**3. Results**

Results of gas permeability of investigated samples are shown in Table 2. For the ease of comparison with other data, results are given in different units: permeability coefficient for hydrogen (PH2)(cm3STP·cm·cm−<sup>2</sup> ·s −1 ·cmHg−<sup>1</sup> (Barrer)); diffusion coefficient (m<sup>2</sup> ·s −1 ); and filtration coefficient (m<sup>2</sup> and mD (milidarcy)). Blend of hydrogen (10%) in methane was used for the permeability tests. Results refer to this particular type of gas. For impermeable samples (10−<sup>11</sup> cm3STP·cm·cm−<sup>2</sup> ·s −1 ·cmHg−<sup>1</sup> or lower), only hydrogen was permeating the sample, so these results refer to the pure hydrogen.



As expected, tests showed a wide range of measured permeability values. The highest gas permeability coefficient has multi-grain materials, like concrete, polymer-concrete, and geopolymer. Filtration coefficient "k" of investigated concrete samples is 10−<sup>17</sup> m<sup>2</sup> or higher. Lower gas permeability was observed for mudstone and salt rock before creep process. Both rocks have the filtration coefficient of 2.13 <sup>×</sup> <sup>10</sup>−<sup>19</sup> <sup>m</sup><sup>2</sup> to 2.99 <sup>×</sup> <sup>10</sup>−<sup>19</sup> <sup>m</sup><sup>2</sup> , respectively. However, these rocks are still permeable for gases. In general, the lowest gas permeability has plain-structured materials, like epoxy resins and salt rock, after the creep process. Range of the filtration coefficient of these materials is of 10−<sup>24</sup> m<sup>2</sup> . Salt rock samples became impermeable after about 12 days of exposure to 2.0 MPa of confining pressure of water. Permeability dropped from 2.99 <sup>×</sup> <sup>10</sup>−<sup>19</sup> <sup>m</sup><sup>2</sup> to 5.80 <sup>×</sup> <sup>10</sup>−<sup>24</sup> <sup>m</sup><sup>2</sup> . Hydrogen permeability of epoxy resin samples varied, depending on the additives in the resin. Admixture of

halloysite or graphite powder caused the increase of hydrogen permeability. An exception is the addition of fly ash. Admixture of 30% of volume gave a similar, but slightly lower permeability, comparing to the pure epoxy resin sample. Significant share of fly ash in sample composition did not cause the deterioration of sealing properties.

Results were calculated for the steady-state diffusion. Usually, it took up to 3 weeks to achieve the steady-state diffusion. Increases in measured concentration of hydrogen per day of an example sample is presented in Figure 3. Because of the significant time required to complete the test for each sample, the hydrogen diffusion test was performed for a single gas pressure, which was 1.0 MPa. To verify the proper workings of the setup and sensitivity of the method, one test was extended and the feed gas pressure, after achieving steady-state diffusion, was increased. Pressure was increased after 24 days, from the value of 1.0 MPa to 1.7 MPa. After the pressure increase, several days were required to achieve the steady-state diffusion for a higher pressure. After that time, the measured concentration became stable again on a higher level. According to the Equations (3) and (4), increases of the pressure and permeability coefficient are linear. Pressure was raised by 70%, which gave the increase of measured concentrations by more than 60% as well (after achieving steady-state diffusion). This confirmed that the measuring methodology was correct. Slightly lower increase in concentration, in comparison with the pressure increase, may be explained by higher confining pressure (double the gas pressure, which was approx. 3.6 MPa). It can cause a compaction of the sample, which caused a slight decrease of the permeability. This phenomenon was described for concrete samples in [19], as well as for the polymer materials, where hydrostatic compression effect occurs [15]. However, the scale of permeability decreased, as well as mechanism responsible for it, is different. *Appl. Sci.* **2021**, *11*, x FOR PEER REVIEW 9 of 12

**Figure 3.** Increase of hydrogen concentration during the Carrier Gas Method test of epoxy resin with fly ash (30% vol.) **Figure 3.** Increase of hydrogen concentration during the Carrier Gas Method test of epoxy resin with fly ash (30% vol.) with 1.0 MPa and 1.7 MPa feed gas pressure.

with 1.0 MPa and 1.7 MPa feed gas pressure.

To compare the gas permeability results of different materials with the microstructure of the samples, SEM imaging of selected samples was done. Structures of the samples are shown in Figure 4. An evident difference is seen in microporous and plain materials. Dark areas representing pores are clearly visible in concrete and mudstone samples under similar magnification (Figure 4a,b). In the plain samples, voids appear mostly on the con-To compare the gas permeability results of different materials with the microstructure of the samples, SEM imaging of selected samples was done. Structures of the samples are shown in Figure 4. An evident difference is seen in microporous and plain materials. Dark areas representing pores are clearly visible in concrete and mudstone samples under similar magnification (Figure 4a,b). In the plain samples, voids appear mostly on the contact surface with grains of additives (Figure 4e).

(**a**) (**b**)

tact surface with grains of additives (Figure 4e).

with 1.0 MPa and 1.7 MPa feed gas pressure.

**Figure 3.** Increase of hydrogen concentration during the Carrier Gas Method test of epoxy resin with fly ash (30% vol.)

tact surface with grains of additives (Figure 4e).

To compare the gas permeability results of different materials with the microstructure of the samples, SEM imaging of selected samples was done. Structures of the samples are shown in Figure 4. An evident difference is seen in microporous and plain materials. Dark areas representing pores are clearly visible in concrete and mudstone samples under similar magnification (Figure 4a,b). In the plain samples, voids appear mostly on the con-

**Figure 4.** SEM imaging of the surface structure of investigated samples: (**a**) concrete "2" (year 2016); (**b**) mudstone (Carbon); (**c**) salt rock (Permian); (**d**) epoxy resin; (**e**) epoxy resin + graphite (5% vol.); (**f**) stainless-steel. **Figure 4.** SEM imaging of the surface structure of investigated samples: (**a**) concrete "2" (year 2016); (**b**) mudstone (Carbon); (**c**) salt rock (Permian); (**d**) epoxy resin; (**e**) epoxy resin + graphite (5% vol.); (**f**) stainless-steel.

## **4. Discussion 4. Discussion**

Differences of the gas permeability of investigated materials is caused by the differences in structure of tested materials, which lead to the different mechanisms of gas migration. Multi-grain materials, such as concrete or mudstone, have many pores and voids within the structure. Fine grains can decrease the gas permeability because the intergranular porosity is lower while the compaction of the material is higher; this phenomenon was also observed in other research [22]. However, gas flow through the sample is still Differences of the gas permeability of investigated materials is caused by the differences in structure of tested materials, which lead to the different mechanisms of gas migration. Multi-grain materials, such as concrete or mudstone, have many pores and voids within the structure. Fine grains can decrease the gas permeability because the intergranular porosity is lower while the compaction of the material is higher; this phenomenon

it is not essential data for the purpose of this paper. Because of the low gas sealing properties of the investigated concretes, this type of material is not suitable for sealing purposes of underground excavations. However, it can still be a reinforcement and base liner. Plain materials, like salt rock, epoxy, or steel, do not have pores and voids in their structure. Gas is not flowing through the sample (there is no pressure gradient along the sample). Hydrogen particles can diffuse through the material by dislocations in crystal structure. It is a linear defect that induces the tensile stress. Gas elements can diffuse much easier through those kinds of zones [23]. Lattice diffusion is also possible, but in much higher temperatures, transcending Tamman temperature (in this temperature atoms in solid material acquire enough energy to make bulk reactivity and mobility significant, usually approximately half of the melting temperature) [24]. In this case, research temper-

Interesting results were obtained with the fly ash epoxy sample. Graphite and halloysite are slightly increasing hydrogen permeability of the samples, while fly ash do not affect the sealing properties. Fly ash used for this research was not grinded but only

ature was much below the Tamman temperature.

was also observed in other research [22]. However, gas flow through the sample is still noticeable and is the main mechanism of gas migration in that kind of material. However, it is not essential data for the purpose of this paper. Because of the low gas sealing properties of the investigated concretes, this type of material is not suitable for sealing purposes of underground excavations. However, it can still be a reinforcement and base liner.

Plain materials, like salt rock, epoxy, or steel, do not have pores and voids in their structure. Gas is not flowing through the sample (there is no pressure gradient along the sample). Hydrogen particles can diffuse through the material by dislocations in crystal structure. It is a linear defect that induces the tensile stress. Gas elements can diffuse much easier through those kinds of zones [23]. Lattice diffusion is also possible, but in much higher temperatures, transcending Tamman temperature (in this temperature atoms in solid material acquire enough energy to make bulk reactivity and mobility significant, usually approximately half of the melting temperature) [24]. In this case, research temperature was much below the Tamman temperature.

Interesting results were obtained with the fly ash epoxy sample. Graphite and halloysite are slightly increasing hydrogen permeability of the samples, while fly ash do not affect the sealing properties. Fly ash used for this research was not grinded but only sieved. Since fly ash from power plants is easily available, it could be a cost-effective filler by reducing the amount of epoxy resin in the sealing liner.

Obtained results of epoxy resin hydrogen permeability is slightly lower than presented in literature. Other research, presented collectively in [16], showed the hydrogen permeability of epoxy resin of approximately 1.0 Barrer, while performed research of investigated samples gave the permeability coefficient of approximately 0.2 Barrer. Results of hydrogen diffusion coefficient presented in [17], which was 6.9 <sup>×</sup> <sup>10</sup>−<sup>11</sup> <sup>m</sup>2/s, was also higher than the obtained 1.5 <sup>×</sup> <sup>10</sup>−<sup>12</sup> from this research. Lower results may be caused by numerous factors, influencing on the gas permeability in polymeric materials like polymer chemistry (epoxide number), free volumes (crystallinity, orientation of molecules), porosity or voids (air inclusions), and fillers presence [16].

Permeability coefficient of 316SS steel was calculated using the Equations (3)–(6), based on the literature data [25]. Permeability of 316 L steel were taken from [26,27]. Because of the sensitivity and construction of the setup, investigation of the steel samples was not possible. Permeability of steel is orders of magnitude lower than materials the setup is meant for. To investigate the steel or alloys, much thinner samples need to be used. The Setup is not designed for that kind of samples, but only for a core-shape samples. Calculated hydrogen permeability PH2 of 316SS steel was 4.6 <sup>×</sup> <sup>10</sup>−<sup>17</sup> cm3STP·cm·cm−<sup>2</sup> ·s −1 ·cmHg−<sup>1</sup> (4.6 <sup>×</sup> <sup>10</sup>−<sup>7</sup> Barrer), and given [26,27], hydrogen diffusion coefficient D of 316L steel was in range from 10−<sup>13</sup> to 10−<sup>15</sup> m2/s.
