## 1 Introduction  
Poland has very minimal oil reserves, and the available natural-gas deposits are not able to cover the demand for natural gas even at the present time. The renewable-energy sources are in our country at an early stage of development, and Polish natural conditions do not favor the development of this type of energy source. That is why the primary energy sources in Poland are coal and lignite, and the acquisition of energy from coal is much more cost effective. However, Poland must meet the European Union's greenhouse-gas emissions requirements, and it is necessary to use clean coal technologies. During the coal combustion process, besides the energy, undesirable substances are also produced. This phenomenon is unavoidable due to the chemical composition of the combusted fuel and the combustion itself. Substances produced during combustion include primarily sulphur oxides, nitrogen, hydrocarbons, carbon monoxide, solids, and so on [1,2]. Currently, the main goal of the researchers is to create methods that limit the emission of harmful products of hard coal combustion. In recent years, the application of membrane techniques has become very promising. It is related to their many advantages, such as: the low capital costs; high energy efficiency and thermal, mechanical and chemical stability; good separation properties; and lack of necessity of membrane regeneration [3; 4]. That is why the main objective of current membrane research is to obtain stable membranes with appropriate permeability and selectivity. Considering the limitations of both inorganic and polymeric membranes, a new type of hybrid membrane, also called MMM, has been proposed. Mixed-matrix membranes (MMMs) are inorganic fillers in solid, liquid, or both solid and liquid forms (e.g., carbon molecular sieves, zeolites, metals, ceramics, silica, metal organic frameworks, graphene, carbon nanotubes (CNTs), etc.) dispersed in a polymer matrix. These membranes offer the potential to combine the easy processability of polymers with the outstanding gas separation properties of inorganic materials [3; 4; 5; 6; 7; 8]. They could be classified into three main groups: the polymer-solid, the polymer-liquid, and the polymer-liquid-solid membranes. However, the polymer-solid MMMs have aroused the greatest interest. For this type of MMM, both zeolitic and nonzeolitic inorganic materials are used as fillers. The zeolites were used as fillers because of their specific adsorption properties, the appropriate thermal stability, and shape selectivity [9]. As a polymer matrix for the preparation of zeolitic or nonzeolitic hybrid membranes, both glassy and rubber polymers are used. In the case of rubbery polymers, the interfacial interaction between them and zeolitic fillers is probably better due to the greater mobility of polymer chains [9]. On the other hand, glassy polymers are characterized by greater mechanical stability and gas transport properties. However, mixed-matrix membranes based on this type of polymer matrix show the presence of interfacial void defects. In order to solve this problem, many types of modifications have been made, such as: application of silane and amine coupling agents to improve interfacial adhesion and gas selectivity (changing the surface properties of fillers from hydrophilic to hydrophobic), coating of nonselective slots with a silicone rubber, and addition of a plasticizer to reduce the intrinsic gas separation performance of polymers [9; 10; 11; 12; 13; 14; 15; 16; 17; 18]. Gas transport through a mixed-matrix membrane is a complicated problem (Figure 1). In order to predict the gas permeability through these matrices, many theoretical models were proposed [1; 19], as well as the model created by [PERSON]. Our research group has been conducting research on the application of inorganic-organic hybrid membranes in the separation of gas mixtures.