# The Role of Clean Coal Technologies in the Development of Renewable Energy Sources
## 1 Introduction
### Membrane Techniques  
Membrane techniques are a clean coal technology that will allow for the separation of greenhouse gases and the acquisition of key elements that are essential during the production of renewable energy technologies. The membrane is a layer that is designed to separate two phases of a feed. Due to its properties, the membrane acts as a passive or active barrier that allows transport between the other two phases. Depending on the type of feed, various membranes can be used, the properties of which enable, for example, the separation of harmful gases such as greenhouse gases from the feed, or the acquisition of valuable rare earth metals [7]. The authors conduct research on membranes that enable obtaining the following:  
* greenhouse gases, mainly CO2 from gases produced during the combustion of hard coal,
* rare earth elements recovered from fly ash generated in the combustion of hard coal. Mixed matrix membranes, i.e., combinations of a polymer matrix with nanotubes, have been used for greenhouse gas separation [8; 9]. The membranes were subjected to numerous modifications, which enabled their efficiency to be increased. The separation process can take place in various ways, for example by diffusion through the membrane, by taking advantage of differences in the solubility of elements in a solution, or by adsorption on the surface of membranes. The air passing through the membrane is divided into two streams: permeate, which is a mixture of gases free of harmful greenhouse gases, and retentate, e.g., CO2. The retentate should be captured and stored for further use. To speed up the search for membranes with the highest efficiency, a computer program was written that allows us to check the properties and performance of the membrane before its physical implementation [10]. For this purpose, mathematical models were used, such  
Figure 3: CCS strategy diagram supplemented with level 4. Source: own elaboration. as the Maxwell, Bruggeman or Felske models. The use of these models also allowed for verification of the industrial suitability of a given membrane. The Bruggeman model is presented below as an example:  
\[(P_{r})^{1/3}\bigg{[}\frac{\lambda_{dm}-1}{\lambda_{dm}-P_{r}}\bigg{]}=(1-\Phi)^{-1} \tag{1}\]  
where  
\(P_{r}\)--relative permeability of components,  
\(\lambda_{dm}\)--Pd/Pm permeability ratio,  
\(\Phi\)--volume fraction of filler particles. A similar process occurs in the case of membranes used for REE (rare earth element) recovery. After passing through the membrane, the separated REEs are purified and concentrated [11]. This makes it possible to obtain the desired chemical compounds. The created computer programs were used to analyze the obtained experimental results and select optimal membranes and sorbents. For this purpose, pseudo-first-order, pseudo-second-order Lagergren, intramolecular diffusion, chemisorption-diffusion and Boyd models were used to investigate various mechanisms. Additionally, in order to describe the equilibrium partition of REE ions between the liquid and solid phases (adsorbent) for different initial concentrations, appropriate adsorption isotherms were used. For this purpose, the REE_isotherm application was created, which is based on three models: Langmuir, Freundlich and Dubinin-Radushkevich [12; 13; 14]. An example diffusion-chemisorption model is presented below [15]:  
\[\frac{t^{0.5}}{q_{t}}=\frac{1}{K_{DC}}+\frac{1}{q_{e}}*t^{0.5} \tag{2}\]  
where:  
\(K_{DC}\)--diffusion-chemisorption constant  
\(q_{e}\)--adsorption capacity of metal ions at equilibrium state (mg/g)  
\(q_{t}\)--adsorption capacity of metal ions at time \(t\)  
--time (min)  
The presented technological solutions will firstly make it possible to keep coal in Poland's energy mix, and additionally provide valuable substances whose use can accelerate the development of renewable energy sources.