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. 2013 Oct 2;6:141. doi: 10.1186/1754-6834-6-141

Table 4.

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

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

a Scaled based on yield of FS and SS to the SS farming energy use;

b For FNG-fueled ethanol plants, producing DDGS as the co-product;

c For FNG-fueled ethanol plants, producing WDGS as the co-product;

d For RNG-fueled ethanol plants, producing DDGS as the co-product;

e For RNG-fueled ethanol plants, producing WDGS as the co-product;

f Based on correspondence with Prof. Jaoquim Seabra;

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.