420-D-81-103
FUEL ECONOMY MEASUREMENT
CARBON BALANCE METHOD
Richard Lawrence
October 1981

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FUEL ECONOMY MEASUREMENT - CARBON BALANCE METHOD
Introduction
This paper gives the equations for determining fuel economy by the
carbon balance method for gasoline, diesel fuel, alcohols and blends
of the above. Derivations of the fuel economy equation constants and
several sample calculations are given. Fuel economy calculation
using compresses natural gas and method for stoichiometric A/F
determinations are included in Appendix 2.
Comparisons of carbon balance and volumetric fuel economy measurement
were made in an earlier study.—^
Summary
The carbon balance equation for determining fuel economy is:
F.E. = 			
y HC + 0.42? CO + 0.273 C02 + z TP
VJhere HC, CO, COj, and TP are in grams per mile and x and y are
given in the following table for some typical fuels. A more complete
table, including A/F, is given in Appendix 1.
Fuel	x	y

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Indolene
2421
.865
Diesel if2
2778
.865
Methanol (MOH)
1124
375
Ethanol (ETOH).
1557
521
90% IND/10% ETOH
2335
.829
TP is the particulate emission level in grams carbon per mile.
It is neglible for computing fuel economy for gasoline fueled
vehicles. For light duty diesel vehicles it is of the same
order of magnitude as the HC contribution (which is very
small). In this paper z is assumed to be 0.85 however available
data ranges from .75 to .95. Note that the "official" fuel
economy equation in the Federal Register does not include
particulate emissions.
3. Discussion
Fuel economy by the carbon balance method is accurate when used
under conditions where certain assumptions are valid. These
assumptions are:
1/ Evaporative and Exhaust Emissions of Two Automobiles Fueled With

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Volatility adjusted Gasohol, David Lawrence, D. Niemczak,
EPA-AA-TEB-81-12

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1	- All carbon in the exhaust comes from carbon in the fuel.
Corrections for carbon in the exhaust from sources other than
the fuel are made (such as background air corrections).
2	- The HC composition of the exhaust is the same as that of the
fuel.
3	- Emissions of HC, CO, COj and total particulate (®/mi) are
measured accurately. This includes proper accounting for
interferences such as water vapor.
A - The vehicle exhaust system does not have any leaks.
5	- The weight fraction carbon (WFc) and specific gravity (SG) are
known. Ideally, they should be accurately determined for each
batch of gasoline or diesel fuel.
6	- For vehicles with particulate traps or trap oxidizers the carbon
trapped and emissions during purge are properly accounted for.
The first four assumptions are valid for gasoline and diesel
fueled vehicles tested in accordence with Fit 40 CFR 86. The
VTF and SG must be accurately determined. This is not
c
difficult for pure fuels, such as the alcohols.
For gasoline and diesel fuels the SG is easily determined from the
API gravity.—'' SG for the alcohols is available from various
handbooks.

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WFc is not easily determined for gasoline and diesel fuels and can
vary by several percent from batch to batch. For fuel economy
comparisons between a base gasoline or diesel fuel and a blend of
alcohol with that base fuel the effect of the uncertainty of WF of
	a		c
the base fuel cancels. Thus, fuel economy comparisons for fuel
blends can be done accurately using the carbon balance method, c.
-Hi t -it""!* 6*.u r*-«l
However, batch to batch fuel economy comparisons of a single fuel
type (e.g. Indolene HO) can induce an error on the order of up to 27,
if the WF and SG are assumed rather than measured. Such a
c
situation exists under current fuel economy regulations (40 CFR part
600) where an assumed value of 2421 grams carbon per gallon of
gasoline and 2778 grams carbon per gallon of diesel fuel are used.
Particulate emissions from diesel fueled vehicles are not included in
the "official" EPA equation given in 40 CFR 600. However, at the
current particulate standard of 0.6 ^/mi the impact of excluding
particulate emissions will cause overstatement of fuel economy,
especially for higher fuel economy vehicles. For example, assuming
that a diesel fueled vehicle particulate consisting of 85% carbon the
impact of excluding the particulate emission will be to overstate
fuel economy by:
TP =• 0.6 e/mi	TP = 0.2 e/mi
0.07 MPG
0.44 MPG
1.80 MPG
0.02 MPG
0.14 MPG
0.61 MPG
(20 MPG vehicle)
(50 MPG vehicle)
(100 MPG vehicle)

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For vehicles with other particulate emission rates the impact of
excluding these emissions from the carbon balance equation will
change proportionately.
4. Calculations
Carbon balance fuel economy is given by:
j, v =	grams carbon / gal fuel = MPG
r • L •	¦¦ ¦ — ¦ — i - i
grams carbon in exhaust / mile
2/ SG =
141.5
131.5 + deg API

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The numerator "N" of equation 2 is determined by:
N = Grams carbon/gal fuel
N - 3785 x SGxWF
c
Where: 3785 « density of water (grams per gallon)
SG = Specific gravity of fuel (§c/gw)
WFc = weight fraction of carbon in the fuel = MWc/MWf
MW^ = molecular weight of carbon per fuel molecule
= molecular weight of fuel.
Example 1: pure _ethanol ¦	C2H60
SG = .789
MW = 2 x 12.011 = 24.022
c
MWf = 2 x 12.011 + 6 x 1.008+ 16.0 = 46.070
WF = 24.02/46.07 = .5214
c
N = 3785 x .789 x .5214
N = 1557 grams carbon/gal fuel
Example 2: Gasoline: CH^ (typical value)
Note that the gasoline is reduced to the	value
simplify calculations.
SG = .740
MW = 1 x 12.01 = 12.011
c
MWf = 1 x 12.011 + 1.86 x 1.008 = 13.88
WF = 12.011/13.886 = .865

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N = 3785 x .740 x .865
N = 2421 grams carbon/gal fuel
Example 3: Diesel Fuel: CH1 BA (Typical value)
SG	= 0.8475
MW	=	1 x 12.011 = 12.011
c
MWf =	1 x 12.011 + 1.86 x 1.008 = 13.886
MF = 12.011/13.886 = .865
c
N = 3785 x 0.8485 x 0.865
N = 2778 grams carbon/gal fuel
Example 4: a mixture of 10% ethanol and 90% gasoline:
Calculate components individually and then weight by volume
fraction.
N = .1 x 1557 + .9 x 2421
N = 2334 grams carbon/gal fuel
Where: 1557 = gc/gal ETOH
2421 = gc/gal Gasoline
B. The Denominator "D" of equation 2 is determined by:
D = WF x HC g/mi + .429 x CO 8/mi + .273 x CO, g/mi
C	£¦
+ 0.85 x TP 8/mi
HC, CO, ' CO2 ®/mi are obtained from the emissions test.

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TP is obtained from the emission test for diesel pueled
vehicles and is assumed equal to zero for other vehicles
with low particulate emission rates.
0.429 is the weight fraction of carbon in CO:
MW /MW - 12.011/(12.011 + 16.0) = 0.429
c CO
0.273 is the weight fraction of carbon in COj:
MW /MW = 12.011/(12.011 + 2 x 16.0)
C COj
The weight fraction carbon of diesel particulate is assumed
to be 0.85

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WFC for single component fuels is determined as in
the calculations for the numerator.
For fuel blends:
WFC = (VF< WF1 SG^)
(VFi SGi)
Example 5 a mixture of 10% ethanol and 90% gasoline:
WT'C = .1 x .5214 x .789 + .9 x .865 x .739 = .6164
.1 x .789 + .9 x .739	.7440
WF£ = .829 grams carbon/gram fuel
D = .829 HC + .429 CO + .273 C02
C. Carbon balance equation:
Combining above information (from ex 4 and 5) for a mixture
of 10% ethanol and 90% gasoline in eq 1 gives:
FE, MPG = 	"Qlll	g^/gal fuel	
(.829 HC + .429 CO + .273 CO-,) g /mile
e. c
The carbon balance equation for one batch of "Anafuel" is
shown to demonstrate the method for combining three fuel
components (Appendix, Table 2).

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APPFNDIX 1
TABLE 1
Fue] Properties - Alcohols, Gasoline, Diesel Fuels
(i)
Fuel
Indolene
112 Diesel
(2)
Formula
C"].86
C"i.86
(3)
MW
13.89
13.89
(A)
SG
.740
.848
(5)
8fnel/GAL
(3785 x SG)_'
2801
3210
(6)
^^carbon
.865
.865
(7)
gc/CAL
(HWc/MWfue]) (5 x 6)
2423 [Note 2]
2776 [Note 3]
(8)
A/F
(STOTCII)
14.5
14.5
Me thanol
Ethanol
N-Propanol
N-Butanol
CII4O
C2II60
c3,,8°
c4h10o
32.04
46.07
60.09
74.12
.792
.789
.804
.810
2997.7
2986.4
3043.1
3065.9
.3749
.5214
.5997
.6482
1124
1557
1825
1987
6.5
9.0
10.3
11.2
'Gasohol"
10% ETOH
in gasoline
10% MOH
in gasoline
,8294
.8138
2335
2179
14.0
13.7
F.E., MPC = 	(7) g^/gal.		
6 x 1IC + .4 29 CO + ."273 C02 gc/mi + z x TP
Where: HC, CO, C02, and TP are in 8/mi
And:	Z is the weight fraction carbon in the particulate of diesel fueled
vehicles. Assume 7. - .85 if no other information is available. 40 CFR 600
does not include TP in fuel economy calculation.
77 i gal = 3785 cc; 1 cc = 1 g water at 4°C.
2/ 40 CFR 600 uses 2421 gc/gal Indolene.

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/M'rr.mjjA i
TABLE 2
Fuel
J ndolene
Casoli ne
Portion of
Anafuel
MOII
BOH
FORMULA
C},1.86
c,,1.71
CII4O
C^HjoO
Anafuel 7/81
9.8% MOII
2.7% BOH
87.5% Gasolene
MW,
Fuel rropertie& - "Anafuel'
WF_
SG	g/CAL
(3785 x SG)I/
13.89 .740
2801
13.73 .76961/ 2913
32.04 .792	2998
74.12 .810	3066
.865
.8748
.3749
.6482
.8191/
gc/GAL
2548
1124
1987
23933/
A/F
2421 [F.R. Value] 14.5
6.5
12.1
13.7
F.F., MPC =
	2393 gr/gal	
(.819 HC + .429 CO ¥ .273 CO2) gc/mi
T7 1 gal = 3785 cc; 1 cc = 1 g water
2/ Calculated
3/ -875 (2548) + .098 (1124) + .027 (1987) = 2393 gc/ga]
4/ (Vf) (Wf) (SC)
(.875 x .875 x .7696) + (.098 x .3749 x .792) + (.027 x .6482 x .810) = .6328 = .ft1q
(.875 x .7696) + (.098 x .792) + (.027 x .810)	.7729 	
(Vf) (SG)

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VjQC jrPS.'-S
I. Method for Calculation of Fuel Economy of Compressed Natural Gas (CNG)
A. An accurate analysis of the fuel giving mole fraction data is require<
Below is given a typical CNG analysis.
Gas Analysis in Mole %
Nitrogen (N2)	4.24 Higher Heating Value = 976- BTU/SCF
C02	1.23
He	.12
90.52	Specific Gravity = .607
C2H6	3.22
C3H8	.45
i-C^H^o	*06
n-C^H^o	*07
i-C5H12	.02
n-C5H12	.02
C6H14	-02
C7H16	.01
C8His	.01
CgH2o	.00
CioH22	.00
CnH24	.00
C12H26	'O0
C13H28	*00
C14H30	.00
H2	.00
B. Calculation of Carbon and Hydrogen Weight Fractions.
1.	The weight of Carbon per constituent is:
// of carbon Atoms x (the weight of a carbon Atom = 12.01115) x mole fractior
The sum of the carbon weight fractions will be the carbon weight fractior
for the fuel.
2.	The molecular weight of the fuel is found by:
(Molecular weight of constituent) x (Mole fraction)
The sum of the weight fractions will be molecular weight for the fuel.
3.	The weight of the hydrogen per constituent is:
(// of Hydrogen Atoms) x (the weight of a Hydrogen Atom = 1.008) x (H;
mole fraction)
The sum of the hydrogen weight fractions will be ' the hydrogen weight
fraction of the fuel.
J]	gy	?ev

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4. Because the CO2 in the fuel will simply pass through the engine (assumed
the carbon fraction of the fuel not counting the CO2 in also needed.
A sample calculation is given below:

Mole
Molecular Weight
Weight
Weight
Molecula
Component
Fraction
of Constituent
Carbon
Hydrogen
Weight
n2
0.0450
28.0134
0
0
1.26060
C02
0.0043
44.00995
0.05165
0
0.18924
He
0.0012
4.0026
0
0
0.00480
CH49O
0.9076
16.0430
10.90132
3.65933
14.56065
C2«6
0.0362
30.0700
0.86961
0.21893
1.08854
C3Hg
0.0039
44.0972
0.14053
0.03145
0.17198
i-C4Hio
0.0005
58.1243
0.02402
0.00504
0.02906
n~c4H10
0.0006
58.1243
0.02883
0.00605
0.03487
i_c5H12
0.0002
72.1513
0.01201
0.00242
0.01443
n-C5Hi2
0.0001
72.1513
0.00601
0.00121
0.00722
C6«i4
0.0002
86.1784
0.01441
0.00282
0.01724
c7Hi6
0.0001
100.2055
0.00841
0.00161
0.01002
c8h18
0.0001
114.2327
0.00961
0.00181
0.01142
TOTALS
1.0000

12.06641
3.93068
17.40007
Carbon weight fraction =
for fuel
weight Carbon
= 12.06641 = .693
molecular weight of fuel 17.40007
weight Carbon - weight CO?
Carbon weight fraction for
.691
fuel not counting CO2	molecular weight of fuel
Hydrogen weight o-f fraction = weight of Hydrogen
of fuel	molecular weight of fuel
12.06641 - .0516.'
17.40007
= 3.93068 = .226
17.40007
C. Carbon Balance Method of Fuel Economy Calculation for CNG.
1.	The weight fraction of carbon in CO is:
12.01115	=
12.01115 + 15.9994
2.	The weight fraction of carbon in CO2 is:
12.01115
12.01115 + 2(15.9994)
= .273
The weight fraction of HC in the vehicle exhaust is assumed to be equal t
that in the fuel not counting CO2.
The gram/mile of carbon in the exhaust is then:
(weight fraction of carbon not)
.429 (CO) + .273 (CO2) + ( counting CO2 in the fuel ) (HO
Where CO, CO2, and HC are in grams/mile from the exhaust analysis.

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The density of the fuel is calculated as follows:
s Pressure x Mass Air (s.G.)
R x T
Where R = Universal Gas Constant = 1545.33 ft - lbf/lbm - °R
T = Temperature in °R
S.G.= Specific gravity compared to air given in the fuel analysis.
example = At atmospheric pressure, 60°F the
= (14.767 psi)(144 in2/fti)(28.967 lbm/lb-mole Air)(453.592 gms/11
(S.G.)	"
"	(1545.33 ft-lbf/lbm-°R)(520°R)
= (34.77 gms/ft3)(S.G.)
for the analysis given previously S.G. = .607
example = (34.77 gms/ft3)(.607) = 21.11 gms/ft3 = 2111 gms/100 SCF
Fuel Economy Calculations
The fuel economy calculations are found by
(Gms/100 SCF)(Carbon weight fraction for the fuel) miles/100 SCF
.429 (CO) + .273(C02) + (Carbon weight fraction for)(HC)
(the fuel not counting CO2)
example: for the analysis given above and HC = 1.0 gms/oile, CO = 7.0 gms/m:
CO2 = 400 gms/mile, = 21.11 gms/Ft3 = 2111 gms/100 SCF
(2111 gms/100SCF)(.693)
(.429)(7.0) + (.273)(400) + (.691)(1.0) = 12'96 miles/100 SCF
Equivalent gasoline MPG Calculations
Using the higher heating value from the CN4 Analysis for 100SCF the lov
heating value must be calculated.
This is because we will need to compare the lower heating values of CNG c
Gasoline. The lower heating value is calculated as follows:
Grams of Hydrogen/100 SCF = (grams of fuel/100SCF)(Weight fraction
Hydrogen)
(in the fuel)
The H2O produced per 100 SCF
= (Grams of Hydrogen/100 SCF)[(2)(1.00797) + 15.9994)]
(2)(1.00797)

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The heating value of H2O at 60°F is:
(H20 produced/100 SCF) x 1059.9 BTU/lbm
453.592 gms/lbm
Where 1059.9 BTU/lbm is the energy required to change 1 lbm of H2O frc
liquid to steam.
The lower heating value = the higher heating value - the heating value 0
H20
Ex. using the same set of example data
Grams of H2/100 SCF = (2111 gm/100 SCF)(.226) = 477.1 gms Ho/10
SCF
H20 produced/100 SCF = 477.1 ,[(2)(1.00797) + 15.9994)] = 4263 58 gms H,o/10
(2)(1.00797)	^
The heating value of the H20 is:
4263.58 gms H20/100 SCF y 1059.9 BTU/lbm = 9962.6 BTU/100 SCF
453.592 gms/lbm
The lower heating value = S7600 - 9962.6 = 87637.4 BTU/100 SCF
The number of SCF of CNG to have an equivelent BTU content of one gallon
is given by
Lower heating value 1 gallon of gasoline (100) = No. of SCF
Lower heating value of 100 SCF of CNG	Gallon of Gasoline
The mile per gallon gasoline equivelent is given by
m^es x No. of SCF	 x 1 = MPG gasoline equivelent.
100 SCF Gallon of Gasoline lOt)
ex. Using same example with BTU/gallon of gasoline = 118,000 BTU/gal.
No. of SCF = 118,000 x 100 = 134.65 SCF/gallon.
Gallon of Gasoline 87637.4
MPG gasoline equivelent = 12.96 miles x 134.65 SCF/Gallon= 17.45 MPG equi
100 SCF 100

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Calculation of Air/Fuel Ratio at Stochiometric A/R.
1.	For any hydrocarbon fuel CxHyOz
2.	The Equation is:
CxHyOz + (x + y/4 - z/2) O2 + 79/21 (x + y/4 - z/2) N2
x CO2 + y/2 H2O + 79/21 (x + y/4 - z/2) N2
A/F«;t0TCH = (x + y/4 - z/2)(32) + 79/21 (x + y/4 - z/2) x (28)
12.011 (x) + 1.008 (y) + 16.0 (z)
A./FsTnTr.H/=	137.333 (x + y/4 - z/z-1)
12.011 (x) + 1.008 (y) + 16.0 (z)

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