NMP Review – Response to Comments, Attachment 1

Responses to Comments

Thomas Armstrong, Relevant Comments:

Reviewer Comment: Dr. Armstrong’s comments cover approximately 4 pages. Selected 

relevant comments have been excerpted as follows:

The error dramatically shifts the shape of the Concentration versus Time series for the scenarios 

so that maximum concentrations generally (but not always) occur after the consumer leaves the 

work zone. This means the correct personal exposure profiles will be dramatically lower than the 

erroneous results given in the current NMP draft. The peak concentrations are also significantly 

affected, but perhaps not quite as dramatically.

The EPA Draft Risk Assessment for NMP uses an incorrect value for the first order exponential 

decay constant (K1) of 10 per hour (0.17 per minute) for NMP. Since this may be difficult to 

believe, this commentary goes into considerable detail to demonstrate the error is real and has 

significant impact in the Draft NMP RA. The second exponential decay constant (K2) for NMP 

appears approximately appropriate. The K1 of 10 per hour is the same value used for DCM in the 

Draft DCM RA. This K1 is an appropriate value for DCM, but is very erroneous for NMP. The 

vapor pressures, a prime determinant of K’s, are vastly different. This K1 is a parameter error 

used in the NMP modeling for Scenarios 1 to 8, and is unfortunately not just a typographical 

error in the list of parameters in the tables. The “downstream” work on NMP Margins of 

Exposure and other subsequent analyses using the results of Scenario 1 to 8 are then also 

significantly in error and will need to be redone. 

Comparative Modeling Results to Demonstrate the K1 Error. 

One of the first indications of the error arises from Figure D-5 in the NMP Draft Risk 

Assessment (see Item 1 below). Another indication is that a K1 of 10 per hour (0.17 per minute) 

means approximately 17 percent of the initial NMP mass evaporates in the first minute, and 17 

percent of the amount remaining each minute thereafter in an exponentially decreasing manner. 

This 17 percent in the first minute is obviously not correct and not plausible given NMP’s low 

vapor pressure. Several scenarios from the NMP draft RA are examined to illustrate the effect of 

the error, but the following is not a complete examination of all the modeled NMP scenarios. 

Rather, the intent is to demonstrate how the wrong K1 of 10 per hour and a more appropriate K1 

of 0.3 per hour alter the peak concentration and concentration versus time results. Note 0.3 per 

hour is an estimate and a proper analysis of Figure D-5 may lead to a slightly different value. 

1. The exposure chamber (MRI, cited as EPA 1994b) results cannot be replicated with the 

incorrect K1 of 10 per hour (0.17 per minute). They can be adequately replicated with a 

K1 of 0.3 per hour (0.005 per minute), which is much more a reasonable value for a low 

vapor pressure material like NMP. See attachment, figures in items 1, 2 and 3. 

2. The MCCEM bathtub refinishing scenario results for NMP can be approximately 

replicated using the incorrect K1 of 10 per hour (0.17 per minute). Using the more 

appropriate K1 value of 0.3 per hour (0.005 per minute), the results are dramatically 

lower and do not approach saturation at Cmax. See figures in attachment, items 4 to 6. 

This is much more in line with expectations for NMP based on the chamber data and 

other real world data.

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NMP Review – Response to Comments, Attachment 1

3. As an additional spot check, an attempt to recreate the results for Scenario 1 is included 

in the attachment. Note that use of the INCORRECT K1 of 10 per hour reasonably but 

not exactly compares to the reported MCCEM results. If a more appropriate value of 0.3 

per hours is used for K1, the results are dramatically different, for Cpeak as well as the 

shape of the C vs. t curve. 

ATTACHMENTS NMP Modeling Issues 

1. Figure D-5 and Table D-3 from page 101 of draft NMP Risk Assessment. These are 

stated as the results of fitting exponentials to the measured chamber concentration on the 

y axis. The Cmax is approximately 65 PPM or 263 mg/M3 since 1 ppm = 4.06 mg/M3. 

These results CANNOT be as they are with a K1 of 10 per hour.

This first order rate constant (K1) 

of 10 per hour cannot be from the fit to the data in the graph above. A K1 of around 0.3 

per hour is consistent with the curve fit to the data. See the results shown in Item 2 

and 3 below.

2. IH Mod Well Mixed Room Model with Exponentially Decreasing Emission Rate, attempt 

to replicate chamber results but using INCORRECT first order decay constant for 

NMP of 10 per hour = 0.17 per minute. Parameters for the NMP quantity and chamber 

conditions as given in US EPA (1994b). Consumer exposure to paint stripper solvents. 

US Environmental Protection Agency, Washington, DC, but converted to PER MINUTE. 

Note Cmax of 248 mg/m3 at 20 minutes. Note this is a version of a predecessor to IH 

Mod. The revised spreadsheet considers the second exponential mass and second 

exponential constant of 0.05 per hour = 0.00083 per minute.

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NMP Review – Response to Comments, Attachment 1

Response: This comment generally can be summarized as follows:

“Dr. Armstrong believes that: 

(1) The parameters reported in the NMP Risk Assessment document, Table D-3 are 

incorrect and CANNOT be used to obtain the results shown in Figure D-5; and 

(2) The k value for the first exponential is unrealistically high. 

Based on the comments, it is clear that the reviewer does not understand the modeling algorithms 

used in this study. For this reason, a reasonably thorough treatise of the double exponential and 

the incremental source models that are used to represent continuous-application scenarios are 

provided in Attachment 1. A summary of the different approaches is presented graphically in 

Figure 1. The time series labeled “Armstrong’s version of the fit in the NMP risk assessment” 

compared to the time series labeled “The fit in the NMP Risk Assessment document” clearly 

demonstrates the misunderstanding. The reviewer mistakenly thinks that the NMP study applied 

a double exponential that does not reflect continuous product application. The construct that the 

reviewer applied is appropriate only for a product where all product mass is instantaneously 

available, as in the case of a room deodorizer placed in a residence. This construct does not apply 

to a product such as paint stripper, where the applied mass steadily increases over time 

throughout the application period. The construct that OPPT applied has been termed an 

incremental source model and is used to mathematically represent a constant application rate 

over time coupled with an emission rate for each instantaneously applied segment that declines 

exponentially over time.

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NMP Review – Response to Comments, Attachment 1

Clearly, if a double exponential without continuous application were used, then the model would 

over-predict the early emissions. However, as noted above, this is not the model that OPPT used. 

As is proven by the results shown in Figure 1 for the incremental model (the fit in the NMP Risk 

Assessment document, which exactly matches our prediction obtained from MCCEM’s 

incremental source model), the parameters given in Table D-3 CAN be used to obtain the results 

shown in Figure D-5.

Figure 1. Comparison of Alternative Modeling Algorithms Applied to the MRI NMP Data.

The question of an appropriate k value for the first exponential and the suggestion that it is 

unrealistically high are both due to a misunderstanding of the model algorithms. As discussed in 

Attachment 1, the two exponentials are used to represent different mass-transfer processes with 

different rates. In the case of paint strippers, surface area is created during the application of the 

product. The first exponential is intended to represent the volatilization of molecules (i.e., DCM 

or NMP) within a few μm of the surface during and shortly after the active application period. 

The second exponential would represent the diffusion and volatilization of molecules in the bulk 

applied product. The percent of applied mass emitted – a result of our "best visual fit" to the 

chamber data – was 26% of the applied mass being emitted, with 2% allocated to the 1st

exponential and 24% allocated to the 2nd. While a k value as high as 10 may seem

counterintuitive for a relatively nonvolatile chemical such as NMP, it is perfectly legitimate 

when used in this context. More specifically, the mass applied to the first exponential (the 

exponential with the “fast” rate constant, in this case 10/hr) is 2% of the total applied NMP, 

representing the limited mass of molecules available for rapid volatilization. The second 

A1-4
NMP Review – Response to Comments, Attachment 1

exponential (with the lower rate constant, in this case 0.05/hr) releases 24% of the applied NMP 

mass, representing the slower emissions.

Also, as discussed in Attachment 1, the incremental form of the double exponential (which 

OPPT applied for predictive purposes) was used to distribute the emissions to account for the 

continuous application of paint stripper over each application event. The continuous application 

spreads the rise out over the duration of the application by considering the time of application as 

the starting time of the exponential representation; therefore, the use of parameters to reflect the 

application rate, the duration of the application, and the percent of applied mass that is released 

impacts the slope of the concentration rise as well as the slope of the tail of the exponentials. The 

2% of applied mass attributed to the first exponential plays a significant role in properly 

representing the initial rise, while the 24% attributed to second exponential plays a significant 

role in properly representing the tail.

By fitting a double exponential without continuous application, as the reviewer did, the resulting 

exponentials necessarily will have an artificially lower rate constant to account for both the 

actual rate of decline as well as the delay due to the duration of the application. The final 

conclusion should be drawn from the fit of the model to the measurement data. As can be seen 

from the MCCEM prediction in Figure 1 (which overlays the visual fit to the data), the structure 

of the data suggests that the incremental version of the double exponential model is best capable 

of representing both the rise and the decay portions of the measured data.

The help provided by MCCEM for emission models makes this distinction clear: 

A single-exponential source is one with an emission rate that declines exponentially over time as 

the reservoir of emitting material is progressively diminished. This source model is most 

appropriate for emitting materials or furnishings that are placed indoors, rather than consumer 

products that are applied in some fashion. The required inputs are the initial emission rate and the 

first-order rate constant that describes the exponential decline in the emission rate over time. A 

source of this type is "placed in" and "removed from" the house in accordance with the start and 

end times specified by the user.

Consumer products that are applied to surfaces (e.g., architectural coatings, all-purpose cleaners) 

are best represented by the incremental source model. This model assumes a constant application 

rate over time, coupled with an emission rate for each instantaneously applied segment that 

declines exponentially. The mathematical expression for the total emission rate resulting from the 

combination of constant application rate and exponential emission rate for each applied segment 

has been developed by Evans (1994).

Depending on the type of applied product, either one or two exponential expressions may be 

needed to characterize the declining emission rate. As described by Wilkes et al. (1996), for a 

product such as latex paint the first exponential typically governs the early phase of emissions 

due to evaporation, whereas the second tends to dominate the later phase of emissions due to 

diffusion through the surface and/or applied product. Although the first exponential is the primary 

determinant of the peak concentration (which usually occurs within or soon after the application 

period), the second exponential typically accounts for a much larger fraction of the total emitted 

mass. The user must specify the fraction of emitted mass associated with the first exponential and 

the rate constant for emissions decline for each of the two exponentials. At the user's option, one 

of the exponentials can be "turned off" by specifying either zero or 100 percent as the fraction of 

mass associated with the first exponential.

A1-5
NMP Review – Response to Comments, Attachment 1

Unfortunately, the current version of MCCEM is not compatible with Windows 7/8. 

Consequently XP computers are retained for the purpose of running models that have not yet 

been ported to Windows 7/8, recognizing that not all modelers have this capability. 

Reviewer Comment: Thomas Armstrong’s Comment 4 on Page 16:

4. NMP Scenarios 1 to 8 evaluated with MCCEM use a double exponential model (Eq. D-5 

page 96) with the two rate constants (K1 and K2) derived from fit to the MRI chamber data 

(EPA 1994b). Given good data from the MRI study, this gives an adequate basis for determining 

the rate of NMP emission to air, under reasonably similar conditions. However, NMP will have a 

reduced vaporization rate at low air velocities. One source to support this is Matthews 1989 cited 

in DCM RA for other reasons. 

In industrial hygiene modeling, this has been called “back pressure” and especially for short 

duration activities with limited and low velocity airflow, a thin saturated vapor layer above the 

evaporating film suppresses further evaporation and saturation concentrations exist only very 

close to the film surface. This then disperses with the air flow, and the general space 

concentration rises, reaching a fraction of saturation that depends on the source NMP generation 

and dispersion, ventilation and volume. Failure to consider this may lead to significant 

overestimation of the NMP concentration in air. This may be handled better via different 

modeling equations than the ones used in MCCEM. A well-mixed (single chamber) equation that 

provides for this is given in Chapter 5 of Keil, C. B., Ed. (2000). Mathematical Models for 

Estimating Occupational Exposure to Chemicals. Fairfax, VA, AIHA Press. Other forms of the 

model exist, including in a freeware spreadsheet [IH Mod, available at:

http://ss4m.aiha.org/insideraiha/volunteergroups/EASC/Pages/EASCTopics.aspx

While very difficult to determine without actual experimental data, the thin film stratification of 

NMP may be significant in a restricted space and a concave surface with limited effective air 

velocity over the surface, such as a bathtub. At low air velocities, there is little turbulence to 

drive dispersion. These considerations place significant doubt on the application of the MRI Ks 

for the bathtub stripping scenario. This could be verified with some simple laboratory scale 

experiments.

Response:

It is certainly likely that the off-gassing rate is affected by turbulence. However, there are no 

readily available data to evaluate this assertion. As the commenter suggests, investigating this 

potential impact would likely require some field and/or laboratory studies. In addition, or 

perhaps alternatively, this investigation would require some sophisticated CFD modeling. 

In deciding upon a course of action to address this comment, the following factors should be 

considered:

1. Is it possible that these boundary layer factors significantly impact exposure? This leads 

to a discussion of the likelihood of a significant reduction in mass-transfer and whether 

the predicted concentrations are near a risk-derived critical concentration. If the 

concentrations are 10-fold different from the critical concentration, this quite possibly is 

irrelevant. On the other hand, if the concentrations are close to the critical concentration, 

A1-6
NMP Review – Response to Comments, Attachment 1

then a preliminary estimate on the possible impact of this factor would be useful in 

determining the importance of this potential impact.

2. The exposure assessment was conducted under a set of realistic conditions, including 

ventilation assumptions. The source cloud assumption is based on estimates of room 

airflow velocities. The higher this velocity, the more the boundary layer is disturbed, 

enhancing mixing. If the surface velocities are expected to be low, such that a boundary 

layer inhibits mass transfer and tends to lower air concentrations, this would imply that 

the source-cloud ventilation would also be lower, tending to increase air concentrations.

3. During the brush-on and scraping activities (which based on label instructions would 

occupy a majority of the time during any paint stripping activity) the user is actively

creating turbulence at the surface.

4. The uncertainty in many of the other parameters, including but not limited to product use 

behavior and ventilation rate near the source, may very well dwarf the uncertainty due to 

the potential impacts of low air velocities. 

5. Per model predictions, the source cloud is at the saturation concentration during most of 

the stripping. Therefore, a small decrease in the mass-transfer rate likely would delay 

reaching the saturation concentration but would have a negligible impact after saturation 

is reached.

Given all these factors and the uncertainties noted above, the relative impact of application to a 

concave or curved surface likely is minor. 

A1-7
NMP Review – Response to Comments, Attachment 1

Attachment 1: Description of Model Algorithms

Double Exponential and Continuous Application

1. The Double Exponential Algorithm

The double exponential empirical model is used to represent the emissions during application 

and the waiting period. The double exponential is the sum of two exponentials as given by 

equation A1-1. The two exponentials are used to represent different mass-transfer processes with 

different rates. In the case of paint strippers, surface area is created during the application of the 

product. The first exponential is intended to represent the volatilization of molecules (i.e., DCM 

or NMP) within a few μm of the surface during and shortly after the active application period. 

The second exponential would represent the diffusion and volatilization of molecules in the bulk 

applied product. 

S t E e E e

k t k t ( ) = + − −

01 02

1 2 (A1-1)

where: S(t) = Source strength as a function of time (mass/time)

E01 = Initial emission rate for first exponential (mass/time)

E02 = Initial emission rate for second exponential (mass/time)

k1 = First-order rate constant for first exponential (time-1)

k2 = First-order rate constant for second exponential (time-1

)

t = Time.

Integrating the mass balance equation for the one-compartment case, using Equation A1-1 for the 

source term and assuming an initial concentration of zero, gives Equation A1-2:

C t

E

V Q

V

k

e e

E

V Q

V

k

e e

k t

Q

V t k t

Q

V t

( ) =

− 



 





− 



 



 +

− 



 





− 



 



 − − − − 01

1

02

2

1 2 (A1-2)

2. General Equation for Emissions from Continuous Application

The double exponential equation is applicable to a short-term product application. For the case of 

a brush- or spray-applied product, such as painting or paint stripping, the application occurs 

gradually by application in relatively continuous strips across the surface being treated. To 

represent the emissions and concentrations during a continuous application event, the application 

can be characterized as short-duration application segments, with each segment represented by 

the double exponential algorithm, as shown in Figure A1-1. The sum of the segment-specific

exponentials is then fitted to the measured data using a sum-of-squared-differences approach.

A single exponential cannot properly represent the rise and tail of the emissions and resulting 

concentrations because of the continuous nature of the product use. The continuous application 

spreads the rise out over the duration of the application, and therefore the application rate and 

duration impact the slope of the concentration rise as well as the slope of the tail of the 

exponentials. An illustrative demonstration of this effect is shown in Figure A1-2, which 

compares the fitted sum of exponentials to a double exponential fit to the same data set. The 

single exponential does not capture the significant features of the dataset, falling short of the 

A1-8
NMP Review – Response to Comments, Attachment 1

peak and then falling off too rapidly after the end of the application period. Furthermore, the 

parameters of the double exponential will change if the length of the application period changes. 

The application period is one of the parameters of the continuous application algorithms.

Figure A1-1. Basis for Continuous Application Algorithm.

Figure A1-2. Comparison of a Double Exponential Fit to the Continuous 

Application Algorithm.

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NMP Review – Response to Comments, Attachment 1

Modeling the emissions of the double exponential source term for an ongoing continuous 

application event was presented in a paper by Evans (1994).1 This algorithm can be used in a 

predictive model to represent the source strength as a function of time for the combination of (1) 

continuous application of a product, such as paint or paint stripper, at an essentially constant rate, 

and (2) a double exponential emission profile for each instantaneously applied segment.

Representation of the time-varying source strength for a double exponential during a continuous 

painting event is given by the following equation:1

( ) [ ( ) ( )( )]

( )

( ) ( ) ( )

[ ( )] ( )

S t

M

t

f e f e

M

t

f e f e H t t

a

k t k t

a

k t t k t t

a

a a

= − + − −

− − + − − −

− −

− − − −

1 1 1

1 1 1

1 2

1 2

(A1-3)

where: M = Total mass to be emitted (mass)

ta = Paint application time (time)

f = Fraction of mass emitted from the first exponential (unitless)

t = Time 

and: ( ) ( )

( ) H t t if t t

if t t a

a

a

− = − ≤

− >







0 0

1 0

;

;

(A1-4)

Equation A1-3 provides a continuous representation of the emission rate during and following 

application, where the source emission for each instantaneously applied segment is represented 

by a double exponential. This equation has been used in the past for representation of emissions 

and concentration profiles during painting by EPA studies.2,3

1 WC Evans, “Development of Continuous-Application Source Terms and Two-Compartment Analytical Solutions,” 

ASTM Symposium on Methods for Characterizing Indoor Sources and Sinks, September 25-28, 1994, Washington, 

DC

2 Wilkes C, Koontz M, Ryan M, and Cinalli C, Estimation of Emission Profiles for Interior Latex Paint, 

Proceedings: The Seventh International Conference on Indoor Air Quality and Climate. Nagoya, Japan, July 21-26, 

1996, Vol. 2: 55-60 3 Wilkes, CR and MD Koontz. Use of Small-Chamber Data to Estimate and Model Chemical Emissions from Latex 

and Alkyd Paints. Final Report No. IE-2812, prepared by GEOMET Technologies, Inc. under EPA Contract No. 

68-D3-0013, WA No. 3-19, 1997.

A1-10

 
Attachment 2: Application of the Model Algorithms

The purpose of the model algorithm is to provide a representation of the emissions and resulting 

air concentrations affecting exposure to the product user and other occupants of the home, with 

the objective of performing model-based exposure assessments to evaluate a variety of exposure 

scenarios. Ideally, to accomplish this the model algorithms need to be scalable across factors 

impacting the exposure, including housing characteristics, product use alternatives, and other 

paint stripping activities.

The basis for the model algorithm was limited to selected chamber studies published in the 

literature as cited in the NMP and DCM Risk Assessment documents. Since no theoretical-based 

model developed and validated was found, the approach pursued for this project was to develop 

semi-empirical algorithms to allow scaling across the important parameters of interest. Based on 

the similarity of paint stripping activities and past studies investigating exposure to paint 

products,2,3 the double exponential was evaluated. Furthermore, the incremental application of 

the double exponential was considered to represent the continuous nature of the product use. 

Selected advantages, disadvantages and shortcomings are listed in Table A2-1.

Table A2-1. Selected Advantages, Disadvantages and Shortcomings of Each 

Considered Model Algorithm 

Algorithm Advantages Disadvantages/Shortcomings A

Single 

Exponential

Captures the general emission characteristics

Scalable to product mass

Cannot capture more than one process. Not 

scalable or translatable to other variables.

Double 

Exponential

Considers fast and slow emissions

Scalable to product mass

Not scalable or translatable to other variables.

Cannot represent the continuous nature of the 

product application

Incremental 

Double 

exponential

Scalable (Partly or Fully)

Product amount

Product Use Rate

Duration of application

Room size 

Ventilation rates

Some variability not explained

Not necessarily translatable to other 

application methods, very different 

formulations. 

A. Not all shortcomings are mentioned. For example, there is not mass-transfer model that accounts for resistance 

to evaporation that may occur as the air concentration approaches saturation.

A comparison of the fit to the NMP data from the MRI study is presented in Figure A2-1. The 

NMP data shown in Figure A2-1 are taken from NMP chamber study results conducted by 

Midwest Research Institute under contract to the US EPA.4 The data shown in Figure A2-1 were 

collected during three chamber tests, referred to as Runs 10, 11, and 12, during which a brush-on 

paint stripper product containing NMP was applied to a 2 x 4 foot painted plywood panel in a 

controlled environment, and the resulting air concentration were monitored. The paint stripper 

4 EPA, 1994. Consumer Exposure to Paint Stripper Solvents. Final Report. U.S. Environmental Protection 

Agency. February 28, 1994.

 
NMP Review – Response to Comments (Continued)

application and scraping activity lasted 107, 112 and 113 minutes for Runs 10, 11 and 12, 

respectively. Approximately 5 hours of airborne concentration data were collected per run.

Two alternative double exponential representations are shown in the figure as well as an 

incremental adaptation of the double exponential (see discussion in Attachment 1). Two of the 

three fits shown in the figure were derived based on minimizing the sum of the squared 

differences between the model predictions and the observed data, allowing the fitting algorithm 

to vary the rate constants and the mass of chemical applied to each algorithm. The incremental 

model shown in Figure A2-1 was fit to the Run 10 data using 8 double exponentials as illustrated 

in Figure A1-1, each representing approximately 14 minutes of painting/scraping activity. The fit 

to chamber test 10 was performed because the data from that test was judged to be best behaved 

data set.

As Figure A2-1 demonstrates, the double exponential does not fit data as well as the incremental 

version of the double exponential model, for both the initial rise and the tail portions of the 

concentration profile. Likewise, the parameters suggested by Armstrong do not result in a fit that 

captures both the shape and the magnitude of the concentration profile.

Figure A2-1. Comparison of the Four Considered Models for Representing 

the Chamber Data.

12