NOTICE

This technical report does not necessarily represent final EPA decisions or 

positions. It is intended to present technical analysis of issues using data 

that 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.

Assessment and Standards Division

Office of Transportation and Air Quality

U.S. Environmental Protection Agency

National Renewable Energy Laboratory

U.S. Department of Energy

Coordinating Research Council

EPAct/V2/E-89: Assessing the Effect 

of Five Gasoline Properties on Exhaust 

Emissions from Light-Duty Vehicles 

Certified to Tier 2 Standards

Final Report on Program Design and 

Data Collection

Appendix A

Re-Design of Fuel Matrices for EPAct 

Program

EPA-420-R-13-004

April 2013
A-2 

RE-DESIGN OF FUEL MATRICES FOR EPACT PROGRAM

(Work Assignment WA 1-08 for Contract EP-C-07-028) 

September, 2008 

Robert L. Mason and Janet P. Buckingham 

Southwest Research Institute

1.0 Introduction

The objective of this project was to re-design the test fuel matrices previously provided to 

the EPA in February and August 2008 for its EPAct Program. The experimental designs 

were to be used to construct prediction equations for light-duty gasoline vehicle 

emissions. Five fuel properties were chosen as the experimental factors. These included 

ethanol (ETOH), T50, T90, aromatics (AROMATICS) and DVPE. The number of levels 

for each factor was 4 for ETOH, 5 for T50, 2 for T90, 2 for aromatics and 2 for DVPE. 

Due to the desire to minimize the number of exhaust emissions test fuels, statistical 

designs were selected using a computer algorithm that generated optimal designs. In 

optimal designs, unlike in standard factorial and fractional factorial experiments, the 

factors are selected to be nearly orthogonal rather than exactly orthogonal, and the 

estimates of the factor effects are correlated rather than uncorrelated with one another. 

Computer-generated optimal designs are labeled non-orthogonal designs.

The process of generating an optimal design requires specification of the linear model 

that is to be estimated as well as a list of candidate design points from which to choose 

the design points. The candidate design points are usually located at the vertices of the 

space generated by the chosen levels of the factors to be included in the experiment, but 

may include any points within the ranges of the chosen factors. 

An optimal design is generated by choosing design points from the candidate design 

point list that maximize or minimize a chosen optimality criterion that is related to the 

specified linear model. There are several different optimality criteria for generating 

optimal designs, and the one chosen for this study was G-optimality. Optimal designs are 

judged by their efficiency, which is usually expressed as a percentage. The efficiency 

value is a function of the number of points in the design, the number and types of factors 

in the model, and the maximum standard error for model prediction over the design 

points. The G-optimality criterion seeks to minimize the maximum standard error for 

prediction over the design points. Since a standard fractional factorial design will have 

an efficiency of 100%, a large G-efficiency value indicates the design is good. 

Generally, a design with a G-efficiency greater than 50-60% is considered adequate for 

prediction purposes. 
A-3 

Different types of search algorithms are available for finding an optimal design. These 

algorithms are based on adding and deleting candidate points to a design and stopping 

when the chosen criterion ceases to improve the design. The search method used in this 

project was the simple exchange algorithm. The initialization of the search process is 

started by specifying a random number. 

Given below is a brief description of the process used in selecting the design requested by 

EPA for studying fuel effects on tailpipe emissions in light-duty vehicles.

2.0 Original Experimental Design #1: 16-Fuel Matrix

Factors and Model 

Five experimental factors were used in this matrix development. The factors and their 

levels are listed in Table 1. 

TABLE 1. EXPERIMENTAL FACTORS AND LEVELS FOR DESIGN #1

Factor Low Level Mid Levels High Level

T50, oF 150 190, 220 240

T90, oF 300 - 340

ETOH, % 0 - 10

DVPE, psi 7 - 10

Aromatics, % 15 - 40

All combinations of the above values would yield 4x2x2x2x2=64 candidate test fuels. 

However, due to problems in blending some of the fuels, EPA eliminated (1) the 8 

candidate fuels with T50=240o

F and ETOH=10%, (2) the 8 candidate fuels with 

T50=150o

F and ETOH=0% and (3) the 4 candidate fuels with T50=150oF, ETOH=10% 

and DVPE=7. This left n = 64-20 = 44 candidate fuels available for usage in generating 

the model. 

EPA requested that the experimental design should generate data to estimate the 

coefficients (labeled b1 to b10) for the following polynomial-type model: 

Response = b0 + b1*T50 + b2*T90 + b3* ETOH + b4*DVPE + b5*Aromatics + 

 b6*T50*T50 + b7*ETOH*T50 + b8*ETOH*T90 + 

b9*ETOH*DVPE + b10*ETOH*Aromatics + Error

where Response indicates the emissions or engine property of interest, and Error denotes 

the random error in the experiment. 

Design Results

An experimental design software package, ECHIP Version 7.01, was used to generate the 

experimental design matrix to meet the above conditions. Several design attempts were 
A-4 

made with varying starting random seeds for the algorithmic process in ECHIP. The 

‘best’ design resulted in a G-efficiency equal to 72.6%. Table 2 lists the experimental 

design fuel matrix, consisting of 16 unique factor-level combinations, that was produced 

using ECHIP. 

TABLE 2. FUEL MATRIX DESIGN #1

Fuel No. T50, o

F

T90, o

F

ETOH, 

%

DVPE, 

psi

AROMATICS, 

%

1 150 300 10 10 15

2 240 340 0 10 15

3 220 300 10 7 15

4 220 340 10 10 15

5 240 300 0 7 40

6 190 340 10 7 15

7 190 300 0 7 15

8 220 300 0 10 15

9 190 340 0 10 40

10 220 340 10 7 40

11 190 300 10 10 40

12 150 340 10 10 40

13 220 340 0 7 40

14 190 340 0 7 15

15 190 300 0 10 40

16 220 300 10 7 40

3.0 Original Experimental Design #2: 25-Fuel Matrix

After the 16-fuel experimental design given in Table 2 was developed, EPA requested 

that additional fuels be added to include an area of the design space that extended the 

ethanol content (ETOH) to 20%, but included points at 15%. An additional criterion was 

that the original 16-fuel design be kept intact and that the additional fuels would be used 

to augment this design. There was also a request to keep the number of additional test 

fuels to 9 so that the total number of fuels was 25. 

Factors and Model 

The factors and their levels are listed in Table 3. 
A-5 

TABLE 3. EXPERIMENTAL FACTORS AND LEVELS FOR DESIGN #2

Factor Low Level Mid Levels High Level

T50, oF 150 160 190

T90, oF 300 - 340

ETOH, % 15 - 20

DVPE, psi 7 - 10

Aromatics, % 15 - 40

All combinations of the above values would yield 3x2x2x2x2=48 candidate test fuels. 

However, due to problems in blending some of the fuels, EPA chose to (1) eliminate the 

4 candidate fuels with T50=150o

F, ETOH=15% and DVPE=7, (2) eliminate the 16 

candidate fuels at ETOH=20% and T50=150oF and 190oF by restricting the candidate

fuels at ETOH=20% to have only T50=160o

F and (3) eliminate the 8 candidate fuels with 

T50=160oF and ETOH=15%. This left a candidate set of n = 48-28 = 20 fuels for usage 

in augmenting the design given in Table 2. 

EPA also requested that the experimental design should generate data to estimate the 

coefficients (labeled b1 to b11) for the following polynomial-type model (which now 

includes a squared term for ETOH): 

Response = b0 + b1*T50 + b2*T90 + b3* ETOH + b4*DVPE + b5*Aromatics + 

 b6*T50*T50 + b7*ETOH*T50 + b8*ETOH*T90 + 

b9*ETOH*DVPE + b10*ETOH*Aromatics + b11*ETOH*ETOH + 

Error

where Response indicates the emissions or engine property of interest, and Error denotes 

the random error in the experiment. 

Design Results

An experimental design software package, ECHIP Version 7.01, was used to 

generate the experimental design matrix to meet the above conditions. Several design 

attempts were made with varying starting random seeds for the algorithmic process in 

ECHIP. The chosen design resulted in a G-efficiency equal to 68.1% and is listed in

Table 4 as Design #2. The experimental design consists of 25 unique factor-level 

combinations. 
A-6 

TABLE 4. FUEL MATRIX DESIGN #2

(WITH G-EFFICIENCY = 68.1%) 

Fuel No. T50, o

F

T90, o

F

ETOH, 

%

DVPE, 

psi

AROMATICS, 

%

1 150 300 10 10 15

2 240 340 0 10 15

3 220 300 10 7 15

4 220 340 10 10 15

5 240 300 0 7 40

6 190 340 10 7 15

7 190 300 0 7 15

8 220 300 0 10 15

9 190 340 0 10 40

10 220 340 10 7 40

11 190 300 10 10 40

12 150 340 10 10 40

13 220 340 0 7 40

14 190 340 0 7 15

15 190 300 0 10 40

16 220 300 10 7 40

17 160 300 20 7 40

18 160 300 20 10 15

19 160 340 20 10 40

20 160 340 20 7 15

21 150 340 15 10 15

22 150 300 15 10 40

23 190 300 15 7 40

24 190 340 15 10 40

25 190 300 15 10 15
A-7 

FIGURE 1. ETOH AND T50 DOMAIN FOR DESIGNS #2 AND #3 

(DVPE=7 AND 10 PSI; T90=300 AND 340OF; AROMATICS=15 AND 40 %) 

4.0 Revised Experimental Design #3: 25-Fuel Matrix

After the 25-fuel experimental design given in Table 4 was developed, EPA, due to a 

problem in blending the fuels at ETOH=15%, requested that the test fuel matrix be 

redesigned. The revised design was to include the 16 original fuels listed in Table 2 in 

addition to 9 new fuels so that the total number of fuels was 25. The additional fuels 

were to include six fuels with the ethanol content (ETOH) set at 20%, and three fuels 

with ETOH set at 15%. The candidate factors and levels for these fuels are listed in 

Table 3 and the proposed model is the same as the model described in Section 3.0. 

Design Results

An experimental design software package, ECHIP Version 7.01, was used to 

generate the experimental design matrix to meet the above conditions. Because of the 

complexity in needing to include six fuels with ETOH=20% and three fuels with 

ETOH=15%, the algorithmic approach was not used. Instead, all combinations of fuels 

meeting the above criteria were individually augmented to the 16-fuel matrix Design #1 

given in Table 2 and the resulting G-efficiency was computed. The design with the 

highest G-efficiency was selected. The chosen design resulted in a G-efficiency equal to 

0

5

10

15

20

140 150 160 170 180 190 200 210 220 230 240 250

T50, F

Ethanol Content, %
A-8 

68.7% and is listed in Table 5 as Design #3. The experimental design consists of 25 

unique factor-level combinations. 

TABLE 5. FUEL MATRIX DESIGN #3

(WITH G-EFFICIENCY = 68.7%) 

Fuel No. T50, o

F

T90, o

F

ETOH, 

%

DVPE, 

psi

AROMATICS, 

%

1 150 300 10 10 15

2 240 340 0 10 15

3 220 300 10 7 15

4 220 340 10 10 15

5 240 300 0 7 40

6 190 340 10 7 15

7 190 300 0 7 15

8 220 300 0 10 15

9 190 340 0 10 40

10 220 340 10 7 40

11 190 300 10 10 40

12 150 340 10 10 40

13 220 340 0 7 40

14 190 340 0 7 15

15 190 300 0 10 40

16 220 300 10 7 40

17 160 300 20 7 15

18 160 300 20 7 40

19 160 300 20 10 15

20 160 340 20 7 15

21 160 340 20 10 15

22 160 340 20 10 40

23 150 340 15 10 40

24 190 340 15 7 15

25 190 300 15 7 40

5.0 Revised CRC Experimental Design #4: 30-Fuel Matrix

At the completion of the above design work, EPA requested that SwRI work with 

Mr. Jim Uihlein from Chevron to prepare a 30-fuel experimental design for the 

Coordinating Research Council. The steps followed in this process are described below. 

1. The response surface model had the same form as the one used in developing EPA’s 

original 25-fuel matrix (i.e., described in Section 3.0), but also included a squared 

term for T90. 

 

2. Three fuels were added to the EPA’s revised 25-fuel matrix given in Table 5 to 

obtain a 28-fuel matrix, and the G-efficiency of this design was determined. The 

three additional fuels had the properties listed in Table 6. 
A-9 

TABLE 6. ADDITIONAL CRC FUELS

Factor Fuel 1 Fuel 2 Fuel 3

T50, oF 215 202 195

T90, oF 325 325 325

ETOH, % 0 9.5 14.5

DVPE, psi 9 9 9

AROMATICS, % 29.5 24.9 22.6

3. The 28 fuels were forced into the model described in Step 1 above, and then a 

single additional fuel was selected that maximized the G-efficiency of the design. 

The candidate fuels for the additional fuel were restricted to the following two 

regions. 

 Region 1: 

T50, ETOH (150, 10) (150, 15) (160, 10) (160, 15) 

T90 300, 325, 340 

DVPE 10 

 ARO 15, 40 

 Region 2: 

T50, ETOH (160, 20) 

T90 300, 325, 340 

DVPE 7, 10 

 ARO 15, 40 

 Taken together there were 4x3x1x2=24 candidate fuels in Region 1 and 

1x3x2x2=12 candidate fuels in Region 2 for a total of 36 candidate fuels. These 

fuels are listed in Table 7. 

4. A second model was fit using the same criteria as given in Step 3 above, but two 

additional fuels (rather than one additional fuel) were selected to yield a 30-fuel 

matrix. This was determined by selecting the best pair of fuels to add to the 28-fuel 

matrix.

Many different experimental designs were generated in this process. Included for each 

were the G-efficiencies of the designs using the new response surface model described in 

Step 1, as well as the G-efficiencies of these same fuel matrices using the original 

response surface model (i.e., without the squared T90 term). CRC preferred the 

experimental design given in Table 8 with G-efficiency = 64.1% for the model with the 

squared T90 term and G-efficiency = 59.4% for the model without the squared T90 term 

(i.e., see model in Section 2). 

 
A-10 

TABLE 7. CANDIDATE FUELS FOR CRC AUGMENTED EXPERIMENTAL 

DESIGNS

Fuel No. T50, o

F

T90, o

F

ETOH, 

%

DVPE, 

psi

AROMATICS, 

%

1 150 300 10 10 15

2 150 300 10 10 40

3 150 325 10 10 15

4 150 325 10 10 40

5 150 340 10 10 15

6 150 340 10 10 40

7 150 300 15 10 15

8 150 300 15 10 40

9 150 325 15 10 15

10 150 325 15 10 40

11 150 340 15 10 15

12 150 340 15 10 40

13 160 300 10 10 15

14 160 300 10 10 40

15 160 325 10 10 15

16 160 325 10 10 40

17 160 340 10 10 15

18 160 340 10 10 40

19 160 300 15 10 15

20 160 300 15 10 40

21 160 325 15 10 15

22 160 325 15 10 40

23 160 340 15 10 15

24 160 340 15 10 40

25 160 300 20 7 15

26 160 300 20 7 40

27 160 325 20 7 15

28 160 325 20 7 40

29 160 340 20 7 15

30 160 340 20 7 40

31 160 300 20 10 15

32 160 300 20 10 40

33 160 325 20 10 15

34 160 325 20 10 40

35 160 340 20 10 15

36 160 340 20 10 40

 

After observing the alternative generated experimental designs, CRC noted that a very 

similar design, with similar G-efficiency values, could be obtained by replacing the test 

fuel No. 29 in Table 6 with the following fuel:
A-11 

T50 T90 Ethanol DVPE Aromatics

 o

F oF % psi %

 150 325 10 10 15 

CRC decided that, if EPA believed that this E10 fuel was considerably easier to blend 

than E10 fuel No. 29 in Table 8, then this could be used as an acceptable alternative. 

 

TABLE 8. FUEL MATRIX DESIGN #4 

(WITH G-EFFICIENCY = 64.1% FOR MODEL WITH T902 TERM)

Fuel No. T50, o

F

T90, o

F

ETOH, 

%

DVPE, 

psi

AROMATICS, 

%

1 150 300 10 10 15

2 240 340 0 10 15

3 220 300 10 7 15

4 220 340 10 10 15

5 240 300 0 7 40

6 190 340 10 7 15

7 190 300 0 7 15

8 220 300 0 10 15

9 190 340 0 10 40

10 220 340 10 7 40

11 190 300 10 10 40

12 150 340 10 10 40

13 220 340 0 7 40

14 190 340 0 7 15

15 190 300 0 10 40

16 220 300 10 7 40

17 160 300 20 7 15

18 160 300 20 7 40

19 160 300 20 10 15

20 160 340 20 7 15

21 160 340 20 10 15

22 160 340 20 10 40

23 150 340 15 10 40

24 190 340 15 7 15

25 190 300 15 7 40

26 215 325 0 9 29.5

27 202 325 9.5 9 24.9

28 195 325 14.5 9 22.6

29 150 325 10 10 40

30 160 325 20 7 40
A-12 

*** THE FOLLOWING SECTION WAS ADDED TO THE ABOVE REPORT 

AND WAS NOT PART OF WORK ASSIGNMENT 1-08, EPA CONTRACT EP-C07-028. IT IS BASED ON WORK ASSIGNMENT 3-02, EPA CONTRACT EP-C07-028. *** 

 

6.0 Final Fuel Matrix Design Tested in Phase 3 of the EPAct/V2/E-89 Program

The fuel matrix design #5 which was tested in Phase 3 of the EPAct/V2/E-89 

Program is shown in Table 9. It was derived by the EPA from the design #4 shown in 

Table 8 in the following manner: 

• Fuels 26, 27 and 28 were removed from the matrix design #4 

• Fuels 17 through 25 and 29 through 30 in fuel matrix design #4 were renumbered 

in design #5 to match designations which were already being used in the blend 

development process 

• Some nominal levels of T50, T90 and aromatic content were adjusted in fuel 

matrix #5 to match levels achievable with the available blending components. 

Specifically, 

o T50 of E15 fuel 26 and all E20 fuels (Table 9) was changed to 165 o

F 

from 150 oF and 160 oF, respectively

o T50 of E15 fuels 27 and 28 was changed from 190 oF to 220 oF 

o High level of aromatic content was changed from 40 vol.% to 35 vol.% 

The G-efficiency of this 27-fuel matrix #5 was computed to equal 51.6 % for the model 

without the squared T90 term.
A-13 

TABLE 9. FUEL MATRIX DESIGN #5 

(WITH G-EFFICIENCY = 51.6% FOR MODEL WITHOUT T902 TERM)

Fuel No. T50, o

F

T90, o

F

ETOH, 

%

DVPE, 

psi

AROMATICS, 

%

1 150 300 10 10 15

2 240 340 0 10 15

3 220 300 10 7 15

4 220 340 10 10 15

5 240 300 0 7 35

6 190 340 10 7 15

7 190 300 0 7 15

8 220 300 0 10 15

9 190 340 0 10 35

10 220 340 10 7 35

11 190 300 10 10 35

12 150 340 10 10 35

13 220 340 0 7 35

14 190 340 0 7 15

15 190 300 0 10 35

16 220 300 10 7 35

20 165 300 20 7 15

21 165 300 20 7 35

22 165 300 20 10 15

23 165 340 20 7 15

24 165 340 20 10 15

25 165 340 20 10 35

26 165 340 15 10 35

27 220 340 15 7 15

28 220 300 15 7 35

30 150 325 10 10 35

31 165 325 20 7 35