United States

Environmental Protection

Agency

Air and Radiation EPA420-P-02-011

March 2002

NR-001a

RVP and Temperature

Corrections for Nonroad

Engine Modeling

 Printed on Recycled Paper
EPA420-P-02-011

March 2002

RVP and Temperature Corrections for

Nonroad Engine Modeling

NR-001a

Assessment and Standards Division

Office of Transportation and Air Quality

U.S. Environmental Protection Agency

NOTICE

This technical report does not necessarily represent final EPA decisions or positions.

It is intended to present technical analysis of issues using data that are currently available.

The purpose in the release of such reports is to facilitate the exchange of

technical information and to inform the public of technical developments which

may form the basis for a final EPA decision, position, or regulatory action.
NR-001a March 26, 2002 1

RVP and Temperature Corrections

 for Nonroad Engine Modeling

Report No. NR-001a

revised March 26, 2002

Assessment and Standards Division

EPA, Office of Transportation and Air Quality

Purpose

This report documents how the draft EPA NONROAD2002 emission inventory model

accounts for the effects of temperature and RVP on diurnal evaporative emissions, as well as

temperature effects on four-stroke exhaust emissions. RVP and temperature also effect vapor

displacement, which is covered in NR-013a, “Refueling Emissions for Nonroad Engine

Modeling.”

Background

The draft EPA NONROAD2002 model estimates diurnal evaporative emissions from

gasoline-fueled engines. Evaporative emissions from diesel-fueled engines are considered

negligible due to the extremely low volatility of diesel fuel and, therefore, are not included in the

NONROAD model. 

Evaporative emissions from most gasoline-fueled engines are very sensitive to the

volatility of the fuel (typically expressed as Reid Vapor Pressure or RVP) as well as the

temperatures that the fuel experiences. In highway vehicles, this sensitivity is mitigated to some

degree by the carbon canister evaporative control systems that have been used for many years,

but such control systems are not currently used on nonroad equipment. 

Modeling of uncontrolled evaporative emissions has been attempted in a variety of ways. 

The EPA MOBILE5b model for highway vehicles uses an algorithm based on the Wade equation

[1, 2]. This is based on the "Ideal Gas Law" which models pressure, temperature, and volume

assuming simplified "ideal" behavior, and the equation also includes a compressibility factor to

account for the non-ideal nature of hydrocarbon vapor. There has also been some limited testing

of nonroad engines, such as lawn mower fuel tanks, to gather diurnal evaporative emission data,

but little or none of this testing has addressed variation of the fuel's base temperature and RVP,

so it is of little value for the purposes of this analysis. 
NR-001a March 26, 2002 2

In addition to effects on diurnal emissions, NONROAD also includes effects of ambient

temperature on exhaust emissions. This has been true in every release of the model including the

1997 beta, but it was inadvertently omitted in the previous version of this technical report. The

method used in NONROAD is taken directly from the MOBILE5b highway vehicle emission

factor model. Only effects on 4-stroke gasoline engine exhaust hydrocarbons (HC), carbon

monoxide (CO), and oxides of nitrogen (NOx) are included. We are not aware of any data that

could be used to estimate temperature effects on the other pollutants in NONROAD, so no such

effects are currently modeled.

Approach

Temperature and RVP Effects on Diurnal Evaporative Emissions

The basic mechanisms of fuel evaporation are the same regardless of whether the

engine/fuel system is a highway vehicle or a nonroad engine. They both use fuel tanks, fuel

lines, and carburetors or fuel injection systems to deliver the fuel to the engine. In terms of their

evaporative emissions, the major difference between highway vehicles and nonroad engines is

that highway vehicles in the U.S. have been required to use evaporative control systems, such as

carbon canisters, to minimize evaporative losses. Thus, test data from controlled vehicles would

not be applicable to nonroad engines, but the principles and test data concerning uncontrolled

evaporative emissions from highway vehicles should be reasonably applicable to nonroad

engines. 

Two existing models of RVP and temperature effects on diurnal emissions were

investigated and considered: the California ARB OFFROAD model and the US EPA

MOBILE5b highway vehicle emissions model. The EPA model used for development of the

national Phase 1 small spark ignition engine rule was not considered in this evaluation since it

did not include any calculation of RVP or temperature effects on evaporative emissions. 

Both the ARB OFFROAD model and MOBILE5b calculate diurnal emissions by

adjusting from base conditions of 9.0 psi RVP and an ambient temperature rise from 60F - 84F

during the day (average temperature of 75F) to the RVP and ambient temperature range being

modeled. However, there are substantial differences in the effects of temperature in the two

models. In MOBILE5b, a day with an average temperature of 90F instead of 75F results in twice

as much diurnal emissions, whereas in ARB's OFFROAD model the 90F day would increase

diurnal emissions by a factor of 3. According to the ARB model documentation, their equation

was derived from EPA highway vehicle data that included both carbureted and fuel injected

vehicles, which means that the vehicles were probably equipped with carbon canister evaporative

control systems. The use of such data could account for the greater rate of increase in diurnal

losses with temperature, since carbon canisters would be more likely to experience

"breakthrough" due to the much greater vapor generation rate at high temperature. Although the

controlled vehicles would probably show lower absolute emissions, they would have a larger

percentage increase in emissions with temperature, when compared with uncontrolled vehicles. 
NR-001a March 26, 2002 3

Thus, EPA does not consider the approach used in the ARB OFFROAD model to adjust

evaporative emissions for RVP and temperature to be appropriate for nonroad engines. By

contrast, the approach used in the EPA MOBILE5b model does not rely on emission data from

highway vehicles to estimate evaporative emissions from nonroad engines. For this reason, EPA

has chosen to rely on the approach used in the EPA MOBILE model for uncontrolled engines to

estimate evaporative emissions from nonroad engines.

The EPA MOBILE5b model 's diurnal evaporative calculations are divided into three

separate parts: (a) a base diurnal emission rate based on test data at standard test conditions: 9.0

psi RVP and a 60F - 84F temperature rise, (b) adjustment of these uncontrolled emissions to the

temperature and RVP of interest, and (c) modification of results to account for the control system

and possible tampering. As described above, the MOBILE5b model uses basic chemistry theory

to model the variation in uncontrolled diurnal emissions with RVP and temperature. Thus, for

purposes of the NONROAD model, it is fairly straightforward to use the appropriate portion of

code directly from the MOBILE5b model's diurnal calculations to adjust the base nonroad

diurnal emissions for temperature and RVP. By applying this code from the MOBILE5b model,

the absence of evaporative control systems can be reflected properly in the calculations.

This approach provides consistency between the NONROAD model and other current

models, but it does not rule out possible changes to the method in a future version of the

NONROAD model based on analysis of any newer data or comparison with updated versions of

other models that may become available. 

Temperature Effects on Four-Stroke Exhaust Emissions

The details of the temperature correction method from the MOBILE5b model are as

follows: 

TCF = EXP [ A * (Tambient -75) ]

where:

TCF = multiplicative Temperature Correction Factor

Tambient = Ambient Temperature, in degrees Fahrenheit

"A" = The coefficient "A" is taken from MOBILE5b for "Bag 2" effects on uncontrolled

light-duty gasoline vehicles (LDGV's). "Bag 2" refers to the hot stabilized portion of the

test sequence, so no cold-start effects are present. The value of "A" in the above equation

depends on high or low temperature (relative to 75F) and on pollutant (HC/CO/NOx). 

Values for A are:
NR-001a March 26, 2002 4

"A" Tambient<75 Tambient>75

HC (4-stroke) - 0.00240 +0.00132

CO (4-stroke) +0.00158 +0.00375

NOx (4-stroke) - 0.00892 - 0.00873

For two-stroke engines, conditions differ significantly from those of on-road motor

vehicles. Therefore, the 4-stroke corrections from MOBILE5b are not applied to 2-stroke or

diesel engines in NONROAD. Due to lack of data for these engine types, temperature effects on

exhaust emissions from 2-stroke and diesel engines are not currently included in the draft version

of NONROAD2002. 

Summary and Recommendations

Due to its applicability to current nonroad engines without evaporative emission controls,

the algorithm used in EPA's MOBILE5b model to predict the effects of ambient temperature and

fuel RVP on evaporative emissions from uncontrolled highway vehicles was chosen for use in

the draft EPA NONROAD2002 model. This algorithm is applied as an adjustment factor to the

base emission rate, expressed as grams per day per gallon of fuel tank capacity, for a given type

of engine to adjust from the base RVP and temperature conditions to the RVP and ambient

temperatures being modeled. The FORTRAN subroutine from MOBILE5b that performs this

adjustment is attached as an appendix. 

The base diurnal emission rates for different equipment types come from limited testing

that has been done of nonroad equipment. The documentation of these base emission rates is

contained in a separate report, “Basic Evaporative Emission Rates for Nonroad Engine

Modeling, NR-0012a". 

References

[1] "Factors Influencing Vehicle Evaporative Emissions,” D.T. Wade, Esso Research and

Engineering Co., Society of Automotive Engineers paper SAE 670126, 1967. 

[2] "Mathematical Models for Prediction of Fuel Tank Carburetor Evaporation," W.J. Koehl, Jr.,

Mobile Research and Development Corp., Society of Automotive Engineers paper SAE 690506,

1969. 

[3] "MOBILE5b" Emission Factor Model, U. S. EPA, Office of Mobile Sources, Assessment and

Modeling Division, 1997. 

Attachment (CALUDI source code from MOBILE5b)
NR-001a March 26, 2002 1

 FUNCTION CALUDI(RVPW,TMIN,TMAX,FILLED)

C

C CALUDI uses passed in fuel RVP levels, minimum and maximum fuel tank

C temperatures and fleet average percent of fuel tank filled to estimate

C an Uncontrolled Diurnal emission rate.

C

C Called by LOCAL

C

C Calls QUITER.

C

C Input on call:

C

C parameter list:

C RVPW,TMIN,TMAX,FILLED

C

C common blocks:

C /REGION/ IREJN

C

C Output on return:

C function: CALUDI

C

C Local array subscripts :

C

C AIRPRE(2) - AIRPRE ( IREJN )

C FUELT(2) - FUELT ( JV )

C VAPOR(2) - VAPOR ( JV )

C

C Local variable / array dictionary:

C Name Type Description

C ------ ---- ----------------------------------------------------

C A R coefficient used to calculate VAPOR(I)

C AIRPRE R air pressure

C A100 R coefficient used to calculate A

C C R constant, used to calculate A100

C DENSTY R fuel density, a function of RVPW

C FILLED R percent of fuel tank filled

C FUELT R incremental fuel tank temperature in degrees Fahrenheit

C GTP R grams of HC loss for temperature pair FUELT

C PI R Greek pi = ratio of circumference of a circle to its diameter.

C Used in computing X.

C RVPW R fuel RVPs used to compute the components of the Wade Index

C TMAX R maximum temperature

C TMIN R minimum temperature

C TP1 R first coefficient for Wade equation

C TP2 R second coefficient for Wade equation

C TP3 R third coefficient for Wade equation

C UDISUM R incremental and, eventually, total Uncontrolled Diurnal rate

C VAPOR R vapor pressure at FUELT (2 temperatures, 1 degree apart)

C VP100 R vapor pressure at 100F, a function of RVPW

C VSPACE R vapor space in cubic feet, a function of FILLED

C WMOLEC R molecular weight, a function of RVPW and fuel temp

C X R coefficient used to calculate A100, a function of VP100

C

C Notes:

C CALUDI is the sum of HC loss at each fuel temperature increment under the

C input conditions.

C CALUDI temperature range "cuts" code changed for MOBILE4.1 so as to

C not lose the last difference pair due to round off. Also added an
NR-001a March 26, 2002 2

C immediate return if TMIN=TMAX.

C

 COMMON /REGION/ FEET(2),IREJN,ALT,INITPR

C

 DIMENSION AIRPRE(2),FUELT(2),VAPOR(2)

C

 DATA AIRPRE/14.696,12.5/,PI/3.14159/

C

 UDISUM=0.0

C

 IF(TMIN.EQ.TMAX) GOTO 99

C

C To calculate the CALUDI value, first compute several parameters and then

C move stepwise through the fuel tank temperature range, adding each

C degree difference pair's contribution to the sum UDI of the grams HC

C loss over the entire range.

C

C Calculate fuel density for given RVPW.

C

 DENSTY=6.4-0.01977*RVPW

C

C Calculate vapor space under given percent of fuel tank filled.

C

 VSPACE=2.4062-0.02139*FILLED

C

C Calculate vapor pressure at 100 (VP100) for given RVPW.

C

 VP100=1.0223*RVPW

 * +(0.0357*RVPW)/(1.0-0.0368*RVPW)

C

C Calculate A100 according to VP100.

C

 IF(VP100.LT.14.18) GOTO 10

 C=80.861

 X=0.11*COS((4.0*VP100-9.0)*PI/14.0)

 * +5.4*ALOG(VP100)

 GOTO 20

C

 10 C=66.561

 X=0.12*COS((VP100-6.0)*PI/4.0)

 * -0.21*SIN(2.0*PI/7.5*(VP100-4.0))

C

 20 A100=C-12.822*VP100

 * +1.3291*VP100**2

 * -0.07991*VP100**3

 * +1.9017E-03*VP100**4-X

C

C Initialize fuel tank temperature pair.

C

 FUELT(1)=TMIN

 FUELT(2)=FUELT(1)+1.0

 IF(FUELT(2).GT.TMAX) FUELT(2)=TMAX

C

C Iteration starts here.

C

 30 CONTINUE

C

C Calculate molecular weight.
NR-001a March 26, 2002 3

C

 WMOLEC=69.69-1.274*RVPW

 * +0.059*(FUELT(1)+FUELT(2))/2.0

C

C Calculate vapor pressures.

C

 DO 40 JV=1,2

 A=A100+(100.0-FUELT(JV))

 * *((262.0/(A100/6.0+560.0))-0.01328)

C

C pass JV's A < 0.0 => CALUDI < 0.0 => diurnal evap < 0.0 => fatal error

C Technically, high RVPW (in A100) and high temperature (in FUELT(JV)) does not

C make sense anyway: the gas tank would blow up.

C

c

cgwilson ----------------------------------------

c

c The following change made to write an error message ---

c

cgwilson IF(A.LT.0.0) CALL QUITER(A,JV,97,INERR)

c

 IF(A.LT.0.0) then

 write(*,'(/,1X,2A)') 'ERROR: Calculating the temperature ',

 & 'adjustment factors for diurnal emissions.'

 write(*,'(9X,2A)') 'Check parameters in /OPTIONS/ packet ',

 & 'of the options file.'

 endif

c

cgwilson ----------------------------------------

c

C

 VAPOR(JV)=14.696

 * -0.53059*A

 * +7.6961E-03*A**2

 * -5.4907E-05*A**3

 * +1.7044E-07*A**4

 40 CONTINUE

C

C Apply Wade equation.

C

 TP1=VSPACE*118040.0*DENSTY/(690.0-4.0*WMOLEC)

 TP2=VAPOR(1)/(AIRPRE(IREJN)-VAPOR(1))

 * +VAPOR(2)/(AIRPRE(IREJN)-VAPOR(2))

 TP3=(AIRPRE(IREJN)-VAPOR(1))/(FUELT(1)+460.0)

 * -(AIRPRE(IREJN)-VAPOR(2))/(FUELT(2)+460.0)

 GTP=TP1*TP2*TP3

C

 UDISUM=UDISUM+GTP

C

 FUELT(1)=FUELT(1)+1.0

 FUELT(2)=FUELT(2)+1.0

 IF(FUELT(2).GT.TMAX) FUELT(2)=TMAX

 IF(FUELT(1).LT.TMAX) GOTO 30

C

 99 CALUDI=UDISUM

C

 RETURN

 END