EPA-AA-SDSB-84-3
Technical Report
Corrections for Variations
in Test Fuel Properties
By
G. D. Thompson
NOTICE
Technical Reports do not necessarily represent final EPA
decisions or positions. They are intended to present
technical analysis of issues using data which 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.
Standards Development and Support Branch
Emission Control Technology Division
Office of Mobile Sources
Office of Air and Radiation
U. S. Environmental Protection Agency
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I. Introduction
General Motors Corporation has recently asserted that the
test fuel used at the EPA/MVEL has varied in energy density and
carbon content since 1975.[1] General Motors has subsequently
requested that a CAFE correction be granted to account for
these variations in fuel properties.
GM has submitted data demonstrating that the test fuel
used by GM has varied since 1975. Since EPA and GM obtain fuel
from the same sources it is probable that the EPA test fuel has
also varied in a similar fashion. If so, this is a change
which would systematically affect the measured fuel economy of
test vehicles and hence corporate average fuel economies
(CAFE). This change is similar to previous test procedure
changes for which CAFE corrections have been proposed.[2]
The report develops a simple correction based on the
energy content per unit carbon of the fuel. The correction
proposed by GM is also discussed, as is the problem of limited
available data on the test fuels.
II. The Correction for Test Fuel Properties
The EPA exhaust emission and fuel economy measurements
determine the quantity of carbon combusted by the vehicle
during the test. The carbon balance equation then computes the
volume of fuel which must have been burned to yield the
measured amount of carbon. The coefficients of the EPA
equation are currently fixed numerical values which in effect
define a reference test fuel.
If the carbon content of the fuel varies in time, as GM
has asserted, then the present carbon balance equation will not
give the true volume of the test fuel consumed. It will,
however, continue to give the correct quantity of the original
reference fuel which would have to be consumed to give the
measured carbon. Therefore the carbon balance equation
automatically adjusts the fuel economy calculation for whatever
fuel is used back to a volume of the reference fuel.
While the carbon balance equation automatically adjusts
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the fuel economy calculation for the carbon content of the
fuel, it does not consider how the engine is affected by the
fuel. For long term variations in the fuel properties, such as
those which appear to have occurred at the EPA/MVEL, the fuel
delivery to the engine will be adjusted to account for the
energy content. This will occur automatically with some closed
loop fuel control systems and manually through calibration
adjustments in other instances. This will be required either
to maintain vehicle driveability or to maintain acceptable HC
and CO emissions.
Ultimately the energy content is the most important aspect of
the fuel to the engine. If the energy content of the fuel
decreases the engine must burn more fuel to provide the same
amount of work output. Therefore, fuel economy corrections for
changes in fuel properties should be formulated in terms of the
energy content per unit carbon of the fuel. Since the
variations in the fuel properties have been small, it is
reasonable to state that the fuel consumption is proportional
to the energy content per unit carbon of the fuel. That is:
= COM
fc
(1)
Where:
COMr =
Er =
the quantity of the reference fuel which would
be consumed
the measured consumption of test fuel
the energy content per unit carbon of the
actual fuel
the energy content per unit carbon of the
reference fuel
Equation 1 simply states that the quantity of carbon which
is burned is proportional to the energy content of the fuel.
If the actual fuel has more energy per unit carbon than the
reference fuel, say 10 percent more, then 10 percent more
carbon of the reference carbon fuel would have to be burned to
provide the necessary energy for the fuel economy or emissions
test.
Fuel economy is proportional to the inverse of fuel
consumption. Therefore equation 1 may alternately be expressed
as:
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MPGr=MPGmET (2)
a
Where:
MPGr = the fuel economy using the reference fuel
MPGm = the measured carbon balance fuel economy
The energy content per unit carbon of the fuel is not a
normally measured parameter but it can be calculated from mass
specific heating value of the fuel and the carbon weight
fraction. That is:
E = L/C (3)
Where:
E = the energy content per unit carbon of the fuel
L = the mass specific lower heating value of the fuel
C = the carbon weight fraction of the fuel
Using equation 3 in equation 2:
L /C
MPGr ' MPGm ITTcr
L C
MPG = MPG _f _
m L C
(4)
The first technical report for fuel economy corrections
demonstrated that if each measured fuel economy was corrected
by a constant proportion then the corporate average fuel
economy (CAFE) would be modified by the same proportion. [ 1]
Therefore:
CAFE1 = CAFE -=- - (5)
JL C
a r
Where :
CAFE1 = the CAFE corrected to the 1975 fuel conditions
CAFE = the measured CAFE
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Subtracting the measured value from each side of equation 5:
Lr Ca
CAFE - CAFE = CAFE ^- ^ - CAFE (6)
LJ C.
a r
or
ACAFE = / r-^ -^- - 1 I CAFE
Where:
4 CAFE = the required CAFE correction or CAFE adjustment
The numerical values for the CAFE corrections, or CAFE
adjustments, are presented later in Section V.
Ill . The General Motors Approach
The correction proposed by GM is a more complex two step
approach. [2] First, the carbon balance measured fuel economy
is corrected to a true volumetric fuel economy based on the
carbon content of the test fuel. Then an empirical sensitivity
coefficient is used to adjust this volumetric fuel economy to a
fuel economy of the 1975 model year fuel.
The correction to the volumetric fuel economy of the test
fuel is:
CV
Where :
MPG^ = the true volumetric fuel economy of the test
MPGm = the measured carbon balance fuel economy
CVa = the carbon volume fraction of the test fuel
CV,.,}-, = the carbon volume fraction assumed in the
carbon balance equation
In order to correct the present volumetric fuel economy to
the fuel economy which would have occurred with 1975 fuel the
GM approach assumes that the correction is proportional to the
change in the volumetric heating values of the fuel. A
dimensionless sensitivity coefficient is defined as:
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MPG. - MPG
LV. - LV
Where :
R =
MPGr =
LVt =
LVr =
the sensitivity coefficient
the fuel economy with the 1975 fuel
the lower volumetric heating value of the test
fuel
the lower volumetric heating value of the
reference fuel
Solving equation 8 for the reference fuel economy gives:
MPGr = MPGfc
(9)
Using equation 7 for the test fuel economy gives the total
correction as:
CV
MPGr '
Equation 10 uses the volumetric heating values and the
volumetric carbon fraction of the fuel. Both of these
parameters are, however, usually measured and reported on a
mass specific basis. The conversion from mass specific to
volume specific for either of these parameters is, using the
carbon fraction as an example:
CV = (C)(S)(MH20)
(11)
Where :
S = the specific gravity of the fuel
MH20 = the mass of a unit of water
Using equation 11 and the similar equation for the heating
value of the fuel in equation 10 gives the final correction
equation by the GM method:
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- S(mH O)
MPG = MPG -- - rV-m L S (mH 0)
r m C ,S , (mH_O) nr t t 2 -, ..
cb CD 2 R|r — = — , \ - 1J + 1
L S (itiH-O)
C S 1
a a
= MPG " " L S
m CcbScb (R JLj^- - 1) + 1
LrSr
Rearranging terms results in:
C S L S
= MPG a a rr
R/L q - Lq \ + L q
m CcbScb R(LtSt ~ LrSr) + LrSr
C S L S r 1
= MPGm %a * * l ITs- LIT
m CcbScbLtSt R(i - JL±) + ^
tt tt
But the carbon balance and the reference parameters are the
same, that is:
Ccb = Cr (14)
scb = sr
And the test and actual parameters are the same:
St = Sa (15)
Therefore:
C S L S f _ 1 _ -,
MPG = MPG T^3- ^ ^ ^ L LS LSJ
r mCSLS^ -rr^.Tr
r r a a R - R --R + --
a a a a
C L i- L -i /i>.\
= MPG ^^ C - ITS - ] U6)
m Cr La R + j±t (i _ R)
a a
IV. Discussion
The correction developed in Section II of this report and
that developed by GM are quite different in their basic
concepts. Mathematically, however, the results are related.
The relationship is most easily shown by considering equation
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16 in the special case where R = 1. In this case:
MPGr ' MPGm (T IT (17>
r a
Equation 17 is identical to equation 4 of the EPA approach.
The parameter R may be considered as the efficiency with
which the vehicle engine adapts to fuel variations.
Mathematically the difference between the EPA and GM methods is
simply this efficiency value. GM proposes an efficiency value
of 0.6 based on tests with multiple fuels in fixed vehicle
configurations. However the variations in the EPA fuel
properties have occurred slowly while the vehicles were
continuously tested and modified. It is unreasonable to expect
that a 1985 vehicle carefully calibrated on 1984 test fuel
would use the higher energy per gallon of this fuel as
inefficiently as would a 1975 vehicle which had been calibrated
on 1975 fuel. As long as the variations are gradual it is more
logical to assume that the vehicles will adapt to these
variations with high efficiency, either automatically through
closed loop fuel control systems or through manual calibration
changes.
A second area of questionable accuracy with the GM
approach occurs when the energy content per unit volume of the
fuel decreases. In this case, the efficiency term reduces or
discounts the calculated correction. For example, if the
energy content per unit volume decreased by 20 percent, the
fuel economy correction would only be about 10 percent. It is
unlikely that vehicles could tolerate a significant decrease in
the energy density of the fuel without experiencing an
equivalent decrease in fuel economy.
V. Results
The EPA approach and the GM approach both require data on
the lower heating value and the carbon weight fraction of the
fuel. Neither of these parameters were routinely measured by
EPA in the past. Therefore, these data are not presently
available at EPA although efforts are being made to acquire
whatever data may be available from fuel suppliers. GM did
submit data on the density and other properties of their test
fuel. The GM data are given in Table 1. Using the
hydrogen/carbon ratios submitted by GM, the carbon weight
fraction of the fuel may be calculated by:
C = (12.011)/(12.011 + 1.008 HC)
(18)
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Table 1
Test Fuel Properties*
Calendar
Year
1979
1980
1981
1982
1983
1984
Speci fie
Gravity
0.739
0.742
0.747
0.749
0.749
0.751
API
Gravity
59.97
59.20
57.92
57.42
57.42
56.92
Aromatics
Volume %
26.5
26
26.7
29.8
31.8
31
Avg. Dist.
Temp. , °F
220
222
219
220.3
220
221
Hydrogen/
Carbon Ratio
1.85
1.86
1.81
1.80
1.79
1.77
Data Submitted by General Motors, Reference 1.
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Where:
HC = the hydrogen/carbon ratio
12.011 = the atomic weight of carbon
1.008 = the atomic weight of hydrogen
The heating values of the fuels may be estimated by
empirical equations developed by ASTM or a simplier equation
from Marks' Mechanical Engineering Handbook.[3,4] The carbon
weight fractions, the specific gravity of the fuel and the
estimated heating values are given in Table 2. Both the
heating values and the variation in the heating values
calculated by the different methods are notably different. The
variations computed by the method of Marks' handbook are so
small that the effect from the change in heating value is
insigni ficant.
Table 2 demonstrates that a major uncertainty in the
computed correction will be the heating values of the present
and past fuels. Measured data would be highly desirable since
both of the methods of this report have questionable aspects.
The AS1M method was developed for aviation fuel, primarily
kerosene-like jet fuels and may not be applicable to automotive
gasoline. The method published by Marks is a much more general
approach for a wide range of petroleum products and its
precision in estimating the heating values for different
automotive gasolines is also questionable.
The results of Table 2, together with a CAFE value, are
sufficient to calculate the correction by either the Ol or EPA
approach. Most manufacturers have CAFE1 s near the CAFE
standards. Therefore, using the CAFE standards is a reasonable
approach to estimate the typical CAFE correction for the fuel
change. These corrections, based on the CAFE standards are
given in Table 3.
VI. Conclusions
It is appropriate to develop a CAFE correction for changes
in test fuel parameters. The following equation is the
simplest and most logical correction:
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Table 2
Test Fuel Properties
Calendar
Year
1979
1980
1981
1982
1983
1984
Specific
Gravity
0.739
0.742
0.747
0.749
0.749
0.751
Carbon
Weight
Fraction
.8656
.8650
.8681
.8688
.8694
.8707
Lower Heating Values
ASTM*
(Btu/lb)
18,517
18,515
18,481
18,434
18,407
18,412
Marks' **
(Btu/lb)
19,035
19,013
19,013
19,008
19,014
19,014
* Calculated by the method given in Reference 3.
** Calculated by the method of Reference 4.
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Table 3
CAFE Correction
CAFE Corrections
Model
Year (1)
1980(4)
1981
1982
1983
1984
CAFE
Standard
(MPG)
20
22
24
26
27
GM Method (5)
ASTM (2)
(MPG)
0
0.022
0.201
0.307
0.362
Marks (3)
(MPG)
0
0.036
0.190
0.259
0.282
EPA Method
ASTM (2)
(MPG)
0
-0.013
0.116
0.214
0.281
Marks' (3)
(MPG)
0
0.010
0.097
0.133
0.148
(1) All vehicles of any model year are assumed to be tested in
the previous calendar year.
(2) Lower heating value from ASTM calculation.
(3) Lower heating value from Marks' Handbook calculation.
(4) 1980 model year (i.e., 1979 calendar year taken as the
reference).
(5) The CAFE corrections as calculated by GM were based on the
GM CAFE's, not the CAFE standards. GM' s calculated CAFE
corrections were .0208, .1934, .2722 and .3228 mpg for
model years 1981 through 1984, respectively.
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Where:
Lr = the lower heating value of the reference fuel
La = the lower heating value of the actual test fuel
Ca = the carbon weight fraction of the actual test fuel
Cr = the carbon weight fraction of the reference fuel
This correction is based only on the energy content per
unit of carbon of the fuel. Other, more complicated correction
equations can also be developed.
Relatively little actual fuel data are available. For
example, no measurements of the heating value of the 1975
reference fuel are known. The lack of data is a major cause of
uncertainty in this correction.
Calculated corrections for model year 1984, the year with
the greatest CAFE correction, range from 0.148 mpg to 0.362 mpg
depending on the method of the calculation used and estimated
heating values of the fuel.
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References
1. Letter to R. E. Maxwell, Certification Division,
Office of Mobile Sources, U.S. EPA, from W.S. Freas, General
Motors Emission and Fuel Economy Operators, August 15, 1984.
2. "CAFE Corrections for Test Procedure Changes,"
Thompson, Glenn D. , U.S. EPA, OAR, CMS, ECTD, SDSB, October
1983.
3. "Standard Methanol for Estimation of Heat of
Combustion of Aviation Fuels," ASTM Standard D 3338, 1979.
4. Marks' Standard Handbook for Mechanical Engineers,
Baumeister, Avallone, Baumeister, McGraw Hill 8th Edition, 1978.
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