# A Thermogravimetric Analysis of Biomass Conversion to Biochar: Experimental and Kinetic Modeling
## 3 Results and Discussion
### Thermal Decomposition Kinetic Modeling  
Solid state kinetics can be investigated using thermal methods by observing changes in the sample property as it is heated or maintained at a constant temperature. In our study, reaction kinetics were analyzed using thermal data collected under non-isothermal conditions at a constant heating rate. Through the decomposition of biomass residues, one can obtain volatile compounds (gas) and solid compounds (char); the decomposition process can be represented by the following global transformation [56]:  
\[Biomass(s)\rightarrow\ Char(s)+Volatiles(g) \tag{1}\]  
The solid samples decomposition in isothermal conditions is usually expressed as:  
\[\frac{d\alpha}{dt}=k\cdot f(\alpha) \tag{2}\]  
where \(k\) is the decomposition rate constant and \(f(\alpha)\) is a function of conversion. The conversion or weight loss rate can be determined using the following equation:  
\[\alpha=\frac{m_{0}-m_{t}}{m_{0}-m_{\infty}} \tag{3}\] \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Residue Type** & \begin{tabular}{c} **Heating Rate,** \\ \({}^{\circ}\)C\(\cdot\)min\({}^{-1}\) \\ \end{tabular} & \begin{tabular}{c} **Peak** \\ **Temperature, \({}^{\circ}\)C** \\ \end{tabular} & \
\begin{tabular}{c} \(\frac{dW}{dt}\) \\ \%\(\cdot\)min\({}^{-1}\) \\ \end{tabular} &
\begin{tabular}{c} **Residue,** \\ \%\(\cdot\)min\({}^{-1}\) \\ \end{tabular} \\ \hline \multirow{8}{*}{Apple peel} & \multirow{4}{*}{10} & 98.3 & 5.76 & \multirow{4}{*}{20.9} \\  & & 205.4 & 55.1 & & \\  & & 329.8 & 26.1 & & \\ \cline{2-5}  & & 101.5 & 5.3 & & \\  & & 212.9 & 49.9 & 20.9 \\  & & 335.9 & 22.5 & & \\ \cline{2-5}  & & 115.7 & 4.5 & & \\  & 20 & 225.6 & 44.4 & 20.1 \\  & & 347.3 & 19.4 & & \\ \cline{2-5}  & & 119.9 & 3.17 & & \\  & 30 & 232.1 & 25.6 & 20.0 \\  & & 350.0 & 12.7 & & \\ \hline \multirow{8}{*}{Potato peel} & \multirow{4}{*}{5} & 93.6 & 4.9 & \multirow{4}{*}{27.5} \\  & & 277.9 & 37.5 & & \\ \cline{1-1} \cline{2-5}  & & 95.9 & 1.81 & & \\ \cline{1-1}  & & 289.3 & 19.6 & & \\ \cline{1-1} \cline{2-5}  & & 20 & 93.7 & 1.51 & \\ \cline{1-1}  & & 297.2 & 14.5 & & 27.4 \\ \cline{1-1} \cline{2-5}  & & 30 & 301.5 & 2.6 & & 26.7 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: TG and DTA main characteristics at different heating rates. where \(m_{0}\) is the initial weight of the sample, \(m_{t}\) is the weight of the sample at a certain time, and \(m_{\infty}\) is the final mass of the sample. For non-isothermal TGA experiments, the heating rate \((\beta)\) can be expressed in relation with time/temperature as:  
\[\frac{d\alpha}{dt}=\frac{d\alpha}{dT}\bigg{(}\frac{dT}{dt}\bigg{)}=\beta\frac{ d\alpha}{dT};\ \ \ \beta=\frac{dT}{dt} \tag{4}\]  
Considering valid the Arrhenius representation of the decomposition rate constant \(k(T)=k_{0}\cdot e^{-\frac{E_{a}}{kT}}\), the conversion dependence of time in Equation (4) can be expressed as:  
\[\frac{d\alpha}{dT}=\frac{k_{0}}{\beta}e^{-\frac{E_{a}}{kT}}f(\alpha) \tag{5}\]  
The methods proposed in the literature for determination of the kinetic parameters from TG data are relying on Equation (5) as it is or in its integral form (differential and integral methods) [57]. Most of these methods use the graphical representation of the data for a fast visual assessment of the form of \(f(\alpha)\) and the calculation of the kinetic parameters \(E_{a}\) and \(k_{0}\). The integral form of relation (5) is defined as:  
\[g(\alpha)=\int\limits_{0}^{\alpha}\frac{d\alpha}{f(\alpha)}=\frac{k_{0}}{ \beta}\int\limits_{T_{0}}^{T}e^{-\frac{E_{a}}{R\cdot T}}dT \tag{6}\]  
where \(T_{0}\) is the initial temperature.