1

MEMORANDUM

Subject: Application of Monte Carlo process to the determination of proposed volume 

requirements for 2014 standards NPRM

From: David Korotney

To: EPA Air Docket EPA-HQ-OAR-2013-0479

This memorandum includes all inputs and outputs for the Monte Carlo process that was

used to develop ranges and point estimates for the proposed 2014 volume requirements for the 

Renewable Fuel Standard (RFS) program in the Notice of Proposed Rulemaking (NPRM). 

A. Standard Distributions

The Monte Carlo analyses were based on three standard distributions. These three 

distributions are defined as follows:

Table A-1

Defining Characteristics of the Three Standard Distributions

Normal Mean = 0.8

St Dev = 0.2

Skewed (Weibull) Shape factor = 0.5

Scale factor = 1.7

Half-normal Mean = 0

St Dev = 0.4

The steps taken to develop a randomly generated distribution of volumes for each type of 

renewable fuel (e.g. biodiesel, domestic advanced ethanol, etc) were as follows:

1. A flat distribution was used to generate random numbers between zero and one. 

These randomly chosen values were used to represent values on the cumulative 

distribution curves shown above (abscissa).

Frequency distribution

Volume surrogate

Skewed

Normal

Half-normal

0.0 0.2 0.4 0.6 0.8 1.0 Volume surrogate

Cumulative distribution

Skewed

Normal

Half-normal
2

2. For each randomly generated value on the cumulative distribution, a corresponding 

volume surrogate1 was determined from one of the three standard distributions 

(ordinate)

3. The volume surrogate determined for the chosen standard distribution was scaled to fit 

the chosen range for the type of renewable fuel in question. To do this, the chosen 

distribution as defined in Table A-1 above was shifted and rescaled such that the 5th 

percentile of the standard distribution corresponded to the low end of the designated 

volume range, and the 95th percentile of the standard distribution corresponded to the 

high end of the designated volume range. 

The results of this shifting and rescaling are shown for all input volumes in Sections B and D

below.

To demonstrate how the three standard distributions affect the means, modes, and percentiles 

differently, the three distributions can be shifted and scaled to align their 5th and 95th 

percentiles. The results are shown below.

Figure A-1

Aligned Standard Distributions

 

1

So-called because it has not yet been converted into a volume representing a specific type of renewable fuel, such 

as biodiesel or sugarcane ethanol.

0.0

0.5

1.0

1.5

2.0

2.5

3.0

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

5th percentile for 

all three curves

95th percentile for 

all three curves

Mean for half-normal Mean for skewed

Mean for normal
3

Table A-2

Aligned Standard Distributions

Mean

Percentiles

5th 50th 95th Mode

Normal 0.607 0.224 0.607 0.988 0.607

Skewed (Weibull) 0.542 0.224 0.503 0.988 0.409

Half-normal 0.519 0.224 0.470 0.988 0.200

B. Input values and distributions for cellulosic biofuel

Table B-1

Inputs for Cellulosic Biofuel Production (mill ethanol-equivalent gallons)

Company Distribution Low end of range High end of range

Abengoa Half-normal 0 18

DuPont Half-normal 0 2

INEOS Bio Skewed 2 5

KiOR Skewed 0 9

Poet Half-normal 0 6

CNG/LNG Producers Normal 35 54

Edeniq Half-normal 0 7

Ensyn Normal 0 5

Abengoa

5th percentile = 0

25th percentile = 3

50th percentile = 6

75th percentile = 10

95th percentile = 18 Mean = 7

0%

5%

10%

15%

20%

25%

025710121517202225272932343739424447 Percent of observations

Million gallons
4

DuPont

5th percentile = 0.01

25th percentile = 0.28

50th percentile = 0.64

75th percentile = 1.14

95th percentile = 1.99 Mean = 0.78

0%

5%

10%

15%

20%

25%

00111122223334444555 Percent of observations

Million gallons

INEOS Bio

5th percentile = 2.0

25th percentile = 2.5

50th percentile = 3.1

75th percentile = 3.8

95th percentile = 5.0 Mean = 3.2

0%

2%

4%

6%

8%

10%

12%

14%

16%

22233344455556667778 Percent of observations

Million gallons

KiOR

5th percentile = 0.0

25th percentile = 1.6

50th percentile = 3.3

75th percentile = 5.3

95th percentile = 8.9 Mean = 3.7

0%

2%

4%

6%

8%

10%

12%

14%

16%

01234567789101112131415161718 Percent of observations

Million gallons
5

Poet

5th percentile = 0

25th percentile = 1

50th percentile = 2

75th percentile = 3

95th percentile = 6 Mean = 2

0%

5%

10%

15%

20%

25%

0122345677891011111213141516 Percent of observations

Million gallons

CNG/LNG Producers

5th percentile = 35

25th percentile = 41

50th percentile = 44

75th percentile = 48

95th percentile = 54 Mean = 44

0%

2%

4%

6%

8%

10%

12%

14%

16% 2527303234363840424547495153555759626466 Percent of observations

Million gallons

Edeniq

5th percentile = 0

25th percentile = 1

50th percentile = 2

75th percentile = 4

95th percentile = 7 Mean = 3

0%

5%

10%

15%

20%

25%

012345678910101112131415161718 Percent of observations

Million gallons
6

C. Results of aggregation of cellulosic biofuel sources

Ensyn

5th percentile = 0.0

25th percentile = 1.5

50th percentile = 2.5

75th percentile = 3.6

95th percentile = 5.0 Mean = 2.5

0%

2%

4%

6%

8%

10%

12%

14%

00112223344555667778 Percent of observations

Million gallons

5th percentile = 5

25th percentile = 9

50th percentile = 12

75th percentile = 17

95th percentile = 25 Mean = 14 Mode = 11

Aggregate of:

Abengoa

DuPont

INEOS Bio

Poet

0%

5%

10%

15%

20%

25%

2581114161922252830333639414447505355 Percent of observations

Million gallons

Cellulosic biofuel - Ethanol only, proposed volumes

5th percentile = 0.0

25th percentile = 1.6

50th percentile = 3.3

75th percentile = 5.3

95th percentile = 8.9 Mean = 3.7 Mode = 3.0

Aggregate of:

KiOR

0%

2%

4%

6%

8%

10%

12%

14%

16%

01234567789101112131415161718 Percent of observations

Million gallons

Cellulosic biofuel - Non-ethanol only, proposed volumes
7

D. Input values and distributions for total renewable fuel and advanced biofuel

Table D-1

Inputs for Total Renewable Fuel and Advanced Biofuel (million ethanol-equivalent gallons)

Distribution Low end of range High end of range

E85 consumption Half-normal 100 300

Available volumes of biomassbased dieselHalf-normal 1,920 2,400

Available volumes of nonethanol advanced biofuelNormal 24 132

Available volumes of nonethanol non-advanced 

renewable fuel

Normal 1 25

Available volumes of domestic 

ethanol advanced biofuel Normal 28 142

Available volumes of imported 

sugarcane ethanol Normal 300 800

Aggregate of:

Abengoa 5th percentile = 8

DuPont 25th percentile = 12

INEOS Bio 50th percentile = 16

KiOR 75th percentile = 21

Poet 95th percentile = 30 Mean = 17 Mode = 16

0%

5%

10%

15%

20%

25%

36101316202326303336404346505357606367 Percent of observations

Million gallons

Cellulosic biofuel - Proposed volumes

Aggregate of: 5th percentile = 53

Abengoa 25th percentile = 61

DuPont 50th percentile = 67

INEOS Bio 75th percentile = 73

KiOR 95th percentile = 83

Poet Mean = 67

CNG/LNG Producers Mode = 67

Edeniq

Ensyn

0%

2%

4%

6%

8%

10%

12%

14%

16%

18% 42464953576064677175788286899397 100 104 108 111 Percent of observations

Million gallons

Cellulosic biofuel - All potential volumes
8

5th percentile = 100

25th percentile = 127

50th percentile = 164

75th percentile = 213

95th percentile = 302

Mean = 178

Mode = 96

0%

5%

10%

15%

20%

25% 94 121 149 176 204 231 259 287 314 342 369 397 424 452 479 507 535 562 590 617 Percent of observations

Million gallons

E85

5th percentile = 1,281

25th percentile = 1,327

50th percentile = 1,386

75th percentile = 1,463

95th percentile = 1,608

Mean = 1,405

Mode = 1,293

0%

5%

10%

15%

20%

25% 1,270 1,314 1,358 1,402 1,446 1,490 1,534 1,579 1,623 1,667 1,711 1,755 1,799 1,843 1,887 1,931 1,975 2,019 2,064 2,108 Percent of observations

Million gallons

Biomass-Based Diesel

5th percentile = 22

25th percentile = 57

50th percentile = 78

75th percentile = 100

95th percentile = 130

Mean = 78

Mode = 77

0%

2%

4%

6%

8%

10%

12%

14%

0102030405061718191 101 111 121 131 141 151 161 172 182 192 Percent of observations

Million gallons

Non-ethanol domestic advanced
9

E. Results of aggregation for total renewable fuel

5th percentile = 1

25th percentile = 8

50th percentile = 13

75th percentile = 18

95th percentile = 24 Mean = 13 Mode = 13

0%

2%

4%

6%

8%

10%

12%

14%

02479111315172022242628303335373941 Percent of observations

Million gallons

Non-ethanol in conventional gasoline

5th percentile = 30

25th percentile = 62

50th percentile = 86

75th percentile = 109

95th percentile = 141 Mean = 86 Mode = 86

0%

2%

4%

6%

8%

10%

12%

0102030405060708090 100 110 120 130 140 150 160 170 180 190 Percent of observations

Million gallons

Ethanol in domestic advanced 

5th percentile = 294

25th percentile = 444

50th percentile = 551

75th percentile = 653

95th percentile = 809 Mean = 549 Mode = 549

0%

2%

4%

6%

8%

10%

12%

14%

16%

060 119 179 238 298 357 417 476 536 595 655 715 774 834 893 953 1,012 1,072 1,131 Percent of observations

Million gallons

Imported sugarcane ethanol 
10

F. Results of aggregation for advanced biofuel

Aggregate of: 5th percentile = 12,954

Ethanol in E85 25th percentile = 12,972

Ethanol in E10 50th percentile = 12,996

75th percentile = 13,028

90th percentile = 13,064

95th percentile = 13,087

Mean = 13,005

Mode = 12,951

0%

5%

10%

15%

20%

25% 12,950 12,968 12,986 13,004 13,023 13,041 13,059 13,077 13,096 13,114 13,132 13,150 13,168 13,187 13,205 13,223 13,241 13,260 13,278 13,296 Percent of observations

Million gallons

Total ethanol

5th percentile = 14,995

25th percentile = 15,084

Aggregate of: 50th percentile = 15,183

Total ethanol 75th percentile = 15,297

Non-ethanol cellulosic 95th percentile = 15,515

Biomass-based diesel Mean = 15,207

Non-ethanol advanced Mode = 15,059

Non-ethanol conventional

0%

5%

10%

15%

20%

25% 14,887 14,961 15,035 15,109 15,184 15,258 15,332 15,406 15,480 15,555 15,629 15,703 15,777 15,851 15,926 16,000 16,074 16,148 16,222 16,297 Percent of observations

Million gallons

Total renewable fuel

Aggregate of: 5th percentile = 2,493

Cellulosic biofuel 25th percentile = 2,679

Biomass-based diesel 50th percentile = 2,824

Domestic advanced ethanol 75th percentile = 2,979

Domestic advanced non-ethanol 95th percentile = 3,225

Sugarcane ethanol Mean = 2,837

Mode = 2,810

0%

2%

4%

6%

8%

10%

12%

14%

16%

18% 2,116 2,206 2,296 2,387 2,477 2,567 2,658 2,748 2,838 2,929 3,019 3,109 3,199 3,290 3,380 3,470 3,561 3,651 3,741 3,832 Percent of observations

Million gallons

Advanced biofuel - Option 1 (availability)
11

G. Results of aggregation for non-advanced ethanol (corn-ethanol)

5th percentile = 2,008

25th percentile = 2,012

50th percentile = 2,016

75th percentile = 2,021

95th percentile = 2,030

Mean = 2,017

Mode = 2,016

Aggregate of:

3,750 advanced

- 1,750 cellulosic

+ Cellulosic biofuel

0%

5%

10%

15%

20%

25% 2,003 2,006 2,010 2,013 2,016 2,020 2,023 2,026 2,030 2,033 2,036 2,040 2,043 2,046 2,050 2,053 2,057 2,060 2,063 2,067 Percent of observations

Million gallons

Advanced - Option 2 (reduce by same as cellulosic)

5th percentile = 2,004

25th percentile = 2,086

50th percentile = 2,178

75th percentile = 2,289

95th percentile = 2,507

Mean = 2,202

Mode = 2,099

Aggregate of:

Cellulosic biofuel

Biomass-based diesel

Non-ethanol advanced

0%

5%

10%

15%

20%

25% 1,928 1,999 2,071 2,142 2,213 2,285 2,356 2,428 2,499 2,571 2,642 2,714 2,785 2,856 2,928 2,999 3,071 3,142 3,214 3,285 Percent of observations

Million gallons

Advanced biofuel under Option 3

5th percentile = 12,082 75th percentile = 12,465

25th percentile = 12,246 95th percentile = 12,624

50th percentile = 12,358 Mean = 12,357

Mode = 12,350

Aggregate of:

Total renewable fuel

- advanced (Option 1)

- non-ethanol conventional

0%

2%

4%

6%

8%

10%

12%

14%

16% 11,728 11,790 11,852 11,914 11,975 12,037 12,099 12,161 12,223 12,285 12,347 12,408 12,470 12,532 12,594 12,656 12,718 12,780 12,841 12,903 Percent of observations

Million gallons

Corn ethanol under Option 1 (availability)
12 5th percentile = 12,966

25th percentile = 13,053

50th percentile = 13,152

75th percentile = 13,266

95th percentile = 13,485

Mean = 13,177

Mode = 13,061

Aggregate of:

Total renewable fuel

- advanced (Option 2)

- non-ethanol conventional

0%

2%

4%

6%

8%

10%

12%

14%

16%

18%

20% 12,853 12,927 13,001 13,075 13,150 13,224 13,298 13,372 13,446 13,520 13,595 13,669 13,743 13,817 13,891 13,966 14,040 14,114 14,188 14,262 Percent of observations

Million gallons

Corn ethanol under Option 2 (reduce by same as 

cellulosic)

5th percentile = 12,940

25th percentile = 12,958

50th percentile = 12,983

75th percentile = 13,015

95th percentile = 13,074

Mean = 12,992

Mode = 12,954

Aggregate of:

Total renewable fuel

- advanced (Option 3)

- non-ethanol conventional

0%

5%

10%

15%

20%

25% 12,914 12,933 12,953 12,973 12,993 13,012 13,032 13,052 13,072 13,091 13,111 13,131 13,150 13,170 13,190 13,210 13,229 13,249 13,269 13,289 Percent of observations

Million gallons

Corn ethanol under Option 3