*4.1. Mass Influence*

To gain an understanding of the e ffect of varying masses in the TGA as explained in Section 2.2, the experiments listed in Table 4 were evaluated using the Arrhenius equation together with all four kinetic models (VM, GM, RPM, and JM). In Figure 1, the frequency factor is plotted over the sample mass for each conversion model. A correction term of an exponential type fits the results for every conversion model to a satisfactory degree ( *R*<sup>2</sup> ≈ 95%), with *b* as the model parameter.

$$\lg(m\_0) = e^{-b \cdot m\_0} \tag{12}$$

(13)

With the addition of this correction term, a determination of the intrinsic gasification rate is possible. Therefore, all further experiments were evaluated with the following rate equation, Equation (13), and the value for *b* is obtained by optimization with Equation (11).

**Figure 1.** Frequency factor over sample mass for all four conversion models.

#### *4.2. Confirmation of Reaction Model*

The kinetic model for the gasification of the char has to describe su fficiently the change in reaction rate with ongoing carbon conversion. In Figure 2, the Arrhenius plot is shown for the CO2 gasification in configurations No. 2 and 5 as well as for the steam gasification in configuration No. 3 and 8 for the volumetric model.

It can be seen that the gradient of the Arrhenius graph (i.e., activation energy) increases with increasing temperature. Generally, two possible explanations exist for the change in reactivity. Firstly, two separate reactions with di fferent activation energies and frequency factors could determine the gasification of the char at di fferent temperatures, e.g., a catalyzed and a non-catalyzed reaction. In this case, a suitable reaction model must be selected. Secondly, the reactivity of the char increases more with ongoing gasification than the volumetric model predicts. In this case, another conversion model

should be used, like the GM, RPM or JM. Only additional runs with different heating rates can make the distinction between those two possible explanations, as stated by Miura et al. [23].

**Figure 2.** Arrhenius plot for (**a**) CO2 gasification (configurations No. 2, 5) and (**b**) steam gasification (configuration No. 3, 8) (VM).

The test configuration No. 1 of the CO2 gasification was repeated with heating rates of 20 K/min and 40 K/min in another oven of the TGA. In Figure 3, one representative run for each heating rate is plotted. The solid lines represent the reaction rate according to the Arrhenius model for both runs. The dashed lines show the reaction rate according to the Arrhenius model, when only inverse temperatures of more than 8.2 × 10−<sup>4</sup> K−<sup>1</sup> are considered. It is apparent that the change in reaction rate happens at different temperatures.

**Figure 3.** Arrhenius plot for CO2 gasification in configuration No. 1 with 20 K/min and 40 K/min heating rate.

Additionally, the samples were acid washed according to ISO 602:2015 to remove the mineral content. The acid washed samples were used in CO2 gasification experiments (Table 2) of the configurations No. 1, 3, 5, and 7. Compared to the non-acid washed samples, the Arrhenius plots have the same shape, but exhibit a shift to lower frequency factors by about 0.15–0.4 log(min−1). This indicates the general catalytic effect of the mineral matter in the ash but without any temperature dependency.

Therefore, it can be concluded that the change in char reactivity has to be explained by a suitable conversion model.

#### *4.3. Determination of Kinetic Parameters*

For the determination of the kinetic parameters, the objective function (11) was minimized for the Arrhenius equation and the L–H model in combination with all four kinetic models (VM, RM, RPM and JM) for both the CO2 gasification as well as the steam gasification. The coe fficients of determination *R*<sup>2</sup> are listed in Table 5. The L–H model generally leads to significantly better results than the Arrhenius model with the coe fficient of determination being larger for any given conversion model except from the GM for CO2 gasification. In this case, R<sup>2</sup> is very similar for the Arrhenius and the L–H model. Regarding the conversion models, the JM is the most suitable for the selected char samples.


**Table 5.** Coe fficient of determination R<sup>2</sup> for all model combinations.

Table 6 shows the kinetic parameters for the L–H model, the parameter α of the JM and the parameter *b* for the mass influence.


**Table 6.** Results for the L–H reaction model with the Johnson conversion model.

A closer look has to be taken at the activation energy *Ea*,2, which is negative for both CO2 and steam gasification. Negative activation energies have been observed for gasification before [6] and are a hint that the L–H model does not completely describe the reaction mechanisms during gasification. In the case of steam gasification, a possible reason is the hydrogen inhibition through the irreversible adsorption of hydrogen on the active char sites, described by Hüttinger et al. [24].

For both, steam and CO2 gasification, the influence of ash acting as a catalyst is another explanation. Still, with a coe fficient of determination at about 98% and 95% for steam and CO2 gasification respectively, the confidence intervals are narrow enough for practical use.

Figure 4 exemplarily shows the results of a steam gasification run in test configuration No. 2 with 20 mL/min steam and 35 mL/min hydrogen for a selection of temperatures with their error bar according to the Allan deviation. Additionally, the predicted reaction rates of the L–H model together with all four conversion models are plotted. For the JM, the 95% confidence interval is marked in the plot, too. The measurements show a digressive change in reaction rate between 900 ◦C and 970 ◦C that was observed in all measurements with steam. Only the JM satisfactorily models this characteristic, leading to the very high coe fficient of determination. The results are in good agreemen<sup>t</sup> with the JM model, especially in the relevant range from 750 ◦C to 950 ◦C.

Figure 5 shows the respective information for a trial with 33% CO2 and 20% CO for the L–H reaction model together with all conversion models. Here, the L–H model emulates the measurements for the CO2 gasification best, too. In addition, similarly to Figure 4, the change in reaction rate decreases between 900 ◦C and 950 ◦C. However, for the CO2 gasification, the JM is not able to model this e ffect correctly. For very high conversions and temperatures, all models overestimate the reaction rate. These deviations are observed for most CO2 measurements and lead to a smaller coe fficient of determination. Still, the results are satisfying in the relevant temperature range for practical use in fluidized bed gasification.

**Figure 4.** Measurement and L–H model results for steam gasification in configuration No. 2 (20 mL/min H2O, 35 mL/min H2); 95% confidence interval for JM is marked with a thin dotted line.

**Figure 5.** Measurement and L–H model results for CO2 gasification in configuration No. 6 (33 mL/min CO2, 20 mL/min CO); 95% confidence interval for JM is marked with a thin dotted line.
