   MEMORANDUM
   
   FROM:	Aron Butler, Assessment and Standards Division
   		David Good, Compliance Division
   		Arvon Mitcham, Assessment and Standards Division
   		Office of Transportation and Air Quality
   		Office of Air and Radiation
   		United States Environmental Protection Agency
   
   TO:	Tier 3 Docket #EPA-HQ-OAR-2011-0135
   
   DATE:	February 28, 2013
   
SUBJECT:   	Analysis of the Effects of Changing Fuel Properties on the EPA Fuel
	Economy Equation and R-Factor

Fuel economy is one important measure of a vehicle's efficiency.  Under federal regulations, it is EPA's responsibility to set specific methods used to measure and calculate fuel economy to be used in determining automobile manufacturers' compliance with the Corporate Average Fuel Economy (CAFE) program, as well as the window stickers on new vehicles that inform consumers of a variety of fuel economy related factors. 
 
The proposed change in test fuel, if finalized, could have implications for the CAFE emissions compliance program and the fuel economy labeling program.  Therefore, it is important to characterize the potential change in fuel economy as a result of the changes in certification fuels proposed in this rule.  As outlined in the preamble to the 2017 and Later Model Year Greenhouse Gas Emissions and Corporate Average Fuel Economy  final rule, if the EPA test fuel used for certification and fuel economy vehicles changes to include ethanol, EPA is committed to address whether the fuel change has a potential to affect the stringency of  the standards.  As a result, we reviewed the parameters and inputs for the fuel economy equation to explore whether changing fuel properties have any affect the equation in its current form. 

Historically, there was no simple, non-invasive method to accurately measure the amount of liquid fuel consumed over the course of a fuel economy and emissions test.  Therefore, the standard method of calculating fuel economy has been to determine the miles per gallon based on the sum of the amount of carbon-containing compounds emitted from the tailpipe (primarily CO2 which can be measured with great accuracy) during a standard emissions test, and then combined with the measured properties of the test fuel (density (specific gravity) and carbon weight fraction which determine the amount of carbon-containing compounds in the fuel), miles per gallon metric can be determined.  This calculation is known as the "volumetric fuel economy" calculation and has also been referred to as the "carbon balance" equation in the literature as shown in Equation 1 below, where "T.fuel" subscript indicates properties of the test fuel and "exh" indicates properties of exhaust hydrocarbons.  

		Eq.1


The Energy Policy and Conservation Act (Pub. Law 94-163 December 22, 1975) requires EPA to: 

      "...measure fuel economy for each model and calculate average fuel economy for a manufacturer under testing and calculation procedures prescribed by the Administrator.  However, except under section 32908 [Fuel economy labeling (new vehicle window sticker) requirements] of this title, the Administrator shall use the same procedures for passenger automobiles the Administrator used for model year 1975 (weighted 55 percent urban cycle and 45 percent highway cycle), or procedures for passenger automobiles the Administrator used for model year 1975(weighted 55 percent urban cycle and 45 percent highway cycle), or procedures that give comparable results."  

In the 1970's, EPA promulgated regulations to calculate fuel economy (mpg) based on the carbon balance (volumetric) fuel economy equation, combined with a specific set of fuel properties which were representative of 1975 gasoline.  A carbon wieght fraction of 0.866 and specific gravity of 0.739 were determined to be representative of 1975 gasoline test fuel and incorporated into the carbon balance fuel economy equation, as shown in Equation 2 below (note that NMHC and CH4 are combined into the HC term here). 

		Eq.2


As outlined above, EPCA also mandated that the fuel economy equation used for passenger cars should account for any future change in test fuel properties such that the test procedure would give comparable results compared to the 1975 test procedures.  

In January, 1982, the U.S. Court of Appeals for the Sixth Circuit remanded a case to EPA concerning the need for CAFE adjustments based on test procedure changes since 1975, so that EPA could initiate rulemaking proceedings concerning any appropriate adjustments for the then current test procedures.  From 1983 to 1986, EPA made various regulatory changes to account for test procedure changes since 1975 which were determined to have an effect on CAFE.  This included revisions to the 1975 fuel economy equation.  Beginning with model year 1988 vehicles, the fuel economy equation was revised from an equation which assumed the test fuel had average 1975 fuel properties to an equation which was based on the measured fuel properties of the test fuel which was used to perform the actual test. The fuel economy equation corrected the fuel economy results to account for the differences in the actual fuel properties of the test fuel compared to the properties of the 1975 baseline test fuel.  

Beginning with model year 1988 vehicles, EPA modified the calculation method so that the fuel economy calculation accounted for difference between the test fuel and the 1975 baseline fuel by accounting for differences in carbon weight fraction (CWF) and net heating value (NHV or volumetric energy content) between the actual test fuel and the 1975 baseline fuel.  Accompanying the NHV adjustment was a sensitivity factor, called "R", which represents the response of a typical vehicle's fuel economy to small changes in the fuel's energy content.  Accordingly, the R-factor can be determined using the general formula shown in Equation 3, where "B.fuel" indicates baseline fuel:

                                       
		Eq.3

Studies of fuel economy data done in 1985 by General Motors and others suggested an R-factor of 0.6 would be appropriate.   Based on this information, EPA regulations currently account for changes in test fuel properties compared to the 1975 baseline fuel by calculating fuel economy as shown in Equation 4.

	 	Eq.4


The constants in Equation 4 (i.e. 5,174 x 10[4] and 5,471) contain values for the baseline fuel's NHV (Btu/gal), CWF, and specific gravity.  The R-factor of 0.6 is also visible in the denominator.

A theoretical analyses done by EPA in 1987 described how only a small fraction of the fuel's chemical energy is used to propel the vehicle, and that the many losses to heat and friction are nonlinear and do not depend on fuel properties.  It concluded that while a maximum R-factor of 0.95 was possible, a value of 0.82 was more plausible.  

Other studies examining the R-factor have been published since then.  For instance, in a 1993 study conducted jointly by members of the automobile and oil industries (known as the Auto/Oil program), the authors suggested that "[f]or the current fleet, R had a value of 0.93 +- 0.05 and for the older fleet, the value of R was 0.92 +- 0.21." 

More recently, EPA staff assessed the R-factor based on the EPAct/V2/E-89 dataset.  The EPAct/V2/E-89 test program was sponsored by EPA, DOE/NREL, and CRC to assess the fuel effects of various fuel parameters on exhaust emissions of Tier-2-compliant passenger cars and light trucks.  This resulting dataset contains 956 emission tests conducted on 15 high-sales vehicles of 2008 model year conducted by Southwest Research Institute between March 2009 and June 2010.  More details on the vehicles, fuels, and test procedures can be found in the program report.   

While the focus of the EPAct/V2/E-89 test program was not to evaluate R-factor, the resulting dataset included volumetric fuel economy results for all emission tests (using Equation 1) as well as NHV measurements for all test fuels.  Since R-factor is defined as sensitivity of fuel economy to NHV, it could be empirically determined from the test program results.  Ethanol content has a significant effect on NHV, an issue of special relevance given the proposed increase in ethanol content in certification fuel used during emissions and fuel economy testing.  Figure 1 shows NHV for all test fuels used in the EPAct/V2/E-89 test program.

  Figure 1.  Net heating value versus oxygen content for EPAct/V2/E-89 fuels.
                                       

For the remainder of this analysis we divide the dataset based on whether the test fuel was E0, E10, or E20.  R-factor was calculated using Equation 5, where the averages were taken for all tests on that fuel type. 

		Eq.5


Since the fuel economy values vary significantly by test vehicle, it was useful to calculate an R-value for each test vehicle individually.  Figure 2 shows the results for composite-cycle weighted values (combined results of cold and hot portions of the emission test) by test vehicle for both E10 and E20 groups compared to E0.  Also shown on Figure 2 are simple averages computed across the test fleet, with both values falling between 0.8 and 0.9.  Though not shown, the average R-factors determined from the cold start portions of the test were very similar to the hot running results.  
                                       
  Figure 2.  Empirical R-factor results for EPAct/V2/E-89 dataset by vehicle.


An important consideration in doing empirical analyses for R-factor is the sensitivity of the result to measurement variability.  Since the differences in fuel economy and fuel NHV being examined are typically small relative to their values, Equation 5 can produce widely varying quotients from test to test as evidenced by the variability in results between vehicles for the same fuel comparison and fuel comparisons for the same vehicle.  This makes it difficult to reply on data of limited sample size or studies where other confounding changes may be occurring.  The EPAct/V2/E-89 dataset is large, with at least 16 tests behind the averages for each ethanol level in Equation 5 when producing each vehicle result on Figure 2. 

These results pointing to an R-factor between 0.8 and 0.9 are generally consistent with findings of the Auto/Oil program and EPA's 1987 theoretical analysis.
