## 3 Results and Discussion
### System Validation with Slaked Lime  
#### 3.2.1 Fixed-Bed FGD Experiments  
Figure 3 shows the breakthrough curves for PC obtained under different experimental conditions, conducted for the purpose of validating the dry fixed-bed FGD system. The samples are labeled according to FGD temperature and RH%, as indicated in Table 1. The discussion that follows will also include the parameters \(\lambda\) and \(\mu_{max}\) (see Figure S8) and the breakthrough sulfur capacity (mg/g) (obtained from Equation (5)), presented in Table 2.  
Figure 3a displays the effect of varying the quantity of the sample within the reactor on the desulfurization process conducted at 75 \({}^{\circ}\)C and 30 RH%. An increase in weight of the adsorbent from 0.10 g to 0.14 g resulted in a rise in both the \(t_{b}\) and \(\lambda\) parameters. On the other hand, the maximum specific breakthrough rate (\(\mu_{max}\)) exhibited similar values in both breakthrough curves, indicating that the adsorbent quantity had a minimal impact on this parameter. The breakthrough sulfur capacity in both experiments was 18 mg/g, as this value was normalized by the PC weight. Notably, the breakthrough lag phase was very short when 0.10 g of PC was utilized. This may be attributed to the low ratio of adsorbent employed to inlet SO\({}_{2}\) adsorbate concentration [17]. Additionally, the geometry of the sample holder within the reactor may have influenced the shape of the breakthrough curve. Indeed, the vertical path of the flux along the adsorbent in the configuration described in Section 2.3 is relatively thin (1.5 mm) compared to that of other tubular reactors described in the literature [29]. Therefore, 0.10 g of adsorbent is considered the sample weight limit for loading the reactor to study the uptake capabilities of the material under these conditions. The desulfurization experiment with 0.14 g of PC at 75 \({}^{\circ}\)C in a humidified stream at 30 RH% was replicated three times to evaluate the repeatability of the fixed-bed FGD experiments. Data plotted in Figure 3b highlight that the breakthrough curves look very similar. The breakthrough sulfur capacities are 18, 19, and 20 mg/g, indicating  
Figure 2: Temperature within the reactor computed for (**a**) case A (heater temperature of 180 \({}^{\circ}\)C) and (**b**) case B (heater temperature of 370 \({}^{\circ}\)C). The scale legends to the right of the models in (**a,b**) connect the temperature data with a color gradient. The computed velocity fields for cases A and B are shown in (**c,d**). The scale legends on the right of the models in (**c,d**) connect the flow velocity values with a color gradient. The red arrows indicate the direction of the flux. that the results are reproducible, with an error of 1 mg/g. An increase in the reactor temperature resulted in a notable variation in all breakthrough variables (Figure 3c). Indeed, at 160 \({}^{\circ}\)C, the breakthrough sulfur capacity was 24 mg/g. Conversely, an increase in stream humidity at 45 RH% resulted in a slight increase in the breakthrough sulfur capacity of PC [75 \({}^{\circ}\)C_45 RH%] to 21 mg/g (Figure 3d). Both humidity and temperature exert an influence on the sulfur uptake process, resulting in prolonged \(t_{b}\) and \(\lambda\). In addition, the breakthrough curve of PC [160 \({}^{\circ}\)C_30 RH%] is distinguished by a more rapid increase in C/C\({}_{0}\) during the logarithmic phase and a longer time to reach the stationary phase. This refers to the condition in which the adsorbent approaches saturation [22].