Formaldehyde Indoor Air Model – Pressed Wood Products, Version 2.0 (FIAM-pwp v2.0):

Model User Manual and Documentation

Exposure Assessment Branch

Economics, Exposure and Technology Division

Office of Pollution Prevention and Toxics

Office of Chemical Safety and Pollution Prevention

U.S. Environmental Protection Agency

1200 Pennsylvania Avenue, N. W.

	Washington, D.C.  20460

July 2012

EPA acknowledges the analytical and draft preparation support of Versar, Inc. of Springfield, Virginia in the preparation of this report, provided under Contract No. EP-W-10-005.

  TOC \o "1-3" \h \z \u    HYPERLINK \l "_Toc332143174"  1.	INTRODUCTION   PAGEREF _Toc332143174 \h  1

  HYPERLINK \l "_Toc332143176"  2.	USER INTERFACE	  PAGEREF _Toc332143176 \h  3

  HYPERLINK \l "_Toc332143177"  2.1	Background – Model Versions	  PAGEREF _Toc332143177 \h  3

  HYPERLINK \l "_Toc332143178"  2.2	House Screen	  PAGEREF _Toc332143178 \h  4

  HYPERLINK \l "_Toc332143179"  2.2.1	Inputs and Options	  PAGEREF _Toc332143179 \h  4

  HYPERLINK \l "_Toc332143180"  2.2.2	Basis for Defaults	  PAGEREF _Toc332143180 \h  8

  HYPERLINK \l "_Toc332143181"  2.3	Source Screen	  PAGEREF _Toc332143181 \h  14

  HYPERLINK \l "_Toc332143182"  2.3.1 	Types of Inputs	  PAGEREF _Toc332143182 \h  14

  HYPERLINK \l "_Toc332143183"  2.3.2 	Adding Default Inputs	  PAGEREF _Toc332143183 \h  15

  HYPERLINK \l "_Toc332143184"  2.3.3 	Adding Custom Inputs	  PAGEREF _Toc332143184 \h  16

  HYPERLINK \l "_Toc332143185"  2.3.3 	Basis for Defaults	  PAGEREF _Toc332143185 \h  16

  HYPERLINK \l "_Toc332143186"  2.4	Exposure Screen	  PAGEREF _Toc332143186 \h  21

  HYPERLINK \l "_Toc332143187"  2.4.1 	Inputs and Options for Age of Sources and Formaldehyde Level of Interest	  PAGEREF _Toc332143187 \h  21

  HYPERLINK \l "_Toc332143188"  2.4.2 	Inputs and Options for Exposure Groups	  PAGEREF _Toc332143188 \h  22

  HYPERLINK \l "_Toc332143189"  2.4.3 	Inputs and Options for Concentrations Outside the Home	  PAGEREF _Toc332143189 \h  23

  HYPERLINK \l "_Toc332143190"  2.4.4 	Basis for Defaults	  PAGEREF _Toc332143190 \h  24

  HYPERLINK \l "_Toc332143191"  2.5	Result Screen	  PAGEREF _Toc332143191 \h  27

  HYPERLINK \l "_Toc332143192"  2.5.1 	Concentration Results	  PAGEREF _Toc332143192 \h  27

  HYPERLINK \l "_Toc332143193"  2.5.2 	Exposure Results	  PAGEREF _Toc332143193 \h  28

  HYPERLINK \l "_Toc332143194"  2.5.3 	Printing Inputs and Results	  PAGEREF _Toc332143194 \h  28

  HYPERLINK \l "_Toc332143195"  2.5.4 	Archiving Inputs and Results for a Run	  PAGEREF _Toc332143195 \h  28

  HYPERLINK \l "_Toc332143196"  2.6	Model Access and Additional Features   PAGEREF _Toc332143196 \h  29

  HYPERLINK \l "_Toc332143197"  2.6.1 	Accessing the IGEMS Website	  PAGEREF _Toc332143197 \h  29

  HYPERLINK \l "_Toc332143198"  2.6.2 	Saving Inputs for Later Access	  PAGEREF _Toc332143198 \h  29

  HYPERLINK \l "_Toc332143199"  2.6.3 	Context-sensitive Help	  PAGEREF _Toc332143199 \h  29

  HYPERLINK \l "_Toc332143200"  2.7 	Example Applications	  PAGEREF _Toc332143200 \h  29

  HYPERLINK \l "_Toc332143201"  2.7.1 	Example 1 – Modeling with Model Default Values	  PAGEREF _Toc332143201 \h  29

  HYPERLINK \l "_Toc332143202"  2.7.2 	Example 2 – Modeling a Hypothetical Chamber Test for CARB Compliance	  PAGEREF _Toc332143202 \h  30

  HYPERLINK \l "_Toc332143203"  2.7.3 	Example 3 – Demonstrating an Equilibrium Concentration	  PAGEREF _Toc332143203 \h  31

  HYPERLINK \l "_Toc332143204"  2.7.4	Example 4 – Examining the Incremental Contribution of a Product	  PAGEREF _Toc332143204 \h  32

  HYPERLINK \l "_Toc332143205"  2.7.5	Example 5 – Varying the Decay Rate (Half Life)	  PAGEREF _Toc332143205 \h  33

  HYPERLINK \l "_Toc332143206"  3.	MODEL CALCULATIONS AND ASSUMPTIONS	  PAGEREF _Toc332143206 \h  35

  HYPERLINK \l "_Toc332143207"  3.1	Generalized Mass-Balance Equation	  PAGEREF _Toc332143207 \h  36

  HYPERLINK \l "_Toc332143208"  3.2	Steady-State Model for Initial Formaldehyde Concentration in One Compartment	  PAGEREF _Toc332143208 \h  37

  HYPERLINK \l "_Toc332143209"  3.3 	Extension of the Steady-State Model to Two Compartments	  PAGEREF _Toc332143209 \h  39

  HYPERLINK \l "_Toc332143210"  3.4 	Matthews Model Compared to HBF Model	  PAGEREF _Toc332143210 \h  40

  HYPERLINK \l "_Toc332143211"  3.5 	Other Potentially Useful Modeling Constructs	  PAGEREF _Toc332143211 \h  42

  HYPERLINK \l "_Toc332143212"  3.6 	Discussion of Indoor Sinks	  PAGEREF _Toc332143212 \h  45

  HYPERLINK \l "_Toc332143213"  3.7	Decay of Indoor Concentrations	  PAGEREF _Toc332143213 \h  45

  HYPERLINK \l "_Toc332143214"  3.8	Default Value for Half Life	  PAGEREF _Toc332143214 \h  48

  HYPERLINK \l "_Toc332143215"  3.9	Temperature and Humidity Adjustments   PAGEREF _Toc332143215 \h  51

  HYPERLINK \l "_Toc332143216"  3.10	Exposure Calculations	  PAGEREF _Toc332143216 \h  53

  HYPERLINK \l "_Toc332143217"  4.	 EVALUATION OF MODEL ALGORITHMS AND PREDICTIONS	  PAGEREF _Toc332143217 \h  55

  HYPERLINK \l "_Toc332143218"  4.1	Mathematical Correctness of Model Algorithms	  PAGEREF _Toc332143218 \h  55

  HYPERLINK \l "_Toc332143219"  4.2	NIST Assessment of Matthews Model Predictions	  PAGEREF _Toc332143219 \h  55

  HYPERLINK \l "_Toc332143220"  4.3	Assessment of FIAM-pwp Predictions – EPA Pilot Study	  PAGEREF _Toc332143220 \h  56

  HYPERLINK \l "_Toc332143221"  4.3.1	Initial Baseline Period	  PAGEREF _Toc332143221 \h  57

  HYPERLINK \l "_Toc332143222"  4.3.2	First Loading	  PAGEREF _Toc332143222 \h  58

  HYPERLINK \l "_Toc332143223"  4.3.3	Air-out Period after First Loading   PAGEREF _Toc332143223 \h  59

  HYPERLINK \l "_Toc332143224"  4.3.4	Second Loading	  PAGEREF _Toc332143224 \h  60

  HYPERLINK \l "_Toc332143225"  4.3.5	Air-out Period after Second Loading	  PAGEREF _Toc332143225 \h  61

  HYPERLINK \l "_Toc332143226"  4.3.6	Third Loading	  PAGEREF _Toc332143226 \h  62

  HYPERLINK \l "_Toc332143227"  4.4	FIAM-pwp Predictions for Recent Residential Field Monitoring Studies	  PAGEREF _Toc332143227 \h  63

Appendix A – Summary of EPA Formaldehyde Pilot Study

Appendix B – Model Sensitivity

Appendix C – Basis for Emission Classes

Appendix D – Historical Testing of PWPs to Derive Slope and Intercept Values

Appendix E – Derivation of Two-zone Steady-state Solution

  TOC \h \z \t "Figure Caption" \c    HYPERLINK \l "_Toc332144055"  Figure 2-1. FIAM-pwp House Screen.	  PAGEREF _Toc332144055 \h  4

  HYPERLINK \l "_Toc332144058"  Figure 2-2. Popup Screen – Create Your Own Structure Type.	  PAGEREF _Toc332144058 \h  5

  HYPERLINK \l "_Toc332144059"  Figure 2-3. U.S. Climate Zones.	  PAGEREF _Toc332144059 \h  5

  HYPERLINK \l "_Toc332144060"  Figure 2-4. Popup Screen – Create Your Own Climate Zone.	  PAGEREF _Toc332144060 \h  6

  HYPERLINK \l "_Toc332144061"  Figure 2-5. FIAM-pwp Source Screen.	  PAGEREF _Toc332144061 \h  14

  HYPERLINK \l "_Toc332144062"  Figure 2-6. Source Screen after Adding Default PWP Types	  PAGEREF _Toc332144062 \h  15

  HYPERLINK \l "_Toc332144063"  Figure 2-7. Source Screen after Adding Custom Values	  PAGEREF _Toc332144063 \h  16

  HYPERLINK \l "_Toc332144064"  Figure 2-8. Exposure Screen	  PAGEREF _Toc332144064 \h  21

  HYPERLINK \l "_Toc332144065"  Figure 2-9. Preparing to Add a New Exposure Group	  PAGEREF _Toc332144065 \h  23

  HYPERLINK \l "_Toc332144066"  Figure 2-10. Result Screen with First Two Exposure Groups Selected	  PAGEREF _Toc332144066 \h  27

  HYPERLINK \l "_Toc332144067"  Figure 2-11. Emission-rate Parameters for FIAM-pwp Default PWPs in an Apartment.	  PAGEREF _Toc332144067 \h  32

  HYPERLINK \l "_Toc332144068"  Figure 2-12. Formaldehyde Concentration Decline with Fast and Slow Decay Periods.	  PAGEREF _Toc332144068 \h  34

  HYPERLINK \l "_Toc332144069"  Figure 3-1. Representation of Declining Emission Rate by Power-law Function vs. Exponential-decay Model.	  PAGEREF _Toc332144069 \h  44

  HYPERLINK \l "_Toc332144070"  Figure 3-2. Representation of Declining Emission Rate by Power-law Function vs. Exponential-decay Model with Periods of Fast and Slow Decay.	  PAGEREF _Toc332144070 \h  44

  HYPERLINK \l "_Toc332144071"  Figure 4-1. FIAM-pwp House-Screen Inputs Used to Model Study of New California Homes.	  PAGEREF _Toc332144071 \h  65

  HYPERLINK \l "_Toc332144072"  Figure 4-2. FIAM-pwp Source-Screen Inputs Used to Model Study of New California Homes.	  PAGEREF _Toc332144072 \h  66

  HYPERLINK \l "_Toc332144073"  Figure 4-3. FIAM-pwp Results for Modeling of New California Homes.	  PAGEREF _Toc332144073 \h  66

  HYPERLINK \l "_Toc332144074"  Figure 4-4. FIAM-pwp Source-Screen Inputs Used to Model CDC Study of Travel Trailers.	  PAGEREF _Toc332144074 \h  67

  HYPERLINK \l "_Toc332144075"  Figure 4-5. FIAM-pwp Results for Modeling of Travel Trailers.	  PAGEREF _Toc332144075 \h  67

  TOC \h \z \t "Table Caption" \c  \* MERGEFORMAT    HYPERLINK \l "_Toc332143577"  Table 2-1. House Dimensions and Calculated Volume for Five Housing Types	  PAGEREF _Toc332143577 \h  9

  HYPERLINK \l "_Toc332143578"  Table 2-2. Summer and Winter Indoor Temperatures from RECS 2005, by Climate Zone	  PAGEREF _Toc332143578 \h  10

  HYPERLINK \l "_Toc332143579"  Table 2-3. Year-round Indoor Temperatures Derived from RECS 2005, by Climate Zone	  PAGEREF _Toc332143579 \h  10

  HYPERLINK \l "_Toc332143580"  Table 2-4. Modeled Year-round Indoor RH Level, by Climate Zone	  PAGEREF _Toc332143580 \h  11

  HYPERLINK \l "_Toc332143581"  Table 2-5. Alternative Analytical/Regulatory Options for EPA Formaldehyde Rule	  PAGEREF _Toc332143581 \h  17

  HYPERLINK \l "_Toc332143582"  Table 2-6. Default Slopes and Intercepts for Six Default PWP Types	  PAGEREF _Toc332143582 \h  18

  HYPERLINK \l "_Toc332143583"  Table 2-7. Default Exposed Surface Areas (in m2) for Six PWP Types, by Structure Type – New-home Case	  PAGEREF _Toc332143583 \h  20

  HYPERLINK \l "_Toc332143584"  Table 2-8. Default Exposed Surface Areas (in m2) for Six PWP Types, by Structure Type – Renovation Case	  PAGEREF _Toc332143584 \h  20

  HYPERLINK \l "_Toc332143585"  Table 2-9. Default Annual Hours at Home and Non-home Locations, by Exposure Group.	  PAGEREF _Toc332143585 \h  24

  HYPERLINK \l "_Toc332143586"  Table 2-10. Default Concentration Values for Non-home Locations	  PAGEREF _Toc332143586 \h  25

  HYPERLINK \l "_Toc332143587"  Table 2-11. Derivation of Baseline Values for Daycare, School and Work Locations	  PAGEREF _Toc332143587 \h  26

  HYPERLINK \l "_Toc332143588"  Table 2-12. Concentration Values for Selected Non-home Locations, by Emissions Scenario	  PAGEREF _Toc332143588 \h  26

  HYPERLINK \l "_Toc332143589"  Table 2-13. Run Notes for Example 1	  PAGEREF _Toc332143589 \h  30

  HYPERLINK \l "_Toc332143590"  Table 2-14. Run Notes for Example 2	  PAGEREF _Toc332143590 \h  31

  HYPERLINK \l "_Toc332143591"  Table 2-15. Run Notes for Example 3	  PAGEREF _Toc332143591 \h  31

  HYPERLINK \l "_Toc332143592"  Table 2-16. Run Notes for Example 4	  PAGEREF _Toc332143592 \h  33

  HYPERLINK \l "_Toc332143593"  Table 2-17. Run Notes for Example 5, Part 1 (fast decay period)	  PAGEREF _Toc332143593 \h  34

  HYPERLINK \l "_Toc332143594"  Table 2-18. Run Notes for Example 5, Part 2 (slow decay period)	  PAGEREF _Toc332143594 \h  34

  HYPERLINK \l "_Toc332143595"  Table 4-1.  Model Inputs (Sources and Sinks) for Initial Baseline Period	  PAGEREF _Toc332143595 \h  57

  HYPERLINK \l "_Toc332143596"  Table 4-2.  Modeling Results for Initial Baseline Period	  PAGEREF _Toc332143596 \h  58

  HYPERLINK \l "_Toc332143597"  Table 4-3.  Model Inputs (Sources and Sinks) for First (Medium) Loading	  PAGEREF _Toc332143597 \h  58

  HYPERLINK \l "_Toc332143598"  Table 4-4.  Modeling Results for First Loading	  PAGEREF _Toc332143598 \h  59

  HYPERLINK \l "_Toc332143599"  Table 4-5.  Model Inputs for Air-out Period after First Loading	  PAGEREF _Toc332143599 \h  59

  HYPERLINK \l "_Toc332143600"  Table 4-6.  Modeling Results for Air-out Period after First Loading	  PAGEREF _Toc332143600 \h  60

  HYPERLINK \l "_Toc332143601"  Table 4-7.  Model Inputs (Sources and Sinks) for Second (High) Loading	  PAGEREF _Toc332143601 \h  60

  HYPERLINK \l "_Toc332143602"  Table 4-8.  Modeling Results for Second Loading	  PAGEREF _Toc332143602 \h  61

  HYPERLINK \l "_Toc332143603"  Table 4-9.  Model Inputs for Air-out Period after Second Loading	  PAGEREF _Toc332143603 \h  61

  HYPERLINK \l "_Toc332143604"  Table 4-10.  Modeling Results for Air-out Period after Second Loading	  PAGEREF _Toc332143604 \h  62

  HYPERLINK \l "_Toc332143605"  Table 4-11.  Model Inputs (Sources and Sinks) for Third (High) Loading	  PAGEREF _Toc332143605 \h  62

  HYPERLINK \l "_Toc332143606"  Table 4-12.  Modeling Results for Third Loading	  PAGEREF _Toc332143606 \h  63

  HYPERLINK \l "_Toc332143607"  Table 4-13. Summary of Recent Formaldehyde Field Monitoring Studies	  PAGEREF _Toc332143607 \h  64

1.	INTRODUCTION

The model described in this document, the Formaldehyde Indoor Air Model - Pressed Wood Products, Version 2.0 (FIAM-pwp v2.0), is intended to assist the user in estimating human inhalation exposure to airborne formaldehyde emissions from composite wood products (CWPs) installed in new or existing residences, including smaller structures such as camper trailers. The model estimates indoor formaldehyde concentrations and associated human inhalation exposures for such situations.

FIAM-pwp is an adaptation of a model developed during the 1980s by Dr. Thomas Matthews and colleagues, at the Oak Ridge National Laboratory. The “Matthews model” was designed to estimate the steady-state indoor formaldehyde concentration due to emissions from wood products in a single indoor compartment or zone. Product emission rates in the model are dependent on the formaldehyde concentration in the vapor phase – as the concentration increases the emission rates decrease, other things being equal. The initial (“steady-state”) indoor concentration calculated by the model is assumed to decrease over time, as the formaldehyde “reservoirs” in various sources (or sinks) are gradually depleted. The decrease over time is assumed to follow a first-order exponential process, at a decay rate that corresponds to an assumed half life for the collective formaldehyde emissions.

In the mid-1990s, an EPA-sponsored pilot study was undertaken by Versar/GEOMET to assess the contribution of UF-bonded wood products to formaldehyde levels in homes and to evaluate current EPA exposure models. Shortly after this study was completed, Versar was tasked by EPA to develop a modified version of the Matthews model. The primary modifications were (1) estimation of steady-state formaldehyde concentrations for the case of a two-zone indoor environment, and (2) incorporation of reversible (re-emitting) indoor sinks. The modified model also included the option to be run in a single-zone mode. The model was not finalized due to shifting priorities at the time of its development.

In 2006, formaldehyde from pressed wood products received national attention when the U.S. Federal Emergency Management Agency (FEMA) provided travel trailers and mobile homes for habitation by residents of the U.S. gulf coast who were displaced by Hurricane Katrina and Hurricane Rita. Some individuals who moved into these temporary homes complained of breathing difficulties, nosebleeds, and persistent headaches. In December 2007 and January 2008, the Centers for Disease Control and Prevention measured formaldehyde levels averaging 77 parts per billion, (ppb; geometric mean) in a random sample of FEMA-supplied occupied travel trailers, park models, and mobile homes. In February 2008 U.S. health officials announced that potentially hazardous HCHO levels were found in both travel trailers and mobile homes provided by FEMA.

In April 2008 the California Air Resources Board (CARB) formally adopted an Airborne Toxic Control Measure (ATCM) to reduce formaldehyde emissions from CWPs sold, offered for sale, supplied, used, or manufactured for sale in California. On July 7, 2010, the Formaldehyde Standards for Composite Wood Products Act (FSCWPA) was signed into law. This statute, which adds a Title VI to TSCA, establishes formaldehyde emission standards for hardwood plywood, particleboard, and medium-density fiberboard that are identical to the CARB ATCM Phase II standards. TSCA Title VI directs EPA to promulgate implementing regulations by January 1, 2013 that address: sell-through dates for products; stockpiling; third-party testing and certification; auditing and reporting of third-party certifiers; recordkeeping; chain of custody; labeling; enforcement; products made with no-added formaldehyde (NAF) and ultra-low emitting formaldehyde (ULEF) resins; laminated products; finished goods; hardboard; and products containing de minimis amounts of composite wood products.

As a result of the activity described above, EPA decided to revise and update, when possible, the formaldehyde model developed in the mid-1990s to facilitate an assessment of exposures before and after the EPA formaldehyde rule goes into effect. FIAM-pwp v1.0 was the initial result of this effort, with FIAM-pwp v2.0 developed in response to peer review and workgroup comments. Version 2.0 adds exposure estimates to the model but indoor sinks have been excluded, for reasons discussed later in this document (see Section 3). Section 2 describes the user interface for the model and Section 3 describes the mathematical basis, underlying calculations and related assumptions. Model evaluation, including comparisons to research-house and field-monitoring data, is provided in Section 4. The EPA pilot study mentioned above is summarized in Appendix A. Analyses related to model sensitivity are presented in Appendix B. The basis for emission classes used on the Source Screen is presented in Appendix C. Historical chamber-test data, conducted primarily during the 1980s but extending into the 1990s and providing part of the basis for emission-rate parameters used in FIAM-pwp, are described and discussed in Appendix D. Appendix E describes the mathematical derivation of the two-zone implementation of the steady-state model.

2.	USER INTERFACE

2.1	Background – Model Versions

In 2009 an on-line, user-friendly version of the formaldehyde model (FIAM-pwp v1.0) was developed along with documentation to guide its use. Later that same year a peer review of the model was facilitated for EPA by Eastern Research Group, Inc. (ERG). The purpose of the peer review was to review and comment on three main aspects of the FIAM-pwp model: the soundness of the algorithms and exposure assumptions; the ease of use of the graphical interface; and the completeness and clarity of the model documentation. Unedited written comments submitted by five reviewers in response to the peer-review charge were organized in a report prepared for EPA by ERG in October 2009.

Version 2, named FIAM-pwp v2.0 and the subject of this document, was developed to run under the Internet Geographical Exposure Modeling System (IGEMS) platform. Some additions to or subtractions from the previous version are related, at least in part, to the peer reviewers’ comments. For example, a decision was made to drop certain FIAM-pwp features that provided particular challenges or difficulties: (1) inputs for indoor sinks, an area of considerable modeling uncertainty; and (2) inputs for emission characteristics of cabinet components, which were very demanding. In addition, exposure groups are being handled differently in the current version, for consistency with the approach used in  EPA’s 2012 formaldehyde exposure assessment.

The user interface for the current version includes three input screens (House, Source and Exposure Screens) and an output screen (Result Screen) that displays the modeling results; these results are continually updated, such that any time the Result Screen is accessed the results displayed reflect all current inputs, much like a spreadsheet. First-time users, in particular, are advised to go through the input screens in sequence (i.e., House then Source then Exposure), examining results either “along the way” or after all inputs have been entered, at the user’s discretion.

The House Screen is described in Section 2.2, the Source Screen in Section 2.3, and the Exposure Screen in Section 2.4. For each of these screens a description of inputs and options is provided first, followed by the basis for model defaults. The Result Screen is described in Section 2.5. Instructions for accessing the model via the IGEMS portal are provided in Section 2.6, along with documentation of ancillary model features such as saving runs for later access, printing inputs and results for a run, archiving inputs and results in Excel, and accessing the context-sensitive help embedded in the model. Example applications are provided in Section 2.7.

2.2	House Screen

This screen (see Figure 2-1) is intended to collect information on the house volume and internal conditions (e.g., temperature, airflows) and to provide certain options pertaining to model calculations. The inputs here can be divided into three screen portions: (1) documentation of the run and selection of structure type and climate zone (upper portion), (2) editable information on the number of zones, zone volumes and airflows (middle portion); and (3) indoor conditions and formaldehyde decay parameters (lower portion).

Figure 2-1. FIAM-pwp House Screen.

Many of the inputs on this screen are optional, in the sense that default values are provided by the model. The choice of structure type on the upper portion of the screen provides default values for zone volumes and airflow rates, which are displayed on the middle portion of the screen. The choice of climate zone on the same line provides default values for indoor temperature and humidity, which are displayed on the lower portion of the screen. Other inputs on the lower portion (e.g., background concentration) are not linked to any user choice but do have default values. Although the model can be run using default values, care should be taken in choosing the type of structure to be modeled and in choosing appropriate values for inputs such as the background concentration, emissions half life, and indoor temperature and relative humidity.

2.2.1	Inputs and Options

Run Title and Run Notes. Text inputs for these two items are intended to assist the user in documenting the purpose of the model run along with certain choices made or options exercised.

Structure Type and Climate Zone. Both of these items have pick lists from which the user can choose to obtain default values, which can either be used “as is” or edited. The user also has the option of creating additional structure types or climate zones and saving them for later use.

There are five default structure types in FIAM-pwp: single-family (SF) detached homes; SF attached homes; apartments; manufactured/mobile homes, and camper trailers. The SF detached/attached homes are two-story structures with two zones (upstairs and downstairs) whereas the others are single-zone structures.

The values associated with FIAM-pwp default structure types are “untouchable” (i.e., they cannot be directly edited), but the choices on the pick list include one called Create Your Own Structure Type – if this choice is made, then the popup screen shown in Figure 2-2 will appear. At that point, the user assigns a structure type name and enters zone descriptions, volumes and airflows, and then clicks the Save button. The MAKEACOPY button (see Figure 2-1, above) is used to copy and then edit/save any of the default choices. Guidance on entering volume and airflow values is provided later in this section, under the heading Zones, Volumes and Air Flows.

Figure 2-2. Popup Screen – Create Your Own Structure Type.

FIAM-pwp uses the U.S. climate zones defined by the Department of Energy (see Figure 2-3) There are five climate zones, numbered 1 though 5, with 1 being the coldest and 5 the warmest.

Figure 2-3. U.S. Climate Zones.

Source: U.S. Energy Information Administration (  HYPERLINK "http://www.eia.doe.gov/emeu/cbecs/climzonenew.gif"  http://www.eia.doe.gov/emeu/cbecs/climzonenew.gif )

As with default structure types, the values associated with default climate zones in FIAM-pwp are “untouchable.” Other values can be assigned and saved via a choice called Create Your Own Climate Zone, which is included on the climate-zone pick list – if this choice is made, then the popup screen shown in Figure 2-4 will appear. At that point, the user assigns a name, enters the desired temperature and humidity values, and clicks the SAVE button. The MAKEACOPY button on the main screen can be used to copy and then edit/save any of the default choices. Regardless of the climate zone chosen, the user can override the associated temperature and humidity values by changing them directly in the lower portion of the House Screen.

Figure 2-4. Popup Screen – Create Your Own Climate Zone.

Air Exchange Rate. This item is “grayed out” because no user entry is allowed here; the rate is displayed for informational purposes only. The value displayed is calculated by FIAM-pwp using volume and airflow information and, thus, can be changed by editing those inputs.

Zones, Volumes and Air Flows. Houses in FIAM-pwp can have either one or two zones. Among the default structure types, single-family detached and attached homes are conceptualized as having two separate zones (upstairs and downstairs) whereas manufactured homes, apartments and camper trailers are conceptualized as having a single zone. The maximum number of zones allowed is two. Thus, for example, to represent a house with three stories, at least two of the three stories would need to be combined into one zone. The indoor-outdoor airflow rates determine the air exchange rate. For example, for an apartment with a volume of 261 m3, the default indoor-outdoor airflow rate of 52.2 m3/h results in an air exchange rate of 0.2 ACH (i.e., 52.2 m3/h / 262 m3 = 0.2/h).

If the user selects Create Your Own Structure Type from the pick list or edits one of the default choices after making a copy, then the popup screen previously shown in Figure 2-2 will appear. The required information includes the name of the structure type, the description and volume for each zone, and airflow rates. For a one-zone house only the first line needs to be completed and only two air flows are needed – Flow from Outside and Flow to Outside. These flows must be equal to provide an overall flow balance for the house. For a two-zone house six airflows are needed – the flow for each zone to and from outdoors plus the flows in both directions between the two zones. Individual flow pairs (e.g., flow from and to outside for zone 1) do not necessarily need to be balanced, but the total flow out of a zone should match the total flow into it. On the main screen, the program updates the total flow per zone as the user provides or edits inputs. If the total flows for any zone are not balanced, then the program raises a flag by assigning a red font to the zone totals. The model still will run in such cases, but the user is advised of the possibility of counterintuitive or misleading results.

The default air flows are balanced, that is, the airflow rate from outdoors to indoors is equal to that from indoors to outdoors. For two-zone structures – SF detached/attached homes – the house volume is equally apportioned between upper/lower stories and identical indoor-outdoor airflow rates are assumed per story. Further, as an expedience, it is assumed that the airflow rate between the two indoor zones is balanced and equal to the indoor-outdoor airflow rate. Thus, for example, for a SF detached home with a volume of 811 m3 or 405.5 m3 per story, both the indoor-outdoor airflow rate per story and the interzonal airflow rate between stories are set at 81.1 m3/h.

If one of the default two-zone homes is selected but the user prefers to treat the home as a single, well-mixed zone, then FIAM-pwp will add the zone volumes and will “collapse” the airflow rates to the single-zone case, meaning that the only flow information needed is the airflow rates from outdoors to indoors and vice versa. For the single-zone case these two airflow rates should have the same value. If the number of zones is changed back to two, then the program will revert to the volumes and airflow rates originally associated with these house types.

Background Concentration. This concentration – the first of eight inputs on the lower portion of the House Screen – is intended to reflect the contribution to the indoor formaldehyde concentration of both the outdoor concentration and indoor sources other than PWPs (e.g., tobacco smoke, permanent press fabrics, paints, cosmetics). The FIAM-pwp default value for the background concentration is 7.5 ppb. If a value of zero is chosen for the background concentration, then the modeling results will reflect only the contributions of the indoor sources selected for the model run via inputs on the Source Screen.

Emissions Half Life. This input governs the rate at which indoor formaldehyde concentrations decay over time. The FIAM-pwp default value is 1.5 years; with this half life, the emission rate 10 years after new construction would be about 1% of the initial value. With a half life of 3.0 years it would take 20 years (i.e., twice as long) to reach 1% of the initial value.

Temperature and Humidity. Model algorithms to predict initial indoor formaldehyde levels include temperature and humidity adjustments for the emission rate from PWPs. Default values for indoor temperature and relative humidity are assigned based on the user’s choice (or creation) of a climate zone. These defaults can be edited directly on the lower portion of the screen, but if that is done then these new values would only be associated with the saved run name. Alternatively, values can be saved for access in any run by creating a new climate zone or by copying and editing an existing one (see Structure Type and Climate Zone, earlier in this section).

Time from ‘Initial Concentration’ and ‘Decay Concentration to'. By default, FIAM-pwp “decays” initial indoor concentrations that are calculated under a steady-state assumption to time points that are 3, 6 and 12 months later than the initial point in time. The input labeled ‘Time from Initial Conc’ (see Figure 2-1) enables the user to specify an additional point in time (in months) over which the model decays the initial concentration values; this input is set to 24 months by default. The input labeled ‘Decay Concentration to’, with a default of 10 ppb, allows the user to specify a concentration for which the model will calculate the time to decay from the initial modeled concentration to that value. For a two-zone structure, the model will calculate this decay time based on the higher of the zone-specific initial modeled concentrations.

Temperature and Humidity Coefficients. The model initially calculates indoor concentrations at an indoor temperature of 23 (C and an indoor relative humidity of 50 percent, and then adjusts the results to the temperature and humidity conditions selected by the user. The temperature and humidity coefficients specified here are used by the model to make these adjustments.

2.2.2	Basis for Defaults

Structure Type. The five default structure types in FIAM-pwp are the same as those used in the EPA’s Formaldehyde from Composite Wood Products: Exposure Assessment dated March 2012. Collectively, they account for the major types reported by the American Housing Survey (AHS) (  HYPERLINK "http://www.census.gov/hhes/www/housing/ahs/ahs.html"  http://www.census.gov/hhes/www/housing/ahs/ahs.html ) and the Residential Energy Consumption Survey (RECS) (  HYPERLINK "http://www.eia.doe.gov/emeu/recs/"  http://www.eia.doe.gov/emeu/recs/ ): single-family (SF) detached homes; SF attached homes; apartments; and manufactured/mobile homes or trailers. For the purpose of estimating structure volume, a further distinction was made for manufactured homes due to size differences – single-wide (SW) versus double-wide (DW). Camper trailers and park models also are of interest because, like manufactured homes, these housing types have been used for some residents displaced by natural disasters such as Hurricane Katrina. Camper trailers were chosen to represent the small-volume temporary housing for displaced residents, as this housing type accounted for 80 percent of the smaller-volume structures that were tested as part of FEMA’s formaldehyde monitoring in temporary housing,.

For SF detached/attached homes, apartments, and manufactured homes, default structure volumes were calculated based on statistics resulting from the U.S. Department of Energy’s 2005 RECS, using the reported average floor area for the most recently built category (years 2000-2005) and assuming a ceiling height of 8.5 feet. For camper trailers, a typical size used for displaced hurricane victims was assigned, with an assumed ceiling height of 7 feet.

The following floor areas and associated dimensions were assumed for the five structure types:

SF detached home – 3456 sq ft (36 ft x 48 ft, 2 stories)

SF attached home – 2240 sq ft (28 x 40 ft, 2 stories)

Apartment – 1120 sq ft (28 ft x 40 ft)

Manufactured home – 1216 sq ft (16 ft x 76 ft) for SW; 1680 sq ft (28 ft x 60 ft) for DW

Camper trailer – 328 sq ft (8 ft x 35 ft with 4 ft x 12 ft “slide-out”).

The dimensions chosen for SF homes and apartments were consistent with their respective average floor areas as reported in the RECS 2005 survey results.

The dimensions listed above are exterior dimensions; for interior volume calculations, 0.5 ft was subtracted from both the length and width to account for the area occupied by exterior cladding, sheathing, studs and wallboard. For SF homes a simplifying assumption was made that the upper and lower floors are of identical dimensions. For manufactured homes, a weighted average of SW and DW volumes was used; based on statistics from the U.S. Census Bureau’s Manufactured Home Survey (MHS) for years 2000-2009 (  HYPERLINK "http://www.census.gov/const/www/mhsindex.html"  http://www.census.gov/const/www/mhsindex.html ), 70 percent of the manufactured homes were assumed to be the double-wide type. The resultant house volumes are listed, along with the house dimensions, in Table 2-1.

Table 2-1. House Dimensions and Calculated Volume for Five Housing Types

Housing Type	Number of Stories	Length,

ft	Width,

ft	Ceiling Height, ft	Volume,

ft3 (m3)

SF Detached	2	48	36	8.5	28,666 (811)

SF Attached	2	40	28	8.5	18,466 (523)

Apartment	1	40	28	8.5	  9,233 (261)

Manufactured

   Single-wide

   Double-wide

   Averagea

1

1

1

16

28

--

76

60

--

8.5

8.5

8.5

  9,947 (282)

13,908 (394)

12,720 (360)

Camper Trailer

   Main body

   Slide-out

1

1

35

12

8

4

7

7

2,147 (61)

a Weighted average of single-wide (30 %) and double-wide (70 %); see text.

Climate Zone / Temperature and Humidity. Default indoor temperature-values were determined for each of five U.S. climate zones using responses to RECS 2005 survey questions about usual temperatures maintained in the residence. One of the questions – “At what temperature does your household usually keep your home in the winter?” – was asked under three conditions: (1) during the day when someone is home; (2) during the day when no one is home; and (3) during sleeping hours. The same set of questions also was posed with reference to the summer season.

As described in the exposure assessment report cited in Section 1 of this document, the RECS database was analyzed for these questions to estimate the year-round average temperature in each climate zone. Table 2-2 summarizes responses to the RECS questions on daytime temperature when someone is home and nighttime (sleeping hours) temperature by climate zone. The columns labeled “Overall” are weighted averages of the daytime and nighttime average temperatures for summer and winter, with weights of 2/3 for daytime and 1/3 for nighttime. The overall summer and winter temperatures, in turn, were averaged to derive a year-round average temperature, by weighting the season-specific averages by the number of months associated with each. The resultant year-round temperature estimates are listed in Table 2-3.

Table 2-2. Summer and Winter Indoor Temperatures from RECS 2005, by Climate Zone

U.S.

Climate

Zone	Average Summer Temperature	Average Winter Temperature

	Day	Night	Overall	Day	Night	Overall

1 (coldest)	73.4	73.3	73.4	69.1	65.8	68.0

2	73.0	73.0	73.0	69.6	67.6	68.9

3	73.2	73.2	73.2	69.8	68.1	69.3

4	73.9	73.2	73.7	70.9	68.6	70.1

5 (warmest)	75.1	74.8	75.0	72.4	70.6	71.8

Table 2-3. Year-round Indoor Temperatures Derived from RECS 2005, by Climate Zone

U.S.

Climate

Zone	Summer Temperature	Winter Temperature	Year-Round

Temperature

	Average Temperature	Number of Months	Average Temperature	Number of Months

	1 (coldest)	73.4	3	68.0	9	69.4

2	73.0	4	68.9	8	70.3

3	73.2	4	69.3	8	70.6

4	73.7	5	70.1	7	71.6

5 (warmest)	75.0	7	71.8	5	73.6

The RECS does not ask about humidity levels maintained in the residence. Consequently, a mass-balance modeling approach was applied to estimate the year-round average indoor relative humidity (RH) level for each climate zone. A representative city was chosen for each zone:

Climate Zone 1 – Milwaukee, WI

Climate Zone 2 – Chicago, IL

Climate Zone 3 – New York, NY

Climate Zone 4 – Charlotte, NC

Climate Zone 5 – Houston, TX.

Hourly outdoor temperatures for a typical meteorological year (TMY) were obtained for each city as inputs to a mass-balance model. The modeling approach, described in the formaldehyde exposure assessment report cited in Section 1, is consistent with methods described in American Society for Heating, Refrigerating and Air-Conditioning Engineers (ASHRAE) Standard 160P (Criteria for Moisture-Control Design Analysis in Buildings). In the mass-balance model, moisture in the indoor air is determined by moisture in the outdoor air, indoor moisture generation by the occupants, and moisture removal by a central air-conditioning (AC) system.

Modeled indoor RH levels for each climate zone are listed in Table 2-4 for two cases – with and without an AC unit. The effect of the AC unit is most pronounced in Houston, due primarily to the higher outdoor temperature and, hence, the greater AC run time leading to greater moisture removal. Because the vast majority of the U.S. housing stock has air conditioning, the estimated RH values with AC were used in assigning default humidity values.

Table 2-4. Modeled Year-round Indoor RH Level, by Climate Zone

Climate Zone	RH Level with AC	RH Level without AC

1 (coldest)	59.1%	63.8%

2	58.1%	64.7%

3	56.3%	66.4%

4	59.8%	72.6%

5 (warmest)	61.4%	85.3%

Air Exchange Rate and Airflows. The default indoor-outdoor airflows in FIAM-pwp were chosen such that the air exchange rate for each of the default structure types is 0.2 air changes per hour (ACH). For the exposure assessment report cited in Section 1, the focus is on PWPs in new housing; thus, a default value was chosen that lies toward the lower end of the distribution, as newer structures tend to be better sealed and have lower air exchange rates. For residences, the Exposure Factors Handbook (EFH) suggests 0.45 ACH as a central value and 0.18 as a lower-end value, based on statistics developed by Koontz and Rector (1995) from a database of perfluorocarbon tracer (PFT) measurement results. The EFH also cites Murray and Burmaster (1995), who used the same PFT database to summarize distributions for data subsets defined by climate region and season; from that analysis, the 10th percentile value ranged from 0.1 to 0.3 ACH across climates and seasons, averaging about 0.20 ACH.

In a more recent study by Offerman et al. (2008) on ventilation and formaldehyde in new California homes, the 25th percentile value for air exchange rate was 0.2 ACH for the two larger subsets of homes that were studied. In a study by Maddalena (2008) concerning chemical emissions in four FEMA temporary housing units (camper trailers), the measured air exchange rate varied from 0.15 to 0.39 ACH across the trailers, averaging 0.25 ACH. Persily et al. (2010) modeled air infiltration rate distributions for the U.S. housing stock; for single-family homes built in 1990 or later, the 25th percentile value was 0.15 ACH and the 50th percentile value was 0.26 ACH. Given the above statistics, 0.2 ACH was chosen as the value to represent new homes, including detached/attached homes, apartments, manufactured homes, and camper trailers.

For the renovation case that also was examined as part of the formaldehyde exposure assessment, a central value such as 0.45 ACH, as suggested in the EFH, may be more appropriate. However, the data on which that suggested value is based are somewhat dated and there has been a general tendency toward increasing airtightness of U.S. homes over time; for example, the median value reported for the Offerman et al. (2008) study was 0.33 ACH. Thus, a value of 0.40 ACH – double that used for new homes – is suggested for the renovation case.

As noted above, the indoor-outdoor airflow rates determine the air exchange rate. For example, for an apartment with a volume of 261 m3, the default indoor-outdoor airflow rate of 52.2 m3/h results in an air exchange rate of 0.2 ACH (i.e., 52.2 m3/h / 262 m3 = 0.2/h). The default air flows are balanced, that is, the airflow rate from outdoors to indoors is equal to the rate from indoors to outdoors. For two-zone structures – SF detached or attached homes – the house volume is equally apportioned between the upper and lower stories/floors and identical indoor-outdoor airflow rates are assumed for each story. Further, as an expedience, it is assumed that the airflow rate between the two indoor zones is balanced and equal to the indoor-outdoor airflow rate. Thus, for example, for a SF detached home with a volume of 811 m3 or 405.5 m3 per story, both the indoor-outdoor airflow rate for each story and the interzonal airflow rate between stories are set at 81.1 m3/h.

Background Concentration. Although no studies have been conducted with the explicit purpose of characterizing the background concentration, such a value conceivably can be inferred from concentration distributions characterized via field monitoring studies. For example, if a field study were to focus on existing (as opposed to new) homes, then those toward the lower end of the concentration distribution presumably would be older homes with aged PWP sources and, thus, indicative of the background formaldehyde concentration. As noted in Section 3.3 of the exposure assessment report cited in Section 1 of this document, the results of field studies, when examined in this manner, indicate that an appropriate value for the residential formaldehyde background concentration would lie between 5 and 10 ppb. The midpoint of this range – 7.5 ppb – was chosen as the FIAM-pwp default value for the background concentration.

Emissions Half Life. As described in Section 3.8 of this document, suggested values for the formaldehyde emissions half life, reflecting its decay indoors over time, range from 1.5 to 3 years. An estimate of 2.92 years was based on a cross-sectional analysis of homes of varying ages, as a proxy for time-series data from one or a few homes. If none of the materials or furnishings in such homes were changed by the occupants, then this approach might provide an unbiased estimate of the half life. However, as a house ages the occupants will tend to add or replace materials and furnishings, some of which may emit formaldehyde. The addition of these new sources will result in higher concentration than in the case where no new sources were introduced. As a result, the cross-sectional analysis will yield an artificially low estimate of the decay rate, which means an artificially high estimate of the half life. Thus, 2.92 years is best viewed as an upper-bound estimate. A more likely value, based on chamber studies of collections of pressed wood products as they age, is within the range of 1.5 to 2 years. A half life of 1.5 years was chosen as the FIAM-pwp default value; with this half life, the emission rate 10 years after new construction would be about 1% of the initial value.

Temperature and Humidity Coefficients. The default values for these coefficients – 9799 for temperature and 0.0175 for humidity – are based on tests by Berge et al. involving two Norwegian particleboard specimens. These default values were used by HUD in setting the 1984 standards for particleboard and hardwood plywood paneling, and also have been used in ASTM, ANSI and Composite Panel Association (CPA) standards or guidelines. The chamber tests underlying these coefficients were conducted at two temperature settings (22 and 28 (C) and two relative humidity settings (30 and 60 %).

An alternative set of coefficients – 8930 for temperature and 0.0195 for humidity – derives from work by Myers, who reviewed the extant literature and based his recommended temperature coefficient on chamber testing of about 40 specimens (particleboard and hardwood plywood paneling) from 11 laboratories. The temperature range of these tests was from 20 to 40 (C. He also developed a humidity coefficient, but expressed little confidence in the number; the relative humidity in the tests on which the correction factor was based ranged from 20 to 90 percent. Thus, his work encompassed more products and wider temperature/humidity ranges than the Berge et al. study. The HUD standard was promulgated before Dr. Myers completed his work.

2.3	Source Screen

This screen (see Figure 2-5) enables the user to specify the types and amounts of wood products used or installed in the house, the zone(s) in which each type is located, and input parameters (slope and intercept) that govern the formaldehyde emission rate. Following a description of each type of input, guidance is given on choosing default inputs and/or adding custom inputs on this screen.

Figure 2-5. FIAM-pwp Source Screen.

2.3.1 	Types of Inputs

PWP Type. There are six default PWP types in FIAM-pwp:

Oriented strand board (OSB) or softwood plywood (SWPW), typically used as underlayment

Particleboard, often used as the platform to which a countertop laminate is affixed

Medium density fiberboard (MDF), often used in cabinet drawers and/or shelves

Coated CWPs (e.g., interior doors that are primed/painted, vinyl-covered molding)

Hardwood plywood (HWPW), often used for wall paneling and sides/backs of cabinets or entertainment centers

HWPW laminate, with uses similar to HWPW but made by affixing a wood veneer to a particleboard, medium-density fiberboard, or veneer-core platform.

A distinction is made between HWPW and HWPW laminate because EPA may regulate these two PWP types differently.

Emission Class. Default values for FIAM-pwp emission-rate parameters (slope and intercept) have been developed for four emission classes: Baseline; CARB1; CARB2; and NAF. As described below, these emission classes correspond to analytical or regulatory options that have been included by EPA as part of the considerations for a formaldehyde rule.

Slope and Intercept. These two parameters govern the emission rate from PWPs, including dependence of the emission rate on the indoor formaldehyde concentration. The slope is a mass transfer coefficient that reflects the “backpressure” effect of the indoor formaldehyde concentration on the emission rate, whereas the intercept reflects the hypothetical emission rate when the indoor formaldehyde concentration is zero.

Equilibrium Concentration. The equilibrium concentration (mg/m3) displayed for each source is a calculated quantity – intercept (mg/m2-hr) divided by slope (m/hr) – that cannot be edited by the user; it is the theoretical maximum concentration that would occur if that were the only indoor source, with an arbitrarily large exposed surface area. The equilibrium concentration is indicative of the relative strength of emissions from each source. Lower-emitting sources, such as oriented strand board (OSB) or softwood plywood (SWPW), can act as net “absorbers” (i.e., indoor sinks) in the presence of higher-emitting sources, due to the backpressure effect.

Location (Zone) and Exposed Surface Area. If a two-zone structure is being modeled, then sources can be assigned to either or both of the two zones. As discussed later (see Section 2.3.2 and Section 2.3.3), one input line is required for each source type in each zone. The default amounts of exposed surface area for sources in FIAM-pwp are the same as those used in EPA’s Formaldehyde from Composite Wood Products: Exposure Assessment dated March 2012. The exposed surface area (in m2) for a PWP can be viewed as its loading rate (in m2/m3) multiplied by the structure volume (in m3).

2.3.2 	Adding Default Inputs

Each input line or row entered on the Source Screen refers to a specific type of source in a specific zone. For any of the five default structure types, the simplest way to add a group of sources is using the Add Default PWP Types button – taking this action loads each of the six default PWP types in each applicable zone (zone 1 for apartments, manufactured homes and trailers; zones 1 and 2 for SF detached/attached structures). Figure 2-6 shows the Source Screen after this action has been taken. In loading these defaults, there is a choice of Emission Class (baseline, CARB1, CARB2, or NAF) and Case (new-home or renovation). The example shown in the figure is for apartments, with baseline emissions and the new-home case. As indicated in the figure, user selections are made, or inputs are provided, in the lower portion of the screen; these choices/entries are then displayed in the upper portion.

Figure 2-6. Source Screen after Adding Default PWP Types

Once added, any default can be removed or edited using the Remove/Edit buttons to the right. Alternatively, sources can be “turned off” by un-checking the corresponding check-box to the left. The column to the left of PWP Type indicates whether a given line or row in the table is a FIAM-pwp default (D), revision (R) of a default, or newly created (C). For example, when a default source is edited, the character in this column will change from D to R. If the line is later changed back to the default values for area, source and intercept (either by re-editing values or by using the Restore button), then the character displayed in the corresponding column will revert to D.

Sources also can be added, one at a time, using the Add button. In addition to Emission Class and Case, choices need to be made for PWP Type and Area. The default area for any combination of PWP and zone, displayed to the right, can be changed before clicking the Add button; after the button is clicked, the area (or any other value on that line) can be changed using the Edit button. In either case, any source for which default values have been changed will be marked with an R in the second column. All sources chosen or added can be removed at once using the Clear List button. The maximum number of sources allowed by FIAM-pwp is 20.

2.3.3 	Adding Custom Inputs

Beyond adding default sources, the user also can add new sources and associated values using the Add Custom Values button; this is the only way to add sources if a structure type other than one of the defaults has been chosen. Inputs are required for the name of the PWP Type, the Emission Class, the Zone (1 or 2), and values for Area, Slope and Intercept. Figure 2-7 shows the appearance of the Source Screen after using this button to add one source line.

Figure 2-7. Source Screen after Adding Custom Values

2.3.3 	Basis for Defaults

As noted above, the default PWP types available in FIAM-pwp are those used in the EPA 2012 formaldehyde exposure assessment. The four emission classes in FIAM-pwp, which correspond to analytical or regulatory options under consideration by EPA for a forthcoming formaldehyde rule, are described briefly in Table 2-5.  EPA is considering some options beyond those listed, such as exclusion of HWPW laminates from the CARB1, CARB2 and NAF options. The basis for these classes is described in some detail in Section 4.4.8 of the report on EPA’s formaldehyde exposure assessment, which is reproduced as Appendix C in this document. In brief, within each emission class or regulatory option, a certain percentage of each product type is assumed to be in compliance with an existing standard such as CARB1; these assumed percentages vary across the emission classes. The procedure for estimating the emission rate for each product type, assuming that it meets a given standard, is described below.

Table 2-5. Alternative Analytical/Regulatory Options for EPA Formaldehyde Rule

Option a	Description

Baseline	Estimated emission levels (year 2013) in the absence of an EPA rule.

CARB1, Including Laminated Products	All CWPs, including laminated products, are at emission levels that meet CARB b Phase 1 standards. Products that meet CARB Phase 1 standards at baseline are assumed to remain at that emission level.

CARB2/Statutory Option,

Including Laminated Products	All CWPs, including laminated products, are at emission levels that meet CARB Phase 2 standards. Products that meet CARB Phase 2 standards at baseline are assumed to remain at that emission level.

NAF c, Including Laminated Products	All CWPs, including laminated products, are at emission levels that meet NAF standards. Products that meet NAF standards at baseline are assumed to remain at that emission level.

a Corresponds to emission class used in FIAM-pwp

b California Air Resources Board

c No added formaldehyde

Slope and Intercept. Appendix D of this document lists emission-rate parameters for various types of PWPs that were derived from sets of chamber tests conducted during the 1980s and up through the mid-1990s. Although the results from these tests are somewhat dated, an important distinguishing feature is that all such tests were conducted at multiple air exchange rates and/or product loading ratios, enabling estimation of model parameters – slope and intercept – that reflect the dependence of the emission rate on the indoor formaldehyde concentration.

Equation 3-6 in Section 3.2 of this document is used as a basis for determining the intercept that is associated with a product meeting a certain emission standard, under the assumption that the air entering the chamber is formaldehyde-free:

	b = CSS * (1 + m * Area / Q) * (Q / Area)	(Eqn. 2.1)

where:

b	=	intercept – the emission rate at zero concentration in the air (mg/m2-hr)

CSS	=	steady-state formaldehyde concentration in the chamber (mg/m3)

m	=	slope – the mass transfer coefficient (m/hr)

Area	=	exposed surface area of the product (m2)

Q	=	airflow rate into / out of the chamber (m3/hr)

	=	air exchange rate (1/hr) x chamber volume (m3)

ASTM E1333-10 is a commonly used method for demonstrating compliance with formaldehyde emission standards. The method prescribes an air exchange rate for testing of 0.5 ACH and product loading ratios of 0.43 m2/m3for PB, 0.95 m2/m3for HWPW, and 0.26 m2/m3for MDF. Using these rates along with an assumed slope (m) for a given PWP type, the corresponding intercept can be determined for a hypothetical source that just meets a given emissions standard. The assumed slope for each PWP type is the average of the slopes across all sets of emission tests for that type (after excluding statistical outliers in certain cases), as listed in Appendix D.

For example, the CARB2 emission standard for MDF is 0.11 ppm or 0.135 mg/m3. An arbitrary chamber volume of 100 m3, which together with an air exchange rate 0.5/hr yields a value of 50 m3/hr for Q, was used in the calculation. The volume does not matter here, as the exposed surface area scales to volume via the loading ratio; with a volume of 100 m3 the corresponding surface area is 26 m2. A slope of 1.06 m/hr is assumed; this value is the average slope from about 30 sets of chamber tests of different MDF specimens.

Substituting the assumed values given above into Eqn. 2-1, the intercept (b) that corresponds to the CARB2 emission standard for MDF is calculated as follows:

b = 0.135 mg/m3 * (1 + 1.06 m/hr * 26m2 / 50 m3) * (50 m3 / 26 m2)

= 0.40 mg/m2-hr

Table 2-6 lists the assumed slopes and calculated intercepts for each default PWP type, using the procedure described above and assuming a mix of products meeting different standards within each emission class, as described in Appendix C.

Table 2-6. Default Slopes and Intercepts for Six Default PWP Types

PWP Type	Slope	Intercept by Emission Class:

Baseline	CARB1	CARB2	NAF

OSB/SWPW a	0.61	0.030	0.030	0.030	0.030

Particleboard	0.70	0.131	0.124	0.122	0.030

MDF	1.06	0.281	0.271	0.269	0.128

Coated CWP	0.52	0.082	0.074	0.071	0.022

HWPW	0.27	0.042	0.025	0.021	0.013

HWPW Laminate	0.27	0.042	0.023	0.021	0.013

		a This relatively low-emitting PWP is not subject to any emissions standard.

Exposed Surface Area. The default amounts of exposed surface area for sources are the same as those used in EPA’s  2012 formaldehyde exposure assessment. As described in Section 4.4.6 of the EPA exposure assessment report, the following philosophy was adopted in determining appropriate loading rates for different types of PWPs in various structure types – technically the specific source (cabinets, countertop, paneling, etc.) of each PWP type does not matter, as the model treats all sources in the same way; thus, for any loading scenario it is sufficient to determine and then sum all exposed surface areas per PWP type. Floor plans were used as a basis for developing the loadings. Spreadsheets were developed to document the loadings of PWP components in items such as cabinets, doors and trim, and to then sum across like components to develop the resultant loadings for each of six PWP types listed in the table above.

The default loading rates differ for the new-home vs. renovation cases. For the renovation case, it was assumed that an entire kitchen was renovated, including cabinets, countertop and ancillary areas such as a pantry. It was further assumed that the vinyl covering the kitchen floor and adjacent hallway floor was replaced with engineered wood. The interior doors, underlayment and trim throughout the house were assumed to remain as before the renovation, as were PWPs in any areas beyond the kitchen other than the adjacent hallway floor. Table 2-7 lists the

FIAM-pwp default values for exposed surface area (in m2), for each of the six PWP types listed above in each of the five default structure types, for the case of new construction. Table 2-8 lists the same information for the renovation case.

Table 2-7. Default Exposed Surface Areas (in m2) for Six PWP Types, by Structure Type – New-home Case

Structure Type	OSB/SWPW	Particleboard	MDF	Coated CWP	HWPW	HWPW Laminate

	Zone	Area	Zone	Area	Zone	Area	Zone	Area	Zone	Area	Zone	Area

Apartment	1	  71.480	1	3.255	1	4.645	1	78.165	1	18.137	1	  7.773

Camper	1	  15.675	1	1.020	1	2.090	1	13.005	1	29.575	1	12.675

Mobile Home	1	  98.478	1	3.906	1	4.366	1	65.786	1	26.610	1	11.404

SF Attached Home	1	  71.645	1	1.390	1	2.175	1	52.910	1	  6.2685	1	  2.687

	2	  71.645	2	5.205	2	4.790	2	57.010	2	15.278	2	  6.548

SF Detached Home	1	110.965	1	1.080	1	2.615	1	65.495	1	  5.474	1	  2.346

	2	110.965	2	3.095	2	4.355	2	65.620	2	16.464	2	  7.056

Table 2-8. Default Exposed Surface Areas (in m2) for Six PWP Types, by Structure Type – Renovation Case

Structure Type	OSB/SWPW	Particleboard	MDF	Coated CWP	HWPW	HWPW Laminate

	Zone	Area	Zone	Area	Zone	Area	Zone	Area	Zone	Area	Zone	Area

Apartment	1	0	1	3.255	1	4.645	1	39.775	1	15.365	1	  6.585

Camper	1	0	1	1.020	1	2.090	1	  4.470	1	17.017	1	  7.293

Mobile Home	1	0	1	3.906	1	4.366	1	23.153	1	34.710	1	14.876

SF Attached Home	1	0	1	1.390	1	2.175	1	10.340	1	  2.286	1	  0.980

	2	0	2	5.205	2	4.790	2	33.205	2	18.680	2	  8.006

SF Detached Home	1	0	1	1.080	1	2.615	1	11.755	1	  2.286	1	  0.980

	2	0	2	3.095	2	4.355	2	31.790	2	27.342	2	11.718

2.4	Exposure Screen

This screen (Figure 2-8) enables the user to provide inputs related to the age of indoor sources and a formaldehyde level of interest (LOI) that is used in certain exposure calculations as well as activity patterns (time spent in different locations or environments) for exposure groups (e.g., infants, workers, retires) and formaldehyde concentrations in environments outside the home. As with the House Screen, the inputs here can be divided into three screen portions: (1) Age of Sources and Formaldehyde LOI (upper portion); (2) Exposure Groups (middle portion); and (3) Concentrations Outside the Home (lower portion).

Figure 2-8. Exposure Screen

2.4.1 	Inputs and Options for Age of Sources and Formaldehyde Level of Interest

Age of Sources. The assumed age of indoor sources at the start of the exposure period (i.e., at the time when an individual moves into the modeled structure) affects the modeled indoor formaldehyde concentrations to which an individual is exposed – in general, the lower the age of sources the higher the indoor concentrations at the start of the exposure period. With a source age of zero years – the model default – FIAM-pwp begins exposure calculations with an initial indoor concentration in a newly constructed home, which is intended to reflect an equilibrium condition shortly (typically within 30 days) after a house has been loaded with PWPs. A source age of zero years also would apply to new materials/furnishings added as part of a major remodeling effort. A model limitation here is that all sources are assumed to be the same age; FIAM-pwp does not allow different ages to be specified for different sources.

Formaldehyde Level of Interest (LOI). One of the exposure calculations is the percent of time an individual is exposed to formaldehyde concentrations at or above some level of interest. By default, the LOI is set to 10 ppb; this is easily changeable by entering a different value.

2.4.2 	Inputs and Options for Exposure Groups

Default Groups. As shown above in Figure 2-8 (middle portion), FIAM-pwp has six default exposure groups:

Infants (0 to < 2 years of age)

Pre-school/school children (age 2 to < 16 years of age)

Non-industry workers (age 16 to <64)

Fabrication-industry workers (age 16 to <64)

Retirees (age 64 or greater)

Part-time workers (age 16 to <64)

The choice of age breaks to distinguish infants and pre-school/school children from adults was driven by the possible age dependency of cancer slope factors. EPA has developed age-dependent adjustment factors (ADAFs) to address the potential for differential potency associated with exposure during early life (below 16 years of age). There is a 10-fold adjustment for ages 0 to <2 years, a 3-fold adjustment for ages 2 to <16, and no adjustment for ages 16 and older. Workers were split into full-time and part-time subgroups; full-time workers were further divided to distinguish non-industry workers from wood-industry segments where higher occupational formaldehyde exposures can occur. In terms of activity patterns, the retiree group also can be used to represent individuals of age 16 to <64 who are unemployed or working at home.

A subset of the exposure groups can be selected for a model run by checking or un-checking the check-boxes on the left for each line. The default values for any group can be modified using the Edit button to the right; the original/default values can be restored using the Restore button. As discussed below, user-defined exposure groups also can be added. The third column from the left on each line indicates whether the inputs for each exposure group are default (D) values, revisions (R) of defaults, or newly created (C).

The inputs for exposure groups are annual hours spent at each of five locations or environments:

In zone 1 at home

In zone 2 at home

At work, school or daycare

In a vehicle

At all other locations

The sum of the default hours at these locations is 8,760, that is, the number of hours in one year; if the edited values do not sum to 8,760, then FIAM-pwp displays the sum in red font to indicate that corrections are in order. For two-zone structures, Zone 1 is conceptualized as upstairs or the sleeping area and Zone 2 is conceptualized as downstairs or the living area. For one-zone structures the sleeping and living areas are grouped together in a single zone.

Custom Groups. User-defined exposure groups can be added via the Add button, in the screen area below the listing of the default groups. Figure 2-9 shows illustrative inputs, just before adding them. Inputs are the name of the group and the annual hours spent in each of the five locations/environments, along with the formaldehyde concentration at the work/school/daycare location (see further discussion below, in Section 2.4.3). The hours by location should sum to 8,760; if not, after the exposure group has been added FIAM-pwp will assign a red font to Total Hours to indicate that some adjustments are in order. Once added, newly defined exposure groups can be later removed by the user. A maximum of three newly defined exposure groups can be added.

For concentrations outside the home, the formaldehyde concentration at the work/school/daycare location can vary by exposure group. Thus, when a new exposure group is added the required inputs include not only the annual hours at each location but also the concentration at the work/school/daycare location.

Figure 2-9. Preparing to Add a New Exposure Group

2.4.3 	Inputs and Options for Concentrations Outside the Home

Locations outside of, or away from, the home are included in FIAM-pwp to provide a total or “around-the-clock” exposure perspective. The concentration values assigned to these locations are displayed on the lower portion of the Exposure Screen (see Figure 2-8 on previous page). The default values shown in the figure can be modified by the user. The changes can be made in either the ppb or µg/m3 column; FIAM-pwp will automatically convert in either direction using the relationship 1 ppb = 1.23 µg/m3. The model defaults can be restored at any time using the Load Default button at the bottom of the screen.

2.4.4 	Basis for Defaults

Exposure Groups. The 2009 Exposure Factors Handbook (EFH) update (External Review Draft) was the primary source of information on activity patterns, that is, how an individual’s time is allocated among residential and non-residential locations. Estimates of annual hours at home and non-home locations are provided for each exposure group in Table 2-9. The total time spent at home was determined from EFH tables that indicate the time spent at home in all rooms combined. The time at home in Zone 1 was defined as the sum of time spent in the bedroom or bathroom. EFH statistics indicate that infants spend, on the average across the population, one hour per day at daycare facilities. Children of school age were assumed to spend 6.5 hours per day at school, for 180 days per year. Full-time workers were assumed to spend 8 hours per day at work, for 250 days per year. The hours at work or school for part-time workers and retirees were based on EFH statistics, as were the hours in a vehicle for each exposure group. The time spent in “all other” environments was determined by subtraction from the total time budget of 8,760 hours per year.

Table 2-9. Default Annual Hours at Home and Non-home Locations, by Exposure Group.

Exposure Group	Location

	Home

 Zone 1 a	Home

 Zone 2	Work or School or Daycare	In

 Vehicle	All

 Other	Total, all Locations

Infants	4,958	1,652	    365	252	1,533	8,760

Pre-school/School 	4,253	1,292	1,170	356	1,689	8,760

Non-industry Workers	3,327	2,032	2,000	590	   811	8,760

Fabrication Workers	3,327	2,032	2,000	590	   811	8,760

Retirees	3,607	3,538	   107	372	1,136	8,760

Part-Time Workers	3,935	2,038	1,000	401	1,386	8,760

a Zone 1 – upstairs (sleeping area); Zone 2 – downstairs (living area).

Concentrations Outside the Home. Unlike the residential concentrations calculated by

FIAM-pwp, which are decayed over time, these concentrations are treated as constant over time. The default concentrations (see Table 2-10) assigned to non-home locations, which assume a baseline emissions scenario, were derived from several sources. In-vehicle and outdoor/other concentrations were based on average values reported from EPA’s air monitoring network (see Section 3.1 of the formaldehyde exposure assessment report). The value assigned to vehicles (6 ppb) is the average reported for the “mobile” land use category; the value assigned to outdoors/other (3 ppb) is the average of values reported for “residential” and “commercial” land use categories, with consideration also given to outdoor formaldehyde levels measured in residential monitoring studies. The value assigned to the fabrication-industry workplace was taken from EPA’s occupational exposure assessment for formaldehyde. The values assigned to daycares, schools and non-industry workplaces involved calculations that are described below.

Table 2-10. Default Concentration Values for Non-home Locations

Location	Formaldehyde Concentration

	ppb	µg/m3

Daycare	9.8	12.0

School	8.7	10.7

Work, Non-Industry	10.0	12.3

Work, Fabrication	199.5	244.9

Vehicle	6.0	7.4

Outdoors/Other	3.0	3.7

In developing the baseline concentrations for daycare, school and non-industry work locations, it was assumed that 10 percent of the buildings in each category were of recent construction or were recently renovated. As with the fabrication-industry workplace, the value for newer buildings associated with the non-industry workplace was taken from the EPA’s 2011 Assessment of Occupational Exposure to Formaldehyde from Composite Wood Products report referenced above. Newer schools were assigned the 95th percentile formaldehyde concentration, thought to represent newer or recently renovated buildings, from a relatively large monitoring study of portable and traditional classrooms in California schools. The value assigned to newer daycare facilities is an average of the concentration for non-industry work and averages from field studies, of newer homes. For older daycare, school and non-industry buildings, the 25th percentile for formaldehyde levels measured in the EPA BASE study was used. Table 2-11 shows the derivation of the age-weighted baseline concentration values for these building types.

Table 2-11. Derivation of Baseline Values for Daycare, School and Work Locations

Location	Formaldehyde Concentration, ppb

	Older Buildings	Newer Buildings	Composite a of Older & Newer

Daycare	  7.0	35.0	  9.8

School	  7.0	24.0	  8.7

Work, Non-Industry	  7.0	36.5	10.0

a Composite value = 90% x (value for older buildings) + 10% x (value for newer buildings).

The values for vehicle and outdoor/other concentrations are assumed to be the same for different  analytical options (baseline, CARB1, etc.) whereas those for the other locations can vary (see Table 2-12), because the formaldehyde concentrations in the fabrication workplace, as well as newer/renovated daycares, schools and non-industry workplaces, could be affected by a new rule for formaldehyde. As with the baseline values, suggested concentration values for other analytical options for newer non-industry workplaces were taken from the recent EPA report referenced above. For daycare facilities, the percent reductions across analytical options used for fabrication and non-industry work were applied. A similar approach was used for schools, except that the percent reductions were lowered slightly (i.e., by 10 percent) to account for generally higher prevailing air exchange rates in schools, which would tend to temper the effect of formaldehyde emission reductions.

Table 2-12. Concentration Values for Selected Non-home Locations, by Emissions Scenario

Location	Formaldehyde Concentration, ppb

	Baseline a	CARB1	CARB2	NAF

Daycare b	9.8	9.5	9.4	8.0

School b	8.7	8.1	8.0	7.3

Work, Non-Industry b	10.0	9.4	9.3	7.9

Work, Fabrication	199.5	192.0	190.8	93.0

a FIAM-pwp provides baseline values as the defaults for non-home locations.

b The values assigned to these locations are a weighted average of those for older and newer buildings; see text .

In calculating total exposure for the exposure groups, FIAM-pwp combines the time spent in various locations with concentrations encountered at those locations. For the work/school/daycare location, FIAM-pwp uses the daycare concentration for infants, the school concentration for children, and the work concentration for workers and retirees. When a new exposure group is added (see Figure 2-9 above), in addition to the time spent at each location the user also needs to enter an appropriate value for the concentration at the work/school/daycare location.

2.5	Result Screen

This screen (Figure 2-10) lists modeled indoor formaldehyde concentrations (upper portion of the screen) together with exposure estimates (lower portion). Further details are provided below.

Figure 2-10. Result Screen with First Two Exposure Groups Selected

2.5.1 	Concentration Results

FIAM-pwp lists the concentrations calculated for Zones 1 and 2 under the temperature and humidity conditions entered by the user; the Zone 2 results are set to the background concentration if the user has specified a one-zone structure. Section 3.9 describes the procedures and gives the equations that are used to adjust modeled concentrations to the user-specified conditions. Concentrations are reported both in volume/volume (ppb) and mass/volume (µg/m3) units.

Initial concentrations – those listed for 0 months under Time from Initial Concentration – reflect the condition shortly after a house has been loaded with PWPs. As described in Section 3.7, estimates of initial indoor concentrations due to PWPs are decayed exponentially by the model, in accordance with a user-specified emissions half life (default of 1.5 years), to develop estimates for subsequent points in time. Results are provided for time points that are 3 months, 6 months and 12 months later than that for the initial concentration values, plus a user-specified point in time (24 months by default). The user-specified value for length of time over which to decay the initial concentration is entered on the House Screen, where the default emissions half life also can be changed.

The results also include the time required for the highest initial indoor concentration to drop below a user-specified concentration (an input on the House Screen). The equation used for this calculation is given in Section 3.7. By definition, the indoor concentration cannot decay to a value that is lower than the background concentration (an input on the House Screen). If the value to which the indoor concentration is to be decayed is less than or equal to the background concentration, then the calculation result is undefined. In such cases, FIAM-pwp reports 0 months as the time to decay.

As described in greater detail in Section 3, the model calculates the initial indoor concentration(s) under an assumed steady-state condition. In real life, a true steady-state is never achieved, due to the dynamics of formaldehyde source emissions and indoor sinks. Formaldehyde sources typically do not emit at a constant rate, but rather at a rate that tends to decline over time as the “reservoir” of initial free formaldehyde, coupled with that formed through hydrolysis, is gradually depleted. Although a true steady-state is never reached, it has been observed in field studies that the combined actions of sources and sinks will result in an initial rise in the indoor concentration, followed by a “leveling off” period that may be fairly brief and then a longer period of gradual decline in concentration. The initial “steady-state” concentrations estimated by FIAM-pwp are intended to approximate the indoor concentrations during the leveling-off period, which typically would occur within 30 days or less following the installation of PWPs.

2.5.2 	Exposure Results

An average daily concentration (ADC) is reported for each zone of the house, or other modeled structure, and for each default or added exposure group selected by the user. The percent of time during which the concentration in each zone is greater than a user-specified level of interest (LOI) is also reported. For each exposure metric, annual averages are reported for the first modeled year and for the next ten years thereafter. ADC calculations for exposure groups are based on time spent, and concentrations encountered, in the two zones of the house together with times and concentrations when the individual is out of the house. Concentrations in the house are calculated by the model and decay over time, whereas out-of-house concentrations are input by the user on the Exposure Screen and are assumed to be constant over time. Further details on exposure calculations, including equations, are provided in Section 3.10.

2.5.3 	Printing Inputs and Results

An option at the top of the Result Screen – Generate pdf – enables the user to create a pdf file that contains both the inputs and results for a model run. The pdf mimics the appearance of the input screens and creates a table listing the same model outputs as shown on the Result Screen.

2.5.4 	Archiving Inputs and Results for a Run

Another option at the top of the Result Screen – Download Excel – enables the user to save a file in Excel format that contains all inputs and results for the current model run. The saved Excel file has three sheets or tabs, named Combined, Inputs and Results. FIAM-pwp creates an Excel file for each run name; if multiple runs are made under the same run name and the download button is pressed after each run, then FIAM-pwp will append each set of inputs and results to the Excel file. The Inputs sheet has one column for each input and creates one Excel row for each model run. The Results sheet has columns for each output and creates 11 rows for each model run, because ADC results are provided for Zone 1, Zone 2, and exposure groups for each of 11 years (year 0-1, year 1-2, etc.). FIAM-pwp concentration results, which relate to single points in time, are duplicated across the 11 rows. Similarly, the Combined sheet containing inputs and results has 11 rows and duplicates both the inputs and the modeled concentrations across the 11 rows that are generated for each run.

2.6	Model Access and Additional Features

2.6.1 	Accessing the IGEMS Website

The IGEMS website that houses FIAM-pwp can be accessed at   HYPERLINK "https://ofmpub.epa.gov/igems-jsp/"  https://ofmpub.epa.gov/igems-jsp/ . After the Privacy Act Notification has been acknowledged, a user can log in if he/she has an account (otherwise set up a new account). After logging in, a user can access FIAM-pwp by selecting it benath Formaldehyde Indoor Air Model from the choices to the left.

2.6.2 	Saving Inputs for Later Access

The first time FIAM-pwp is used, the Run FIAM button at the bottom will not be available until inputs have been provided or choices have been made on the House Screen, Source Screen and Exposure Screen. When the run button is pressed, FIAM-pwp will prompt for a Run File Name. Up to 20 characters can be used in naming the file. After the SAVE button is pressed, FIAM-pwp will show the Result Screen. A new run file can be created, or a current one saved, at any time – creating, opening and saving run files works much like similar functions in Microsoft Windows. Once a run file has been named and saved, it will be included on the list that can be accessed by pressing the Open File button. If the SAVE button is pressed using a file name that already exists, FIAM-pwp will ask whether the existing run file should be overwritten.

2.6.3 	Context-sensitive Help

FIAM-pwp provides context-sensitive help via a series of buttons with a “?” icon. When the icon is pressed a dialog box appears with help specific to the input or option with which it is associated. Pressing the Close button returns the user to the input or output screen. There is also an Overview button for each of the input screens that; when this button is pressed FIAM-pwp displays a brief description of the purpose of the screen and the types of inputs required. All of the help dialogs provided by FIAM-pwp can be saved by pressing the Save FIAM Help button that is accessed on the Result Screen.

2.7 	Example Applications

Six examples are provided in this section to illustrate certain FIAM-pwp features and options as well as the insights that can be obtained from making model runs, particularly a series of related runs.

2.7.1 	Example 1 – Modeling with Model Default Values

This example illustrates how FIAM-pwp results can be obtained quickly when using default values for items such as type of structure, climate zone, indoor sources, and exposure groups. As described in previous sections, the default values reflect decisions or choices made in the EPA 2012 formaldehyde exposure assessment (see footnote 10 in Section 1). The example further illustrates how minor changes from the defaults can be made to view complementary results.

The key choices for this example are indicated in the run notes provided in Table 2-13 for Part 1. First, on the House Screen, Apartment (a one-zone structure) was selected as the structure type and Zone 5 was selected as the climate zone. Second, default PWP types were loaded on the source screen with the choices of baseline emissions and new construction (as opposed to renovation). Third, default exposure groups were chosen on the Exposure Screen. Model defaults were used for all other inputs not mentioned above. The modeling results indicated an initial indoor formaldehyde concentration of 78.6 ppb.

Table 2-13. Run Notes for Example 1

Screen	Notes

Part 1

House	Select Apartment and Climate Zone 5; defaults otherwise

Source	Select "Add Default PWP Types" with Emission Class = baseline, Case = new-home (six sources will appear, all checked)

Exposure	Select default exposure groups (no action needed; all checked by default)

Result	Initial concentration – 78.6 ppb (97.1 µg/m3) for Zone 1, N/A for Zone 2

Part 2

House	Keep Apartment and Climate Zone 5

Source	Select "Add Default PWP Types" with Emission Class = CARB2, Case = new-home (Note: clear previous list before adding new sources)

Result	Initial concentration – 68.5 ppb (84.6 µg/m3) for Zone 1, N/A for Zone 2

Part 3

House	Keep Apartment and Climate Zone 5; change air exchange rate to 0.4 ACH by changing flows to and from outside from 52.26 to 104.52 m3/h

Source	Select default PWP types – Emission Class = baseline, Case = renovation (Note: clear previous list before adding new sources)

Result	Initial concentration – 49.0 ppb (60.5 µg/m3) for Zone 1, N/A for Zone 2

Part 4

House	Select SF Detached; keep Climate Zone 5

Source	Program will issue a warning due to change in structure type; click OK.

Select default PWP types – Emission Class = baseline, Case = new-home

(Note: clear previous list before adding new sources; 12 sources will appear)

Result	Initial concentration – 57.1 ppb (70.5 µg/m3) for Zone 1,

59.9 ppb (74.0 µg/m3) for Zone 2

Next (see Part 2), the emission class was changed to CARB2, which has lower emissions than baseline. All other inputs were kept the same as for Part 1. The modeled initial concentration in this case was 68.5 ppb. Then (Part 3) the emission class was changed back to baseline while choosing the loading rates for renovation instead of new construction and changing the air exchange rate from 0.2 to 0.4 ACH, by doubling the airflow rates to/from outdoors; the modeled initial concentration in this case was 49.0 ppb. Last (Part 4), baseline emissions and new construction were chosen while changing the structure type to SF detached (a two-zone structure). The initial modeling results in this case were 57.1 ppb for Zone 1 (sleeping area) and 59.9 ppb for Zone 2 (living area).

2.7.2 	Example 2 – Modeling a Hypothetical Chamber Test for CARB Compliance

This example is drawn from the 2012 EPA exposure assessment report previously cited in Section 1. ASTM E1333-10, Standard Test Method for Determining Formaldehyde Concentrations in Air and Emission Rates from Wood Products Using a Large Chamber (ASTM 2010), is commonly used to demonstrate compliance with formaldehyde emission standards. The method prescribes an air exchange rate for testing of 0.5/hr and product loading ratios of 0.43 m2/m3for PB, 0.95 m2/m3 for HWPW, and 0.26 m2/m3for MDF. Using these rates and an assumed slope, the intercept can be determined for a hypothetical source that just meets a given emissions standard. The CARB2 emission standard for MDF is 0.11 ppm (110 ppb) or 0.135 mg/m3. Per the 2012 EPA exposure assessment, a MDF specimen complying with the standard would have an intercept value of 0.40 mg/m2-hr, assuming a slope of 1.06 m/hr based on historical chamber tests of MDF specimens.

FIAM-pwp was used to model a hypothetical chamber test with an MDF specimen that just meets the standard (see notes for this example in Table 2-14). An assumed air exchange rate of 0.5/hr and chamber volume of 100 m3 equates to an airflow rate of 50 m3/hr into and out of the chamber. The volume assumed does not matter, as the exposed surface area scales to the volume via the loading ratio – with a volume of 100 m3 the corresponding MDF surface area is 26 m2. The assumed slope was 1.06 m/hr, the average value from ~ 30 historical tests of various MDF specimens (see Appendix D of this report). The modeling result – an initial concentration of 108.5 ppb – confirms compliance of the hypothetical MDF specimen with the standard (110 ppb).

Table 2-14. Run Notes for Example 2

Screen	Notes

House	Use “Add Your Own Structure Type” to create new type named Chamber Zone 1 (Chamber) – volume = 100.0 m3; flow to/from outside = 50.0 m3/hr

Check box next to “Check here if one-zone case”

Create climate zone named Standard Conditions, 23 °C and 50 % RH

Change background concentration to 0.0 ppb

Source	Add custom values for PWP type MDF, Emission Class Meet CARB2 110 ppb

Area = 26.0 m2, Slope = 1.06 m/hr; Intercept = 0.4 mg/m2-hr

Exposure	No exposure group selected (uncheck all)

Result	Initial concentration = 108.5 ppb (134.1 µg/m3)

2.7.3 	Example 3 – Demonstrating an Equilibrium Concentration

The default MDF source in FIAM-pwp has a baseline emission rate characterized by an intercept of 0.28122 mg/m2-hr and a slope of 1.06 m/hr. The formaldehyde equilibrium concentration, obtained by dividing the intercept by the slope, is 0.2653 mg/m3 or 265.3 µg/m3. Attainment of an equilibrium concentration can be demonstrated via modeling. FIAM-pwp was run with a hypothetical chamber volume of 100 m3 and an airflow rate of 50 m3/hr, as in the previous example. An arbitrarily large exposed surface area of 100,000 m3 was assumed. The modeled concentration in the chamber (265.2 µg/m3; see run notes in Table 2-15) is consistent with the calculated value for the equilibrium concentration.

Table 2-15. Run Notes for Example 3

Screen	Notes

House	Use created structure type named Chamber

Zone 1 (Chamber) – volume = 100.0 m3; flow to/from outside = 50.0 m3/hr

Check box next to “Check here if one-zone case”

Use created climate zone named Standard Conditions, 23 °C and 50 % RH

Change background concentration to 0.0 ppb

Source	Add PWP type MDF, Emission Class = baseline, Case = new-home

Area = 100,000 m2, Slope = 1.06 m/hr; Intercept = 0.28122 mg/m2-hr

Exposure	No exposure group selected (uncheck all)

Result	Initial concentration = 214.6 ppb (265.2 µg/m3)

2.7.4	Example 4 – Examining the Incremental Contribution of a Product

As described in Section 2.1, a prior online version of FIAM-pwp (v1.0) was subjected to a peer review. In commenting on the backpressure effect, one of the reviewers noted the following:

Assessment of acute/chronic exposure is associated with different uncertainties and conceptual models. In the acute setting, the backpressure effect may attenuate the contribution of a new product such that the total acute indoor exposure concentration is not affected. However, in a chronic or long-term timeframe, it is reasonable to expect that the majority of available formaldehyde and precursors ultimately will partition from the product into the indoor space. My recommendation is that a conceptual framework be developed or documented to ensure that users take these factors into consideration when investigating acute versus chronic timeframes. For the acute timeframe, it is important to consider the total collection of assembled indoor products. For chronic exposure, a more accurate characterization of dose attributable to a single product is likely obtained by considering the decay profile of that product in the absence of other products; the attenuation due to the backpressure effect is temporary and, eventually, a source that is initially attenuated will begin to emit formaldehyde as the indoor-air concentration decreases.

To illustrate some of the reviewer’s points, the incremental contributions of illustrative CWPs were examined by modeling them both as a single source and in the presence of other CWPs. As shown in Figure 2-11, FIAM -pwp has loadings of six default PWP types for apartments; these were used in a series of model runs with an apartment as the structure types (see run notes in Table 2-16). For these runs, the background concentration was set to 0.0 ppb.

Figure 2-11. Emission-rate Parameters for FIAM-pwp Default PWPs in an Apartment.

For the first run, only MDF was selected (by checking the corresponding check-box), resulting in a modeled initial concentration of 23.4 ppb. Next, the model was run checking all sources except MDF, with a resultant modeled initial concentration of 70.7 ppb. The modeled initial concentration when all sources, including MDF, were selected was 77.3 ppb – less than the sum of results from the first two runs and, thus, illustrating the suppression of emissions in the presence of other sources. A similar series of runs was made with OSB/SWPW as the focus. The modeled concentration for OSB/SWPW only was 22.9 ppb – similar to that for MDF, but with an exposed surface area about 15 times as large. The modeled concentration with all sources except OSB/SWPW (88.3) ppb) was higher than that obtained with all sources, including OSB/SWPW (77.3 ppb). This outcome illustrates that OSB/SWPW acts as a “net absorber” in the presence of the other default PWP types used in the example. The relative emissions strength of each PWP type is apparent from its equilibrium concentration, which for MDF is more than five times that of OSB/SWPW (equilibrium concentrations are listed in Figure 2-11).

Table 2-16. Run Notes for Example 4

Screen	Notes

Part 1

House	Select Apartment and Climate Zone 5; background = 0; defaults otherwise

Source	Select default PWP types – Emission Class = baseline, Case = new-home

Check only the MDF type

Exposure	No exposure group selected (uncheck all)

Result	Initial concentration – 23.4 ppb (28.9 µg/m3)

Part 2

House	Keep Apartment, Climate Zone 5, and background = 0

Source	Keep default PWP types – Emission Class = baseline, Case = new-home

Check all PWP types except MDF

Result	Initial concentration – 70.7 ppb (87.4 µg/m3)

Part 3

House	Keep Apartment, Climate Zone 5, and background = 0

Source	Keep default PWP types – Emission Class = baseline, Case = new-home

Check all PWP types, including MDF

Result	Initial concentration – 77.3 ppb (95.5 µg/m3)

Part 4

House	Keep Apartment, Climate Zone 5, and background = 0

Source	Keep default PWP types – Emission Class = baseline, Case = new-home

Check only the OSB/SWPW type

Result	Initial concentration – 22.9 ppb (28.3 µg/m3)

Part 5

House	Keep Apartment and Climate Zone 5

Source	Keep default PWP types – Emission Class = baseline, Case = new-home

Check all PWP types except OSB/SWPW

Result	Initial concentration – 88.3 ppb (109.0 µg/m3)

2.7.5	Example 5 – Varying the Decay Rate (Half Life)

As discussed later in this report (see Section 3.5), several peer reviewers suggested multiple or changing decay rates to represent, for example, “fast” (earlier) and “slow” (later) periods of exponentially declining formaldehyde emissions. Such an undertaking, although a “stretch” of FIAM-pwp’s capabilities, is possible provided that adequate care is taken. The key to varying the decay rate is having a means to predict the initial concentration for the point in time at which this rate is changed.

For this example it was assumed that the fast decay could be represented by a half life of one year and the slow decay by a half life of three years. The fast-decay period was assumed to last one year, followed by a slow-decay period of nine years. The resultant indoor-concentration time series over the 10 years, calculated externally from the model, is shown in Figure 2-12 together with the default background concentration (7.5 ppb) that was assumed for the example. The change in the decay rate can be seen as the “kink” in the time series at an elapsed time of one year.

Figure 2-12. Formaldehyde Concentration Decline with Fast and Slow Decay Periods.

Inputs for the example were simplified by assuming a single emitter – MDF. For the first run (Part 1; see Table 2-17), a half life of 1.0 years was assumed together with an MDF exposed surface area of 18.5 m2; the modeled initial concentration was 63.7 ppb and the modeled concentration after one year was 35.6 ppb. For the second run (Part 2; see Table 2-18), the assumed half life was changed to 3.0 years. For this run it also was necessary to adjust the source inputs such that the modeled initial concentration would be 35.6 ppb. Through trial and error it was determined that this outcome could be obtained by changing the intercept for the MDF emission rate from the default value of 0.28122 to 0.1455 mg/m2-hr. The modeled initial concentration in this case was 35.6 ppb and the modeled concentration after 108 months (9 years, or 10 years cumulative) was 11.0 ppb. The collective results from the two runs are consistent with the time series in Figure 2-12.

Table 2-17. Run Notes for Example 5, Part 1 (fast decay period)

Screen	Notes

House	Select Apartment as the structure type

Use created climate zone named Standard Conditions, 23 °C and 50 % RH

Half life = 1.0 years

Source	MDF/baseline/new-home with surface area = 18.35 m2 and default values for slope/intercept (add only this type with default surface area; edit surface area)

Result	Initial concentration = 63.7 ppb (78.7 µg/m3)

Concentration at 12 months = 35.6 ppb (44.0 µg/m3)

Table 2-18. Run Notes for Example 5, Part 2 (slow decay period)

Screen	Notes

House	Change half life to 3.0 years

Change time from initial concentration to 108 months (to get to 10 years)

Source	Change intercept for MDF to 0.1455 mg/m2-hr (by editing)

Result	Initial concentration = 35.6 ppb (44.0 µg/m3)

Concentration at 108 months = 11.0 ppb (13.6 µg/m3)

3.	MODEL CALCULATIONS AND ASSUMPTIONS

This section describes the technical basis for the calculation routines in the software, which consist of two major components. The first of these predicts the initial “steady-state” formaldehyde concentration(s) in one or two zones of the house due to the combined actions of sources and sinks in a newly constructed home. The primary input for this component is an empirical emission-rate algorithm (i.e., estimated initial emission rate as a function of formaldehyde concentration and other environmental variables) for various types of pressed-wood products. For more information regarding formaldehyde emissions from pressed-wood products, the reader is referred to an EPA report.

The second component of the model is a decay function that gradually reduces the estimated initial steady-state concentration(s) due to indoor sources and sinks over a specified period of time. The concentrations are reduced in accordance with an exponential decay function, using a decay rate that is determined from a user input for the formaldehyde emissions half life. With this function, the concentrations at any point in the “life” of a home can be predicted, on the assumption that the materials in the house do not change over time and the air exchange rate, indoor temperature and indoor humidity also remain constant.

The first model component is based on the fundamental principle of conservation of mass in an indoor environment, as described in Section 3.1. A model (see Section 3.2) was developed during the 1980s to predict the formaldehyde concentration in a single indoor compartment under an assumed steady-state condition, taking into account the dependence of formaldehyde emission rates on the prevailing indoor concentration. This model has been extended (see Section 3.3) to predict formaldehyde concentrations in two indoor compartments under the same assumption. Whether a one-chamber or two-chamber model is used in the calculations depends on the type of structure selected by the model user (see Section 2.2).

An alternative formulation of the model, with an embedded calculation of the equilibrium concentration, is described and discussed in Section 3.4. Other potentially useful modeling constructs are presented and discussed in Section 3.5. Although the model, as currently formulated, technically has the capability to represent indoor sinks, this model feature has been dropped due to several uncertainties together with the lack of supporting data. Some discussion of this topic is provided in Section 3.6.

Section 3.7 describes the basis for the equation used to decay the initial steady-state concentration(s) over time and provides examples to illustrate calculations for concentrations at any point in time and for the time to reach a pre-defined concentration such as 10 ppb. Section 3.8 documents the basis for selection of a default value for the formaldehyde concentration half life, which is needed to decay the concentration over time. Section 3.9 describes the equations used to adjust indoor formaldehyde concentrations calculated by the model, under baseline indoor conditions of 23 ( C and 50 % relative humidity, to the user’s inputs for temperature and humidity conditions. Section 3.10 describes the exposure calculations used in the model.

3.1	Generalized Mass-Balance Equation

The formaldehyde concentration in an indoor environment is dependent on two types of factors: (1) those that increase the concentration, such as emissions from formaldehyde sources, and (2) those that decrease the concentration, such as dilution with outdoor air assumed to be lower in concentration than that indoors. Although the two types of factors would appear to be distinct entities, they actually are interdependent because of formaldehyde’s general behavior – emission rates from pressed-wood products are dependent on the concentration in the indoor volume, and the formaldehyde concentration, in turn, is dependent on these emission rates as well as removal mechanisms.

The principle of conservation of mass in an indoor environment is fundamental to the formaldehyde modeling process. Simply stated, this principle means that the rate of change over time in the formaldehyde mass indoors is determined by the rates of generation and removal. This principle can be expressed mathematically for an indoor compartment or zone as follows:

 	(Eqn. 3-1)

where:

V	=	indoor volume (m3)

C	=	formaldehyde concentration (mg/m3)

t	=	time (hr)

i, j	=	indoor compartments (0 signifies the outdoors)

Q	=	airflow rate between indoor zones or between indoor zone and outdoors (m3/hr)

Ei,k	=	emission rate for formaldehyde source k in zone i (mg/hr)

Si,p	=	sorption rate for formaldehyde absorbent p in zone i (mg/hr).

Model results are presented in both volume/volume units (ppb) and mass/volume units (µg/m3). Conversion between these unit conventions is performed using the ideal gas law, assuming constant pressure (1 atmosphere) and the user-specified temperature.

3.2	Steady-State Model for Initial Formaldehyde Concentration in One Compartment

A model developed in the 1980s by Matthews and colleagues was designed to estimate the steady-state formaldehyde concentration resulting from emission sources in a single indoor compartment. The following discussion is in large part excerpted from Matthews et al. The underlying model theory and its derivation are described in the same document and in a paper by Matthews et al.

At steady state, the formaldehyde (CH2O) concentration in a single compartment can be expressed as follows:

[CH2O]SS = [CH2O]out + CH2OER/(F * ACH * VOL)	(Eqn. 3-2)

where:

[CH2O]SS	=	steady-state formaldehyde concentration inside the compartment (mg/m3)

[CH2O]out	=	formaldehyde concentration outside the compartment (mg/m3), assumed to be constant over time

CH2OER	=	emission rate of a formaldehyde source inside the compartment (mg/h)

F	=	fraction of air coming into the compartment that mixes within the volume (i.e., the mixing factor)

ACH	=	air exchange rate with outdoors for the compartment (hr-1)

VOL	=	volume of the compartment (m3).

Assuming that F is equal to unity and using Q (airflow rate into and out of the compartment, in m3/hr) to denote the product of ACH * VOL, Equation 3-2 becomes:

[CH2O]SS = [CH2O]out + CH2OER/Q	(Eqn. 3-3)

Application of the model as expressed in Equation 3-3 is simplified by assuming that all parameters in the equation remain constant (at steady state) and that there are no permanent losses of formaldehyde due to irreversible sorption to sinks.

Emissions from pressed-wood sources are area-dependent in that the magnitude of the emission is a direct function of the surface area (Area) of the source in the compartment. The equivalent of Equation 3-3 for an area-dependent source is:

[CH2O]SS = [CH2O]out + (CH2OER( * Area)/Q	(Eqn. 3-4)

with CH2OER( in units of mg/m2-hr and Area in m2.

The formaldehyde emission rate, CH2OER(, is formulated consistent with a one-dimensional representation of Fick’s Law, describing the emission rate as the release rate when the formaldehyde air concentration is zero, reduced by the product of the mass transfer coefficient and the vapor-phase concentration. This formulation can be expressed as follows:

CH2OER( = -m * [CH2O]V + b		(Eqn. 3-5)

where:

m	=	the mass transfer coefficient (m/hr)

[CH2O]V	=	the CH2O concentration in the vapor phase (mg/m3)

b	=	a constant; the emission rate at zero CH2O concentration in the air (mg/m2-hr).

As noted by Matthews, Hawthorne and Thompson (see footnote on this page):

Thus, the modeled CH2O emission rates maximize at zero CH2O concentration and decrease linearly to a net emission rate of zero at some equilibrium CH2O concentration. If the CH2O concentration is raised beyond the equilibrium level with the addition of new CH2O sources, extrapolation of the model to higher CH2O concentrations indicates that sorption of the CH2O by the original ‘emitter’ is expected to occur. Experimental results of individual and paired emitters in small-scale environmental chambers by Pickrel et al. and Godish et al. are consistent with this theory. Paired source contributions of pressed-wood products, insulation, carpeting and UFFI typically yielded CH2O concentrations less than the sum of the concentrations for the individual emitters. In addition, Godish found that the CH2O emission strength of many weaker emitters in paired source combinations was enhanced following brief exposure to a stronger emitter. This suggests a temporary sorptive mechanism for CH2O followed by reemission of CH2O at reduced CH2O concentrations.

The vapor-phase concentration, [CH2O]V, by definition is equal to [CH2O]SS at steady state; therefore, substitution of [CH2O]SS and Equation 3-5 into Equation 3-4 results in the following expression:

 	(Eqn. 3-6)

In the case of multiple pressed-wood sources, Equation 3-4 becomes:

[CH2O]SS = [CH2O]out + ((CH2OER(k* Areak) /Q	(Eqn. 3-7)

where the subscript k refers to the kth source. By extension, Equation 3-6 then becomes:

 	(Eqn. 3-8)

3.3 	Extension of the Steady-State Model to Two Compartments tc \l2 "3.3 	Extension of the Steady-State Model to Two Compartments

The formulation for the single-compartment case is adapted for use with a two-compartment case, by solving appropriate mass-balance equations. The mass-balance equation for each compartment, neglecting sinks (see Section 3.6), is as follows:

 	(Eqn. 3-9)

where:

Vi	=	volume of compartment i (m3)

Ci	=	concentration in compartment i (mg/m3)

t	=	time (hrs)

i,j	=	indoor compartments (0 signifies the outdoors)

Qij	=	flow rate from compartment i into compartment j (m3/hr)

Ei,k	=	emission rate for formaldehyde source k in zone i (mg/hr)

It is acknowledged here that there are formaldehyde sources other than pressed-wood products in the indoor environment; however, such emitters (e.g., tobacco smoke, permanent press fabrics, paints, cosmetics) typically are comparatively weak. Together, the outdoor concentration and these weaker emitters contribute to what can be described as a "background" concentration. As an expedience, for purposes of this model, the background concentration is treated as if all such contributions can be represented by the outdoor concentration. Studies of background concentrations indicate that the concentrations indoors are generally offset from outdoors due to these other sources by approximately 5 ppm (see Section 2.2.2). Although the emission rate of these other formaldehyde sources can be impacted by the presence of new sources such as PWPs, this impact is expected to minimal. Therefore, treating these other sources as an outdoor contribution provides a meaningful construct for isolating the impact of the new sources, by providing a constant background offset.

With this representation, equation 3-9 can be alternately expressed as follows:

 	(Eqn. 3-10)

where:

CB	=	background concentration, which is defined as the outdoor concentration plus the contribution from indoor sources other than pressed-wood products (assumed to be constant over time).

Considering the source equation as described in Equation 3-5 for multiple pressed-wood products in either zone, the sum of these emission sources in each compartment can be expressed as:

 	(Eqn. 3-11)

where:

CH2OER(i,k	=	unit emission rate of source k located in compartment i (mg/m2-hr)

Areai,k	=	area of source k located in compartment i (m2)

mi,k	=	mass transfer coefficient of source k located in compartment i (m/hr)

bi,k	=	emission rate at zero CH2O air concentration for source k located in compartment i (mg/hr)

Ci	=	CH2O air concentration in compartment i (mg/m2).

Considering the combined Equations 3-10 and 3-11 for each compartment, and solving simultaneously for the steady-state condition (see Appendix A), the following equations are obtained:

 	(Eqn. 3-12)

 	(Eqn. 3-13)

where:

SS	=	indicates the steady-state solution

   for the k sources located in compartment 1

   for the k sources located in compartment 1.

   for the k sources located in compartment 2

   for the k sources located in compartment 2.

3.4 	Matthews Model Compared to HBF Model

An alternative to the Matthews model is the HBF model (name coined by Myers), a model developed by Hoetjer for which mathematically identical versions have been developed by Berge et al. and by Fujii et al. The underlying theory and derivation of the model have been summarized by Myers.

The HBF model formulation for the steady-state concentration for a single source is as follows:

CSS = CEQ / (1 + N / kL) 	(Eqn. 3-14)

where:

CSS	=	the steady-state formaldehyde concentration (mg/m3)

CEQ	=	the formaldehyde equilibrium concentration (mg/m3)

N	=	the air exchange rate (1/hr)

k	=	mass transfer coefficient (analogous to m in Matthews model) (m/hr)

L	= 	product loading ratio (m2/m3)

It can be shown that the Matthews and HBF formulations are identical models and that CEQ = b/m. The only difference between the two models is in the regression equations that are used to derive the parameters, not their theoretical constructs.

The Matthews formulation, under the assumption that the outdoor concentration is zero, can be expressed as follows by substituting Equation 3-5 into Equation 3-4:

CSS = (-m * CSS + b) * Area / Q	(Eqn. 3-15)

where CSS is as defined above and m, b, Area and Q are as defined previously in Section 3.2.

Substituting ACH * VOL for Q, Equation 3-15 can be expressed as:

	CSS = (-m * CSS + b) * Area / (ACH * VOL) 	(Eqn. 3-16)

Equation 3-16 can be expressed using the same terms as in Equation 3-14, by setting N = ACH and by setting L = (Area / VOL):

	CSS = (-m * CSS + b) / (N/L) 	(Eqn. 3-17)

Equation 3-17 can be solved for CSS as follows:

 	(Eqn. 3-18)

Setting the Matthews (Equation 3-18) and HBF (Equation 3-14) formulations equal to each other yields the following equality:

 		(Eqn. 3-19)

Equation 3-19 can be solved for CEQ as follows:

	(Eqn. 3-20)

Therefore, setting CEQ = b/m leads to identical model formulations.

3.5 	Other Potentially Useful Modeling Constructs

One of the peer reviewers commented on the potential utility of the saturation concentration (Csat) of formaldehyde in air over an emitter of interest, as follows:

Equation 3-5 is reproduced below with slightly different notation along with an equivalent equation from my previous work:

       (Equation 3-5 with different notation)

Gss 	= steady state emission rate (mg/m2-hr).  Equivalent to CH2OER’

Gmax = the maximum emission rate which occurs at zero backpressure; that is, at zero concentration of formaldehyde in the air (mg/m2-hr).  Equivalent to b.

m 	= the mass transfer coefficient (m/hr)

Css 	= vapor-phase concentration of formaldehyde at steady state (mg/m3).  Equivalent to        [Ch2O]v

Equation 3-5 above is essentially identical to an algorithm that I have often used for backpressure modeling, shown below:

Csat = the saturation concentration (mg/m3) of formaldehyde in the air over the emitter of interest. That is the concentration that would be expected in a volume (with high surface area/volume ratio) in which the emitting walls were made up entirely of the emitter of interest and there is zero ventilation. Note the equivalence of this last equation to Equation 3-5 above and the identity of m:

Clearly, the relatively straightforward analytical measurement of Csat could provide a potentially valuable extended methodology for the evaluation and development of the model’s parameters relative to specific emitters.

Several peer reviewers suggested possible alternatives to the exponential-decay model used in FIAM-pwp to represent declining formaldehyde emissions over time. One suggestion was that a power-law model may be more suitable and another suggestion was the use of an expression with multiple or changing decay rates to represent, for example, “fast” (earlier) and “slow” (later) periods of exponentially declining emissions. Brown fitted a double-exponential model to results from chamber experiments, noting that “the high but decreasing emission rates in the first 3 months were consistent with free formaldehyde and formaldehyde produced from easily hydrolysed chemical bonds” and that  “longer-term, near-constant emissions may be due to ongoing hydrolysis of resins used in the wood panels.” One peer reviewer noted a conceptual model with three exponential-decay compartments, attributed to three potential sources of formaldehyde emissions:

Free formaldehyde (short-term compartment);

Decay of paraformaldehyde and other complex structures (medium-term compartment); and

Hydrolysis of the resin (long-term compartment).

A single-exponential model for declining formaldehyde emissions over time has the following form:

	ER(t) = ER(0) e -kt

	Where:

	ER(t) is the emission rate at time t (e.g., elapsed hours);

	ER(0) is the initial emission rate (t = 0); and

	k is the rate constant governing the exponential decline in the emission rate.

The power-law function takes the following form:

	ER(t) = at -k

	Where a is a constant and k is an exponential index, dimensionless.

Although the power-law function is undefined when t is zero, an initial emission rate can be “set” by assigning an arbitrarily small value to t (the rate is highly sensitive to the value chosen for t).

The plots in Figure 3-1 illustrate the declining behavior of the power-law function, with a set to 50 and k set to 0.25, in comparison to the single-exponential model, with ER(0) set to 90 and k set to either 0.1 or 0.5. The power-law function generally has a sharper curvature than the exponential model. This sharper curvature can be matched to an extent with the exponential model, but only by choosing a more rapidly declining emission rate (e.g., with k set to 0.5 as in the figure). The shape of the time-related decline obtained using the power-law function can be nearly matched by the exponential-decay model, however, when it is modified to have an initial period of faster decline followed by a second period of slower decline, as illustrated in Figure 3-2. If, for example, the conceptual model above with three potential sources of formaldehyde emission is a representative construct, then the approach of using multiple exponentials as a semi-empirical approximation may be preferable (recognizing the associated need for estimating multiple parameters) because first-order processes are exponential in form. An example application of FIAM-pwp with a varying decay rate is provided in Section 2.7.5.

The above constructs, although potentially useful, currently share one limitation – little existing data to provide a basis for assigning appropriate parameter values. They should be kept in mind, however, for future research efforts and modeling applications. By comparison, as described in Section 3.8, there has been a fair amount of research on the formaldehyde emissions half life, providing some basis for choosing a value for the rate of decline for the simpler single-exponential decay model.

Figure 3-1. Representation of Declining Emission Rate

by Power-law Function vs. Exponential-decay Model.

Figure 3-2. Representation of Declining Emission Rate by Power-law Function

vs. Exponential-decay Model with Periods of Fast and Slow Decay.

3.6 	Discussion of Indoor Sinks tc \l2 "3.4 	Treatment of Indoor Sinks

In concept, the treatment of indoor sinks in the calculation module could be accomplished within the model framework by recognizing that the emission term, as given by Equation 3-5, is comprised of two components. The first component (-m*[CH2O]v) is in the same form as a first-order sink representation. The second component (b) is a constant, representing a constant emission rate. By setting b equal to zero and m to a nonzero value, this “source” representation actually reflects the behavior of a first-order sink. Alternatively, setting m to zero and b to a nonzero value represents a product as a constant emitter.

Recognizing these behaviors, the source term could be used to represent a simplistic sink by assigning a large enough value to m to result in a net flux of formaldehyde into a material that acts as a sink.  However, this simplistic approach does not allow a fully realistic representation of the re-emission from sinks that has been observed in laboratory and field studies. In the model, the concentration in a compartment is assumed to decline from an initial “steady-state” concentration in accordance with a user-specified half-life. This model representation tends to diminish the effect of the sink over time, much like the emission rates for materials that act as sources. In reality, sinks for formaldehyde tend to accumulate mass when air concentrations are high, and to re-emit this mass as the air concentration decreases. The accumulation rate in the sink at any point in time is a function of the air concentration and the mass residing in the sink at that point, as well as other sink characteristics.

Because the complex relationships such as those described above cannot be fully captured by using the current modeling framework to represent sinks, it is recommended that users do not attempt to model sinks using FIAM-pwp. Ignoring the potential effects of indoor sinks will tend to result in a more conservative estimate, that is, higher modeled concentrations. The magnitude of prediction error with exclusion of indoor sinks is believed to be relatively small, on the order of 10 % for most formaldehyde modeling situations.

3.7	Decay of Indoor Concentrations tc \l2 "3.5	Decay of Indoor Concentrations

The initial (steady-state) indoor formaldehyde concentration, as calculated by the model described above, is assumed to decrease over time as the reservoir of formaldehyde in various sources and sinks is gradually depleted. The decrease in the initial value over time is assumed to follow a first-order exponential process, expressed as follows:

 	(Eqn. 3-21)

where:

Ct	=	formaldehyde concentration indoors (ppb) at time t (in years), due to the combination of background concentration and emissions from PWPs (Note: Ct = Ci at t = 0)

CB	=	background concentration (ppb), which is defined as the outdoor concentration plus the contribution from indoor sources other than    pressed-wood products (assumed constant)

Ci	=	initial concentration indoors (ppb)

k	=	first-order rate constant for the exponential decline (years-1).

Note that, in Equation 3-21, only the contribution from the new PWPs (i.e., Ci - CB) is decayed because the background contribution is assumed to be constant, as discussed in Section 3.3. The value of k is determined from the user-specified half life for the indoor formaldehyde concentration, assumed to be dominated by an exponential decay in formaldehyde source strength.  Solving for t results in the following equation:

 	(Eqn. 3-22)

Solving for k results in the following equation:

 	(Eqn. 3-23)

Neglecting for the moment the background contribution to the indoor concentration (i.e., assuming that the background concentration is zero), Equation 3-23 reduces to:

 	(Eqn. 3-24)

By definition, Ct is equal to half of Ci when the half-life is reached:

 	(Eqn. 3-25)

where:

T = half-life (in years).

By substitution, Equation 3-24 becomes:

 	(Eqn. 3-26)

Substituting the default half life of 1.5 years (see Section 2.2) for T in the above equation gives:

k = 0.462 years-1

Indoor concentrations at later points in time (i.e., subsequent to the initial, steady-state values for each zone) are calculated by decaying only the portion of the indoor concentration that is attributable to indoor pressed-wood products. For example, to obtain the indoor concentration 3 months (0.25 years) after the initial value, with an assumed half-life of 1.5 years, Equation 3-21 would apply:

C(0.25 yr) = CB + (Ci - CB) e-0.462*0.25	(Eqn. 3-27)

If Ci were 50 ppb and the background concentration were zero, then the indoor concentration three months later would be 44.5 ppb. With the default background concentration of 7.5 ppb (see Section 2.2), the indoor concentration would be 57.5 ppb initially and 52 ppb after three months. In either case, the portion of the initial indoor concentration due to indoor pressed-wood products (50 ppb) would be reduced by 5.5 ppb over three months with a half life of 1.5 years.

The time required for the initial indoor concentration to decay to a user-specified concentration (e.g., 10 ppb, the default value) can be determined from the first-order exponential process using Equation 3-22 as follows, given an initial indoor concentration greater than the specified concentration and assuming a background concentration of zero:

t = ln (Ci / 10) / k	(Eqn. 3-28)

Continuing with the above example, where k is 0.462 years-1 and Ci is 50 ppb, by substitution into Equation 3-28 we get:

t = ln (50 / 10) / 0.462	(Eqn. 3-29)

for which the value of t is 3.48 years, or 41.8 months.

The model uses the higher of the two initial indoor concentrations, when a two-zone model is selected, for the calculation. Because the user is allowed to specify a background concentration other than zero, which is assumed to be constant over time, Equation 3-22 can be used to account for the background contribution while decaying only the component due to indoor sources and sinks:

 	(Eqn. 3-30)

With the default background concentration of 7.5 ppb and an initial concentration of 57.5 ppb, the value for t would be 6.48 years. The result from Equation 3-30 is multiplied by 12 and reported in months. If the highest initial indoor concentration is lower than the background concentration, then zero months is reported as the time required for the indoor concentration to decay to background.

3.8	Default Value for Half Life

Ideally, an appropriate half-life value for representing the long-term decay of formaldehyde emissions and concentrations in residences would be determined by taking measurements in a house soon after it was loaded with pressed-wood products and at periodic points in time over the next several years. Continuing with this ideal situation, the products would not change throughout the measurement period and factors such as indoor temperature and humidity, as well as the indoor-outdoor air exchange rate, would change only minimally in response to outdoor weather conditions and occupant activities indoors. Further, the experiment would be repeated in several houses. The data for each house would be analyzed to fit a nonlinear (e.g., exponential) decay function to the time-varying indoor concentrations, and the resultant estimates would be compared across houses (or the data would be pooled across houses) to determine an appropriate central value for the concentration half life.

The ideal data set has not been collected, however, most likely because the complexities and costs of multiple measurements over time, coupled with the need to restrict certain occupant activities over several years (or to operate a research house to gain experimental control), would be prohibitive.  There are two practical alternatives to the ideal experimental situation, both of which have been attempted: (1) collect or assemble point-in-time measurements from houses of varying ages, as a proxy for the time-related decay in one or a series of houses; and (2) conduct chamber tests at periodic points in time for pressed-wood products, either individually or in combination.

Either alternative has significant limitations. For example, cross-sectional data from many houses are, at best, a crude proxy for the time-related behavior of a single house, or of a limited set of well-characterized houses – the analysis is confounded by varying, and generally unknown, construction features, occupant activities and weather conditions at the times of measurement. Chamber tests, on the other hand, have the advantage of careful experimental control. However, for multiple tests over time, the material to be tested typically would not be kept in the chamber-controlled environment throughout the testing period, but rather during only the relatively brief occasions when measurements were to be taken. Further, most such tests have been conducted only for a single product or material. The time-related rate of decline depends on the formaldehyde concentration; the rate of decline is more rapid for a single product because other products are not present to increase the formaldehyde concentration and thereby retard its rate of formaldehyde release. Limited tests of product/material ensembles have been conducted, but none have included the full array of sources and sinks that typically would be present in an occupied house. With these limitations in mind, some previous investigations into the half life of formaldehyde emissions or concentrations are summarized below.

As summarized in a Versar 1988 report, estimates of decay half lives for formaldehyde concentrations in residences range from 2 to 44 years, with most estimates below 5 years. These estimates have been based largely on pooled cross-sectional data across a variety of residences, as a proxy for time-series data from one or a few houses. It is noteworthy that the higher estimates (20 to 44 years) are from data sets involving houses aged from new to 50 years, whereas the lower estimates (2 to 4 years) are from data sets where the houses generally were 10 years old at most. If none of the materials or furnishings in a house were to be changed, and if the occupants were to avoid using consumer products that emit formaldehyde, then the indoor concentration could be expected to eventually decay to some background level, similar to that if no sources were present. As a house ages, however, occupants will tend to add or replace materials and furnishings, some of which may emit formaldehyde. Such changes, then, will introduce new sources, thereby raising the formaldehyde concentration relative to the no-change case and artificially inflating the half-life estimate.

The above conjecture is partly supported by limited studies involving repeat measurements at different points in time from one or two houses, for which the half-life estimate ranged from 2.0 to 2.6 years. A careful analysis by Versar of a cross-sectional data set for 396 manufactured homes, as described in the 1988 report referenced on the previous page, resulted in a half-life estimate of 2.92 years. This estimate is believed to be an upper bound for the true half life in a house that has some significant formaldehyde sources from the outset of its construction and occupancy history.

Chamber studies to investigate the decay of formaldehyde have focused primarily on individual sources and, not surprisingly, have produced shorter half-life estimates than most residential studies. As summarized in the same (1988) Versar report, the estimated half lives from chamber studies have ranged from 0.2 to 2.58 years. One noteworthy investigation, conducted by Matthews et al., involved a combination of sources (particleboard, hardwood plywood paneling and MDF) under controlled environmental conditions (23 ( C and 50 % relative humidity). The “slow” decay study, with an air exchange rate of 0.4 air changes per hour (ACH) in the chamber, produced a half-life estimate of 1.52 years. The “fast” decay study was conducted with relatively high air exchange rates designed to keep the chamber formaldehyde concentration below 0.1 ppm. The lower background concentration was expected to increase the emission rates and, thus, shorten the decay periods relative to the “slow” decay study. Resultant half-life estimates were 0.76, 0.62 and 1.08 years for particleboard, paneling and MDF, respectively.