### MEMORANDUM

FROM: James Warila United States Environmental Protection Agency

Office of Air and Radiation Office of Transportation and Air Quality

Assessment and Standards Division

TO: Tier 3 Docket EPA-HQ-OAR-2011-0135

DATE: February 28, 2013

RE: Statistical Analysis of the Effects of Changing Fuel Properties on CO 2



### Emissions from Light-Duty Gasoline-Powered Vehicles based on EPAct/V2/E-89 Test Program Results

The change in test fuel described in the Tier 3 Notice of Proposed Rulemaking, if finalized, could have implications for the CAFE and GHG emissions compliance programs, as well as the fuel economy labeling program. Therefore, it is important to characterize the potential impact on

CO 2 

### emissions from the change in certification test fuel proposed in this rule. As outlined in the preamble to the 2017 and Later Model Year Greenhouse Gas Emissions and Corporate Average Fuel Economy (CAFE) 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 Greenhouse Gas and CAFE standards. 1 

### As a result, we used data from the EPAct Program to examine the effects of changing fuel properties on CO 2 

### emissions.

Using results from Phase 3 of the EPAct Program (also known as EPAct/V2/E-89), we performed a statistical analysis of the effects of five fuel properties on the CO 2 

### emissions of 15 late-model light-duty vehicles. To our knowledge, this is the most comprehensive study of fuel

effects on CO 2 

### emissions on recent model year vehicles.

The project was conducted as a controlled experiment, in which the design can be characterized as “randomized block with repeated measures”, in which vehicles are treated as blocks and fuel properties as “treatments.” A statistically optimal study design was developed to represent variation in five fuel properties: ethanol volume (%), aromatic content (%), RVP (psi), T50 (°F) and T90 (°F). These five parameters were selected based on previous studies as having potential to affect exhaust emissions, and were included in the design at the levels shown in Table 1. A critical feature of the study design is that the properties of the test fuels are assigned to span the ranges of in-use fuel properties, with the intent of providing a basis for the development of statistical models capable of predicting emissions for the majority of in-use fuels. Following a process in which statistical power, fuel-blending feasibility and budget were balanced, the final design included 27 test fuels.

1 77 FR 62624, 62777-62778 (October 15, 2012).

### A set of 15 test vehicles, all in model year 2008, with the majority certified to Tier-2/Bin-5

standards, was selected on the basis of sales levels, vehicle and engine sizes, and representation of manufacturers. Emissions were measured on the LA92 test cycle at a nominal temperature of 75°F. Emissions measured include carbon dioxide (CO 2 

### ), carbon monoxide (CO), total hydrocarbons (THC), methane (CH 4 

### ), non-methane hydrocarbons (NMHC), oxides of nitrogen (NO

x 

### ), and particulate matter (PM2.5). Following the completion of data collection, in June 2010, construction of the dataset involved intensive evaluation and quality assurance.

More details on the vehicles, fuels, and test procedures can be found in the program report. 2



### Table 1. Levels assigned to Experimental Factors (Fuel parameters) for the Phase-3 EPAct

**program.**

Factor No. Levels Levels

Low Middle High

Ethanol (%) 4 0 10, 15 20

Aromatics 2 15 35

RVP (psi) 2 7 10

T50 ( ° F) 5 150 165, 190, 220 240

T90 ( ° F) 3 300 325 340



## Analysis

Each of the vehicles was tested on each of the 27 fuels, with replication. On most vehicle fuel combinations two replicates were performed, whereas on some combinations, 3 replicates were performed. The total dataset includes 956 observations.

For this analysis we used cycle composites for the LA92 results, in which the three phases of the cycle (cold start, hot running and hot start) were weighted in the same manner as a composite calculated for the FTP cycle.



## Data Review

Figure 1 shows a summary of the entire CO 2 

### dataset as the common logarithm of the cycle composites, presented by vehicle and fuel. As expected, measurements are consistent and precise for each vehicle, with variability among vehicles considerably larger than variability within vehicles. Overall, the measurements range from 290 to 600 g CO 2 

### /mi.

2 US EPA, “EPAct/V2/E-89: Assessing the Effect of Five Gasoline Properties on Exhaust Emissions from LightDuty Vehicles Certified to Tier 2 Standards, Final Report on Program Design and Data Collection”, Report Number EPA-420-R-13-004, March 2013. Available at http://www.epa.gov/otaq/models/moves/epact.htm

### Figure 1. Common logarithms of CO **2** 

### measurements (Composites on LA92 cycle).



### As a next step, we averaged the data across all levels of each of the fuel properties in turn, and by vehicle, as shown in Figure 2 through Figure 6. The plots make it clear that, at the scales shown, visible effects are apparent only for aromatics.

**Figure 2. CO 2**  

### (Composite): Results averaged by four levels of ethanol and by vehicle.

### Figure 3. CO **2** 

### (Composite): Results averaged by two levels of aromatics and by vehicle.

**Figure 4. CO 2**  

### (Composite): Results averaged by two levels of RVP and by vehicle.

### Figure 5. CO **2** 

### (Composite): Results averaged by five levels of T50 and by vehicle.

**Figure 6. CO 2**  

### (Composite): Results averaged by three levels of T90 and by vehicle.



### In addition, we investigated whether graphing the results might indicate the possibility of an interaction effect between aromatics and ethanol. In this case we averaged the data by both its

### four ethanol and two aromatics levels and plotted the means, as shown in Figure 7. In this plot

we show trends against aromatics with a different series for each ethanol level. As in Figure 3, the effect of aromatics is visible, but it is not apparent that the aromatics effect differs systematically by ethanol level.

**F igure 7. CO**  **2** 

### (Composite): Emissions vs. Aromatics by Ethanol Level.



## Statistical Modeling

We followed up on the graphical presentation of the data by performing statistical modeling.

Response variable : As mentioned above, the response variable was CO 2 

### emissions, as the cycle composite on the LA92 cycle. Unlike other emissions, such as NO

x 

### , PM or NMOG, it was not necessary to perform a natural log transformation of the data before modeling, as the CO 2 

### results are approximately normally distributed with respect to the fuel properties.

Design Model : The properties of the test fuels form a five-dimensional study design optimized to estimate emissions as efficiently as possible for set of pre-specified model terms. These terms include a linear term for each of the five fuel properties, two squared terms for ethanol and T50, and four interaction terms, for combinations of ethanol with each of the remaining four properties. A model including this set of 11 terms is shown Equation 1.



### T90etOH T50etOH RVPetOH Arom etOH T50T50 etOH etOH T90 T50 RVP Arom etOH CO

11 10 9 8 7 6 5 4 3 2 102



### 

       

           

Equation 1

### The model including all 11 terms will be referred to as a “full model,” indicating that it contains

all available candidate terms.

Standardization : Prior to modeling, all terms were “standardized.” That is, each fuel property measurement was “centered” by subtracting its mean (for all measurements), and then “scaled” by dividing the difference by its corresponding standard deviation (for all measurements). For the five linear terms, this process was performed using individual fuel property measurements. The resulting “ Z score” has a mean of 0.0 and a standard deviation of 1.0. For 2 nd 

### –order terms, cross products terms were constructed not from the original measurements, but rather from the Z scores for the applicable linear terms. Then the standardization process was repeated, after calculating the means and standard deviations of the cross products of the Z scores. Thus, these “two-stage” standardized values for the 2 nd 

### -order terms will be referred to using the notation

“ ZZ .” For example, the term for the etOH×etOH quadratic term is notated as ZZ
ee 

### , and that for

the etOH×Aromatics interaction as ZZ
ea 

### . This process is performed to neutralize any remaining correlations among terms, particularly between linear effects and corresponding 2 nd 

### -order terms, and is described in greater detail in section 2.3.1 of the EPAct analysis report. Thus the models actually fit are represented in Equation 2, in which each term corresponds to its counterpart in Equation 1.

e911e510er9ea8 557ee6 9554r3a2e102 

### CO

ZZ ZZ ZZZZ ZZZZ ZZZZZ

       

  

      Equation 2



### Model Fitting : Starting with a “full model” including all 11 terms in Equation 2, we performed model fitting to identify and remove terms not contributing to the fit of the model to the dataset. This process was performed by backwards elimination. In the first step, after fitting the full model, any terms with p -values for their Type-III tests greater than 0.10 were removed and the model refit without them. The model with fewer terms is termed a “reduced model,” which is said to be “nested” in the full model. Then, as a test of goodness of fit between the two models, a likelihood ratio test was performed. The test statistic was the difference in the -2 log likelihood statistics between the nested and full models (known as the “reference model” for purposes of the test). This statistic is assumed to follow a χ 2 

### distribution with degrees of freedom equal to the difference in the number of parameters between the two models. If the test gave a p -value greater than 0.10, the null hypothesis of no difference in fit between the two models was retained, and the term(s) under consideration were dropped in subsequent model-fitting steps, under the assumption that they did not make a statistically significant improvement in the model fit. On the other hand, if the p -value was < 0.10, the null hypothesis was dropped, and one or more of the term(s) would be retained in the model, pending successive fitting steps. In this circumstance, one or more of the terms is assumed to make a statistically significant improvement in model fit.

If terms dropped in the first step are not retained, the “reduced model” with fewer terms becomes the “reference model” and the process is repeated. Successive model fitting steps are performed until a significant result is obtained and all remaining terms have p -values < 0.10.

## Results

The process is summarized in Table 2 through Table 4. Table 2 shows the set of reduced models fit. Table 3 shows the results of successive tests fit during the process. Table 4 shows the coefficients, standard errors and tests of effect for the full model and the reduced model having

the best fit to the dataset.

**T able 2. Models fit for CO**  **2** 

### (composite): (all models include an intercept term).

Model Term Notation Model

Full FM6 1 FM7 FM8

etOH Z

e • • • •

Arom Z

a • • • •

RVP Z

r • • • ×

T50 Z

5 • • • •
T90 Z

9 • ×

etOH × etOH ZZ
ee • ×

T50 × T50 ZZ 55 • ×

etOH × Arom ZZ
ea • • ×

etOH × RVP ZZ
er • ×

etOH × T50 ZZ e5 • ×

etOH × T90 ZZ e9 • ×

1 denotes “full minus 6.”

“x” denotes a term that was removed



### Table 3. CO **2** 

### (Bag 1): Model Fitting History, starting with the 11-term Full model.



### Fit Parameters Test with respect

to

Previous Model



### Model p

- 2 ln L BIC 1 

### Dev. d Pr> χ 2

Full 12 -7591.08 -7553.17

FM6 6 -7582.70 -7561.03 8.380 6 0.212

FM7 5 -7580.88 -7561.92 1.820 1 0.177

FM8 2 4 -7578.22 -7561.97 2.660 1 0.103

1 A lower value indicates a better fit.

2 Best fit with respect to the 11-term design model.

### Table 4. CO **2** 

### (Composite): Coefficients and Tests of Effect for the Full and Reduced Models, with **respect to the 11-term design model.**

Effect Full Model Reduced Model (FM8)

Estimate 1 Std.Err. 1 d.f. t

- value Pr> t Estimate 1 Std.Err. 1 d.f. t

- value Pr> t Intercept 433.7 25.59 15 16.95 0.000000 433.7 25.59 15 16.95 0.000000

Z
e 0.9796 0.2043 941 4.795 0.000002 0.9877 0.1678 941 5.886 0.000000

Z
a 7.784 0.1424 941 54.67 0.000000 7.766 0.1414 941 54.92 0.000000

Z
r - 0.1993 0.1626 941 -1.225 0.22 0.8249 0.1730 941 4.768 0.000002

Z 5 0.7546 0.2051 941 3.679 0.00025

Z 9 - 0.0243 0.1424 941 -0.170 0.86

ZZ
ee 0.2269 0.2741 941 0.8276 0.41

ZZ 55 - 0.2038 0.2053 941 -0.993 0.32

ZZ
ea 0.2050 0.1393 941 1.472 0.14

ZZ
er - 0.1770 0.1421 941 -1.246 0.21

ZZ e5 - 0.0867 0.2942 941 -0.295 0.77

ZZ e9 - 0.0459 0.1398 941 -0.328 0.74

2

veh 

###  9,822 9,821

2

 

###  18 18

1 Ex pressed in units of g/mi per a change in the fuel property of 1.0 standard deviation (g/mi

- σ ).



## Interpretation

The results shown in Table 4 are presented graphically in Figure 8, in which the bars represent the magnitude and signs of the coefficients, excluding the intercept (434 g/mi). Error bars on the coefficients represent 90% confidence intervals based on the standard errors shown in the table. The terms dropped from the reduced model can be seen as those with error bars spanning 0.0.

### Figure 8. CO **2** 

### (Composite): Standardized Model Coefficients for Full and Reduced Models (Error **bars represent 90% confidence intervals).**



### The reduced model is simple, retaining only three linear effects and no 2 nd 

### -order terms. The linear terms are ethanol, aromatics, and T50, with the values for ethanol and T50 being similar in size, with values of approximately 1.0 g/mi- σ . The term for aromatics is considerably larger, at approximately 8.0 g/mi- σ

.

Because, as mentioned above, the fuel properties are “standardized” before model fitting, and because the response variable is CO 2 

### emissions (g/mi), as a composite on the LA92, the coefficients represent a change in CO 2 

### emissions corresponding to changes in the fuel properties of 1.0 standard deviation ( σ ), as calculated for the fuel matrix used in the study. In addition, the coefficients represent the effect on the emission rate for each fuel property, as though the remaining properties would be held constant while varying the property under consideration. This assumption is entirely artificial but very useful in assessing the behavior of emissions in relation to changing fuel properties.

An interpretation of each of the terms is provided below:

Ethanol : The coefficient takes a value of 0.98 g/mi- σ . As the σ for ethanol is 7.9 vol.%, the coefficient indicates an increase of ~0.124 g CO 2 

### /mi per % increase in ethanol volume, assuming aromatics and T50 are held constant. For example, with the other two properties constant, we would predict a 1.25 g/mi increase in CO 2 

### from an E10 blend relative to an E0 blend. Note, however, that the change is very small, e.g., an average rate of 350 g/mi on E0 would increase to 351.24 g/mi on E10, which represents an increase of 0.4%.

### Aromatics : This coefficient takes a value of 7.8 g/mi- σ . The σ for aromatics is 10.0 vol.%.

Thus, the coefficient indicates an increase of 0.78 g CO 2 

### /mi per % increase in aromatics volume, assuming ethanol and T50 are held constant. For example, with the other two properties constant, we would predict a 7.8 g/mi increase in CO 2 

### from a 15% aromatics to one with 25% aromatics. While larger than the ethanol effect, this change is also small relative to the base level, e.g., an average rate of 350 g/mi on a fuel with 15% aromatics would increase to 357.8 g/mi on a fuel with 25% aromatics, which represents an increase of 2.2%.

T50 : This coefficient takes a value of 0.83 g/mi- σ . The σ for T50 is 28.6°F. The coefficient thus indicates an increase of 0.029 g CO 2 

### /mi per an increase in T50 of 1.0 F°, assuming ethanol and aromatics are held constant. For example, with the other two properties held constant, we would predict a 0.88 g/mi increase in CO 2 

### from a fuel with T50 at 220°F relative to a fuel with T50 at 190°F. An average rate of 350 g/mi on a fuel with T50 at 220°F would increase to 350.88 g/mi on a fuel with T50 at 190°F, which represents an increase of 0.3%.



## Conclusion

The analysis of results from the EPAct program indicates that changes in fuel properties are associated with measurable changes in CO 2 

### emissions. In particular, three fuel properties, ethanol, aromatics and T50 are associated with statistically significant changes in CO 2 

### emissions that are, however, small to very small in absolute terms.

Of the three properties, the effect for aromatics is clearly the most important, with the aromatics coefficient 8 times and 9.4 times larger than those for ethanol and T50, respectively (based on

the standardized coefficients s hown above in Figure 8).

While it is useful to consider the coefficients in isolation, it is critical to remember that in practice the fuel properties cannot be cleanly separated. Thus, when applying the models, it is necessary to account for the effects of multiple properties varying simultaneously.

For example, while noting that the ethanol coefficient predicts that a shift from E0 to E10 blends

would result in a small increase in CO 2 

### emissions, accounting for simultaneous decreases in aromatics (and possibly T50) due to dilution and/or octane match-blending by refiners, we would expect the aromatics effect would be opposite the ethanol effect and of an equal or greater magnitude. For example, the model suggests that the increase in CO 2 

### due to an increase in ethanol from 0 to 10 vol% (1.25 g/mi CO 2 

### increase) would be offset by a reduction in aromatics of 1.6 vol% (1.25 g/mi CO 2 

### decrease), not accounting for potential changes in T50. Stated differently, the model predicts that a gasoline with 0 vol% ethanol and 25 vol% aromatics would

have the same CO 2 

### emissions as a fuel with 10 vol% ethanol and 23.4 vol% aromatics.

In general, we conclude that the data and analysis support a conclusion that, aside from improbable cases in which ethanol and aromatics increase simultaneously, the addition of ethanol to gasoline is expected to have no appreciable effects on CO 2 

### emissions.