## 4 Results of Kinetic Modeling
### Calcination Kinetics Comparative Analysis
Studies typically suggest that the decomposition reaction can be modeled by either Avrami nucleation [26] or first-order chemical reaction F1 [32; 58], which is logical when taking into account that F1 is a special case of nucleation. As a further means of comparison, the model-fitting results presented previously were compared with published results which employed the isoconversonal Friedman method, carried out by the authors using the same experimental data [24]. The results of the analysis are summarized in Table 4, which also presents average values of \(E_{a}\) over the course of the reaction (\(E_{o}\)). A detailed explanation of the assumption of single-step reaction kinetics is presented elsewhere [30]. The equilibrium pressure, \(P_{0}\) (kPa), of the gaseous product is seen to have a significant influence on d\(\alpha\)/d\(t\) and, hence, the activation energies under the 100% CO2 atmosphere [24] (see Table 4). The compensation effect was used as an alternative means of determining a reaction mechanism for calcination. This method was only applied for calcination under N2, due to the large variation in kinetic parameters under CO2[24] (see Section 3.3). Figure 5 shows a comparison of the experimental and theoretical reaction models, which are compared to suggest a reaction mechanism. The plot shows that the best fitting reaction mechanism is the R2 (contracting area) geometric reaction model, which produces a correlation coefficient of 0.9919. This model also produced a high correlation coefficient in the Coats-Redfern analysis (R\({}^{2}\) > 0.999; see Table 2). The activation energy determined with Coats-Redfern is 30% higher than the average Friedman value (213 compared to 164 kJ mol\({}^{-1}\)), although the values are still within the range obtained in the literature for CaCO3 calcination [30]. In conclusion, the R2 model (contracting area) is the mechanism which most accurately models the calcination of CaCO3 under pure N2, in agreement with the literature [50], which has been verified using both Coats-Redfern and compensation effect methods. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Experimental Atmosphere** & **CO2** & **N2** \\ \hline \(E_{a}\) **(k) mol\({}^{-1}\))** & 430–171 & 171–147 \\ \(E_{o}\) **(k) mol\({}^{-1}\))** & 307 & 164 \\ \(A_{a}\) **(min\({}^{-1}\))** & \(3.8\times 10^{34}\)–\(2.9\times 10^{5}\) & \(1.5\times 10^{7}\)–\(3.7\times 10^{4}\) \\ \(A_{o}\) **(min\({}^{-1}\))** & – & 3.13\(\cdot 10^{6}\) \\ **Max k (min\({}^{-1}\))** & 0.023 & 0.012 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Kinetic parameters for calcination obtained from P-CaO material using the Friedman method [24]. Figure 5: Comparison of theoretical reaction models and experimental model-fitting curve (compensation effect) for calcination under N2. It is important to note that the nucleation models and the R2 reaction model are proposed as the mechanisms most consistent with kinetic data for calcination of CaCO\({}_{3}\) under 100% CO\({}_{2}\) and N\({}_{2}\), respectively. As set out by [PERSON] and [PERSON] in their discussion of the solid state reactions and the extraction of Arrhenius parameters from thermal analysis, one of the fundamental tenets of chemical kinetics is that no reaction mechanism can ever be proved on the basis of kinetic data alone [64]. Despite not allowing for complete isolation of the experimental reaction without influence from physical processes (i.e., diffusion, adsorption, desorption), the suggested reaction models are useful for drawing reasonable mechanistic conclusions.