*3.1. Elemental Compositions*

Before performing a regression analysis, it is required to examine the relationship between the variables. Figure 1 shows how the C, H and N contents of torrefied woody biomass vary with solid yield using scatter plots. From Figure 1a, it is observed that the carbon content decreases linearly with the increase of solid yield for every type of feedstock. Almost every type of wood forms a data cluster. Figure 1b indicates that the hydrogen percentage increases with increasing solid yield. As the amount of nitrogen is very low, its change is not significant. However, Figure 1c shows that the nitrogen content increases with an increase in the solid yield for some of the data of pine, willow and eucalyptus, but it decreases for other types of wood. Figure 2 depicts the HHV of torrefied wood versus the carbon and hydrogen yields. A linear relation between the heating value and the carbon content is evident in Figure 2a for all types of torrefied wood. However, no distinct relation between HHV and hydrogen content can be seen in Figure 2b.

**Figure 1.** *Cont.*

**Figure 1.** Variation of (**a**) Carbon (% wt.) (**b**) Hydrogen (% wt.) and (**c**) Nitrogen (% wt.) with solid yield for different types of torrefied wood.

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

As mentioned previously, 152 samples have been used in regression analysis to develop correlations for C and H contents and HHV of torrefied wood. Table 3 provides five different regression equations that are evaluated for three dependent variables and their corresponding prediction measures. For instance, in the case of Cr*,* the first regression equation that includes only Y*s* as the independent variable, Equation (13), results in an R<sup>2</sup> of 81.52% and RMSE of 0.037. By including C as a second independent variable, Equation (14), the R<sup>2</sup> value increases to 89.86% and RMSE decreases to 0.028. Similar observations are made for Hr. That is, an R<sup>2</sup> of 79.01% and RMSE of 0.059 are found for the model when Ys is used as the only independent variable, Equation (15), whereas the second regression model, Equation (16), yields an R<sup>2</sup> value of 88.45% and RMSE of 0.043.

$$\mathbf{C\_r = a\_1 + b\_1 Y\_s} \tag{13}$$

$$\mathbf{C\_r = a\_2 + b\_2 Y\_s + a\_3 C} \tag{14}$$

$$\mathbf{H}\_{\mathbf{r}} = \mathbf{a}\_3 + \mathbf{b}\_3 \mathbf{Y}\_{\mathbf{s}} \tag{15}$$

$$\mathbf{H}\_{\mathbf{f}} = \mathbf{a}\_{4} + \mathbf{b}\_{4}\mathbf{Y}\_{8} + \mathbf{a}\_{4}\mathbf{H} \tag{16}$$

$$\text{HHV}\_{\text{I}} = \mathbf{a}\_{\text{5}} + \mathbf{b}\_{\text{5}} \mathbf{C}\_{\text{r}} \tag{17}$$

**Table 3.** Regression models for predicting the C and H contents and HHV of torrefied wood.


**Figure 2.** Relationship between HHV with (**a**) C content and (**b**) H content of torrefied wood.

For prediction of the HHVr, an R<sup>2</sup> value of 92.80% with an RMSE of 0.023 is obtained by taking Cr as the only independent variable. Hr is not included as an additional variable because it does not have significance impact on HHV, which is also evident in Figure 2b. The values of the coefficients of Equations (13)–(17) in Table 3 are given in Table 4.


**Table 4.** The coefficients of Equations (13)–(17).

Figure 3 shows the deviation between the experimental and predicted values obtained from the regression models of Equations (14), (16) and (17) for Cr, Hr and HHVr, respectively. The predicted values that are in the close vicinity of the solid lines in Figure 3a–c imply a good accuracy of prediction by the model. The data points in Figure 3a show that they form a cluster at the upper region of the solid line. The maximum points of Cr lie between 0.7 and 1. However, data for Hr are distributed through the solid line as shown in Figure 3b with 96% of the data being in the range 0.5 to 1. On the other hand, for HHVr in Figure 3c, most of the data points are gathered in the upper region of the solid line like Cr. All the data points of HHVr point lie between 0.65 and 1.

**Figure 3.** *Cont.*

**Figure 3.** Regression model plot for (**a**) C*r* (**b**) H*r* and (**c**) HHVr.

Introducing Equations (7)–(9) into Equations (13)–(17) and using the values of the coefficients given in Table 4, the final form of the correlations for carbon and hydrogen contents and HHV of a torrefied biomass can be represented as:

$$\frac{\text{C}}{\text{C}\_{\text{o}}} = 0.7405 + \frac{28.47}{\text{Y}\_{\text{s}}} \tag{18}$$

$$\frac{\text{C}}{\text{C}\_{\text{o}}} = \frac{-0.47289 + 9.8562 \times 10^{-3} \text{Y}\_{\text{s}}}{0.01 \text{Y}\_{\text{s}} - 0.010633 \text{C}\_{\text{o}}} \tag{19}$$

$$\frac{\text{H}}{\text{H}\_{\text{0}}} = 1.067 - \frac{11.45}{\text{Y}\_{\text{s}}} \tag{20}$$

$$\frac{\rm H}{\rm H\_o} = \frac{-0.55735 + 9.9884 \times 10^{-3} \rm Y\_s}{0.01 \rm Y\_s - 0.086329 \rm H\_o} \tag{21}$$

$$\frac{\text{HHV}}{\text{HHV}\_{\text{o}}} = \frac{4.6508}{\text{Y}\_{\text{s}}} + 0.94497 \frac{\text{C}}{\text{C}\_{\text{o}}} \tag{22}$$

where C, H and Ys are expressed on a dry mass percentage basis.

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

As discussed previously, the proposed correlations in the literature are based on proximate analysis of raw biomass. The predictability of the correlations developed in this study are compared with those proposed by others. Parikh et al. [10] and Shen et al. [11] developed equations based on proximate analysis to predict elemental composition of raw biomass. Nhucchen [17] used the proximate analysis to predict the *C* and *H* percentage of both raw and torrefied biomass. To compare the HHV model, five different correlations from three different sources [12,13,18] are selected. Yin [12] and Friedl et al. [13] correlations are based on the proximate and ultimate analysis, whereas Nhucchen et al. [18] estimates the HHV of torrefied biomass using either proximate or ultimate analysis of torrrefied biomass.

Table 5 compares the proposed correlations for C, H and HHV in the current study to other published correlations. Average biased error (ABE) and root-mean-square error (RMSE) are calculated for all models using additional 12 samples obtained from Refs. [48,49]. Bridgeman et al. [48] torrefied willow and miscanthus at 240 ◦C and 290 ◦C with a residence time of 10 and 60 min. Broström et al. [49] reported the ultimate analysis of spruce torrefied at 260, 280 and 310 ◦C and a residence time of 8, 16.5 and 25 min. Although, miscanthus is a non-woody biomass, it is considered here to examine the applicability of the correlations developed in this study to non-woody biomass.


**Table 5.** Comparison of the newly developed C, H and HHV correlations with others.

a*ABE* = 1*n* n∑ i=1 (y<sup>∗</sup>i − yi)/yi, b carbon content calculated using Equation (18), c carbon content calculated using Equation (19).

The first model developed in this study for carbon content, Equation (18), gives an ABE of −2.4% and RMSE of 2.12 whereas the second correlation, Equation (19), yields an ABE of 4% and RMSE of 3.3. The correlations of Parikh et al. [10] and Shen et al. [11] give higher negative values of −12.1% and −11.7% for ABE with RMSE of 7.39 and 7.23, respectively, as their models are originally developed for raw biomass. The correlation proposed by Nhucchen [17] shows an ABE of −6.1% and RMSE of 3.86. In the case of hydrogen*,* the correlations of this study, Equations (20) and (21), show an ABE of −2.4% and −4.8% with an RMSE of 0.24 and 0.88, respectively. The highest ABE is found for the correlation of Nhucchen [17]. The correlation developed by Prikh et al. [10] gives an ABE of −1.8% and RMSE of 0.26 and that of Shen et al. [11] yields an ABE of −1.4% and RMSE of 0.26.

For HHV, this study shows an ABE of −3.1% and RMSE of 1.02 when Equation (18) is used to determine the carbon content. These figures slightly change to 2.93% and 1.24 if the carbon content is calculated using Equation (19). Yin et al. [12] developed two correlations for HHV of raw biomass. As shown in Table 5, the first one gives an ABE of −8.7% and RMSE of 2.32 whereas the second relation yields an ABE of −3.2% and RMSE of 0.92. Friedl et al. correlation [13] developed using raw biomass data shows an ABE of 1.3% and RMSE of 0.44. The two correlations developed by Nhucchen et al. [18] give ABE of −0.6% and 2.2% with RMSE of 0.78 and 0.55.

Figure 4 compares the predicted values of the carbon content, the hydrogen content, and heating value obtained from Equations (18)–(22) with the measured data reported in Refs. [48,49]. It is evident from Figure 4a that Equations (18) and (19) satisfactorily predict the *C* content. A maximum error of 7.23% is found for miscanthus when C is predicted by Equation (18). For woody biomass, a maximum error of 8.6% is found for spruce from Equation (19). In the case of H*,* as shown in Figure 4b, the largest difference between the predicted and measured values found for miscanthus is 12.33% when Equation (21) is used. Also, a reasonable accuracy of prediction is found for HHV in Figure 4c with a maximum error of 8.2%. Overall, the agreemen<sup>t</sup> between the predicted and measured values in Figure 4 is acceptable for engineering applications.

It must be noted that as the proposed correlations are obtained using the data of different types of wood, their application to a non-woody biomass is not recommended. Furthermore, the new correlations are developed for a solid yield in the range 58% to 97%. Whether torrefied biomass is used in a combustion or gasification process, one would need to know the composition of the torrefied solid to accurately predict the gaseous products (combustion gases or producer gas). For this, Equations (18)–(22) are expected to be a useful tool for designers and researchers.

**Figure 4.** *Cont.*

**Figure 4.** Comparison of the predicted and measured values of (**a**) Carbon content, (**b**) Hydrogen content and (**c**) HHV.
