## 4 Selecting a Suitable Metal Oxide
### Removal Efficiency
The reported kinetic prefactors show considerable variation, even among the same metal oxides. This is in part due to the different methods used for evaluating the experimental data. Also, we notice that except in the case of calcium-based sorbents, the activation energies are relatively small. On the one hand, this may hint to an adsorption-desorption mechanism accompanying the sulfidation reaction [67]. On the other hand, the low activation energies may also be caused by \"pollution\" of the measured reaction rate by transport phenomena: Likewise to the reaction rate function; transport coefficients also increase with temperature, although to a much lesser extent. For instance, molecular diffusivity of gases follow \(D_{M}\sim T^{1.75}/P\) while Knudsen diffusivity follows \(D_{k}\sim T^{0.5}\)[44]. Transport limitations might become relevant at high temperature. The weaker increase of the transport coefficient with temperature compared to the (intrinsic) reaction rate might cause a reduction of the measured activation energy. Taking together the considerations on the equilibrium and on the kinetics, it can be seen that the kinetics benefits from increasing the temperature while the equilibrium becomes less favorable. Hence, the upper bound for the operating temperature for a given metal oxide is determined by the equilibrium while the lower bound is controlled by kinetic limitations [74]. Specifically, from the equilibrium data and the specified amount of H\({}_{2}\)S removal, the maximum operating temperature for a metal oxide is derived from Equation (11) as:  
\[T_{\rm max}\approx\frac{\Delta G}{R}\bigg{[}\ln\bigg{(}\frac{C_{\rm H_{2}S, \infty}}{C_{\rm H_{2}O,0}+\gamma(C_{\rm H_{2}S,0}-C_{\rm H_{2}S,\infty})}\bigg{)} \bigg{]}^{-1} \tag{15}\]  
where \(C_{\rm H_{2}S,0}\) and \(C_{\rm H_{2}O,0}\) are the inlet (or initial) concentrations of H\({}_{2}\)S and H\({}_{2}\)O, respectively (if the inlet stream does not contain any steam \(C_{\rm H_{2}O,0}=0\)), and \(C_{\rm H_{2}S,\infty}\) is the desired concentration of H\({}_{2}\)S after the removal is completed, i.e., the concentration after the gas has passed the packed bed before breakthrough. Similarly, the minimum operating temperature is estimated treating reaction \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**MO** & **Temperature Range** & **Prefactor \(k_{0}\)** & **Activation Energy \(E_{a}\)** & **Method** & **Ref.** \\ \hline Iron-based: & & & & & \\ Fe\({}_{2}\)O\({}_{3}\) & 600–900 \({}^{\circ}\)C & 2.5 \(\times 10^{-3}\) cm/s & 13.8 kJ/mol & Grain model & [67] \\ Fe\({}_{2}\)O\({}_{3}\) & 500–800 \({}^{\circ}\)C & - & 14.7 kJ/mol & (not specified) & [68] \\ Manganese-based: & & & & & \\ MnO & 300–800 \({}^{\circ}\)C & 0.456 cm/s & 23.8 kJ/mol & Initial kinetics & [50] \\ Mn-ore & 400–600 \({}^{\circ}\)C & 0.93 cm/s & 30.6 kJ/mol & Initial kinetics & [66] \\ MnO & 800–920 \({}^{\circ}\)C & 4.16 cm/s & 37.42 kJ/mol & Shrinking core model & [69] \\ Zinc-based: & & & & & \\ ZnO & 300–750 \({}^{\circ}\)C & 0.110 cm/s & 30.3 kJ/mol & Initial kinetics & [50] \\ ZnO & 400–800 \({}^{\circ}\)C & 1.31 cm/s & 43.11 kJ/mol & Initial kinetics & [70] \\ ZnO & 550–650 \({}^{\circ}\)C & 3.7 \(\times 10^{-3}\) cm/s & 16.2 kJ/mol & Grain model & [51] \\ Calcium-based: & & & & & \\ CaO & 300–800 \({}^{\circ}\)C & 0.038 cm/s & 21.6 kJ/mol & Initial kinetics & [50] \\ CaO & 650–900 \({}^{\circ}\)C & 640 m/s & 155 kJ/mol & Grain model & [48] \\ CaCO & 560–670 \({}^{\circ}\)C & 5200 m/s & 163 kJ/mol & Grain model & [71] \\ Copper-based: a & & & & & \\ CuCeO\({}_{x}\) & 350–750 \({}^{\circ}\)C & - & 16 kJ/mol & Initial kinetics & [73] \\ Cu-Cr\({}_{2}\)O\({}_{3}\) & 650–850 \({}^{\circ}\)C & - & 19.8 kJ/mol & Initial kinetics & [72] \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Kinetic parameter for different metal oxides. (Equation (1)) as an irreversible reaction taking place in a well mixed continuous reactor.