# Correlations to Predict Elemental Compositions and Heating Value of Torrefied Biomass

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Methodology

#### 2.1. Biomass Samples

#### 2.2. Data Analysis

#### 2.3. Error Estimation

^{*}, y and $\overline{\mathrm{y}}$ represent the predicted, measured and average value of the dependent variables, respectively, and n is the number of data points used for the derivation of a particular correlation. The RMSE is considered as the absolute measure of the model’s fit to the data and preferred over the mean absolute error as it places more weight on the larger error terms. On the other hand, the ${\mathrm{R}}^{2}$ value is the relative measure of the model’s fit and represents the explained percentage of variability in the response variable as compared to the mean alone. RMSE is used for measuring the accuracy of the model along with the ${\mathrm{R}}^{2}$ value when the main objective of the model is prediction. Small RMSE values and high ${\mathrm{R}}^{2}$ values (between 0 and 1) imply a good fit for the model. The bias of a model measures the degree of overestimation or underestimation of the prediction as obtained from the model. Positive values of bias error suggest that the predicted values by the model will be greater than the actual values and vice versa [47].

## 3. Results

#### 3.1. Elemental Compositions

#### 3.2. Modeling of C, H and HHV

#### 3.3. Comparison with the Existing Correlations in the Literature and Experimental Data

## 4. Conclusions

## Nomenclature and Subscript

C | Carbon content (%wt.) |

O | Oxygen content (%wt.) |

HHV | Higher heating value (MJ/kg) |

VM | Volatile matter (%) |

${\mathrm{Y}}_{\mathrm{s}}$ | Solid mass yield (%) |

${\mathrm{y}}^{*}$ | Predicted value |

$\overline{\mathrm{y}}$ | Average value |

daf | Dry and ash free |

RMSE | Root mean square error |

H | Hydrogen content (%wt.) |

N | Nitrogen content (%wt.) |

FC | Fixed carbon (%) |

ASH | Ash content (%) |

n | Number of measurements |

y | Measured value |

N | Number of data |

ABE | Average biased error (%) |

_{o} | Raw biomass |

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Variation of (

**a**) Carbon (% wt.) (

**b**) Hydrogen (% wt.) and (

**c**) Nitrogen (% wt.) with solid yield for different types of torrefied wood.

**Figure 3.**Regression model plot for (

**a**) ${\mathrm{C}}_{r}$ (

**b**) ${\mathrm{H}}_{r}$ and (

**c**)${\mathrm{HHV}}_{\mathrm{r}}$.

**Figure 4.**Comparison of the predicted and measured values of (

**a**) Carbon content, (

**b**) Hydrogen content and (

**c**) HHV.

**Table 1.**Summary of the experimental conditions of torrefaction (categorized by the feedstock type).

Feedstock Type | Temperature (°C) | Residence Time (min) | References | ||
---|---|---|---|---|---|

Minimum | Maximum | Minimum | Maximum | ||

Birch | 200 | 280 | 10 | 60 | [20,21,22,23,24] |

Pine | 200 | 300 | 15 | 60 | [22,25,26,27,28,29,30] |

Spruce | 200 | 300 | 5 | 60 | [21,23,31,32,33] |

Willow | 230 | 300 | 30 | 60 | [32,34,35] |

Eucalyptus | 240 | 290 | 15 | 60 | [25,34,36] |

Poplar | 220 | 300 | 20 | 50 | [27,37] |

Beech Wood | 240 | 300 | 15 | 60 | [38] |

Leaucaena | 240 | 300 | 5 | 40 | [39,40] |

Wood Mixture | 230 | 290 | 30 | 60 | [34,41] |

Lauan | 220 | 250 | 30 | 60 | [35] |

Sawdust | 220 | 300 | 10 | 60 | [42] |

Cedarwood | 200 | 290 | 50 | 50 | [43] |

Black Locust | 225 | 250 | 60 | 60 | [44] |

Ash | 250 | 265 | 39 | 43 | [32] |

Aspen | 240 | 280 | 15 | 60 | [20] |

Wood | Parameter | n | Min | Max | Mean | Wood | Parameter | n | Min | Max | Mean |
---|---|---|---|---|---|---|---|---|---|---|---|

Birch | ${\mathrm{Y}}_{\mathrm{s}}$(%) | 19 | 58.01 | 97 | 76.33 | Pine | ${\mathrm{Y}}_{\mathrm{s}}$(%) | 24 | 65 | 95 | 80.53 |

C (% wt.) | 19 | 49.61 | 56.92 | 52.65 | C (% wt.) | 24 | 49.47 | 59.03 | 53.74 | ||

N (% wt.) | 19 | 0.06 | 0.15 | 0.12 | N (% wt.) | 24 | 0.06 | 0.55 | 0.17 | ||

H (% wt.) | 19 | 5.51 | 6.18 | 5.88 | H (% wt.) | 24 | 4.78 | 6.74 | 5.8 | ||

HHV (MJ/kg) | 19 | 18.83 | 22.93 | 20.97 | HHV (MJ/kg) | 24 | 18.07 | 25.38 | 20.96 | ||

Spruce | ${\mathrm{Y}}_{\mathrm{s}}$(%) | 26 | 68.40 | 97 | 81.3 | Eucalyptus | ${\mathrm{Y}}_{\mathrm{s}}$(%) | 13 | 58 | 86.0 | 71.64 |

C (% wt.) | 26 | 50.6 | 57.49 | 53.89 | C (% wt.) | 13 | 50.92 | 63.5 | 55.37 | ||

N (% wt.) | 26 | 0.06 | 0.21 | 0.1 | N (% wt.) | 13 | 0.00 | 0.2 | 0.1 | ||

H (% wt.) | 26 | 5.60 | 6.39 | 5.9 | H (% wt.) | 13 | 5.3 | 6.31 | 5.85 | ||

HHV (MJ/kg) | 26 | 20.46 | 22.97 | 21.6 | HHV (MJ/kg) | 13 | 19.45 | 25 | 21.9 | ||

Willow | ${\mathrm{Y}}_{\mathrm{s}}$(%) | 4 | 63 | 68.76 | 66.09 | Poplar | ${\mathrm{Y}}_{\mathrm{s}}$(%) | 7 | 73 | 95.0 | 82.14 |

C (% wt.) | 4 | 54.0 | 56.9 | 55.65 | C (% wt.) | 7 | 47.12 | 55.1 | 50.69 | ||

N (% wt.) | 4 | 0.00 | 0.42 | 0.16 | N (% wt.) | 7 | 0.2 | 0.31 | 0.24 | ||

H (% wt.) | 4 | 5.7 | 6.41 | 6.02 | H (% wt.) | 7 | 5.3 | 5.98 | 5.78 | ||

HHV (MJ/kg) | 4 | 21.3 | 23.71 | 22.5 | HHV (MJ/kg) | 7 | 18.5 | 20.8 | 19.6 | ||

Beech Wood | ${\mathrm{Y}}_{\mathrm{s}}$(%) | 10 | 60 | 91 | 76.35 | Leaucaena | ${\mathrm{Y}}_{\mathrm{s}}$(%) | 5 | 60.0 | 79.8 | 67.92 |

C (% wt.) | 10 | 48.22 | 55.86 | 50.6 | C (% wt.) | 5 | 53.2 | 60.2 | 56.59 | ||

N (% wt.) | 10 | 0.13 | 0.23 | 0.16 | N (% wt.) | 5 | 0.7 | 0.9 | 0.81 | ||

H (% wt.) | 10 | 4.9 | 5.88 | 5.46 | H (% wt.) | 5 | 5.06 | 5.9 | 5.61 | ||

HHV (MJ/kg) | 10 | 19.01 | 22.00 | 19.93 | HHV (MJ/kg) | 5 | 21.3 | 24.7 | 22.84 | ||

Lauan | ${\mathrm{Y}}_{\mathrm{s}}$(%) | 3 | 59.8 | 82.3 | 74.73 | Sawdust | ${\mathrm{Y}}_{\mathrm{s}}$(%) | 16 | 58.0 | 97 | 86.85 |

C (% wt.) | 3 | 54.33 | 64.4 | 57.88 | C (% wt.) | 16 | 46.9 | 61.0 | 51.16 | ||

N (% wt.) | 3 | 0.12 | 0.17 | 0.15 | N (% wt.) | 16 | 0.02 | 0.1 | .06 | ||

H (% wt.) | 3 | 6.37 | 6.99 | 6.73 | H (% wt.) | 16 | 5.1 | 6.0 | 5.61 | ||

HHV (MJ/kg) | 3 | 23.2 | 26.92 | 24.45 | HHV (MJ/kg) | 16 | 16.6 | 26.0 | 18.61 | ||

Wood Mixture | ${\mathrm{Y}}_{\mathrm{s}}$(%) | 14 | 58.8 | 90.5 | 73.07 | Cedar Wood | ${\mathrm{Y}}_{\mathrm{s}}$(%) | 5 | 69 | 85 | 77.9 |

C (% wt.) | 14 | 45.1 | 61.4 | 53.82 | C (% wt.) | 5 | 48.82 | 56.13 | 53.34 | ||

N (% wt.) | 14 | 0.0 | 0.21 | 0.83 | N (% wt.) | 5 | 0.48 | 0.83 | 0.61 | ||

H (% wt.) | 14 | 4.75 | 6.3 | 5.64 | H (% wt.) | 5 | 4.01 | 5.49 | 4.76 | ||

HHV (MJ/kg) | 14 | 17.8 | 24.3 | 21.34 | HHV (MJ/kg) | 5 | 19.35 | 21.25 | 20.62 | ||

Black Locust | ${\mathrm{Y}}_{\mathrm{s}}$(%) | 2 | 79 | 87.0 | 83 | Ash & Aspen | ${\mathrm{Y}}_{\mathrm{s}}$(%) | 4 | 64.5 | 86.4 | 74.23 |

C (% wt.) | 2 | 50.59 | 52.77 | 51.68 | C (% wt.) | 4 | 50.0 | 53.0 | 51.65 | ||

N (% wt.) | 2 | 0.21 | 0.23 | 0.22 | N (% wt.) | 4 | 0.02 | 0.16 | 0.08 | ||

H (% wt.) | 2 | 3.45 | 4.39 | 3.92 | H (% wt.) | 4 | 5.9 | 6.1 | 6.0 | ||

HHV (MJ/kg) | 2 | 19.35 | 20.38 | 19.86 | HHV (MJ/kg) | 4 | 20.0 | 21.1 | 20.55 |

Dependent Variable | Independent Variable(s) | RMSE | Bias | ${\mathbf{R}}^{2}(\%)$ | Eq. No. |
---|---|---|---|---|---|

${\mathrm{C}}_{\mathrm{r}}$ | ${\mathrm{Y}}_{\mathrm{s}}$ | 0.037 | $1.4\times {10}^{-19}$ | 81.52 | 13 |

${\mathrm{Y}}_{\mathrm{s}}$, C | 0.028 | $1.5\times {10}^{-19}$ | 89.86 | 14 | |

${\mathrm{H}}_{\mathrm{r}}$ | ${\mathrm{Y}}_{\mathrm{s}}$ | 0.059 | $3.2\times {10}^{-21}$ | 79.01 | 15 |

${\mathrm{Y}}_{\mathrm{s}}$, H | 0.043 | $8.4\times {10}^{-20}$ | 88.45 | 16 | |

${\mathrm{HHV}}_{\mathrm{r}}$ | ${\mathrm{C}}_{\mathrm{r}}$ | 0.023 | $-4.7\times {10}^{-19}$ | 92.80 | 17 |

Eq. No | Eq. No | |||||
---|---|---|---|---|---|---|

13 | ${\mathrm{a}}_{1}$ | ${\mathrm{b}}_{1}$ | 14 | ${\mathrm{a}}_{2}$ | ${\mathrm{b}}_{2}$ | ${\mathrm{c}}_{2}$ |

0.2847 | $7.405\times {10}^{-3}$ | −0.47289 | $9.8562\times {10}^{-3}$ | $1.0633\times {10}^{-2}$ | ||

15 | ${\mathrm{a}}_{3}$ | ${\mathrm{b}}_{3}$ | 16 | ${\mathrm{a}}_{4}$ | ${\mathrm{b}}_{4}$ | ${\mathrm{c}}_{4}$ |

−0.1145 | $1.067\times {10}^{-2}$ | −0.55735 | $9.9884\times {10}^{-3}$ | $8.6329\times {10}^{-2}$ | ||

17 | ${\mathrm{a}}_{5}$ | ${\mathrm{b}}_{5}$ | ||||

$4.6508\times {10}^{-2}$ | 0.94497 |

Correlation | Reference | ABE ^{a} (%) | RMSE |
---|---|---|---|

$\frac{\mathrm{C}}{{\mathrm{C}}_{\mathrm{o}}}=0.7405+\frac{28.47}{{\mathrm{Y}}_{\mathrm{s}}}$ $\frac{\mathrm{C}}{{\mathrm{C}}_{\mathrm{o}}}=\frac{-0.47289+9.8562\times {10}^{-3}{\mathrm{Y}}_{\mathrm{s}}}{0.01{\mathrm{Y}}_{\mathrm{s}}-0.010633{\mathrm{C}}_{\mathrm{o}}}$ | Current Study | −2.4 4.0 | 2.12 3.30 |

$\mathrm{C}=0.637\mathrm{FC}+0.455\mathrm{VM}$ | [10] | −12.1 | 7.39 |

$\mathrm{C}=0.635\mathrm{FC}+0.460\mathrm{VM}-0.095\mathrm{ASH}$ | [11] | −11.7 | 7.23 |

$\mathrm{C}=-35.9972+0.7698\mathrm{VM}+1.3269\mathrm{FC}+0.3250\mathrm{ASH}$ | [17] | −6.1 | 3.86 |

$\frac{\mathrm{H}}{{\mathrm{H}}_{\mathrm{o}}}=1.067-\frac{11.45}{{\mathrm{Y}}_{\mathrm{s}}}$ $\frac{\mathrm{H}}{{\mathrm{H}}_{\mathrm{o}}}=\frac{-0.55735+9.9884\times {10}^{-3}{\mathrm{Y}}_{\mathrm{s}}}{0.01{\mathrm{Y}}_{\mathrm{s}}-0.086329{\mathrm{H}}_{\mathrm{o}}}$ | Current Study | −2.4 −4.8 | 0.24 0.88 |

$\mathrm{H}=0.052\mathrm{FC}+0.062\mathrm{VM}$ | [10] | −1.8 | 0.26 |

$\mathrm{H}=0.059\mathrm{FC}+0.060\mathrm{VM}+0.010\mathrm{ASH}$ | [11] | −1.4 | 0.26 |

$\mathrm{H}=55.3678-0.4830\mathrm{VM}-0.5319\mathrm{FC}-0.5600\mathrm{ASH}$ | [17] | 11.9 | 0.82 |

$\frac{\mathrm{HHV}}{{\mathrm{HHV}}_{\mathrm{o}}}=\frac{4.6508}{{\mathrm{Y}}_{\mathrm{s}}}+0.94497\frac{\mathrm{C}}{{\mathrm{C}}_{\mathrm{o}}}$ | Current Study | −3.1 ^{b} | 1.02 |

2.93 ^{c} | 1.24 | ||

$\mathrm{HHV}=0.1905\mathrm{VM}+0.2521\mathrm{FC}$ | [12] [12] | −8.7 | 2.32 |

$\mathrm{HHV}=0.2949\mathrm{C}+0.8250\mathrm{H}$ | −3.2 | 0.92 | |

$\mathrm{HHV}=3.55{\mathrm{C}}^{2}-232\mathrm{C}-2230\mathrm{H}+51.2\mathrm{CH}+131\mathrm{N}+20600$ | [13] | 1.3 | 0.44 |

$\mathrm{HHV}=0.1846\mathrm{VM}+0.3525\mathrm{FC}$ | [18] [18] | −0.6 | 0.78 |

$\mathrm{HHV}=32.7934+0.0053{\mathrm{C}}^{2}-0.5321\mathrm{C}-2.8769\mathrm{H}+0.0608\mathrm{CH}-0.2401\mathrm{N}$ | 2.2 | 0.55 |

^{a}$ABE=\frac{1}{n}\sum _{\mathrm{i}=1}^{\mathrm{n}}\left({\mathrm{y}}_{\mathrm{i}}^{*}-{\mathrm{y}}_{\mathrm{i}}\right)/{\mathrm{y}}_{\mathrm{i}}$,

^{b}carbon content calculated using Equation (18),

^{c}carbon content calculated using Equation (19).

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## Share and Cite

**MDPI and ACS Style**

Hasan, M.; Haseli, Y.; Karadogan, E. Correlations to Predict Elemental Compositions and Heating Value of Torrefied Biomass. *Energies* **2018**, *11*, 2443.
https://doi.org/10.3390/en11092443

**AMA Style**

Hasan M, Haseli Y, Karadogan E. Correlations to Predict Elemental Compositions and Heating Value of Torrefied Biomass. *Energies*. 2018; 11(9):2443.
https://doi.org/10.3390/en11092443

**Chicago/Turabian Style**

Hasan, Mahmudul, Yousef Haseli, and Ernur Karadogan. 2018. "Correlations to Predict Elemental Compositions and Heating Value of Torrefied Biomass" *Energies* 11, no. 9: 2443.
https://doi.org/10.3390/en11092443