## 4 Process Description  
The selection of an appropriate membrane material is based on the feed blue stream main indicators (especially pressure and temperature) and its characteristics (e.g., CO\({}_{2}\), NO\({}_{x}\), and SO\({}_{x}\)). For the process design, the membrane method is applied after a pre-treatment system such as blue gas desulphurization (FGD) and DeNO\({}_{x}\) to remove the harmful gases (acid) due to the damage it may cause to the recovery operation [54]. Even though membrane technology exhibits a high energy efficiency and lower cost choice to remove carbon dioxide from blue gases, the limited implementations of the technology are the major challenge. Nevertheless, multi-stage designs and recycle flow utilization are substantially required to obtain a high CO\({}_{2}\) recovery rate with high purity. In CFPP, the blue gas generated mainly has a low CO\({}_{2}\) concentration and low pressure; therefore, the use of compression and/or vacuum pump units is fundamental to increasing the driving force for carbon dioxide transfer [55; 56; 57]. Table 1 below shows the lignite fuel features and contents, where the low heating value for the coal considered is 28,141 kJ/kg. Three various membrane process configurations have been prepared for the current article to obtain the minimum energy needed for a 90% carbon dioxide recovery rate and 99% purity. An elevated CO\({}_{2}\) purity is required for different industries' utilization [12]. It is widely accepted that the compressors and vacuum pumps' power required with membrane area are the essential indicators influencing the capture rate and process total cost. As a comprehensive concept for the membrane process, the purity of the carbon dioxide captured essentially relies on the poor membrane area. The polyacrylamide polymer was integrated with an enzyme called CA in a research project (CO\({}_{2}\) hybrid project) examined in 2020 [59]; this material was selected for the current paper due to specific advantages such as its characteristic of high permeability and selectivity, in addition to its availability in the market. The minor components, such as H\({}_{2}\)S and SO\({}_{2}\), have an effect on membrane materials which has been addressed by [PERSON] et al. [60]; the authors declared that these compounds may influence the material of plasticization and aging, which limits the membrane process performance and reduces its lifetime. However, five years is the efficient working period for the membrane material, and reparations must be considered after that duration [61; 62]. CHEMCAD model 8.1 is the simulation platform harnessed to investigate all the operations in the present paper. Table 2 demonstrates the prime indicators of coal power plants assumed. The membrane configurations integrated with the CFPP used for the present paper were ordered as three cases; in each case, various variables have been simulated (such as membrane surface area, compression ratio,... etc.) to achieve the prime goal of the research (high efficiency and purity of CO\({}_{2}\) captured with lowest cost). Based on the proposal of [PERSON] et al. (2013) [34], we investigated different values regarding the first membrane area to mitigate the total price to demonstrate an economically efficient membrane process design. The considered cases for the current paper with the schemes are presented below, check Figure 3:  
* Case 1: One stage of a membrane with compression and vacuum pump units;
* Case 2: Two stages of a membrane with a compression unit before each membrane module;
* Case 3: Three stages of a membrane with several compression units. \begin{table}
\begin{tabular}{c c} \hline \hline
**Lignite Detail** & **Value (\%)** \\ \hline Carbon & 72.3 \\ Ash & 13.89 \\ Oxygen & 7.45 \\ Hydrogen & 4.11 \\ Nitrogen & 1.69 \\ Sulfur & 0.56 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The fuel-utilized contents [58]. For each case assumed, the 80,460 kmol/h of flue gas produced from the CFPP was introduced into units of water and impurity elimination before the membrane system.