Temperature and RVP Effects on Diurnal Emissions
for Nonroad Engine Modeling
Report No. NR-001
November 12, 1997
Craig Harvey
U.S. EPA Office of Mobile Sources, Assessment and Modeling
Division
Purpose
This report documents how the EPA NONROAD emission inventory
model accounts for the effects of temperature and RVP on diurnal
evaporative emissions.
Background
The EPA NONROAD 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 MOBILE 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.
Approach
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 MOBILE 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 MOBILE 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 MOBILE, 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. 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 MOBILE 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 MOBILE 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 MOBILE 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 MOBILE
model's diurnal calculations to adjust the base nonroad diurnal
emissions for temperature and RVP. By applying this code from
the MOBILE 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.
Summary and Recommendations
Due to its applicability to current nonroad engines without
evaporative emission controls, the algorithm used in EPA's
MOBILE5 model to predict the effects of ambient temperature and
fuel RVP on evaporative emissions from uncontrolled highway
vehicles was chosen for use in the EPA NONROAD 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 MOBILE5 that performs
this adjustment is attached.
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.
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)
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
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
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
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
C immediate return if TMIN=TMAX.
C
INCLUDE 'REGION.I'
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.
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
IF(A.LT.0.0) CALL QUITER(A,JV,97,INERR)
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