## 3 Results and Discussion  
In the initial stage of research, the authors created a computer program MOT (membrane optimization tool) in the Java programming language. In this programme, the user will be able to choose the optimal gas permeation model for the MMMs, such as [PERSON]'s, [PERSON]'s, [PERSON]'s, [PERSON]'s, [PERSON]'s modified model or the Felske model. Within a chosen model, there will be a possibility to simulate the efficiency of the designed membranes and select the suitable components (organic, such as polylimides, polyphenylene oxide; and inorganic, such as modified carbon nanotubes, zeolites, etc.). In order to verify the correct functioning of the designed tool, the appropriate laboratory tests would be performed, and the experimental results will be compared with the predicted ones. Within the study, membranes identified as optimal for reducing emissions of undesirable substances or enrichment of gaseous mixtures in a desirable component will be created. The programme will allow us to verify the behavior and efficiency of innovative membranes before they are performed, to determine their performance and the properties of alternative membranes, and to reduce costs of research and their time. It will be an excellent tool for research scientists to study the separation of various gas mixtures using inorganic-organic hybrid membranes. As a result, the proposed method will allow the reduction of gaseous emissions in line with EU standards, which will allow further use of coal--Poland's strategic energy source. In this article, the experimental results obtained by the authors and the results found throughout the literature [39; 41] were compared with the theoretical data predicted by means of the most popular model (Maxwell) used by many researchers to predict membrane permeability. The users will also have the possibility to model the gas permeation through various hybrid membranes applying other models such as [PERSON], [PERSON]\(-\)[PERSON], [PERSON], modified [PERSON]'s model or [PERSON] model [9; 19; 28; 29; 34; 35; 36; 37; 38; 39; 40; 41; 42; 43; 44; 45; 46; 47]. The programme consists of the following windows:main window for model selection (Figure 2). Individual models are selected from the combo box. The user could enter the membrane parameters, such as volume fraction of filler particles, phi \(\Phi\), \(P_{d}/P_{m}\) permeability ratio, lambda \(\lambda_{dm}\) and polymer permeation \(P_{m}\) for two gases, in [PERSON]'s model window (Figure 3). The programme calculates the value of \(P_{1}\) and \(P_{2}\), and the value of alpha \(\alpha_{1/2}\). The user has the possibility to select the Robeson upper bound for such combinations of gases as \(\mathrm{O_{2}/N_{2}}\), \(\mathrm{CO_{2}/CH_{4}}\), \(\mathrm{H_{2}/N_{2}}\), \(\mathrm{H_{2}/CH_{4}}\), \(\mathrm{He/N_{2}}\), \(\mathrm{He/H_{2}}\), \(\mathrm{He/CH_{4}}\), \(\mathrm{CO_{2}/N_{2}}\), \(\mathrm{N_{2}/CH_{4}}\), \(\mathrm{H_{2}/CO_{2}}\), \(\mathrm{He/CO_{2}}\). * the additional tools, such as the diffusion and sorption coefficient calculator, as well as the ability to add the user's experimental data, are located in the More options menu (Figure 4). The average absolute relative error (AARE) and root-mean-square error (RMSE) were calculated in order to compare the theoretical MOT-predicted results with the experimental data, derived from the literature and our own research. Average absolute relative error was calculated as follows [48]:  
\[\%AARE=\frac{100}{NDP}\sum_{i=1}^{NDP}\left|\frac{p_{i}^{estim}-p_{i}^{exp}}{ p_{i}^{exp}}\right|, \tag{5}\]  
where:  
\(NDP\)--number of data points,  
\(p_{i}^{estim}\)--estimated value, and  
\(p_{i}^{exp}\)--experimental value. The root-mean-square error [49]:  
\[RMSE=\sqrt{\frac{1}{NDP}\sum_{i=1}^{NDP}\left(p_{i}^{estim}-p_{i}^{exp}\right) ^{2}}. \tag{6}\]  
So, the application will have an additional option of the average absolute relative error and the root-mean-square error calculation. Figure 2: The main window for model selection.