Online supporting information for the following article published in Indoor Air
DOI: 10.1111/ina.12198
Understanding and Controlling Airborne Organic Compounds in the
Indoor Environment: Mass-transfer Analysis and Applications
Yinping Zhang1,*, Jianyin Xiong2, Jinhan Mo1,Mengyan Gong1, Jianping Cao1
1-Institute of Built Environment, Tsinghua University, 100084, Beijing, China
2-School of Mechanical Engineering, Beijing Institute of Technology, Beijing 100081,
China
*Corresponding author. E-mail: zhangyp@tsinghua.edu.cn
Table S1. List of some representative works on mass transfer on characteristics of
emissions of airborne organic compounds from indoor materials.
Works
Scenario features, solving methods, limitations and comments
Problem type 3.1.1: Describe or estimate emission process characteristics.
The problem studied is defined as the Little problem for convenience
in the present paper and features: Single-layer homogeneous material
with one surface emitting; well-mixed chamber air; Cin, Ca (t=0)=0;
constant C0, D and K; hm is infinite; one-dimensional mass transfer;
equilibrium between the
contaminant concentrations in the
air/material interface.
Little et al. (1994)
Fully analytical solution of C(x, t), m  t  and Ca(t) by using a variable
separation method.
Overestimates early stage emissions due to the assumption that hm is
infinite.
Seminal work in modeling indoor organic compound source/sink
characteristics.
Yang et al. (2001b)
The Little problem except that hm is not considered infinite.
1
Numerical solution for 3D convective mass transfer in air and 1D mass
transfer for internal diffusion and partition at the material/air interface.
The Little problem except that hm is estimated using convective mass
transfer correlations.
Huang and
Numerical solution based on a finite difference method and fully
Haghighat (2002)
analytical solution for C(x, t), m  t  and Ca(t) under the condition that
Ca(t) << Ca(x=L, t)/K, which is not always applicable.
Emission/sorption between a double-layer material and indoor air.
The model allows non-uniform initial material-phase concentrations in
Kumar
and
Little
(2003a)
each of the two layers and a transient influent gas-phase concentration.
Not fully explicit analytical solution of C(x, t), m  t  by using
Laplace transformation.
Assuming that hm is infinite.
Diffusion-controlled porous material with one surface that emits/absorbs
VOCs to/from the air.
A generalized sink model that allows for a non-uniform initial material
Kumar
and
(2003b)
Little
phase concentration and a transient influent gas phase concentration.
Not fully explicit analytical solution of C(x, t), m  t  by using
Laplace transformation.
Assuming that hm is infinite.
Murakami
et al. (2003)
Porous material with one surface that emits/absorbs VOCs to/from the
air.
Numerical solution using CFD.
The Little problem except that hm is not considered infinite, Cin(t),
Ca(t=0) are not necessarily zero.
Fully analytical solutions of C(x, t), m  t  and Ca(t) if Cin(t) and Ca(t=0)
Xu and Zhang
are constant by using Laplace transformation.
(2003)
Not fully explicit analytical solution of C(x, t), m  t  and Ca(t) that
requires a finite difference method if Cin(t) is time-dependent or nonzero
Ca(t=0).
Deng and Kim
Same as that of Xu and Zhang (2003) except that Cin(t=0) and Ca(t=0)
(2004)
are zero; air exchange rate of chamber.
2
Fully explicit analytical solutions of C(x, t), m  t  and Ca(t) by using
Laplace transformation which are quite convenient to use.
Same as those of Xu and Zhang (2003) except that C0(x,t=0) is not
Xu and Zhang
constant but is a function of x.
(2004)
Not fully explicit analytical solution of C(x, t), m  t  and Ca(t) and
requires a finite difference method to calculate from initial conditions.
Zhang and Niu
(2004)
Multiple multi-layer homogeneous materials coexisting with each other
acting either as a source or a sink.
Numerical solution using single-zone method.
Porous material with one surface that emits/adsorbs VOC to/from
well-mixed air by considering primary and secondary source and sink
effects.
Lee et al. (2005)
Not fully explicit analytical solution of C(x, t), m  t  and Ca(t), and may
require a finite difference method to calculate from initial conditions.
So-called multi-phase model.
Single-layer homogeneous material with one surface that emits SVOC
(DEHP) to well-mixed air.
Not fully analytical solution of C(x, t), m  t  and Ca(t).
Xu and Little (2006)
Same as those of Xu and Zhang (2003) except for considering the
sorption of SVOCs on interior chamber surfaces.
It may overestimate early stage emissions due to the assumption that hm
on sorption surfaces is infinite.
Single-layer homogeneous material with one surface that adsorbs VOC
from well-mixed air
Deng et al. (2007)
Includes time-dependent Cin.
Fully analytical solution of C(x, t), m  t  and Ca (t) by using Laplace
transformation.
Single-layer homogeneous material with one surface emitting, non-well
Deng and Kim
(2007)
mixed air, a typical Korean apartment unit with different ventilation
scenarios, ignoring adsorption/desorption of VOCs to/from other
building materials; Ca(t=0) is zero.
Numerical solution using 3-D CFD model.
Hu et al. (2007)
Arbitrary layer homogeneous material with two surface emissions to
3
well-mixed air.
C0, D and K of each layer are constant.
For each surface, hm is estimated using a convective mass transfer
correlation; C0 (x,t=0) is not constant but a function of x.
Not fully explicit analytical solution of C(x, t) for each layer, m  t  for
each surface and Ca(t) is obtained by Laplace transformation that
requires a finite difference method to calculate from initial conditions.
Multi-layer homogeneous materials with one surface emitting, poorly
mixed air, a typical small office room with different ventilation scenarios
(sometimes with an air cleaner), considering sorption of VOCs of other
Li and Niu (2007)
indoor materials; Ca(t=0) is nonzero; C0(x, t=0) for each layer can be
non-uniform.
Numerical solution.
Multiple single-layer homogeneous materials coexisting with each other
acting as either a source or a sink; one surface emitting; Ca is zero, C0(x,
t=0) for each layer is constant (if it is zero, the material is a sink),
Deng et al. (2008)
well-mixed air, K and D for each layer is constant.
Fully analytical solution of Ca(t) and m  t  for each layer obtained by
Laplace transformation.
“The state-space method, was first introduced to indoor environmental
quality modeling by Yan and his coworkers in 2009” (Guo, 2013).
Yan et al. (2009)
The advantage of this method is that it reduces the computational
complexity by transforming a partial differential equation problem into a
series of discrete, ordinary differential equations that are more suitable
for computing.
Based on the Hu et al. (2007) model, except that the chemical reaction
rate within each material layer may be nonzero.
Wang and Zhang
(2011)
Not fully explicit analytical solution for C(x, t) in each layer, m  t  for
each surface and Ca(t) obtained by variable separation method and
Green’s function method.
“Currently, the most general and most complicated analytical solution”
(Liu et. al., 2013b).
Guo (2013)
Developed a framework for modeling the dynamic concentrations of
SVOCs indoors by using a modified state space method.
4
It can be used to develop a high performance indoor air quality program
or software.
Problem type 3.1.2: Find the generalized emission correlations.
First approach using dimensionless analysis to obtain the generalized
VOC emission correlations for a building material placed in a ventilated
Xu and Zhang
chamber or room.
(2003)
Under the model conditions, the dimensionless emission rate of VOCs is
a function of Bim/K and Fom. The applied condition of the Little et al.
model is presented.
Under dimensionless analysis, the dimensionless concentration and
Zhang and Xu
emission rate are the functions of Bim/K and Fom.
(2003)
Several correlations describing the VOC emission characteristics from
building material are developed by using a least square analysis.
Correlations
for
characterizing
the
relationship
between
the
dimensionless emission rate and four dimensionless parameters are
Qian et al. (2007)
derived.
The emission rate under practical conditions can be conveniently
obtained from the results under chamber (ventilated) test conditions.
Correlations applicable to airtight conditions are deduced.
Xiong et al. (2011c)
The emission rate under practical conditions can be conveniently
obtained from the results under chamber (airtight) test conditions.
A dimensionless mass transfer analysis to determine the SVOC emission
process characteristics in a test chamber. The specific conditions are
Liu et al (2013)
presented by using it in three simplified cases.
Several practical and quantifiable ways to improve chamber design are
proposed.
Problem type 3.1.3: Rapidly and accurately determine the emission characteristic
parameters.
Cup method with measured parameter D.
Kirchner et al.
Just one VOC can be tested at a time due to the use of purified VOC
(1999)
liquid.
Extraordinarily high concentration inside the cup may overestimate D.
Static twin chamber method with measured parameters D and K.
Bodalal et al. (2000)
External convection is ignored, which will underestimate D.
Air leakage and pressure difference between chambers may lead to error.
5
Hansson
and
Stymne (2000)
Cup method with measured parameter D (other features are similar to
Kirchner et al. (1999) thus not listed here, the same below).
Twin chamber method with measured parameters D and K.
Concentration level can be controlled at a required level.
Meininghaus et al.
Several VOCs can be tested in one experiment.
(2000)
External convection is ignored, which will underestimate D when the
airflow is slow.
Nonlinear regression method with measured parameters C0, D and K.
K is pre-determined by empirical correlations.
Yang et al. (2001)
Maximum concentration in the chamber is difficult to detect, which may
result in uncertainties for the measured C0 and D.
FBD method with measured parameters C0.
Short experimental time (within 7 hours).
Cox et al. (2001a)
Complicated experimental system.
Grinding process changes the physical properties of the material-VOC
combination, which may cause unpredictable measurement errors.
Microbalance method with measured parameters D and K.
Cox et al. (2001b)
Independent approach to measure the two parameters.
External convection is ignored.
Tiffonnet
et
al.
(2002)
Headspace method with measured parameter K.
Multi-injection can increase the measurement accuracy.
Nonlinear regression
method
(inverse
method) with
measured
parameters D and K.
Li and Niu (2005)
There is a risk of multiple solutions due to the inter-dependence of the
two parameters when they are estimated/fitted at the same time.
Nonlinear regression method with measured parameters C0, D and K.
He et al. (2005)
Prediction of K is more dependent on data abundance compared with
other two parameters.
There is a risk of multiple solutions.
Luo and Niu (2006)
Nonlinear regression method with measured parameters D and K.
Measuring emission rate of DEHP (SVOC) from vinyl flooring in FLEC.
Clausen et al (2007)
Relative humidity does not significantly influence emission rate of
DEHP.
Xu et al. (2009)
Twin chamber method with measured parameters D and K.
6
A similarity relationship between VOC and water vapor transport is
established.
Farajollahi et al.
Twin chamber method with measured parameters D and K.
(2009)
The effects of temperature and relative humidity are analyzed.
Extraction method with measured parameter C0.
Simple experimental system.
Smith et al. (2009)
Long experimental time (about 4 weeks).
Grinding process changes the physical properties of the material-VOC
combination, which may cause unpredictable measurement error.
A method for measuring the parameters C0, D and K.
Wang and Zhang
Experiments take about 7 days.
(2009)
Peak concentration after injection is hard to detect, which will affect the
measurement accuracy.
A method for measuring the parameters C0 and K.
Xiong et al. (2009)
Reducing experimental time significantly (i.e., 3 weeks) since it is not
necessary to let the target VOCs completely emit from the material;
Ito and Takigasaki
Nonlinear regression method (concurrent method) with measured
(2011)
parameters C0 and K.
C-history method for a closed chamber with measured parameters C0, D
and K.
Short experimental time (1~3 days).
Xiong et al. (2011a)
High measurement accuracy (RSD<10%).
Multiple samplings in airtight conditions may result in VOC mass loss if
the chamber volume is small, which may result in uncertainty (this is not
the case for large chambers).
VVL method with measured parameters C0 and K.
Xiong et al. (2011b)
Performing tests in parallel can decrease the experimental time (to within
24 hours).
With some improvements this method can be used to measure D and hm.
Measuring emission parameters of DEHP (SVOC) from vinyl flooring in
FLEC.
Clausen et al. (2012)
DEHP concentration adjacent to vinyl flooring surface is close to the
vapor pressure of pure DEHP.
DEHP steady-state concentration increases greatly, adsorption to chamber
7
walls decreases greatly, with increasing temperature.
Measuring emission parameters of phthalates (SVOC) from vinyl
flooring in a specially-designed chamber.
Xu et al. (2012)
Significantly reduces the time to reach steady state by increasing the
ratio of emission area to sorption area.
hm and y0 cannot be measured simultaneously.
Xu et al. (2012a)
Determination of D and K of formaldehyde in selected building materials
and the impact of relative humidity.
C-history method for a ventilated chamber with measured parameters C0,
D and K.
Huang et al. (2013)
Experimental time is less than 12 hours and R2 ranges from 0.96 to 0.99.
One test is performed in airtight conditions while other tests are
performed in ventilated conditions, thus some common measurement
instruments (e.g., GC/MS, HPLC) can be used.
Non-fitting method for determining parameters C0 and D with just two
sequential observations from a chamber test.
Li M (2013)
Standard deviations can be estimated without any assumption about the
distribution of experimental errors.
K is not determined; requirement of Fom>0.1 must be fulfilled.
Measures phthalate emissions from vinyl flooring in a specially designed
chamber.
Liang and Xu
Reduces experiment duration by improving chamber design, i.e., high
(2014a)
ratio of emission surface to sorption surface and improving air mixing.
Determines y0 by combining the equilibrium concentration and hm
obtained by empirical formula.
Simple method for estimating the ranges of D and C0 using gas-phase
VOC concentration data obtained from ventilated chamber tests.
Validated using the Monte-Carlo method and the National Research
Ye et al. (2014)
Council of Canada’s emissions database.
This simple method has more benefits when only a few data points are
available.
K is not determined.
Problem type 3.1.4: Evaluate the accuracy of the test results
A PMP standard emission sample is designed
Cox et al. (2010)
Its emission behavior is similar to a building material with determined
8
C0, D and K.
The requirement of storing at low temperature may result in leakage
during shipping, which may affect the measurement accuracy.
A LIFE standard emission sample is designed.
Constant emission rate during usage.
Wei et al. (2012)
Long emission durations.
Easy to store, apply and maintain.
Problem type 3.1.5: Obtain the relationship between C0, D, K and the influencing
factors.
Bodalal
et
al.,
(2001)
By analyzing the experiment data, correlations between D and molecular
weight (M), K and vapor pressure (p) are obtained.
A parallel pore model is developed to establish the relationship between
Blondeau et al.
D and pore structure.
(2003)
Considers the pores to be connected in parallel.
The determined D is much larger than that from chamber test results.
A mean pore model is developed to establish the relationship between D
and pore structure.
Seo et al. (2005)
It reduces all kinds of pores into an average pore.
The determined D is much larger than that from chamber test results.
A theoretical correlation between K and temperature is deduced from the
Zhang et al. (2007)
Langmuir kinetic equation.
K decreases with increasing temperature.
Wang et al. (2008)
A correlation between K and the VOC liquid molar volume based on the
theory of adsorption potential.
A macro-meso two-scale model is proposed to establish the relationship
between D and pore structure.
Xiong et al. (2008)
The connection between the macro and meso pore are in series.
The determined D is of the same magnitude as that from the chamber
test
A correlation between D and temperature is derived.
Deng et al. (2009)
Molecular diffusion is assumed to be dominant.
D increases with increasing temperature.
A correlation between the emittable ratio (C0/Ctotal) and temperature is
derived based on statistical physics theory.
9
Huang et al. (2014)
C0 increases with increasing temperature.
C0 is much smaller than the total concentration (Ctotal) at room
temperature.
Problem type 3.1.6: Reduce the VOC emission rates of indoor materials.
A low diffusive barrier layer is developed to reduce emissions.
Yuan et al. (2007)
The existence of nanoparticles in the barrier layer can greatly reduce D
thus decreasing the emission rate.
A dynamic-static chamber method was developed to simultaneously
measure the VOC solid-phase diffusion coefficient and solid/air partition
coefficient in barrier layers based on the solution of a mass transfer
He et al. (2010)
model with appropriate boundary conditions.
Results showed that barrier layers could greatly reduce indoor VOC
concentrations and therefore, the barrier layers could act as a promising
approach in the design of low-emission building materials.
Doping adsorbents into wood-based panels is proposed as a way to
He
and
Zhang
(2013)
control formaldehyde emissions.
The doped adsorbents increase the sorption property, which leads to a
high K and reduced emission rate.
1. Diffusivity for Knudsen diffusion
The diffusivity for Knudsen diffusion is obtained from the self-diffusion coefficient
derived from the kinetic theory of gases (Welty et al., 2009). For species A, it can
expressed as:
Le 8 RgT
(S1)
3  MA
For Knudsen diffusion, the path length Le is replaced by the pore diameter dp, as
DAA* 
species A is now more likely to collide with the pore wall than with another molecule.
The Knudsen diffusivity for diffusing species A, DK, is thus represented by:
DK 
dp
8 RgT
(S2)
3  MA
where, Rg is the gas constant, 8.314 J/(mol.K); MA is the molecular weight of species A,
kg mol-1; T is the temperature, K.
10
Equation (S2) indicates that Knudsen diffusivity DK is dependent on the pore
diameter, species molecular weight and temperature. Generally, the Knudsen process is
significant only at low pressure and small pore diameter. However, there must be a wide
range of conditions where both Knudsen diffusion and molecular diffusion are
significant. In the intermediate regime both wall collisions and intermolecular collisions
contribute to diffusion, which is called transitional diffusion. For species A in a binary
mixture of A and B, the transitional diffusivity D is determined by (Ruthven, 1984):
1 1  YA
1


D
D1
DK
where,   1 
(S3)
NB
; NA, NB are the fluxes of species A and B; YA is the mole fraction of
NA
species A; D1 is the molecular diffusivity of species A.
For cases where α=0, (NA=-NB), or where YA is close to zero, the equation reduces
to:
1
1
1


D D1 DK
(S4)
2. Fugacity
Fugacity is linearly, or nearly linearly related to concentration and can be regarded
physically as the partial pressure in an ideal gas or the escaping potential exerted by a
chemical in one physical phase on another (Mackay, 2001).
At low concentrations, the fugacity and concentration of chemicals are linearly
related, i.e., fugacity is proportional to concentration. This suggests the use of a
relationship of the form:
CZ f
(S5)
where, C is the chemical concentration, mol m-3; f the fugacity, Pa; Z the fugacity
capacity, mol m-3Pa-1.
11
Fugacity directly indicates the direction of mass transfer: from a high fugacity
medium to a low fugacity medium. The difference of fugacity acts as the driving force
behind mass transfer. Fugacity can be used to directly address the equilibrium status of
a system. If, and only if, the fugacity in all compartments is equal, can equilibrium be
attained. Therefore, for partitioning between two compartments at equilibrium, the
concept of fugacity overcomes the discontinuity at the interface associated with
concentration. The statement above makes fugacity perfectly analogous to the concept
of temperature in heat transfer, which directly indicates direction of heat transfer, acts as
the driving force and criterion of equilibrium and gives a continuous curve for
compartments at equilibrium.
The fugacity capacity defines the holding capacity of a material for a chemical
based on the properties of both the material and the chemical. When two or more
compartments are in equilibrium, the fugacity is the same in all phases. Therefore, the
aim of the fugacity approach is to deduce Z for the chemicals in air, water and other
phases, as this is the key quantity for assessing environmental partitioning.
Based on thermodynamic analysis, the solution for Z in the gas phase is:
Z
1
 RT
(S6)
where, ϕ is a fugacity coefficient; R is the gas constant.
For solution in the liquid phase, the solution for Z is:
Z
1
v w i f R
(S7)
where, vw is the molar volume per amount; γi is the activity coefficient; fR is a reference
fugacity. More expressions for Z are available in (Mackay, 2001).
12
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15