## 2 Materials and Methods
### Experimental Conditions for the Pyrolysis and Combustion Experiments  
The configurations of the drop tube furnace used for the pyrolysis of the coal particles and for the combustion of the resulting coal char particles are presented in Figure 1.  
The silica-alumina reactor of the drop tube furnace is 1.7 m high and its radius \(R_{r}\) is equal to 3.5 cm. This reactor is placed inside a furnace whose temperature is controlled. For the combustion experiments on the coal char particles, three constant regulation temperatures of the reaction zone of the drop tube furnace were considered: 1100, 1200 and 1300 \({}^{\circ}\)C.  
The first main difference between the two configurations of the drop tube furnace deals with the injection system. For the pyrolysis experiments, the coal particles were injected through an injection probe at a rate equal to 17 \(\times\) 10\({}^{-13}\) kg.h\({}^{-1}\), Figure 1a, together  
\begin{table}
\begin{tabular}{c c c} \hline \hline  & **Coal** & **Coal Char** \\ \hline Proximate analysis (wt\%, ar 1) & & \\ Volatile matter & 24.0 & 0.7 \\ Ash & 13.8 & 20.0 \\ Fixed Carbon & 54.7 & 78.5 \\ Moisture & 7.5 & 0.8 \\ Ultimate analysis (\%, daf 2) & & \\ C & 67.64 & 76.63 \\ H & 3.77 & 0.89 \\ O 3 & 26.02 & 20.69 \\ N & 1.81 & 1.26 \\ S & 0.76 & 0.53 \\ \hline \hline \end{tabular} 1  
\end{table}
Table 1: Proximate and ultimate analyses of the South African coal considered in the present study and of the coal char produced from the coal particles through pyrolysis experiments in the drop tube furnace.  
Figure 1: A schematic representation of the drop tube furnace used for the pyrolysis experiments applied to coal particles (**a**), and for the combustion of the resulting coal char particles (**b**).  
with a nitrogen flow of 400 L.h\({}^{-1}\) pre-heated at 1300 \({}^{\circ}\)C. The drop distance was 1 m length. Concerning the combustion experiments, for each injection sequence, 2 mg of coal char particles were injected through a water cooled injector with a primary gas flow (40 L.h\({}^{-1}\)), under an oxidative atmosphere (12% oxygen, balance nitrogen). Then, the coal char particles were entrained by a secondary nitrogen flow (360 L.h\({}^{-1}\)) preheated at 900 \({}^{\circ}\)C, Figure 1b.  
Concerning the outlet in the case of the pyrolysis experiments, the coal char particles were collected through a sample probe which was water cooled, Figure 1a. For the combustion experiments, the particle temperature was recorded by a two-color pyrometer IMPAC ISR 12-LO, placed at the bottom of the drop tube furnace and vertically pointing to the reaction zone of the drop tube furnace, Figure 1b. This particle temperature measured during its fall in the reactor is the only experimental data which are available. For a regulation temperature equal to 1200 \({}^{\circ}\)C, a shift of 75 \({}^{\circ}\)C was observed between the lowest and the highest maxima of the particle temperature, with a mean temperature equal to 1353 \({}^{\circ}\)C. This roughly corresponds to an uncertainty equal to 38 \({}^{\circ}\)C, which is in agreement with [PERSON] et al. who wrote in [PERSON] et al. (2013) that temperature measurements by optical methods are given within an uncertainty equal to \(\pm\)50 \({}^{\circ}\)C, when the particle is observed along its overall trajectory.  
For the combustion experiments of the coal char particles, at least nine injections were performed.