## 2 Materials and Methods
### Statistical Analysis  
An analysis of the fit of the measurement points and individual models was performed using the coefficient of determination, R\({}^{2}\); the sum of squares of errors, ERRSQ (The Sum Square of Errors); the composite fractional error function, HYBRD (Hybrid Fractional Error Function); the average relative error, ARE (Average Relative Error); the Fisher F test; and the \(\chi^{2}\) test [54]. The relevant formulas are shown below.  
\[\rm ERRSQ=\sum_{i=1}^{K}\Bigl{(}q_{exp}-q_{calc}\Bigr{)}^{2} \tag{9}\]  
\[\rm HYBRD=\frac{100}{k-P}\sum_{i=1}^{k}\left(\frac{\Bigl{(}q_{exp}-q_{calc} \Bigr{)}^{2}}{q_{exp}}\right) \tag{10}\]  
\[\rm ARE=\frac{100}{k}\sum_{i=1}^{k}\left|\frac{q_{exp}-q_{calc}}{q_{exp}}\right| \tag{11}\]  
\[\rm F=\frac{(k-p)\cdot\sum_{i=1}^{k}\Bigl{(}q_{exp}-\frac{1}{k}\cdot\sum_{i=1 }^{k}q_{exp}\Bigr{)}^{2}}{(k-1)\cdot\sum_{i=1}^{k}\Bigl{(}q_{exp}-q_{calc} \Bigr{)}^{2}} \tag{12}\]  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Lp.** & **General Form** & **Linear Form** & **References** \\ \hline
1 & \(\rm q=\frac{q_{max}\,K_{L}\,C_{o}}{1+K_{L}\,C_{o}}\) (3) & & [47; 49] \\ \hline
2 & Linearization according to [PERSON] & \(\rm\frac{C_{o}}{q}=\frac{1}{q_{max}\,K_{L}}+\frac{C_{o}}{q_{max}}\) (4) & [47; 49] \\ \hline
3 & Linearization according to & \(\rm\frac{1}{q}=\frac{1}{q_{max}\,K_{L}}\cdot\frac{1}{C_{o}}+\frac{1}{q_{max}}\) (5) & [47; 49] \\ \hline
4 & Linearization according to [PERSON] & \(\rm\frac{q}{C_{o}}=-K_{L}\cdot q+q_{max}\,K_{L}\) (6) & [47; 49] \\ \hline
5 & Linearization according to & \(\rm q=\left(\frac{\pi}{K_{L}}\right)\cdot\frac{q}{C_{o}}+q_{max}\) (7) & [47; 49] \\ \hline \hline \end{tabular} Notation: qmax—maximum sorption capacity, given in mg/g; K\({}_{\rm L}\)—Langmuir isotherm constant, given in L/mg.  
\end{table}
Table 1: Langmuir sorption isotherm models in general and linear form.  
\[\chi^{2}=\sum_{i=1}^{k}\left(\frac{\left(q_{\text{exp}}-q_{\text{calc}}\right)^{2} }{q_{\text{calc}}}\right) \tag{13}\]  
Here, \(q_{\text{exp}}\) denotes the sorption obtained from measurements, \(q_{\text{calc}}\) denotes the sorption obtained from calculations using the model in general form, \(k\) is the number of measurement points, and \(p\) is the number of model parameters.  
Statistical studies of the effect of temperature on sorption were performed using the GLM (generalized linear model) [55], with the dependent variable \"q\", the quantitative variable \"C\({}_{e}\)\", and temperature as the qualitative variable.  
In addition, in order to show whether there are significant differences between the sorption capacity at different process temperatures and Rockfos\({}^{\text{\textregistered}}\) material granulations, an analysis of variance was performed. The normality of distributions in individual groups was tested using the Shapiro-Wilk test, and the homogeneity of variance was tested using [PERSON]'s test. When the tested variables followed a normal distribution and the homogeneity of variance was maintained, differences between groups were analyzed with the ANOVA test. To identify which means differed significantly, post hoc NIR tests were applied. When variables within groups did not follow a normal distribution (according to the Shapiro-Wilk test), differences between groups were analyzed using the nonparametric Kruskal-Wallis ANOVA test. Significant differences between groups were then identified through multiple comparisons of the mean ranks for all samples. Statistical analyses were performed using STATISTICA 13.3.