United States Air and Radiation EPA420-P-02-011
Environmental Protection March 2002
Agency NR-001a
4>EPA 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.
-------
RVP and Temperature Corrections
for Nonroad Engine Modeling
Report No. NR-OOla
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 MOBILESb 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-OOla March 26, 2002
-------
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 MOBILESb 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
MOBILESb 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 MOBILESb 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 MOBILESb, 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-OOla March 26, 2002
-------
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 MOBILESb 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 MOBILESb 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 MOBILESb 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 MOBILESb model's diurnal calculations to adjust the base nonroad
diurnal emissions for temperature and RVP. By applying this code from the MOBILESb 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 MOBILESb 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 MOBILESb 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-OOla March 26, 2002
-------
"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 MOBILESb 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
ofNONROAD2002.
Summary and Recommendations
Due to its applicability to current nonroad engines without evaporative emission controls,
the algorithm used in EPA's MOBILESb 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 MOBILESb 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," WJ. Koehl, Jr.,
Mobile Research and Development Corp., Society of Automotive Engineers paper SAE 690506,
1969.
[3] "MOBILESb" Emission Factor Model, U. S. EPA, Office of Mobile Sources, Assessment and
Modeling Division, 1997.
Attachment (CALUDI source code from MOBILESb)
NR-OOla March 26, 2002
-------
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-OOla March 26, 2002
-------
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*COSt(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(l)=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-OOla March 26, 2002
-------
c
WMOLEC=69.69-1.274*RVPW
* +0 . 059* (FUELT(l)+FUELT(2) )/2.0
C
C Calculate vapor pressures.
C
DO 4 0 JV=1,2
A=A100+(100.O-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.O.O) CALL QUITER(A,JV,97,INERR)
c
IF(A.LT.O.O) then
write(*,'(/,IX,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(l).LT.TMAX) GOTO 30
C
99 CALUDI=UDISUM
C
RETURN
END
NR-OOla March 26, 2002
------- |