Formaldehyde Indoor Air Model – Pressed Wood Products 

(FIAM-pwp): 

Model Documentation 

Prepared for: 

 U.S. Environmental Protection Agency 

 Office of Pollution Prevention and Toxics 

 1200 Pennsylvania Avenue, N. W. 

 Washington, D.C. 20460 

Under: 

 EPA Contract No. EP-W-04-035, 

 Work Assignment No. 4-2 

Prepared by: 

Versar, Inc. 

 6850 Versar Center 

 Springfield, VA 22151 

August 2009 
i 

DISCLAIMER 

This is a draft document; it has not yet been reviewed in accordance with U.S. Environmental 

Protection Agency policy or approved for publication. Mention of trade names or commercial 

products does not constitute endorsement or recommendation for use.
ii 

TABLE OF CONTENTS

Section Page

1. INTRODUCTION............................................................................................................. 1-1 

2. USER INTERFACE.......................................................................................................... 2-1 

2.1 Main Screen................................................................................................................. 2-1 

2.2 House Screen............................................................................................................... 2-3 

2.3 Sources - General Screen............................................................................................. 2-8 

2.4 Sources - Cabinets Screen...........................................................................................2-17 

2.5 Sinks Screen ...............................................................................................................2-24 

2.6 Exposures Screen .......................................................................................................2-27 

2.7 Results Screen ............................................................................................................2-29 

3. MODEL CALCULATIONS AND ASSUMPTIONS......................................................... 3-1 

3.1 Generalized Mass-Balance Equation ............................................................................ 3-2 

3.2 Steady-State Model for Initial Formaldehyde Concentration in One Compartment........ 3-3 

3.3 Extension of the Steady-State Model to Two Compartments........................................ 3-5 

3.4 Treatment of Indoor Sinks ........................................................................................... 3-6 

3.5 Decay of Indoor Concentrations................................................................................... 3-8 

3.6 Default Value for Half Life .........................................................................................3-10 

3.7 Temperature and Humidity Adjustments .....................................................................3-12

3.8 Exposure Calculations.................................................................................................3-13 

4. SUMMARY OF EPA FORMALDEHYDE PILOT STUDY.............................................. 4-1 

4.1 Study Objectives and Design........................................................................................ 4-1 

4.2 Study Methods ............................................................................................................ 4-3 

4.3 Study Results............................................................................................................... 4-6 

4.4 Study Conclusions ......................................................................................................4-10 

5. ASSESSMENT OF MODEL ACCURACY....................................................................... 5-1 

5.1 Mathematical Correctness of Model Algorithms........................................................... 5-1 

5.2 NIST Assessment of Matthews Model Predictions ....................................................... 5-1 

5.3 Assessment of Predictions by the Current Model.......................................................... 5-2 

6. REFERENCES.................................................................................................................. 6-1 

Appendix A – Derivation of Two-zone Steady-state Solution
iii 

LIST OF TABLES

Table Page

2-1. Summary of Default House Types Available in the Model............................................... 2-5 

2-2. Linear Formaldehyde Emission Models Based on Environmental Chamber Data Taken 

at 23 °C, 50 % RH or at 25 °C, 50 % RH ......................................................................2-10 

2-3. Linear Slopes and Calculated Intercepts for Sources Just Meeting HUD/ANSI 

 and CARB Phase 1/Phase 2 Emission Standards ............................................................2-15 

2-4. Default Values for Emitting Components of Kitchen Wall Cabinets................................2-21 

2-5. Default Values for Emitting Components of Kitchen Base Cabinets................................2-22 

2-6. Default Values for Emitting Components of Vanities .....................................................2-23 

4-1. Initial Emission Characteristics of Products Used in the Pilot Study ................................ 4-4 

4-2. Loading Areas for Pressed-wood Products at the Conventional House............................ 4-4 

4-3. Summary of Monitoring Results for Loadings 1, 2, and 3................................................ 4-6 

4-4. Computed Emission Rates for UF-Bonded Products ....................................................... 4-8 

5-1. Model Inputs (Sources and Sinks) for Initial Baseline Period........................................... 5-3 

5-2. Modeling Results for Initial Baseline Period.................................................................... 5-4 

5-3. Model Inputs (Sources and Sinks) for First (Medium) Loading ....................................... 5-4 

5-4. Modeling Results for First Loading................................................................................. 5-5 

5-5. Model Inputs for Air-out Period after First Loading........................................................ 5-5 

5-6. Modeling Results for Air-out Period after First Loading.................................................. 5-6 

5-7. Model Inputs (Sources and Sinks) for Second (High) Loading 3 ..................................... 5-6 

5-8. Modeling Results for Second Loading............................................................................. 5-7 

5-9. Model Inputs for Air-out Period after Second Loading.................................................... 5-7 

5-10. Modeling Results for Air-out Period after Second Loading ............................................. 5-8 

5-11. Model Inputs (Sources and Sinks) for Third (High) Loading ........................................... 5-8 

5-12. Modeling Results for Third Loading................................................................................ 5-9 
iv 

LIST OF FIGURES

Figure Page

2-1. Main Screen before Logging in ....................................................................................... 2-1 

2-2. Main Screen after Logging in.......................................................................................... 2-2 

2-3. House Screen with Default Selections............................................................................. 2-3 

2-4. House Screen with Conventional House 2 Selected......................................................... 2-7 

2-5. Sources - General Screen Prior to Selection of Any Sources ........................................... 2-8 

2-6. Sources - General Screen with Four Source Types Selected...........................................2-16 

2-7. Sources - Cabinets Screen Prior to Selection of Any Cabinets ........................................2-17 

2-8. Sources - Cabinets Screen with Medium-emitting Wall Cabinet Selected........................2-19 

2-9. Sources - Cabinets Screen with Medium-emitting Base Cabinet Selected........................2-19 

2-10. Sinks Screen with Initial Values .....................................................................................2-24 

2-11. Sinks Screen with Equilibrium Values ............................................................................2-25 

2-12. Exposures Screen with Default Selections......................................................................2-27 

2-13. Results Screen (Concentrations) for Default Case ..........................................................2-29 

2-14. Results Screen (Exposures) for Default Case .................................................................2-31 

2-15. Concentration Results after Addition of Sources and Sinks ............................................2-32 

2-16. Exposure Results after Addition of Sources and Sinks....................................................2-32 

4-1. Upstairs Formaldehyde Concentrations over Time for Three Loadings ............................ 4-7 
1-1 

1. INTRODUCTION 

The model described in this document, Formaldehyde Indoor Air Model – Pressed Wood Products or 

FIAM-pwp, is intended to assist the user in estimating human inhalation exposure to airborne 

formaldehyde (HCHO) emissions from pressed wood products installed in new or existing residences 

or small structures such as portable classrooms or camper trailers. The model estimates indoor 

formaldehyde concentrations and associated human inhalation exposures for such situations. 

The model described herein is an adaptation of a model developed during the 1980s by Dr. Thomas 

Matthews and colleagues at the Oak Ridge National Laboratory (Matthews et al. 1983a; Matthews et 

al. 1987). The “Matthews model” was designed to estimate the steady-state formaldehyde 

concentration resulting from emission sources such as pressed wood products in a single indoor 

compartment or zone. Product emission rates in the model are dependent on the HCHO concentration 

in the vapor phase, in accordance with Fick’s Law describing the bulk-vapor interphase at the surface 

of a pressed wood emission source. The initial (steady-state) indoor concentration calculated by the 

model is assumed to decrease over time as the reservoir of formaldehyde in various sources (or sinks) 

is gradually depleted. The gradual decrease over time is assumed to follow a first-order exponential 

process, at a decay rate that depends on the chosen emissions half life for HCHO. 

 

In the mid-1990s an EPA-sponsored pilot study was undertaken by Versar/GEOMET (Koontz et al. 

1996) 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 April 2008 the California Air Resources Board adopted an airborne toxics control measure to 

reduce formaldehyde emissions from composite wood products sold in that state. This new regulation 

governs the formaldehyde content in both raw composite wood products and finished products sold 

or used in California. In 2008 EPA was petitioned to adopt the California regulation as a national 

standard. EPA denied the petition but, in so doing, stated its intention to gain a greater scientific 

understanding of potential health risks of formaldehyde’s use in pressed wood products. 

The recent petition has caused OPPT to renew interest in the model, the current version of which is 

documented in this manual. In addition to the modifications noted above, this version of the model 

has a third modification – the addition of exposure estimates. Section 2 describes the user interface 

for the model and Section 3 describes the mathematical basis and underlying calculations and related 

assumptions. The EPA pilot study mentioned above is summarized in Section 4 and an assessment of 

the model’s accuracy is provided in Section 5. References cited in the document are listed in Section 

6. Appendix A describes the mathematical derivation of the two-zone implementation of the steadystate model.
2-1 

2. USER INTERFACE 

The user interface consists of a Main Screen (introductory screen), five input screens (House, 

Sources - General, Sources - Cabinets, Sinks and Exposures), and a Results Screen that displays 

modeling results after inputs have been provided and calculations have been executed (the 

calculations are executed automatically each time the Results Screen is accessed). The components of 

the main, input and results screens are described below. Model calculations and related assumptions 

are documented in Section 3. 

2.1 Main Screen

The model should be accessed using Internet Explorer (version 8 or later). The Main Screen, which is 

an introductory or opening screen (see Figure 2-1), enables the user to “log in” to the program, to 

choose options relating to the visual display and audio help files, and to access previously saved 

inputs or create a new set of inputs. 

After a User Name and Password have been entered, tabs for accessing the input screens will appear 

at the top (see Figure 2-2). Currently, User Names and Passwords are assigned by EPA or by Versar. 

At this point audio help files and/or visual help (larger fonts) can be enabled by checking the 

appropriate box(es). Either of these options can be disabled by un-checking the corresponding box. 

The next step is to choose a file name for new inputs or to access previously saved inputs, if any, by 

selecting a name from the drop-down list. The file name can contain any combination of uppercase 

and lowercase letters along with numbers and blanks/spaces. The maximum number of characters for 

a file name is 16. 

Figure 2-1. Main Screen before Logging in. 
2-2 

Figure 2-2. Main Screen after Logging in. 

The input screens can be accessed in any order; however, as a general rule it is advisable to access the 

screens by going from left to right, starting with the House Screen. Inputs are saved automatically as 

the user progresses through the input screens. 
2-3 

2.2 House Screen

This screen (see Figure 2-3) is intended to collect information from the user on the house volume and 

airflows and to provide certain options pertaining to model calculations. More specifically, the inputs 

for this screen are in three areas: (1) documentation of the run and selection of indoor conditions and 

formaldehyde decay parameters (upper-left portion of the screen); (2) choice of house type, house 

volume and number of zones (upper-right portion); and (3) input of zone volumes and airflow rates 

(lower portion). 

Most of the inputs on this screen are optional, in the sense that default values are provided by the 

model. Although the model can be run using all defaults, care should be taken in your choice of values 

for the background concentration, emissions half life, temperature and humidity, and type of house or 

structure (e.g., portable classroom) to be modeled. 

Figure 2-3. House Screen with Default Selections. 

2.1.1 Upper-left Portion

Inputs for this portion of the House Screen relate to documentation of the run and choices for indoor 

conditions and formaldehyde decay parameters. 

Title and Notes. Text inputs for title and notes are intended to assist the user in documenting specific 

features or options that are chosen in making the model run; these inputs are “echoed back” on the 

Results Screen. 

Air Exchange Rate. The air exchange rate is “grayed out” because no user entry is allowed here. 

Instead, the rate is calculated by the program using the volume and airflow information from the 

lower portion of the screen, as described later (see Lower Portion subsection). 
2-4 

Background Concentration. The background concentration, with a default value of 0.000 ppm, is 

intended to reflect the contribution to the indoor concentration of the outdoor concentration plus 

indoor sources other than pressed wood products (e.g., tobacco smoke, permanent press fabrics, 

paints, cosmetics). Normally a value between 0.001 and 0.010 ppm would be appropriate for this 

input. If the background concentration is left at its default value of zero, then the modeling results will 

reflect the contributions of pressed wood products and indoor sinks only. 

Emissions Half Life. The emissions half life is used by the model to “decay” indoor concentrations 

over time from the initial values calculated by the model under a steady-state assumption. As 

described in Section 3.6, the default half life of 2.92 years is based on a regression analysis of 

formaldehyde concentrations in residences of various ages.

The default choice is considered to be conservative; that is, assuming that initial concentrations in a 

structure are predicted accurately, the value of 2.92 years likely will cause the modeled concentrations 

to decay at a slower rate than might be observed in a stable setting (i.e., one in which no new pressed 

wood products are added after initial construction). A half life on the order of 1.5 to 2.0 years is 

suggested as a less conservative value.

Temperature and Humidity. The model calculates and reports indoor concentrations assuming an 

indoor temperature of 23 ° C and an indoor relative humidity of 50 percent (base conditions). The 

inputs provided here enable the user to specify an additional set of temperature and humidity values; 

the model also provides results that are adjusted to these user-specified conditions. The temperature 

and humidity coefficients provided as options on this screen are used by the model to make the 

adjustments (see Section 3.7). By default, the user-specified temperature and humidity values also are 

set at 23 ° C and 50 percent, respectively, as shown above in Figure 2-3. Exposure measures included 

in the model results, such as average daily dose and percent of time above a formaldehyde 

concentration of concern (COC), are determined using indoor concentrations that are calculated 

under user-specified conditions. 

Time from Initial Concentration and Decay Concentration. By default, the model will “decay” 

initial indoor concentrations that are calculated under a steady-state assumption to time points that 

are 3 months, 6 months and 12 months later than that for the initial concentration values (see Section 

2.7 and Section 3.5). The input labeled “Time from Initial Conc.” enables the user to specify an 

additional point in time (in months) over which the model will decay the initial concentration values; 

this input is set to 24 months by default (see Figure 2-3). 

By default, the model calculates the time required for the highest indoor concentration to decay to 

0.01 ppm. The input labeled “Decay Concentration to,” with a default value of 0.01 ppm, allows the 

user to specify an additional concentration (in ppm) for which the model will calculate the time to 

decay to that value. 
2-5 

2.1.2 Upper-right Portion

Inputs for this portion of the House Screen relate to choices for the type of house to be modeled, the 

house volume, and the number of modeled zones in the house. 

Type of House. The choices for type of house are based on the availability of house/zone volume and 

airflow information. As summarized in Table 2-1, either a conventional (choice of two types) or a 

manufactured house can be selected. Default volumes and air flows will be displayed for the selected 

house type, but these values can be changed manually. A structure such as a portable classroom or a 

camper trailer can be represented by choosing a manufactured house and editing the house volume. 

Table 2-1. Summary of Default House Types Available in the Model

Volume, m3

House Type No. of 

Stories Configuration Zone 

1 

Zone 

2 Total 

Air 

Exchange 

Rate, ACH 

Conventional 

1 3 Two upper floors (zone 1) and basement (zone 2) 304.0 167.0 471.0 0.59 

Conventional 

2 2 Upstairs (zone 1) and Downstairs (zone 2) 318.5 205.7 524.2 0.33 

Manufactured 1 One floor (zone 1) 221.9 -- 221.9 0.50 

If the first conventional house (Conventional 1) is selected, as shown in Figure 2-3, then the user 

interface will display information on volumes and air flows for the conventional house that was used 

in the pilot study for the USEPA Indoor Air Formaldehyde Testing Program (Koontz et al. 1996). 

This is a three-story house with two zones – Zone 1 is the upper floors (first and second) combined, 

and Zone 2 is the basement. If the user selects the second conventional house (Conventional 2), then 

the program will display volumes and air flows for a “generic” conventional house consisting of two 

stories and two zones – upstairs and downstairs. The default volumes and air flows for this house are 

based on analysis of a database containing results from field studies in which airflow rates were 

measured using multiple tracer gases. If the user selects a manufactured house, then the user interface 

will display the volume and air flows for a single-story, one-zone house with an assumed length of 

21.34 meters (70 ft), width of 4.27 meters (14 ft), and ceiling height of 2.44 meters( 8 ft).

House Volume. The default house volume can be changed by entering a new value here. If a new 

value is entered, then the program will adjust the zone-specific volumes in the lower portion of the 

screen so that they add up to the new volume. The airflow rates in the lower portion of the screen will 

remain at their default values, meaning that the calculated air exchange rate will change. The air 

exchange rate can be adjusted by changing the airflow rates to and from outside for each zone in the 

lower portion of the screen. 

As an alternative to entering a house volume, the “Calculate Volume” option can be used to enter 

inputs for number of stories, length, width and height; the program will calculate the volume by 

multiplying these values. Default values are provided for the volume components as “placeholders” 

that can be edited. The model assumes that each story has the same length, width and height when 
2-6 

calculating the volume, but different volumes can be assigned to each zone in the lower portion of the 

screen. 

Number of Zones. Houses can have either one or two zones. Both of the conventional houses are 

conceptualized as having two separate zones or compartments whereas the manufactured house is 

conceptualized as a single zone. The model cannot represent more than two zones. Representing a 

house with more than two stories would require some stories be combined into one zone, as with the 

configuration of the Conventional 1 house (i.e., the two upper floors are combined into one zone). 

If either conventional house is chosen and the user selects “One Zone” as the number of zones, then 

the program will “collapse” the airflow rates in the lower portion of the screen 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 from one to two, then the model will assign the entire volume, as well as air flows 

to/from outside, to Zone 1. This assignment is made for the purpose of providing “placeholder 

values” that can be edited. The original volumes and air flows for the house type that was selected can 

always be obtained by re-selecting it at the top-right of the screen (it may be necessary to first select 

another house type and then re-select the desired house type). 

2.1.3 Lower Portion

This portion of the House Screen enables the user to enter zone-specific descriptions, volumes and 

airflow rates. That is, the user can enter or edit descriptions and volumes for each zone as well as air 

flows between zones and between indoors and outdoors. If the volume of either zone is changed, then 

the program will automatically update the total house volume. 

As noted above, the air exchange rate in the upper-left part of the screen cannot be changed directly 

by the user – the air flows provided near the bottom of the screen, which are used in executing model 

calculations, also are used by the software to calculate the air exchange rate (total flow into the 

house, divided by its volume) for display. 

If the user selects a one-zone house, then 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 the case of 

a two-zone house, six airflows are needed – the flow of 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 must match the 

total flow into it. The program updates these total flows as the user provides or edits inputs. If the 

total flows for any zone are not balanced, then the program will issue a warning but will allow access 

to other screens. 

The airflow matrix on the House screen actually shows eight air flows, but two of these are 

redundant. The Flow From Other Zone on the first line (Zone 1) is the same as the Flow To Other 

Zone on the second line (Zone 2), and The Flow To Other Zone on the first line (Zone 1) is the same 

as the Flow From Other Zone on the second line (Zone 2). If the user edits any of these flows, then 

the corresponding redundant flow automatically is updated by the program. 

As shown previously in Table 2-1, the default air exchange rates for houses provided by the model are 
2-7 

0.59 air changes per hour (ACH) for Conventional house 1, 0.33 ACH for Conventional house 2, and 

0.5 ACH for the manufactured house. If the user wishes to change the default air exchange rate while 

maintaining a flow balance in each zone, the simplest means of adjustment is to multiply all airflows 

by the ratio of the target or new air exchange rate to that of the default air exchange rate. For 

example, if the default rate is 0.33 ACH and the target rate is 0.5 ACH, then the target/default ratio is 

0.5/0.33, or 1.5. In this case, all airflow rates would be increased by 50 % (i.e., multiplied by 1.5) to 

achieve the target air exchange rate while maintaining a flow balance. 

The default air exchange rate and air flows for Conventional 1 are based on 24-hour measurements 

with perfluorocarbon tracers (PFTs) taken at the house used in the USEPA formaldehyde pilot study. 

The air exchange rate (but not interzonal air flows) for the pilot-study conventional house also was 

measured using sulfur hexafluoride (SF6) as a tracer. Air exchange rates estimated with SF6 were 

systematically about a third lower (i.e., average of about 0.4 ACH) than rates estimated with PFTs. 

As noted in the pilot study report, the SF6 method involves periodic injection and mixing of the tracer 

through the HAC system followed by real-time analysis of the concentration decline due to infiltrating 

outdoor air, whereas the PFT method relies on near-constant release of tracers from multiple 

locations accompanied by time-integrated sampling over a 24-hour period. The limited resources 

available for the pilot study did not allow investigation of the differences between the two methods. 

Should the user wish to replace the default air exchange rate with a lower value such as 0.4 ACH, 

then the corresponding interzonal air flows can be estimated by the method described above. 

The default volume, air exchange rate and airflow rates for the house labeled as Conventional 2 (see 

Figure 2-4) are based on analysis of a database with PFT measurement results, using only houses that 

were configured as two zones – upstairs and downstairs/basement. The default air exchange rate (an 

arbitrary choice) for the manufactured house is 0.5 ACH, meaning that the flows from/to outside are 

exactly half the house volume. For a more conservative estimate of formaldehyde concentrations 

indoors, lower air flows (resulting in a lower air exchange rate) can be entered. 

Figure 2-4. House Screen with Conventional House 2 Selected.
2-8 

2.3 Sources - General Screen

This screen (see Figure 2-5) enables the user to specify the types and amounts of pressed-wood 

products used in the house and the zone(s) in which each product is located (Zone 1 is selected by 

default). The user has the option of (1) selecting one or more emission sources from a menu of source 

types for which emission rate modeling parameters (i.e., “Slope” and “B” values; see Section 3.2) 

have been developed from results of chamber tests, or (2) entering a source with one's own emission 

rate modeling parameters, by editing the modeling parameter values for one of the many choices 

provided here. The source area, set to zero by default, must be edited to “activate” a source. 

Each input line or row on this screen refers to a specific type of source in a specific zone. 

Consequently, to represent a source that is present in both zones of a house, two input lines need to 

be provided for that source – one line for Zone 1 and one line for Zone 2. Once a source has been 

selected, it can be deselected or “turned off” by either of two methods: (1) choosing “None Selected” 

in the Source Type list, or (2) entering a value of zero for the source’s area. 

One of the Source Types available on this screen is Kitchen Cabinet, but there also is a separate 

screen that is specific to cabinets (Sources - Cabinets; see Section 2.4). The emission rate modeling 

parameters for cabinets that are available on the Sources - General screen are based on chamber 

testing of an ensemble of kitchen wall and base cabinets. Alternatively, on the Sources - Cabinet 

screen one can essentially “build” cabinets, component by component, and specify the emission rate 

modeling parameters for each component, but the process is fairly involved. In the absence of detailed 

information on specific cabinet components and appropriate values for their modeling parameters, it is 

recommended that the cabinet ensemble available on this screen be used. 

Figure 2-5. Sources - General Screen Prior to Selection of Any Sources.
2-9 

As described in a previous report (Versar 1989), the emission rate modeling parameters provided with 

the software have been developed from the results of indoor-air chamber tests on pressed wood 

products that were conducted at multiple air exchange rates and/or product loading ratios. The model 

currently contains emission rate modeling parameters for one or more chamber-tested products within 

each of the following source types: 

• Particleboard underlayment 

• Mobile home decking 

• Industrial particleboard 

• Medium density fiberboard 

• Hardwood plywood paneling (with a print face) 

• Hardwood plywood paneling (with a paper face) 

• Hardwood plywood paneling (with a wood veneer face) 

• Hardwood plywood paneling (unspecified face material) 

• Softwood plywood (phenol-formaldehyde resin) 

• Hardboard (phenol-formaldehyde resin) 

• Kitchen cabinets 

• Interior doors. 

Table 2-2 lists all of the products (and emission rate modeling parameters) contained in the model for 

each source type. This table also provides references for the data in the table and additional 

information, as available, on chamber testing conditions (air exchange rate and loading ratio). 

Correlation coefficients listed in the right-hand column of the table are based on regression analysis 

between calculated emission rates and measured chamber concentrations for tested products, from 

which the modeling parameters (slope and intercept) were estimated. Not all investigators reported a 

correlation coefficient; coefficients are listed in cases where they were reported. 

The abbreviated names assigned to individual available sources in the table reflect the organization 

(e.g., EPA, ORNL) or individual that performed the testing from which modeling parameters were 

estimated. Several Available Sources – EPA-PBU for Particleboard Underlayment, EPA-HWP for 

Hardwood Plywood Paneling (Unspecified), EPA-CABINET for Kitchen Cabinets, and EPA-DOOR 

for Interior Doors – are based on chamber testing performed as part of the EPA pilot study on 

formaldehyde (Koontz et al. 1996), which was conducted using the house labeled as Conventional 1. 

Most source types have more than one available source; in such cases, the model also provides an 

“average” source as well as a maximum-certifiable HUD/ANSI (i.e., U.S. Dept. of Housing and 

Urban Development; American National Standards Institute) source, for which the modeling 

parameters were derived from the products (i.e., available sources) that were tested. The average for 

a given source type has slope and intercept values that are averaged across all available sources; in the 

case of medium density fiberboard (mdf), three cases with a suspect slope or intercept (unusually high 

value) were deemed potential outliers and excluded from the calculation. Such averages are suggested 

choices unless detailed information on emission characteristics is available for the product(s) selected. 
2-10 

Table 2-2. Linear Formaldehyde Emission Models Based on Environmental Chamber Data Taken at 23 °C, 50 % RH 

 (Listed Model Parameters are for Conditions of 23 °C and 50 % RH) 

Matthew’s Emissi

ER = m (con

Source Type Available Sourcesb

No. of Data 

Pointsc N/L Ranged

Measured 

Concentration 

Range (ppm) 

Slope (m/hr) Intcpt. (mg/

Particleboard Underlayment 

ORNL-PCB #1 ORNL-PCB #2 ORNL-PCB #3 ORNL-PBU 1 #4 ORNL-PBU 3 #3 ORNL-PBU 3 #6 GP-2 GP-4 GP-5 NBS-USM2-2B NBS-USM2-3B NBS-USM5-1A NBS-U-5,8,9,12,18 EPA-PBU AVG PBU MAX HUD 

3 4 4 4 4 3 

0.127 to 0.633 

0.316 to 5.70 

0.101 to 0.949 

0.159 to 9.18 0.444 to 6.67 0.586 to 2.37 

0.077 to 0.162 0.057 to 0.354 0.084 to 0.158 0.084 to 0.215 0.058 to 0.442 0.062 to 0.118 

-0.32 -0.70 -0.88 -1.72 -0.70 -0.93 -0.84 -1.57 -0.76 -0.36 -0.38 -0.62 -0.60 -1.25 -0.83 -0.83 

0.09 0.44 0.19 0.46 0.51 0.47 0.40 0.37 0.58 0.18 0.27 0.33 0.18 0.28 0.34 0.74 

Mobile Home Decking 

LEH-B GP-MHD AVG MHD MAX HUD 

-1.35 -0.77 -1.06 -1.06 

0.66 0.39 0.52 0.82 

Industrial Particleboard 

ORNL-PBI 3#2 LEH-C LEH-D LEH-H LEH-I LEH-J LEH-K LEH-L LEH-M LEH-N LEH-O LEH-P LEH-Q 

4 8 9 6 6 6 6 6 6 6 6 6 6 

0.316 to 3.31 

0.76 to 6.10 0.31 to 6.10 0.59 to 3.82 0.59 to 3.82 0.59 to 3.82 0.59 to 3.82 0.59 to 3.82 0.59 to 3.82 0.59 to 3.82 0.59 to 3.82 0.59 to 3.82 0.59 to 3.82 

0.096 to 0.457 -0.47 

-1.00 -0.54 -1.02 -0.87 -1.30 -0.96 -1.07 -0.40 -1.32 -0.58 -1.58 -0.98 

 0.42 

1.24 0.36 0.45 0.60 0.27 0.32 0.53 0.14 0.24 0.22 0.37 0.39 
2-11 

Matthew’s Emissi

ER = m (con

Source Type Available Sourcesb

No. of Data 

Pointsc N/L Ranged

Measured 

Concentration 

Range (ppm) 

Slope (m/hr) Intcpt. (mg/

Industrial Particleboard (continued) 

GP-1A GP-3A GP-6A GP-7A GP-8A GP-9A GP-11A NBS-USM7-1B NBS-USM2-1A NBS-USM6-1B NBS-USM6-2A NBS-USM6-3B NBS-USM4-1B GP-1N GP-2N GP-3N GP-4N GP-5N GP-6N GP-7N AVG PBI MAX HUD 

 -0.41 

-0.63 -0.46 -0.38 -0.63 -0.62 -0.55 -0.45 -0.39 -0.80 -0.33 -0.64 -0.28 -0.70 -0.72 -0.81 -0.55 -0.50 -0.46 -0.58 -0.70 -0.70 

0.12 0.33 0.34 0.24 0.33 0.35 0.29 0.12 0.30 0.18 0.18 0.29 0.20 0.53 0.53 0.35 0.27 0.37 0.34 0.48 0.35 0.39

Medium Density Fiberboard 

ORNL-MDF 1 #5 ORNL-MDF 3 #5 ORNL-MDF 1 #4 ORNL-MDF 2 #4 ORNL-MDF-U LEH-E LEH-F LEH-G GP-1 GP-2 GP-3 GP-4 GP-5 GP-6 

4 4 9 9 

15 

1.47 to 12.5 1.33 to 12.5 0.31 to 6.10 0.31 to 6.10 0.15 to 7.09 

0.170 to 0.952 0.160 to 0.936 

-0.89 -1.00 -1.25 -1.58 -0.91 -0.48 -0.80 -0.80 -4.98 -1.17 -2.00 -2.22 -3.87 -0.78 

2.78 2.49 1.62 1.09 4.24 0.32 0.79 0.83 1.27 0.77 0.84 1.33 0.80 0.50 

Medium Density GP-7 -0.73 0.58 
2-12 

Matthew’s Emissi

ER = m (con

Source Type Available Sourcesb

No. of Data 

Pointsc N/L Ranged

Measured 

Concentration 

Range (ppm) 

Slope (m/hr) Intcpt. (mg/

Fiberboard (continued) 

GP-8 GP-9 GP-10 GP-11 GP-12 GP-13 GP-14 GP-15 NBS-LMDF-1C NBS-LMDF-2B NBS-MDF 1 NBS-MDF 2 NBS-MDF 3 NBS-MDF 4 NBS-MDF 5 AVG MDF MAX NPA MDF 

-0.43 -0.69 -1.83 -0.81 -1.45 -0.90 -1.30 -0.77 -0.88 -0.71 -1.50 -1.16 -1.09 -0.76 -0.65 -1.28 -1.28 

0.46 0.32 0.92 0.58 1.31 0.63 0.75 0.39 0.64 0.73 1.73 1.14 1.31 1.29 1.43 0.13 1.18

Hardwood Plywood Paneling (Print) 

ORNL-PNPR 2 #3 ORNL-PNPR 3 #3 ORNL-PNPR 2 #5 ORNL-PNPR 3 #1 ORNL-PAN #2 AVG PNPR MAX HUD 

4 4 4 

0.313 to 6.57 0.445 to 3.34 0.316 to 1.90 

0.085 to 0.719 0.029 to 0.127 0.021 to 0.055 

-0.46 -0.37 -0.40 -0.85 -0.48 -0.51 -0.51 

0.67 0.13 0.25 0.26 0.05 0.27 0.25 

Hardwood Plywood Paneling (Paper) 

ORNL-PNP 2 #4 ORNL-PNP 3 #1,2h

ORNL-PNP 3 #1,2iAVG PNP MAX HUD 

4 4 3 

0.313 to 6.57 0.202 to 1.11 0.171 to 1.11 

0.037 to 0.426 0.063 to 0.225 0.129 to 0.402 

-0.27 -0.10 -0.27 -0.21 -0.21 

0.27 0.09 0.22 0.19 0.18 

Hardwood Plywood Paneling (Veneer) 

ORNL-PND 1 #1,2h

ORNL-PND 1 #1,2iORNL-PND 3 #5 ORNL-PAN #1 AVG PND MAX HUD 

4 4 3 4 

0.152 to 0.355 

0.125 to 1.06 0.318 to 1.11 

0.136 to 0.949 

0.105 to 0.194 0.055 to 0.248 0.062 to 0.137 0.072 to 0.162 

-0.19 -0.11 -0.34 -0.45 -0.27 -0.27 

0.08 0.08 0.11 0.13 0.10 0.19

Hardwood Plywood NBS-P6-1 8 0.04 to 1.91 0.022 to 0.253 -0.12 0.05 
2-13 

Matthew’s Emissi

ER = m (con

Source Type Available Sourcesb

No. of Data 

Pointsc N/L Ranged

Measured 

Concentration 

Range (ppm) 

Slope (m/hr) Intcpt. (mg/

Paneling (Unknown) NBS-P8-1 

NBS-P10-1 NBS-P14-1 NBS-P17-1 NBS-P21-1 EPA-HWP AVG MAX HUD 

5 

11 

8 5 

0.03 to 1.14 0.04 to 4.86 0.18 to 5.20 0.08 to 7.36 

0.263 to 1.04 

0.027 to 0.239 0.045 to 0.370 0.014 to 0.098 0.020 to 0.224 0.066 to 0.106 

-0.12 -0.45 -0.67 -0.52 -0.22 -0.96 -0.44 -0.44 

0.04 0.30 0.08 0.15 0.03 0.16 0.12 0.24 

Softwood Plywood (PF Resin) 

ORNL-PFPLY #1 5 0.23 to 1.05 0.017 to 0.029 -0.61 0.03 

Hardboard (e.g., "Masonite") 

ORNL-HBD 1 7 -- 0.02 to 0.095 -1.39 0.17 

Kitchen Cabinets EPA-CABIN 3 0.390 to 2.29 0.023 to 0.075 -0.49 0.08 Interior Doors EPA-DOOR 3 0.585 to 2.44 0.022 to 0.061 -0.52 0.08 

a The data listed in this table are based on the results of emission rate tests performed at Oak Ridge National Laboratory (ORNL) for the Consumer Product 

the National Bureau of Standards (NBS) for EPA and CPSC, at Georgia Pacific Corp. (GP), and at Weyerhauser Co. by Dr. W. F. Lehmann. The data 

sources were obtained from or are based on the results reported in Progress Reports No. I, II, XIV, XV, XVI, and XVIII submitted to CPSC by ORNL; NB

CPSC; a 1987 NBS report to EPA (Grot et al. 1987); comments submitted by Georgia Pacific Corp. to EPA (Howlett 1988); Lehmann (1987) (also persoLehmann (Weyerhauser Co.) and G. Schweer (EPA) on June 30, 1987); and Koontz et al. 1996. The ORNL reports listed the Matthew’s model parameters for the individual sources and presented summary test data for the tested N/L conditions. The Min the table are as listed in the ORNL reports. Lehmann (1987) and Howlett (1988) reported HBF model parameters for the tested boards; Matthews mod

were calculated from the HBF model parameters. The NBS report listed Matthews model parameters. 

b Product codes are reported as listed in the ORNL Progress Reports (except for interior plywood, hardboard, and MDF-U) for the ORNL products. The 

(1987) are denoted by "LEH" followed by the letter code used in his report. The products reported in the NBS reports are denoted by "NBS" followed by t

products tested by Georgia Pacific Corp. are denoted by "GP" followed by a digit representing the order presented in the report’s tables. The products (Koontz et al. 1996) are denoted by "EPA." 

c Refers to the number of distinct N/L experiments conducted. d N/L is the ratio of the experimental air exchange rate (N), in air changes per hour, to the product loading in the chamber (L), in m2 of product surface ae ER is the emission rate of the product in units of mg of formaldehyde per m2 of product surface area per hour; the intercept has the same units. The slo
2-14 

f The emission rate parameters (i.e., slope and intercept values) for "average" source types (i.e., AVG) are the means of the slope and intercept values for th

type. The emission rate parameters for the "Maximum-HUD/ANSI certifiable" board types (i.e., MAX HUD/ANSI) were calculated using the "average" sl

chamber concentrations allowed by HUD/ANSI standards for pressed-wood products used in manufactured housing (i.e., 0.37 mg/m3 for particleboard/m

plywood paneling; see, for example, ANSI 1999 and ANSI 2002), at loading rates specified by HUD/ANSI and summarized in ASTM D 1333 (i.e., 0.43 0.95 m2/m3for hardwood plywood paneling, and 0.26 m2/m3for mdf), and at an air exchange rate of 0.5 air changes/hour.. 

g Correlation coefficient between calculated emission rate and measured chamber concentration. h Only decorative side exposed. i Both sides exposed. REFERENCES ANSI 1999. American National Standard: Particleboard. ANSI 208.1-1999, approved February 8, 1999. ANSI 2002. American National Standard: Particleboard. ANSI 208.2-2002, approved May 13, 2002. R.A Grot, S. Silberstein, and K. Ishiguro. 1985. Validation of Models for Predicting Formaldehyde Concentrations in Residences Due to Pressed Wood Prod

National Bureau of Standards. Report #NBSIR 85-3255. R.A. Grot, S. Nabinger, and S. Silberstein. 1987. Formaldehyde from Low-emitting Pressed Wood Products and the Effectiveness of Various Remedial Measu

Emissions. U.S. Dept. of Commerce, National Bureau of Standards. C.T. Howlett. 1988. Data provided to EPA on January 14, 1988, and on June 6, 1988 by C.T. Howlett (Georgia Pacific Corp.). 

M.D. Koontz, H.E. Rector, D.R. Cade, C.R. Wilkes, and L.L. Niang. 1996. Residential Indoor Air Formaldehyde Testing Program: Pilot Study. Report No. IE

Technologies, Inc. for the U.S. Environmental Protection Agency, Washington, DC, under EPA Contract No. 68-D3-0013. W.F. Lehmann. 1987. Effect of Ventilation and Loading Rates in Large Chamber Testing of Formaldehyde Emissions from Composite Panels. Forest Prod
2-15 

A “MAX HUD/ ANSI” source type is a hypothetical source that just meets the HUD/ANSI standard 

(e.g., 0.30 ppm for particleboard/mdf or 0.20 ppm for hardwood plywood paneling), based on a 

chamber test at the air exchange rate (0.5 ACH) and product loading rate (0.43 m2/m3for 

particleboard/decking, 0.95 m2/m3for hardwood plywood paneling, and 0.26 m2/m3for mdf) 

prescribed in ASTM E 1333-96 (ASTM 1996a). Using these rates along with the “average” slope 

value for the applicable Source Type, a one-chamber formaldehyde model was applied to solve for the 

B (intercept) value that would result in the source just meeting the applicable HUD standard. 

More recently, the California Air Resources Board (CARB) has put forth emission standards for 

composite wood products as part of an airborne toxic control measure (see Table 1 in CARB 2008). 

There is a phased implementation of the CARB standards, with a Phase 1 target date of July 2009 and 

Phase 2 (stricter standards) targeted for July 2012. Using the approach described above for the MAX 

HUD/ANSI source types, hypothetical sources just meeting the CARB Phase 1 and Phase 2 standards 

(termed MAX CARB P1 and MAX CARB P2, respectively) have been added to the model. Slope 

and intercept values so determined, for both the MAX HUD/ANSI and MAX CARB source types, 

are summarized in Table 2-3 together with the corresponding emission standards. 

Table 2-3. Slopes and Calculated Intercepts for Sources Just Meeting 

HUD/ANSI and CARB Phase 1/Phase 2 Emission Standards 

Emission Standard, ppm Calculated Intercept 

Source Type 

HUD/ANSI CARB P1 CARB P2 

Slope 

HUD/ANSI CARB P1 CARB P2 

Particleboard 

Underlayment 0.30 0.18 0.09 -0.83 0.74 0.44 0.22 

Mobile Home 

Decking 0.30 0.18 0.09 -1.06 0.82 0.49 0.24 

Industrial 

Particleboard 0.30 0.18 0.09 -0.7 0.69 0.41 0.20 

Medium Density 

Fiberboard 0.30 0.21 0.11 -1.06 1.10 0.77 0.40 

HP Paneling 

(print) 0.20 0.08 0.05 -0.51 0.26 0.10 0.06 

HP Paneling 

(paper) 0.20 0.08 0.05 -0.21 0.18 0.07 0.04 

HP Paneling 

(veneer) 0.20 0.08 0.05 -0.27 0.20 0.08 0.05 

HP Paneling 

(unknown) 0.20 0.08 0.05 -0.44 0.24 0.10 0.06 

The user can select any of the individual products available within each source type by first selecting a 

source type on the Sources - General Screen and then selecting a specific source from the available 

sources. When an available product is selected, the “Slope” and “B” values for that product will 

appear automatically on the screen. If the user wishes to input his/her own Slope and B values, then 

these values must be entered into the Slope and B fields.
2-16 

After selecting a product, the user must enter the area (in units of m2) of that product and the house 

zone in which the product is located (Zone 1 is selected by default). The area value is set to zero by 

default, which is equivalent to “turning off” the source. As noted previously, if the selected product is 

present in both house zones then two line entries are required – one entry for Zone 1 and one for 

Zone 2. The model allows the user to select up to 15 product/zone combinations. 

The Slope value is a mass transfer coefficient that reflects the “backpressure” effect of the indoor 

formaldehyde concentration on the emission rate. The B value is an intercept that reflects the emission 

rate when the indoor formaldehyde concentration is zero. The default Slope and B values can be 

changed either by selecting a different source type and available source or by directly editing the 

values. The source’s area can be changed only via editing. There should be a valid basis for editing the 

default Slope and B values, such as results of chamber emission tests. 

All inputs for emission rate modeling parameters are in metric units. The intercept, in mg/m2-hr, is 

multiplied by the source area (in m2) to give an emission rate, in mg/h. The slope, in units of m/h, is 

multiplied by the indoor concentration (mg/m3) and by the source area (m2), with resultant units of 

mg/h. The slope value usually is negative, to reflect the backpressure effect (i.e., the emission rate 

tends to decrease as the indoor formaldehyde concentration increases). A slope of zero indicates no 

backpressure effect. See Section 3.2 for further details. 

For the example shown below in Figure 2-6, four source types were selected: underlayment; interior 

doors; kitchen cabinets; and counter top (industrial particleboard). For the first three types, products 

from the EPA pilot study (EPA-PBU, EPA-DOOR and EPA-CABINET) were selected. For counter 

top, an “average” product (AVG INDUSTRIAL P) was selected. All products were assigned to Zone 

1 of the house. 

Figure 2-6. Sources - General Screen with Four Source Types Selected. 
2-17 

2.4 Sources - Cabinets

There are three ways to include cabinets as formaldehyde sources in this model: 

1) On the Sources - General Screen, select the “Kitchen Cabinet” choice under the “Source 

Types” drop-down list. This choice reflects the cabinet ensemble that was used in the EPA 

formaldehyde pilot study. 

2) On the Sources - Cabinet Screen (Figure 2-7), use the design assistance program to develop a 

cabinet ensemble. Any combination of low-, medium-, or high-emitting cabinets can be chosen 

for use as kitchen wall cabinets, kitchen base cabinets or vanity cabinets. A cabinet type is 

selected by first choosing one of the Available Cabinets at the top of the screen and then using 

the right arrow (-->) button to move that choice to the Selected Cabinets area; the choice can 

be deselected using the left-arrow button. The corresponding cabinet components and their 

characteristics, which can be edited, will be displayed in the Cabinet Component 

Characteristics area in the lower part of this screen. Specify the desired number of cabinets of 

each type and the location (zone) in which each type is placed. 

3) Design individual cabinets and their components on the Sources - Cabinets screen, by choosing 

“Custom Cabinet” in the drop-down list under Available Cabinets. Choose the number of 

custom cabinets, and then specify the individual components and their emission parameters and 

location in the Cabinet Component Characteristics area. 

Figure 2-7. Sources - Cabinets Screen Prior to Selection of Any Cabinets.

As with the Sources - General and Sinks screens, the emission modeling parameters include Slope, B 

and Area values. Given the multiple emitting components and the many available choices of slopes, B 

values and areas to represent each, there is greater uncertainty in the aggregate emission rate 

developed from this screen than when using the cabinet ensemble from the Sources - General Screen. 

The limitation when using the Sources - General Screen for cabinet representation is that only one 

type of cabinet ensemble is available. 
2-18 

The available cabinet types include kitchen wall cabinet, kitchen base cabinet, and vanity. The cabinet 

components include the top, side, bottom, back, front door/drawer, frame, shelves and, in the case of 

a base cabinet or vanity, toe kick. The user can choose any combination of low-, medium- or highemitting cabinets of each type, and can specify the number of each. Generally, in going from lower to 

higher emitters, the number of emitting components, the emission rate and/or the exposed surface 

area increases. The process described above – selecting a cabinet type from one of the Available 

Cabinets at the top of the screen and then moving that choice to the Selected Cabinets area – is 

continued until all cabinet types have been selected for the user’s desired ensemble (e.g., mediumemitting wall cabinet plus medium-emitting base cabinet plus high-emitting vanity). 

After an available cabinet has been selected (i.e., moved to the Selected Cabinets area), the number of 

cabinets associated with it can be changed and the characteristics of its components can be 

viewed/changed. By default, one cabinet is specified for each type. The default value can be changed 

by highlighting one of the selected cabinets and then entering the desired number in the box labeled 

“Change # Cabinets for Highlighted Selected Cabinet Below.” This process is continued until the 

desired number of cabinets of each type has been specified. 

The program displays one cabinet type at a time but keeps track of inputs for all types. The 

component characteristics for a chosen cabinet type can be viewed by clicking on that type under 

Selected Cabinets. Figure 2-8 shows the default components and associated Slope, B and Area values 

when a medium-emitting kitchen wall cabinet has been selected; Figure 2-9 shows the same 

information for a medium-emitting kitchen base cabinet. 

Note that not all components shown are emitters, as some have blank values for Slope, B and Area. 

For example, of the seven wall-cabinet components shown in Figure 2-8, only three – shelves, door 

and back – are emitters. The applicable components vary with the type of cabinet selected and its 

general emission characteristics (i.e., low, medium or high emitting). If custom cabinet is selected, 

then no components are displayed because a cabinet is being “built from scratch” in this case. 

The Slope and B values for any cabinet component can be modified either by selecting a different 

combination from the Source Types and Available Sources or by directly editing these values. There 

should be a valid basis for editing Slope or B values, such as results of chamber emission tests. The 

value for Area can be changed only through editing. 

As with the Sources-General screen, all inputs for cabinet modeling parameters are in metric units. 

The intercept, in units of mg/m2 hr, is multiplied by the source area (m2) to give an emission rate, in 

mg/h. The slope, in units of m/h, is multiplied by the indoor concentration (mg/m3) and by the source 

area (m2), with resultant units of mg/h. The slope value usually is negative, to reflect the backpressure 

effect (i.e., the emission rate decreases as the indoor formaldehyde concentration increases). The 

slope value can be set to zero to reflect no backpressure effect. 
2-19 

Figure 2-8. Sources - Cabinets Screen with Medium-emitting Wall Cabinet Selected. 

Figure 2-9. Sources - Cabinets Screen with Medium-emitting Base Cabinet Selected. 
2-20 

Table 2-4 lists the emitting components and associated default choices/values for the three available 

types of kitchen wall cabinets – low-emitting, medium-emitting and high-emitting. The low-emitting 

cabinet has two emitting components – shelves and back – with a collective area of 0.66 m2. The 

medium-emitting cabinet has three emitting components with a collective area (1.82 m2) that is nearly 

three times that of low-emitting cabinets. The high-emitting cabinet has seven emitting components 

with a collective area (3.52 m2) that is about twice that of medium-emitting cabinets. 

Table 2-5 provides the same information for three types of kitchen base cabinets. The low-emitting 

cabinet has four emitting components with a collective area of 1.45 m2. The medium emitter has five 

emitting components with a collective area (2.81 m2) that is nearly twice that of low-emitting 

cabinets. The high emitter has nine emitting components with a collective area (6.38 m2) that is more 

than twice that of medium-emitting cabinets. 

Table 2-6 provides information for three types of vanities. The low-emitting vanity has three emitting 

components with a collective area of 0.96 m2. The medium emitter has four emitting components with 

a collective area (2.12 m2) that is a little more than twice that of low-emitting vanities. The high 

emitter has seven emitting components with a collective area (4.86 m2) that is more than double that 

of medium-emitting vanities. 
2-21 

Table 2-4. Default Values for Emitting Components of Kitchen Wall Cabinets 

Component Source Type Source Slope (m/hr) B (mg/m2-hr) Area (m2) 

Low-emitting Ensemble 

Shelves industrial 

particleboard avg industrial -0.7 0.3 0.023 

Back hardboard 

(pf resin) 

ornlhardboard -1.39 0.17 0.639 

Total Area 0.66 

Medium-emitting Ensemble 

Shelves industrial 

particleboard 

avg industrial 

p 

-0.7 0.3 0.023 

Door hp paneling avg veneer 

panel -0.27 0.09 1.161 

Back industrial 

particleboard avg industrial -0.7 0.3 0.639 

Total Area 1.82 

High-emitting Ensemble 

Side industrial 

particleboard 

max hud 

industrial -0.7 0.56 0.465 

Bottom industrial 

particleboard 

max hud 

industrial -0.7 0.56 0.465 

Top industrial 

particleboard 

max hud 

industrial -0.7 0.56 0.465 

Shelves industrial 

particleboard 

max hud 

industrial -0.7 0.56 0.023 

Frame alkyd urea 

coated wood avg epa-rti 0.0 0.45 0.299 

Door alkyd urea 

coated wood avg epa-rti 0.0 0.45 1.161 

Back med density 

fiberboard avg mdf -1.28 0.95 0.639 

Total Area 3.52 
2-22 

Table 2-5. Default Values for Emitting Components of Kitchen Base Cabinets 

Component Source Type Source Slope (m/hr) B (mg/m2-hr) Area (m2) 

Low-emitting Ensemble 

Shelves industrial 

particleboard avg industrial -0.7 0.3 0.023 

Back hardboard 

(pf resin) 

ornlhardboard -1.39 0.17 0.74 

Toe Kick industrial 

particleboard avg industrial -0.7 0.3 0.188 

Countertop industrial 

particleboard avg industrial -0.7 0.3 0.503 

Total Area 1.45 

Medium-emitting Ensemble 

Shelves industrial 

particleboard 

avg industrial 

p 

-0.7 0.3 0.023 

Door and 

Drawer hp paneling avg veneer panel -0.27 0.09 1.355 

Back industrial 

particleboard avg industrial -0.7 0.3 0.74 

Toe Kick industrial 

particleboard avg industrial -0.7 0.3 0.188 

Countertop industrial 

particleboard avg industrial -0.7 0.3 0.503 

Total Area 2.81 

High-emitting Ensemble 

Side industrial 

particleboard 

max hud 

industrial -0.7 0.56 1.084 

Bottom industrial 

particleboard 

max hud 

industrial -0.7 0.56 0.929 

Shelves industrial 

particleboard 

max hud 

industrial -0.7 0.56 0.023 

Frame alkyd urea 

coated wood avg epa-rti 0.0 0.45 0.325 

Door and 

Drawer Front

alkyd urea 

coated wood avg epa-rti 0.0 0.45 1.355 

Back med density 

fiberboard avg mdf -1.28 0.95 0.74 

Toe Kick industrial 

particleboard 

max hud 

industrial -0.7 0.56 0.188 

Drawer Sides 

and Back 

industrial 

particleboard 

max hud 

industrial -0.7 0.56 1.23 

Countertop industrial 

particleboard 

max hud 

industrial -0.7 0.56 0.503 

Total Area 6.38 

Table 2-6. Default Values for Emitting Components of Vanities 
2-23 

Component Source Type Source Slope (m/hr) B (mg/m2-hr) Area (m2) 

Low-emitting Ensemble 

Back hardboard 

(pf resin) 

ornlhardboard -1.39 0.17 0.639 

Toe Kick industrial 

particleboard avg industrial -0.7 0.3 0.188 

Countertop industrial 

particleboard avg industrial -0.7 0.3 0.132 

Total Area 0.96 

Medium-emitting Ensemble 

Door Front hp paneling avg veneer 

panel -0.27 0.09 1.161 

Back industrial 

particleboard avg industrial -0.7 0.3 0.639 

Toe Kick industrial 

particleboard avg industrial -0.7 0.3 0.188 

Countertop industrial 

particleboard avg industrial -0.7 0.3 0.132 

Total Area 2.12 

High-emitting Ensemble 

Sides industrial 

particleboard 

max hud 

industrial -0.7 0.56 1.626 

Bottom industrial 

particleboard 

max hud 

industrial -0.7 0.56 0.813 

Frame alkyd urea 

coated wood avg epa-rti 0.0 0.45 0.299 

Door Front alkyd urea 

coated wood avg epa-rti 0.0 0.45 1.161 

Back med density 

fiberboard avg mdf -1.28 0.95 0.639 

Toe Kick industrial 

particleboard 

max hud 

industrial -0.7 0.56 0.188 

Countertop industrial 

particleboard 

max hud 

industrial -0.7 0.56 0.132 

Total Area 4.86 
2-24 

2.5 Sinks Screen

The purpose of this screen (shown in Figure 2-10 with initial values, discussed below) is to enable the 

user to specify the types and amounts of indoor sinks present in the house and the house zone in 

which each chosen sink is located (Zone 1 is selected by default). Although indoor sinks are 

represented in the model using the same parameters (i.e., Slope and B values) as used for sources, 

they are included on a separate input screen for clarity. 

As with the Sources - General Screen, one can either select an available sink from a menu of sink 

types for which modeling parameters have been developed or enter a sink with one's own modeling 

parameters, by editing the parameter values for one of the choices that are provided. Once a sink has 

been selected, it can be deselected or “turned off” by either of two methods: (1) choosing “None 

Selected” in the Sink Type list, or (2) entering a value of zero for the Area. 

Each line or row on the screen refers to a specific type of sink in a specific zone. Consequently, to 

specify a sink that is present in both zones of a house, two line entries are required – one entry for 

Zone 1 and one for Zone 2. 

Figure 2-10. Sinks Screen with Initial Values. 

As described in greater detail in Section 3.4, the treatment of indoor sinks in the calculation routine is 

accomplished by recognizing that the “emission” term has two components. The first (Slope, usually 

with a negative value) is in the form of a first-order sink representation, and therefore can be used to 

represent absorption by the sink. The second (B, or intercept) is in the form of a constant emission 

rate, and therefore can be used to represent re-emissions from the sink. The slope has units of m/h; it 

is multiplied by the indoor concentration (mg/m3) and by the sink area (m2), with resultant units of 

mg/h. The intercept, in units of mg/m2-hr, is multiplied by the sink area (m2) to give a re-emission 

rate, also in mg/h. 

Default parameters are provided with the model for two types of indoor sinks – carpeting and painted 
2-25 

wallboard. For each type of sink two sets of parameter values are provided with the model, one 

labeled “initial” and one labeled “equilibrium.” Initial values reflect a sink’s behavior at the time when 

a house is first loaded with formaldehyde sources. At this stage, the sink acts as a net “absorber” and 

will accumulate formaldehyde mass much more quickly than it releases (re-emits) mass. Equilibrium 

values reflect a sink’s behavior at some later time, after it has accumulated significant mass and is 

nearing or has reached a state of equilibrium where its re-emission rate is similar to its absorption rate. 

It may still act as a net absorber, but its net absorption rate is considerably lower than during the 

initial stage. 

Depending in part on the prevailing formaldehyde concentration, indoor sinks may approach a state of 

equilibrium in as little as 30 days after a house has been loaded with sources. Because this model is 

designed to estimate the steady-state formaldehyde concentration that would occur around this time, 

it is suggested that equilibrium rather than initial values be used. If there is uncertainty regarding how 

to apply indoor sinks in the model, then it is suggested that sinks be ignored (i.e., left out) as a 

conservative modeling approach. 

The default initial and equilibrium values assigned to indoor sinks currently available in the model are 

based primarily on an analysis of small-chamber test data, as described more fully in Section 3.4. In 

brief, the analysis indicates that the B value (i.e., the re-emission rate) is dependent on the 

formaldehyde concentration in air, increasing roughly in proportion to the concentration. The default 

B values shown in Figure 2-11 for an equilibrium case – higher than those for the default initial case in 

Figure 2-10 – are thought to be appropriate for an indoor-air concentration on the order of 40 ppb.

Figure 2-11. Sinks Screen with Equilibrium Values. 

The default B value for an initial condition for carpeting (0.003 mg/m2-h), intended to represent a 
2-26 

point in time before the sink has accumulated any significant mass, is based on small-chamber 

emission tests using carpeting and padding that had not yet been placed in an indoor setting with any 

significant formaldehyde sources. The default B value for an initial condition for wallboard (0.004 

mg/m2-h) is based on the formaldehyde content by weight in paint that was applied to the wallboard in 

the conventional house for the USEPA formaldehyde pilot study. 

For the equilibrium condition, results from small-chamber tests for painted wallboard that were 

conducted at the time of the EPA pilot study suggest a B value of about 0.0375 mg/m2-h per 10 ppb 

indoor formaldehyde concentration (e.g., 0.0375 mg/m2-h at 10 ppb, 0.075 at 20 ppb, and 0.1125 at 

30 ppb). Results for carpeting and padding suggest a B value of about 0.016 mg/m2-h per 10 ppb 

indoor formaldehyde concentration. As an aid to choosing an appropriate B value for a sink, a 

preliminary model run can be made to estimate the concentrations that would prevail with the sources 

of choice activated while “turning off” all sinks. As a check on the reasonableness of assumed 

modeling parameters for indoor sinks, modeled concentrations when including the sinks should be 

somewhat lower than when excluding them. See Section 5.3 for an example application, where the 

addition of indoor sinks lowered the modeled concentrations by about 10 percent. 
2-27 

2.6 Exposures Screen

This screen (Figure 2-12) accommodates two population groups or exposure scenarios – adults (left 

side) and children (right side). The two scenarios require the same types of inputs, except that items 

related to an individual’s lifetime do not apply to the child scenario. For children, an age group needs 

to be chosen as a basis for displaying default values for the exposure factors. 

The upper part of the screen has exposure factors such as the age of formaldehyde sources (pressed 

wood products) at the start of the exposure period, the length of the exposure period, and average 

body weight. The lower part of the screen has exposure factors related to activity patterns, including 

time spent in/out of the house and average inhalation rates at different locations. 

Figure 2-12. Exposures Screen with Default Selections. 

The age of sources at the start of the exposure period (i.e., the time when an individual moves into 

the modeled house) affects the initial indoor formaldehyde concentrations to which the individual is 

exposed. In general, the lower the age of sources the higher the indoor concentrations at the start of 

the exposure period. Entering a source age of zero will cause the model to begin exposure 

calculations with the initial indoor concentrations shown on the results page, which are intended to 

reflect an equilibrium condition shortly (typically within 30 days) after a house has been loaded with 

pressed wood products. A source age of zero also would apply for the case of exposures following a 

major remodeling effort. For the purpose of model calculations, all sources are assumed to be the 

same age; the model does not allow different ages to be specified for different sources. 

The length of the exposure period should reflect the number of years that a person would reside in the 

modeled house. Normally the exposure period would be relatively short (e.g., 5-10 years or less) for 

children. 
2-28 

The model will begin calculations with the specified age of sources and continue the calculations for 

the specified length of the exposure period. For example, if 5 years is entered for the age of sources 

and 10 years for the length of the exposure period, then the model will begin calculations with the 

sources aged 5 years and will continue the calculations until the sources have aged 15 years. 

Default values for years in lifetime and average body weight during one’s lifetime (both applicable 

only to the adult scenario) are taken from the Exposure Factors Handbook. Average body weight 

during the exposure period applies to both adults and children. For children there are five choices for 

age range, with different default body weights: Youth (13-19 years); Child (6-12 years); Small Child 

(3-5 years); Infant 1-2 years; and Infant <1 year. 

In the case of children, the default body weight reflects the child’s weight at the start of the exposure 

period. Depending on the length of exposure period that is chosen, the body weight may need to be 

adjusted upward from the default value to reflect the child’s average weight during the exposure 

period. Suppose, for example, that an infant (age 1-2 years) is chosen with a body weight of 12.3 kg 

and an exposure period of 5 years. According to the Exposure Factors Handbook, the average body 

weight for a child of age 6-7 years (i.e., 5 years later) is close to 24 kg. The average body weight 

during the exposure period, then, would be on the order of 18 kg.

One of the exposure calculations is the percent of time an individual is exposed to a concentration 

above a formaldehyde concentration of concern (COC). The model automatically calculates the 

percent of time above 0.01 ppm. The COC input here allows the user to select a second level of 

concern for the calculations. Different COC values are allowed for the adult and child scenarios. 

The formaldehyde concentration out of the house is used in exposure calculations for times when the 

individual is not in Zone 1 or Zone 2 within the house. This concentration is an average value 

representing all time away from the house, including time spent outdoors, commuting, at work or 

school, in stores, etc. A concentration of zero should be selected if the exposure calculations are 

intended to reflect only the exposures incurred while in the house. As with the formaldehyde COC, 

different values can be chosen for the adult and child scenarios for this factor. 

Separate inputs are required for weekdays and weekend days for time spent in Zones 1 and 2 of the 

house. The two zones can be used, for example to distinguish sleeping areas from the remainder of 

the house or to distinguish finished and unfinished areas. The default values distinguish time spent 

upstairs (Zone 1) vs. in the basement (Zone 2). By default, all time in the house is assigned to Zone 1 

(where the formaldehyde sources are located by default) as a conservative approach. Time spent out 

of the house is “grayed out” because it is automatically calculated by the model. If a one-zone house 

is selected (on the House Screen), then the hours for Zone 2 automatically will be set to zero and 

grayed out. Similarly, separate inputs are required for breathing rates while in each zone and out of 

the house. Default values for both time spent and breathing rate, taken from the Exposure Factors 

Handbook, vary with the child age range that is selected.
2-29 

2.7 Results Screen

This screen “echoes back” user inputs from the House Screen for the title of the model run and 

associated notes, and provides modeled indoor formaldehyde concentrations together with exposure 

estimates. The example screen shot in Figure 2-13, showing the upper portion of the Results Screen 

that includes modeled concentrations, corresponds to the default case where the user has made no 

changes to any of the input screens. In the default case all results are zero, both for concentrations 

and for exposures, because no sources have been selected, the background concentration has been set 

to zero (on the House Screen), and the concentration encountered when outside the house also has 

been set to zero (on the Exposures Screen). 

If the air flows entered on the House Screen are not balanced, then a note to this effect will appear at 

the top of the screen, to the right of the screen title. A button to the right near the top of the screen, 

labeled “SAVE RESULTS TO MS EXCEL,” can be used to save a summary of inputs and results for 

the current model run. The summary is saved as a comma-delimited file (i.e., with an extension of 

.csv) that can be opened with Microsoft Excel. On some computers, the file may be saved with an 

extension of .xls; in such cases, it is necessary to rename the extension to .csv to view the file. 

Figure 2-13. Results Screen (Concentrations) for Default Case. 

Concentration results are listed for both Zone 1 and Zone 2 (or just Zone 1 if the user has specified a 

one-zone house) under two sets of temperature/humidity conditions – base (left side, fixed at 23 ° C 

and 50 % RH) and user-specified (right side, as entered on the House Screen and listed at the top 

right of the concentration results). Section 3.7 describes the procedures and gives the equations that 

are used to adjust concentrations under base conditions to user-specified conditions. Concentrations 

are reported both in volume/volume (ppm) and mass/volume (mg/m3) units. 
2-30 

The initial concentrations reflect the condition shortly after a house has been loaded with pressed 

wood products. As described in Section 3.5, estimates of initial indoor concentrations due to sources 

and sinks are decayed exponentially by the model, in accordance with a user-specified emissions half 

life (default of 2.92 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 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 (under userspecified conditions) to drop below 0.01 ppm and below a user-specified concentration (an input on 

the House Screen). The equation used for this calculation is given in Section 3.5. 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 model reports 0 months as the time to decay. 

As described in 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. Similarly, indoor 

sinks typically do not absorb and release formaldehyde at a constant rate. When formaldehyde sources 

are first introduced, the sinks essentially are formaldehyde-free and, thus, act as net “absorbers.” At 

some later point in time, each sink eventually reaches a transient “steady state” whereby the mass 

absorbed and the mass released are virtually identical. Thereafter, as the indoor sources continue to 

decay in strength, the sink may act as a net “emitter.” 

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. Steady-state (initial) concentrations estimated by the model 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 pressed wood products. 

Exposure estimates (Figure 2-14) are provided for both adult (left side) and child (right side) 

exposure scenarios, based on modeled indoor concentrations under user-specified temperature and 

humidity conditions. The first two outputs (House Age at Start and Length of Exposure Period) are 

simply carried over from the user’s inputs on the Exposure Screen. The remaining outputs are 

different types of exposure metrics, including average daily dose and average daily concentration as 

well as the percent of time during which an individual is exposed to a formaldehyde concentration at 

or above a level of concern (e.g., 0.01 ppm). The exposure estimates shown in the figure all are equal 

to zero because initial indoor concentrations are equal to zero for the default case. 

Lifetime Average Daily Dose (LADD) and Lifetime Average Daily Concentration (LADC) apply only 

to adults, whereas Average Daily Dose (ADD) and Average Daily Concentration (ADC) apply to 

both adults and children. The LADD/ADD calculations share the same numerator – cumulative dose 
2-31 

over the number of years living in the house (input on the Exposure Screen). The difference is in the 

denominator – for LADD the denominator is the number of years in the individual’s lifetime (N/A for 

a child), whereas for ADD the denominator is the number of years living in the house. Similarly, the 

LADC and ADC share the same numerator but have different denominators. Further details on 

exposure calculations, including equations, are provided in Section 3.8. 

Figure 2-14. Results Screen (Exposures) for Default Case. 

The percent of time during which an individual (either adult or child) is exposed to a formaldehyde 

concentration at or above 0.01 ppm is reported along with the percent of time at or above one other 

concentration of concern (COC). The second COC is a user-specified value that is input on the 

Exposures Screen. 

The dose, concentration and percent-of-time calculations 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 the out-of-house concentration is input by the user on the Exposure Screen and is 

assumed to be constant over time. 

The example screen in Figure 2-15 shows concentration results after some sources and sinks have 

been added. The inputs chosen for this example correspond to a “medium” loading that was used in 

the Conventional 1 house for the USEPA pilot study. The sources (see Figure 2-6) are underlayment 

(area of 46 m2), interior doors (35 m2), cabinets (59 m2) and countertop (4 m2, input as industrial 

particleboard). The sinks (see Figure 2-11) are carpet and padding (94 m2) and painted wallboard 

(420 m2). The initial concentrations under baseline conditions – 23 ° C and 50 % RH – are 0.051 

mg/m3 (0.42 ppm) in Zone 1 and 0.044 mg/m3 (0.35 ppm) in Zone 2. Concentrations 36 months later 

– slightly longer than the 2.92-year default half life – are just under half the initial values. Indoor 

concentrations of this magnitude would take 72 months (i.e., 6 years) to decline to 0.01 ppm under 

the assumed half life of 2.92 years. 
2-32 

Figure 2-15. Concentration Results after Addition of Sources and Sinks. 

The exposure estimates for the same run (Figure 2-16) are appreciably higher than for the default 

case, due to the addition of sources. Default values were used on the Exposure Screen for this run. 

The higher values for exposure metrics for the child scenario, as compared to the adult, are due to the 

shorter exposure period; that is, with a shorter exposure period the child would encounter higher 

concentrations on average because indoor HCHO concentrations decline with the passage of time. 

Figure 2-16. Exposure Results after Addition of Sources and Sinks.
3-1 

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. 

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 default decay rate 

that is based on historical data for formaldehyde levels in manufactured homes of various ages. 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 house selected by the model user (see Section 

2.2). 

A second adaptation of the model was to explicitly address indoor sinks. Although the model, as 

initially formulated, always had the capability to represent indoor sinks, this facet of the model has been 

incorporated more formally in the user interface (see Section 2.5), with inclusion of default model 

parameters for selected types of potential sinks (carpeting and painted wallboard). The treatment of 

sinks and the basis for estimation of sink parameters are described in Section 3.4.

Section 3.5 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 0.01 ppm. Section 3.6 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 3.7 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 a new set of user-selected temperature and humidity conditions. Section 3.8 describes the 

exposure calculations used in the model.
3-2 

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 background concentration in the indoor volume, and the formaldehyde 

concentration, in turn, is dependent on these emission rates. 

The principle of conservation of mass in an indoor environment is fundamental to the formaldehyde 

modeling process. Simply stated, this principle means that the flows of formaldehyde mass into and out 

of a fixed volume must be equal and, further, 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: 

∑ ∑ ∑ ∑ = =

≠ ≠

= − + − + −

in Zone i

num sinks

p

i p

in Zone i

num sources

k

i k

j i

j

ij i

j i

j

i B i i ji j

i

i Q C Q C Q C Q C E S

dt

dC

V

1

,

1

0 0 ,

 (Eqn. 3-1) 

where: 

V = indoor volume (m3) 

C = formaldehyde concentration (mg/m3) 

t = time (hr) 

CB = background concentration, which is defined as the outdoor concentration plus 

the contribution from indoor sources other than pressed-wood products 

(assumed constant) 

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 release site k in zone i (mg/hr) 

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

Model results are presented in both volume/volume units (ppm) and mass/volume units (mg/m3). 

Conversion between these unit conventions is performed using the ideal gas law, assuming constant 

pressure (1 atmosphere) and the user-specified temperature. 
3-3 

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

A model developed in the 1980s by Matthews and his colleagues was designed to estimate the steadystate formaldehyde concentration resulting from emission sources in a single indoor compartment. The 

following discussion is in large part excerpted from Matthews et al. (1983a). The underlying model 

theory and its derivation are described in Matthews et al. (1983a, 1983b). 

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 = steady-state formaldehyde concentration outside the 

compartment (mg/m3) 

CH2OER = the emission rate of a formaldehyde source inside the 

compartment (mg/h) 

F = the fraction of air coming into the compartment that mixes 

within the volume (i.e., the mixing factor) 

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

VOL = the volume of the compartment (m3). 

The product of F and ACH is termed by Matthews et al. as PEX, the effective pollutant exchange rate 

(in units of hr-1). With this notation, Equation 3-2 becomes: 

[CH2O]SS = [CH2O]out + CH2OER/(PEX * VOL) (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 of the source in the compartment. The equivalent of Equation 3-3 for 

an area-dependent source is: 

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

with CH2OER′ in units of mg/m2

-hr and area in m2. 

Fick’s Law describes the bulk-vapor interphase at the surface of a pressed-wood emission source. If 

one assumes that the mass transport coefficient and the formaldehyde concentration in the bulk phase 
3-4 

are independent of the formaldehyde concentration in the vapor phase, then the emission rate of a solid 

source is: 

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). 

If the vapor-phase concentration, [CH2O]V, is assumed to equal [CH2O]SS at steady state, then 

Equation 3-5 can be substituted into Equation 3-4 to obtain the following equation: 

[ ]

[ ]

D

CH O

PEX VOL

b Area

CH O

out

SS

2

2

*

*

+

= (Eqn. 3-6) 

where: 

PEX VOL

m Area D

*

*

= 1+

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

[CH2O]SS = [CH2O]out + Σ(CH2OER′k* Areak) / (PEX * VOL) (Eqn. 3-7)

where the subscript k refers to the k

th source. By extension, Equation 3-6 then becomes: 

[ ]

( )

[ ]

D

CH O

PEX VOL

b Area

CH O

out

k

k k

SS

2

2

*

*

+

=

∑

(Eqn. 3-8)

where: 

( )

PEX VOL

m Area

D

k

k k

*

*

1

∑

= +
3-5 

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, given 

that sinks can be represented in the model using source terminology (see Section 3.4), is: 

∑=

= + − − +

in Zone i

num sources

k

i B ji j i i ij i i k

i

i Q C Q C Q C Q C S

dt

dC

V

1

0 0 ,

 (Eqn. 3-9) 

where: 

Vi = volume of compartment i (m3) 

Ci = concentration in compartment i (mg/m3) 

t = time (hrs) 

CB = background concentration, which is defined as the outdoor concentration plus 

the contribution from indoor sources other than pressed-wood products 

(assumed constant) 

i,j = indoor compartments 

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

ΣSi,k = sum of k sources in compartment i (mg/hr) 

Considering the source equation as described in Equation 3-5 for multiple pressed-wood products in 

either zone, the sum of formaldehyde sources (and sinks) in each compartment can be expressed as: 

∑ =∑ = ∑(− + )

k k

i k i k i i k i k

k

Si k CH OERi k Areai k m Area C b Area , , , , ,

'

, 2 ,

* * * * (Eqn. 3-10) 

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 3-9 and 3-10 for each compartment, and solving simultaneously 

for the steady-state condition (see Appendix A), the following equations are obtained: 

( ) ( )

( ) 10 20 10 21 10 2 12 20 12 2 1 20 1 21 1 2

01 20 01 21 01 2 21 02 20 21 2 1 21 2

,1 Q Q Q Q Q z Q Q Q z z Q z Q z z

Q Q Q Q Q z Q Q C Q Q z y Q y

C

B

SS + + + + + + +

+ + + + + + +

= (Eqn. 3-11) 

( ) ( )

( ) 20 10 20 12 20 1 21 10 21 1 2 10 2 12 2 1

02 10 02 12 02 1 12 01 10 12 1 2 12 1

,2 Q Q Q Q Q z Q Q Q z z Q z Q z z

Q Q Q Q Q z Q Q C Q Q z y Q y

C

B

SS + + + + + + +

+ + + + + + +

= (Eqn. 3-12) 

where: 
3-6 

SS = indicates the steady-state solution 

z1 = k

in Zone

num sources

k

∑mk Area

=

1

1

 for the k sources located in compartment 1 

y1 = k

in Zone

num sources

k

∑bk Area

=

1

1

 for the k sources located in compartment 1. 

z2 = k

in Zone

num sources

k

∑mk Area

=

2

1

 for the k sources located in compartment 2 

y2 = k

in Zone

num sources

k

∑bk Area

=

2

1

 for the k sources located in compartment 2. 

3.4 Treatment of Indoor Sinks

The treatment of indoor sinks in the calculation module is 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 can 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. 

The complex relationships described above are not fully captured by the sink representation that is used 

in the model. On the other hand, the sink representation is believed to be indicative of a sink’s behavior 

around the time, usually within 30 days after installation of source and sink materials in a residence, 

when the time-varying indoor concentration has reached its maximum value and is changing at a 

relatively slow rate. 

Default parameter values for sinks in the model have been derived from an analysis of data collected for 

conventional house 1. There were two major types of potential sinks in this house – carpeting and 

painted wallboard. As noted above, sinks can be represented in the model using the same parameters as 

used for sources. The Langmuir isotherm model described in the formaldehyde pilot study report 

(Koontz et al. 1996) was used to develop default parameter estimates for sinks. With this type of 
3-7 

model, the mass-balance equation for the change in mass residing in a sink over time is as follows: 

k C k M

dt

dM = a − d

(Eqn. 3-13) 

where: 

M = mass per unit area of sink, mg/m2

ka = adsorption rate constant, m/h 

C = indoor formaldehyde concentration, mg/m3 

kd = desorption rate constant, h-1. 

Estimates for the adsorption and desorption rates were developed by fitting air-concentration data from 

several small-chamber tests to the corresponding Langmuir isotherm mass-balance equation for the 

chamber. The adsorption rate for the Langmuir isotherm model has units of m/h and, thus, is directly 

compatible with the slope term for sources or sinks in the Matthews model. The desorption rate 

constant has units of inverse hours; when this rate is multiplied by the mass per unit area in the sink 

(mg/m2), as in the above equation, the resultant product has units of mg/m2-h, consistent with those for 

the intercept term in the Matthews model. 

In the presence of indoor formaldehyde sources, the accumulated mass in the sink increases over time 

but eventually will reach a transient “steady-state” value. A linear relationship between the maximum 

accumulated mass in the sink and the (assumed constant) indoor-air concentration was found, by 

running the Langmuir model to steady state for different indoor-air concentrations. This procedure was

used to determine appropriate values for the intercept terms for wallboard and carpeting at different 

indoor-air concentrations. 

For painted wallboard, estimation of parameters for the Langmuir model suggested that an appropriate 

value for the slope was -3.0 m/h and that an appropriate value for the intercept, under an assumed 

equilibrium condition, was about 0.0375 mg/m2-h per 10 ppb indoor-air formaldehyde concentration

(i.e., 0.0375 mg/m2-h at 10 ppb, 0.075 at 20 ppb, 0.1125 at 30 ppb, 0.15 at 40 ppb, etc.). For 

carpeting, the Langmuir model estimates indicated that an appropriate value for the slope was -1.3 m/h

and that an appropriate intercept value was about 0.016 mg/m2-h per 10 ppb of indoor concentration. 

The default intercept value for an initial condition for carpeting (0.003 mg/m2-h), intended to represent 

a point in time before the sink has accumulated any significant formaldehyde mass, was based on smallchamber emission tests using carpeting and padding that had not yet been placed in an indoor setting 

with any significant formaldehyde sources. The default intercept value for an initial condition for paint 

(0.004 mg/m2-h) was based on the reported formaldehyde content by weight in the paint. 
3-8 

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: 

( )

-kt

t B i B C = C + C − C e (Eqn. 3-14) 

where: 

Ct = formaldehyde concentration indoors (ppm) at time t (in years) 

CB = background concentration (ppm), which is defined as the outdoor 

concentration plus the contribution from indoor sources other than 

pressed-wood products (assumed constant) 

Ci = initial concentration indoors (ppm) 

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

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: 

k

C C

C C

t

t B

i B













−

−

=

ln

(Eqn. 3-15) 

Or, solving for k results in the following equation: 

t

C C

C C

k

t B

i B













−

−

=

ln

(Eqn. 3-16) 

Neglecting for the moment the background contribution to the indoor concentration (i.e., assuming that

the background concentration is zero), Equation 3-16 reduces to: 

t

C

C

k

t

i













=

ln

(Eqn. 3-17) 

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

= 5.0

i

T

C

C

(Eqn. 3-18) 

where: 

T = half-life (in years). 
3-9 

By substitution, Equation 3-17 becomes: 

( )

T

k

ln 2

= (Eqn. 3-19) 

Substituting the default half life of 2.92 years (see Section 3.6) for T in the above equation gives: 

k = 0.237 years-1

Indoor concentrations at later points in time (i.e., subsequent to initial, steady-state values for each 

zone) are calculated by the 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 2.92 years, Equation 3-14 would apply: 

C(0.25 yr) = CB + (Ci - CB) e-0.237*0.25 (Eqn. 3-20) 

If Ci were 0.05 ppm and the outdoor concentration were zero, for example, then the indoor 

concentration 3 months later would be 0.047 ppm. Small outdoor concentrations, which typically 

would be the case, have a minor impact on the relationship. For example, with an outdoor 

concentration of 0.001 ppm, the indoor concentration would be 0.051 ppm initially and 0.048 ppm 

after 3 months. 

Given an initial concentration greater than 0.01 ppm and assuming an outdoor concentration of zero, 

the time required to reach 0.01 ppm can be determined from the first-order exponential process using 

Equation 3-15 as follows: 

t = ln (Ci / 0.01) / k (Eqn. 3-21) 

Continuing with the above example where k is 0.237 years-1 and Ci is 0.05 ppm, by substitution into 

equation 3-15, we get: 

t = ln (0.05 / 0.01) / 0.237 (Eqn. 3-22) 

for which the value of t is 6.79 years, or 81.5 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 3-15 is used to account for the outdoor 

contribution while decaying only the component due to sources and sinks: 

k

C

C C

t

B

i B













−

−

=

01.0

ln

(Eqn. 3-23) 

The result from Equation 3-23 is multiplied by 12 and reported in months. If the highest initial indoor 

concentration is lower than 0.01 ppm, then zero months is reported as the time required for the indoor

concentration to decay to 0.01 ppm. The same equation is used to calculate the time required for the 

highest indoor concentration to decay to a user-specified concentration of concern (COC). 
3-10 

3.6 Default Value for Half Life

Ideally, an appropriate half-life value for representing the long-term decay of formaldehyde 

concentrations in residences would be determined by taking measurements in a house soon after it was 

loaded with formaldehyde sources and sinks, and at periodic points in time over the next several years. 

Continuing with this ideal situation, the sources and sinks would not change throughout the 

measurement period, and factors such as indoor temperature and humidity, as well as the indooroutdoor 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 then would be analyzed to fit a nonlinear (e.g., exponential) decay function to the timevarying 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 a formaldehyde-bearing material, or for some ensemble of such materials. 

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 wellcharacterized 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 timerelated rate of decline depends on the formaldehyde concentration, and the rate of decline is more rapid 

for a single material, because other materials are not present to increase the formaldehyde 

concentration and thereby retard its rate of formaldehyde release. Limited tests of 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 

formaldehyde concentration half life 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, 
3-11 

then, will introduce new sources, thereby raising the formaldehyde concentration relative to the nochange 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 (1988) of a cross-sectional data set for 396 manufactured homes 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 Versar (1988) 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. (1985), 

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. 

Of the two decay studies by Matthews et al., the “slow” study is believed to be more indicative of 

formaldehyde behavior in residences. However, the authors add the caution that care should be taken in

interpreting the study results. For example, the duration of the study may have been inadequate to 

accurately measure the emission decay period for the collection of sources. In addition, the data may 

reflect a relatively rapid decay of emissions from a few of the strongest emitting sources, as opposed to 

the entire collection of products, whereas in real life one might typically expect to find a combination of 

relatively strong and weak emitters, or of sources and sinks. 

For the various reasons noted in the above review and discussion, there is considerable uncertainty as

to the most appropriate value to represent the central tendency for the decay rate of formaldehyde, in a 

residence where construction features, house contents and occupant activities remain relatively stable

over time. The cross-sectional data from residential studies are believed to yield estimates erring on the 

high side (i.e., longer estimated than actual half life), and the temporal data from chamber studies are 

believed to yield estimates erring in the opposite direction. 

The collective evidence indicates that an appropriate half-life value probably lies between 1.5 and 3.0 

years. The default value currently provided with the model – 2.92 years – will tend to err on the 

conservative side. That is, assuming that the initial concentration in a house is predicted accurately, the 

2.92-year value likely will cause the modeled concentration to decay at a slower rate than might be 

observed in a stable residential setting. 

A recent paper by Groah (2005) focused on the topic of decay in formaldehyde concentrations over 

time. The author notes that “newer sources of formaldehyde are continually being brought into homes 
3-12 

as they age.” Examples would include installation of new kitchen cabinets when remodeling or addition 

of new furnishings such as furniture or shelving that may contain pressed-wood products. To the extent

that such situations exert an upward bias on half-life estimates that are based on an analysis of homes of 

different ages, it could be argued that the default half-life value of 2.92 years is too conservative, as 

mentioned above. Two studies were noted by Groah that involved chamber testing of a collection of 

pressed-wood products as they aged. One (Matthews et al. 1985, cited above) estimated the emissions 

half life to be 1.52 years and the other (Groah and Gramp 1988) indicated a half life of 2.10 years. 

Based on these studies, a half life on the order of 1.5 to 2.0 years is suggested should the user wish to 

apply a less conservative value. 

3.7 Temperature and Humidity Adjustments

As noted in Section 2 and in the introduction to this section, the model initially estimates the 

formaldehyde concentration(s) in a residence under baseline indoor conditions of 23 ° C temperature 

and 50 % relative humidity – these are consistent with the conditions under which most chamber tests 

have been conducted, in accordance with ASTM standard E 1333, for estimation of emission rates 

under an assumed steady-state condition. The model then adjusts the initial concentration estimates to a 

second (user-specified) set of temperature and humidity conditions. 

The temperature adjustment used in the model is of the form: 

[ ( U )] R TB T

T C C e

1 1

0

−

= (Eqn. 3-24) 

where: 

CT = Temperature-adjusted formaldehyde concentration 

C0 = Formaldehyde concentration at the baseline temperature 

R = Temperature coefficient for adjustment 

TU = User-specified temperature, ° K 

TB = Baseline temperature, 296 ° K (23 ° C). 

The humidity adjustment, applied to the temperature-adjusted concentration, is of the form: 

( ) B U

T

TH A H H

C

C

+ −

=

1

 (Eqn. 3-25) 

where: 

CTH = Temperature- and humidity-adjusted formaldehyde concentration 

CT = Temperature-adjusted formaldehyde concentration 

A = Humidity coefficient for adjustment 

HU = User-specified relative humidity, % 

HB = Baseline relative humidity, 50 %. 

Combining equations 3-24 and 3-25, the temperature- and humidity-adjusted concentration can be 

expressed as follows: 

CTH = C0KTH (Eqn. 3-26) 

where KTH is the combined temperature and humidity adjustment factor: 

[ ( )]

( ) B U

R T T

TH A H H

e

K

B U

+ −

=

−

1

1 1

(Eqn. 3-27) 
3-13 

Thus, the adjustments require temperature and humidity coefficients, for which the model provides two 

sets of default values. The first set of coefficients was calculated by Berge et al. (1980) for two 

Norwegian particleboard specimens. These coefficients 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. Chamber tests underlying these 

coefficients were conducted at two temperatures (22 and 28 ° C) and at two relative humidities (30 and 

60 %). The coefficients reported by Berge et al. were 9799 for temperature (assumes an Arrhenius type 

of model) and 0.0175 for humidity (assumes a linear model). 

The second set of coefficients was reported by Myers (1985), who reviewed the extant literature and 

developed his recommended temperature coefficient based on chamber testing of about 40 specimens 

(particleboard and hardwood plywood paneling) from 11 laboratories. The temperature range of the 

product tests was from 20 to 40 ° C. Dr. Myers also developed a humidity coefficient, but expressed 

little confidence in the number; the relative humidities 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. It is worth noting that the HUD standard was 

promulgated before Dr. Myers completed his work. His reported correction coefficients were 8930 for 

temperature and 0.0195 for relative humidity, using the same model assumptions as Berge et al. 

The temperature and humidity adjustments modify the emission rate from pressed-wood products and, 

therefore, the portion of the indoor concentration due to indoor sources and sinks. That is, the 

temperature and humidity adjustment is applied only to the portion of the steady-state concentration 

contributed by pressed-wood products. The adjustment applied to the two-zone concentrations 

calculated using equations 3-11 and 3-12 takes the following form: 

( ) C ,1 SS ,adjusted = C ,1 SS −CB KTH + CB

 (Eqn. 3-28) 

( ) C ,2 SS ,adjusted = C ,2 SS − CB KTH + CB

 (Eqn. 3-29) 

Similarly, the adjustment applied to the one-zone concentration calculated using equation 3-8 takes the 

following form: 

[ ] ([ ] ) CH2O SS ,adjusted = CH2O SS −CB KTH + CB

 (Eqn. 3-30) 

3.8 Exposure Calculations

As noted in Section 2.6, the model calculates the following exposure metrics: 

• Lifetime average daily concentration (LADC) and average daily concentration (ADC) 

• Lifetime average daily dose (LADD) and average daily dose (ADD) 

• Percent of time at or above 0.01 ppm and a user-specified COC. 

To determine the LADC and ADC values, the model first calculates daily indoor concentrations over 

the duration of the exposure period (defined as the number of years in the house, as input on the 

Exposure Screen). A simplifying assumption used here is that the indoor concentration is constant over
3-14 

any 24-hour period. In actuality, there will be a marginal concentration decrease throughout the day 

due to the long-term formaldehyde decay indoors. 

The average concentration (Caverage)for any given day is a weighted average of the concentrations in 

Zone 1, Zone 2, and while away from the house, with the weights being the fraction of time spent by 

the individual in each location (the weights can differ for weekdays vs. weekend days): 

Caverage = (C1 * F1)+ (C2 * F2) + (Cout * Fout) (Eqn. 3-31) 

where C refers to concentration, F to fraction of time, and the subscripts 1, 2 and out to Zone 1, Zone 

2 and out of the house, respectively. The ADC is simply the average of the daily-average 

concentrations over the exposure period, or the sum of the daily-average concentrations divided by the

length of the exposure period, in days. The LADC calculation shares the same numerator but has a 

denominator of length of lifetime, in days. 

To determine the LADD and ADD values, the model first calculates the daily dose (Ddaily) at each 

location (Zone 1, Zone 2 and out of the house): 

Ddaily = Cdaily * BRdaily * TSdaily (Eqn. 3-32) 

where: 

Cdaily = Daily-average concentration at location, mg/m3

BRdaily = Breathing rate at location, m3/hr 

Tdaily = Time spent at location, hr 

The daily dose per location, in mg, is summed across locations to get total daily dose. The total daily 

doses are then summed over the entire exposure period. Division by the length of the exposure period, 

in days, and by body weight, in kg, yields average daily dose in mg/kg-day. The LADD calculation 

shares the same numerator but has a denominator of length of lifetime, in days. 

To determine the percent of time at or above 0.01 ppm (or user-specified COC), the model tests 

whether the daily concentration at each location is ≥ 0.01 ppm. If so, then the number of daily hours 

spent at that location is accumulated. The accumulated hours, across the three locations and over the 

entire exposure period, are then divided by the length of the exposure period, in hours, and multiplied 

by 100 to express the result as a percent. 

 
4-1 

4. SUMMARY OF EPA FORMALDEHYDE PILOT STUDY1

4.1 Study Objectives and Design 

At a public meeting in January 1993, EPA representatives outlined a plan for a proposed formaldehyde 

(HCHO) study that was to be conducted in two phases – a main study and a pilot study. The main 

study was to involve testing using passive monitors in 108 newly constructed conventional and 

manufactured houses located throughout the United States. A smaller pilot study was to be conducted 

first to evaluate the feasibility and logistical considerations of the experimental design for the larger 

main study.

In September 1994 the National Particleboard Association (NPA) signed a Cooperative Research and 

Development Agreement (CRDA) with EPA to fund a pilot study in newly constructed conventional 

and manufactured houses. The general purpose of the pilot study was to evaluate methods used to 

measure the contribution of UF-bonded building materials to indoor HCHO concentrations in newly 

constructed conventional and manufactured houses. 

The specific objectives of the pilot study were to:

• Test logistical considerations relevant to carrying out experimental procedures for the 

testing program in a single conventionally-built single-family house and in several 

manufactured houses. 

• Demonstrate that experimental variables or conditions likely to affect formaldehyde 

concentrations in new houses (i.e., UF-bonded wood product emission characteristics and 

loading rates, temperatures and indoor air exchange rates) can be controlled, individually 

and jointly varied, held sufficiently constant, and that the response can be measured to a 

specified precision. 

• Demonstrate that test results can be obtained across a range of different experimental 

conditions, similar to that which can be present in new houses. 

• Estimate the extent of variability of the experimental results and the variation with changes 

in experimental conditions. 

• Determine how to account for, or to eliminate or minimize, residual formaldehyde 

carryover between test runs in the conventional house due to effects of inherent sinks. 

• Evaluate the ability to control and vary the air exchange rate of houses using an adjustable 

mechanical air handling system. 

The study was guided by a Quality Assurance Project Plan (QAPP; GEOMET 1994) with a detailed 

description of the experimental design and variables, monitoring protocols, and quality 

assurance/control procedures that would be employed. According to the QAPP, the pilot study would 

include one unoccupied, conventionally built, single-family house and four unoccupied manufactured 

houses. Four manufactured houses were specified in the pilot study because it was not practical to 

install and remove products in a manufactured house. The conventional house was to be a two-story 

house on a slab or crawlspace. The manufactured-house portion of the pilot study eventually was 

dropped due to resource limitations. 

 

1 Portions of this section have been extracted or adapted from Hare et al. (1996) and Koontz et al (1996). 
4-2 

The QAPP also specified that the following variables would be evaluated in the pilot study: 

• Product emission characteristics: Only “medium” emitting products were to be used. 

Emissions from particleboard and from plywood wall paneling (as measured by ASTM 

method E 1333; ASTM 1996a) were to be between 0.12 and 0.14 ppm. Because there were 

no established protocols for measuring formaldehyde emissions from kitchen/bathroom 

cabinets, commercially available cabinets constructed with “medium” emitting materials 

(melamine-wrapped particleboard) were to be used. 

• Product loading rate: Two different loading combinations of products – Medium and High 

(defined later) – were to be installed in the house. 

• Environmental conditions in the house: 

- Temperature of 75 °F 

- Ventilation rate of 0.5 air changes per hour (ACH) 

Relative humidity in the house, while not a controlled variable, was targeted at 50 percent. Air leakage 

was to be determined through blower-door tests, with efforts to make the house as airtight as possible. 

Ventilation rates were to be controlled by a mechanical heat recovery ventilator (HRV) attached to the

heating and air conditioning system (HAC). Air exchange rates were to be measured by two tracer gas 

methods – constant release of perfluorocarbon tracers (PFTs, EPA Method IP-4A; USEPA 1990) and 

periodic injection/decay of sulfur hexafluoride (SF6, EPA Method IP-4B; USEPA 1990). 

Four product loadings were to be used – two Medium and two High. Prior to loading the products in 

the house, a baseline value for the house without any experimental UF-bonded wood products was to 

be determined. The products then would be installed in the house and indoor formaldehyde 

concentration measurements taken over approximately a 30-day period. At the completion of 30-day 

period, the products were to be removed from the house. The house would be allowed to “air out” for 

a period of time until a new equilibrium level (baseline) was reached, after which the next set of 

products would be installed. The order of the loading configurations in the house was to be 

randomized, with the single constraint that Loadings 1 and 2 would be different (i.e., one High and one 

Medium). 

Indoor and outdoor formaldehyde concentrations (24-hour time-integrated values) were to be 

measured by EPA method IP-6A (Solid Adsorbent Cartridge; USEPA 1990) 7, 12, 28, and 33 days 

after products were installed in the house. If necessary, additional testing could take place to confirm 

any trends or unexpected results. Readings on days 12 and 33 were considered statistical replicates of

readings on days 7 and 28, respectively. Indoor formaldehyde concentrations were to be measured in 

the kitchen, living room, upstairs bedroom, basement, and outdoors. One duplicate sample was to be 

collected on each sampling occasion, at a location to be varied systematically. 

Product emission tests were to be conducted in a large chamber in accordance with ASTM E 1333, at 

three different air exchange rates. Because there were no established protocols for large-chamber 

testing of doors and cabinets, the following loading rates were be used: 

• Doors – five doors, at a total loading rate of 0.125 ft2

/ft3
4-3 

• Kitchen cabinets/countertops – one base and one wall cabinet with doors closed, at a 

loading rate of 0.133 ft2

/ft3. A section of countertop was to be placed on the base cabinet 

during testing. 

The above loading rates were similar to those established by the Department of Housing and Urban 

Development (HUD) for large-chamber testing of particleboard and industrial panels. 

For sink-effect testing of painted gypsum wallboard and carpet/padding, products were to be placed in 

a small clean environmental chamber. A known concentration of formaldehyde gas was to be injected 

into the chamber. By accurately measuring time-varying concentrations in the chamber, it could be 

determined whether the material was absorbing formaldehyde gas and then re-emitting it after the 

source was turned off. 

4.2 Study Methods

Securing a house builder or owner who was willing to participate in the study proved to be more 

difficult and costly than anticipated, due mainly to the constraint that the house could not be occupied 

during the test period. A homeowner was located in Centreville, MD, who was building a rental house 

and was willing to lease it for as long as needed. The house was a conventionally built, 1326 ft2

, twostory Cape Cod style with a full basement (volume of 168 m3

). The QAPP had called for a house with 

crawl space, but efforts to find such a house in the study area were unsuccessful. The total volume of

the finished living space was 10,746 ft3

 (304 m3). The first floor of the house (712 ft2 floor area) had 

5931 ft3 (168 m3) of living space that consisted of a living room, kitchen, bathroom/laundry room, and 

bedroom. The second floor of the house (614 ft2 floor area) had 4815 ft3 (136 m3) of living space that 

consisted of two bedrooms and a bathroom. The door from the first-floor finished living space to the 

unfinished basement was sealed shut during the entire project. The house contained no furniture or 

draperies. 

Industry representatives were responsible for procuring all pressed-wood products that would be used 

in the pilot study. Sufficient quantities of 5/8” particleboard underlayment, 3/4” industrial particleboard 

for countertops, 1/4” hardwood plywood wall paneling (3-ply birch face, tropical hardwood back and 

core with 7 cut grooves along the length of each panel to simulate random-width lumber planking), 

interior partition doors, and kitchen and bathroom cabinets were obtained from member companies or 

participating associations, or were purchased at local building supply centers. Emission characteristics 

of the particleboard and plywood wall paneling used in the study were determined prior to selecting the 

materials for testing. 

Initial emission characteristics of the products used in the study (see Table 4-1) were determined by 

ASTM E 1333 at 0.5 ACH. All products were stored in a controlled-access warehouse until they were 

installed in the house. During storage, products were wrapped in 6-mil plastic to minimize 

formaldehyde off-gassing. It was discovered during the study that temperature control in the warehouse

was marginal and that temperatures ranged up to 85 ° F. 

Products were installed in the house according to manufacturers’ recommended installation 

instructions, and conventional practices were followed. The particleboard underlayment was installed 

with screws for easy removal. The kitchen and bath cabinets were screwed tightly against the wall. The

plywood wall paneling was nailed to the wall to minimize damage to the gypsum wallboard. 
4-4 

Table 4-1. Initial Emission Characteristics of Products Used in the Pilot Study 

Product Emissions, ppm Loading Rate, ft2/ft3

Particleboard Underlayment 0.144 0.130 

Plywood Wall Paneling 0.114 0.290 

Cabinets 0.053 0.133 

Interior Doors 0.052 0.125 

Loading areas for pressed-wood products are shown in Table 4-2. For the Medium loading scenario, 

particleboard underlayment was installed on the first floor, along with interior doors on both floors and 

a full set of kitchen/bathroom cabinets and countertops. For the High loading scenario, particleboard 

underlayment was installed on both the first and second floors. In addition, twelve 4’ X 8’ sheets of 

plywood wall paneling were installed. To establish a relatively uniform loading and to avoid using 

partial panels, four full-size sheets were installed in an upstairs bedroom, in the downstairs bedroom, 

and in the living room. Interior doors and a full set of kitchen and bathroom cabinets and countertops

(same number as for Medium loading) also were installed. The total exposed surface area for cabinets 

was calculated to be 631 ft2

 (59 m2). Particleboard underlayment was not installed in the kitchen and 

bathroom areas of the house, as those areas were covered by vinyl sheet goods that had been 

permanently installed during final preparation of the house before field testing was initiated. 

Table 4-2. Loading Areas for Pressed-wood Products at the Conventional House 

Loading Area, ft2

1st Floor 2nd Floor Component 

Medium 

Loading

High 

Loading

Medium

Loading

High 

Loading

Underlayment 496.2 496.2 --- 519.3 

Paneling --- 256.0 --- 128.0 

Doors 203.6 169.6 

Countertop 37.9 5.65 

Blower-door tests indicated that the house had numerous leaks in the building shell and between the 

first floor and basement. Air leakage sites were identified (service penetrations between the basement

and first floor and along the base plate) and sealed with caulk and foam. Numerous leaks also were 

found in the forced-air HAC distribution system. Sealing procedures reduced the leakage rate by more 

than 50 percent, from ~ 10 ACH at 50 Pa (corresponding to ~ 0.5 ACH under moderate environmental 

conditions) to ~ 4 ACH at 50 Pa. 

Initial study plans did not include measurement of formaldehyde concentrations in the basement, 

because it was thought that the combination of house sealing procedures and a closed interior door at 

the top of the stairwell to the basement would minimize air communication with the remainder of the 

house. However, during tracer gas studies to characterize the air exchange rate for the house it became 

obvious that tracer injected into the living area was being transferred to the basement. Consequently, it 
4-5 

was decided to include formaldehyde measurements in the basement. In addition, PFT sources and 

samplers were configured so that the average airflow rate between the basement and living area could 

be quantified during each sampling event. 

Following initial baseline testing, products for Loading 1 (Medium) were installed and indoor 

concentration levels were measured in accordance with the protocols outlined in the QAPP. It became 

evident during this time that there was difficulty in controlling relative humidity levels in the house, 

which reached over 70 percent. Humidity levels were lowered to the desired range by adding additional 

dehumidification equipment in the house. Because high humidity causes higher formaldehyde emissions, 

the house was declared to be in an “upset condition” during this time and it was decided that Loading-1 

products should be left in the house until conditions stabilized. The final readings for Loading 1 were 

taken 78 days after product loading. 

It also was determined during this time that resource constraints would not permit the full 

implementation of the loading schedule established in the study plan, which was modified for conduct 

of only three loadings in the house – one Medium and two High loadings. In addition, the air-out 

period between successive loadings was fixed at seven days instead of waiting for formaldehyde levels 

to reach equilibrium. 

Following the removal of Loading-1 products from the house and a seven-day airing-out period, 

Loading-2 (High) products were installed. Formaldehyde concentrations were measured on days 7, 12, 

28, and 33. Following removal of Loading-2 products from the house and a seven-day airing-out 

period, Loading-3 (High) products were installed. Formaldehyde concentrations again were measured 

on days 7, 12, 28, and 33 after loading. Following removal of Loading 3 products, the house was 

returned to the homeowner. 

A limited amount of sink-effect testing was conducted as part of the pilot study. From results of the 

laboratory sink-test results and results from Loadings 1, 2 and 3, it appeared that the gypsum wall 

board was acting as a significant sink. Because the exposed surface area of the wallboard was greater 

than all of the UF-bonded products installed in the house, it was considered critical to fully characterize 

the sink effect behavior of painted gypsum wallboard. It also was considered important to determine 

whether the carpet/padding used in the house was acting as a sink or had any barrier effect on 

formaldehyde emissions from the particleboard underlayment. 

The original protocol for “barrier testing” was modified to evaluate the floor system with both 

particleboard underlayment and carpet/padding, instead of just the carpet/padding. A sample of 

particleboard underlayment was placed in a stainless-steel pan and inserted in a small chamber. 

Formaldehyde concentrations in the chamber were measured continuously with a real-time (Interscan) 

analyzer. As a separate test, a second sample of particleboard with carpet/padding directly above it was 

placed in a stainless-steel pan and inserted in the chamber. Differences in the concentration profiles for 

the two tests would reflect the barrier effect of the carpet/padding used in the pilot study. To minimize 

the inherent variability within a piece of particleboard, specimens used for these tests were prescreened 

via small-chamber emission tests (ASTM 1996b) – the two pieces with the closest emission rates were 

used for the tests. 

4.3 Study Results
4-6 

The results of formaldehyde, temperature, humidity and air-exchange measurements during the formal 

“runs” associated with each loading, as well as their respective baseline periods, are compiled in Table 

4-3. Formaldehyde concentrations measured in the upstairs rooms generally were similar to one another 

and higher than those measured in the basement. The highest concentration measured in the house – 76 

ppb – was in the kitchen during Loading 3 (High). The monitoring results collectively indicate that, for 

all three loadings, indoor HCHO concentrations had peaked by the time of measurements taken 33 days 

after product loading. The formaldehyde results also indicate that monitored levels for Loadings 2 and

3 generally were consistent with one another and that these “high” loadings had higher HCHO levels 

(but also a higher baseline) than the “medium” loading (Loading 1). 

Although measured air exchange rates generally were in the target range of 0.4 to 0.6 ACH, the PFT 

estimates consistently were higher than those based on SF6. One possible reason for the discrepancy is 

the inherent difference between the two measurement technologies. The SF6 method involves periodic 

injection and mixing of the tracer through the HAC system, followed by real-time analysis as the 

concentration declines. The PFT method relies on a near-constant release of tracers from multiple 

locations near the perimeter of the house, with time-integrated sampling over a 24-hour period. 

Table 4-3. Summary of Monitoring Results for Loadings 1, 2, and 3 

Formaldehyde Concentration, ppb Temperature, °F RH, % Air Exchange, ACH Run* 

LR KIT BR BMT AMB LR KIT BR BMT AMB LR 2ND AMB SF6 PFT 

Loading 1 (Medium) 

Baseline 9.1 9.8 9.5 9.1 1.3 75.7 75.8 74.0 63.4 49.0 22.8 24.4 55.2 -- 0.50 

1 27.5 29.9 20.1 -- 1.0 73.8 73.4 73.2 68.5 56.9 43.2 41.0 60.2 0.44 0.54 

2 29.6 31.3 29.9 26.5 7.0 73.8 73.6 73.4 66.7 52.4 46.2 43.2 76.8 0.44 0.54 

3 41.7 43.9 36.3 28.2 2.1 75.1 75.0 74.9 71.1 69.6 63.1 60.2 93.9 0.40 0.54 

4 36.8 39.4 31.1 -- 1.7 75.5 74.8 73.4 73.1 66.0 50.4 49.8 60.6 0.40 0.57 

Loading 2 (High) 

Baseline 23.0 23.7 22.1 25.7 2.8 75.2 73.1 74.3 77.0 84.4 54.5 52.3 80.3 0.39 -- 

1 60.1 60.8 60.5 39.7 2.9 75.3 73.5 74.5 76.2 81.5 57.1 55.5 88.2 0.38 0.61 

2 55.8 58.1 54.7 40.0 2.3 75.1 73.4 74.3 75.4 80.1 50.9 49.3 74.1 0.38 0.71 

3 46.7 48.5 53.3 38.0 1.4 74.4 73.9 75.6 75.7 75.4 50.7 43.8 71.2 0.36 0.59 

4 39.0 40.8 48.1 30.7 0.9 73.4 73.2 73.2 73.6 63.1 51.6 43.2 71.6 0.39 0.60 

Loading 3 (High) 

Baseline 26.0 25.8 27.7 25.0 <1.0 73.3 72.8 73.3 73.3 61.4 54.9 44.3 85.0 0.41 -- 

1 71.9 76.1 65.6 42.6 1.1 75.0 73.2 72.5 73.6 76.1 62.7 65.3 95.1 0.39 0.69 

2 53.8 55.2 54.7 29.9 1.1 72.3 72.4 72.0 70.7 60.3 49.7 47.1 86.7 0.36 0.64 

3 43.2 46.2 39.5 20.3 1.1 71.7 71.8 69.5 66.6 49.1 43.8 43.7 87.2 0.42 0.62 

4 42.3 40.4 44.1 22.8 1.4 71.7 71.9 70.7 66.9 55.4 46.1 44.9 88.8 0.35 0.53 

 Legend: * Run 1 occurred 7 days after product loading; 

 LR = living room; KIT = kitchen; Run 2 occurred 12 days after product loading; 

 BR = bedroom; BMT = basement; Run 3 occurred 28 days after product loading; 

 AMB = ambient; 2ND = second floor. Run 4 occurred 33 days after product loading. 

Upstairs measurements (average of kitchen, living room and bedroom locations) for the three loadings 

are plotted in Figure 4-1 against elapsed time after UF-bonded wood products were installed (day 

“zero” indicates baseline measurements). The curvature of the lines is due to the spline fit that was 

applied and is not meant to imply that values between measurement points can be readily interpolated. 
4-7 

The figure illustrates the general consistency across Loadings 2 and 3 and their differences from 

Loading 1. Although concentrations for Loading 1 are similar to those for Loadings 2 and 3 toward the 

end of their respective test periods, indoor humidity levels were relatively high near the end of Loading 

1. 

Figure 4-1. Upstairs Formaldehyde Concentrations over Time for Three Loadings.

Differences in baseline levels and in the general shape of the time series for Loading 1 versus Loadings 

2 and 3 can be explained partly by the wallboard sink effect. The wallboard sink was largely “empty” at 

the outset of Loading 1 but was largely “pre-loaded” at the outset of Loadings 2 and 3, as reflected in 

the higher baseline values for the later loadings. The time series for Loadings 2 and 3 have a shape 

consistent with that of an exponentially declining emitter, as would be expected when the dominant sink 

(wallboard) has been pre-loaded and becomes a “net zero emitter,” such that the declining rate of 

emissions from aging wood products drives the concentration profile. For Loading 1, however, this 

profile is dampened by the relatively large mass being absorbed by the wallboard sink in an “unloaded”

state. Some of the difference in baseline values for Loading 1 versus Loadings 2 and 3 also may be due

to the relatively low humidity level at the time when baseline measurements were taken for Loading 1. 

The key measurement parameter for the study, formaldehyde by the DNPH method, was in control 

across all measurement periods. QA spikes indicated that recoveries were consistently in the range of 

90-110 percent, well within the accuracy goal of ±20 percent. Results of duplicate DNPH samples 

indicated a combined sampling and analytical precision of ±10 percent or better, again well within the

corresponding data quality objective. The standard deviation across the high loadings, for 

measurements at the same location and at the same elapsed time since loading of UF-bonded wood 

0

10

20

30

40

50

60

70

80

0 5 10 15 20 25 30 35

Formaldehyde Concentration, ppb

Time from Loading, days

Loading 1

Loading 2

Loading 3
4-8 

products, was not much larger than that for duplicate measurements (i.e., at the same time and location 

within any given loading). This finding points to the repeatability of high-loading results for the 

conventional house, after the sinks were pre-loaded as a result of the preceding medium loading. 

Emission rates for UF-bonded wood products that were installed in the pilot study house, based on 

large-chamber concentrations that were adjusted to standard conditions of 77 ° F and 50% RH per 

ASTM E 1333, are listed in Table 4-4. Each product was tested at target air exchange rates of 0.25, 

0.5 and 1.0 ACH. Two patterns that were evident for all products are noteworthy. First, as the air 

exchange rate is increased, the emission rate also increases, but at a rate that is less than proportional to 

the increase in air exchange. This trend is indicative of a concentration “backpressure” effect, as applied 

in the Matthews model. Second, for each product the emission rate was lower for products used for 

later loadings (products were tested near the time of each loading). These results indicate that some 

emissions decay likely occurred during storage, even though products were wrapped in plastic. The 

elevated temperature in the warehouse may have accelerated the decay process somewhat. 

Table 4-4. Computed Emission Rates for UF-Bonded Products 

Emission Rate, μg/m2-h 

Loading 

Underlayment Paneling Cabinets Doors 

At Target ACH of 0.25* 

1 

2 

3 

104.9 (0.25 ACH) 

99.2 (0.25 ACH) 

90.4 (024 ACH) 

Not Used 

42.9 (0.25 ACH) 

32.9 (0.25 ACH) 

45.6 (0.17 ACH) 

45.2 (0.24 ACH) 

45.7 (0.25 ACH) 

52.0 (0.24 ACH) 

Not Tested 

49.9 (0.25 ACH) 

At Target ACH of 0.50 

1 

2 

3 

178.3 (0.50 ACH) 

162.6 (0.50 ACH) 

149.9 (0.51 ACH) 

Not Used 

72.3 (0.50 ACH) 

56.8 (0.50 ACH) 

77.1 (0.51 ACH) 

69.9 (0.50 ACH) 

68.5 (0.50 ACH) 

74.2 (0.50 ACH) 

Not Tested 

68.4 (0.51 ACH) 

At Target ACH of 1.0 

1 

2 

3 

221.9 (1.01 ACH) 

200.6 (0.99 ACH) 

190.2 (1.01 ACH) 

Not Used 

104.9 (0.99 ACH) 

77.0 (1.01 ACH) 

82.8 (1.00 ACH) 

73.4 (0.99 ACH) 

74.9 (1.01 ACH) 

79.9 (1.00 ACH) 

Not Tested 

74.2 (1.00 ACH) 

* Actual air exchange rates during each test are given in parentheses. 

Other products used in the house were assessed for formaldehyde emission characteristics. For the 

paint used on the wallboard and interior doors at the study house, the manufacturer’s data indicated 

that the wallboard paint contained 0.001% formaldehyde by weight and the door paint contained 

0.007% formaldehyde. A carpet/padding sample was sent to EPA’s Air and Energy Engineering 

Research Laboratory (AEERL) in Research Triangle Park for small-chamber testing. Results of the 

chamber tests, conducted at 0.5-0.55 ACH, 74 ° F and 55-60 % RH, indicated an emission rate of 1.4 

μg/m2-h for the carpet and the same rate for the padding (after subtracting the chamber background) at 
4-9 

an elapsed time of 24 hours following insertion in the chamber, or an emission rate of 2.8 μg/m2-h for 

these two constituents combined. The combined emission rate is one to two orders of magnitude lower 

than that for UF-bonded wood products. 

Small-chamber tests were conducted to evaluate sink characteristics of the carpet and padding. Two 

tests were conducted under identical air exchange rates of 1.5 ACH, but with different formaldehyde 

concentrations in the input stream because the rate of adsorption to the sink was suspected to be a 

function of the air concentration. In both tests, a 7.1-inch square piece of carpet and padding was 

placed in a tight-fitting aluminum pan with edges equal to the depth of the carpet and padding. The pan 

containing the carpet and pad was then placed horizontally on the chamber floor. The chamber was 

sourced with a formaldehyde stream of 0.2 ppm during the first test and 0.12 ppm during the second. 

Comparison of the theoretical (concentrations that would be expected in the absence of sinks) and 

measured concentrations indicated that formaldehyde was adsorbed by the carpet, and the trend in the 

data appeared to reflect a first-order removal process. 

Chamber tests for gypsum wallboard were conducted to evaluate its sink characteristics. As with the 

carpet tests, these two tests were conducted under identical conditions with the exception of the 

formaldehyde feed-stream concentration, to evaluate the effect of concentration on the rate of mass 

transfer to and from the wallboard. For each test, two 10.5-inch square pieces of painted wallboard 

were securely fastened back-to-back and edge sealed with sodium silicate, leaving a total of 220.5 

square inches of exposed wallboard surface area. The wallboard was then placed in the center of 

chamber in a vertical position, supported by stainless steel wire. The chamber was sourced with a 

formaldehyde stream of 0.2 ppm during the first test and 0.12 ppm for the second, at 1.5 ACH. The 

resulting data from these tests indicated that the sink effect was more pronounced for wallboard than 

for the carpet/padding ensemble. The concentration data were fit to a Langmuir isotherm model (see 

Section 3.4) to estimate adsorption and desorption rate constants for the two types of sinks. 

Tests to evaluate the behavior of underlayment both with and without a carpet/padding barrier were 

conducted under identical chamber conditions using a tight-fitting aluminum pan with edges equal to 

the depth of the underlayment, carpet and padding. In the first test, a 7.1-inch square piece of 

underlayment was placed in the pan with nothing above it. In the second test, a 7.1-inch square piece of 

underlayment was placed in the pan with an equally sized piece of padding and carpet placed above it. 

For both tests, the pan was then placed horizontally on the chamber floor. The resulting data indicated 

that the underlayment was releasing formaldehyde. While it was tempting to conclude from the results 

that the carpet and padding had no effect on the emission of formaldehyde, the carpet/padding sink test 

described above indicated otherwise. 
4-10 

4.4 Study Conclusions

The following conclusions, primarily related to the objectives given in Section 4.1, were reached as a

result of the pilot study: 

• Some logistical difficulties were encountered that prevented the study from being 

completed as outlined in the QAPP. Among the greatest difficulties were locating a study 

house and maintaining humidity levels in the house within the prescribed range. Humidity 

was not a primary experimental variable for the study, but was considered to be an 

important covariate that should be tightly controlled. Logistical aspects such as acquiring, 

storing and accessing the materials associated with house loading went remarkably 

smoothly, due in part to the high level of cooperation from various industry representatives 

and their close working relationship with the study team. 

• Little difficulty was encountered in controlling most experimental variables at the study 

house. The primary variables – product loading rate, emission rate, temperature, and air 

exchange – all were generally kept within their respective target ranges. Some emissions 

decay was evident for wood products stored for successively later loadings. 

• It was demonstrated that different test results could be obtained across different 

experimental conditions and that sufficient precision in measurement response could be 

obtained. Differences across the experimental conditions (medium versus high loading) 

could be distinguished, although these differences were partially dampened by the 

substantial sink effect of the gypsum wallboard. Appropriate precision was obtained largely 

because of the consistently high resolution, accuracy and precision for the sampling method 

(solid adsorbent cartridge) with a 24-hour sampling duration. 

• The study data were marginally sufficient for estimating the extent of variability of results 

and the variation with changes in experimental conditions. The limited number of loadings, 

coupled with the unique circumstances of the first loading (little mass in the indoor sinks at 

the outset), made it difficult to properly estimate the variance component associated with 

repeats of the same loading configuration. However, it was demonstrated that the variance 

across repeats of the high loading, for a specific sampling location at the same elapsed time 

relative to loading of the house, was only marginally higher than the variance for duplicate 

formaldehyde samples. 

• Formaldehyde carryover between successive tests at the conventional house, due to 

inherent sinks, was not trivial. The sink effect, due largely to adsorption of formaldehyde by 

painted gypsum wallboard, was not eliminated by the prescribed “airing out” of the house. 

The monitoring results, however, did suggest that baseline formaldehyde values were 

reasonably reproducible once the house had been loaded with UF-bonded wood products. 

• The ability to control and vary the air exchange rate of the conventional house using a heat 

recovery ventilator (HRV) was demonstrated. This ability was demonstrated for two of the 

three target air exchange rates (0.2 and 0.5 ACH) planned for the full study; the third target 

(1.2 ACH) could not be addressed because the HRV lacked sufficient capacity. Achieving 

the lower target of 0.2 ACH was made possible by sealing procedures that substantially 

reduced the air leakage of the house and, thus, the sensitivity of its air exchange rate to 

weather conditions.
5-1 

5. ASSESSMENT OF MODEL ACCURACY 

The accuracy of the model has been assessed from two perspectives: (1) independent checks on the 

correctness of model algorithms; and (2) comparison of model predictions with measurements in realworld situations. 

5.1 Mathematical Correctness of Model Algorithms

An Excel spreadsheet has been developed as a tool for assessing the mathematical correctness of 

algorithms used in the model. The Excel tool includes individual sheets for inputs corresponding to 

model input screens – House, Source, Sinks and Cabinets – together with a separate sheet that 

displays the calculation results (predicted HCHO concentrations). Input areas within each screen are 

set up similarly to those in the model, with the exception that no drop-down selections are provided 

for sources, sinks or cabinets. Instead, input areas (cells) are designated for direct entry of Slope, B

and Area values. Results are provided for both the one-zone and two-zone implementation of the 

model, in concentration units of mg/m3

 and ppm. 

Results in the Excel tool were compared with those reported by the model for a variety of cases 

representing different combinations/values for background concentrations, sources, sinks and 

cabinets, for both one-zone and two-zone implementations. This exercise led to discovery of minor 

errors in the handling of ppm vs. mg/m3

 units for the background concentration and in the 

temperature/humidity adjustment for indoor formaldehyde concentrations. Other than those 

discrepancies, the results agreed exactly in all cases. The errors discovered in the model’s calculation 

routine have been corrected. 

5.2 NIST Assessment of Matthews Model Predictions

An effort was undertaken by researchers (Silberstein et al. 1988) at the National Institute of Standards 

and Technology (NIST) to validate the Matthews model on which this model is based. Particleboard 

underlayment, hardwood-plywood paneling and medium-density fiberboard (mdf) products initially 

were characterized in chambers by measuring their HCHO surface emission rates over a range of 

formaldehyde concentrations, air exchange rates and two combinations of temperature and relative 

humidity. The products then were installed in a two-room prototype house in different combinations, 

and equilibrium HCHO concentrations were monitored in the house. 

The following findings are excerpted directly from the authors’ abstract: 

Particleboard underlayment and mdf, but not paneling, behaved as the emission model predicted 

over a large concentration range, under both sets of temperature and relative humidity. Good 

agreement was also obtained between measured formaldehyde concentrations and those 

predicted by a mass-balance indoor air quality model. 

The mass-balance model referenced here is the Matthews model. The following excerpt, taken 

directly from the authors’ conclusions, provides some further insights on model performance: 

In developing its models, ORNL assumed that there is relatively free formaldehyde diffusion 

within the "bulk phase" of pressed-wood products. Formaldehyde emission results from the 

difference in concentration between this "bulk phase" and the atmosphere, in accordance with 

Fick's first diffusion law. This assumption is apparently fairly descriptive of particleboard and 
5-2 

mdf, but not of hardwood plywood paneling. It is hypothesized that internal diffusion is 

important in formaldehyde emission by pressed-wood products, and layering of solid thin sheets 

of plywood obstructs diffusion to a greater extent than do chips and pieces in the other pressedwood products. In other words, formaldehyde emission may not be as diffusion-limited in 

plywood as it is in other pressed-wood products. This would explain why formaldehyde 

emission by plywood appeared relatively insensitive to temperature and RH used in the present 

study. Higher temperature and RH increase resin degradation to formaldehyde and increase the 

formaldehyde diffusion rate. Apparently, the small changes of temperature and RH used in the 

present study did not increase the "bulk phase" formaldehyde concentration or the diffusion rate 

sufficiently to overcome the obstructing layers of the relatively low-emitting plywood used in 

this study. 

It is noteworthy here that particleboard and mdf generally are much higher HCHO emitters than 

plywood or hardwood plywood paneling. Thus, the NIST validation effort indicated accurate model 

predictions for the major HCHO emitters among pressed-wood products. 

5.3 Assessment of Predictions by the Current Model

An assessment undertaken by the author of this document involved comparison of model predictions 

with concentrations measured in the EPA pilot study house under various conditions, including before 

and after loading the house with pressed-wood products. The assessment was conducted by using 

known/measured factors such as zone volumes, airflow rates, indoor temperature and humidity, and 

source/sink loading areas together with estimates of emission model parameters for each type of 

source or sink. Model inputs were developed for six cases (time periods within the pilot study) at the

conventional house – initial baseline, first loading, air-out after first loading, second loading, air-out 

after second loading, and third loading. Inputs supplied for model input screens – House, Sources and 

Sinks – are described in a general manner below. Further details specific to each of the six cases are

given in the subsections that follow. 

The house screen requires inputs for the type of house, the zone volumes and airflow rates, the 

background formaldehyde concentration, and the indoor temperature and humidity conditions. The 

house used for the pilot study – Conventional 1 – was selected. Airflow measurements with PFTs on 

14 different occasions during the pilot study averaged 0.59 ACH and varied over a relatively narrow 

range of 0.5 to 0.7 ACH. The default airflow rates provided with the model for this conventional 

house, which correspond to an air exchange rate of 0.59 ACH, were used for all model runs. 

Outdoor formaldehyde concentration measurements during the pilot study varied over the narrow 

range of 0.001 to 0.003 ppm, averaging about 0.002 ppm. The average of 0.002 ppm was used for 

this input rather than case-specific values. The model calculates formaldehyde levels in each zone of 

the house under a base set of temperature/humidity conditions (23 ° C, 50 %) and a user-supplied set 

of conditions. The user-supplied conditions were chosen to represent the average of the values 

measured upstairs for each case at the conventional house. The major formaldehyde sources all were 

located upstairs. The default temperature and humidity coefficients provided with the model, for 

adjustment of modeled formaldehyde concentrations from the base conditions to the user-supplied 

conditions, were used for all model runs. 
5-3 

Model parameters for sources – Slope and B – have been estimated previously from large-chamber

emission tests conducted by industry or the USEPA, and are supplied with the model. The major 

sources installed in the conventional house – underlayment, kitchen/bathroom cabinets, interior doors,

and hardwood plywood – were chamber tested under three different air exchange rates as part of the 

pilot study. Source loading areas for the model runs are described later as they pertain to each 

modeled case. 

There are two major types of potential sinks in conventional house 1 – carpet/padding and painted 

wallboard. Sinks can be represented in the Matthews model using the same parameters as those for 

sources. The Langmuir isotherm model described in the formaldehyde pilot study report (p. 6-44) was 

used to develop parameter estimates for sinks, for use in the Matthews model. The estimation process 

is described in Section 3.4. 

The modeling approach, rationale and assumptions for each of the six modeled cases are described 

below. The results of this evaluation exercise collectively indicate that the modified (two-zone) 

Matthews model can predict measured values quite well for the conventional house, but errs 

somewhat on the conservative side (i.e., it tends to “over-predict”). The greatest area of uncertainty

in applying the model appears to be in choosing appropriate values for indoor sinks. One additional 

area of uncertainty stems from the fact that humidity levels were not measured downstairs; as noted 

previously, upstairs values for temperature and humidity were used in constructing the model inputs. 

5.3.1 Initial Baseline Period

Model inputs for this period are summarized in Table 5-1. The only source present in the house 

during the initial baseline period was the plywood subfloor, and the only sink was painted wallboard 

(carpet was not yet installed). The area for plywood was taken as the product of the upstairs volume 

(304 m3) and an assumed loading ratio of 0.43 m2/m3, or 131 m2. For wallboard the loading ratios for 

walls (0.95 m2/m3) and ceilings (0.43 m2/m3) were used to estimate a total area of 420 m2. Model 

source/sink parameters (intercept and slope) were taken from the model defaults for softwood 

plywood. An intercept value of 0.04 mg/m2

-h was chosen for wallboard after running the model with 

plywood only and obtaining an indoor formaldehyde concentration in the vicinity of 10 ppb. 

Table 5-1. Model Inputs (Sources and Sinks) for Initial Baseline Period 

Source/Sink Slope (m/h) Intercept (mg/m2-h) Area (m2) 

Softwood plywood -0.61 0.03 131 

Painted wallboard -3.00 0.04 420 

Modeling results for the initial baseline are shown in Table 5-2. With plywood as the only source, and

without including wallboard as a sink, the modeled values for the conditions under which 

measurements were taken (23.98 ° C, 23.6 % RH) were 8 ppb upstairs and 7 ppb downstairs, close to 

the measured values of 9.5 and 9.1 ppb for the respective zones. Addition of wallboard as a sink had 

no appreciable effect on the modeled values. It is plausible that, at this point in time, the wallboard 
5-4 

had reached a state of equilibrium and, thus, acted as neither a net source nor a net sink. When the 

intercept parameter for wallboard was arbitrarily halved (to 0.02 mg/m2

-h), to cause it to behave as 

net sink, the modeled values were 5.0 ppb upstairs and 4.4 ppb downstairs under the conditions when 

measurements were taken. 

Table 5-2. Modeling Results for Initial Baseline Period 

Results (ppb) for Base/Measured Conditions

23 ° C, 50 % RH 23.98 ° C, 23.6 % RH Source/Sink Inputs

Upstairs Downstairs Upstairs Downstairs 

Softwood plywood as a source 10.3 9.0 7.8 6.9 

Add wallboard as a sink 10.7 9.4 8.2 7.2 

Measured values -- -- 9.5* 9.1 

*The measured value is an average across 3 monitoring sites (living room, kitchen and bedroom). 

5.3.2 First Loading 

The modeled sources for the first (medium) loading included underlayment, cabinets, interior doors 

and countertop (Table 5-3). Plywood was not included as a source because it was covered by 

underlayment or by floor tile. Loading areas for the sources were taken from Section 3.5 of the pilotstudy report, and slopes and intercepts were taken from the pilot-study values provided with the 

model for underlayment, doors and cabinets. For countertop, industrial particleboard was selected to 

obtain slope/intercept parameters (average values were used). The intercepts chosen for carpeting and 

wallboard were predicated on an indoor-air concentration near 40 ppb. 

Table 5-3. Model Inputs (Sources and Sinks) for First (Medium) Loading 

Source/Sink Slope (m/h) Intercept (mg/m2-h) Area (m2) 

Underlayment -1.27 0.28 46 

Cabinets -0.48 0.08 59 

Interior doors -0.50 0.08 35 

Countertop -0.70 0.30 4 

Carpeting -1.30 0.065 94 

Painted wallboard -3.00 0.15 420 
5-5 

The modeling results for this case (Table 5-4) are compared with measured values taken at run 4 (28 

days after loading), by which time the indoor-air concentrations appeared to have reached a secular 

equilibrium. The addition of carpeting lowered the modeled concentrations slightly, and further 

addition of wallboard lowered the modeled values by about 10 percent compared to estimates with no 

sinks. The modeled concentrations for measured conditions, with carpeting and wallboard included, 

were 5-10 ppb higher than measured values under those conditions. 

Table 5-4. Modeling Results for First Loading 

Results (ppb) for Base/Measured Conditions

23 ° C, 50 % RH 23.65 ° C, 50.1 % RH Source/Sink Inputs

Upstairs Downstairs Upstairs Downstairs 

Underlayment, cabinets, doors and 

countertop as sources 

47 40 51 43 

Add carpeting as a sink 46 39 49 42 

Add wallboard as a sink 42 36 45 39 

Measured values (run 3, day 28) -- -- 41 28 

 

5.3.3 Air-out Period after First Loading 

For this air-out period, plywood again was the only source and wallboard was the only sink. In this 

case, however, it was necessary to account for the fact that the wallboard had adsorbed significant 

mass during the first loading. Some of this mass would be lost during the air-out period, which lasted

7 days, but the amount lost was uncertain. Consequently, the intercept for the first loading (see Table 

5-5) was used as an upper bound when developing inputs and half this value was used as a lower 

bound. 

Table 5-5. Model Inputs for Air-out Period after First Loading 

Source/Sink Slope (m/h) Intercept (mg/m2-h) Area (m2) 

Softwood plywood -0.61 0.03 131 

Painted wallboard -3.00 0.15/0.075* 420 

*Two runs were made, one with 0.15 as the intercept and one with 0.075. 

As shown in Table 5-6, the modeling results with the alternative intercept values for wallboard 

surround the measured values. The model estimates with the smaller intercept value, to account for 

the likely possibility that the wallboard had released a fair amount of mass during the air-out period, 

are closer to the measurement results. 
5-6 

Table 5-6. Modeling Results for Air-out Period after First Loading 

Results (ppb) for Base/Measured Conditions

23 ° C, 50 % RH 23.44 ° C, 53.4 % RH Source/Sink Inputs 

Upstairs Downstairs Upstairs Downstairs 

Softwood plywood as a source 10.3 9.0 11.5 10.0 

Add wallboard as a re-emitting sink 

(intercept = 0.15) 34 29 38 33 

Change wallboard intercept to 0.075 18 16 20 18 

Measured values -- -- 23 26 

5.3.4 Second Loading 

For the second (high) loading, the sources (Table 5-7) were similar to those for the first loading, but 

with a larger area for underlayment and with the addition of hardwood plywood paneling as another 

source. The intercept values chosen for carpet and for wallboard were based on concentration 

estimates obtained from running the model without any sinks. 

Table 5-7. Model Inputs (Sources and Sinks) for Second (High) Loading

Source/Sink Slope (m/h) Intercept (mg/m2-h) Area (m2) 

Underlayment -1.27 0.28 94 

Cabinets -0.48 0.08 59 

Interior doors -0.50 0.08 35 

Countertop -0.70 0.30 4 

Paneling -0.98 0.16 36 

Carpeting -1.30 0.095 94 

Painted wallboard -3.00 0.225 420 

Modeled values (Table 5-8) were compared to measurements taken at run 2 (day 12), by which time 

it appeared that a secular equilibrium already had been reached. This earlier time of equilibrium, 

relative to that for the first loading, was likely due to the wallboard sink being substantially “preloaded” with formaldehyde mass as a result of the first loading. The modeling results without sinks 

were 70-75 ppb upstairs and 60-65 ppb downstairs. The addition of carpeting and wallboard as sinks 
5-7 

lowered the modeled values by about 10 percent. The modeled values with sources and sinks were 

about 10 ppb higher than those measured upstairs (differences similar to those for the first loading),

and about 15 ppb higher than the measured downstairs values. 

Table 5-8. Modeling Results for Second Loading 

Results (ppb) for Base/Measured Conditions

23 ° C, 50 % RH 23.48 ° C, 50.1 % RH Source/Sink Inputs 

Upstairs Downstairs Upstairs Downstairs 

Underlayment, cabinets, doors, 

countertop and paneling as sources 

70 60 74 63 

Add carpeting as a sink 68 58 72 61 

Add wallboard as a sink 63 54 67 57 

Measured values (run 2, day 12) -- -- 56 40 

5.3.5 Air-out Period after Second Loading

For the air-out period after the second loading, the only sources and sinks again were plywood and 

wallboard (Table 5-9). As with the first air-out period, it was necessary to account for the fact that

the wallboard had adsorbed mass during the second loading and then had lost some of this mass 

during the air-out period. To accommodate uncertainty in the amount of mass in the wallboard near 

the beginning of this air-out period, an intercept close to that for the second loading was used as an

upper bound, and half that value was used as a lower bound. 

Table 5-9. Model Inputs for Air-out Period after Second Loading 

Source/Sink Slope (m/h) Intercept (mg/m2-h) Area (m2) 

Softwood plywood -0.61 0.03 131 

Painted wallboard -3.00 0.19/0.095* 420 

*Two runs were made, one with 0.19 as the intercept and one with 0.095. 

As shown in Table 5-10, the model results with alternative intercept values for wallboard surround 

the measured values, and the model estimates with the smaller intercept value are closer to the 

measurement results. This pattern is the same as that observed for the comparison of modeling and 

measurement results for the first air-out period. 
5-8 

Table 5-10. Modeling Results for Air-out Period after Second Loading 

Results (ppb) for Base/Measured Conditions

23 ° C, 50 % RH 22.83 ° C, 49.6 % RH Source/Sink Inputs 

Upstairs Downstairs Upstairs Downstairs 

Softwood plywood as a source 10.3 9.0 10.0 8.7 

Add wallboard as a re-emitting sink 

(intercept = 0.19) 43 36 41 35 

Change wallboard intercept to 0.095 22 19 22 19 

Measured values -- -- 27 25 

5.3.6 Third Loading 

For this repeat of the high loading, the model inputs for sources and sinks (Table 5-11) were the same

as those used for the second loading, including the intercepts for carpeting and wallboard. 

Table 5-11. Model Inputs (Sources and Sinks) for Third (High) Loading 

Source/Sink Slope (m/h) Intercept (mg/m2-h) Area (m2) 

Underlayment -1.27 0.28 94 

Cabinets -0.48 0.08 59 

Interior doors -0.50 0.08 35 

Countertop -0.70 0.30 4 

Paneling -0.98 0.16 36 

Carpeting -1.30 0.095 94 

Painted wallboard -3.00 0.225 420 

The measurement results for this loading indicated that a secular equilibrium had been reached even 

sooner than in previous cases (i.e., by run 1 on day 7), and the measured values for run 1 therefore 

were used as a basis for comparison with modeling results. The modeled values were about 10 ppb 

higher than measured upstairs but about 25 ppb higher downstairs (Table 5-12). One possible 

explanation for the greater difference downstairs is that the humidity level, which was not measured 

downstairs, may have been lower than the value used in the model run. 
5-9 

Table 5-12. Modeling Results for Third Loading 

Results (ppb) for Base/Measured Conditions

23 ° C, 50 % RH 22.63 ° C, 64 % RH Source/Sink Inputs 

Upstairs Downstairs Upstairs Downstairs 

Underlayment, cabinets, doors, 

countertop and paneling as sources 70 60 89 76 

Add carpeting as a sink 68 58 86 74 

Add wallboard as a sink 63 54 80 69 

Measured values (run 1, day 7) -- -- 72 43 
6-1 

6. REFERENCES 

ASTM. 1996a. Standard Test Method for Determining Formaldehyde Concentrations in Air and 

Emission Rates from Wood Products Using a Large Chamber. Designation E 1333-96 (Reapproved 

2002), American Society for Testing and Materials, Philadelphia, PA.

ASTM. 1996b. Standard Test Method for Determining Formaldehyde Concentrations in Air from 

Wood Products Using a Small-Scale Chamber. Designation D 6007-02 (Reapproved 2008), American 

Society for Testing and Materials, Philadelphia, PA.

A. Berge, B. Mellagaard, P. Hanetho, and E. Ormstad. 1980. Formaldehyde Release from 

Particleboard – Evaluation of a Mathematical Model. Holz Als Roh-und Werkstoff 38: 252-255. 

CARB. 2008. Final Regulation Order: Airborne Toxic Control Measure to Reduce Formaldehyde 

Emissions from Composite Wood Products. California Air Resources Board. 

GEOMET. 1994. Residential Indoor Air Formaldehyde Testing Program: Pilot Study, Quality 

Assurance Project Plan. Report No. IE-2695, prepared by GEOMET Technologies, Inc. for the 

USEPA Office of Pollution Prevention and Toxics under Contract No. 68-D3-0013. 

W. Groah and G. Gramp. 1988. An Estimate of Home Occupant Exposures to Formaldehyde Gas 

from Plywood and Reconstituted Wood Products Bonded with Formaldehyde Based Adhesives. 

CPA/HPVA 1988 Exposure and Assessment Package Report, Hardwood Plywood and Veneer 

Association, Reston, VA.

W. Groah. 2005. Decay or the Decrease in Formaldehyde Concentrations or Emissions over Time and 

UF-bonded Wood Panel Products. Report prepared for the Composite Panel Association, 

Formaldehyde Council Inc., Hardwood Plywood and Veneer Association, and the Kitchen Cabinet 

Manufacturers Association. 

D. Hare, R. Margosian, W. Groah, S. Abel, G. Schweer, and M. Koontz. 1996. Evaluating the 

Contribution of UF-bonded Building Materials to Indoor Formaldehyde Levels in a Newly 

Constructed House. In Proceedings of the 30th International Particleboard/Composite Materials 

Symposium, Washington State University, Pullman, WA, pp. 93-108. 

M. Koontz, H. Rector, D. Cade, C. Wilkes, and L. Niang. 1996. Residential Indoor Air 

Formaldehyde Testing Program: Pilot Study. Report No. IE-2814, prepared by GEOMET 

Technologies, Inc. for the USEPA Office of Pollution Prevention and Toxics under EPA Contract 

No. 68-D3-0013.

T. Matthews, T. Reed, B. Tromberg, C. Daffron, and A. Hawthorne. 1983a. Formaldehyde Emissions 

from Combustion Sources and Solid Formaldehyde Resin Containing Products: Potential Impact on 

Indoor Formaldehyde Concentration and Possible Corrective Measures. Proceedings of ASHRAE 

Symposium “Management of Atmospheres in Tightly Enclosed Spaces,” Santa Barbara, CA. 

T. Matthews, A. Hawthorne, C. Daffron, T. Reed, and M. Corey. 1983b. Formaldehyde Release from 

Wood Products. In Proceedings of the 17th International Particleboard Symposium, Washington 

State University, Pullman, WA. 

T. Matthews, T. Reed, B. Tromberg., K. Fung, C. Thompson, J. Simpson, and A. Hawthorne. 1985. 
6-2 

Modeling and Testing of Formaldehyde Emission Characteristics of Pressed-Wood Products: Report 

XVIII to the U.S. Consumer Product Safety Commission. ORNL/TM-9867, Oak Ridge National 

Laboratory, Oak Ridge, TN. 

T. Matthews, A. Hawthorne, and C Thompson. 1987. Formaldehyde Sorption and Desorption 

Characteristics of Gypsum Wallboard. Environmental Science & Technology 21: 629-634.

G. Myers. 1985. The Effects of Temperature and Humidity on Formaldehyde Emission from UFbonded Boards: A Literature Critique. Forest Products Journal 1985: 35:20-31. 

S. Silberstein, R. Grot, K. Ishiguro, and J. Mulligan. 1988. Validation of Models for Predicting 

Formaldehyde Concentrations in Residences due to Pressed-Wood Products. JAPCA 38: 1403-1411.

USEPA. 1990. Compendium of Methods for the Determination of Air Pollutants in Indoor Air. 

Report No. EPA/600/4-90/010, Atmospheric Research and Assessment Laboratory, U.S. 

Environmental Protection Agency, Research Triangle Park, NC. 

Versar. 1988. Formaldehyde Exposure in Residential Settings: Sources, Levels, and Effectiveness of 

Control Options. Update (September 30, 1988) of 1986 report by Versar, Inc. for the USEPA Office 

of Toxic Substances, prepared under Contact No. 68-02-3968. 

Versar. 1989. Indoor Formaldehyde Concentration from Pressed-Wood Products Model 

Documentation. Prepared by Versar, Inc. for the USEPA Office of Toxic Substances under Contact 

No. 68-02-4254.
Appendix A 

Derivation of Two-zone Steady-state Solution
A-1 

Mass balance equation for zone 1 (well-mixed assumption): 

01 0 21 2 10 1 12 1 1

1

1 Q C Q C Q C Q C S

dt

dC

V = + − − + (1) 

where: 

1 1 1 1

S = − z C + y (Matthew’s implementation) (2) 

1

1

1

z1 m Area

in Zone

num sources

k

∑ k

=

= m3/hr (3) 

k

in Zone

num sources

k

y ∑bk Area

=

=

1

1

1

 mg/hr (4) 

m = mass transfer coefficient, m/hr 

b = emission rate when the air concentration is zero, mg/(m2 hr) 

Q = flow rates, m3/hr 

C = concentrations, mg/m3 

Area = emission area, m2

t = time, hr 

V = volume, m3

Mass balance equation for zone 2 (well-mixed assumption): 

02 0 12 1 20 2 21 2 2

2

2 Q C Q C Q C Q C S

dt

dC

V = + − − + (5) 

Q12

Q21

Q01 Q10 Q02 Q20

Zone 1 

V1

S1

Zone 2 

V2

S2
A-2 

where: 

2 2 2 2

S = − z C + y (6) 

2

2

1

z2 m Z Area

in Zone

num sources

k

= ∑ k +

= (7) 

2

2

1

y2 m C

in Zone

num sources

k

∑ k

=

=

(8) 

Assume flows are constant and set dC/dt = 0 (steady state condition): 

01 0 21 2 10 1 12 1 1 1 1

0 = Q C + Q C − Q C − Q C − z C + y (9) 

And: 

02 0 12 1 20 2 21 2 2 2 2

0 = Q C + Q C − Q C − Q C − z C + y (10) 

Solving for C1: 

10 12 1

01 0 21 2 1

1 Q Q z

Q C Q C y

C

+ +

+ +

= (11) 

Solving for C2: 

20 21 2

02 0 12 1 2

2 Q Q z

Q C Q C y

C

+ +

+ +

= (12) 

Substitute equation 12 into equation 11: 

10 12 1

1

20 21 2

02 0 12 1 2

01 0 21

1 Q Q z

y

Q Q z

Q C Q C y

Q C Q

C

+ +

+















+ +

+ +

+

=

 (13) 
A-3 

Rearranging and combining terms: 

( )

20 21 2

21 02 0 21 12 1 21 2

10 12 1 1 01 0 1 Q Q z

Q Q C Q Q C Q y

Q Q z C Q C y

+ +

+ +

+ + − − =

(( ) ) ( ) 10 12 1 1 01 0 1 20 21 2 21 02 0 21 12 1 21 2 Q + Q + z C − Q C − y Q + Q + z = Q Q C + Q Q C + Q y

21 02 0 21 12 1 21 2

01 20 0 01 21 0 01 2 0 20 1 21 1 2 1

10 20 1 10 21 1 10 2 1 12 20 1 12 21 1 12 2 1 1 20 1 1 21 1 1 2 1

Q Q C Q Q C Q y

Q Q C Q Q C Q z C Q y Q y z y

Q Q C Q Q C Q z C Q Q C Q Q C Q z C z Q C z Q C z z C

= + +

− − − − − −

+ + + + + + + +

( )

( ) ( ) 01 20 01 21 01 2 21 02 0 20 21 2 1 21 2

10 20 10 21 10 2 12 20 12 2 1 20 1 21 1 2 1

Q Q Q Q Q z Q Q C Q Q z y Q y

Q Q Q Q Q z Q Q Q z z Q z Q z z C

+ + + + + + +

+ + + + + + + =

( ) ( )

( ) 10 20 10 21 10 2 12 20 12 2 1 20 1 21 1 2

01 20 01 21 01 2 21 02 0 20 21 2 1 21 2

1 Q Q Q Q Q z Q Q Q z z Q z Q z z

Q Q Q Q Q z Q Q C Q Q z y Q y

C

+ + + + + + +

+ + + + + + +

=

 (14) 

Similarly: 

( ) ( )

( ) 20 10 20 12 20 1 21 10 21 1 2 10 2 12 2 1

02 10 02 12 02 1 12 01 0 10 12 1 2 12 1

2 Q Q Q Q Q z Q Q Q z z Q z Q z z

Q Q Q Q Q z Q Q C Q Q z y Q y

C

+ + + + + + +

+ + + + + + +

= (15)