health NMSE normalized mean square error NRC National Research Council Canada OSB oriented strand board VOC volatile organic compound

2012). A short-term test is preferred in terms of practicality and cost. However, it is important to understand the long- term emissions since both labeling and life-cycle assessment aim to reduce emissions over the entire stage of a lifetime of a building product, not just for short-term emissions. Although it is well recognized that emission data should be used within the period of measurements, the models based on short-term measurements are frequently extrapolated to predict long-term emissions (Won et al. 2008). Therefore, the question would be whether short-term test results can be used to predict long-term emissions. As demonstrated by Won et al. (2008), a high level of uncertainties (up to 1000%

of prediction error) could be introduced into predicting long-term emissions.

A subsequent dilemma is to define the difference between short term and long term. To the authors’ best knowledge, there is no clear consensus on this. In the past, VOC emissions testing is usually conducted for days or up to a few weeks (Won et al. 2005), and at present, the labeling schemes for material emission testing could take up to nearly a month (28 days) (AgBB 2012; Liu et al. 2012). Thus, we could say that a 3-day duration typically represents the short-term emission and 28-day the long-term emission in material emissions tests. However, the testing duration of 28 days

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may not always represent “long-term” emissions, because it is expected that the emission process can take months or years to complete for certain VOCs emitted at very low levels (Han et al. 2012; Ye et al. 2014a). Given that approximately the first 10% of the emission duration could be considered as unsteady state (Qian et al. 2007), the unsteady-state emissions could last longer than one month. In other words, even the emission level on the 28th day of the testing may not be applicable to represent the steady-state or long-term emissions for all VOCs emitted to indoor air.

Regardless of the emission duration, the process of VOC emissions from solid building materials is usually con-sidered as internal diffusion, following the Fick’s second law. Theoretical models that use fundamental mass-transfer mechanisms such as diffusion are mainly derived with three key parameters, i.e., the material-phase diffusion coefficient, D (m2∙s−1); the material/air partition coefficient, K (—); and the initial material-phase emittable concentration, C0 (μg∙m−3) (Little et al. 1994; Xu and Zhang 2003). Typically, we can find C0, D and K ranges of (105–108) μg∙m−3, (10−9–10−13) m2∙s−1 and (102–105), respectively, for solid indoor materials (Cox et al. 2001a,b; Haghighat et al. 2002). In general, mass- transfer models have advantages over empirical models since the parameters of mass-transfer models have physical meanings (Liu et al. 2015) and, therefore, are theoretically easier to apply to different testing conditions.

Despite the existence of the more advanced modeling approach based on mass-transfer mechanisms, empirical models are still prevailingly used to predict VOC emissions due to the complexity of measuring/determining at least three key parameters involved in the theoretical models. That is, additional tests need to be conducted to obtain these model parameters of C0, D and K (Liu et al. 2013), or the current testing procedure needs to be changed to incorporate methods that can simultaneously obtain multiple key parameters (Xiong et al. 2011; Huang et al. 2013). In consequence, experimental data, in particular, on material properties (i.e., D and K) are currently limited in terms of applying the mass-transfer model (Li and Niu 2005). Liu et al. (2015) also pointed out the lack of information to describe formaldehyde emissions from composite wood products with mass-transfer models. While it is desirable to work on theoretical models that are based on mass-transfer mechanisms, it would be more practical to study and improve the prediction capacity of empirical models.

The issue associated with emission modeling is further complicated with the fact that the available literature on the topic of long-term (year-long) emissions from building materials is still rare, and only a small portion of the studies specifically focused on the legitimacy of using empirical or theoretical models to predict VOC emissions over a long period of time. A nine-month emission test was conducted (Han et al. 2012) and reported a less than 6% difference

variance to apply a source identification method for VOCs from aged materials in actual indoor environment. Both empirical and theoretical models were used to fit the data. However, one concern in the study is that using emission data alone to fit the three key parameters simultaneously is not rigorous or robust, because the solution is not unique or is extremely sensitive to small perturbations (Li 2013). To avoid multivariate regressions, more robust methods have been proposed (Xiong et al. 2011; Huang et al. 2013; Li 2013). However, if certain criteria (e.g., sampling interval) could not be met, the prediction methods would be applicable only at screening-level (Ye et al. 2014a).

Recently, Liu et al. (2015) measured formaldehyde emissions from composite and solid wood furniture for a period from 400 h to 4000 h. Liang et al. (2015) also reported formaldehyde concentrations in an actual building with temperature and RH variations for 29 months, in addition to an eighteen months’ study on VOC long-term emission record for a newly-built apartment (Liang et al. 2014). The studies provide valuable information on long-term emissions under a laboratory condition and actual building condition (Liang et al. 2015). The need still exists for more diverse experimental data on long-term emissions and discussion on the applicability of short-term data to long-term emissions.

In this paper, the applicability of empirical models based on short-term emission data to predict long-term material emissions has been investigated. Among various empirical models as reviewed (Guo 2002a), three types of empirical models, including constant, power-law and exponential models, were selected partly due to their inclusion in labeling schemes and testing standards (e.g., BIFMA and ASTM). The discrepancies were analyzed between the emission factors and gas-phase concentrations predicted by the empirical models and the true values, which were generated based on a diffusion-based model for materials that are single-layered, uniform and solid with random variations involved. Measures to improve the accuracy of long-term prediction or effects of shortening the testing duration were discussed. Additionally, experimental data, i.e., one-year-long emission data con-ducted by National Research Council Canada (NRC) with oriented strand boards (OSBs), were applied to validate the applicability of empirical models in long-term emission predictions.

2 Methodology

2.1 Diffusion-controlled emissions model

A schematic representation of a chamber for testing diffusion-controlled emissions of a solid material, which means the emission process can be considered as internal diffusion and described with Fickian diffusion, is shown in Fig. 1.

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Fig. 1 Schematic representation of a chamber for testing diffusion- controlled emissions of a solid material with description of parameters (Little et al. 1994)

Assuming D and K are independent of concentration

and C0 is uniform within the material, a diffusion-based model that can be used to predict emissions is given by Little et al. (1994). The material-phase compound concentration can be derived as Eq. (1). The convective mass transfer process was ignored in this model and, therefore, overestimation is expected for the early-stage emissions (Xu and Zhang 2003). However, the overestimation usually lasts for a short period of time (e.g., hours). From the long-term emission perspective, the overestimation of the early stage emissions is less likely to affect the total amount of the VOC that would be emitted to the air in the long run. Therefore, Little et al. (1994) is considered to be a suitable model to simulate long-term VOC emissions.

( )( )( ) ( )

( ) ( ) ( )

2 2

0 22 21

exp cos, 2

cosn n n

n n n n

Dq t h uq q xC x t C

L h uq q L u h q L

¥

=

ì üï ï- -ï ïï ï= í ýé ùï ï- + + +ï ïê úï ïî ë û þå

(1) where

( )/h Q A D K= ⋅ ⋅ (2)

( )/u V A K= ⋅ (3)

The qn’s are the positive roots of Eq. (4).

( ) 2tann n nq q L h uq= - (4)

If ( )

( ) ( )

2

22 2( ) n n

n

n n

h uq qH q

L h uq q L u h

-=

é ù- + + +ê úë û

, the theoretical

emission factor (E(t)) can be derived as

( )

( ) ( ) ( )

20

1

,( )

2 tan exp

x L

n n nn

C x tE t D

x

C D H q q L Dq t

=¥

=

=-

= -å (5)

Also, the gas-phase compound concentration is given by

( )( ) ( )0 2

1

, 2( ) expx Ln n

n

C x t Cy t H q Dq tK K

¥=

=

= = -å (6)

Since we can take Fom(t) = Dt/L2 = 2.0 as the criterion for the emissions to be approximately finished (Xiong et al. 2013), the characteristic time for the completion of emissions can be derived as t = 2L2/D. Therefore, the characteristic emission factor, which can be used to represent the average emission factor during the life time of a material, is defined as (Ye et al. 2014a)

0 02

ˆ22 /

C L C DELL D

= = (7)

2.2 Analyzing discrepancies of using empirical models

2.2.1 Empirical model selections

Four empirical models, selected from existing classification and labelling schemes for building materials, are used to evaluate the emission characteristics of materials as summarized in Table 1.

Table 1 Empirical models selected from classification and labelling schemes for building materials

Model Prediction methods References

M1 Constant model without prerequisites: ( ) constantE t = or ( ) (336h)E t E= ASTM D5116 (ASTM 2010) CS 01350 (CDPH 2010)

M2

Constant model with a prerequisite: ( )1 2( )(72h 336h) 2E t E tE t +

£ £ = , where

( )1 2

2 1

ln ln ( ) ( 0.15,0.15)ln lnE t E tb t t

-= = -

-,

(t1 = 72 h, t2 = 336 h), b is also used in the power-law model (M3)

BIFMA M7.1 (BIFMA 2011)

M3 Power-law model: (72h 336h) bE t at-£ £ = , where ( ) ( )1 1 2 2  b ba E t t E t t= = , (t1 = 72 h, t2 = 336 h) BIFMA M7.1 (BIFMA 2011)

M4 Exponential model: ( )( ) 0

0e ekt ktR t RE t EA A

- -= = = ASTM D5116 (ASTM 2010) ASTM D6670 (ASTM 2013)

Note: For models M2 and M3, t2 = 168 h (7 days) is originally recommended by BIFMA mainly to reduce the testing cost. However, t2 = 336 h (14 days) was used in this study for the following reasons: (1) it could be better to test the applicability of M2 by running the simulation to 14 days because it is more likely to achieve steady state at 336 h; (2) it could also be potentially useful to set t2 to 336 h for the comparison of M1 and M2; (3) according to Section 3.1.2, the applicability of M2 is not favorable even with t2 = 336 h, and the applicability would be worse if t2 = 168 h was used.

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2.2.2 Discrepancy ratio for average emission factors predicted with empirical models

(1) Model M1 (constant with no prerequisite)

A constant model (see models M1 and M2 in Table 1), which is the simplest of all empirical models, is still widely used to indicate an emission level. It assumes that the emission factor does not change significantly after a certain period of time. For example, the emission rate at 336 h (14 days) or the average emission rate between 72 h (3 days) and 336 h (14 days) that is considered to have reached steady-state, as recommended by CS 01350 (CDPH 2010) can be used to represent the constant emissions.

This assumption can be tested by comparing the constant emission factor at 336 h and the characteristic emission factor that is expressed as Eq. (7).

1(33 h)

ˆ6E

ER = (8)

R1 that is far from unity illustrates there is a discrepancy between the average emission factor over the characteristic time and the emission factor at 336 h.

However, it should be noted that R1 can also be expressed as the ratio of the constant emission factor at 336 h and the average emission factor during steady state (Es) to compare the two emissions from a steady-state perspective (Ye et al. 2014b). For simplicity, E rather than Es was adopted in deriving R1 in this paper.

(2) Model M2 (constant with prerequisite)

For BIFMA M7.1 (BIFMA 2011), model M2 serves as a supplementary for model M3. The idea is to use a constant emission factor for cases where the emission factor changes slowly, which can be represented with small b in a power-law model, e.g., b = (−0.15, 0.15). This can also mean that the emissions reach steady state in a relatively short period time (e.g., 72 h), satisfying the following conditions:

( ) ( )( ) ( )

m 2

1 2

336 3600 0.2

ln ln0.15 0.15

ln 336 3600 ln 72 3600

DFoL

E t E t

ì ´ïï = ³ïïïí -ïï- £ £ïï ´ - ´ïî

(9)

or

( )( )

2 7

1

2

/ 1.65 10

1.26 1.26

D LE tE t

-ì ³ ´ïïïïíï- £ £ïïïî

(10)

According to Eq. (10), besides general parameters specified in Section 2.1, D and K ultimately determine if the criterion of b = (−0.15, 0.15) is met. Therefore, the

relationship of D, K and b was investigated through simulations (see Section 2.2.3).

R2, which is shown in Eq. (11), was used to test the discrepancy of the average emission factor between 72 h and 336 h and the characteristic emission factor once the criterion for b is fulfilled.

( )2

72h (336h)ˆ2

E ER

E+

= (11)

Besides general parameters for chamber testing such as V, Q, A and L, both R1 and R2 are functions of D and K.

(3) Models M3 and M4

M3 and M4 represent a popular form of power-law and exponential model that are used by BIFMA (2011) and ASTM (2010), respectively. M3 is a pure data-fitting model with parameters bearing no physical meanings (Guo 2002a). M3 utilizes the emission rate at 72 h and 336 h and no regression technique is needed to determine the two emission model parameters, i.e., a and b. However, it is better to determine a and b with regression when more than 2 data points are available. Therefore, a and b were determined by a regression method, in which two parameters need to be fitted simultaneously.

Equation (12) was derived to compare the average emission factor using an empirical model (in this case, M3), E , and the characteristic emission factor, E . Because E represents the life-time average emission factor, E was also determined using the same time span (t = 2L2/D). The discrepancy ratio of the averaged emission factor using model M3 and the characteristic emission factor, R3, can be expressed as follows:

( )( )

22 /2

03

02 1

ˆd / 2 /

/ 21 2

1

t L Db

b

o

at t L DR

C D La L

C L b D

EE

=-

- +

= =

=- +

ò( )

( )( )( )

(12)

R3 needs to get closer to 1 to indicate a good level of prediction.

M4 is widely used since it is built on the theoretical consideration that the emission rate is proportional to the pollutant mass remaining in the source (Guo 2002a). Also, it can lead to a simple solution when it is integrated for a time period close to infinity, as shown in calculating the life-time exposure of a VOC emitted from a building product (Park et al. 2016). Since the initial emission factor, E0, is typically determined by the sampling data at early stage or from a product formulation, only one empirical parameter needs to be fitted for M4. The main purpose of putting the initial emission factor into the model is to reduce the

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complexity of parameter fitting as well as to make the model look more “inherently legit” to some extent by providing a physical meaning to E0. However, two parameters (E0 is taken as a variable, marked as 0E ¢ ), instead of one, could enhance the flexibility of the exponential model, leading to better fitting results. Therefore, M4 is also fitted with two parameters. R4, which is similar to R3, is used to evaluate the ratio of the average emission factor using model M4 and the characteristic emission factor.

( )( )

2

2

2 /2

00

40

20

e d / 2 /

/ 2ˆ

1 1 e

t L Dkt

kLD

o

EE

E t L DR

C D LE

C L k

=-

-

¢= =

¢= -

ò( )

( )( )( )

(13)

Both R3 and R4 are the function of D, K and L, as well as the parameters of empirical models.

Determining E in Eqs. (12) and (13) requires a known D value that may be difficult to determine in practice from an emission test conducted with a purpose of using an empirical model. However, Eqs. (12) and (13) provide a way to thoroughly investigate the suitability of the empirical model compared to the mass-transfer model at a life-long emission scale. Therefore, R3 and R4 were calculated for simulated data with known D’s, but not for experimental data.

2.2.3 Procedures to determine the ratios of averaged emission factors with potential measurement errors involved

The true values of emission factors and chamber concentrations were generated based on Eq. (5) and Eq. (6), respectively. Among the parameters required, general parameters for chamber testing such as V, Q, A and L were set to the values that match the test conditions of two emissions tests (material ID: OSB6a and OSB6b) in the NRC database (Won et al. 2008) (Table 2). Because C0 is not coupled with D and K in Little et al.’s model (Little et al. 1994), C0 has no impact on the fitting accuracy. Therefore, for simplicity, C0 was assumed to be 106 μg∙m−3 for all cases. On the contrary, various combinations of D and K were used to cover the range of 10−13 – 10−9 m2·s−1 and 102 – 106, respectively, which are typical for solid indoor materials (Cox et al. 2001a,b; Haghighat et al. 2002). A value of D was selected so that the range of

10−13 – 10−9 m2·s−1 could be evenly covered on a logarithmic scale. For a chosen D, K was randomly selected within 102 – 106 using the Monte-Carlo method by assuming an equal distribution of K within the range. Selection of K was repeated at least 1000 times. Then, R1 was calculated for each combination of D and K. Additionally, L was varied in five levels for a given set of D and K to test the effects of material thickness (see Section 3.1.1). Since not all sets of D and K meet the requirements for M2, R2 was calculated for a smaller set of D and K (see Section 3.1.2).

More steps were involved to determine R3 and R4. Step 1, D and K were categorized into 16 groups that cover one order of magnitude of each parameter (e.g., D~10−12 – 10−11 m2·s−1 and K~103 – 104). The reason for this grouping is that the shapes of an emission curve used to fit the empirical models do not vary considerably for both D and K within each range. Therefore, each group could have unique characteristics such as fast/slow decay curves. For example, fast diffusion (high D) and small resistance (small K) would result in a fast decay curve, while slow diffusion (low D) and big resistance (big K) would produce a slow decay curve. The applicability of an empirical model could be different for different shapes of emission curves. Then, D and K were randomly selected within each category using the Monte- Carlo method with more than 1000 times repetition. Step 2, for a given set of D and K, the true values of chamber concentrations were generated based on Eq. (6) for the sampling times in Table 2. Step 3, to account for potential measurement errors, the chamber concentrations were further varied using the following method. Additive, uncorrelated, and normally distributed random errors were assumed for each gas-phase concentration measurement (yexp) or

( ) ( )exp iy t y t δ= + (14)

δi lies within the range of [−2.576σ, 2.576σ] with 99% confidence level, where the standard deviation σ is given by Eq. (15) (Li and Niu 2005):

maxσ β y= ⋅ (15)

β ranges from 0 to 10%. Equation (15) was adopted to account for the maximum variations based on the emission intensity. Steps 1 and 3 were specifically designed to cover the effects of the variations in D, K and measurements on

Table 2 Testing conditions for material ID OSB6a and OSB6b in the NRC database

A 0.200 m2 V 0.048 m3

L 0.0145 m N 1.04 h−1

Sampling time Δti

(30 samplings)

0.98 h, 2.7 h, 11.5 h, 23.5 h, 35.5 h, 47.6 h, 71.8 h, 100.7 h, 143.6 h, 149.5 h, 154.9 h, 160.9 h, 196.1 h, 239.0 h, 340.4 h, 479.2 h, 677.5 h, 892.4 h, 1346.0 h, 1899.7 h, 1924.9 h, 2547.7 h, 3098.8 h, 3888.1 h, 4608.8 h, 4894.6 h, 6628.4 h, 6866.2 h, 8140.1 h, 8760.1 h

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R3 and R4. This is an alternative to a conventional sensitivity analysis, which requires a complex calculation procedure since the parameters of the empirical models depend on D and K.

Step 4, short-term emission factors, for which the test period varies and is typically less than one month, i.e., 0 – 3 d / 7 d /14 d /28 d, were obtained by converting gas-phase compound concentrations based on the mass balance shown in Eq. (16). It should be noted that the determined first emission factor, E(t1), may be smaller than the second emission factor, E(t2), because y(t=0)=0 and it takes time for the chamber concentration to increase. Therefore, to get a better fit of M3 or M4, E(t1) may need to be excluded. The importance of capturing the maximum emission factor is discussed later (see Section 3.1.3). Step 5, model parameters for M3 and M4 were fitted and the empirical models were used to predict long-term (year-long, i.e., 2nd month – 12th month) emission factors (or gas-phase concentrations). Step 6, comparison of the emission factor predicted by the empirical and theoretical model can be performed based on R3 and R4.

d ( ) ( )dy tV A E N V y t

t= ⋅ - ⋅ ⋅ (16)

2.2.4 Procedures to determine the overall discrepancy based on discrete data points

In addition to the discrepancy ratio (R1 to R4) that is based on the emission factor averaged over a life-time of a material, the applicability of a model can also be assessed for discrete data points. This is relevant for M3 and M4 (both determined by a regression method) since they are meant to reproduce the emission characteristics along with time. Among various tools to assess model performance (ASTM 2014), the normalized mean square error (NMSE) was adopted to evaluate the overall prediction capability of M3 and M4. NMSE is calculated as the average of the squared differences between the true and predicted value, which is subsequently divided by the average of true values and the average of predicted values (ASTM 2014). NMSE will have a value of 0 when there is perfect agreement for all pairs of the predicted year-long (2nd – 12th month) gas-phase concentrations based on empirical models and the observed (simulated) gas-phase concentrations. NMSE will tend toward higher values as the pairs differ by greater magnitudes. NMSE of 0.25 or lower is considered to indicate the adequacy of a model (ASTM 2014).

2.2.5 Testing with experimental data

To further validate the applicability of the empirical models (i.e., M3 and M4), experimental data were also used. The data were selected from the NRC database with material ID

OSB6a and OSB6b that were tested for ~ 1 year in 50-L chambers. The difference between two specimens was whether the specimen was cut from a corner (OBS6a) or a center (OSB6b) from a large panel of oriented strand board (14.5 mm in thickness / T&G Sub-Floor). Sample dimensions and chamber configurations are shown in Table 2. Air samples were taken on 2,4-dinitrophenylhydrazine (DNPH) cartridges for carbonyl compounds and sorbent tubes for other VOCs, analyzed by a high performance liquid chromatography and a thermal desorption-gas chromatography-mass spectrometry, respectively (Won et al. 2005, 2008). A total of 59 and 58 VOCs were detected in OSB6a and OBS6b from both methods, respectively. Since the applicability of using an empirical model to predict long-term emissions for a specific group of VOCs (i.e., aldehydes) has been conducted by Won et al. (2008), this paper will be focusing on validating the applicability of the model for more diverse compounds based on theoretical and statistical discrepancies derived in the previous sections.

Similar to the procedures described in Section 2.2.3, it also took four steps to validate the applicability of empirical models using experimental data. First, both the short-term and long-term experimental data (gas-phase compound concentrations) were obtained; Second, the emission factors were obtained from the short-term concentration data; Third, an empirical model was used to fit the emission factors; Fourth, the long-term gas-phase concentrations were predicted using the fitted model and compared with the long-term experimental data. Detailed results using the experimental data of OSB6a and OSB6b to validate both the power-law and exponential model can be found in Section 3.2.

3 Results and discussion

3.1 Examining the applicability of empirical models

3.1.1 Model M1 (constant with no prerequisites)

Figure 2 shows the discrepancy ratio (Eq. (8)) for M1 that was used to predict emission levels for solid materials. The error bars are standard deviations of R1 which were caused by different K values. Since L has an impact on the emission factor (and also Fom), several levels of L (L ~10−3 – 10−1 m) are also added into Fig. 2 to illustrate the effects of L on R1.

As shown in Fig. 2, R1 value depends on diffusion coefficient, D, and material thickness, L. Under the physical testing condition in Table 2 (e.g., L = 0.0145 m), the emission factor at 336 h, E(336h), would overestimate the characteristic emission factor, E , during the long-term emission unless D is approximately greater than 10−10 m2·s−1. For thicker materials, R1 tends to increase as it takes more

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Fig. 2 Discrepancy ratio between the emission factor at 336 h (model M1) and the characteristic emission factor

time to reach steady state under the same D value and, therefore, emission factor at 336 h tends to be closer to the emission factor at time zero. On the contrary, E(336h) would underestimate E with bigger D and/or thinner L, which would boost the emission process. It is difficult to predict an exact combination of D and L that produces an accurate estimation of the average emissions since there are numerous possibilities depending on material characteristics (e.g., thickness). Despite this disadvantage, the constant model still has its value for its simplicity and, possibly, low cost of testing. If we consider overestimation is better than underestimation, the constant model has a better chance to predict emissions from a thicker material with a small diffusion coefficient.

There are two more noteworthy observations. First, the effect of K is not significant throughout the whole range compared to that of D or L. Second, due to the fact that the Y axis is on a logarithmic scale to show a wide range of R1

better, it seems that the relative variations due to K are bigger

with bigger D for a particular thickness. However, the absolute variations reach a peak when D is around 1.7×10−12 m2·s−1. And the absolute variations tend to be smaller when D is either higher or lower than 1.7×10−12 m2·s−1. These observations are reasonable because K would only significantly affect the early stage emissions, i.e., Fom = Dt/L2 < 0.01 (Ye et al. 2014a), which means the effect of K on emissions at 336 h can be considered marginal for D ≥ 1.7×10−12 m2·s−1 (under the condition of t = 336 h and L = 0.0145 m). When D < 1.7×10−12 m2·s−1, the emissions are slow and the effects of K on the emissions at 336 h would be inherently negligible since the main reason for slow emissions is the low D.

3.1.2 Model M2 (constant with a prerequisite)

Because the prerequisite condition (–0.15<b<0.15) would not be fulfilled for some materials, the applicability of the prerequisite condition of M2 is first illustrated in Fig. 3(a), in which the circles and triangles mean whether the prerequisite condition can and cannot be fulfilled, respectively, using the test conditions in Table 2.

Figure 3(a) shows that the prerequisite condition is more likely to be fulfilled for VOCs with bigger resistance (bigger K) and faster diffusion (bigger D) for that the emission factor needs to reach steady state towards 72 h and 336 h of sampling times (see Section 2.2.1). The emissions with big gas-phase resistance (especially with fast diffusion) usually fall in the category of external-controlled emissions because the limiting factor for emissions is more likely to be in the gas-phase (although the external convective mass transfer coefficient, hm, is beyond the scope of this paper, gas-phase resistance is often referred to hm. However, compared to D, K is more of a gas-phase resistance as well). On the other hand, small gas-phase resistance and slow diffusion emissions are more likely to be internal-controlled (diffusion-controlled)

Fig. 3 Applicability of model M2 examined for multiple combinations of D and K

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emissions, for which the dominating resistance would be in the material phase (D). Therefore, it can be concluded from Fig. 3(a) that the prerequisite condition is difficult to meet for VOC emissions, because the emission curve of VOCs would not be steady between 72 h and 336 h with smaller K (i.e., the decay curve would be steeper) or smaller D (i.e., the time to reach steady state would be longer than 336 h). Although it is theoretically feasible to enlarge the area that fulfills the prerequisite by increasing A and L and decreasing N and V, it is not always practical to get different chamber configurations and sample dimensions.

Once the prerequisite condition is accomplished, the discrepancy ratio between the averaged emission factor at 72 h and 336 h and the characteristic emission factor, R2, can also be quantified (Fig. 3(b) with the original general parameters in Table 2). It shows that even after meeting the criterion, the averaged emission factor at 72 h and 336 h is still expected to overestimate the characteristic emission factor when D is smaller than 3×10−10 m2·s−1. Overall, R2 values tend to be smaller than R1 values since R2 is based on the assumption that the emission is steady at 72 h and 336 h, which makes the emission factor at 72 h and 336 h is closer to the averaged emission factor.

3.1.3 Model M3 (power-law model)

The discrepancy ratio and NMSE involved with M3 to predict long-term emission factors are shown in Fig. 4, which was generated with the procedures in Sections 2.2.3 and 2.2.4. The first 28 days of data were used to fit M3. And the fitted M3 was used to predict year-long emissions with

the original sampling intervals used in the test of OSB6a and OSB6b. The mean values and the standard deviations (error bars) of R3 and NMSE are summarized for 16 groups of D and K. The idea of error bars is adopted in Fig. 4 to show the expected variations of R3 and NMSE values caused by various D’s, K’s and simulated variations involved in gas-phase concentration data used to fit the model.

Figure 4 provides a comprehensive picture for the applicability of using a power-law model to predict long-term emissions. First, the criterion of NMSE of 0.25 or lower is mostly met by the cases with slow emission, i.e., slow diffusion (low D) or big resistance (big K). On the other hand, the prediction of M3 is not good (NMSE > 8) for cases with high D and small K. This can be explained by the fact that the power-law model favors a relatively slow decay curve in terms of predicting long-term emissions. A fast emission process, i.e., a case with high D and small K, produces a sharply decaying emission factor during the short-term emissions and much lower emissions in a slowly decaying pattern during the long-term emissions. Therefore, most of the predicted concentrations for long-term emissions with power-law models would be too big compared to the true values of the simulated concentrations with high D and small K.

However, according to Fig. 4, NMSE values seem to be improved for some fast emission scenarios when random measurement errors (β) are increased. This is reasonable because the variations can provide a chance for the simulated concentration to be corrected from either being too big or too small.

Fig. 4 Applicability of model M3 using 28 days of data to predict long-term (2nd month to 12th month) emissions with original sampling intervals

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Second, R3 values in Fig. 4 show the adequacy of predicting the average life-long emission factor ( E ) using the power-law model. R3=1 indicates a good prediction of E for life-long emissions. It can be concluded that R3 values were approximately 1 ( E ≈ E ) for most cases with the exceptions that the E values would be either one-order-of-magnitude- bigger than E (for high D and small K, the power-law model overestimated the long-term emissions) or one-order-of- magnitude-smaller than E (for high D and big K, the power-law model underestimated the long-term emissions). That is, R3 in Fig. 4 indicates reasonable agreements between the mass-transfer model and the power-law model in terms of life-long emissions for slow diffusion process (D < 10−11 m2·s−1). Another issue is that, in all 16 categories (sub-figures), the trends of R3 are insensitive to random variations of the simulated data for a given D and K. This is likely due to the fact that the discrepancy ratio is based on the emission factor averaged over a long-time period.

Figure 4 examines the applicability of M3 using relatively “long” short-term emission data (28 days) to study its long-term prediction capability. However, in practice, the cost of an emission test can be lowered if the testing time can be reduced while maintaining a fairly reasonable confidence for predicting long-term emissions. Therefore, the applicability of M3 was further investigated using the 3, 7 or 14 days of data to predict long-term emissions. Since the patterns in all 16 scenarios are similar, one scenario (D ~10−12 to 10−11 m2·s−1; K ~103 to 104) was taken as an example (Fig. 5(a)). Additionally, it is expected that the shape of the fitted M3 would depend on the sampling intervals at early stage. Therefore, the effects of the first sampling time on the fitting results were investigated. In addition to the original ~1 h as the first sampling time, 0.5 h and 2.0 h were taken for comparison and the results are shown in Fig. 5(b).

Interestingly, it can be found from Fig. 5(a) that using data with longer emissions within the first 28 days would

not result in better prediction of long-term emissions in terms of both R3 and NMSE values, based on the fact that all four lines are overlapping. This indicates that, if the prediction capability is judged based on R3 and NMSE values, testing a material for 3 days appears to be long enough for a diffusion-controlled emission material to get a confident prediction of long-term emissions when a power-law model is used.

Figure 5(b) shows that NMSE values considerably depend on the first sampling time. In this case with the second sampling time at 2.7 h (see Table 2), 2 h appears to be a better choice as the first sampling time compared to 0.5 h or 1.0 h (see Fig. 5(b)). However, caution should be taken to interpret the results. That is, it doesn’t mean that 2 h would always be the best choice as the first sampling point under all test conditions. This is because the chamber concentrations tend to change drastically with a peak at early stage, the shape of which depends on the emission rate and chamber air change rate. Also, it takes at least first two samplings to determine the highest emission level (Eq. (16)). E(t1) needs to be excluded if E(t1)< E(t2). Otherwise, the fitting results would be compromised because mathematically, E(t = 0) = +∞, for a power-law model. To obtain a good fit of the power-law model, the determined emissions during the time period between t1 and t2 need to be high enough. However, it can be difficult to capture the accurate shape of the early-stage emission curve by only two samplings. On the other hand, it may not be practical to add more sampling points during the first few hours of the testing. In short, Figs. 5(a) and 5(b) indicate that, although it may be difficult to plan in advance, capturing the highest average emission level at initial stage of emission is more important than extending the testing period to improve the model predictability of a power-law model. The same conclusion can be made in the analysis with other ranges of D and K than the example range (D ~10−12 to 10−11 m2·s−1; K ~103 to

Fig. 5 Effects of test duration and sampling intervals for early stage emissions on the applicability of model M3 to predict long-term emissions

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104 in Fig. 5), although the results are not shown in this paper. With the limited simulation cases employed in this paper, it is difficult to generalize how the predictability of M3 would be affected by different initial sampling schedules. More research is recommended to understand the issue. However, the initial sampling should be done within the first hours when the ACH is around 1 h−1. Theoretically, the time for the peak concentration to occur after the material being placed in the chamber is approximately at (1/ACH) h, because the average emission rate during the first (1/ACH) h is the highest.

3.1.4 Model M4 (exponential model)

Figure 6 summarizes the applicability of using an exponential model (M4) to predict long-term emissions, which was produced following the similar procedure described in the previous sections. Both 0E ¢ and k in M4 were fitted as variables. Error bars are not included for NMSE in some of the sub-figures when the standard deviation is larger than the mean value of NMSE, which indicates that extremely high NMSE values were collected.

At least two conclusions can be made from Figs. 4 and 6. First, the similarity to R3 is that R4 was not sensitive to variations associated with the simulated data for a given D and K. However, the difference from R3 is that R4 would be close to 1 for cases with fast diffusion and small resistance, while R4 would be smaller than 1 for most cases where diffusion is slow or resistance is high. This means the exponential model can predict the average life-long emission factors for materials with confidence for all emission scenarios

with high D or low K. Second, although the NMSE values would get worse for most cases when variations increased, M4 generally showed the best performance with D ~ 10−11 to 10−10 m2·s–1, for which the characteristic emission time would be approximately one year (equivalent to the time scale used in NMSE determinations). And NMSE values tend to be bigger with M4 than with M3 for a given set of D and K. This indicates that power-law model is generally preferred to exponential model for predicting long-term emissions. However, both M3 and M4 would result in high NMSE values for fast emissions with small gas-phase resistance. This is because the emission curve for fast emissions would be decaying rapidly and the characteristic emission time would be approximately only a few days to a few weeks. Therefore, neither power-law nor exponential model would be adequate to predict long-term emissions under these conditions.

Similar to Fig. 5(a), the applicability of M4 for short- term data was also investigated using the 3, 7 or 14 days of data to predict long-term emissions. The scenario with D ~10−12 to 10−11 m2·s−1 and K ~103 to 104 was taken as an example (Fig. 7(a)). It can be seen that “longer” short-term data sets are preferable for predicting long-term emissions with M4. That is, poor NMSE values would be expected even for using 14-day data, not to mention 3- or 7-day data. The R4 values are also closer to 1 when using “longer” short-term data, although the difference caused by different short-term data sets is not as big as that for NMSE. This is possibly due to the fact that R4 is the term averaged over time.

Fig. 6 Applicability of model M4 using 28 days of data to predict long-term (2nd month to 12th month) emissions with original sampling intervals

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Since the initial emission factor (E0) is usually pre- determined in practice, the effects of estimation of E0 were tested with the results in Fig. 7(b), in which E0 in M4 was pre-determined using the first data point and only k was fitted. As expected, determining E0 in advance would worsen the agreement between predicted and simulated year-long concentrations (higher NMSE values). On the contrary, the disadvantage of using the pre-determined E0 was not pronounced with R4, which happened to be close to 1- using 7- or 14-day data. However, by increasing the test duration, R4 values would change from being smaller than 1 to being bigger than 1, suggesting that the best shape of an exponential model was not obtained. This is because E0 was pre-determined, resulting in either underestimating or overestimating the life-long emissions.

3.2 Examining the applicability of the empirical models using experimental data

The experimental data from OSB6a and OSB6b measured for up to 28 days (~ 700 h) were used to develop models M3 and M4 (ran twice, one for 0E ¢ was fitted and one for E0 was pre-determined). Figrues 8(a) and (b) are to illustrate the model fitting process according to Section 2.2.5 using hexanal as an example. The models developed based on 28 days (Fig. 8(b)) were used to predict the 1-year data of hexanal in Fig. 8 (a). The NMSE values indicate that the power-law model (M3) is preferable to the exponential model (M4).

The analysis was extended to all VOCs emitted from OBS6a and OSB6b. The resulting NMSE values are provided in Figs. 8(c) and (d) to indicate the agreement between experimental and predicted long-term gas-phase concentrations. Each symbol represents one VOC emitted

from OSB6a or OSB6b and the X axis of vapor pressure is applied only to distinguish different VOCs. The presentation is not meant to derive any relationship between vapor pressure and NMSE values. In Fig. 8(c), fitting results using 3-day and 7-day data are also added for comparison. R3 and R4 values are not included in Fig. 8, since the true values of C0 and D for the detected VOCs are unknown and only the ranges of D (10−11 to 10−12 m2·s−1) on a screening level are reported (Ye et al. 2014a).

When using 28-day experimental data, about 4% of VOCs (OSB6a: isopropyltoluene, formaldehyde and butanal, OSB6b: camphene and formaldehyde) meet the criterion of NMSE of 0.25 or lower in Fig. 8(c), which indicates the performance of M3 was adequate for predicting long-term emissions for these VOCs. The majority of NMSE values (88.9%) were below 8, which corresponds to the difference between the predicted and experimental data of one order of magnitude. Therefore, it can be roughly said that the power-law model based on 28-day data can predict the year-long emissions within the accuracy of one order of magnitude for most VOCs in OSB6a and OSB6b. On the other hand, about 1% of VOCs (OSB6b: butanal) meet the same criterion for M4 and only 22% of the NMSE values were below 8. Overall, M3 seems to be a better tool to predict year-long emissions.

For the power-law model (Fig. 8(c)), using 3-day, 7-day or 14-day data (14-day data were not shown due to too many overlaps) resulted in 74.4%, 83.8% and 88.9% of the NMSE values that were below 8, respectively. The results are similar to those of using 28-day data. Although 14-day testing seems equivalent to 28-day testing in this case, the results indicate that 3-day or 7-day testing would also be long enough to provide the long-term prediction capability similar to that of 28-day test.

Fig. 7 Effects of data length and initial emission factor (E0) on the applicability of model M4 to predict long-term emissions

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4 Summary and conclusions

This paper investigates the adequacy of using empirical models to predict long-term emissions with short-term data that are typically less than one month. Four empirical models, i.e., (1) constant with no prerequisites, M1; (2) constant with a prerequisite, M2; (3) power-law model, M3; and (4) exponential model, M4, were selected. This research uses a mass-transfer model based on diffusion to generate reference data for comparison. The key parameters for the mass-transfer model were selected randomly using the Monte-Carlo method. Additionally, random errors were further introduced to account for potential errors that can be caused by measurements or other mechanisms.

For both constant models, the discrepancy ratios between the predicted and simulated emission factors, i.e., R1 and R2, were derived. While there was a narrow range of D that led to R1 ~ 1, overestimation was more prevalent for the constant model, in particular, for fast diffusion (high D). Emission

sources with big resistance (big K) and fast diffusion (high D) were shown to have greater chances to fulfill the prerequisite condition of M2 with steady emission factors between 72 h and 336 h. However, the discrepancy ratios for M2 (R2) could still be far from 1. As expected, this indicates that overestimation could be expected if constant models were used.

The discrepancy ratios of average life-long emission factor ( E ) and the characteristic emission factor, i.e., R3 and R4, were derived for the power-law (M3) and exponential (M4) model. NMSE values were also adopted to evaluate the overall adequacy based on individual data points. Several conclusions were made based on these parameters. First, when year-long emissions are of interest, M3 favors slow emissions, while M4 favors emissions with the characteristic emission time of one year that is roughly equivalent to the time used in the NMSE determinations. Overall, M3 was more accurate than M4 to predict year-long emissions using short-term data. Second, by testing the life-long average

Fig. 8 Applicability of M3 and M4 using 28 days of experimental data (OSB6a and 6b) to predict long-term emissions

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emissions predicted by the empirical and mass-transfer models using R3 and R4, both M3 and M4 resulted in good agreements for most cases. However, M3 prefers slow emission scenarios and M4 favors fast emissions. Third, testing a material for 3 or 7 days appears to lead to long- term predictions with similar confidence levels to those from 28-day testing if M3 is applied. However, a “longer” short-term test is preferable for M4. Also, the early-state samplings can pose significant impacts on the applicability of both M3 and M4 because the accuracy of both models is affected by whether the early high emissions are captured or not. This is expected to be particularly important for M4 when the pre-determined initial emission factor is used as a parameter.

Additionally, the validation with the measured chamber data conducted by National Research Council Canada (NRC) shows that the long-term prediction capability of M3 could be within the accuracy of one order of magnitude for most VOCs emitted from two OSB specimens. On the other hand, M4 had less favorable prediction capability than M3 with larger NMSE values in general.

Although the conclusions on the applicability of the power-law model and the exponential model based on the simulated data generally agree with those based on experimental data, a bigger question would be whether it is feasible to assume that the emission characteristics and/or emission mechanisms do not change over time and, therefore, the long-term emissions can be predicted with short-term data. It was shown that the empirical models based on 3-day to 28-day data can predict reasonably well the year-long emissions simulated with a mass-transfer model. However, if the diffusion process changes over time possibly due to the changes in material characteristics (e.g., change in diffusion coefficient) and/or the emission process is associated with secondary emissions based on chemical reactions that are triggered by environmental condition changes (e.g., hydrolysis due to water) during the usage of a material, using a short- term model to predict long-term emissions may not be reasonable. More research is recommended to understand the emission mechanisms that might change over time and their impacts on long-term emissions.

Acknowledgements

The material emissions database by National Research Council Canada (NRC) is the outcome of two consortium projects, i.e., CMEIAQ I and II. The authors would like to thank the members of the consortiums and the technical advisory committees. This project is also funded by the National Natural Science Foundation of China through Grant No. 21507102 and China Postdoctoral Science Foundation through Grant No. 2015M570386.

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