## 4 Results of Kinetic Modeling  
### Calcination Kinetics Comparative Analysis  
Calcination kinetics were modeled using Coats-Redfern, master plots, and isoconversional methods with compensation effects for two different atmospheres, as explained previously (see Section 3.1). The Coats-Redfern analysis under 100% N\({}_{2}\) will be discussed first. Figure 2a displays the Coats-Redfern Arrhenius plots for all of the theoretical reaction models (see Section 3.1), while Figure 2b shows selected reaction models with the highest correlation coefficients, which are also presented in Table 2. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Kinetic Model** & \(E_{a}\) **(kJ mol\({}^{-1}\))** & \(A\) **(min\({}^{-1}\))** & **Correlation Coefficient (R\({}^{2}\))** & **Material and Reference** \\ \hline
**A2** & 108.73 & \(3.5\times 10^{4}\) & 0.9924 & P-CaCO\({}_{3}\) \\  & & & & This work \\
**A3** & 67.11 & \(1.7\times 10^{2}\) & 0.9913 & This work \\
**A4** & 46.30 & \(1.1\times 10^{1}\) & 0.9900 & This work \\
**R2** & 203.57 & \(2.1\times 10^{9}\) & 0.9995 & This work \\
**R3** & 213.12 & \(5.0\times 10^{9}\) & 0.9982 & This work \\
**F1** & 233.59 & \(2.3\times 10^{11}\) & 0.9933 & This work \\
**D1** & 371.14 & \(1.0\times 10^{18}\) & 0.9985 & This work \\
**R2** & 180.12 & \(1.2\times 10^{7}\) & - & CaCO\({}_{3}\)[50] \\
**F1** & 190.46 & \(3.4\times 10^{7}\) & - & CaCO\({}_{3}\)[58] \\
**R3** & 187.1 & - & - & CaCO\({}_{3}\)[54] \\
**D1** & 224.21 & \(3.0\times 10^{4}\) & - & CaCO\({}_{3}\)[59] \\ \hline \hline \end{tabular}  
* The kinetic models are classified as follows. A2–4 are the Avrami–Erofeyev nucleation models, where 2–4 refer to the exponential in the algebraic function. R2–3 are the geometric contraction models, where R2 uses a contracting area model and R3 uses a contracting volume model. F1 refers to a first-order reaction model and D1 to a first-order diffusion model.  
\end{table} 
Table 2: Kinetic parameters for calcination obtained from P-CaCO\({}_{3}\) (100% N\({}_{2}\) atmosphere) (average over four heating rates) compared with literature results (CaCO\({}_{3}\) decomposition under inert atmosphere). Figure 2: Coats–Redfern Arrhenius plots for P-CaCO\({}_{3}\) (10 K min\({}^{-1}\)) under 100% N\({}_{2}\): **(a)** All models; **(b)** selected models with highest R\({}^{2}\) values. Correlation coefficients are seen to be very high for all reaction mechanisms, while calculated activation energies vary between 47 and 370 kJ mol\({}^{-1}\). By a small margin, the highest correlation coefficient is produced by the R2 geometric model, which determined an \(E_{a}\) of 204 kJ mol\({}^{-1}\). These kinetic parameters are typical for the calcination of CaCO\({}_{3}\) under an inert atmosphere. Literature results generally produce values of \(E_{a}\) between 180 and 224 kJ mol\({}^{-1}\)[30], showing a lack of consensus on the calcination reaction model (see Table 2). Physical descriptions of the reaction models referenced in Table 2 are provided in a review of kinetics applied to CaL [30]. As for the experiment under N\({}_{2}\), Coats-Redfern Arrhenius plots (Figure 3) and kinetic parameters for selected reaction models (Table 3) are presented for an experiment under 100% CO\({}_{2}\). Under this atmosphere, calculated activation energies are much higher, ranging from 300 to 600 kJ mol\({}^{-1}\) when modeled by the nucleation models to 1200 kJ mol\({}^{-1}\) when fitted with a first-order model. This is due to the high gradients in the Arrhenius plots under 100% CO\({}_{2}\), which mathematically leads to high activation energies. High values of \(E_{a}\) are also obtained in the few literature studies carried out under 100% CO\({}_{2}\)[31; 60]. [PERSON] et al. attribute this to the fact that the temperature range of decomposition becomes higher and narrower as the percentage of CO\({}_{2}\) increases, resulting in a higher apparent activation energy [31]. decompose more quickly [30; 61].