# Kinetic Models of Wood Biomass Drying in Hot Airflow Systems
## 3 Empirical Investigation of the Process
The model that best adapted to the experimental data obtained in the drying of rubber was that of [PERSON] and [PERSON], for which they found that for a drying temperature of 90 \({}^{\circ}\)C, the value of \(k\) is equal to 0.0008, and that of a is equal to 1.038 (with an \(R^{2}\) = 0.9963 and a mean square error of 0.00015). However, the coefficients a and \(k\) are influenced by the process temperature in such a way that, as the temperature increases, the drying rate is also higher. They also indicated that the physical properties of the rubber might vary, and the equations obtained might not be applicable to different rubbers. In addition, the conditions of their experimentation might not make this model applicable to other drying processes with different test conditions. [PERSON] et al. (2020) [54] proposed an estimation of the value of the overall mass transfer resistance (\(K\)) through the equation:  
\[\frac{1}{K}=\alpha_{0}\exp\biggl{(}\frac{c_{0}}{T_{K}}\biggr{)}e+b_{0}\ \exp \biggl{(}\frac{c_{0}}{T_{K}}\biggr{)}v^{-p}\exp\biggl{(}\frac{-z}{x_{FSP}-x_{e}} \biggr{)}\]  
where \(x_{FSP}-x_{e}\) is the difference between the saturation point of the fibres and the moisture content at equilibrium for a specified air temperature and relative humidity. \(T_{\text{K}}\) is the temperature in degrees Kelvin (K), \(e\) is the thickness of the solids to be dried, and \(v\) is the air velocity. The parameters of this equation particularised for spruce (_Picea abies_) and beech (_Fagus sylvatica_) wood establish the model:  
\[x_{c}=0.063829\cdot\dot{m}_{w}-0.00168\cdot T_{bh}+0.250371\]0  
Note that the overall mass transfer resistance only depends on the process temperature, fibre saturation moisture, and moisture at equilibrium. The fibre saturation moisture \(x_{FSP}\) could be close to the critical moisture \(x_{c}\). [PERSON] and [PERSON] (2023) [55], in order to compare the effectiveness of different drying methods from a kinetic point of view, evaluated the drying constant \(\beta\). For this, they assumed that the evaporation rate of the dried material is proportional to the difference between the mass at one instant \(m\) and the mass at wet equilibrium \(m_{e}\):  
\[x_{c}=0.063829\cdot\dot{m}_{w}-0.00168\cdot T_{bh}+0.250371\]1  
where \(m_{e}\) is the equilibrium in the bulk sample. Thus, they obtained the following solution to the above equation:  
\[x_{c}=0.063829\cdot\dot{m}_{w}-0.00168\cdot T_{bh}+0.250371\]2  
obtaining the value of the drying constant \(C\) experimentally. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Model Name** & **Model Equation** & **Reference** \\ \hline Page & \(MR=\frac{x-x_{e}}{x_{0}-x_{e}}=exp(-k,\ t^{n})\) & [48] \\ [PERSON] & \(MR=\frac{x-x_{e}}{x_{0}-x_{e}}=\text{a}\ast\exp(-k,\ t)\) & [49] \\ Logarithmic & \(MR=\frac{x-x_{e}}{x_{0}-x_{e}}=\exp(-k,\ t)+c\) & [50] \\ Two-term exponential & \(MR=\frac{x-x_{e}}{x_{0}-x_{e}}=\exp\left(-k,\ t\right)+(1-a)\exp(-k,\ a,\ t)\) & [51] \\ Diffusion approach & \(MR=\frac{x-x_{e}}{x_{0}-x_{e}}=\exp(-k,\ t)+(1-a)\exp(-k,\ b,\ t)\) & [52] \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Models for calculating the moisture ratio (MR) in drying processes. [PERSON] and [PERSON] (2013) [56] continued their line of research by modelling drying processes of porous and wet materials from experimental data. In this case, hot air drying of potato sheets of predefined dimensions (4 \(\times\) 2 \(\times\) 2 \(\times\) 2 cm) was studied, with the dryer air temperatures varying between 40, 50, 60, and 70 \({}^{\circ}\)C. The air speed was always 2 m/s. Since 1965, researchers have reached a number of interesting conclusions. The first of these was that, in the first instants of the process, the drying rate is very fast, since the moisture content is high, so at the beginning, the material loses the free water from its surface, for which little energy is required, which is quickly provided by the hot air hitting the object.