## 3 Results and Discussion
They concerned hybrid membranes consisting of the hyperbranched polyimide matrix (ODPA-MTA) and zeolite 4A. It was observed (experimental data in Table 4) that with the increasing filler addition, the zeolite 4A-HSPI hybrid membranes were characterized by the rise of the selectivity coefficient and decrease of the permeability coefficient, as in the case of [PERSON] and [PERSON]'s research [39, 41]. In spite of this, it was found that the measurement points were approaching [PERSON]'s line (Figures 8 and 9) along with the increase in filler content. That indicates that after earlier proposed modifications, it will be possible to obtain more productive membranes. It was also found that for the value of a volume fraction of filler particles \(\Phi\) bigger than 0.2, the observed difference between experimental results and theoretical data is large. This is directly related to higher values of calculated \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Membrane**} & \multirow{2}{*}{\(\Phi\)} & \multicolumn{2}{c}{**Experimental data**} & \multicolumn{2}{c}{**Theoretical data**} & \multirow{2}{*}{**AARE (\%)**} & \multirow{2}{*}{**RMSE (\%)**} \\ \cline{3-3} \cline{5-6}  & & \(\mathbf{\kappa_{02/N_{2}}}\) & & \(\mathbf{PO_{2}}\) (Barrer) & & \(\mathbf{\kappa_{02/N_{2}}}\) & \(\mathbf{PO_{2}}\) (Barrer) & \\ \hline M1 & 0.15 & 7.50 & 0.45 & 7.40 & 0.54 & & \\ M2 & 0.25 & 8.40 & 0.40 & 8.65 & 0.56 & 36 & 29 \\ M3 & 0.40 & 10.10 & 0.32 & 11.03 & 0.60 & & \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Experimental [41] and theoretical MOT-predicted data for the zeolite 4A-poly (vinyl acetate) mixed-matrix membranes. Figure 7: Comparison of experimental results (navy blue point) for the zeolite 4A-poly (vinyl acetate) mixed-matrix membranes with 3 different filler additions (M1, M2 and M3) with Maxwell theoretical results (red point) and their position relative to the Robeson upper bound line (green line). errors. That is why this method is not the appropriate gas transport description through MMMs with large filler loading. It was observed that for all chosen examples, the mean absolute relative error percentage ranges from 29% to 36%, while the root-mean-square error was in the range of 10% to 29%. The proposed MOT application also gives the possibility of simulation for further models of gas permeation through mixed-matrix membranes. The above article presents preliminary results from the comparison of gas transport data through zeolite 4A-HBPI membranes obtained with two models, namely Maxwell and Bruggeman (Figure 10). It was found that the theoretical data obtained from the Bruggeman model regarding the selectivity coefficient was worse than those obtained based on the Maxwell model, while the MOT-predicted data regarding the permeability coefficient were slightly better. Finally, the errors calculated within the Bruggeman model are comparable with errors obtained based on the Maxwell model proposed earlier; namely, AARE was 33% and RMSE was 18%. Because the calculated errors show that both the Maxwell and Bruggeman models are not accurate enough for description of proposed membranes, further research will focus on two solutions. The first one will be the application of next-generation permeation models for the description of transport in more complex systems. And the second one will be the appropriate modification of analysed mixed-matrix membranes, leading to an ideal system. Figure 8: _Cont._  
So we can see that thanks to the tools gathered in one place (application MOT), the researchers will be able to quickly and comprehensively evaluate potential membranes. Figure 8: Comparison of experimental results (navy blue point) for the zeolite 4A-HBPI mixed-matrix membranes with 6 different filler additions (M1–M6) with Maxwell theoretical results (red point) and their position relative to the Robeson upper bound line (green line).