**2. Experimental Methodology and Materials**

**2. Experimental Methodology and Materials** Setup used to investigate the hydrogen permeability was built in the Laboratory of Unconventional Gas and CO<sup>2</sup> 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 con-Setup used to investigate the hydrogen permeability was built in the Laboratory of Unconventional Gas and CO<sup>2</sup> 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.

centration 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,

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. *Appl. Sci.* **2021**, *11*, x FOR PEER REVIEW 3 of 12

**Figure 2.** Steady-State Method/Carrier Gas Method setup.

**Figure 2.** Steady-State Method/Carrier Gas Method setup. 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 periodi-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).

$$q = \left(\frac{\left(\frac{p\_i \cdot V\_{res}}{Z\_i \cdot R \cdot T}\right) - \left(\frac{p\_f \cdot V\_{res}}{Z\_f \cdot R \cdot T}\right)}{t}\right) \cdot 22.4 \cdot 10^{-3} \tag{1}$$

pressure gradient through the sample, by adjusting the pressure on the upstream and

where:

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* = gas flow, m3/s *pi* , *p<sup>f</sup>* = initial pressure (*p<sup>i</sup>* ) and final pressure (*p<sup>f</sup>* ) in reservoir, Pa *Vres* = reservoir volume, m<sup>3</sup> *Zi* , *Z<sup>f</sup>* = gas compressibility factor at the initial (*Z<sup>i</sup>* ) and final (*Z<sup>f</sup>* ) pressure *R* = gas constant (8.314463 m<sup>3</sup> ·Pa·mol−<sup>1</sup> ·K−<sup>1</sup> ) *T* = gas temperature in reservoir, K *t* = time, s

> 

*Zi*, *Z<sup>f</sup>* = gas compressibility factor at the initial (Zi) and final (Zf) pressure

$$k = \frac{2 \cdot q \cdot p\_o \cdot L \cdot \mu}{A \cdot \left(p\_i^2 - p\_o^2\right)}\tag{2}$$

*t*

  (1)

where:

*k* = permeability coefficient, m<sup>2</sup>

*t* = time, s

*q* = gas flow, m3/s

where: *q* = gas flow, m<sup>3</sup> /s *pi*, *p<sup>f</sup>* = initial pressure (*pi*) and final pressure (*pf*) in reservoir, Pa *pi* , *p<sup>o</sup>* = average inlet (*p<sup>i</sup>* ) and outlet (*po*) gas pressure (pressure gradient), Pa *L* = sample length, m *µ* = gas viscosity, Pa·s

*Vres* = reservoir volume, m<sup>3</sup> *A* = sample cross area, m<sup>2</sup>

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.

$$V = \frac{\mathcal{R} \cdot T}{p} \tag{3}$$

where:

*V* = molar volume in test conditions, m<sup>3</sup> ·mol−<sup>1</sup> *<sup>R</sup>* = gas constant: 8.314463 J·mol−<sup>1</sup> ·K−<sup>1</sup>

*T* = gas temperature, K

*p* = gas pressure, Pa

An amount of hydrogen diffused through the sample in a certain time can be calculated, using the Equation (4). In this case the volume of the downstream side of the setup needs to be determined. This was done by approximation of the inner volume of the pipes, based on the manufacturer's data and measurements of the setup. The volume of the downstream in the setup was 12.0 cm<sup>3</sup>

$$N\_{H\_2} = \frac{c \cdot \left(\frac{N\_A}{V}\right) \cdot v\_{downstream}}{10^6} \tag{4}$$

where:

*NH*<sup>2</sup> = amount of hydrogen, diffused through the sample *c* = measured hydrogen concentration on downstream side, ppm *<sup>N</sup><sup>A</sup>* = Avogadro's constant: 6.02214076·1023, mol−<sup>1</sup> *V* = molar volume, m<sup>3</sup> ·mol−<sup>1</sup>

*vdownstream* = volume of downstream side of setup, m<sup>3</sup>

By knowing the molar volume of one mole of gas in Standard Temperature and Pressure conditions (STP: 0 ◦C, 100 kPa), the volume of gas in STP can be calculated, using Equation (5).

$$V\_{H\_2} = \frac{N\_{H\_2} \cdot 22.414}{N\_A} \tag{5}$$

where:

*VH*<sup>2</sup> = volume of hydrogen diffused through the sample, cm3STP *<sup>N</sup><sup>A</sup>* = Avogadro's constant: 6.02214076·1023, mol−<sup>1</sup> 22.414 = mole volume of ideal gas in STP, cm<sup>3</sup>

Using the calculation above, gas permeability coefficient can be calculated with Equation (6).

$$P\_{H\_2} = \frac{V\_{H\_2} \cdot l}{A \cdot t \cdot p} \tag{6}$$

where:

*PH*<sup>2</sup> = hydrogen permeability coeficcient, barrer *VH*<sup>2</sup> = volume of hydrogen diffused through the sample, cm3STP *l* = sample length, cm

*A* = sample cross section area, cm<sup>2</sup>

*t* = time, s

*p* = gas pressure (feed gas), cmHg (1 bar = 75 cmHg)

Permeability coefficient of hydrogen is given in Barrer unit [18], presented in Equation (7). Barrer unit is commonly used for presenting the permeability of membranes. However, it does not refer to the SI system, because of the pressure given in cmHg. Transforming the

pressure into the SI unit (for example bar or Pa) is possible, however the results will not be comparable with the common literature data.

$$1bar{r} = \frac{\text{cm}^3\_{\text{STP}} \cdot \text{cm}}{\text{cm}^2 \cdot \text{s} \cdot \text{cm} \text{Hg}} 10^{-10} \tag{7}$$

Hydrogen diffusion is calculated as a diffusion coefficient D, given in m2/s, using the Fick's law [19] and following set of Equations (8)–(12), as well as values received from the Equations (3) and (4). For a gas diffusion through the polymer materials, the transport mechanism described by Fick's Law is accepted [20].

$$J = -D\frac{\partial\phi}{\partial x} \tag{8}$$

where:

*<sup>J</sup>* = flux, amount of hydrogen diffusing through the area in time, mol·m−<sup>2</sup> ·s −1 *D* = diffusion coefficient, m<sup>2</sup> ·s −1 *<sup>φ</sup>* = hydrogen concentration, mol·m−<sup>3</sup>

*x* = length of hydrogen path, m

$$D = -J \frac{\varkappa\_2 - \varkappa\_1}{\Phi\_{downstream} - \Phi\_{upstream}} \tag{9}$$

where:

*D* = diffusion coefficient, m<sup>2</sup> ·s −1

*<sup>J</sup>* = flux, amount of hydrogen diffused through the area in time, mol·m−<sup>2</sup> ·s −1 *<sup>φ</sup>upstream* = concentration of hydrogen (upstream), mol·m−<sup>3</sup>

*<sup>φ</sup>downstream* = concentration of hydrogen (downstream), mol·m−<sup>3</sup>

*x*<sup>2</sup> − *x*<sup>1</sup> = diffusion distance (sample length), m

For a non-porous polymer material, the tortuosity is equal to 1, thus the assumption can be made, that the hydrogen path is equal to sample length [21].

$$J = -\frac{\left(\frac{N\_{H2}}{N\_A}\right)}{A \cdot t} \tag{10}$$

where:

*<sup>J</sup>* = flux, amount of hydrogen diffused through the area in time, mol·m−<sup>2</sup> ·s −1 *NH*<sup>2</sup> = amount of hydrogen elements, diffused through the sample, from Equation (4) *<sup>N</sup><sup>A</sup>* = Avogadro's constant: 6.02214076 <sup>×</sup> <sup>10</sup>23, mol−<sup>1</sup> *A* = sample cross area, m<sup>2</sup> *t* = time, s

$$
\phi\_{upstream} = \frac{c\_{up}}{V \cdot 100} \tag{11}
$$

where:

*<sup>φ</sup>upstream* = concentration of hydrogen (upstream), mol·m−<sup>3</sup> *cup* = concentration of hydrogen in refenrence gas, % *<sup>V</sup>* = molar volume of gas mol·m−<sup>3</sup> , from Equation (3)

$$\phi\_{downstream} = \frac{\left(\frac{N\_{H2}}{v\_{downstream}}\right)}{N\_A} \tag{12}$$

where:

*<sup>φ</sup>downstream* = concentration of hydrogen (downstream), mol·m−<sup>3</sup> *NH*<sup>2</sup> = amount of hydrogen elements, diffused through the sample, from Equation (4) *vdownstream* = volume of downstream side of setup, m<sup>3</sup> *<sup>N</sup><sup>A</sup>* = Avogadro's constant: 6.02214076 <sup>×</sup> <sup>10</sup>23, mol−<sup>1</sup>

Measurements of concentrations at the downstream side were done every 2–4 days and given in the diffusion ratio in time (ppm of H2/24 h). Structure of the samples was investigated, using HRSEM SUPRA 35 (Carl Zeiss AG, Oberkochen, Germany) Scanning Electron Microscope, since the chemical composition of the samples was not the scope of this study; the Energy Dispersive Spectrometry was not used for this research.

For the purpose of the study, several materials that could be used as a liner in underground excavation were selected. Samples under investigation can be divided into three general groups: epoxy resins with different additives; concrete; polymer-concrete and rocks (mudstone and rock salt). Materials were selected based on their common availability, low cost, and ease of preparation. Resin samples were prepared by mixing resin and cured for at least 7 days. During the pot time, samples were held in the oven in a temperature of 30 ◦C to accelerate the venting of the samples. Relative low temperature was set to simulate the thermal conditions in the excavations. Higher temperatures would be more efficient in the samples venting but would not be related with the actual underground temperature conditions, where the resins might be applied. Concrete and polymer-concrete samples were prepared by companies, according to their recipes and general standards for curing the concretes. Concrete samples were cored using a diamond core drill of 2.54 mm (1 inch) diameter. In Table 1 detailed description of samples is given.


**Table 1.** Details of investigated samples.

\* CEM I, CEM II—cement types according to Polish Standard: PN-EN 197-1:2012, PN-B-19707:2013.

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