## 2 Experimental Methodology and Materials  
Setup used to investigate the hydrogen permeability was built in the Laboratory of Unconventional Gas and CO\({}_{2}\) Storage at the Silesian University of Technology. Setup is combining the Steady-State Flow Method and Carrier Gas Method. Setup can be switched between mentioned methods, depending on the permeability coefficient of investigated samples. A scheme of the setup is shown in the Figure 2. It consists of the gas cylinder, pressure regulation valves, sample holder, precise gas pressure transducers, and gas concentration detector. The upstream side is a reference gas. A blend of 10% of hydrogen in methane was used as a reference gas on the upstream side. Gas is applied on the sample, held in the PVC sleeve with confining pressure of water. Tests were conducted at 1.0 MPa feed gas pressure. During the test, the downstream side was filled with carrier gas (helium) at the pressure of 100 kPa. A single gas detector for hydrogen, with sensitivity of 2-2000 ppm, was plugged on the end of the setup for gas concentration measurements made periodically. After the measurement is done, the same socket is used to plug the carrier gas (helium), the downstream side is filled with after vacuuming. There is also a back pressure valve,  
Figure 1: Scheme of the LRC linings. which can be used to adjust the pressure on the downstream side, when there is a flow of gas through the sample. Back pressure valve is giving the possibility to set a steady pressure gradient through the sample, by adjusting the pressure on the upstream and downstream side. Depending on the behavior of the sample, a proper method can be used. When a pressure increase on the downstream side is observed, there is a gas flow through the sample. It occurs, when the permeability of the sample is high enough to allow the gas to flow through the sample. Steady-State Flow Method is based on the pressure gradient in the sample, caused by the gas flow. Pressure gradient in the sample and gas pressure (together with temperature) in the reservoir are measured with precise pressure transducers (accuracy 0.5% FS). Filtration coefficient \"k\" can be calculated, using the Equations (1) and (2). \[q=\left(\frac{\left(\frac{p_{i}\cdot V_{res}}{Z_{i}\cdot R\cdot T}\right)- \left(\frac{p_{f}\cdot V_{res}}{Z_{f}\cdot R\cdot T}\right)}{t}\right)\cdot 22.4 \cdot 10^{-3} \tag{1}\]  
where:  
\(q=\) gas flow, m\({}^{3}\)/s  
\(p_{i}\), \(p_{f}=\) initial pressure (\(p_{i}\)) and final pressure (\(p_{j}\)) in reservoir, Pa  
\(V_{res}=\) reservoir volume, m\({}^{3}\)  
\(Z_{i}\), \(Z_{f}=\) gas compressibility factor at the initial (\(Z_{i}\)) and final (\(Z_{f}\)) pressure  
\(R=\) gas constant (8.314463 m\({}^{3}\cdot\)Pa\(\cdot\)mol\({}^{-1}\cdot\)K\({}^{-1}\))  
\(T=\) gas temperature in reservoir, K  
\(t=\) time, s  
\[k=\frac{2\cdot q\cdot p_{o}\cdot L\cdot\mu}{A\cdot\left(p_{i}^{2}-p_{o}^{2} \right)} \tag{2}\]  
where:  
\(k=\) permeability coefficient, m\({}^{2}\)  
\(q=\) gas flow, m\({}^{3}\)/s  
\(p_{i}\), \(p_{o}=\) average inlet (\(p_{i}\)) and outlet (\(p_{o}\)) gas pressure (pressure gradient), Pa  
\(L=\) sample length, m  
\(\mu=\) gas viscosity, Pa\(\cdot\)s  
\(A=\) sample cross area, m\({}^{2}\)  
Figure 2: Steady-State Method/Carrier Gas Method setup. When the gas permeability of the sample is low enough to prevent the gas flow through the sample, gas diffusion can be measured. In this case, Carrier Gas Method is used, which is based on the difference in gas concentration gradient through the sample. It is possible to measure it precisely with a single-gas hydrogen detector. Knowing the parameters of a reference gas on the upstream side, calculations of the permeability coefficient P are made, using a set of Equations (3)-(6). Using helium as a carrier gas, an ideal gas law can be assumed.