# Research on Pure Hydrogen Production Using a Fuel-Processing System Combined with a PSA System
## 4 PSA (Pressure Swing Adsorption) System  
When a gas is physically adsorbed into a solid surface, an adsorption equilibrium is achieved between gas molecules and the adsorbed sites on the surface of the adsorbent (activated carbon). The expression of the coverage is defined as the ratio of the area occupied by gas molecules to the total surface area of the adsorbent, which depends on the partial pressure of the gas and is called the adsorption isotherm [42; 43]. To calculate the adsorption isotherm, several models have been proposed, such as the Langmuir isotherm, the Langmuir-Freundlich isotherm, IASR, DSL, and VSM. Among \begin{table}
\begin{tabular}{c c c} \hline \hline  & **Reactions** & **Energy Amount** \\ \hline Steam reforming & \(CH_{4}+H_{2}O\ \to CO+3H_{2}\) & \(\Delta H_{298K}^{0}|\text{mol}^{-1}=205,800\) \\ Steam reforming + Water–gas shift & \(CH_{4}+2H_{2}O\ \to CO_{2}+4H_{2}\) & \(\Delta H_{298K}^{0}|\text{mol}^{-1}=164,600\) \\ Dry reforming & \(CH_{4}+CO_{2}\ \to 2 CO+2H_{2}\) & \(\Delta H_{298K}^{0}|\text{mol}^{-1}=247,000\) \\ Combustion & \(CH_{4}+2O_{2}\ \to CO_{2}+2H_{2}O\) & \(\Delta H_{298K}^{0}|\text{mol}^{-1}=-802,600\) \\ Partial oxidation & \(CH_{4}+0.5O_{2}\ \to CO+2H_{2}\) & \(\Delta H_{298K}^{0}|\text{mol}^{-1}=-36,000\) \\ CO oxidation & \(CO+0.5O_{2}\ \to CO_{2}\) & \(\Delta H_{298K}^{0}|\text{mol}^{-1}=-282,993\) \\ Hydrogen oxidation & \(H_{2}+0.5O_{2}\ \to H_{2}O\) & \(\Delta H_{298K}^{0}|\text{mol}^{-1}=-241,856\) \\ Water–gas Shift & \(CO+H_{2}O\ \to CO_{2}+H_{2}\) & \(\Delta H_{298K}^{0}|\text{mol}^{-1}=-41,200\) \\ Methanation I & \(CO+3H_{2}\ \to CH_{4}+H_{2}O\) & \(\Delta H_{298K}^{0}|\text{mol}^{-1}=-205,800\) \\ Methanation II & \(CO_{2}+4H_{2}\ \to CH_{4}+2H_{2}O\) & \(\Delta H_{298K}^{0}|\text{mol}^{-1}=-164,600\) \\ Methanation III & \(CO_{2}+H_{2}\ \to CH_{4}+CO_{2}\) & \(\Delta H_{298K}^{0}|\text{mol}^{-1}=-247,000\) \\ Endothermic water–gas shift & \(CO_{2}+H_{2}\ \to CO+H_{2}O\) & \(\Delta H_{298K}^{0}|\text{mol}^{-1}=41,200\) \\ Methane decomposition & \(CH_{4}\to C+2H_{2}\) & \(\Delta H_{298K}^{0}|\text{mol}^{-1}=74,500\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Possible reactions in methane steam reforming. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Temperature (\({}^{\circ}\)C)** & \(K_{SR}\) & \(K_{WGS}\) \\ \hline
400 & \(5.93\times 10^{-8}\) & 1.17 \\
600 & \(5.22\times 10^{-1}\) & 2.55 \\
800 & \(1.69\times 10^{2}\) & 1.04 \\
1000 & \(1.0934\times 10^{-4}\) & 0.58 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Equilibrium constant for temperature. them, the Langmuir and Langmuir-Freundlich isotherms are commonly used to predict the adsorption equilibrium compared to the IAST (Ideal Adsorbed Solution Theory) or VSM (Vacancy Solution Model) models, which have a large number of parameters and relatively complex equations [42; 43]. DSL (Dual-Site Langmuir) also has many parameters, but its shape is similar to the existing Langmuir model, which is not complicated and is easy to predict [42; 43]. Understanding the dynamics of adsorption beds filled with porous particles such as zeolites or activated carbon in PSA processes is essential for understanding mathematical models for controlling and estimating hydrogen purification [27]. For the analysis of the PSA system, the mass balance and energy balance were calculated along with the extended Langmuir isotherm for gas consumption using the following assumptions [31; 32]. 1. Radial gradients for flow velocity, concentration, and temperature can be ignored, and the flow of fluid is a one-dimensional plug flow. 2. There is no pressure drop due to friction between the fluid and the adsorbent in the chamber. 3. The temperature of the adsorbent is constant at any point, and there is always a thermal equilibrium between the fluid and the adsorbent. 4. The main resistance of material transfer exists in the adsorbent, and the external epidural material transfer resistance is ignored.