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Table 4 Probability distribution functions of key parameters of sorghum-based ethanol production pathways

From: Life-cycle energy use and greenhouse gas emissions of production of bioethanol from sorghum in the United States

Parameter

Mean

P10

P90

PDF Typeg

GS farming

    

Energy use, MJ/kilogram of grain[ [27]

0.68

0.40

0.97

Normal

N, gram/kilogram of grain [9]

24

19

29

Weibull

P2O5, gram/kilogram of grain [9]

6.4

1.3

12

Logistic

K2O, gram/kilogram of grain [9]

0.70

0.16

1.2

Uniform

Grain yield, tonne/hectare [9]

3.4

2.5

4.4

Lognormal

N content of GS stalk, gram/kilogram of grain [28]

10

7.6

11

Triangular

N2O conversion rate of N fertilizer:% [20]

1.5

0.41

3.0

Weibull

SS farming

Energy use, MJ/wet tonne of SS [20]

100

90.4

110

Normal

N, gram/wet kilogram of SS [29]

1.5

1.1

1.8

Lognormal

P2O5, gram/wet kilogram of SS [29]

0.56

0.37

0.76

Normal

K2O, gram/wet kilogram of SS [29]

0.89

0.58

1.0

Weibull

Herbicide, gram/wet kilogram of SS [29]

0.069

0.058

0.080

Lognormal

Biomass yield, wet tonne/hectare [29]

76

58

95

Uniform

Grain yield, wet tonne/hectare [30]

1.8

1.0

2.6

Normal

Sugar yield, tonne/hectare [29]

7.0

4.9

9.4

Lognormal

Bagasse yield, wet tonne/hectare [29]

12

8.7

15

Gamma

FS farming

Energy use, MJ/wet tonne of FSa

113

102

124

Normal

N, gram/wet kilogram of FS [29, 31]

2.2

1.2

3.2

Logistic

P2O5, gram/wet kilogram of FS [29]

0.41

0.34

0.49

Uniform

K2O, gram/wet kilogram of FS [29]

0.82

0.67

0.96

Uniform

Herbicide, gram/wet kilogram of FS [29]

0.067

0.056

0.079

Uniform

FS dry matter yield, tonne/hectare [9]

23

11

36

Weibull

Ethanol Production

Grain-based ethanol production

Ethanol plant energy use, MJ/liter of ethanolb[20]

8.1

6.7

9.5

Normal

Ethanol plant energy use, MJ/liter of ethanolc[19]

5.1

4.2

6.0

Normal

Ethanol plant energy use, MJ/liter of ethanold

8.3

6.9

9.8

Normal

Ethanol plant energy use, MJ/liter of ethanole

5.3

4.4

6.2

Normal

Ethanol production yield, liter/kilogram of grain [31–35]

0.42

0.40

0.44

Normal

DDGS yield, kilogram /liter of ethanol [20]

0.68

0.61

0.74

Triangular

WDGS yield, kilogram /liter of ethanol [20]

1.9

1.7

2.1

Triangular

Enzyme use, kilogram/tonne of grain [20]

1.0

0.94

1.2

Normal

Yeast use, kilogram/tonne of grain [20]

0.36

0.32

0.40

Normal

Sugar-based ethanol production

    

Ethanol plant energy use, MJ/liter of ethanol [36]

9.2

9.0

9.3

Uniform

Electricity demand of ethanol production, MJ/liter of ethanolf

1.4

1.3

1.5

Uniform

Ethanol production yield, liter/kilogram of sugar [29, 31, 32, 35, 37–44]

0.58

0.53

0.62

Lognormal

Yeast use, kilogram/tonne of sugar [42–45]

5.2

4.2

6.2

Uniform

Cellulosic ethanol production

    

Ethanol production yield, liters/dry kilogram of bagasse [20]

0.38

0.33

0.42

Normal

Enzyme use, kilogram/dry tonne of bagasse [46]

16

9.6

23

Triangular

Yeast use, kilogram/dry tonne of bagasse [46]

2.5

2.2

2.7

Triangular

  1. a Scaled based on yield of FS and SS to the SS farming energy use;
  2. b For FNG-fueled ethanol plants, producing DDGS as the co-product;
  3. c For FNG-fueled ethanol plants, producing WDGS as the co-product;
  4. d For RNG-fueled ethanol plants, producing DDGS as the co-product;
  5. e For RNG-fueled ethanol plants, producing WDGS as the co-product;
  6. f Based on correspondence with Prof. Jaoquim Seabra;
  7. g We employed EasyfitTM, a curve-fitting toolbox [47], to find the probability distribution type from a pool of 55 distributions, e.g. Normal distribution, Weibull distribution, Uniform distributions, etc., that best fits each set of the data points we collected for each parameter. For many parameters, we also applied a weighting factor to fit the distribution. The higher the value of the weighting factor corresponding to a sample value of the parameter, the higher possibility the parameter has the sample value in the probability distribution function to be fitted for the parameter. The toolbox uses one of the four well-known methods to estimate distribution parameters based on available sample data: maximum likelihood estimates; least squares estimates; method of moments; and method of L-moments. The toolbox calculates the goodness-of-fit statistics including the Kolmogorov Smirnov statistic, the Anderson Darling Statistic, and the Chi-squared statistic, for each of the fitted distributions. Then, the toolbox ranks the distributions based on the goodness-of-fit statistics. We then selected the distribution with the highest rank primarily based on the Kolmogorov Smirnov statistic. The curve-fitting requires at least five data points for each parameter. We collected sufficient data for the parameters in Table 4 to meet this criterion, except for N content of GS stalk, herbicide use for FS farming, and electricity demand of ethanol production, which we were able to collect only two or three data points. Accordingly, we assumed a uniform or triangular distribution for these parameters.
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Biotechnology for Biofuels and Bioproducts

ISSN: 2731-3654

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