## 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 2009i 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. Ment ion 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 Concentra tion in One Compartment........ 3-3 3.3 Extension of the Steady-State Model to Two Compartme nts........................................ 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 Solutioniii 

### 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 Environ mental 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 Jus t Meeting HUD/ANSI

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

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

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

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

................................................... 2-23

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

4-2. Loading Areas for Pressed-wood Products at the Convent ional 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) Loadi ng ....................................... 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 Loadin g.................................................. 5-6

5-7. Model Inputs (Sources and Sinks) for Second (High) Loadin g 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 Loadin g ............................................. 5-8

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

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

................................................... ......... 5-9iv 

### 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 An y Sources ........................................... 2-8

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

2-7. Sources - Cabinets Screen Prior to Selection of A ny 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 S inks ............................................2-32

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

4-1. Upstairs Formaldehyde Concentrations over Time for Three Loadings ............................ 4-71-1



### 1. INTRODUCTION

The model described in this document, Formaldehyde Indoor A ir Model – Pressed Wood Products or FIAM-pwp , is intended to assist the user in estimating human inh alation exposure to airborne formaldehyde (HCHO) emissions from pressed wood products in stalled in new or existing residences or small structures such as portable classrooms or campe r trailers. The model estimates indoor formaldehyde concentrations and associated human inhalat ion exposures for such situations.

The model described herein is an adaptation of a model dev eloped during the 1980s by Dr. Thomas Matthews and colleagues at the Oak Ridge National Laborat ory (Matthews et al. 1983a; Matthews et al. 1987). The “Matthews model” was designed to estimate th e steady-state formaldehyde concentration resulting from emission sources such as pr essed wood products in a single indoor compartment or zone. Product emission rates in the mode l are dependent on the HCHO concentration in the vapor phase, in accordance with Fick’s Law descri bing the bulk-vapor interphase at the surface of a pressed wood emission source. The initial (steady-s tate) 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 assum ed to follow a first-order exponential process, at a decay rate that depends on the chosen emis sions 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 t his study was completed, Versar was tasked by EPA to develop a modified version of the Matthews mo del. 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-e mitting) indoor sinks. The modified model also included the option to be run in a single-zone mode. The m odel was not finalized due to shifting priorities at the time of its development.

In April 2008 the California Air Resources Board adopted an a irborne toxics control measure to reduce formaldehyde emissions from composite wood products s old 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 th e California regulation as a national standard. EPA denied the petition but, in so doing, stated i ts intention to gain a greater scientific understanding of potential health risks of formaldehyde’s us e 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 modification s noted above, this version of the model has a third modification – the addition of exposure estima tes. 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 summar ized 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 th e two-zone implementation of the steadystate model.2-1



### 2. USER INTERFACE

The user interface consists of a Main Screen (introduc tory screen), five input screens (House, Sources - General, Sources - Cabinets, Sinks and Exposure s), and a Results Screen that displays modeling results after inputs have been provided and calculat ions have been executed (the calculations are executed automatically each time the R esults 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 (vers ion 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 hel p 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 Pas swords are assigned by EPA or by Versar. At this point audio help files and/or visual help (larger f onts) can be enabled by checking the appropriate box(es). Either of these options can be disa bled 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/space s. 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 infor mation from the user on the house volume and airflows and to provide certain options pertaining to mode l 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 sc reen); (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, car e 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 do cumentation 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 t he 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 ent ry is allowed here. Instead, the rate is calculated by the program using the v olume 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 conc entration of the outdoor concentration plus indoor sources other than pressed wood products (e.g., tobac co 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 defa ult value of zero, then the modeling results will reflect the contributions of pressed wood products and indoo r 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 mo del under a steady-state assumption. As described in Section 3.6, the default half life of 2.92 year s is based on a regression analysis of formaldehyde concentrations in residences of various age s.

The default choice is considered to be conservative; th at is, assuming that initial concentrations in a structure are predicted accurately, the value of 2.92 years l ikely 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 a ssuming an indoor temperature of 23 ° C and an indoor relative humidity of 50 percent (base con ditions). The inputs provided here enable the user to specify an additiona l 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 scre en are used by the model to make the adjustments (see Section 3.7). By default, the user-specifi ed 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 percen t of time above a formaldehyde concentration of concern (COC), are determined using in door 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 mo del 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 c hoices 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 availab ility 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 st ructure such as a portable classroom or a camper trailer can be represented by choosing a manufact ured house and editing the house volume.

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

Volume, m 3
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 s elected, as shown in Figure 2-3, then the user interface will display information on volumes and air f lows 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 se cond conventional house (Conventional 2), then the program will display volumes and air flows for a “gene ric” conventional house consisting of two stories and two zones – upstairs and downstairs. The defaul t 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 h eight 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-s pecific volumes in the lower portion of the screen so that they add up to the new volume. The airflo w rates in the lower portion of the screen will remain at their default values, meaning that the calcula ted air exchange rate will change. The air exchange rate can be adjusted by changing the airflow rat es to and from outside for each zone in the lower portion of the screen.

As an alternative to entering a house volume, the “Cal culate Volume” option can be used to enter inputs for number of stories, length, width and height; th e program will calculate the volume by multiplying these values. Default values are provided for th e volume components as “placeholders” that can be edited. The model assumes that each story h as the same length, width and height when2-6

calculating the volume, but different volumes can be assi gned 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 compartmen ts whereas the manufactured house is conceptualized as a single zone. The model cannot represe nt more than two zones. Representing a house with more than two stories would require some stor ies be combined into one zone, as with the configuration of the Conventional 1 house (i.e., the tw o upper floors are combined into one zone).

If either conventional house is chosen and the user se lects “One Zone” as the number of zones, then the program will “collapse” the airflow rates in the l ower 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 airfl ow rates should have the same value. If the number of zones is changed from one to two, then the model wi ll 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 t ype).

2.1.3 Lower Portion

This portion of the House Screen enables the user to e nter zone-specific descriptions, volumes and airflow rates. That is, the user can enter or edit des criptions 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 volum e.

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 calculat e 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 a ir flows are needed – flow from outside and flow to outside; these flows must be equal to provide an overal l 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. Indiv idual 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 flow s 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 t he program. As shown previously in Table 2-1, the default air exchange rates for houses provided by the model are2-7

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 t o that of the default air exchange rate. For example, if the default rate is 0.33 ACH and the target rat e 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 i ncreased by 50 % (i.e., multiplied by 1.5) to achieve the target air exchange rate while maintainin g a flow balance.

The default air exchange rate and air flows for Convent ional 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 (SF 6 ) as a tracer. Air exchange rates estimated with SF 6 were systematically about a third lower (i.e., average of a bout 0.4 ACH) than rates estimated with PFTs. As noted in the pilot study report, the SF 6 method involves periodic injection and mixing of the tr acer 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-con stant 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 r ate with a lower value such as 0.4 ACH, then the corresponding interzonal air flows can be est imated 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/base ment. 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 conservativ e estimate of formaldehyde concentrations indoors, lower air flows (resulting in a lower air exc hange 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 pr oduct 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, m ust be edited to “activate” a source.

Each input line or row on this screen refers to a spec ific type of source in a specific zone. Consequently, to represent a source that is present in b oth 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 K itchen Cabinet, but there also is a separate screen that is specific to cabinets (Sources - Cabine ts; see Section 2.4). The emission rate modeling parameters for cabinets that are available on the So urces - General screen are based on chamber testing of an ensemble of kitchen wall and base cabine ts. 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 i s fairly involved. In the absence of detailed information on specific cabinet components and appropriat e values for their modeling parameters, it is

recommended that the cabinet ensemble available on th is 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 emissio n rate modeling parameters provided with the software have been developed from the results of in door-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 fo r 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 mo deling parameters) contained in the model for each source type. This table also provides references f or the data in the table and additional information, as available, on chamber testing conditi ons (air exchange rate and loading ratio). Correlation coefficients listed in the right-hand colum n of the table are based on regression analysis

between calculated emission rates and measured chamber c oncentrations 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 so urces in the table reflect the organization (e.g., EPA, ORNL) or individual that performed the testin g from which modeling parameters were

estimated. Several Available Sources – EPA-PBU for Par ticleboard Underlayment, EPA-HWP for Hardwood Plywood Paneling (Unspecified), EPA-CABINET for Kitchen Cabinets, and EPA-DOOR for Interior Doors – are based on chamber testing perfo rmed as part of the EPA pilot study on formaldehyde (Koontz et al. 1996), which was conducted using t he 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 Institut e) source, for which the modeling parameters were derived from the products (i.e., availabl e sources) that were tested. The average for a given source type has slope and intercept values that ar e averaged across all available sources; in the case of medium density fiberboard (mdf), three cases wit h 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 charac teristics is available for the product(s) selected.2-10Table 2-2. Linear Formaldehyde Emission Models Based on Environmental Chamber Data Taken at 23°C, 50 % RH or at 25°C, 50 % RHa(Listed Model Parameters are for Conditions of 23°C and 50 % RH)Matthew’s Emission Modelse,fER = m (conc) + bSource TypeAvailable SourcesbNo. of DataPointscN/L RangedMeasuredConcentrationRange (ppm)Slope (m/hr)Intcpt. (mg/m2/hr)Corr. Coeff.gParticleboardUnderlaymentORNL-PCB #1ORNL-PCB #2ORNL-PCB #3ORNL-PBU 1 #4ORNL-PBU 3 #3ORNL-PBU 3 #6GP-2GP-4GP-5NBS-USM2-2BNBS-USM2-3BNBS-USM5-1ANBS-U-5,8,9,12,18EPA-PBUAVG PBUMAX HUD3444430.127 to 0.6330.316 to 5.700.101 to 0.9490.159 to 9.180.444 to 6.670.586 to 2.370.077 to 0.1620.057 to 0.3540.084 to 0.1580.084 to 0.2150.058 to 0.4420.062 to 0.118-0.32-0.70-0.88-1.72-0.70-0.93-0.84-1.57-0.76-0.36-0.38-0.62-0.60-1.25-0.83-0.830.090.440.190.460.510.470.400.370.580.180.270.330.180.280.340.74-0.96-0.99-0.96-0.88-0.98-0.72-0.90-0.99-0.65-0.87Mobile HomeDeckingLEH-BGP-MHDAVG MHDMAX HUD-1.35-0.77-1.06-1.060.660.390.520.82IndustrialParticleboardORNL-PBI 3#2LEH-CLEH-DLEH-HLEH-ILEH-JLEH-KLEH-LLEH-MLEH-NLEH-OLEH-PLEH-Q48966666666660.316 to 3.310.76 to 6.100.31 to 6.100.59 to 3.820.59 to 3.820.59 to 3.820.59 to 3.820.59 to 3.820.59 to 3.820.59 to 3.820.59 to 3.820.59 to 3.820.59 to 3.820.096 to 0.457-0.47-1.00-0.54-1.02-0.87-1.30-0.96-1.07-0.40-1.32-0.58-1.58-0.980.421.240.360.450.600.270.320.530.140.240.220.370.39-0.942-11Matthew’s Emission Modelse,fER = m (conc) + bSource TypeAvailable SourcesbNo. of DataPointscN/L RangedMeasuredConcentrationRange (ppm)Slope (m/hr)Intcpt. (mg/m2/hr)Corr. Coeff.gIndustrialParticleboard(continued)GP-1AGP-3AGP-6AGP-7AGP-8AGP-9AGP-11ANBS-USM7-1BNBS-USM2-1ANBS-USM6-1BNBS-USM6-2ANBS-USM6-3BNBS-USM4-1BGP-1NGP-2NGP-3NGP-4NGP-5NGP-6NGP-7NAVG PBIMAX HUD-0.41-0.63-0.46-0.38-0.63-0.62-0.55-0.45-0.39-0.80-0.33-0.64-0.28-0.70-0.72-0.81-0.55-0.50-0.46-0.58-0.70-0.700.120.330.340.240.330.350.290.120.300.180.180.290.200.530.530.350.270.370.340.480.350.39-0.99-0.82-0.99-0.57-0.97-0.99Medium DensityFiberboardORNL-MDF 1 #5ORNL-MDF 3 #5ORNL-MDF 1 #4ORNL-MDF 2 #4ORNL-MDF-ULEH-ELEH-FLEH-GGP-1GP-2GP-3GP-4GP-5GP-64499151.47 to 12.51.33 to 12.50.31 to 6.100.31 to 6.100.15 to 7.090.170 to 0.9520.160 to 0.936-0.89-1.00-1.25-1.58-0.91-0.48-0.80-0.80-4.98-1.17-2.00-2.22-3.87-0.782.782.491.621.094.240.320.790.831.270.770.841.330.800.50-0.99-0.90Medium DensityGP-7-0.730.582-12Matthew’s Emission Modelse,fER = m (conc) + bSource TypeAvailable SourcesbNo. of DataPointscN/L RangedMeasuredConcentrationRange (ppm)Slope (m/hr)Intcpt. (mg/m2/hr)Corr. Coeff.gFiberboard(continued)GP-8GP-9GP-10GP-11GP-12GP-13GP-14GP-15NBS-LMDF-1CNBS-LMDF-2BNBS-MDF 1NBS-MDF 2NBS-MDF 3NBS-MDF 4NBS-MDF 5AVG MDFMAX NPA MDF-0.43-0.69-1.83-0.81-1.45-0.90-1.30-0.77-0.88-0.71-1.50-1.16-1.09-0.76-0.65-1.28-1.280.460.320.920.581.310.630.750.390.640.731.731.141.311.291.430.131.18Hardwood PlywoodPaneling (Print)ORNL-PNPR 2 #3ORNL-PNPR 3 #3ORNL-PNPR 2 #5ORNL-PNPR 3 #1ORNL-PAN #2AVG PNPRMAX HUD4440.313 to 6.570.445 to 3.340.316 to 1.900.085 to 0.7190.029 to 0.1270.021 to 0.055-0.46-0.37-0.40-0.85-0.48-0.51-0.510.670.130.250.260.050.270.25-0.93-0.97-0.88Hardwood PlywoodPaneling (Paper)ORNL-PNP 2 #4ORNL-PNP 3 #1,2hORNL-PNP 3 #1,2iAVG PNPMAX HUD4430.313 to 6.570.202 to 1.110.171 to 1.110.037 to 0.4260.063 to 0.2250.129 to 0.402-0.27-0.10-0.27-0.21-0.210.270.090.220.190.18-0.78-0.83-0.99Hardwood PlywoodPaneling (Veneer)ORNL-PND 1 #1,2hORNL-PND 1 #1,2iORNL-PND 3 #5ORNL-PAN #1AVG PNDMAX HUD44340.152 to 0.3550.125 to 1.060.318 to 1.110.136 to 0.9490.105 to 0.1940.055 to 0.2480.062 to 0.1370.072 to 0.162-0.19-0.11-0.34-0.45-0.27-0.270.080.080.110.130.100.19-0.60-0.90-0.95-0.92Hardwood PlywoodNBS-P6-180.04 to 1.910.022 to 0.253-0.120.05-0.912-13Matthew’s Emission Modelse,fER = m (conc) + bSource TypeAvailable SourcesbNo. of DataPointscN/L RangedMeasuredConcentrationRange (ppm)Slope (m/hr)Intcpt. (mg/m2/hr)Corr. Coeff.gPaneling (Unknown) NBS-P8-1NBS-P10-1NBS-P14-1NBS-P17-1NBS-P21-1EPA-HWPAVGMAX HUD511850.03 to 1.140.04 to 4.860.18 to 5.200.08 to 7.360.263 to 1.040.027 to 0.2390.045 to 0.3700.014 to 0.0980.020 to 0.2240.066 to 0.106-0.12-0.45-0.67-0.52-0.22-0.96-0.44-0.440.040.300.080.150.030.160.120.24-0.98-0.84-0.81-0.85-0.42-0.99Softwood Plywood(PF Resin)ORNL-PFPLY #150.23 to 1.050.017 to 0.029-0.610.03--Hardboard(e.g., "Masonite")ORNL-HBD 17--0.02 to 0.095-1.390.17-0.99Kitchen CabinetsEPA-CABIN30.390 to 2.290.023 to 0.075-0.490.08-0.97Interior DoorsEPA-DOOR30.585 to 2.440.022 to 0.061-0.520.08-0.93a The data listed in this table are based on the results of emission rate tests performed at Oak RidgeNational Laboratory (ORNL) for the Consumer Product Safety Commission (CPSC), atthe National Bureau of Standards (NBS) for EPA andCPSC, at Georgia Pacific Corp. (GP), and at Weyerhauser Co. by Dr. W. F. Lehmann. The data listed in the table for individualsources 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; NBS Report #NBSIR 85-3255 toCPSC; a 1987 NBS report to EPA (Grot et al. 1987);comments submitted by Georgia Pacific Corp. to EPA(Howlett 1988); Lehmann (1987) (also personal communication between B.Lehmann (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 Matthews model parameters listedin the table are as listed in the ORNL reports. Lehmann (1987) and Howlett (1988) reported HBF model parameters for the tested boards; Matthews model parameters for these productswere calculated from the HBF model parameters. TheNBS report listed Matthews model parameters.b Product codes are reported as listed in the ORNLProgress Reports (except for interior plywood, hardboard, and MDF-U) for the ORNL products. The products reported in Lehmann(1987) are denoted by "LEH" followed by the lettercode used in his report. The products reported in the NBS reports are denoted by "NBS" followed by thecode used in the reports. Theproducts tested by Georgia Pacific Corp. are denoted by "GP" followed by a digit representing the order presented in the report’s tables. The products tested for the EPA Pilot Study(Koontz et al. 1996) are denoted by "EPA."c Refers to the number of distinct N/L experimentsconducted.d N/L is the ratio of the experimental air exchangerate (N), in air changes per hour, to the productloading in the chamber (L), in m2of product surface area per m3of chamber volume.e ER is the emission rate of the product in units of mg of formaldehyde per m2of product surface area per hour; the intercept has the same units. The slope units are m/hr.2-14f 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 valuesfor the tested sources of a given sourcetype. The emission rate parameters for the "Maximum-HUD/ANSI certifiable" board types (i.e., MAX HUD/ANSI) were calculated using the "average" slope values and the maximum testchamber concentrations allowed by HUD/ANSI standards for pressed-wood products used in manufactured housing (i.e., 0.37 mg/m3for particleboard/mdf and 0.25 mg/m3for hardwoodplywood 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 m2/m3for particleboard/decking,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.REFERENCESANSI 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 Products. U.S. Dept. of Commerce,National Bureau of Standards. Report #NBSIR 85-3255.R.A. Grot, S. Nabinger, and S. Silberstein. 1987. Formaldehyde from Low-emitting Pressed Wood Productsand the Effectiveness of Various Remedial Measuresfor Reducing FormaldehydeEmissions. U.S. Dept. of Commerce, National Bureauof Standards.C.T. Howlett. 1988. Data provided to EPA on January14, 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-2814, prepared by GEOMETTechnologies, 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 Products Journal37(4):31-37.2-15

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 plywo od paneling), based on a chamber test at the air exchange rate (0.5 ACH) and produc t loading rate (0.43 m 2 /m 3 for particleboard/decking, 0.95 m 2 /m 3 for hardwood plywood paneling, and 0.26 m 2 /m 3 for mdf) prescribed in ASTM E 1333-96 (ASTM 1996a). Using these rates alo ng with the “average” slope value for the applicable Source Type, a one-chamber form aldehyde model was applied to solve for the B (intercept) value that would result in the source just m eeting the applicable HUD standard.

More recently, the California Air Resources Board (CA RB) has put forth emission standards for composite wood products as part of an airborne toxic cont rol 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 correspondin g 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 availab le within each source type by first selecting a source type on the Sources - General Screen and then se lecting a specific source from the available sources. When an available product is selected, the “Slo pe” 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 m 2 ) 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 r eflects 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 zer o. The default Slope and B values can be changed either by selecting a different source type and av ailable source or by directly editing the values. The source’s area can be changed only via editin g. There should be a valid basis for editing the default Slope and B values, such as results of chamber emi ssion tests.

All inputs for emission rate modeling parameters are in metric units. The intercept, in mg/m 2 -hr, is multiplied by the source area (in m 2 ) to give an emission rate, in mg/h. The slope, in unit s of m/h, is multiplied by the indoor concentration (mg/m 3 ) and by the source area (m 2 ), 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 concentrati on 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 type s were selected: underlayment; interior doors; kitchen cabinets; and counter top (industrial partic leboard). For the first three types, products from the EPA pilot study (EPA-PBU, EPA-DOOR and EPA-CAB INET) were selected. For counter top, an “average” product (AVG INDUSTRIAL P) was selecte d. All products were assigned to Zone

1 of the house.

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

2.4 Sources - Cabinets

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

1) On the Sources - General Screen, select the “Kitch en 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 de sign assistance program to develop a cabinet ensemble. Any combination of low-, medium-, o r high-emitting cabinets can be chosen for use as kitchen wall cabinets, kitchen base cabinet s or vanity cabinets. A cabinet type is selected by first choosing one of the Available Cabin ets at the top of the screen and then using the right arrow (-->) button to move that choice to t he Selected Cabinets area; the choice can be deselected using the left-arrow button. The correspondi ng cabinet components and their characteristics, which can be edited, will be displayed in the Cabinet Component Characteristics area in the lower part of this scree n. Specify the desired number of cabinets of each type and the location (zone) in which each type i s placed.

3) Design individual cabinets and their components on the Sources - Cabinets screen, by choosing “Custom Cabinet” in the drop-down list under Available Ca binets. Choose the number of custom cabinets, and then specify the individual component s and their emission parameters and location in the Cabinet Component Characteristics ar ea.

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

As with the Sources - General and Sinks screens, the e mission modeling parameters include Slope, B and Area values. Given the multiple emitting components a nd the many available choices of slopes, B values and areas to represent each, there is greater unc ertainty in the aggregate emission rate developed from this screen than when using the cabinet e nsemble 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 cabine t, 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 choos e any combination of low-, medium- or highemitting cabinets of each type, and can specify the numb er 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 pl us 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 char acteristics of its components can be viewed/changed. By default, one cabinet is specified for e ach type. The default value can be changed by highlighting one of the selected cabinets and then en tering 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 specifi ed.

The program displays one cabinet type at a time but keeps t rack of inputs for all types. The component characteristics for a chosen cabinet type c an 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 se lected; 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 sho wn in Figure 2-8, only three – shelves, door and back – are emitters. The applicable components vary w ith 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 be ing “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 cab inet modeling parameters are in metric units. The intercept, in units of mg/m 2 hr, is multiplied by the source area (m 2 ) to give an emission rate, in mg/h. The slope, in units of m/h, is multiplied by the in door concentration (mg/m 3 ) and by the source area (m

2 ), with resultant units of mg/h. The slope value usually i s negative, to reflect the backpressure effect (i.e., the emission rate decreases as the indo or formaldehyde concentration increases). The slope value can be set to zero to reflect no backpressur e effect.2-19

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

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

Table 2-4 lists the emitting components and associated def ault choices/values for the three available types of kitchen wall cabinets – low-emitting, medium-emi tting and high-emitting. The low-emitting cabinet has two emitting components – shelves and back – with a collective area of 0.66 m 2 . The medium-emitting cabinet has three emitting components wi th a collective area (1.82 m 2 ) that is nearly three times that of low-emitting cabinets. The high-e mitting cabinet has seven emitting components with a collective area (3.52 m 2 ) 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 m 2 . The medium emitter has five emitting components with a collective area (2.81 m 2 ) that is nearly twice that of low-emitting cabinets. The high emitter has nine emitting component s with a collective area (6.38 m 2 ) that is more than twice that of medium-emitting cabinets.

Table 2-6 provides information for three types of vaniti es. The low-emitting vanity has three emitting components with a collective area of 0.96 m 2 . The medium emitter has four emitting components with a collective area (2.12 m 2 ) that is a little more than twice that of low-emit ting vanities. The high emitter has seven emitting components with a collecti ve area (4.86 m 2 ) 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/m 2 -hr) Area (m 2 ) 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 3.522-22

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

Component Source Type Source Slope (m/hr) B (mg/m 2 -hr) Area (m 2 ) 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 Vanities2-23

Component Source Type Source Slope (m/hr) B (mg/m 2 -hr) Area (m 2 ) 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 4.862-24

2.5 Sinks Screen

The purpose of this screen (shown in Figure 2-10 with initi al values, discussed below) is to enable the user to specify the types and amounts of indoor sinks prese nt in the house and the house zone in which each chosen sink is located (Zone 1 is selected b y 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 t he choices that are provided. Once a sink has been selected, it can be deselected or “turned off” by e ither 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 treatm ent of indoor sinks in the calculation routine is accomplished by recognizing that the “emission” term ha s 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 int ercept) is in the form of a constant emission rate, and therefore can be used to represent re-emissio ns from the sink. The slope has units of m/h; it is multiplied by the indoor concentration (mg/m 3 ) and by the sink area (m 2 ), with resultant units of mg/h. The intercept, in units of mg/m 2 -hr, is multiplied by the sink area (m 2 ) to give a re-emission rate, also in mg/h.

Default parameters are provided with the model for two ty pes of indoor sinks – carpeting and painted2-25

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 thi s 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 abso rption rate is considerably lower than during the initial stage.

Depending in part on the prevailing formaldehyde concentrat ion, 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 concen tration 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 tha t 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 c oncentration on the order of 40 ppb.

Figure 2-11. Sinks Screen with Equilibrium Values.

The default B value for an initial condition for carpeti ng (0.003 mg/m 2 -h), intended to represent a2-26

point in time before the sink has accumulated any signifi cant mass, is based on small-chamber emission tests using carpeting and padding that had not yet b een placed in an indoor setting with any significant formaldehyde sources. The default B value for an initial condition for wallboard (0.004 mg/m 2 -h) is based on the formaldehyde content by weight in pa int that was applied to the wallboard in the conventional house for the USEPA formaldehyde pilot study.

For the equilibrium condition, results from small-chambe r tests for painted wallboard that were conducted at the time of the EPA pilot study suggest a B val ue of about 0.0375 mg/m 2 -h per 10 ppb indoor formaldehyde concentration (e.g., 0.0375 mg/m 2 -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 abo ut 0.016 mg/m 2 -h per 10 ppb indoor formaldehyde concentration. As an aid to choosin g an appropriate B value for a sink, a preliminary model run can be made to estimate the conce ntrations 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 concentratio ns 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 concentration s 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 ch ild 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 len gth of the exposure period, and average body weight. The lower part of the screen has exposure f actors related to activity patterns, including time spent in/out of the house and average inhalation ra tes 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 formaldehy de concentrations to which the individual is exposed. In general, the lower the age of sources the hi gher the indoor concentrations at the start of the exposure period. Entering a source age of zero will ca use the model to begin exposure

calculations with the initial indoor concentrations s hown on the results page, which are intended to reflect an equilibrium condition shortly (typically with in 30 days) after a house has been loaded with pressed wood products. A source age of zero also would apply fo r the case of exposures following a major remodeling effort. For the purpose of model calculat ions, 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 relativ ely 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, i f 5 years is entered for the age of sources and 10 years for the length of the exposure period, then th e model will begin calculations with the sources aged 5 years and will continue the calculations unt il the sources have aged 15 years.

Default values for years in lifetime and average body we ight 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 y ears); 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 reflect s the child’s weight at the start of the exposure period. Depending on the length of exposure period that is ch osen, 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 t he user to select a second level of

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

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

individual is not in Zone 1 or Zone 2 within the house. T his 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 sho uld 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 sc enarios 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 distingui sh 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 defaul t, all time in the house is assigned to Zone 1 (where the formaldehyde sources are located by default) a s 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 brea thing rates while in each zone and out of the house. Default values for both time spent and breath ing 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 Scr een for the title of the model run and associated notes, and provides modeled indoor formaldehyde c oncentrations together with exposure estimates. The example screen shot in Figure 2-13, showin g 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 tit le. A button to the right near the top of the screen, labeled “SAVE RESULTS TO MS EXCEL,” can be used to sav e a summary of inputs and results for the current model run. The summary is saved as a comma-de limited file (i.e., with an extension of .csv) that can be opened with Microsoft Excel. On som e 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 Cas e.

Concentration results are listed for both Zone 1 and Zo ne 2 (or just Zone 1 if the user has specified a one-zone house) under two sets of temperature/humidity con ditions – base (left side, fixed at 23 ° C and 50 % RH) and user-specified (right side, as entered on th e House Screen and listed at the top right of the concentration results). Section 3.7 describ es 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 (m g/m 3 ) units.2-30

The initial concentrations reflect the condition sho rtly after a house has been loaded with pressed wood products. As described in Section 3.5, estimates of in itial indoor concentrations due to sources and sinks are decayed exponentially by the model, in acco rdance with a user-specified emissions half life (default of 2.92 years), to develop estimates for subs equent 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 def ault). 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-s pecified 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 l ower than the background concentration (an input on the House Screen). If the value to which the i ndoor concentration is to be decayed is less than or equal to the background concentration, then the m odel 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 ste ady-state is never achieved, due to the dynamics of formaldehyde source emissions and indoor sinks. Formal dehyde sources typically do not emit at a constant rate, but rather at a rate that tends to decl ine over time as the “reservoir” of initial free formaldehyde, coupled with that formed through hydrolysis, i s 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 formalde hyde-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 be en 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 pre ssed wood products.

Exposure estimates (Figure 2-14) are provided for both adult (l eft side) and child (right side) exposure scenarios, based on modeled indoor concentration s under user-specified temperature and humidity conditions. The first two outputs (House Age at St art 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 Avera ge 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 shar e the same numerator – cumulative dose2-31

over the number of years living in the house (input on t he 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 numbe r of years living in the house. Similarly, the

LADC and ADC share the same numerator but have differen t denominators. Further details on exposure calculations, including equations, are provided in Se ction 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 t he 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 calculation s are based on time spent, and concentrations encountered, in the two zones of the house together wit h times and concentrations when the

individual is out of the house. Concentrations in the ho use are calculated by the model and decay over time, whereas the out-of-house concentration is input b y the user on the Exposure Screen and is

assumed to be constant over time.

The example screen in Figure 2-15 shows concentration res ults after some sources and sinks have been added. The inputs chosen for this example correspond t o 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 m

2 ), interior doors (35 m 2 ), cabinets (59 m 2 ) and countertop (4 m 2 , input as industrial particleboard). The sinks (see Figure 2-11) are carpet and paddi ng (94 m 2 ) and painted wallboard (420 m

2 ). The initial concentrations under baseline condition s – 23 ° C and 50 % RH – are 0.051 mg/m 3 (0.42 ppm) in Zone 1 and 0.044 mg/m 3 (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 an d Sinks.

The exposure estimates for the same run (Figure 2-16) are a ppreciably 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 sce nario, 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 concentr ations decline with the passage of time.

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

3. MODEL CALCULATIONS AND ASSUMPTIONS

This section describes the technical basis for the c alculation 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 compon ent 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-w ood products.

The second component of the model is a decay function th at gradually reduces the estimated initial steady-state concentration(s) due to indoor sources and s inks over a specified period of time. The concentrations are reduced in accordance with an exponen tial decay function, using a default decay rate that is based on historical data for formaldehyde level s 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 pri nciple of conservation of mass in an indoor environment, as described in Section 3.1. A model (see S ection 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 formaldehy de emission rates on the prevailing indoor concentration. This model has been extended (see Secti on 3.3) to predict formaldehyde concentrations in two indoor compartments under the same assumption. Whe ther a one-chamber or two-chamber model is used in the calculations depends on the type of ho use 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 repre sent 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 (carpeti ng and painted wallboard). The treatment of sinks and the basis for estimation of sink parameters a re described in Section 3.4.

Section 3.5 describes the basis for the equation used to de cay the initial steady-state concentration(s) over time, and provides examples to illustrate calculatio ns 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 concen tration half life, which is needed to decay the concentration over time. Section 3.7 describes the equat ions used to adjust indoor formaldehyde concentrations calculated by the model, under baseline i ndoor conditions of 23 ° C and 50 % relative humidity, to a new set of user-selected temperature and hum idity 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 environmen t is dependent on two types of factors: (1) those that increase the concentration, such as emiss ions 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 appea r 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 env ironment 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 rat e of change over time in the formaldehyde mass indoors is determined by the rates of generation a nd removal. This principle can be expressed mathematically for an indoor compartment or zone as f ollows:



## ∑ ∑ ∑ ∑

= = ≠ ≠

−

+

− +

− = i Zone in sinks num

p p i i Zone in sources num

k k

i i j

j i ij i j

j j ji i i B i i

i S E C Q C Q C Q C Q dt dC V

1 , 1 , 0 0 (Eqn. 3-1)

where:

V = indoor volume (m 3 )

C = formaldehyde concentration (mg/m 3 )

t = time (hr)

C B = background concentration, which is defined as the outdoo r 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 indoo r zone and outdoors (m

3 /hr)

E i,k = emission rate for formaldehyde release site k in zone i (mg/hr)

S i,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/m 3 ). Conversion between these unit conventions is performe d 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 emissio n sources in a single indoor compartment. The following discussion is in large part excerpted from Matth ews et al. (1983a). The underlying model theory and its derivation are described in Matthews et al. (1983a, 1983b).

At steady state, the formaldehyde (CH 2 O) concentration in a single compartment can be expres sed as

follows:

[CH 2 O] SS = [CH

2 O] out + CH

2 OER/(F * ACH * VOL) (Eqn. 3-2)

where:

[CH

2 O] SS = steady-state formaldehyde concentration inside the

compartment (mg/m 3 )

[CH 2 O] out = steady-state formaldehyde concentration outside the compartment (mg/m 3 )

CH 2 OER = the emission rate of a formaldehyde source inside th e

compartment (mg/h)

F = the fraction of air coming into the compartment th at mixes

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

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

VOL = the volume of the compartment (m 3 ).

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:

[CH 2 O] SS = [CH

2 O] out + CH

2 OER/(PEX * VOL) (Eqn. 3-3)

Application of the model as expressed in Equation 3-3 is sim plified 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 th e compartment. The equivalent of Equation 3-3 for an area-dependent source is:

[CH 2 O] SS = [CH

2 O] out + (CH

2 OER ′ * Area)/(PEX * VOL) (Eqn. 3-4)

with CH

2 OER ′ in units of mg/m 2 -hr and area in m 2

.

Fick’s Law describes the bulk-vapor interphase at the surf ace of a pressed-wood emission source. If one assumes that the mass transport coefficient and th e formaldehyde concentration in the bulk phase3-4

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

source is:

CH 2 OER ′ = -m * [CH

2 O] V + b (Eqn. 3-5)

where:

m = the mass transfer coefficient (m/hr)

[CH 2 O] V = the CH 2 O concentration in the vapor phase (mg/m 3 )

b = a constant; the emission rate at zero CH 2 O concentration in the

air (mg/m

2 -hr).

If the vapor-phase concentration, [CH 2 O] V , is assumed to equal [CH 2 O] SS at steady state, then Equation 3-5 can be substituted into Equation 3-4 to obtain th e following equation:



## [ ] [ ]

D O CH VOL PEX Area b

O CH out

SS 2

2 *

* +

= (Eqn. 3-6)

where:

VOL

PEX Area m D

*

* 1 + =

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

[CH 2 O] SS = [CH

2 O] out + Σ (CH 2 OER ′

k * Area k ) / (PEX * VOL) (Eqn. 3-7)

where the subscript k

refers to the k

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



## [ ] ( ) 

## [ ]

D O CH VOL PEX Area b

O CH out

k k k

SS 2

2 *

*

+

= 

## ∑

(Eqn. 3-8)

where:



## ( )

VOL PEX Area m

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 adapt ed for use with a two-compartment case, by solving appropriate mass-balance equations. The mass-bala nce equation for each compartment, given that sinks can be represented in the model using source te rminology (see Section 3.4), is:



## ∑

= +

− − + = i Zone in sources num

k k

i i ij i i j ji B i i

i S C Q C Q C Q C Q dt dC V

1 , 0 0 (Eqn. 3-9)

where:

V i = volume of compartment i (m 3 )

C i = concentration in compartment i (mg/m 3 )

t = time (hrs)

C B = background concentration, which is defined as the outdoo r concentration plus the contribution from indoor sources other than pressed -wood products (assumed constant) i,j = indoor compartments Q ij = flow rate from compartment i into compartment j (m 3 /hr)

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

Considering the source equation as described in Equation 3-5 f or multiple pressed-wood products in either zone, the sum of formaldehyde sources (and sinks) in each compartment can be expressed as:


# ( ) ∑ ∑ ∑ +

− = =

k k k i k i i k i k i

k k i k i k i Area b C Area m Area OER CH S

, , , , , '

, 2

, * * * * (Eqn. 3-10)

where:

CH

2 OER ′

i,k = unit emission rate of source k located in compartment i (mg/m

2 -hr)

Area i,k = area of source k located in compartment i (m 2 )

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

b i,k = emission rate at zero CH 2 O air concentration for source

k located in compartment i (mg/hr)

C i = CH 2 O air concentration in compartment i (mg/m 2 ).

Considering the combined Equations 3-9 and 3-10 for each compartment, and solving simultaneously for the steady-state condition (see Appendix A), th e following equations are obtained:



## ( ) ( ) ( )

2 1 21 1 20 1 2 12 20 12 2 10 21 10 20 10 2 21 1 2 21 20 02 21 2 01 21 01 20 01 ,1 z z Q z Q z z Q Q Q z Q Q Q Q Q y Q y z Q Q C Q Q z Q Q Q Q Q C B
SS + + + + + + + + + + + + + +

= (Eqn. 3-11)



## ( ) ( ) ( )

1 2 12 2 10 2 1 21 10 21 1 20 12 20 10 20 1 12 2 1 12 10 01 12 1 02 12 02 10 02 ,2 z z Q z Q z z Q Q Q z Q Q Q Q Q y Q y z Q Q C Q Q z Q Q Q Q Q C B

SS + + + + + + + + + + + + + +

= (Eqn. 3-12)

where:3-6 SS = indicates the steady-state solution

z 1 = k

Zone in sources num

k k Area m 

# ∑

= 1

1 for the k

sources located in compartment 1

y 1 = k

Zone in sources num

k k Area b 

# ∑

= 1

1 for the k

sources located in compartment 1.

z 2 = k

Zone in sources num

k k Area m 

# ∑

= 2

1 for the k

sources located in compartment 2

y 2 = k

Zone in sources num

k k Area b 

# ∑

= 2

1 for the k

sources located in compartment 2.

3.4 Treatment of Indoor Sinks

The treatment of indoor sinks in the calculation mo dule 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*[CH 2 O]

v ) is in the same form as a first-order sink represe ntation. The second component ( b ) is a constant, representing a constant emission r ate. By setting b equal to zero and m to a nonzero value, this “source” representation actua lly reflects the behavior of a first-order sink. Alternatively, setting m to zero and b to a nonzero value represents a product as a const ant 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 mat erial that acts as a sink. However, this simplistic approach does not allow a fully realistic representation of the re-emission f rom sinks that has been observed in laboratory and fiel d 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 ten d to accumulate mass when air concentrations are high, a nd 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 concentrati on and the mass residing in the sink at that point, as well as other sink characteristics.

The complex relationships described above are not f ully captured by the sink representation that is us ed in the model. On the other hand, the sink represent ation is believed to be indicative of a sink’s beha vior around the time, usually within 30 days after insta llation of source and sink materials in a residence

, when the time-varying indoor concentration has reac hed its maximum value and is changing at a relatively slow rate.

Default parameter values for sinks in the model hav e been derived from an analysis of data collected f or conventional house 1. There were two major types of potential sinks in this house – carpeting and painted wallboard. As noted above, sinks can be rep resented in the model using the same parameters as used for sources. The Langmuir isotherm model desc ribed in the formaldehyde pilot study report (Koontz et al. 1996) was used to develop default pa rameter estimates for sinks. With this type of3-7

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

M k C k dt dM

d

a − = (Eqn. 3-13)

where:

M = mass per unit area of sink, mg/m 2

k

a = adsorption rate constant, m/h

C = indoor formaldehyde concentration, mg/m 3

k d = desorption rate constant, h -1

.

Estimates for the adsorption and desorption rates w ere developed by fitting air-concentration data fro m several small-chamber tests to the corresponding La ngmuir isotherm mass-balance equation for the chamber. The adsorption rate for the Langmuir isoth erm 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 sin k (mg/m

2 ), as in the above equation, the resultant product has units of mg/m 2 -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 const ant) indoor-air concentration was found, by running the Langmuir model to steady state for diff erent indoor-air concentrations. This procedure was used to determine appropriate values for the interc ept 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 approp riate value for the intercept, under an assumed equilibrium condition, was about 0.0375 mg/m 2 -h per 10 ppb indoor-air formaldehyde concentration (i.e., 0.0375 mg/m 2 -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 t hat an appropriate value for the slope was -1.3 m/h and that an appropriate intercept value was about 0 .016 mg/m 2 -h per 10 ppb of indoor concentration. The default intercept value for an initial conditio n for carpeting (0.003 mg/m 2 -h), intended to represent a point in time before the sink has accumulated anysignificant 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 defa ult intercept value for an initial condition for pa int (0.004 mg/m

2 -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 conc entration, as calculated by the model described above, is assumed to decrease over time as the rese rvoir 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

B i B t e

C C C C

−

+ = (Eqn. 3-14)

where:

C

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

C B = background concentration (ppm), which is defined as the outdoor concentration plus the contribution from indoor sou rces other than pressed-wood products (assumed constant)

C i = initial concentration indoors (ppm)

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

The value of k

is determined from the user-specified half life fo r the indoor formaldehyde concentration, assumed to be dominated by an expone ntial decay in formaldehyde source strength. Solving for t

results in the following equation:

k C C C C

t B

t B i      

− −

= ln

(Eqn. 3-15)

Or, solving for k

results in the following equation:

t C C C C

k B

t B i      

− −

= ln

(Eqn. 3-16)

Neglecting for the moment the background contributi on to the indoor concentration (i.e., assuming that the background concentration is zero), Equation 3-1 6 reduces to:

t C C

k t

i      

= ln (Eqn. 3-17)

By definition, C t is equal to half of C i 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 2 ln

= (Eqn. 3-19)

Substituting the default half life of 2.92 years (s ee 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 ea ch zone) are calculated by the decaying only the porti on of the indoor concentration that is attributable to indoor pressed-wood products. For example, to obtai n 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) = C

B + (C i - C

B ) e -0.237*0.25 (Eqn. 3-20)

If C i were 0.05 ppm and the outdoor concentration were z ero, for example, then the indoor concentration 3 months later would be 0.047 ppm. Sm all outdoor concentrations, which typically would be the case, have a minor impact on the relat ionship. For example, with an outdoor concentration of 0.001 ppm, the indoor concentratio n would be 0.051 ppm initially and 0.048 ppm

after 3 months.

Given an initial concentration greater than 0.01 pp m and assuming an outdoor concentration of zero, the time required to reach 0.01 ppm can be determin ed from the first-order exponential process using Equation 3-15 as follows:

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

Continuing with the above example where k is 0.237 years -1 and C i 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 mon ths.

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

B i      

− −

= 01.0 ln

(Eqn. 3-23)

The result from Equation 3-23 is multiplied by 12 a nd reported in months. If the highest initial indoo r concentration is lower than 0.01 ppm, then zero mon ths is reported as the time required for the indoor concentration to decay to 0.01 ppm. The same equati on is used to calculate the time required for the highest indoor concentration to decay to a user-spe cified concentration of concern (COC).3-10

3.6 Default Value for Half Life

Ideally, an appropriate half-life value for represe nting 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 a nd sinks would not change throughout the measurement period, and factors such as indoor temp erature and humidity, as well as the indooroutdoor air exchange rate, would change only minima lly in response to outdoor weather conditions and occupant activities indoors. Further, the experimen t would be repeated in several houses. The data for each house then would be analyzed to fit a nonlinea r (e.g., exponential) decay function to the timevarying indoor concentrations, and the resultant es timates 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 n eed to restrict certain occupant activities over several years (or to operate a research house to ga in experimental control), would be prohibitive. There are two practical alternatives to the ideal e xperimental situation, both of which have been attempted: (1) collect or assemble point-in-time me asurements from houses of varying ages, as a proxy for the time-related decay in one or a series of ho uses; and (2) conduct chamber tests at periodic poi nts 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 o f a single house, or of a limited set of wellcharacterized houses – the analysis is confounded b y varying, and generally unknown, construction features, occupant activities and weather condition s at the times of measurement. Chamber tests, on th e other hand, have the advantage of careful experimen tal control. However, for multiple tests over time, the material to be tested typically would not be ke pt in the chamber-controlled environment throughout the testing period, but rather during only the rela tively 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 rap id for a single material, because other materials are not present to increase the formaldehyde concentration and thereby retard its rate of formal dehyde release. Limited tests of material ensembles have been conducted, but none have included the ful l array of sources and sinks that typically would b e present in an occupied house. With these limitation s 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 e stimates below 5 years. These estimates have been based largely on pooled cross-sectional data across a variety of residences, as a proxy for time-serie s data from one or a few houses. It is noteworthy tha t the higher estimates (20 to 44 years) are from da ta sets involving houses aged from new to 50 years, wh ereas 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 furnishing s 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 b e expected to eventually decay to some background level, similar to that if no sources wer e present. As a house ages, however, occupants will tend to add or replace materials and furnishings, s ome of which may emit formaldehyde. Such changes,3-11

then, will introduce new sources, thereby raising t he formaldehyde concentration relative to the nochange case and artificially inflating the half-lif e 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 th e half-life estimate ranged from 2.0 to 2.6 years. A careful analysis by Versar (1988) of a cross-sectio nal 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 lif e in a house that has some significant formaldehyde source s from the outset of its construction and occupancy history.

Chamber studies to investigate the decay of formald ehyde have focused primarily on individual sources, and not surprisingly have produced shorter half-lif e estimates than most residential studies. As summarized in the same Versar (1988) report, the es timated half lives from chamber studies have ranged from 0.2 to 2.58 years. One noteworthy inves tigation, conducted by Matthews et al. (1985), involved a combination of sources (particleboard, h ardwood plywood paneling and MDF) under controlled environmental conditions (23 ° C and 50 % relative humidity). The “slow” decay st udy, with an air exchange rate of 0.4 air changes per hour (A CH) in the chamber, produced a half-life estimate o f 1.52 years. The “fast” decay study was conducted wi th 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, th us, shorten the decay periods relative to the “slow ” decay study. Resultant half-life estimates were 0.7 6, 0.62 and 1.08 years for particleboard, paneling and MDF, respectively.

Of the two decay studies by Matthews et al., the “s low” study is believed to be more indicative of formaldehyde behavior in residences. However, the a uthors add the caution that care should be taken in interpreting the study results. For example, the du ration of the study may have been inadequate to accurately measure the emission decay period for th e 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 combinati on of relatively strong and weak emitters, or of sources and sinks.

For the various reasons noted in the above review a nd discussion, there is considerable uncertainty as to the most appropriate value to represent the cent ral tendency for the decay rate of formaldehyde, in a residence where construction features, house conten ts and occupant activities remain relatively stable

over time. The cross-sectional data from residentia l 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 a re believed to yield estimates erring in the opposite direction.

The collective evidence indicates that an appropria te half-life value probably lies between 1.5 and 3. 0 years. The default value currently provided with th e model – 2.92 years – will tend to err on the conservative side. That is, assuming that the initi al concentration in a house is predicted accurately , the 2.92-year value likely will cause the modeled conce ntration 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 forma ldehyde are continually being brought into homes3-12

as they age.” Examples would include installation o f new kitchen cabinets when remodeling or addition of new furnishings such as furniture or shelving th at may contain pressed-wood products. To the extent that such situations exert an upward bias on half-l ife estimates that are based on an analysis of home s 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 th at involved chamber testing of a collection of pressed-wood products as they aged. One (Matthews e t 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 th is 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 w ith the conditions under which most chamber tests have been conducted, in accordance with ASTM standa rd 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 humi dity conditions.

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

( ) [ ]

U B T T R

T 

### e C C 1

1

0 − 

### = (Eqn. 3-24)

where:

C T = Temperature-adjusted formaldehyde concentration

C 0 = Formaldehyde concentration at the baseline tempe rature

R = Temperature coefficient for adjustment

T U = User-specified temperature, ° K

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

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



## ( )

U B T

TH H

H A C C

− + = 1 (Eqn. 3-25)

where:

C TH = Temperature- and humidity-adjusted formaldehyde c oncentration

C T = Temperature-adjusted formaldehyde concentration

A = Humidity coefficient for adjustment

H U = User-specified relative humidity, %

H B = Baseline relative humidity, 50 %.

Combining equations 3-24 and 3-25, the temperature- and humidity-adjusted concentration can be expressed as follows:

TH TH K C C 0 = (Eqn. 3-26)

where K

TH is the combined temperature and humidity adjustmen t factor:

( ) [ ] 

## ( )

U B T T R

TH H

H A e K U B

− + = −

1 1

1 (Eqn. 3-27)3-13

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

sets of default values. The first set of coefficien ts was calculated by Berge et al. (1980) for two Norwegian particleboard specimens. These coefficien ts were used by HUD in setting the 1984 standards for particleboard and hardwood plywood pa neling, 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. we re 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 Myer s (1985), who reviewed the extant literature and developed his recommended temperature coefficient b ased 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 humid ities in the tests on which the correction factor w as based ranged from 20 to 90 percent. Thus, his work encompassed more products and wider temperature/humidity ranges than the Berge et al. s tudy. It is worth noting that the HUD standard was promulgated before Dr. Myers completed his work. Hi s 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 adjustmen t applied to the two-zone concentrations calculated using equations 3-11 and 3-12 takes the following form:



# ( )

B

TH B SS adjusted SS 

### C

K C C C +

− = ,1

, ,1 (Eqn. 3-28)



# ( )

B

TH B SS adjusted SS 

### C

K C C C +

− = ,2

, ,2 (Eqn. 3-29)

Similarly, the adjustment applied to the one-zone c oncentration calculated using equation 3-8 takes th e following form:



## [ ] [ ]



## ( )

B TH B SS adjusted SS 

### C K C O CH O CH +

− = 2

, 2 (Eqn. 3-30)

3.8 Exposure Calculations

As noted in Section 2.6, the model calculates the f ollowing exposure metrics:

• Lifetime average daily concentration (LADC) and ave rage daily concentration (ADC)

• Lifetime average daily dose (LADD) and average dail y dose (ADD)

• Percent of time at or above 0.01 ppm and a user-spe cified COC.

To determine the LADC and ADC values, the model fir st 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 her e is that the indoor concentration is constant over3-14

any 24-hour period. In actuality, there will be a m arginal concentration decrease throughout the day due to the long-term formaldehyde decay indoors.

The average concentration ( C average )for any given day is a weighted average of the con centrations 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 di ffer for weekdays vs. weekend days):

C average = (C 1 * F

1 ) + (C

2 * F 2 ) + (C

out * F out ) (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 si mply 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 ca lculation shares the same numerator but has a denominator of length of lifetime, in days.

To determine the LADD and ADD values, the model fir st calculates the daily dose ( D daily ) at each location (Zone 1, Zone 2 and out of the house):

D daily = C

daily * BR daily * TS daily (Eqn. 3-32)

where:

C

daily = Daily-average concentration at location, mg/m 3

BR daily = Breathing rate at location, m 3 /hr

T daily = Time spent at location, hr

The daily dose per location, in mg, is summed acros s locations to get total daily dose. The total dail y doses are then summed over the entire exposure peri od. 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 p pm (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 accumula ted hours, across the three locations and over the entire exposure period, are then divided by the len gth of the exposure period, in hours, and multiplie d by 100 to express the result as a percent.4-1

4. SUMMARY OF EPA FORMALDEHYDE PILOT STUDY 1

4.1 Study Objectives and Design

At a public meeting in January 1993, EPA representa tives 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 S tates. A smaller pilot study was to be conducted first to evaluate the feasibility and logistical co nsiderations of the experimental design for the lar ger main study

.

In September 1994 the National Particleboard Associ ation (NPA) signed a Cooperative Research and Development Agreement (CRDA) with EPA to fund a pil ot 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 mate rials 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 si ngle-family house and in several

manufactured houses.

• Demonstrate that experimental variables or conditio ns 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 acros s a range of different experimental conditions, similar to that which can be present in new houses.

• Estimate the extent of variability of the experimen tal results and the variation with changes in experimental conditions.

• Determine how to account for, or to eliminate or mi nimize, residual formaldehyde carryover between test runs in the conventional hou se due to effects of inherent sinks.

• Evaluate the ability to control and vary the air ex change 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 variable s, monitoring protocols, and quality assurance/control procedures that would be employed . According to the QAPP, the pilot study would include one unoccupied, conventionally built, singl e-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-hou se portion of the pilot study eventually was dropped due to resource limitations.

1 Portions of this section have been extracted or ad apted from Hare et al. (1996) and Koontz et al (199 6).4-2

The QAPP also specified that the following variable s 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 construct ed 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 control led variable, was targeted at 50 percent. Air leaka ge was to be determined through blower-door tests, wit h efforts to make the house as airtight as possible

. Ventilation rates were to be controlled by a mechan ical heat recovery ventilator (HRV) attached to the heating and air conditioning system (HAC). Air exch ange rates were to be measured by two tracer gas methods – constant release of perfluorocarbon trace rs (PFTs, EPA Method IP-4A; USEPA 1990) and periodic injection/decay of sulfur hexafluoride (SF 6 , 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 a ny 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 ho use. The house would be allowed to “air out” for a period of time until a new equilibrium level (bas eline) was reached, after which the next set of products would be installed. The order of the loadi ng configurations in the house was to be randomized, with the single constraint that Loading s 1 and 2 would be different (i.e., one High and on e Medium).

Indoor and outdoor formaldehyde concentrations (24- hour time-integrated values) were to be measured by EPA method IP-6A (Solid Adsorbent Cartr idge; USEPA 1990) 7, 12, 28, and 33 days after products were installed in the house. If nece ssary, additional testing could take place to confi rm any trends or unexpected results. Readings on days 12 and 33 were considered statistical replicates of readings on days 7 and 28, respectively. Indoor for maldehyde concentrations were to be measured in the kitchen, living room, upstairs bedroom, basemen t, 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 la rge chamber in accordance with ASTM E 1333, at three different air exchange rates. Because there w ere no established protocols for large-chamber testing of doors and cabinets, the following loadin g rates were be used:

• Doors – five doors, at a total loading rate of 0.12 5 ft 2 /ft 34-3

• Kitchen cabinets/countertops – one base and one wal l cabinet with doors closed, at a loading rate of 0.133 ft 2 /ft 3 . A section of countertop was to be placed on the b ase cabinet during testing.

The above loading rates were similar to those estab lished by the Department of Housing and Urban Development (HUD) for large-chamber testing of part icleboard 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 concen tration of formaldehyde gas was to be injected into the chamber. By accurately measuring time-vary ing concentrations in the chamber, it could be determined whether the material was absorbing forma ldehyde 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 t o participate in the study proved to be more difficult and costly than anticipated, due mainly t o the constraint that the house could not be occupi ed 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 ft 2 , twostory Cape Cod style with a full basement (volume o f 168 m 3 ). The QAPP had called for a house with crawl space, but efforts to find such a house in th e study area were unsuccessful. The total volume of the finished living space was 10,746 ft 3 (304 m 3 ). The first floor of the house (712 ft 2 floor area) had

5931 ft 3 (168 m

3 ) of living space that consisted of a living room, kitchen, bathroom/laundry room, and bedroom. The second floor of the house (614 ft 2 floor area) had 4815 ft 3 (136 m 3 ) 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 enti re project. The house contained no furniture or draperies.

Industry representatives were responsible for procu ring all pressed-wood products that would be used in the pilot study. Sufficient quantities of 5/8” p articleboard underlayment, 3/4” industrial particle board for countertops, 1/4” hardwood plywood wall panelin g (3-ply birch face, tropical hardwood back and core with 7 cut grooves along the length of each pa nel 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 lo cal building supply centers. Emission characteristi cs of the particleboard and plywood wall paneling used in the study were determined prior to selecting th e materials for testing.

Initial emission characteristics of the products us ed 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 we re 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 m anufacturers’ recommended installation instructions, and conventional practices were follo wed. 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 min imize 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, ft 2 /ft 3

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 i n Table 4-2. For the Medium loading scenario, particleboard underlayment was installed on the fir st floor, along with interior doors on both floors and

a full set of kitchen/bathroom cabinets and counter tops. For the High loading scenario, particleboard underlayment was installed on both the first and se cond 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 installe d in an upstairs bedroom, in the downstairs bedroom

, and in the living room. Interior doors and a full s et of kitchen and bathroom cabinets and countertops (same number as for Medium loading) also were insta lled. The total exposed surface area for cabinets

was calculated to be 631 ft 2 (59 m 2 ). Particleboard underlayment was not installed in the kitchen and bathroom areas of the house, as those areas were co vered by vinyl sheet goods that had been permanently installed during final preparation of t he house before field testing was initiated.

Table 4-2. Loading Areas for Pressed-wood Products at the Convent ional House

Loading Area, ft 2

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 nume rous leaks in the building shell and between the first floor and basement. Air leakage sites were id entified (service penetrations between the basement and first floor and along the base plate) and seale d with caulk and foam. Numerous leaks also were found in the forced-air HAC distribution system. Se aling procedures reduced the leakage rate by more than 50 percent, from ~ 10 ACH at 50 Pa (correspond ing 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 hous e sealing procedures and a closed interior door at the top of the stairwell to the basement would mini mize air communication with the remainder of the house. However, during tracer gas studies to charac terize the air exchange rate for the house it becam e obvious that tracer injected into the living area w as being transferred to the basement. Consequently, it4-5

was decided to include formaldehyde measurements in the basement. In addition, PFT sources and samplers were configured so that the average airflo w rate between the basement and living area could be quantified during each sampling event.

Following initial baseline testing, products for Lo ading 1 (Medium) were installed and indoor

concentration levels were measured in accordance wi th the protocols outlined in the QAPP. It became evident during this time that there was difficulty in controlling relative humidity levels in the hous e, which reached over 70 percent. Humidity levels were lowered to the desired range by adding additional dehumidification equipment in the house. Because hi gh 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 conditio ns stabilized. The final readings for Loading 1 wer e taken 78 days after product loading.

It also was determined during this time that resour ce 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 an d two High loadings. In addition, the air-out period between successive loadings was fixed at sev en days instead of waiting for formaldehyde levels to reach equilibrium.

Following the removal of Loading-1 products from th e house and a seven-day airing-out period, Loading-2 (High) products were installed. Formaldeh yde 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. F ormaldehyde 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 conduct ed as part of the pilot study. From results of the laboratory sink-test results and results from Loadi ngs 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 charact erize the sink effect behavior of painted gypsum wallboar d. It also was considered important to determine whether the carpet/padding used in the house was ac ting as a sink or had any barrier effect on formaldehyde emissions from the particleboard under layment.

The original protocol for “barrier testing” was mod ified to evaluate the floor system with both particleboard underlayment and carpet/padding, inst ead of just the carpet/padding. A sample of particleboard underlayment was placed in a stainles s-steel pan and inserted in a small chamber. Formaldehyde concentrations in the chamber were mea sured continuously with a real-time (Interscan) analyzer. As a separate test, a second sample of pa rticleboard with carpet/padding directly above it w as 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 t he carpet/padding used in the pilot study. To minim ize the inherent variability within a piece of particle board, specimens used for these tests were prescree ned via small-chamber emission tests (ASTM 1996b) – the two pieces with the closest emission rates were

used for the tests.

4.3 Study Results4-6

The results of formaldehyde, temperature, humidity and air-exchange measurements during the formal “runs” associated with each loading, as well as the ir respective baseline periods, are compiled in Tab le 4-3. Formaldehyde concentrations measured in the up stairs 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). T he monitoring results collectively indicate that, f or all three loadings, indoor HCHO concentrations had peaked by the time of measurements taken 33 days after product loading. The formaldehyde results als o indicate that monitored levels for Loadings 2 and 3 generally were consistent with one another and th at these “high” loadings had higher HCHO levels (but also a higher baseline) than the “medium” load ing (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 SF 6 . One possible reason for the discrepancy is

the inherent difference between the two measurement technologies. The SF 6 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 tim e-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 SF 6 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 occurr ed 12 days after product loading; BR = bedroom; BMT = basement; Run 3 occurre d 28 days after product loading; AMB = ambient; 2ND = second floor. Run 4 occur red 33 days after product loading. Upstairs measurements (average of kitchen, living r oom and bedroom locations) for the three loadings are plotted in Figure 4-1 against elapsed time afte r UF-bonded wood products were installed (day “zero” indicates baseline measurements). The curvat ure of the lines is due to the spline fit that was applied and is not meant to imply that values betwe en measurement points can be readily interpolated.4-7

The figure illustrates the general consistency acro ss Loadings 2 and 3 and their differences from Loading 1. Although concentrations for Loading 1 ar e similar to those for Loadings 2 and 3 toward the end of their respective test periods, indoor humidi ty levels were relatively high near the end of Load ing

1.

Figure 4-1. Upstairs Formaldehyde Concentrations over Time for T hree Loadings.

Differences in baseline levels and in the general s hape of the time series for Loading 1 versus Loadin gs 2 and 3 can be explained partly by the wallboard si nk effect. The wallboard sink was largely “empty” a t the outset of Loading 1 but was largely “pre-loaded ” at the outset of Loadings 2 and 3, as reflected i n 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 sin k (wallboard) has been pre-loaded and becomes a “net zero emitter,” such that the declining rate of emissions from aging wood products drives the conce ntration profile. For Loading 1, however, this profile is dampened by the relatively large mass be ing absorbed by the wallboard sink in an “unloaded”

state. Some of the difference in baseline values fo r Loading 1 versus Loadings 2 and 3 also may be due to the relatively low humidity level at the time wh en baseline measurements were taken for Loading 1. The key measurement parameter for the study, formal dehyde 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 ±2 0 percent. Results of duplicate DNPH samples indicated a combined sampling and analytical precis ion 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 e lapsed time since loading of UF-bonded wood 0 10 20 30 40 50 60 70 80

0 5 10 15 20 25 30 35Formaldehyde Concentration, ppb

Time from Loading, days Loading 1

Loading 2

Loading 34-8

products, was not much larger than that for duplica te measurements (i.e., at the same time and locatio n within any given loading). This finding points to t he 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 wer e 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 proporti onal to the increase in air exchange. This trend is indicat ive of a concentration “backpressure” effect, as ap plied 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, eve n though products were wrapped in plastic. The elevated temperature in the warehouse may have acce lerated the decay process somewhat.

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

Emission Rate, μg/m 2 -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 gi ven 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 t he study house, the manufacturer’s data indicated that the wallboard paint contained 0.001% formaldeh yde by weight and the door paint contained 0.007% formaldehyde. A carpet/padding sample was se nt to EPA’s Air and Energy Engineering Research Laboratory (AEERL) in Research Triangle Pa rk 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/m 2 -h for the carpet and the same rate for the padding (after subtracting the chamber background) at4-9

an elapsed time of 24 hours following insertion in the chamber, or an emission rate of 2.8 μg/m 2 -h for

these two constituents combined. The combined emiss ion 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 r ates 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 e qual to the depth of the carpet and padding. The pa n containing the carpet and pad was then placed horiz ontally on the chamber floor. The chamber was sourced with a formaldehyde stream of 0.2 ppm durin g 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 proc ess.

Chamber tests for gypsum wallboard were conducted t o 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. Th e wallboard was then placed in the center of chamber in a vertical position, supported by stainl ess steel wire. The chamber was sourced with a formaldehyde stream of 0.2 ppm during the first tes t 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 abo ve 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 horizontall y on the chamber floor. The resulting data indicate d 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 em ission of formaldehyde, the carpet/padding sink tes t
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 greate st 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 stu dy, but was considered to be an important covariate that should be tightly controll ed. 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 cooperat ion from various industry representatives and their close working relationship with the study team.

• Little difficulty was encountered in controlling mo st experimental variables at the study house. The primary variables – product loading rate , emission rate, temperature, and air exchange – all were generally kept within their res pective target ranges. Some emissions decay was evident for wood products stored for succ essively later loadings.

• It was demonstrated that different test results cou ld be obtained across different experimental conditions and that sufficient precisi on in measurement response could be obtained. Differences across the experimental condi tions (medium versus high loading) could be distinguished, although these differences were partially dampened by the substantial sink effect of the gypsum wallboard. Ap propriate precision was obtained largely because of the consistently high resolution, accura cy and precision for the sampling method (solid adsorbent cartridge) with a 24-hour sampling duration.

• The study data were marginally sufficient for estim ating the extent of variability of results and the variation with changes in experimental cond itions. 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 marginal ly 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, d ue 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 b aseline formaldehyde values were reasonably reproducible once the house had been loa ded with UF-bonded wood products.

• The ability to control and vary the air exchange ra te of the conventional house using a heat recovery ventilator (HRV) was demonstrated. This ab ility was demonstrated for two of the three target air exchange rates (0.2 and 0.5 ACH) p lanned for the full study; the third target (1.2 ACH) could not be addressed because the HRV la cked sufficient capacity. Achieving the lower target of 0.2 ACH was made possible by se aling 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 tw o perspectives: (1) independent checks on the correctness of model algorithms; and (2) comparisonof model predictions with measurements in realworld situations.

5.1 Mathematical Correctness of Model Algorithms

An Excel spreadsheet has been developed as a tool f or assessing the mathematical correctness of algorithms used in the model. The Excel tool includ es individual sheets for inputs corresponding to model input screens – House, Source, Sinks and Cabi nets – together with a separate sheet that displays the calculation results (predicted HCHO co ncentrations). Input areas within each screen are set up similarly to those in the model, with the ex ception that no drop-down selections are provided for sources, sinks or cabinets. Instead, input area s (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/m 3 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 back ground concentrations, sources, sinks and cabinets, for both one-zone and two-zone implementa tions. This exercise led to discovery of minor errors in the handling of ppm vs. mg/m 3 units for the background concentration and in the temperature/humidity adjustment for indoor formalde hyde concentrations. Other than those discrepancies, the results agreed exactly in all ca ses. The errors discovered in the model’s calculati on routine have been corrected.

5.2 NIST Assessment of Matthews Model Predictions

An effort was undertaken by researchers (Silberstei n et al. 1988) at the National Institute of Standar ds and Technology (NIST) to validate the Matthews mode l 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 H CHO 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 panelin g, behaved as the emission model predicted over a large concentration range, under both sets o f temperature and relative humidity. Good agreement was also obtained between measured formal dehyde concentrations and those predicted by a mass-balance indoor air quality mode l.

The mass-balance model referenced here is the Matth ews model. The following excerpt, taken directly from the authors’ conclusions, provides so me further insights on model performance:

In developing its models, ORNL assumed that there i s relatively free formaldehyde diffusion within the "bulk phase" of pressed-wood products. F ormaldehyde emission results from the difference in concentration between this "bulk phas e" and the atmosphere, in accordance with Fick's first diffusion law. This assumption is appa rently fairly descriptive of particleboard and5-2 mdf, but not of hardwood plywood paneling. It is hy pothesized 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 emissio n may not be as diffusion-limited in plywood as it is in other pressed-wood products. Th is 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 deg radation 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" for maldehyde 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 ge nerally are much higher HCHO emitters than plywood or hardwood plywood paneling. Thus, the NIS T validation effort indicated accurate model predictions for the major HCHO emitters among press ed-wood products.

5.3 Assessment of Predictions by the Current Model

An assessment undertaken by the author of this docu ment 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 produ cts. The assessment was conducted by using known/measured factors such as zone volumes, airflo w rates, indoor temperature and humidity, and source/sink loading areas together with estimates o f 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 loadin g, air-out after first loading, second loading, air -out after second loading, and third loading. Inputs sup plied for model input screens – House, Sources and Sinks – are described in a general manner below. Fu rther details specific to each of the six cases are given in the subsections that follow.

The house screen requires inputs for the type of ho use, the zone volumes and airflow rates, the background formaldehyde concentration, and the indo or temperature and humidity conditions. The house used for the pilot study – Conventional 1 – w as selected. Airflow measurements with PFTs on 14 different occasions during the pilot study avera ged 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 dur ing 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 mo del 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 ch osen 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 humid ity coefficients provided with the model, for adjustment of modeled formaldehyde concentrations f rom 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 – under layment, kitchen/bathroom cabinets, interior doors, and hardwood plywood – were chamber tested under th ree different air exchange rates as part of the pilot study. Source loading areas for the model run s are described later as they pertain to each

modeled case.

There are two major types of potential sinks in con ventional 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 t he 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 fo r each of the six modeled cases are described

below. The results of this evaluation exercise coll ectively indicate that the modified (two-zone) Matthews model can predict measured values quite we ll for the conventional house, but errs somewhat on the conservative side (i.e., it tends t o “over-predict”). The greatest area of uncertainty in applying the model appears to be in choosing app ropriate values for indoor sinks. One additional area of uncertainty stems from the fact that humidi ty levels were not measured downstairs; as noted previously, upstairs values for temperature and hum idity were used in constructing the model inputs.

5.3.1 Initial Baseline Period

Model inputs for this period are summarized in Tabl e 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 plywoo d was taken as the product of the upstairs volume (304 m

3 ) and an assumed loading ratio of 0.43 m 2 /m 3 , or 131 m

2 . For wallboard the loading ratios for walls (0.95 m

2 /m 3 ) and ceilings (0.43 m 2 /m 3 ) were used to estimate a total area of 420 m 2 . Model source/sink parameters (intercept and slope) were t aken from the model defaults for softwood plywood. An intercept value of 0.04 mg/m 2 -h was chosen for wallboard after running the model with plywood only and obtaining an indoor formaldehyde c oncentration in the vicinity of 10 ppb.

Table 5-1. Model Inputs (Sources and Sinks) for Initial Bas eline Period

Source/Sink Slope (m/h) Intercept (mg/m 2 -h) Area (m 2 )

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 downst airs, close to the measured values of 9.5 and 9.1 ppb for the resp ective 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 wallboar d5-4

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 h alved (to 0.02 mg/m 2 -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 monitori ng 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 include d as a source because it was covered by underlayment or by floor tile. Loading areas for th e 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 cou ntertop, industrial particleboard was selected to obtain slope/intercept parameters (average values w ere used). The intercepts chosen for carpeting and wallboard were predicated on an indoor-air concentr ation near 40 ppb.

Table 5-3. Model Inputs (Sources and Sinks) for First (Me dium) Loading

Source/Sink Slope (m/h) Intercept (mg/m 2 -h) Area (m 2 )

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 4205-5

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 c oncentrations 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 cond itions, with carpeting and wallboard included, were 5-10 ppb higher than measured values under tho se 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 wo uld be lost during the air-out period, which lasted 7 days, but the amount lost was uncertain. Conseque ntly, the intercept for the first loading (see Tabl e 5-5) was used as an upper bound when developing inp uts and half this value was used as a lower

bound.

Table 5-5. Model Inputs for Air-out Period after First Loadi ng

Source/Sink Slope (m/h) Intercept (mg/m 2 -h) Area (m 2 )

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 th e alternative intercept values for wallboard

surround the measured values. The model estimates w ith the smaller intercept value, to account for the likely possibility that the wallboard had relea sed 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, bu t with a larger area for underlayment and with the ad dition 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 a ny sinks.

T able 5-7. Model Inputs (Sources and Sinks) for Second (High ) Loading

Source/Sink Slope (m/h) Intercept (mg/m 2 -h) Area (m 2 )

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 measure ments 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 f irst loading. The modeling results without sinks were 70-75 ppb upstairs and 60-65 ppb downstairs. T he addition of carpeting and wallboard as sinks5-7

lowered the modeled values by about 10 percent. The modeled values with sources and sinks were about 10 ppb higher than those measured upstairs (d ifferences similar to those for the first loading), and about 15 ppb higher than the measured downstair s 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, th e only sources and sinks again were plywood and wallboard (Table 5-9). As with the first air-out pe riod, it was necessary to account for the fact that the wallboard had adsorbed mass during the second l oading and then had lost some of this mass during the air-out period. To accommodate uncertain ty 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 lowe r bound.

Table 5-9. Model Inputs for Air-out Period after Second Loadi ng

Source/Sink Slope (m/h) Intercept (mg/m 2 -h) Area (m 2 )

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 alte rnative intercept values for wallboard surround the measured values, and the model estimates with t he smaller intercept value are closer to the measurement results. This pattern is the same as th at 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 inpu ts 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 (Hi gh) Loading

Source/Sink Slope (m/h) Intercept (mg/m 2 -h) Area (m 2 )

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 da y 7), and the measured values for run 1 therefore were used as a basis for comparison with modeling r esults. The modeled values were about 10 ppb higher than measured upstairs but about 25 ppb high er downstairs (Table 5-12). One possible explanation for the greater difference downstairs i s 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)

-- -- 72 436-1



### 6. REFERENCES

ASTM. 1996a. Standard Test Method for Determining F ormaldehyde Concentrations in Air and Emission Rates from Wood Products Using a Large Cha mber. Designation E 1333-96 (Reapproved 2002), American Society for Testing and Materials, Philadelphia, PA.

ASTM. 1996b. Standard Test Method for Determining Formaldehyde C oncentrations 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 T esting Program: Pilot Study, Quality Assurance Project Plan. Report No. IE-2695, prepare d by GEOMET Technologies, Inc. for the

USEPA Office of Pollution Prevention and Toxics und er Contract No. 68-D3-0013.

W. Groah and G. Gramp. 1988. An Estimate of Home Oc cupant Exposures to Formaldehyde Gas from Plywood and Reconstituted Wood Products Bonded with Formaldehyde Based Adhesives. CPA/HPVA 1988 Exposure and Assessment Package Repor t, Hardwood Plywood and Veneer Association, Reston, VA.

W. Groah. 2005. Decay or the Decrease in Formaldehy de Concentrations or Emissions over Time and UF-bonded Wood Panel Products. Report prepared for the Composite Panel Association, Formaldehyde Council Inc., Hardwood Plywood and Ven eer Association, and the Kitchen Cabinet

Manufacturers Association.

D. Hare, R. Margosian, W. Groah, S. Abel, G. Schwee r, and M. Koontz. 1996. Evaluating the Contribution of UF-bonded Building Materials to Ind oor 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. Ni ang. 1996. Residential Indoor Air Formaldehyde Testing Program: Pilot Study. Report N o. IE-2814, prepared by GEOMET Technologies, Inc. for the USEPA Office of Pollutio n 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 Resi n Containing Products: Potential Impact on Indoor Formaldehyde Concentration and Possible Corr ective Measures. Proceedings of ASHRAE Symposium “Management of Atmospheres in Tightly Enc losed 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. Tho mpson, J. Simpson, and A. Hawthorne

. 1985.6-2

Modeling and Testing of Formaldehyde Emission Chara cteristics of Pressed-Wood Products: Report XVIII to the U.S. Consumer Product Safety Commissio n. ORNL/TM-9867, Oak Ridge National Laboratory, Oak Ridge, TN.

T. Matthews, A. Hawthorne, and C Thompson. 1987. Fo rmaldehyde Sorption and Desorption Characteristics of Gypsum Wallboard. Environmental Science & Technology 21: 629-634.

G. Myers. 1985. The Effects of Temperature and Humi dity on Formaldehyde Emission from UFbonded Boards: A Literature Critique. Forest Products Journal 1985: 35:20-31.

S. Silberstein, R. Grot, K. Ishiguro, and J. Mullig an. 1988. Validation of Models for Predicting Formaldehyde Concentrations in Residences due to Pr essed-Wood Products. JAPCA 38: 1403-1411.

USEPA. 1990. Compendium of Methods for the Determin ation of Air Pollutants in Indoor Air. Report No. EPA/600/4-90/010, Atmospheric Research a nd 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 198 6 report by Versar, Inc. for the USEPA Office of Toxic Substances, prepared under Contact No. 68- 02-3968.

Versar. 1989. Indoor Formaldehyde Concentration fro m Pressed-Wood Products Model Documentation. Prepared by Versar, Inc. for the USE PA Office of Toxic Substances under Contact

No. 68-02-4254.Appendix A

Derivation of Two-zone Steady-state SolutionA-1

Mass balance equation for zone 1 (well-mixed assump tion):

1 1 12 1 10 2 21 0 01 1

1 S C Q C Q C Q C Q dt dC V +

− − + = (1)

where:

1 1 1 1 y C z S +

− = (Matthew’s implementation) (2)

1 1

1 1 Area m z Zone in sources num

k k 

# ∑

= = m 3 /hr (3)

k Zone in sources num

k k Area b y 

# ∑

= = 1

1 1 mg/hr (4)

m = mass transfer coefficient, m/hr

b = emission rate when the air concentration is zero , mg/(m 2 hr) Q = flow rates, m 3 /hr

C = concentrations, mg/m3

Area = emission area, m 2

t = time, hr

V = volume, m

3

Mass balance equation for zone 2 (well-mixed assump tion):

2 2 21 2 20 1 12 0 02 2

2 S C Q C Q C Q C Q dt dC V +

− − + = (5)

Q 12 Q 21

Q 01 Q 02 Q 10 Q 20 Zone 1

V 1 S 1 Zone 2

V 2 S 2A-2

where:

2 2 2 2 y C z S +

− = (6)

2 2

1 2 Area

Z m z Zone in sources num

k k + = 

# ∑

= (7)

2 2

1 2 C m y Zone in sources num

k k 

# ∑

= = (8)

Assume flows are constant and set dC/dt = 0 (steady state condition):

1 1 1 1 12 1 10 2 21 0 01 0 y C z C Q C Q C Q C Q +

− − − + = (9)

And:

2 2 2 2 21 2 20 1 12 0 02 0 y C z C Q C Q C Q C Q +

− − − + = (10)

Solving for C 1 :

1 12 10 1

2 21 0 01

1 z

Q Q y C Q C Q C

+

+ + +

= (11)

Solving for C 2 :

2 21 20 2

1 12 0 02

2 z

Q Q y C Q C Q C

+

+ + +

= (12)

Substitute equation 12 into equation 11:

1 12 10 1

2 21 20 2

1 12 0 02

21 0 01

1 z

Q Q y

z Q Q y C Q C Q Q C Q

C

+

+ +

       

+ + + + +

= (13)A-3

Rearranging and combining terms:



## ( )

2 21 20 2 21 1 12 21 0 02 21

1 0 01 1 1 12 10 z Q Q y

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

+ + + +

=

− − + +



## ( ) ( ) ( )

2 21 1 12 21 0 02 21 2 21 20 1 0 01 1 1 12 10 y Q C Q Q C Q Q z Q Q y C Q C z Q Q + + = + +

− − + +

2 21 1 12 21 0 02 21 1 2 1 21 1 20 0 2 01 0 21 01 0 20 01 1 2 1 1 21 1 1 20 1 1 2 12 1 21 12 1 20 12 1 2 10 1 21 10 1 20 10

y Q C Q Q C Q Q y

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

+ + = −

− − − − − + + + + + + + +



## ( )

( ) ( )

2 21 1 2 21 20 0 02 21 2 01 21 01 20 01 1 2 1 21 1 20 1 2 12 20 12 2 10 21 10 20 10

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

+ + + + + + + = + + + + + + +



## ( ) ( ) ( )

2 1 21 1 20 1 2 12 20 12 2 10 21 10 20 10 2 21 1 2 21 20 0 02 21 2 01 21 01 20 01

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

+ + + + + + + + + + + + + +

= (14)

Similarly: 

## ( ) ( )

( )

1 2 12 2 10 2 1 21 10 21 1 20 12 20 10 20 1 12 2 1 12 10 0 01 12 1 02 12 02 10 02

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

+ + + + + + + + + + + + + +

= (15)