## 3 Results
The operating temperature of 950 \({}^{\circ}\)C was chosen for these preliminary tests to show agglomeration problems, which did not occur in any of the samples studied. The analysis of the samples in an H\({}_{2}\) atmosphere gave positive results in terms of reactivity; in addition, the samples treated with Cu showed higher reduction and oxidation conversions at 30 seconds. On the other hand, the analysis in a CO atmosphere showed similar results in OXMN009P for the reduction of Mn SOC and more excellent oxidation conversion at 30 seconds. However, this result is insufficient since the impregnation of Cu reactivity would have improved TSO with CO as fuel. From the TGA data, reduction (Mred) and oxidation (Mox) conversion curves as a function of time can be generated using Equations (1) and (2), where Xred = reduce conversion; Xox = oxidation conversion; mx = rusty mass; m = mass at an instant in time t. With these data, the conversions of TO in oxidation and reduction can be quantified with the weights of the TGA analysis because the other parameters are known. \[X_{red}=\frac{m_{ox}-m}{m_{ox}R_{max,\ T\text{O}}X_{Mco}} \tag{1}\]  
\[X_{ox}=1-\frac{m_{ox}-m}{m_{ox}R_{max,\ T\text{O}}X_{Mco}} \tag{2}\]  
[PERSON] et al. (2004) determined the reaction rate index (RI) as a variable in solid oxygen carriers and established Equations (3) and (4). \[RI=100\times 60\times Ro\times\left(\frac{dx}{dt}\right)_{norm} \tag{3}\]  
\[\left(\frac{dX}{dt}\right)_{norm}=\frac{p_{ref}}{p_{TGA}}\times\left(\frac{ dX}{dt}\right) \tag{4}\]  
where (dX/dt) is the derivative of the TSO conversion to time; pref is the reference partial pressure of the fuel gas; p TGA is the partial pressure of the fuel in TGA experiments; and the subscript norm is used to express the product p ref/p_TGA \(\times\) (dX/dt) [11]. Table 6 shows the reaction rate indices (RI) obtained for the preliminary analyses carried out on each sample, which were calculated according to Equation (1), facilitating the comparison of the reaction rate between different SOCS, indicated in Equation (1), in the conversion delta between 0 and 0.15 when the reaction is faster, and the \(Pr\) was set at 0.15 atm, which is commonly used in the literature [11; 15]. OXMN009P has a higher RI than OXMN009, and both materials present RI in the range reported in the literature for other Mn materials (see Table 7). \begin{table}
\begin{tabular}{l c c} \hline \multicolumn{3}{c}{**RI (\%/min)**} \\ \hline
**Material** & **CO** & **H\({}_{2}\)** \\ \hline OXMN009 & 5.8 & 15.1 \\ OXMN009P & 6.1 & 20.1 \\ Ilmenita \({}^{\text{a,1}}\) & 2.5 & 7.9 \\ Residuo de Bauvita \({}^{\text{1}}\) & 3.9 & 10.5 \\ Mineral (hematita) \({}^{\text{1}}\) & 3.4 & 12.4 \\ MnSA \({}^{\text{2}}\) & 5.1(5.3) \({}^{\text{a}}\) & 14.2 (11.8) \\ MnGBHNE \({}^{\text{2}}\) & 6.4 (1.4) & 19.2 (9.0) \\ MnGBMPB \({}^{\text{2}}\) & 9.0 (2.4) & 26.4 (14.8) \\ \hline \end{tabular}
\end{table} 
Table 6: RI (%/min) in TGA tests at 950 \({}^{\circ}\)C of the Mn minerals reported in the literature. The activation energies (_Ea_) obtained for OXMN009 and OXMN009P using CO, H\({}_{2}\), and CH\({}_{4}\) as reactive gases are between 5 and 18.7 kJ/mol, a similar range to that found in the literature for Mn-based SOC (10.2 to 19.5 kJ/mol) [24] and lower than that reported for the synthetic SOC of Fe, Cu, Ni, and Mn (14 to 33 kJ/mol) [8] and other materials of natural origin, such as activated Ilmenite (25.5 to 80.7 kJ/mol) [26]. The _Ea_ reported for OXMN009P are lower than those of OXMN009 in the reduction reactions, indicating that OXMN009P presents a greater reactivity concerning OXMN009 and a lower energy barrier for the reaction to take place [1], according to the kinetic results in Table 8 [27]. However, the oxidation of a lower _Ea_ was obtained in SOC OXMN009. The kinetic parameters (K) found for OXMN009 and OXMN009P are similar in order of magnitude in all the reactions studied and are close to those reported in the literature [23] for the oxidation of MnO to Mn\({}_{3}\)O\({}_{4}\) m/s(mol/m\({}^{3}\))\({}^{\rm n}\).