EPA 600/R-13/212 | November 2013 | www.epa.gov/ord
United States
Environmental Protection
Agency
Simulation Program i-SVOC
User's Guide
Office of Research and Development
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EPA/600/R-13/212
November 2013
Simulation Program i-SVOC
User's Guide
Software Version: 1.0
by
Zhishi Guo
Air Pollution Prevention and Control Division
National Risk Management Research Laboratory
U.S. EPA Office of Research and Development
Research Triangle Park, NC 27711, USA
National Risk Management Research Laboratory
Office of Research and Development
U.S. Environmental Protection Agency
Cincinnati, Ohio 45268
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Disclaimer
The computer software described in this document was developed by the U.S. EPA for its own
use and for specific applications. The Agency makes no warranties, either expressed or implied,
regarding this computer software package, its merchantability, or its fitness for any particular
purpose, and accepts no responsibility for its use. Mention of trade names and commercial
products does not constitute endorsement or recommendation for use. The views expressed in
this document are those of the author and do not necessarily represent the views or policies of the
Agency.
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Abstract
This document is the User's Guide for computer program i-SVOC, which estimates the
emissions, transport, and sorption of semivolatile organic compounds (SVOCs) in the indoor
environment as functions of time when a series of initial conditions is given. This program
implements a framework for dynamic modeling of indoor SVOCs developed by the author, and
covers six types of indoor compartments: air (gas phase), air (particle phase), sources, sinks (i.e.,
sorption by interior surfaces), contaminant barriers, and settled dust. Potential applications of this
program include: (1) use as a stand-alone simulation program to obtain information that the
current equilibrium models cannot provide, including evaluation of the effectiveness of certain
pollution mitigation methods such as variable ventilation rates, source removal, and source
encapsulation; (2) reducing the uncertainties in the existing multimedia models; and (3) use as a
front-end component for stochastic exposure models to provide information about the SVOC
distribution in indoor media in the absence of experimental data. This program is intended for
advanced users, who are involved in and familiar with indoor environmental quality (IEQ)
modeling or indoor exposure assessment. Because dynamic modeling of SVOCs in indoor media
is a relatively new research field, a number of issues need to be resolved in future research. For
example, efforts should be made to reduce the uncertainties in parameter estimation. There is a
need to develop a data and knowledge base for key parameters for modeling indoor SVOCs,
including, but not limited to, solid-air partition coefficient, solid-phase diffusion coefficient, and
gas-phase mass transfer coefficient.
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Acknowledgements
The author thanks the following testers for their contributions to the development of the
simulation program and this User's Guide. Their feedback has enabled the author to locate and
correct several errors in the code, remove a glitch in the setup program, and improve the
usefulness and readability of this document.
External Testers:
Charles Weschler, Robert Wood Johnson Medical School and Rutgers University, USA
Doyun Won, National Research Council Canada
B. Beverly Guo and J. Jensen Zhang, Syracuse University, USA
Ying Xu, University of Texas at Austin, USA
John Little and Yaoxing Wu, Virginia Polytechnic Institute and State University, USA
Yinping Zhang, Tsinghua University, China
Xinke Wang, Xi'an Jiaotong University, China
Heidi Hubbard, ICF International, USA
EPA Internal Testers:
Kent Thomas, National Exposure Research Laboratory
Xiaoyu Liu, National Risk Management Research Laboratory
Christina Cinalli and Charles Bevington, Office of Pollution Prevention and Toxics
Laureen Burton, Office of Radiation and Indoor Air
Emmet Keveney, Region 2
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Table of Contents
Disclaimer i
Abstract ii
Acknowledgements iii
Table of Contents iv
List of Tables viii
List of Figures ix
1. Introduction 1
1.1 What is i-SVOC? 1
1.2 Main features 1
1.3 Potential applications 2
1.4 Intended users 2
1.5 Limitations 3
1.6 Hints on parameter estimation 3
1.6.1 Parameter estimation is the user's responsibility 3
1.6.2 Solid-air partition coefficient 4
1.6.3 Solid-phase diffusion coefficient 4
1.6.4 Gas-phase mass transfer coefficient 4
2. Software Installation and Technical Support 5
2.1 Hardware and software requirements 5
2.2 Installing program i-SVOC 5
2.3 Uninstalling program i-SVOC 5
2.4 Contact information 6
iv
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2.5 Technical support 6
3. Getting Started 7
3.1 User interface 7
3.1.1 General appearance 7
3.1.2 Pages and forms for user input 8
3.1.3 Output tables 9
3.1.4 Display adjustment 9
3.2 Creating a model for a diffusional source 10
3.2.1 Creating a model 10
3.2.2 Error checking 15
3.2.3 Running the model 15
3.2.4 More output options 16
3.2.5 Where are the temperature and air velocity in this model? 17
3.3 Adding a diffusional sink 17
3.3.1 Example sink parameters 17
3.3.2 Open an existing model file 18
3.3.3 Create and run the new model 18
3.3.4 Include mass fluxes in the output options 20
3.4 Creating a model for settled dust 21
3.4.1 Creating a constant emission source 21
3.4.2 SVOC accumulation in settled dust 24
3.4.3 SVOC re-emission from settled dust after the source is removed 27
3.5 Creating a model for airborne particles 28
3.6 Modeling phthalate emissions from vinyl flooring 31
3.6.1 Parameters 32
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3.6.2 Modeling the chamber concentrations 33
3.7 When a simulation fails 35
3.7.1 Causesof simulation failure s 35
3.7.2 Using the command 35
3.7.3 Using the command 35
3.7.4 A failed simulation will not hurt the operating system 35
4. More Features 36
4.1 Time-varying ventilation rates 36
4.2 Source removal 38
4.3 Double-layer sources 39
4.4 Encapsulation 43
4.5 Pulse release of airborne particles 45
4.6 Episodic sources for airborne particles 45
4.7 Using the command 46
4.8 Using the command 47
4.9 Calculating the total SVOC concentration in room air 48
5. Program Specifications 49
6. Inside i-SVOC 51
6.1 Programming language and supporting software 51
6.2 Numerical method 51
6.3 Modified state-space method 51
6.3.1 Diffusional sources and sinks 51
6.3.2 Permeable particles 52
6.4 Mass transfer equations 52
6.4.1 Diffusional sources and sinks 52
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6.4.2 Dynamic Langmuir sink 54
6.4.3 Dynamic Freundlich sink 55
6.4.4 Permeable particles 56
6.4.5 Impermeable particles 57
6.4.6 Particles with a liquid film over an impermeable solid core 57
6.4.7 SVOC mass fluxes 58
6.5 Differential equations 58
6.5.1 Room Air 59
6.5.2 Diffusional sources and sinks 59
6.5.3 Surface adsorption 60
6.5.4 Permeable particles 60
6.5.5 Impermeable particles 61
6.5.6 Particles with a liquid film over an impermeable solid core 61
6.5.7 Number concentration of airborne particles for a pulse release 62
6.6 Initial Conditions 62
6.7 Unit Conversion 62
6.7.1 SVOC Concentration in sources and sinks 63
6.7.2 Particle-air partition coefficient 63
6.7.3 Particle mass and number concentrations in air 63
6.7.4 SVOC concentration for impermeable particles 64
6.7.5 Dust loading versus number of dust 64
6.8 Miscellaneous calculations 65
6.8.1 Calculating the average particle-phase SVOC concentration in air in (ug/g particles) 65
6.8.2 Calculating the total particle-phase SVOC concentration in air in (ug/m3 air) 65
6.8.3 Simulating episodic emission sources for airborne particles 66
vii
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6.8.4 Calculating the average SVOC concentration in settled dust 68
6.9 SVOC migration from sources to settled dust due to direct contact 69
7. References 70
Appendix A SVOC transfer to settled dust due to direct contact with a source 73
Appendix B Parameter estimation for the dynamic Freundlich adsorption model 77
List of Tables
Table 1. Speed buttons and their corresponding menu items. 8
Table 2. Example parameters for modeling PCB-52 emissions from a caulking material. 10
Table 3. Example parameters for concrete walls as a diffusional sink for PCB-52. 18
Table 4. Example parameters for simulating DEP sorption by settled dust with diameters
of 2.5, 10, and 50 urn. 22
Table 5. Example parameters for simulating DEP sorption by airborne particles with
diameters of 0.1, 1, 2.5, and 10 urn. 29
Table 6. Parameters for DEHP emissions from vinyl flooring (from Xu et al., 2006). 32
Table 7. Estimated parameters for the dynamic Freundlich adsorption model
(see Section 6.4.3). 33
Table 8. Example parameters for demonstration of time-varying ventilation rates. 36
Table 9. Example parameters for simulating a double-layer source. 40
Table 10. Example parameters for simulating an encapsulated source. 43
Table 11. Maximum allowable number of components in a model. 49
Table 12. List of options for simulation output. 50
Table 13. Selection of the slicing methods for diffusional sources and sinks. 52
Table 14. Selection of the slicing method for permeable particles. 52
Table 15. Representing an episodic particle-release event by four consecutive pulse
releases 67
VIII
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List of Figures
Figure 1. User interface of program i-SVOC: (1) parameter entry page for building properties. 7
Figure 2. User interface of program i-SVOC: (2) parameter entry form for diffusional sources.
Note the two form tabs near the lower-left corner. 9
Figure 3. Data entry form for diffusional sources. 12
Figure 4. The page. Click the
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Figure 20. Completed parameter entry form for type I airborne particles. 30
Figure 21. Simulated DEP concentrations in airborne particles as a function of time. The
residence time (tr) shown is for 2.5 urn-diameter particles. 31
Figure 22. Simulated DEHP concentrations in the CLIMPAQ due to emissions from vinyl
flooring (This figure was generated from four simulations with different source areas). 34
Figure 23. Simulated DEHP concentrations in the FLEC due to emissions from vinyl flooring. 34
Figure 24. Defining variable ventilation rates (parameters from Table 8). 37
Figure 25. Simulation results for varying ventilation rates (file "Varying_ACH.svoc"). 37
Figure 26. Defining the source removal time. 38
Figure 27. Air concentrations before and after the source removal at 7000 elapsed hours. 39
Figure 28. The double-layer source was first created as two single-layer sources. 41
Figure 29. The form for grouping two single-layer sources into a double-layer source. 41
Figure 30. The two single-layer sources have been grouped into a double-layer source.
Note the changes in source IDs. 42
Figure 31. Air concentration due to emissions from a hypothetical double-layer source
(see Table 9). 42
Figure 32. Define the encapsulation time in the source-grouping form. 44
Figure 33. Simulated effect of source encapsulation on indoor air concentration using
hypothetical parameters in Table 10. 44
Figure 34. Simulated total particle-phase SVOC concentration in air due to three consecutive
pulse releases of particles; created by demonstration model "Airborne PM-pulse.svoc". 45
Figure 35. Calculation sheet for simulating an episodic source by a series of pulse releases. 46
Figure 36. After running model "MyModel-02" with the command, the
concentration gradient in the source at 10000 hours is posted on the source form. Similar
changes were made to the sink form. 47
Figure 37. Simulated particle concentrations in room air due to an episodic particle-release
event; created by demonstration model "PM-episodic.svoc". 68
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1. Introduction
1.1 What is i-SVOC?
I-SVOC is a Microsoft Windows-based computer program for dynamic modeling of the
emissions, transport, and sorption of semivolatile organic compounds (SVOCs) in the indoor
environment. This program implements a modeling framework recently developed by this author
(Guo, 2013, 2014).
This program covers six types of indoor media (i.e., compartments): air (gas phase), air (particle
phase), sources, sinks (i.e., sorption by interior surfaces), contaminant barriers, and settled dust.
The key input parameters of the program include the solid-air partition coefficients, solid-phase
diffusion coefficients, and gas-phase mass transfer coefficients.
Program i-SVOC is more of a model shell than a model. It can be regarded as a modeling
platform on which the users can build and experiment with their own models. This program:
• Covers the functions of most commonly used models for indoor SVOC.
• Ensures that the calculated results are consistent with the existing mass transfer and
empirical models.
• Provides the user with more flexibility than the existing models.
• Frees the user from numerical computations.
1.2 Main features
Over the past two decades, more than 20 mass transfer models and nearly 10 multimedia models
have been developed for indoor VOCs and SVOCs (Liu, et al., 2013; Guo, 2013; and references
herein). While the mass transfer models have contributed significantly to better understanding of
the behavior of diffusional sources, sinks, and barriers in buildings, their applications in the real
world have been somewhat limited because of two major issues: model incompatibility and
computational complexity (Guo, 2013). As a result, it is difficult to use those models to simulate
the cases where multiple sources and sinks are present. Particulate matter plays an important role
in human exposure to SVOCs. Most existing multimedia models assume that there is an
instantaneous equilibrium between the gas-phase and particle-phase SVOCs. It has been
demonstrated that such assumption tends to overestimate the particle-phase SVOC
concentrations in room air when the particle-air partition coefficient is large (Guo, 2014).
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Program i-SVOC resolves the above-mentioned problems by adopting a new modeling
framework, as described in Section 6. The key features of this program include:
• It is the first general-purpose tool for dynamic modeling of indoor SVOCs.
• It allows multiple diffusional sources and sinks to be present in a simulation.
• It includes components for dynamic modeling of SVOC interactions with suspended and
settled particles, which can be size-segregated.
• It frees the user from tedious numerical computations and allows them to focus on
developing models and conducting simulations.
• There are multiple options for the simulation output, including SVOC concentrations in
indoor media and mass fluxes.
Details about the specifications of this program are given in Tables 11 and 12 in Chapter 5.
1.3 Potential applications
Program i-SVOC may be useful in the following areas:
• It can be used as a stand-alone simulation program to obtain information that the current
equilibrium models cannot provide. For example, i-SVOC can evaluate the effectiveness
of certain pollution remediation methods such as variable ventilation rates, source
removal, and source encapsulation.
• It can help reduce the uncertainties in the existing multimedia models. For instance, for
the SVOCs with large solid-air partition coefficients, the instantaneous equilibrium
assumption tends to overestimate the particle-phase SVOC concentrations in room air.
Program i-SVOC can provide an estimate of the degree of sorption saturation (DSS),
which can be used as an adjusting factor.
• It can be used as a front-end component for stochastic exposure models, such as the
EPA's Stochastic Human Exposure and Dose Simulation (SHEDS) model
(http://www.epa.gov/heasd/research/sheds.html). Program i-SVOC can provide estimates
of the SVOC distributions in indoor media in the absence of experimental measurements.
1.4 Intended users
Program i-SVOC is mainly for advanced users who are involved in and familiar with indoor
environmental quality (IEQ) modeling or indoor exposure assessment.
Many resources are available for those who would like to learn more about IEQ modeling. For
example, a general introduction of IEQ modeling is given by Sparks (2001); commonly used
parameter estimation methods for IEQ modeling are reviewed by Guo (2002); methods for
modeling indoor particles are described by Nazaroff (2004).
2
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1.5 Limitations
Dynamic modeling of SVOC distributions in buildings is a relatively new research field. There
are many unresolved issues. Potential users should be aware of the limitations of the current
program.
• The uncertainties in the simulation results are directly linked to the uncertainties in the
model parameters such as the partition and diffusion coefficients. There have been many
discussions in the literature on how to estimate the partition coefficients. On the other
hand, data and models for the solid-phase diffusion coefficient remain scarce. While there
are well-established methods for estimating the gas-phase mass transfer coefficient for
flat surfaces, there is great uncertainty in this parameter associated with airborne and
settled particles. Thus, reducing the uncertainties in parameter estimation is a key for
future research.
• The current version of program i-SVOC is for a single air zone and a single SVOC. The
program does not support chemical reactions.
• Program i-SVOC ignores the interactions between the settled dust and the surface which
the dust particles are in contact with.
• Direct contact of settled dust with a source is an important mass transfer mechanism by
which SVOCs migrate from the substrate into the dust. The current version of i-SVOC
cannot simulate this mass transfer process. A simple method for estimating the upper
bound of SVOC migration is given in Appendix A.
• Many indoor pesticides are SVOCs. This program does not contain any mass transfer
models for liquid applications.
• Program i-SVOC does not perform stochastic simulations.
• Program i-SVOC is mainly a research tool. It is not intended for regulatory purposes.
1.6 Hints on parameter estimation
1.6.1 Parameter estimation is the user's responsibility
As a general-purpose simulation tool for indoor SVOCs, program i-SVOC and this User's Guide
do not provide any default values for the conditions that the users want to simulate, or
recommend any specific methods for parameter estimation. It is the user's responsibility to select
proper parameter values. Among the many parameters used in i-SVOC, solid-air partition
coefficient, solid-phase diffusion coefficient, and gas-phase mass transfer coefficient are critical.
There is a vast pool of literature that discusses the methods for estimating these parameters. To
further improve our ability to model indoor SVOCs, it is a logical next step to compile and
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evaluate the existing parameter estimation methods and, if necessary, develop new methods.
Very brief discussions on estimating the above-mentioned parameters are provided below.
1.6.2 Solid-air partition coefficient
Many methods are available for estimating the solid-air partition coefficient for interior surface
materials and particles. It can be estimated from either the vapor pressure or octanol-air partition
coefficient of the chemical. It appears that more researchers are in favor of using the latter (for
example, Finizio et al., 1997; Weschler & Nazaroff, 2010). Although experimentally determined
partition coefficients are scarce, some data are available for certain SVOCs (For example, Xu &
Little, 2006; Guo et al., 2012).
1.6.3 Solid-phase diffusion coefficient
Solid-phase diffusion coefficient is difficult to predict because it depends on not only the
properties of the chemical but also those of the substrate. This parameter is commonly related to
the molecular weight of the chemical (Schwope, et al., 1990 and the references herein).
Correlations for the chemicals within the same class are well established (Guo, 2002 and
references herein). Limited experimental data are available for this parameter (For example,
Schwope et al., 1990; Xu & Little, 2006; Guo et al, 2012).
1.6.4 Gas-phase mass transfer coefficient
Several methods are available for estimating the gas-phase mass transfer coefficient for materials
with flat surfaces (e.g., building materials and furniture). Computer program PARAMS (Guo,
2005) implements three methods, among which the method based on Sherwood number is most
commonly used. The information needed to compute this parameter includes the formula of the
chemical, air velocity (or speed), temperature in the room, and surface area.
Methods for estimating the gas-phase mass transfer coefficient for airborne particles are also
available (For example, Li & Davis, 1996). However, there is great uncertainty in this parameter.
The cited values for indoor particles differ by several orders of magnitude. Furthermore, little
information is available about the range of gas-phase mass transfer coefficient for settled dust.
More research is needed to reduce the uncertainty associated with this parameter.
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2. Software Installation and Technical Support
2.1 Hardware and software requirements
Program i-SVOC runs on personal computers with Microsoft Windows as the operating system.
The program has been tested for Windows XP, 7, and 8. A minimum of 5 MB free disk space is
required. The screen resolution should be at least 1024 by 768 pixels. Internet connection is
required only for downloading the installation package from the EPA website.
2.2 Installing program i-SVOC
If your computer is connected to a local network, it is likely that you need the "Administrative
Privileges" to install this program.
After the setup program is downloaded, use the File Explorer to locate the file. Double click the
file name and then follow instructions. The default target folder for installation is "C:\Program
Files\EPA_ISVOC\" for Windows XP and "C:\Program Files (x86)\EPA_ISVOC\" for Windows
7 and 8. During the installation, the setup program will create an icon on your desktop screen.
For Windows 8, a "tile" for the application will also be created on the start screen. Click the icon
or tile to start the simulation program. You can also start the program from the Programs menu.
During the installation, the User's Guide will be copied to the target folder. It can be accessed
from the Programs menu. There is also an icon on your desktop screen.
The setup program has been scanned by anti-virus software Symantech Endpoint Protection
(Symantech, Mountain View, CA) and is free of known viruses.
2.3 Uninstalling program i-SVOC
For Windows XP or 7, go to Windows Control Panel, select , select
i-SVOC from the program list, and then click .
For Windows 8, right-click the tile from the start screen and then click ,
which is located at the bottom-right corner of the screen. This will bring up a list of apps. Click
and then click . In the next window, select
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, . Select program i-SVOC from the list and then
click .
2.4 Contact information
If you have any questions or would like to report bugs and errors, please contact the developer:
Zhishi Guo
US EPA Office of Research and Development
National Risk Management Research Laboratory
Air Pollution Prevention and Control Division
Indoor Environment Management Branch
Mail Code E305-03
Research Triangle Park, NC 27711, USA
Telephone: +919-541-0185
Email: guo.zhishi@epa.gov
2.5 Technical support
Limited technical support is provided by the developer. Communications by electronic mails are
highly preferred. If your problem is associated with a particular model, please attach the model
file to your message.
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3. Getting Started
3.1 User interface
3.1.1 General appearance
This simulation program features a multi-page design. As shown in Figure 1, there is a menu bar
on top. Nine "speed buttons" below the menu bar provide quick access to frequently used menu
items. Table 1 lists the names of the speed buttons and their corresponding menu items. If you
move the cursor over a speed button, a hint will be displayed momentarily.
Menu bar
Speed buttons
Page tabs f _aj _aj
~
i-SVOC 1.0: model-1 .svoc
| File Model Simulate Tools Utilities
j/J ^J J_ *
uilding Sources Sinks | Settled Dust Airborne PM | Conditions Output |
Notepad
[Write roles here.)
Current form = Building
Room and ventilation rate
Room volume (
Base ventilation rate (1/h)
Ventilation mode
o Constant
'" Varialble
Figure 1. User interface of program i-SVOC: (1) parameter entry page for building properties.
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Table 1. Speed buttons and their corresponding menu items.
Button
Group
File
manager
Error
checking
Simulation
mode
Position
(from left)
1
2
3
4
5
6
7
8
9
Button
Name
New
Open
Open recent
Save
Compile
Inspect
Run
Run slow
Run & save
Corresponding
Menu Item
File/New
File/Open
File/Open recent file
File/Save
Model/Compile
Model/Inspect
Simulate/Run
Simulate/Run slow
Simulate/Run & save
Hint Text
Create a new model
Open an existing model
Open a recent model
Save current model
Compile current model
Inspect current model
Run model at normal speed
Run model at reduced speed
Run model & put back output [a]
Described in Section 4.7.
3.1.2 Pages and forms for user input
Below the menu bar and speed buttons, there are seven button-like tabs, and they are labeled
"Building," "Sources," "Sinks," "Settled dust," "Airborne PM," "Conditions," and "Output"
(Figure 1). All the input parameters are grouped into the first six pages. For example, to enter a
source, click the "Sources" tab. Note that there are two data entry forms in the page:
"Diffusional sources" and "Other sources," with the form tabs located near the lower-left corner,
as shown in Figure 2.
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i-SVOC 1.0: model-Lsvoc
File Model Simulate lools Utilities About
Form tabs
_oj jaj _aj jft]
luilding Sources Sinks Settled Dust Airborne Ptvl Conditions Output
Diffusional Sources
ID (Internal)
Source name
Areafm2)
Thickness (m)
Solid/air partition coef (-)
Solid-phase diffus on coef (rnVh)
Gas-phase mass transfer coef (m/h)
Exposed side(s)
Re in oval/en cap 1 me (h)
Initial content in sli e 0 (ug/rn3)
Initial content in sli el (ug/rn5)
Initial content in sli e 2 (ug/nf)
Initial content in sli e 3 (ug/rrf)
Initial content in sli e A (ug/rn*)
C
1
2
3
4
5
6 A
fll
•Diffusional Sources Other Sources
Current form = Ditfusinal source
J|_Quit
Figure 2. User interface of program i-SVOC: (2) parameter entry form for diffusional sources. Note the
two form tabs near the lower-left corner.
3.1.3 Output tables
The simulation results are posted to the
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3.2 Creating a model for a diffusional source
Making a simulation with i-SVOC involves three steps: creating a model, checking the model for
errors, and running the model.
3.2.1 Creating a model
The first example model you will create is for polychlorinated biphenyl (PCB) emissions from a
caulking material in a hypothetical room with a volume of 100 m3 and a ventilation rate of 1 air
change per hour. PCBs were once used as a plasticizer for caulk, sealants, and paint. These
applications were banned in the U.S. in 1978.
Table 2 lists the required parameters. The solid-air partition coefficient and solid-phase diffusion
coefficient are for PCB congener 52. These values are for a specific type of caulk and, thus, may
not be applicable to other types of caulk. Also note that this program uses dimensionless solid-air
partition coefficient.
Table 2. Example parameters for modeling PCB-52 emissions from a caulking material.
Page/Form
Building
Sources/
Diffusional
sources
Simulation
conditions
Parameter Name
Room volume (m3)
Ventilation rate (h"1)
Source name
Exposed area (m2)
Thickness of source material (m)
Solid-air partition coefficient (dimensionless)
Solid-phase diffusion coefficient (m2/h)
Gas-phase mass transfer coefficient (m/h)
Initial concentration in the source (ug/m3)
Exposed side(s)
Initial concentration in room air (ug/m3)
Simulation duration (h)
Output data points
Output options
Value
100
1
Caulk
0.2
0.01
6.54xl07
2.25X10'11
2.2
8.07xl09
top
0
10000
200
~
Notes
[a]
[a]
[b]
[a][c][d]
[e]
[a] Data from Guo et al. (2011), page 104.[bj Estimated by computer program PARAMS (Guo, 2005).
[c] Assume the concentration in the source is uniform initially. [d] Pay attention to the units; use equation
41 in Section 6.7.1 to convert (ug/g) to (ug/m3); there is a unit converter under the menu.
[e] Explained in the text below Figure 4.
10
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To get started, run i-SVOC. After the title window appears, click . Now your screen should
look like Figure 1 in Section 3.1.1. There is a notepad on the left side for making notes. It is
always a good idea to describe your model in detail for future reference. Try to type a few words
there, such as "This is my first model..." Next, enter the room volume and ventilation rate. Now
you are done with the first data entry form.
To enter the parameters for the diffusional source, click the page tab. If the current
form is not for diffusional sources, click the tab at the lower-left corner.
Now your screen should look like Figure 2 in Section 3.1.2.
To add a source, click the button. A data entry form will be displayed (Figure 3). This
program requires that each source be given a name, any name except a blank. This requirement
may seem superfluous. However, its importance will become apparent as the source name is the
only information that can help you identify the data columns in the output table.
Now enter the required parameters on the left side of the form. Program i-SVOC accepts
numerical values in either general or exponential formats:
CORRECT: 3.15 1256 1.23E8 1.23e8 3.45E-12
INCORRECT: 1,256 1.23*10A8
There is a check box near the bottom for "Source removal." Ignore it at this moment. It will be
explained later in Sections 3.4.2 and 4.2.
11
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1 Add New Diffusional Source Elfnlfxl
(Internal ID = S)
Source name
Area [rrf]
Thickness (m)
Solid/air partition coef (-)
Solid-phase diffusion coef (nrfVh)
Gas-phas mass transfer coef (m/h)
Sidefs] exposed to air JTop T |
|~~ Source removal
Initial Concentrations (ug/m5;)
Layer ID
Layer 0
Layer 1
Layer 2
Layer 3
Layer 4
Layer 5
Layer 6
Layer 7
Layer 8
Layer 9
Concentration (ug/m5]
0
0
0
0
0
0
0
0
0
V^ OK X Cancel
7'?c Load
as.
to
Figure 3. Data entry form for diffusional sources.
Next, move to the right side of the form to enter the initial concentrations in the source.
Remember, i-SVOC is based on the modified state-space (MSS) method, which divides the
source into a finite number of slices (Guo, 2013). In this program, a source made of the same
material (i.e., a single layer source) is divided into ten slices. Program i-SVOC does not require
that the initial concentrations in the source be uniform. Because we have assumed that the
concentration is uniform initially (see Table 2), all the layers will have the same concentration
value (i.e., 8.07x 109 ug/m3). If you do not want to type in 10 identical numbers, there is a
shortcut: click on the first cell, type in "8.07E9," and then click the button.
After all is done, click the button. If an error message pops up, fix the problem and then
click . This program allows the user to enter multiple sources. To add another source, click
the button again.
You can make changes to the parameters that you have already entered in the form. To do so,
click the source name first, and then click the button. To delete a source, click the souece
name first, and then click .
To enter the parameters for simulation conditions, click the page tab. As shown in
Figure 4, the user is asked to enter three parameters on the left side of the form: initial
12
-------
concentration in air, simulation duration, and the number of data points to be provided in the
output table. Enter the values according to Table 2.
Simulation Duration and Output Data Points
Simulation duration i rjQQQ (hours
Max. 500,000 hours |~57 years]
Number ol data points 200
73
Current form - Simulation conditions
/
_fl_Quit
Figure 4. The page. Click the
-------
Simulation Output Options
Available Output
00) Air: gas-phase only (ug/m^
01) Diffusional sources/sinks: individual slices (ug/m3 solid)
02) Diffusional sources/sinks: average (ug/m3 solid)
03) Surface adsorption: Langrnuir or Freundlich sinks (ug/rn7 surface)
04) Settled dust: size-segregated concentration in dust (ug/g dust)
05) Settled dust: average concentration in dust (ug/g dust)
06) Settled dust: individual hollow spheres (Type I only) (ug/m3 dust)
07) Airborne PM: size-segregated particle-phase SVOC (ug/g PM)
08) Airborne PM: average particle-phase SVOC (ug/g PM)
09) Airborne PM: total particle-phase SVOC (ug/m3 air)
10) Airborne PM: total number concentration (counts/nf3 air)
11) Airborne PM: total mass concentration (ug PM/m3 air)
12) SVOC mass fluxes (ug/m2/h)
u n x
Selected Output
,/ OK
Figure 5. Form for selecting the output data types.
i-SVOd.O: MyModel-OLsvoc
File Model Simulate lools Utilities About
J|jjj
Building Sources Sinks Settled Dust Airborne PM Conditions Output
Simulation Conditions
Initial Concentration in Air (Gas Phase)
Simulation Duration and Output Data Points
Simulation duration
|1DOOO |hours
Max 5QO.OOCI hours [~57years]
Number of data points 200
Output Options
00) Air: gas-phase only (ug/m5)
Current form = Simulation conditions
Figure 6. Completed form for simulation conditions.
14
-------
Before moving any further, let's save the model for future use. To save the current model, click
the speed button (the fourth from left) or select / from the main menu.
Name the file "MyModel-01" and save it to a folder. Note that i-SVOC uses file extension
".svoc" for model files.
3.2.2 Error checking
The next step is to check the input parameters for potential errors. Program i-SVOC provides two
ways for error checking: and . The former allows i-SVOC to read your
model and check for potential errors; the latter allows the user to check for errors.
To compile the current model, click the speed button (the one with a red check sign)
or select / from the main menu. Try it now. If you see an error message, fix
the problem and try again.
To check for errors by yourself, click the speed button (the one with a magnifying
glass) or select / from the main menu. Program i-SVOC will generate a
laundry list for the parameters in the current model. It tells you how the program interprets your
model. It is highly recommended that you go over the list to confirm the correctness of the
parameters. The parameter list can be printed.
3.2.3 Running the model
To start the simulation, click the speed button (the one with a calculator glyph) or select
/ from the main menu. If you entered the parameters correctly, there should
be no problem during the simulation.
The simulation results are posted to the first data table (the one with the "Concentrations" tab)
located in the
-------
0.60
0.50 -
,_ 0.40 -
<
E
c 0.30 -
£ 0.20 -
01
u
E
u 0.10 -
0.00
0
2000 4000 6000
Elapsed Time (h)
8000
10000
Figure 7. Simulated PCB-52 concentrations in room air (model MyModel-Ol.svoc).
3.2.4 More output options
This program can do more than just calculating the air concentrations. Go to the
page, click the
-------
o
to
re
01
o
u
•t = 10 h
•t = 100 h
•t = 1000 h
•t = 10000 h
234
Depth (mm)
Figure 8. Concentration profiles for PCB-52 in the source as functions of depth and time. The exposed
surface is at depth = 0.
3.2.5 Where are the temperature and air velocity in this model?
Temperature and air velocity (or air speed) are both important parameters for mass transfer. Why
aren't they listed in Table 2? This program does not require these parameters explicitly because
they are imbedded in other key parameters. For example, room temperature is reflected in the
partition, diffusion, and mass transfer coefficients. Similarly, air velocity is imbedded in the gas-
phase mass transfer coefficient.
3.3 Adding a diffusional sink
3.3.1 Example sink parameters
Sorption of SVOCs by interior surfaces is an important issue in both exposure assessment and
contamination remediation. Program i-SVOC allows simulations with multiple sinks. Let's add a
17
-------
diffusional sink to the model that you have just created. The sink is the concrete walls with a
9
total area of 80 m . The new parameters are given in Table 3.
Table 3. Example parameters for concrete walls as a diffusional sink for PCB-52.
Page/Form
Sinks/
Diffusional sinks
Parameter Name
Sink name
Exposed area (m2)
Thickness of sink material (m)
Solid-air partition coefficient (dimensionless)
Solid-phase diffusion coefficient (m2/h)
Gas-phase mass transfer coefficient (m/h)
Initial concentration in the sink (ug/m3)
Exposed side(s)
Value
Concrete
80
0.025
2.11xl07
2.98X10'11
0.68
0
top
Notes
[a]
[a]
[b]
[ J From Guo et al. (2012), page 73. [bj Estimated by computer program PARAMS (Guo, 2005) by
assuming the average area of each wall is 20 m2.
3.3.2 Open an existing model file
In this practice, we will use file MyModel-Ol.svoc that you created earlier. There are two
methods to open an existing model file: (1) Click the speed button (the second from left)
or by selecting / from the main menu. (2) If the file was saved recently, click the
speed button (i.e., the third from the left), or select /
from the main menu.
3.3.3 Create and run the new model
Click the page tab. This page contains two forms: and . Go to the former. The data entry form for diffusional sinks is almost
identical to the one for diffusional sources (i.e., Figure 3). Enter the parameter values provided in
Table 3. Then, click the button.
Now compile and then inspect your model just as you did for your first model. Next, save the
new model to file "MyModel-02" for future use by clicking , from the main
menu. Note that, if you click , or the speed button, the new model will be
saved to "MyModel-01". Now, run the model and you will get the results shown in Figures 9 and
10. Note that the travel distance for SVOCs in a sink is rather short, and that the average
concentration in the sink depends on the thickness selected. To obtain the concentration profiles
like Figure 10, a proper thickness should be selected by trial and error.
18
-------
0.60
0.50 -
0.40 -
~ 0.30 -
,g
'^
2 0.20 -
01
u
§ o.io H
u
0.00
No sink
With sink
2000 4000 6000
Elapsed Time (h)
8000
10000
Figure 9. Simulated PCB-52 concentration in room air by using models MyModel-Ol.svoc (no sink) and
MyModel-02.svoc (with sink).
3.0E+6
0.25
•t = 10 h
•t = 100 h
•t = 1000 h
•t = 10000 h
-K-
0.5 0.75
Depth (mm)
1.25
1.5
Figure 10. Concentration profiles in the sink substrate as functions of depth and time. The exposed
surface is at depth = 0.
19
-------
3.3.4 Include mass fluxes in the output options
In addition to calculating the SVOC concentrations in indoor media, i-SVOC can also calculate
SVOC fluxes (i.e., emission or sorption rates) between indoor media. To include SVOC fluxes in
the simulation output, add the following item to the output options:
12) SVOC mass fluxes (ug/m2/h)
Re-run the model and the mass flux data will be posted to the second data table. Note that mass
fluxes can be either positive or negative. A positive value means emission and a negative value
sorption (Figures 11 and 12).
Note that the distinction between a diffusional source and a diffusional sink is superficial. A
source can become a sink and vice versa. It all depends of the fugacity difference between the
source (or, sink) and room air. In other words, the mass transfer models treat the diffusional
sources and sinks the same (Kumar and Little, 2003a).
300
250 -
200 -
x 150 -
_3
LL.
S 100 H
GO
U
Q_
50 -
0
Emission from caulk
0
200 400 600
Elapsed Time (h)
800
1000
Figure 11. PCB-52 flux between the source (caulk) and room air; positive values mean emissions from
source.
20
-------
0.00
_ -0.05 -
f
(N
-I. -0.10 -
3
* -0.15 -
LL.
(N
f
GQ
U
Q_
-0.20 -
-0.25 -
-0.30
0
Sorption by concrete walls
200 400 600
Elapsed Time (h)
800
1000
Figure 12. PCB-52 flux between for the sink (concrete walls) and room air; negative values mean
sorption from air.
3.4 Creating a model for settled dust
Program i-SVOC can simulate both permeable and impermeable settled dust (Guo, 2014). For
each category, multiple size bins and dust types are allowed, as shown in the example below.
The dust models are fully compatible with the source and sink models. Table 4 lists the example
parameters for sorption of di-ethyl-phthalate (DEP) by settled dust.
3.4.1 Creating a constant emission source
Program i-SVOC includes several non-diffusional source models (i.e., empirical source models)
and they serve for two purposes:
• They are useful for modeling the data from test chambers; and
• They can be used to simplify the model, especially in the cases where airborne or settled
particles are involved.
In this practice, we will use an empirical emission model to keep the gas-phase DEP
concentration at 1 ng/m3 in the absence of any sinks. To start from scratch, click the
speed button (i.e., the first from left) or select , from the main menu. Complete the
page by entering 30m3 for the room volume and 1 h"1 for the base ventilation rate.
21
-------
Then, go to the page. Click the tab near the lower left corner. Click
to bring up the data entry form (Figure 13). Click on the dropdown list at the top-left
corner and then select "Constant source (rate)". The form will display the model description and
the required parameters (Figure 14). Give the source a name and then enter 30 ug/h for the
emission rate. In the absence of any sinks, this value gives a steady-state DEP concentration of 1
ug/m3 for a 30-m3 room with a ventilation rate of one air change per hour. Ignore the "Shut-off
time at this moment. Click .
Table 4. Example parameters for simulating DEP sorption by settled dust with diameters of 2.5, 10, and
50 urn.
Page/Form
Building
Other sources
Dust Type I
(Permeable)
Simulation
conditions
Parameter Name
Room volume (m3)
Ventilation rate (h"1)
Source type
Emission rate (ug/h)
Dust name
Diameter (nm)
Particle-air partition coefficient (dimensionless) [a]
Particle -phase diffusion coefficient (m2/h) [b]
Gas-phase mass transfer coefficient (m/h) [cl
Initial SVOC concentration in particles (ng/g)
Dust particle density (g/cm3)
Number of dust particles[d]
Initial concentration in air (ug/m3)
Simulation duration (h)
Number of output data points
Output options
Value
30
1
Constant source (rate)
30
D2.5
2.5
1.24xl08
IxlO-13
5
0
1
2.44x10"
DIG
10
1.24xl08
IxlO-13
4.5
0
1
3.82xl09
D50
50
1.24xl08
IxlO-13
4
0
1
3.06xl07
0
100
100
[e]
Average value based on two estimation methods, from Weschler et al. (2008).
1 Rough estimate based on several references.
' Best guesses.
1 Assuming a dust loading of 0.2 g/m2 for each size bin and a floor area of 10 m2. A unit converter is
available under the menu.
' The output option is: 04) Settled dust: size-segregated concentration in dust (ug/g dust).
22
-------
Figure 13. Parameter entry form for empirical source models before the model is selected.
Select source model
| Constant source (rate)
Source type: Constant Source (as Rate)
Expression: R = Constant
Emission rate (ug/h) 30
NOTE: The shut-off time is the time when the source
is terminated or removed. If the source is continuous,
leave it as "n.a." (for not applicable!
Figure 14. Parameter entry form for empirical source models after the model is selected and parameters
are entered.
23
-------
3.4.2 SVOC accumulation in settled dust
Go to page . Click form tab near the lower-left corner.
In the parameter entry form (Figure 15), enter the parameters for D2.5 first. Because the
remaining two sets of parameters are quite similar, you can save some typing by using the
command. First, click the dust name ("D2.5") and then click the button.
Note that the dust name for the replicate data set has an extra "x" because i-SVOC does not
allow replicate names in a form. Click on dust name "D.25x" and then click the button.
Now you can make changes. Enter the third set of parameters in a similar manner. After you
finish, the screen should look like Figure 16.
Name of dust
Diameter (urn)
Particle/air partition coef (-)
Particle-phase diffusion coef (rn2/h)
Gas-phase mass transfer coef (m/h)
Initial concentration in dust(ug/g)
Particle density (g/cm8)
Number of particles
Figure 15. Parameter entry form for permeable settled dust.
24
-------
i-SVOC 1.0: MyModel_Dust.SVOC
File Model Simulate lools Utilities About
JtJ
Building Sources Sinks Settled Dust Airborne PM Conditions Output
Settled dust (Type I: porous/permeable)
Dust name
Diameter (urn)
Particle/eir partition coef (-)
Particle-phase diffusion coef (rn*/h)
Gas-phase mass transfer coet (m/h)
Initial SVOC concentration (ug/g)
Density of dust particles (g/cm3)
Number of particles
m'/h)
1 (m/h)
/a)
1
1* I3
D2.5
25
1.24E8
1E-13
5
0
1
2.44E11
D10
10
1.21EB
1E-13
1.5
0
1
3.82E3
D5CI
50
1.24E8
1E-13
A
D
1
3J1F.E7
1
5
6
•
Type II Dust (Lamgmuir & Freundlich)
Current form = Settled dust (Type I)
SI Edit
..Rppllr
Figure 16. The form for type I dust with input parameters for three size bins.
In the page, enter the remaining parameters. The completed form should look like
Figure 17.
25
-------
' J-SVOC1.0: MyModel_Dust.SVOC
hie IVodel birnulate ion IE NtilitieB About
- n x
Building Sources Sinks Settled Dust Airborne PM Conditions Output
I'll Settler: rl.iE.i 'Ei:e-Beqieq.= ed crrrenttotirr in c:us (uq/q dust)
Figure 17. Completed form for simulation conditions.
Now save the model to external file "MyModel_dust.svoc". Next, and then
the model. When you are ready, click the speed button. In case the simulation
fails, try the option (the second speed button from right). The simulation results are
shown in Figure 18.
26
-------
150
I
1
100 -
0'= 2.5(jrn
•v= 10|.m
o
w
50 -
d=50 Mm
20 40 60
ElapsedTime (h)
80
100
Figure 18. Simulation DEP concentrations in settled dust with three size bins.
3.4.3 SVOC re-emission from settled dust after the source is removed
Let's make a slight modification to the model you have just created. Go to the
form, click on the source name, and then click . In the data entry form, the shut-off time is
"n.a." (for not applicable). Change it to 100. Click . Then go to the page.
Change the simulation duration to 200 hours. Re-compile the model and click the speed
button. The results are shown in Figure 19.
27
-------
50 1' 'j 150
Elapsed Time (h)
200
Figure 19. Simulated DEP losses from settled dust after the source is removed.
3.5 Creating a model for airborne particles
Under typical indoor environmental conditions, airborne particles can stay suspended for only a
short period of time. The residence time is usually less than an hour (Qian et al., 2008; Guo,
2014). Typically, the simulation duration for airborne particles should be no longer than several
hours. Simulation results for airborne particles without consideration of residence time can be
misleading. In most cases, long-term simulations are useful only for studying the SVOC
interactions with individual particles, not for the particle "population".
In this practice, we will use the parameters listed in Table 5 to investigate the DEP sorption by
airborne particles in four size bins. Go to the to enter the room volume and
ventilation rate. Next, go to the under the page to define the source.
28
-------
Table 5. Example parameters for simulating DEP sorption by airborne particles with diameters of 0.1, 1, 2.5, and 10 um.
Page/Form
Building
Sources/
Other sources
Airborne PM/
Type I
(permeable)
Simulation
conditions
Parameter Name
Room volume (m3)
Ventilation rate (h"1)
Source type
Emission rate (ng/h)
Shut-off time (h)
Name of airborne particles
Particle release mode
Diameter (um)
Number concentration (counts/m3) [a]
Initial SVOC concentration in particles (ug/g)
Particle-air partition coefficient (dimensionless) [b]
Particle -phase diffusion coefficient (m2/h) [c]
Particle density (g/cm3)
Gas-phase mass transfer coefficient (m/h) [d]
Deposition rate constant (h"1) [e]
Initial concentration in air (ug/m3)
Simulation duration (h)
Number of output data points
Output options
Value
30
1
Constant source (rate)
30
(Leave it as is)
APMO.l
Constant
0.1
3.82xl010
0
1.24xl08
IxlO-13
1
2000
0.45
APM1
Constant
1
3.82xl07
0
1.24xl08
IxlO-13
1
1000
0.45
APM2.5
Constant
2.5
2.45xl06
0
1.24xl08
IxlO-13
1
500
0.6
APM10
Constant
10
3.82xl04
0
1.24xl08
IxlO-13
1
300
0.75
1
2
100
See text below
Each of these values is equivalent to a mass concentration of 20 ug/m3. Thus, the total particle concentration in air is 60 ug/m
b] Average value based on two estimation methods, from Weschler et al. (2008).
cl Rough estimate based on several references.
d] Best guesses based on Shi & Zhao (2012).
[e] Rough estimates based on Qian et al. (2008).
29
-------
Airborne particles are defined in the page, which contains three forms for,
respectively, permeable particles, impermeable particles (i.e., Langmuir and Freundlich
adsorption), and solid particles covered with a liquid film. Go to the first form and then click the
button. Enter the parameters in Table 5. The completed form should look like Figure 20.
1 i-SVOC 1.0: MyModel-APM.SVOC
F i le Mode I S irnulate Too Is Uti I ities About
Eg |
uilding Sources Sinks Settled Dust | Airborne PM Conditions Output
Airborne particulate matter (Type I: porous/permeable)
Serial No.
Particle name
Particle release mode
Diameter (urn)
Number concentration (
Initial SVOC content (ug/g)
Particle/air partition coef(-)
Particle density (g/cm3)
Deposition rate constant (1/h)
PM pulse release time (h)
//m8)
/g)
Jf(-)
coef (ms/h)
er coef (m/h)
it(1/h)
(h)
1
APMO.l
Constant
0.1
3.B2E10
0
1.24E8
1E-13
1
2000
0.15
n a
2
APM1
Constant
1.0
3.82E7
0
1.24E8
1. OE-13
1
1000
0.45
n.a.
3
APM2.5
Constant
2.5
2.15E6
0
1.21E8
1 OE-13
1
500
0.6
n.a.
3
APM10
Constant
10
3.82E1
0
1.21E8
1. OE-13
1
300
0.75
n.a.
5
6
Type I (Permeable) Type II (Langmuir) & Freundlich | Type III (Liquid film) |
Current form = Airborne PM (Type 1)
Figure 20. Completed parameter entry form for type I airborne particles.
In the page, enter 1 for the initial air concentration, 2 for simulation duration, and
100 for the number of output data points. For the output option, select
07) Airborne PM: size -segregated particle-phase SVOC (ug/g PM).
Save the model as "MyModel-APM.svoc." After error-checking, click the speed
button (the second speed button from right). The difference between and is
discussed in Section 3.7 below.
CAUTION: The simulation results for airborne particles should be interpreted with discretion.
The results in Figure 20 are the time history for individual particles. For a given particle size or
type, the SVOC concentration at the residence time is representative of the particle "population"
30
-------
if the particle concentration remains constant during the simulation (Guo, 2014). Particles with
different sizes may have different deposition rates and, thus, slightly different residence times.
The value shown in Figure 21 is for 2.5 um-diameter particles.
CAUTION: It is also recommended that, when simulating airborne particles with constant
release rates, the gas-phase SVOC concentration remain constant.
150
3: ioo -
0.
LLJ
Q
01
CD
Q.
•3 50 H
E
CD
0.
d= 0.1 urn ^<
X
/
' d= 1 urn
I ,/
t= 0.625 h
of= 2.5 urn
of = 10
0.5
1.5
Elapsed Time (h)
Figure 21. Simulated DEP concentrations in airborne particles as a function of time. The residence time
(tr) shown is for 2.5 um-diameter particles.
3.6 Modeling phthalate emissions from vinyl flooring
Until now, we have dealt with hypothetical cases. In the next example, we will use the
parameters in the literature to predict the concentrations of di-2-ethlhexyl phthalate (DEHP) in
two types of test chambers, known as CLEVIPAQ (Chamber for Laboratory Investigations of
Materials, Pollution and Air Quality) and FLEC (Field and Laboratory Emission Cell). The data
were generated by Clausen et al. (2004) and the model parameters by Xu and Little (2006). We
will create a model to calculate the chamber concentrations with different loading factors.
31
-------
3.6.1 Parameters
The parameters for the CLIMPAQ chamber data reported by Xu and Little (2006) are
summarized in Table 6. Note that the unit for time has changed from second to hour.
Table 6. Parameters for DEHP emissions from vinyl flooring (from Xu et al., 2006).
Parameter
Group
Chamber
Source
Sink
Parameter Name and Units
Chamber volume (m3)
Ventilation rate (h"1)
Initial concentration in source (ng/m3)
Source area (m2)
Source thickness (m2) [a]
Solid-phase diffusion coefficient (m2/h) [b]
Gas-phase mass transfer coefficient (m/h) [c]
Material-air partition coefficient (-)
Area of chamber walls (m2)
Freundlich equilibrium constant [d]
Freundlich index [d]
Symbol
V
—
C0
As
6
D
hm
K
A,
Kf
n
Parameter Value
CLIMPAQ
0.051
10
2.6x10"
0.2 to 1.6
0.0025
3.6X10'10
1.44
2.3x10"
1.6
3800
1.5
FLEC
3.5xlO'5
780
2.6x10"
0.018
0.0025
3.6X10'10
5.04
2.3x10"
0.018
6000
0.47
aJ Fctimntfrl hv thiQ mithnr ^ ' Thp nrioinnl unit wnQ m /Q LCJ Thp nrioinnl unit wnQ m/Q ^ ' TniQ
parameter is defined by equation 14; as explained in Section 6.4.3, it is not used in the simulations.
Program i-SVOC includes two dynamic adsorption models for impermeable surfaces: the
Langmuir and Freundlich adsorption models (See Sections 6.4.2 and 6.4.3 below for more
details). However, this program does not support the adsorption models that are based on the
assumption of instantaneous equilibrium. Thus, i-SVOC cannot use the sink parameters (Kfand
ri) listed in Table 6. The dynamic Freundlich adsorption model requires four parameters:/a, a,fd,
and ft (See equation 13 in Section 6.4.2). For the CLFMPAQ chamber, a was set to 1 and ft 0.67.
These values satisfy n = a/ft =1.5 given in Table 6. Similarly, for the FLEC, a and ft were set to
0.47 and 1.0, so their ratio is n = 0.47. In both cases, the non-linear adsorption and desorption
rate constants (fa andfd) were estimated by trial and error. The estimated sink parameters are
summarized in Table 7.
32
-------
Table 7. Estimated parameters for the dynamic Freundlich adsorption model (see Section 6.4.3).
Parameter Name
Nonlinear adsorption rate constant (fig1"" m3a"2 h"1)
Index for non-linear adsorption (dimensionless)
Nonlinear desorption rate constant (|ig1"pm2p"2h"1)
Index for non-linear desorption (dimensionless)
Symbol
fa
a
fa
13
Value
CLIMPAQ
5
1
0.025
0.67
FLEC
10
0.47
0.0015
1
The method used to estimate parameters/a andfd in Table 7 was essentially a data-fitting process
which, in this case, is time-consuming and requires some experience. A much simpler method
for converting the equilibrium Freundlich model to a roughly equivalent dynamic Freundlich
model is described in Appendix B.
3.6.2 Modeling the chamber concentrations
Two models are needed for the parameters listed in Tables 6 and 7, one for the CLIMPAQ and
the other for the FLEC. To create a new model, click the speed button (the first to the
left) or select , from the main menu. This model will need the following
pages/forms:
•
• /
• /
•
Now enter the parameters listed in Tables 6 and 7. In the page, enter the following
information. Then, compile and inspect the model. Save the model to an external file.
Initial concentration in air:
Simulation duration:
Number of output data points:
Output options:
0 (Hg/m3)
10000 (h)
200
00) Air: gas-phase only (|ag/m3)
CAUTION: The model for the CLIMPAQ can be run at the normal speed, but the one for the
FLEC cannot, as explained in Section 3.7. The latter should be run with the
command, and it may take several minutes to complete the simulation because of the long
duration.
33
-------
As shown in Figures 22 and 23, the simulation results compare favorably to the experimental
results (i.e., Figures 2 and 6 in Clausen et al., 2004).
1.00
~ o.so H
~ 0.60 H
o
'S
CD
01
u
0.40 -
0.20 -
0.00
1.6 m2
^^
. 0.8ml
-.-•*"""""""
^'-''* 0.4 m2 .
^ _« • ^^^
X
0.2m2
50 100 150 200 250
Elapsed Time (days)
300
Figure 22. Simulated DEHP concentrations in the CLIMPAQ due to emissions from vinyl flooring (This
figure was generated from four simulations with different source areas).
1.0
m
"SB o-s
k.
< 0.6 -
• 0.4 -
CD
01
O
u
0.2 -
0.0
0 100 200 300
Elapsed Time (days)
400
500
Figure 23. Simulated DEHP concentrations in the FLEC due to emissions from vinyl flooring.
34
-------
3.7 When a simulation fails
3.7.1 Causes of simulation failures
Simulations may fail from time to time. Most failures are caused by the extreme values — in the
context of numerical computation — in the input parameters. The following conditions are
known to cause problems:
• The solid- or liquid-phase diffusion coefficient is very large (e.g., > 10~8 m2/h)
• The particle diameter is very small (e.g., <0.5 jam)
• The chamber volume is very small and the air flow rate very large (e.g., the FLEC).
Program i-SVOC provides the following remedies when a simulation cannot continue.
3.7.2 Using the command
When a simulation fails, the user can re-run his/her model at a slower pace by clicking the speed button (i.e. the one with the glyph of a walking man) or, equivalently, by selecting
the / command from the main menu. This simulation mode can resolve
many problems. For example, the command can handle particles as small as 0.001
um in diameter. The tradeoff is that it takes more time to run a simulation.
3.7.3 Using the command
The command under the menu can handle even more difficult
cases. However, this simulation mode is very time-consuming and, thus, should be used
occasionally and only for short-term simulations (e.g., no longer than several hours).
3.7.4 A failed simulation will not hurt the operating system
When numerical integration fails, the program will halt the simulation and then exit gracefully
without affecting the operating system. In such cases, an error message will be displayed.
35
-------
4. More Features
4.1 Time-varying ventilation rates
Program i-SVOC allows simulations with time-varying ventilation rates. In the page,
click the radio button to display the table, where the user
defines all the ventilation rates other than the base ventilation rate. Demonstration model
"Varying_ACH.svoc" uses the parameters shown in Table 8. To open a demonstration file, select
/ from the main menu. The page of the model is shown in
Figure 24 and the simulation results in Figure 25.
Table 8. Example parameters for demonstration of time-varying ventilation rates.
Page/Form
Building
Sources/
Other sources
Conditions
Parameter Name
Room volume (m3)
Base ventilation rate (h"1)
Ventilation rate between 24 and 48 hours
Ventilation rate between 70 and 80 hours
Source type
Emission rate (ug/h)
Initial air concentration
Simulation duration
Output data points
Output selection
Value
30
1
2
3
Constant rate
30
0
100
100
00) Air: gas phase only (ng/m3)
36
-------
i-SVOC1.0: Varying_ACH.svoc
File Model Simulate lools Utilities About
- n X
0 B
Building Sources Sinks Settled Dust Airborne PM Conditions Output
Notepad
Demonstration of variable ventilation rate
Base ventilation rate = 1
Ventilation rate from 2.A to 48 hours = 2
Ventilation rate from 70 to 80 hours = 3
Current form = Building
Room volume and ventilation rate
Room volume (m*) |3Q
Base ventilation rai
Ventilation rate changes
Statttime(h) End time (h) Ventilation rate (1/h)
JLQuit
Ventilation mode
<~ Constant
<* Varialble
Figure 24. Defining variable ventilation rates (parameters from Table 8).
1.2
ST 1.0 -
a o.
8 -
c
o
•i3 0.6
£
4-1
§ 0.4
c
o
u 0.2
0.0
20 40 60
Elapsed Time (h)
80
100
Figure 25. Simulation results for varying ventilation rates (file "Varying_ACH.svoc").
37
-------
4.2 Source removal
Program i-SVOC allows the user to "stop" a source at any time during a simulation. This feature
is useful in the following cases:
• To study the re-emissions from the sink materials after the SVOC sources are removed.
• To simulate chamber conditions in which the source is cut off during the experiment.
You have tried to shut off a non-diffusional source in Section 3.4.2. Shutting off a diffusional
source is similar. Open model file "MyModel-02" that you created in Section 3.3. Go to the
form in the page. To edit the source, click the source name and
then click . Check the source removal check box and then enter 7000 for the "removal
time" (see Figure 26). Now re-run the model. As shown in Figure 27, the re-emission from the
sink can last for a long time.
View/Edit Diffusive Source
_ n x
(Internal ID = S)
Source name
Area (nf)
Thickness (m)
Solid/air partition coef (-)
|6.54E7
Solid-phase diffusion coef (irf/h) J2.25E-11
Gas-phas mass transfer coef [m/h] 12.2
Side(s) exposed to air
|Top
Source removal at time (h) 1 7QQQ
Initial Concentrations (ug/nr")
Layer 1
Layer 2
Layer 3
Layer 4
Layer 5
Layer S
Layer 7
Layer £
Layer 3
8.07E9
8.07E9
8.07E3
G.07E9
8.07E9
8.07E9
G.07E9
9.07E9
8.07E9
Figure 26. Defining the source removal time.
38
-------
0.4
1
0.3 -
•- 0.2 -
CD
O
u
0.1 -
0.0
0 2000 4000 6000 8000 10000
Elapsed Time (h)
Figure 27. Air concentrations before and after the source removal at 7000 elapsed hours.
4.3 Double-layer sources
Program i-SVOC can simulate double-layer sources (e.g., painted wood board and laminated
composite wood board). Two steps are needed to create a double-layer source:
• Define the top and bottom layers as two single-layer sources, and
• Use the command to combine the two.
For demonstration purposes, we will create a model with the parameters listed in Table 9.
39
-------
Table 9. Example parameters for simulating a double-layer source.
Page/Form
Building
Sources/
Diffusional
sources
Simulation
conditions
Parameter Name
Room volume (m3)
Ventilation rate (h"1)
Source area (m2)
Gas-phase mass transfer coefficient
Layer ID
Material thickness (m)
Solid-air partition coefficient (dimensionless)
Solid-phase diffusion coefficient (m2/h)
Initial concentration in layer (ng/m3)
Side(s) exposed
Initial concentration in air (ng/m3)
Simulation duration (h)
Number of output data points
Output options
Values
30
1
1
1
Top
0.001
l.OxlO6
l.OxlO'10
2.0xl07
Top
Bottom
0.01
2.0xl07
S.OxlO'11
2.0xl09
Neither
0
10000
200
00) Air: gas-phase only (ng/m3)
After entering two single-layer sources, the form should look like Figure
28. Note that, although the bottom layer does not need the gas-phase mass transfer coefficient,
the program still requires a numerical value, which eventually will be ignored.
Now click the button to bring up the source grouping form (Figure 29). On the left side
of the form, select the top and bottom layers. Ignore the right side, which is for encapsulation.
Click to return to the < Diffusional sources> form. Note the changes in the top row
(Figure 30). Run the model. Figure 31 was created by demonstration file "2-layer-l.svoc."
40
-------
* i-SVOC 1.0: : Z-layer-1 .svoc
File Model Simulate Tools Utilities About
iuilding | Sources Sinks | Settled Dust Airborne PM I Conditions Output
Diffusional Sources
ID (Internal)
Source name
Area (m2)
Thickness (m)
Solid/air partition coef(-)
Solid-phase diffusion coef (ms/h)
Gas-phase mass transfer coef (m/h)
Exposed side(s)
Removal/encap time (h)
nitial content in slice 0 (ug/m*)
Initial content in slice 1 (ug/m3)
nitial contenl in slice 2 (ug/m3)
nitial content in slice 3 (ug/m1)
Initial content in slice A (ug/m3)
Mrfpri^l.rfrolSAnM)
S
layer!
1
0001
1EB
1E-10
1
Top
n.a.
2E7
2E7
2E7
2E7
2E7
9F7
S
Iayer2
1
O.D1
2E7
5E-11
1
Top
n.a.
2E3
2E9
2E9
2E9
2E9
'"
3
A
5
6
-
f6\
DiHusional Sources Other Sources
Current form - Diffusinal source
Figure 28. The double-layer source was first created as two single-layer sources.
1 Creating a double-layer source or sink
OH*
Select the top layer
| layer!
Select the bottom layer
Is the top layer an encapsulant?
No
C Yes
Enter time for encapsulation (h)
|E dill
X Cancel
Figure 29. The form for grouping two single-layer sources into a double-layer source.
41
-------
ID (Internal)
Source name
Area (m^
Thickness (m)
Solid/air partition co ef(-)
Solid-phase diffusion co
ef(m*/h)
Gas-phase mass transfer coet (m/h)
Exposed side(s)
Removal/encap time (h)
Initial content in slice 0 (ug/m3)
Initial content in slice 1 (ug/m3)
Initial content in slice 2 (ug/m3)
Initial content in slice 3 (ug/m3)
Initial content in slice A (ug/m3)
lni,i.l^n,= n,moli™trnn/m^
Diffusiorml Sources
Current torn
D1Aop
Dl/btm
H layer^
1 1
0.001 0.01
1EB
1E-10
1
Top
n.a.
2E7
2E7
2E7
2E7
2E7
2E7
5E-11
1
Top
n.a.
2E9
2E9
2E3
ZE9
2E3
3
<\
9P7 I7FH
I
6 «•
-
Other Sources |
= Diffusirml source
fjAdd |
S Edit |
f, Delete |
[j ® Group ||
Jlfluit |
Figure 30. The two single-layer sources have been grouped into a double-layer source. Note the changes
in source IDs.
0
0 2000 4000 6000 8000 10000
Elapsed Time
Figure 31. Air concentration due to emissions from a hypothetical double-layer source (see Table 9).
42
-------
4.4 Encapsulation
An encapsulated source is equivalent to a double-layer source except that the initial
concentration in the encapsulant layer is often zero. Parameters used by demonstration program
"encap-l.svoc" are given in Table 10.
Table 10. Example parameters for simulating an encapsulated source.
Page/Form
Building
Source/
Diffusional
Sources
Simulation
conditions
Parameter Name
Room volume (m3)
Ventilation rate (h"1)
Source area (m2)
Gas-phase mass transfer coefficient
Layer ID
Material thickness (m)
Solid-air partition coefficient (dimensionless)
Solid-phase diffusion coefficient (m2/h)
Initial concentration in layer (ng/m3)
Side(s) exposed
Time for encapsulation (h)
Initial concentration in air (ng/m3)
Simulation duration (h)
Number of output data points
Output options
Value
30
1
1
1
Encapsulant
(top)
0.001
l.OxlO6
l.OxlO'10
2.0xl07
Top
2000
Source
(Bottom)
0.01
2.0xl07
S.OxlO'11
2.0xl09
Top[a]
n.a.
0
10000
200
00) Air: gas-phase only (ng/m3)
Before encapsulation, the top-side of the source is exposed to air.
Creating an encapsulated source is similar to creating a double-layer source. During the
"grouping" process, the user can specify the time when the encapsulant is applied (Figure 32).
The next step is to edit the parameters for the bottom layer by setting the "Exposed side(s)" to
"Top." Figure 33 was created by demonstration file "encap-l.svoc."
43
-------
1 Creating a double-layer source or sink _ G X
Select the top layer
| layer! T |
Select the bottom layer
|layer2 T |
! '•T'OK
Is the top layer an encapsulant?
r No (f Yes
I- f I • n *
tnter time ror encapsulation [nj
J2000
X Cancel
Figure 32. Define the encapsulation time in the source-grouping form.
4.0
3.0
2.0 -
o
'&
CD
0 2000
4000 6000
Elapsed Time
8000 10000
Figure 33. Simulated effect of source encapsulation on indoor air concentration using hypothetical
parameters in Table 10.
44
-------
4.5 Pulse release of airborne particles
When particles are injected into room air in a pulse, all the particles have the same age and thus
the same residence time. These conditions make the simulation results much easier to interpret
than those for other particle release modes.
Figure 34 was created with demonstration model "Airborne PM-pulse.svoc", in which l|am-
diameter particles are released into room air at 1,2, and 3 elapsed hours. Please open the model
file for more details. Note that, in the pulse release mode, the PM number concentration is the
initial concentration for the pulse release, and that you can create multiple pulse releases for the
same particles and for different particles.
0.05
2 3
Elapsed Time (h)
Figure 34. Simulated total particle-phase SVOC concentration in air due to three consecutive pulse
releases of particles; created by demonstration model "Airborne PM-pulse.svoc".
4.6 Episodic sources for airborne particles
Many indoor PM sources such as particle resuspension, cooking, smoking, and incense burning,
are episodic in nature. These sources can be represented by a series of pulse releases. Program i-
SVOC includes a calculation sheet to assist the user to convert the expected number
concentration during the episode to a series of pulse releases. To bring up the calculation sheet
45
-------
(Figure 35), select from the menu. The calculation
method is described in Section 6.8.3.
Pulse release schedule
1 Simulating intermittent PM sources with pulse injections
Enter parameters for intermittent PM source
Target number concentration (Ulnf) |1 E7
Episode start time (h)
Episode end time (h)
Ventilationrate(1/h)
Deposition rate constant (1/h)
Number of pulse releases
Release ID | Release time (h) Initial if cone. (1/m3)
2
2
2.4
1.168E-07
3.200E-06
3.200E-06
2.6
3.200E-06
2.8
3.200EXJ6
A
rise
Figure 35. Calculation sheet for simulating an episodic source by a series of pulse releases.
4.7 Using the command
Some legacy pollutants may have existed in a building for decades and a pseudo-steady state is
often reached. In these cases, the concentration gradients within the diffusional sources and sinks
are unique to the specific building. Modelers are often interested in the current status instead of
the history of the contamination. The command allows the user to simulate the
contamination history for a given building and save the current status for future use. When you
run a model with the command, the results at the end of the simulation will be
put back to the model. For demonstration, open "MyModel-02.svoc" and then select ,
from the main menu. At the end of the simulation, the concentration gradients
will be posted (Figure 36). If you save it with a new file name, it can be used as the starting point
for new simulations. This feature works only for diffusional sources and sinks. Also note that the
SVOC concentration in room air at the end of the simulation will also be posted to the
page.
46
-------
i-SVOC 1.0: MyModel-Z.svoc
I File Model Simulate _ools Utiht PE. About
uilding|| Sources Sinks Settled Dust Airborne PM Conditions Output
Diffusional Sources
ID (Internal)
Source name
Area (nf)
Thickness (m)
Solid/air partition coef (-)
Solid-phase diffus on coef (m2/h)
Gas-phase mass transfer coef (m/h)
Exposed side(s)
Rernoval/encaptirne (h)
Initial ontent in sli e 0 (ug/rn3)
Initial ontent in sli e1 (ug/m3)
Initial ontent in sli e2(ug/nf;)
Initial ontent in sli e 3 (ug/m3!
Initial ontent in sli e 4 (ug/m3)
<
S
a^
0.2
0.01
6.54E7
2.25E-11
2.2
Top
ri.a.
4.1683E»09
4.2320E-.09
4.411 1E*09
4.7572E»09
5.3974E-.09
R j^n^nq
2
3
1
5
6 •*
•
Diflusional Sources Other Sources
Current form = Diifusmal source
jflQuit
Figure 36. After running model "MyModel-02" with the command, the concentration
gradient in the source at 10000 hours is posted on the source form. Similar changes were made to the sink
form.
4.8 Using the command
The command under the menu allows the user to run multiple models
unattended. This feature is especially useful for screening multiple chemicals and for models that
take a long time to run.
To use this feature, all the models should be saved in the same folder. It is highly recommended
but not required to compile each model. After clicking on / , an open-
file dialog will appear. Select model files and then click the button. The program will
run the selected models sequentially. A run-batch report is available after the work is done.
The output data will be saved in the same folder where the model files are located. The output
file names will be the same as the model files except with the "csv" extension, which stands for
comma separated values. Below is an example:
Model file
Output for concentrations
Output for mass fluxes
MyModel -xyz. svoc
MyModel-xyz. csv
MyModel-xyz(Rate) .csv
47
-------
CAUTIONS: (1) If you would like to re-run a batch for some reason, the old csv files will be
overridden. (2) Make certain that none of the csv files is open by other applications such as Excel
because writing data to an open file causes an I/O error.
4.9 Calculating the total SVOC concentration in room air
This program computes the gas-phase and particle-phase concentrations in air separately. To
obtain the total SVOC concentration in air, the following output options should be included in
the model.
00) Air: gas-phase only (ng/m3)
09) Airborne PM: total particle-phase SVOC (ug/m3 air)
After the simulation is done, copy and paste the results to a spreadsheet and then sum the two
data columns up.
48
-------
5. Program Specifications
The program specifications are provided in Tables 11 and 12. In Table 11, the total number of
ordinary differential equations is an overall limiting factor. When a model exceeds the maximum
allowable number of differential equations, the user will receive an error message.
Table 11. Maximum allowable number of components in a model.
Model Components
SVOC species
Air zone
Ventilation rate changes
Single-layer diffusional sources or sinks
Double-layer diffusional sources or sink
Non-diffusional sources
Langmuir/Freundlich sinks
Airborne particle type I (permeable)
Airborne particle type II (surface sorption)
Airborne particle type III (liquid film over solid core)
Settled particle type I (permeable)
Settled particle type II (surface sorption)
Total number of ordinary differential equations
Maximum simulation duration (h)
Maximum number of output data points
Max.
1
1
6
10
3
10
10
10
10
10
10
10
150
5xl06
1000
Notes
[a]
[b]
[b]
[b]
[b]
[b]
[c]
One base ventilation rate plus 5 changes.
[b] Number of size bins or particle types (i.e., same size but different properties).
[c] When the number of equations exceeds this limit, an error message will be displayed.
49
-------
Table 12. List of options for simulation output.
Data Group
SVOC
concentrations
Airborne PM
concentrations
SVOC fluxes
Output Option
00) Air: gas-phase only (ug/m3 air)
01) Diffusional sources/sinks: individual slices (ug/m3 solid)
02) Diffusional sources/sinks: average (ug/m3 solid)
03) Surface adsorption: Langmuir or Freundlich sinks (ug/m2 surface)
04) Settled dust: size-segregated concentrations in dust (ug/g dust)
05) Settled dust: average concentration in dust (ug/g dust)
06) Settled dust: individual hollow spheres (Type I only) (ug/m3 dust)
07) Airborne PM: size-segregated particle -phase SVOC (ug/g PM)
08) Airborne PM: average particle-phase SVOC (ug/g PM)
09) Airborne PM: total particle-phase SVOC (ug/m3 air)
10) Airborne PM: total number concentration (counts/m3 air)
11) Airborne PM: total mass concentration (ng PM/m3 air)
12) SVOC mass fluxes (ug/m2/h)
Notes
Gas-phase SVOC concentration in room air
SVOC concentrations as a function of depth in the
material
Average SVOC concentrations in the material
For non-diffusional sinks
SVOC concentrations in settled dust by size bins
Weighted mean concentration in dust, from Eq. 5 1
SVOC concentrations in settled dust as a function of
depth inside the particle and by size bins
Size -segregated particle-phase SVOC concentrations
in room air
Weighted mean of all PM sizes and types, from Eq. 47
Weighted sum of all PM sizes/types, from Eq. 49
Total number concentration of airborne particles
Total mass concentration of airborne particles
Positive values mean emissions; negative values mean
sorption
50
-------
6. Inside i-SVOC
6.1 Programming language and supporting software
Program i-SVOC was written in Delphi XE Professional Edition (Embarcadero Technologies,
San Francisco, CA). The installation package was created by Install Simple 2.7 PRO
(InstallSimple Solutions, www.installsimple.com).
6.2 Numerical method
The ordinary differential equations are solved by the fourth/fifth-order Runge-Kutta-Fehlberg
method (Cheney and Kincaid, 1980). The original code was written in Fortran (Forthythe et al.,
1977). This author translated it into Delphi and made several minor adjustments to the code.
6.3 Modified state-space method
In program i-SVOC, the diffusion processes inside a solid material or particle are represented by
the modified state-space (MSS) method, which divides the solid phase into a finite number of
slices or hollow spheres. The methods for dividing the flat materials and particles are presented
below. More details about the method development and validation can be found in Guo (2013
and 2014).
6.3.1 Diffusional sources and sinks
The method for dividing a flat material is as follows: (1) The thickness of the exposed slice is
ultra thin (1 x 10"6 m); (2) The inner slices are divided according to equation 1:
(1)
where ALj = thickness of the inner slice of two adjacent slices (m)
ALi = thickness of the outer slice of two adjacent slices (m)
p = 0or 1.
The value ofp is determined by the thickness and solid-phase diffusion coefficient of the
substrate, as shown in Table 13.
51
-------
Table 13. Selection of the slicing methods for diffusional sources and sinks.
Substrate thickness (L)
(mm)
L<2
L>2
Value of Dm
(m2/h)
n/a
>io-9
5
Number of layers w
(»)
1
2
3
5
Thickness of top
hollow sphere (um)
d/2[b]
0.1
0.1
0.1
Value of p for inner
hollow spheres
n/a
n/a
1
1
LaJ Including («-l) hollow spheres and one solid sphere.L J This is a solid sphere
6.4 Mass transfer equations
This section contains all the mass transfer equations used in the program. More detailed can be
found in Guo (2013, 2014) and the references herein.
6.4.1 Diffusional sources and sinks
Mass transfer between the top slice and room air:
c
(2)
-------
-=+- P)
H K h
ma m
where Rma = rate of mass transfer from the top (exposed) slice to air (ug/h)
A = exposed area of the source or sink (m )
Ha = overall gas-phase mass transfer coefficient (m/h) from equation 3 (m/h)
Cmi = SVOC concentration in the top (exposed) slice of the source or sink (ug/m3)
Kma = solid-air partition coefficient (dimensionless)
Ca = SVOC concentration in room air (ug/m3).
ha = gas-phase mass transfer coefficient (m/h)
hm = solid-phase mass transfer coefficient, from equation 4 (m/h)
Dm = solid-phase diffusion coefficient (m2/h)
ALj = thickness of the top (exposed) slice (m).
Note that the solid-phase mass transfer coefficient is not only a function of diffusion coefficient
but also a function of the thickness of the slice.
Mass transfer between two adjacent slices of the same material:
(5)
where Rtj = rate of mass transfer from slice / to slicey (ug/h)
hm = solid-phase mass transfer coefficient (m/h)
Dm = solid-phase diffusion coefficient (m2/h)
AZ/j, AZy = thicknesses of slices /' and7 (m)
(ALZ-+ ALj)/2 = travel distance for inter-slice diffusion (m)
Cmi = concentration in slice / (ug/m3)
Cmj = concentration in slicey (ug/m3).
Mass transfer between two adjacent slices of the different materials:
This type of mass transfer applies only to double-layer sources or sinks. Equation 7 is for the
mass transfer across the material-material interface:
53
-------
R2l=AHml(KuCm2-Cj (7)
1 l £L (8)
Hml hml
(9)
Ku=±- (11)
12 j^ V '
Ama2
where R2i = rate of mass transfer from material 2 to material 1 (ug/h)
^4 = area of the material/material interface (m )
Hmi = overall mass transfer coefficient with respect to material 1, from equation 8 (m/h)
Kn = solid-solid partition coefficient for materials 1 and 2, from equation 11
(dimensionless)
Cm2 = concentration in the slice of material 2 in contact with material 1 (ug/m3)
Cmi = concentration in the slice of material 1 in contact with material 2 (ug/m3)
hmi, hm2 = solid-phase mass transfer coefficients for materials 1 and 2 (m/h)
Dmi, Dm2 = solid-phase diffusion coefficients for materials 1 and 2 (m2/h)
ALj, AL2 = thicknesses of the two contacting slices for materials 1 and 2 (m)
Kmai, Kma2 = material/air partition coefficients for materials 1 and 2 (dimensionless).
6.4.2 Dynamic Langmuir sink
The net adsorption rate for the dynamic Langmuir sink is given by equation 12 (Tichenor, et al.,
1991):
RL=A(kaCa-kdC,) (12)
54
-------
where RL = net adsorption rate for the Langmuir sink (ug/h)
A = area of sink surface (m2)
ka = adsorption rate constant (m/h)
Ca = concentration in air (ug/m3)
kd = desorption rate constant (h"1)
Cs = concentration on sink surface (ug/m2).
6.4.3 Dynamic Freundlich sink
The net adsorption rate for the dynamic Freundlich sink is given by equation 13 (Van Loyd et al.,
1997):
RP=A(faCaa-f
-------
This program does not support the equilibrium model (equation 14). However, it can be
converted to a roughly equivalent dynamic model (equation 13) if parameters Kfand n are
known. Details are given in Appendix B.
CAUTION: The behavior of the Freundlich adsorption models (equations 13 and 14) is poorly
understood. Little is known about the dependence of the model parameters on the properties of
the adsorbate and adsorbent. Thus, they should be used with caution.
6. 4. 4 Permeable particles
SVOC interactions with permeable particles, either suspended or settled, are represented by the
modified state-space (MSS) method, which divides the particle of a given size into several
hollow spheres and one solid sphere at the core (Guo, 2014).
Mass transfer between room air and the top hollow sphere:
(17)
Kpahp ha
(19)
where Rap = rate of mass transfer from room air to airborne particles (ug/h)
A = surface area of the particle (m2)
Ha = overall gas-phase mass transfer coefficient, from equation 18 (m/h)
Cpi = concentration in the exposed hollow sphere (ug/m3)
Kpa = particle-air partition coefficient (dimensionless)
Ca = concentration in room air (ug/m3).
hp = particle-phase mass transfer coefficient, from equation 19 (m/h)
Dp = particle-phase diffusion coefficient (m /h)
r0 = radius of the particle (m)
rtd = radius that divides the top hollow sphere into two parts with equal volumes
(equation 20).
56
-------
(2°)
where ro = outside radius of the top hollow sphere (m)
r i = inside radius of the top hollow sphere (m).
Mass transfer within the particle:
The rate of mass transfer between two adjacent hollow spheres, /' andy, is determined by equation
21:
(21)
(22)
hp = -?£— (23)
V V
'tdi 'tdj
where Ry = rate of mass transfer from hollow sphere /' to hollow sphere y' (ng/h)
r\
At = contact area for hollow spheres /' andy, from equation 22 (m )
hp = particle-phase mass transfer coefficient between hollow spheres /' andy, from
equation 23 (m/h)
rt = inside radius of hollow sphere / (i.e., the outer hollow sphere) (m)
rtdi = radius for travel distance in hollow sphere /', from equation 20 (m)
rtdj = radius for travel distance in hollow sphere y, from equation 20 (m)
(rtdi - rtdj} = travel distance for diffusion between the two hollow spheres (m).
6.4.5 Impermeable particles
The surface adsorption of SVOCs by impermeable particles is represented by the dynamic forms
of the Langmuir or Freundlich adsorption models (equations 12 and 13).
6.4.6 Particles with a liquid film over an impermeable solid core
The rate of mass transfer between indoor air and the liquid film is determined by equation 24:
±-} (24)
57
-------
- = —+ - (25)
Ha KLahL ha
hL=~^T (26)
where Rap = rate of mass transfer from indoor air to the particle (|-ig/h)
Ap = surface area of the particle (m2)
Ha = overall gas-phase mass transfer coefficient, from equation 25 (m/h)
Ca = gas-phase concentration in indoor air (|ag/m3)
CL = concentration in the liquid film of the particle (ng/m3)
Kia = liquid-air partition coefficient (dimensionless)
hi = liquid-phase mass transfer coefficient, from equation 26 (m/h)
ha = gas-phase mass transfer coefficient (m/h)
DL = liquid-phase diffusion coefficient (m2/h)
YQ = radius of the particle (m)
rtd = radius for travel distance in the liquid film, from equation 20 (m)
ro - rtd = travel distance in the liquid film (m).
6.4.7 SVOC mass fluxes
The SVOC mass fluxes are calculated from equation 27, where the mass transfer rate (R) is from
equations 2, 12, 13, 17, or 24.
X = ^ (27)
where X= SVOC mass flux (ug/m2/h)
R = mass transfer rate
A = contact area of the two phases (m2).
The mass flux is a signed value. In this program, a positive flux means SVOC emission into
room air while a negative value means sorption from room air.
6.5 Differential equations
All i-SVOC models are in the form of a system of first-order, ordinary differential equations.
The differential equations for individual indoor media (i.e., compartments) are presented in
Sections 6.5.1 through 6.5.7 below.
58
-------
6.5.1 Room Air
The mass balance for the gas-phase concentration is given by equation 28:
»2 «3 «4
Rsai-^Ranj-YjnDkRadk-VYJNplRap
i=\ j=\ t=i /=i
where V= room volume (m3)
Ca = gas-phase SVOC concentration (|ag/m3)
t = time (h)
Q = air change flow rate (m3/h)
p = penetration factor for the gas-phase SVOC in ambient air (fraction)
Camb = gas-phase SVOC concentration in ambient air (|ag/m3)
RSai = rate of emission from source /' (ng/h)
Ran/ = rate of mass transfer from gas phase to sink material y (|-ig/h)
nDk = total number of settled dust particles in size bin/particle type k in the room (counts)
Radk = rate of mass transfer from gas phase to a single settled dust in size bin/dust type k
Npi = number concentration of airborne particles in size bin/particle type / (counts/m3)
Rapi = rate of mass transfer from gas phase to a single airborne particle in size bin/particle
type / (|ag/h)
nj = number of sources
«2 = number of sinks
n3 = number of size bins/particle types for settled dust
114 = number of size bins/particle types for airborne particles.
6.5.2 Diffusional sources and sinks
Equations 29, 30, and 31 are for, respectively, the exposed slice, interior slices, and bottom slice
with no mass transfer:
For the top slice that is exposed to air:
v^=-Rla+R2l (29)
For interior slices within the same material:
59
-------
For the bottom slice (n) without mass transfer to other media:
where vi, v7, vn, = volumes of top slice, interior slicey, and bottom slice (m3)
Cmi, Cmj, Cmn, = concentrations in top slice, interior slicey, and bottom slice (ng/m3)
Ria = rate of mass transfer from the top slice to air, from equation 2 (ng/h)
R2i = rate of mass transfer from the slice 2 to slice 1, from equation 5 (ng/h)
Rji = rate of mass transfer from the slicey to slice /' (/'=/'+ 1), from equation 5 (ng/h)
Rjk = rate of mass transfer from the slicey to slice k (k=j+l), from equation 5 (ng/h)
Rnn-i = rate of mass transfer from the slice n (the bottom slice) to slice n-l, from equation
5 (ng/h).
6.5.3 Surface adsorption
Adsorption of SVOCs on impermeable surface materials is represented by the dynamic form of
the Langmuir model (equation 32) or the Freundlich model (equation 33):
A- = RL (32)
F (33)
dt
r\
where A = surface area (m )
Cs = concentration on sink surface (ug/m )
t = time (h)
RL = net adsorption rate for dynamic Langmuir model, from equation 12 (ug/h)
RF = net adsorption rate for dynamic Freundlich model, from equation 13 (ug/h).
6.5.4 Permeable particles
For permeable particles, equations 34 and 35 are for, respectively, the top and interior hollow
spheres; equation 36 is for the solid sphere at the core.
60
-------
• = Rap-Rn (34)
at '=R»~R* (35)
vn r\ //•* /-\
vn ?-=-Rm_l (36)
where vi, y,-, vn = volumes of hollow spheres 1 andy, and solid sphere n, from equation 37 (m3)
Cpi, Cry, Cpn = SVOC concentrations in hollow spheres 1 andy, and solid sphere n
(Hg/m3)
Rap = rate of mass transfer from air to the top hollow sphere, from equation 17 (ng/h)
Rn = rate of mass transfer from the top hollow sphere to the adjacent hollow sphere,
from equation 21 (ng/h)
Ry = rate of mass transfer from hollow sphere /' to hollow spherey' (/=/+!), from equation
21 (ng/h)
Rjk = rate of mass transfer from hollow sphere y' to hollow sphere k (£=/+!), from
equation 21 (ng/h)
Rnn-i = rate of mass transfer from solid sphere n to adjacent hollow sphere n-l, from
equation 21 (ng/h).
^n ( 3 A ,>>n\
v = — (r0 ~r, ) (37)
j
where v = volume of the hollow sphere (m3)
r0 = outside radius of the hollow sphere (m)
Yi = inside radius of the hollow sphere (m).
6. 5. 5 Impermeable particles
The differential equations for impermeable particles are the same as equations 32 and 33.
6. 5. 6 Particles with a liquid film over an impermeable solid core
The differential equation for the liquid layer of particles is given by equation 38:
VL=R"L (38)
where v/, = volume of the liquid film, from equation 37 (m3)
61
-------
CL = SVOC concentration in the liquid film (|ag/m3)
t = time (h)
Rai = rate of mass transfer from air to the liquid film, from equation 24 (ng/h).
(39)
where TO = radius of the particle (m)
r i = radius of the solid core (m).
6.5.7 Number concentration of airborne particles for a pulse release
The number concentration of airborne particles following a pulse release is given by equation 40
with initial conditions oft=tp and Np = Npo.
dN
~^ = -(a+kl}Np (40)
where t = elapsed time (h)
tp = time for the pulse release (h)
Np = number concentration at time t (counts/m3)
a = ventilation rate (h"1)
ki = first-order deposition rate constant (h"1).
6.6 Initial Conditions
The program sets the initial time at t = 0 hour. All other initial conditions are defined by the user.
For example, the initial concentration in indoor air is defined in the page; the
initial concentrations in different slices of the source are defined in form
in page . After the model is compiled successfully, the user can view the initial
conditions by clicking the speed button or select , from the main
menu.
6.7 Unit Conversion
This program uses (u.g/m3) as the base unit for SVOC concentrations in all indoor media. The
concentration units for the output data vary. This section presents the equations for unit
conversion.
62
-------
6. 7. 1 SVOC Concentration in sources and sinks
The program gives the SVOC concentration in sources and sinks in (|ag/m3), which can be
converted to (i-ig/g) by equation 41 :
P
(41)
where Cmw = SVOC concentration in source or sink material in (ug/g)
Cmv = SVOC concentration in source or sink material in (ug/m3)
p = material density (g/cm3).
Note that, if the output is the concentrations in different slices (see Section 6.3), the unit
conversion must be done for individual slices because the slices have different thicknesses.
6.7.2 Particle-air partition coefficient
The particle-air partition coefficient is sometimes given in (m3/ug). It can be converted to the
dimensionless value by using equation 42:
Kp=lOl2Kp/p (42)
where Kp = particle-air partition coefficient (dimensionless)
Kp = particle-air partition coefficient (m3/ug)
p = particle density (g/cm3).
6.7.3 Particle mass and number concentrations in air
For airborne particles in a given size bin or particle type, the conversion between the mass and
number concentrations are done with equation 43:
",=6x10-^ (43)
where Np = particle number concentration (counts/m )
63
-------
Mp = particle mass concentration (ug/m3)
p = particle density (g/cm3)
d= particle diameter (um).
A unit converter is available for this purpose ( / / ).
6. 7.4 SVOC concentration for impermeable particles
The basic unit for SVOC sorption by impermeable particles is (ug/m2). Equation 44 is used to
convert the result to common unit (ug/g particles):
(44)
dp
where Q™, = SVOC concentration in impermeable particles (ug/g particle)
Cps = SVOC concentration adsorbed by impermeable particles (ug/m2 particle)
d = diameter of particles (um)
p = density of particles (g/cm3).
A unit converter is available for this purpose ( / /
).
6. 7.5 Dust loading versus number of dust
For a given size bin or particle type, equations 45 and 46 can be used to convert between dust
loading and number of dust particles:
(45)
(46)
6x10"
r\
where ND = number of settled dust particles per unit area (counts/m )
LD = dust loading (g/m2)
p = density of dust particles (g/cm3)
d= diameter of dust particles (|-im).
64
-------
To calculate the total number of dust particles in a given size bin or dust type, multiply ND by the
surface area. Note that both equations 45 and 46 are size-dependent. A unit converter is available
for this purpose ( / / ).
6.8 Miscellaneous calculations
6.8.1 Calculating the average particle-phase SVOC concentration in air in (jug/g particles)
The particle-phase SVOC concentration in air can be expressed in either (ug SVOC/g particles)
or (ug SVOC/m3 air). These concentration units require different calculation methods, as
described below.
When expressed in (ug/g particles), the average particle-phase SVOC concentration is the
weighted mean of all particles in room air, from equation 47:
(47)
i=\
•pl2
~ P, (48)
where Cpw = average SVOC concentration in particle-phase in air (ug/g)
n = number of size bins/particle types
Npi = number concentration for particles in size bin/particle type /' (counts/m3)
Wi = weight of one particle in size bin/particle type /', from equation 48 (g)
Cwi = SVOC concentration in particles in size bin/particle type /' (ug/g)
di = diameter of particles in size bin/particle type / (um)
PI = density of particles in size bin/particle type /' (g/cm3).
6.8.2 Calculating the total particle-phase SVOC concentration in air in fiug/m3 air)
When expressed in (ug/m3 air), the total particle-phase SVOC concentration is the weighted sum
of all particles in room air. Equation 49 takes into consideration both the number concentrations
and particle-phase SVOC concentrations:
65
-------
r =TTV r w (49s)
.pv / , J v pi ^- wi W i \*yJ
where Cpv = total particle-phase SVOC concentration in air (ug/m3)
n = number of size bins/particle types
Npi = number concentration for particles in size bin/particle type /' (counts/m3)
wt = weight of one particle in size bin/particle type /', from equation 48 (g)
Cwi = SVOC concentration in particles in size bin/particle type /' (ug/g).
6.8.3 Simulating episodic emission sources for airborne particles
Many indoor particle sources, such as vacuuming, cooking, smoking, and incense or candle
burning, feature episodic particle generation. These sources are neither constant nor pulse
injection. As a practical tactic, an episodic source of particles can be represented by a series of
pulse injections (Guo, 2014). To do so, the number of pulse releases and the initial number
concentration for each release must be determined. If the target number concentration during the
episode is given, the amount of particles to be released in each pulse release can be estimated
from equation 50 by using a root-trapping algorithm. It is assumed that the release times are
equally spaced.
i n l\
NE =737 ^ }N* ^^^ dt (50)
li lo -i tpi
where NE = average number concentration during the episode (counts/m3)
ti = episode end time (h)
to = episode start time (h)
n = number of pulse releases
Npi = initial number concentration for the /'* pulse release (counts/m3)
a = ventilation rate (h"1)
ki = first-order deposition rate constant (h"1)
t = elapsed time (h)
tpi = release time for the /'* pulse release (h).
This program contains a calculator (, ) for
determining the initial number concentration for each pulse release. To use this equation, the
ventilation rate during the episode must remain constant. Figure 36 shows the simulated particle
concentrations for the following hypothetical case:
66
-------
Particle release event occurs between 2 and 3 elapsed hours
Particle diameter = 1 (jam)
Particle density = 1 (g/cm3)
Particle mass concentration during the episode = 200 (|ag/m3), which is equivalent to a
number concentration of 3.82^108 (counts/m3) for the particles with the diameter and
density mentioned above.
The event was represented by four consecutive pulse releases and the initial particle
concentrations (Table 15) were calculated with the tool under
the menu. Figure 36 shows the simulated number concentrations with demonstration
model "PM-episodic.svoc". In most cases, the difference between the target and simulated
number concentrations during the episode is within 2%.
Table 15. Representing an episodic particle-release event by four consecutive pulse releases
Release No.
1
2
3
4
Release time
(h)
2.00
2.25
2.50
2.75
Initial concentration
(counts/m3)
4.634xl08
1.528xl08
1.528xl08
1.528xl08
67
-------
6.0E+8
2 3
Elapsed Time (h)
Figure 37. Simulated particle concentrations in room air due to an episodic particle-release event; created
by demonstration model "PM-episodic.svoc".
6.8.4 Calculating the average SVOC concentration in settled dust
When there are multiple size bins/particle types for settled dust, the average SVOC concentration
in the dust particles is the weighted mean of the concentrations of different size bins/particle
types:
IX
€*.=-&-
IX ^
(51)
where Cdw = average SVOC concentration in settled dust (ug/g)
n = number of size bins/particle types
rid = number of dust particles in size bin/particle type /' (counts/m3)
Wj = weight of one dust particle in size bin/particle type /', from equation 48 (g)
Cwi = SVOC concentration in dust particles of size bin/particle type /' (ug/g).
68
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6.9 SVOC migration from sources to settled dust due to direct contact
Program i-SVOC does not contain any models for SVOC transfer between sources and settled
duct due to direct contact of the two phases. A simple method for estimating the upper bound of
the SVOC concentration in the duct particles is given in Appendix A.
69
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7. References
(Website accessibility was last verified on September 20, 2013)
Cheney, R. L. and Kincaid, D. (1980). Numerical Mathematics. Brooks/Cole Publishing Co.,
Pacific Grove, CA, pp 194-197.
Clausen, P. A., Hansen, V., Gunnarsen, L., Afshari, A., Wolkoff, P. (2004). Emission of di(2-
ethylhexyl) phthalate from vinyl flooring into air and uptake in dust: emission and sorption
experiments in FLEC and CLIMPAQ, Environmental Science and Technology, 38: 2531-2537.
Forthythe, G. E., Malcolm, M. A., and Moler, C. B. (1977). Computer Methods for Mathematical
Computation. Prentice-Hall, Inc., Englewood Cliffs, NJ, pp 136-147.
Guo, Z. (2002). Review of indoor emission source models - Part 2. Parameter estimation,
Environmental Pollution, 120: 551-564.
Guo, Z. (2005). Program PARAMS User's Guide, U.S. EPA, EPA/600/R-05/066,
32pp.
Guo, Z., Liu, X., Krebs, K. A., Stinson, R. A., Nardin, J. A., Pope, R. H., Roache, N. F. (2011).
Laboratory study of polychlorinated biphenyl (PCB) contamination and mitigation in buildings
— Part 1. Emissions from selected primary sources, U.S. EPA, EPA/600/R-11/156, 107 pp.
Guo, Z., Liu, X., Krebs, K. A., Greenwell, D. J., Roache, N. F., Stinson, R. A., Nardin, J. A.,
and Pope, R. H. (2012). Laboratory study of polychlorinated biphenyl (PCB) contamination
and mitigation in buildings — Part 2. Transport from primary sources to building materials and
settled dust, U.S. EPA, EPA/600/R-ll/156a, 166 pp.
Guo, Z. (2013). A framework for modeling non-steady state concentrations of semivolatile
organiccompoundsindoors—lEmissionsfromdiffusionalsourcesandsorptionbyinterior
surfaces, Indoor and Built Environment, 22: 685-700.
Guo, Z. (2014). A framework for modeling non-steady state concentrations of semivolatile
organic compounds indoors — II. Interactions with particulate matter, Indoor and Built
Environment, 23:26-43.
70
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Kumar, D. and Little, J. C. (2003a). Single-layer model to predict the source/sink behavior of
diffusion controlled building materials. Environmental Science & Technology, 37:3821-3827.
Kumar, D. and Little, J. C. (2003b). Characterizing the source/sink behavior of double-layer
building materials. Atmospheric Environment, 37: 5529-5537.
Li, W. G., and Davis, E. J. (1996). Aerosol evaporation in the transition regime, Aerosol Science
and Technology, 25: 11-21.
Liu, Z., Ye, W., and Little, J. C. (2013). Predicting emissions of volatile and semivolatile organic
compounds from building materials: a review, Building and Environment, 64: 7-25.
Nazaroff, W. W. (2004). Indoor particle dynamics, Indoor Air, 14 (Suppl. 7): 175-183.
Qian, J., Ferro, A. R., and Fowler, K.R. (2008), Estimating the resuspension rate and residence
time of indoor particles, JAWMA, 58(4):502-516.
Schwope, A. D., Goydan, R., and Reid, R. C. (1990). Methods for assessing exposure to
chemical substances. Volume 11: Methodology for estimating the migration of additives and
impurities from polymeric materials. U.S. EPA, EPA 560/5-85/015, 148 pp.
Shi, S. and Zhao, B. (2012). Comparison of the predicted concentration of outdoor originated
indoor polycyclic aromatic hydrocarbons between a kinetic partition model and a linear
instantaneous model for gas-particle partition, Atmospheric Environment, 59:93-101.
Sparks, L. E. (2001). Indoor air quality modeling, in Spengler, J. D., Samet, J. M., and
McCarthy, J. F. (eds.), Indoor Air Quality Handbook, McGraw-Hill, New York, NY, pp 58.1-
58.23.
Takigami, H., Suzuki, G., Hirai, Y., and Sakai, S. (2008). Transfer of brominated flame
retardants from components into dust inside television cabinets. Chemosphere, 73: 161-169.
Tichenor, B. A., Guo, Z., Dunn, J. E., Sparks, L. E., Mason, M. A. (1991). The interaction of
vapor phase organic compounds with indoor sinks, Indoor Air, 1:23-35.
Van Loy, M. D., Lee, V. C., Gundel, L. A., Daisey, J. M., Sextro, R. G, Nazaroff, W. W. (1997).
Dynamic behavior of semivolatile organic compounds in indoor air. 1. Nicotine in a stainless
steel chamber, Environmental Science and Technology, 31:2554-2561.
Weschler, C. J., Salthammer, T., and Fromme, H. (2008). Partitioning of phthalates among the
gas phase, airborne particles and settled dust in indoor environments, Atmospheric Environment,
42:1449-1460.
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Webster, T. F., Harrad, S., Millette, J. R., Holbrook, R. D., Davis, J. M., Stapleton, H. M., Allen,
J. G., McClean, M. D., Ibarra, C., Abdallah, M. A., and Covaci A. (2009). Identifying transfer
mechanisms and sources of decabromodiphenyl ether (BDE 209) in indoor environments using
environmental forensic microscopy, Environmental Science & Technology., 43(9):3067-3072.
Xu, Y. and Little, J. C. (2006). Predicting emissions of SVOCs from polymeric materials and
their interaction with airborne particles, Environmental Science and Technology., 40: 456-461.
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Appendix A
SVOC transfer to settled dust due to direct contact with a source
SVOC can migration from a source to settled dust by direct contact (Webster et al., 2009;
Takigami et al., 2009). This mass transfer mechanism is especially important for chemicals with
very low vapor pressures. The current version of i-SVOC does not include this mechanism
because there are no published dynamic models that take into consideration both solid-solid and
solid-air mass transfers. The two highly simplified models described below allow rough
estimation of the SVOC concentration in settled dust that is in direct contact with a source. Both
models ignore the SVOC transfer between the dust and air.
A.I Equilibrium model
When equilibrium is reached between two solid materials that are in direct, firm contact, the
distribution of the SVOC between the two phases is determined by equation A.I:
Kdm= ^- (A.I)
^m
where Kdm = solid-solid partition coefficient between the dust and source material (dimensionless)
Cd = equilibrium SVOC concentration in dust ((^g/m3)
Cm = equilibrium SVOC concentration in source material
Although few, if any, experimentally determined solid-solid partition coefficients are available
for common building materials and dust, parameter Kdm can be estimated from the solid-air
partition coefficients for the two phases (Kumar and Little, 2003b):
v
(A.2)
am v
Kma
where Kda = solid-air partition coefficient for dust particles (dimensionless)
K^ = solid-air partition coefficient for source material (dimensionless).
Thus, the equilibrium SVOC concentration in the dust can be estimated from equation A.3:
Cd=^Cm (A.3)
ma
73
-------
The values of Q calculated from equation A.3 should be treated as the upper bound of the
absorption because the calculation ignores the SVOC mass fluxes between the dust and room air
and because it takes much longer time for large dust particles to reach equilibrium than for small
particles.
The solid-solid partition coefficient, Kdm, can be either greater or smaller than 1, depending on
the values of the two solid-air partition coefficients in Equation A.2. Takigami et al. (2009)
observed that, in some cases, the concentrations of polybrominated diphenyl ethers (PBDEs) in
settled dust collected from inside the television casing were higher than their concentrations in
the sources (i.e., the casing and circuit boards).
A.2 Dynamic model
The rate of mass transfer between two solids that are in direct contact is given by Equations 7
through 11 in Section 6.4.1. For SVOC transfer from source to dust, Equation A4 applies:
Rsd=AHd(KdmCm-Cd) (A.4)
where Rsd = rate of mass transfer from source to dust particle
A = contact area (m2)
Hd = overall mass transfer coefficient with respect to the dust phase (m/h)
Kdm = solid-solid partition coefficient, from equation A.2 (dimensionless)
Cm = concentration in the source
Cd = concentration in the dust
If the source is a large reservoir for the SVOC, which is the case for many SVOCs including
phthalates and flame retardants, the sorption by the settled dust has little effect on the SVOC
concentration in the source. Thus, we can assume that Cm is constant and, therefore, Equation A4
can be simplified because the overall mass transfer coefficient is no longer needed:
Rsd=Ahd(KdmCm-Cd) (A.5)
where hd = solid-phase mass transfer coefficients for dust particle (m/h).
74
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Dust particles are in different shapes. To use Equation A.5, we further assume that the dust
particle can be represented by a cube with a contact area of A and a height of &. The solid-phase
mass transfer coefficient, hd, can then be estimated from Equation A.6:
hd =L (A.6)
where Dd = solid-phase diffusion coefficients for dust particle (m2/h)
& = height of the dust particle "cube" (m).
Equation A.7 gives the mass balance for the dust cube:
dC
'J_
'' D
dt
=Ahd(KdmCm-Cd] (A.7)
where vd = volume of the dust cube (m3)
t = time (h).
Given the initial conditions of t = 0 and Cd = 0, Equation A.7 can be solved to give an exact
solution for Q (Equation A.8). Note that Equation A.8 contains neither VD nor A.
Cd=KdmCm\l-e *2 I (A.8)
where Cd = SVOC concentration in the dust (ng/m3)
Kdm = solid-solid partition coefficient, from Equation A.2 (dimensionless)
Cm = SVOC concentration in the source, treated as a constant (ng/m3)
Dd = solid-phase diffusion coefficient for dust particle (m2/h)
& = height of the dust cube (m)
t = time (h).
To determine the value of & in Equation A.8, the dust particle of whatever shape must be
"converted" to an equivalent cube. This can be done in three steps: (1) calculate the volume of
the dust particle (VD)', (2) define the contact area (A); and (3) calculate & from & =
Figure A.I was created with the following parameters:
& = IxlO'5, 2xlO'5, and 5xlO'5 (m)
= 0.5
,-12
-.10
Dd= 10'12m2/h
Cm = 10 ng/m (equivalent to 10000 ng/g if density = 1 g/cm)
75
-------
6000
100 200 300 400 500
Elapsed Time (h)
Figure A.I SVOC migration from a constant source to settled dust due to direct contact of the two phases
(assuming dust density = 1).
76
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Appendix B
Parameter estimation for the dynamic Freundlich adsorption model
B.I. Purpose
This appendix describes a method for converting the equilibrium Freundlich adsorption model to
a roughly equivalent, dynamic counterpart.
B.2 Equilibrium Freundlich model
The adsorption model proposed by Xu and Little (2006) assumes that a nonlinear,
instantaneously reversible, Freundlich equilibrium relationship exists between the air and the
surface, and that the SVOC concentration adsorbed on the surface at any time can be calculated
from equation B.I:
Cs=KfC"a (B.I)
r\
where Cs = concentration on sink surface (ug/m )
Kf = constant for a given chemical and sink material at a given temperature (ng1"11 m3""2)
Ca = concentration in air (ug/m3)
n = constant for a given pair of chemical and sink material at a given temperature
(dimensionless).
B.3 Dynamic Fruendlich model
The dynamic Freundlich adsorption model (Van Loyd et al., 1997) uses equations B.2 and B.3 to
calculate the adsorption and desorption rates:
Ra=AfaC: (B.2)
! (B.3)
where Ra = adsorption rate (ug/h)
Rd = desorption rate (ug/h)
A = area of sink surface (m2)
fa = nonlinear adsorption rate constant (ug1"™ m3™"2 h"1)
1 R 9R 9 1
fd = nonlinear desorption rate constant (ug m p" h" )
Ca = concentration in air (ug/m3)
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Cs = concentration on sink surface (ug/m )
a and/? = dimensionless constants.
It is easy to prove that the equilibrium and dynamic Freundlich models are linked by equations
B.4andB.5:
(f Y"
Kf=27- (B-4)
n = — (B.5)
B.4 Estimating parameters a, /?,/«, and/,/ from K/ and «
When the parameters for the equilibrium Freundlich model — Kf and n — are known, the
parameters for the dynamic model — a, ft, fa, andfd — can be estimated in three steps, as
described below.
Step 1: Determine the values of a and ft based on the value of n as follows:
lfn> 1, seta= 1, andjff= l/n
Ifn < 1, seta = n, and/? = 1
In either case, the ratio a//? is equal to n (see Equation B.5). It should be noted that the case with
n>\ is rare because, although equation B. 1 is purely empirical, parameter n usually varies
between 0 and 1.
Step 2: Assign a reasonably large value for/a. As shown in equation B.4, it is the ratio fa/fd that
really matters. The instantaneous equilibrium assumption implies that the adsorption rate is large.
Thus, the value for/a should be large. In the examples below,/a is set to 10 (ug "a m3a"2 h"1). An
fa value much greater than 10 is not recommended because it can cause numerical instability
during the simulation.
Step 3: Calculatefa from equation B.6, which is derived from equation B4:
(B.6)
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B.5 Examples
Table B.I summarizes the parameters for the examples described in Section 3.6. The simulation
results are presented in Figures B.I and B.2.
Table B.I. Sink parameters for DEHP emissions from vinyl flooring[
Model
Equilibrium
Dynamic
Parameter
Name
Kf
n
a
P
fa
fd
Parameter Values
CLIMPAQ
3800
1.5
1
0.67
10
0.040
FLEC
6000
0.47
0.47
1
10
0.0017
Notes
Xu & Little, 2006
Xu & Little, 2006
From step 1
From step 1
From step 2
From step 3
Other required parameters for creating the models are given in Table 6 in Section 3.6.
CD
01
u
O
U
1.0
— 0.8 -
~ 0.6 -
0.4 -
0.2 -
0.0 -1
1.6m2
0.8m2 _.
_„---""
,--***" 0.4 m2
0.2m2
0 50 100 150 200
Elapsed Time (days)
250
300
Figure B.I. Simulated DEHP concentrations in the CLIMPAQ chamber with the sink parameters
given in Table B.I. Results are from four simulations.
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1.0
0.8 -
< 0.6 -
_c
o
S 0.4 -\
01
u
0.2 -
0.0
100 200 300
Elapsed Time (days)
400
500
Figure B.2. Simulated DEHP concentrations in the FLEC chamber with the sink parameters
given in Table B.I.
B.6 Caution
This method was tested with very limited data and, thus, should be used with caution.
80