## 3 Results
Under the minimal CO\({}_{2}\)/Ar ratio of 5, the global carbon conversion was equal to 0.52 at \(t=0.20\) s, to 0.66 at \(t=0.25\) s, to 0.80 at \(t=0.30\) s and to 0.84 at \(t=0.40\) s. These values of the carbon conversion are higher than that presented in Figure 3a, but the furnace temperature was higher than the ones considered in the present study. The authors considered a spherical particle that they decomposed in hundreds of equally spaced concentric shells. They wrote an energy balance to compute the evolution of the particle temperature. They did not compute the oxygen concentration inside the particle, but they computed the effectiveness factor \(\eta\) through Equation (1) from Thiele modulus. In [10], the authors obtained a global carbon conversion approximately equal to 0.82 at time 1.3 s, when applying a regulation temperature of 1200 \({}^{\circ}\)C and an oxygen concentration of 21%. This is a much lower conversion than that observed in the present study for the same regulation temperature. One explanation for such a high difference could be the significant differences in the characteristics of the coals used for the experiments. Nevertheless, the simulations the authors obtained using CFD tools and the Thiele modulus method are in good agreement with their experimental conversions. When changing the value of the particle radius with a variation of \(\pm 20\%\), the maximal difference between the simulated global carbon conversions obtained for \(R_{p}=65\)\(\upmu\)m and \(R_{p}=52\)\(\upmu\)m is equal to 0.05, and that between the simulated conversions obtained for \(R_{p}=65\)\(\upmu\)m and \(R_{p}=78\)\(\upmu\)m is equal to 0.07. This proves that a variation of \(\pm 20\%\) of the particle radius from the selected value (65 \(\upmu\)m) does not significantly modify the simulations (relative difference of 5 and 7%, respectively). The values of the effectiveness factor \(\eta_{p}\) defined in (11) exhibit a sharp decrease between 0.15 and 0.30 s, whatever the regulation temperature, Figure 3b, corresponding to a sharp increase of the particle temperature already observed in Figure 2. These low values of the effectiveness factor \(\eta_{p}\) prove the existence of high oxygen diffusion limitations, characteristic of zone II burning conditions. Even for the lowest regulation temperature of 1100 \({}^{\circ}\)C, these diffusional limitations are present (\(\eta_{p}\) is less than 0.3 for times between 0.3 and 0.5 s). Figure 3c shows that the normalized particle radius \(R_{p}(t)/R_{p}(0)\) regularly decreases after the removal of the first outer volume element which occurs at times 0.73, 0.36 or 0.29 s, in the case of a regulation temperature equal to 1100, 1200 or 1300 \({}^{\circ}\)C, respectively. In the case of the regulation temperature of 1100, 1200 or 1300 \({}^{\circ}\)C, the number of volume elements decreases to 434, 235 or less than 94, respectively. As previously discussed, the computations were stopped at \(t=0.85\) s for the regulation temperature of 1300 \({}^{\circ}\)C, because the global carbon conversion \(X_{C}\) was higher than 0.99, Figure 3a, although the particle radius was not equal to 0 at this final time, Figure 3c. As the volume elements have the size thickness, they contain less carbon when they are close to the center of the particle.