Gas diffusion property of compacted GMZ bentonite with consideration of saturation and gas pressure

doi:10.21203/rs.3.rs-3993917/v1

Download PDF

Research Article

Gas diffusion property of compacted GMZ bentonite with consideration of saturation and gas pressure

https://doi.org/10.21203/rs.3.rs-3993917/v1

This work is licensed under a CC BY 4.0 License

You are reading this latest preprint version

During the long-term operation of a deep geological repository, hydrogen, methane and carbon dioxide, etc. could be generated and accumulated in bentonite around canisters, threatening integrity and safety of engineering barrier systems. In this work, self-designed test apparatuses were developed. Gas diffusion tests were conducted on GMZ bentonite specimens under both rigid and flexible boundary conditions with consideration of initial saturations and gas pressures. After experienced the gas diffusion tests, the specimens were cut and submitted for the mercury intrusion porosimetry (MIP) tests. Results revealed that gas diffusion coefficient was obviously influenced by the initial saturations and gas pressures. As gas pressure increased from 1 to 4 MPa, a decrease of 55.3% ~ 58.8% and 17.7% ~ 73.4% in the diffusion coefficient were recorded for the specimens tested under rigid and flexible boundary, respectively. Compared to the rigid boundary conditions, the effective pore volume for gas molecule diffusion was further compressed under flexible boundary, resulting in a relatively poor pore connectivity and a lower gas diffusion coefficient. Meanwhile, the diffusion coefficient decreased with increasing initial saturations for the flexible boundary specimens, while an opposite trend was recorded for the rigid boundary ones. Explanations to this observation could be that under the rigid boundary conditions, specimens with higher initial saturations have larger diameter macro-pores, facilitating the gas diffusion.

GMZ bentonite

gas diffusion coefficient

initial saturation

gas pressure

boundary conditions

Development of nuclear energy usage produces a large amount of radioactive waste, especially the high-level radioactive wastes (Marsh et al. 2021; Ortiz et al. 2002). How to safely dispose these wastes has been becoming an international critical issue. Previous studies proved that deep geological repositories with multi-barriers including natural barrier (surrounding rocks) and artificial barriers (engineering-barriers and canisters) can effectively isolate nuclides from the human environments (Horseman et al. 1999; Tawara et al. 2012). Due to its ultra-low permeability, high adsorption and good swelling capacities, compacted bentonite is commonly recognized as the most preferred buffer/backfill material for constructing engineering-barriers in the geological repository (Ohazuruike and Lee 2023; Ye et al. 2009).

Studies also proved that during the long-term operation of a repository, due to physicochemical processes such as metal anaerobic corrosion, degradation of microorganisms and irradiation of water and organic matters, gases including hydrogen, methane and carbon dioxide, etc., could be generated (Graham et al. 2016; Kim et al. 2023). More importantly, the gas produced will accumulate in the bentonite around the waste canisters inducing a gradually increase of gas pressure, which could reach an extremely high value of 30 MPa, due to the ultra-low permeability of the bentonite. Consequently, some preferential pore channels could be generated during this gas accumulation process, resulting in gas breakthrough and possible nuclides leakage, and eventually threatening the integrity and safety of the engineering-barrier system.

Meanwhile, researches confirmed that for the gas migrations in the porous media materials with an extremely low permeability, as the gas injection pressure increases, gas diffusion, viscous-capillary flow or two-phase flow, dilatancy controlled gas flow and gas flow along the macro-fractures, etc., can be observed successively (Marschall et al. 2005; Ye et al. 2014). Unfortunately, for gas transport in compacted bentonites, previous work mainly focused on the investigations related to gas breakthrough properties, rarely involving gas diffusion (Cui et al. 2022; Cui et al. 2020).

In fact, in the deep geological repositories, usually, the gas generation rate is very slow and the pressure growth rate of the gas accumulated in the engineering-barriers is also very low. Consequently, gas migration based on the molecule diffusion could last for a long time in the bentonite with an ultra-low permeability (Cui et al. 2023; Jacops et al. 2013). At the same time, due to the intricate and variable pore networks of bentonite, the coexistence of gas diffusion and advection could occur in the different sized pores (Liu et al. 2016). Early investigations also ascertained that bentonite was in an unsaturated state for a period of time, due to the inevitable evolutions of drying and wetting processes during the long-term operation of the repository (Alonso et al. 2005; Seiphoori et al. 2014).

Different from gas advection, which is driven by a gas pressure gradient, gas diffusion involves the stochastic thermal movement of molecules, which is governed by the gas concentration gradient (Rouf et al. 2016; Strangfeld 2021). The diffusion behavior is usually described by the gas diffusion coefficient D. In fact, in a porous media, gas molecule diffusions could include: (1) collisions among gas molecules; (2) collisions between gas molecules and pore walls. Different collisions are governed by different diffusion mechanisms. According to the mechanism of gas diffusion in porous media, gas diffusion can be categorized by the Knudsen number $Kn$ (Sercombe et al. 2007), which is defined as the ratio of the mean free path of the gas molecule to the characteristic length of the porous channel.

$$Kn={\lambda \mathord{\left/ {\vphantom {\lambda {{d_n}}}} \right. \kern-0pt} {{d_n}}}$$

Where, $\lambda$ is the mean free path of gas molecules (nm); d_n is the pore diameter (nm). When $Kn$≥ 10, the mean free path of gas molecules substantially exceeds the pore diameter, and the collisions between the gas molecules and pore wall play the major role, resulting in “Knudsen diffusion”. When $Kn$≤ 0.1, the pore diameter vastly surpasses the mean free path of gas molecules, diffusion is primarily driven by collisions among the individual gas molecules, inducing “Fick diffusion”. When 0.1<$Kn$<10, a balance is reached between the mean free path of gas molecules and the pore diameter, and the significance of collisions among the free gas molecules is commensurate with that of collisions between molecules and the pore wall, and the diffusion is combined by Fick diffusion and Knudsen diffusion, namely, a “transition diffusion”.

In fact, the mechanism governing gas molecule diffusion within porous media mainly depends on the properties of gas (e.g., gas type, gas pressure, viscosity) and porous medium (e.g., pore size distribution, dry density, initial saturation, etc.) (Jacops et al. 2015; Sercombe et al. 2007). Meanwhile, the macroscopic variations of gas diffusions in the media are closely related to the microstructure of pores. Previous studies also confirmed that pore structure and pore size distributions, as well as the saturations and boundary conditions, exert important influences on the connectivity degree and internal morphology of pores (Jacops et al. 2015; Owusu et al. 2023; Strangfeld 2021). However, for the media with identical pore structures, it is evident that gas diffusion capability could be notably enhanced by decreasing gas pressure (Li et al. 2019; Sun et al. 2021). Consequently, these factors could alter gas diffusion in the porous media.

In this work, the two-chamber method was employed to investigate gas diffusion in unsaturated GMZ bentonite specimens under both rigid and flexible boundary conditions. Helium gas and nitrogen gas were separately filled into the two compartments on both ends of the bentonite specimen and equal gas pressures were maintained in the two compartments. During the test, the helium gas diffusing from one end to the other end of the specimen due to the concentration gradient was recorded. Changes of concentration over time in the two compartments were also carefully monitored. Meanwhile, variations in volume, mass, density and saturation of the compacted bentonite specimens were measured. The helium gas diffusion coefficients were calculated. Then, MIP tests were performed on the specimens experienced the diffusion tests and pore structures were analyzed.

2.1 Materials and specimen preparation

The materials tested in this work was Gaomiaozi (GMZ) bentonite, which originated from the Inner Mongolia Autonomous Region, China. It has been selected as the preferred buffer/backfill material for the deep geological disposal of high-level radioactive waste in China. The GMZ bentonite powder tested in this work was a white granular material with the main mineral component of montmorillonite, which has a strong cation exchange ability, good adsorption capacity and well swelling capacity. Some basic properties of GMZ bentonite were listed in Table 1.

Table 1

Basic physical and chemical properties of GMZ bentonite (Wen 2006).
Property	Description
Specific gravity of soil grain	2.66
pH	8.68–9.86
Liquid limit (%)	276
Plastic limit (%)	37
Total specific surface area (m²/g)	597
Cation exchange capacity (mmol/100g)	77.3
Main exchanged cation (mmol/100g)	Na⁺ (43.36), Ca²⁺ (29.14), Mg²⁺ (12.33), K⁺ (2.51)
Main minerals	Montmorillonite (75.4%), quartz (11.7%), cristobalite (7.3%), feldspar (4.3%)

For specimen preparation, first of all, according to the target water content, deionized water was evenly sprayed on the bentonite powder. Then, the wetted bentonite powder was sealed and homogenized. In this way, three initial water contents (11.10, 18.29 and 23.03%) bentonite powders were prepared.

According to the target dimensions (50 mm in diameter, 10 mm in height) and dry density (1.5 g/cm³), the homogenized powder prepared was weighed and poured slowly into a compaction mold. Static compaction was performed with a piston moving at a speed of 0.1 mm/min. After the pre-set displacement being reached, compaction was stopped and the maximum load was kept for 60 minutes for homogenizing the specimen (Cui et al. 2019). Finally, the compaction load was removed and the compacted specimen was obtained.

The procedures mentioned above were repeated until all the specimens listed in Table 2 were compacted. The three initial saturations 38.18, 62.43 and 79.38% of the specimens corresponded to the three initial water contents 11.10, 18.29 and 23.03% of the bentonite powder pre-prepared.

2.2 Test apparatus

The experimental apparatuses self-developed in this work were presented in Fig. 1. They could be employed for conducting gas diffusion tests under (a) flexible boundary and (b) rigid boundary conditions, respectively, using the two-chamber method.

1) The flexible boundary gas diffusion test

The apparatus for conducting flexible boundary gas diffusion tests (Fig. 1a) includes a flexible boundary stainless-steel specimen cell, left and right diffusion compartments, two high-pressure sampling needle valves, two pressure transmitters, a vacuum pump, some stainless-steel gas pipelines for connecting the specimen cell to the two compartments, two high purity gas sources (helium gas and nitrogen gas), a volume/pressure controller, a gas chromatograph and data acquisition system.

The flexible boundary specimen cell was made of 316L stainless steel for holding specimen, which was effectively sealed with some latex film, Teflon tube and O-ring. A volume/pressure controller, which has a measurement range of 0–16 MPa and an accuracy of ± 1 mm³ in volume and ± 1 kPa in pressure, was employed for controlling the confining pressure during the test. Two diffusion compartments were made of 316L stainless steel and internal O-rings to ensure a good gas tightness. A high precision pressure transmitter (0–6 MPa range, < ±0.3%FS precision) fixed at the top of the diffusion compartment was used to monitor and control the changes of gas pressure with data being collected/recorded by the data acquisition system. The high-pressure sampling needle valve (Swagelok SS-ORS2) was a directly connected double ferrules one with a pressure rating of 5000 psig (approx. 35 MPa), which has an excellent gas tightness and a system pressure loss of a single gas sampling within 10 kPa. The vacuum pump, which can reach a vacuum degree within 2 Pa, was adopted for: a) vacuuming all the gas compartments and pipelines before the tests to eliminate the influence of atmospheric impurity gases on the test results; b) vacuuming the pipeline connecting the needle value to the gas chromatograph before each sampling to eliminate the residual gas in the last sampling. The gas chromatograph equipped with two thermal conductivity detectors (TCD) was employed for simultaneously analyzing gas composition and concentration in two diffusion compartments. Two six-way valves (the volume of the internal quantitative loop is 1 ml) were connected to the inlet of the gas chromatograph to ensure the smoothly transport of gases and minimize gas loss during sampling. A computer with chromatograph workstation installed was used to analyze and record data from the gas chromatograph. The gas pipelines in the whole test system used 1/8inch stainless steel tubing with double ferrules, ensuring a good tightness.

2) The rigid boundary gas diffusion test

The apparatus for conducting the rigid boundary gas diffusion tests in Fig. 1b includes a rigid boundary stainless-steel specimen cell, left and right diffusion compartments, two high-pressure sampling needle valves, two pressure transmitters, a vacuum pump, some stainless-steel gas pipelines for connecting the specimen cell and compartments, two high purity gas sources (helium gas and nitrogen gas), a gas chromatograph and data acquisition system.

The rigid boundary specimen cell made of 316L stainless steel was designed for holding specimen. It consists of a top cap, a basement and a specimen ring. During the test, the top cap and basement with two O-rings were tightly fixed with the specimen ring by four high-strength bolts to ensure a good tightness and constant volume of the specimen. Two ports at the top and bottom of the rigid boundary specimen cell were connected to the two diffusion compartments, respectively. The other components are the same to that in the apparatus for conducting the flexible boundary diffusion tests.

2.3 Test procedures

Firstly, a compacted bentonite specimen was installed into the flexible or rigid boundary specimen cell and a confining pressure was applied by the volume/pressure controller. The whole system was stabilized for 60 minutes, and then the two diffusion compartments and the connecting stainless-steel pipelines were vacuumed by the vacuum pump for 60 minutes to eliminate the air impurities. Then, the helium gas and nitrogen gas were injected into the two compartments separately. When the gas pressure in the two diffusion compartments reached the target value correspondingly, the pressure regulating valves were closed immediately. After 10 minutes of stabilization, the valves connecting to the two diffusion compartments at both sides of the flexible or rigid boundary specimen cell were opened and the diffusion process began. The gas was sampled every 12–48 hours using the needle valve, which was connected to the gas chromatograph, for gas concentration analysis. In order to prevent the gas sampled from being affected by the atmospheric impurity gases and the residual gas of the last measurement, a vacuum pump was used to vacuum for 60 minutes at the outlet of the six-way valve before the needle valve was opened for sampling. Meanwhile, the data were analyzed and recorded by the computer workstation. After 7–14 concentration data being continuously recorded and analyzed, the diffusion test was stopped. Finally, the test apparatus was dismantled, the water content and dry density of the specimen were immediately measured. Meanwhile, some small cubic bentonite blocks were cut and prepared for the MIP microscopic tests.

It should be noted that the gas sampling process will inevitably cause gas pressure loss (reduction) in the test system, influencing accuracy of the diffusion measurement. Therefore, the gas sampling using the high-pressure needle valve should be careful, minimizing the disturbance as small as possible (Jacops et al. 2013).

In this work, 18 specimens with three initial saturation were tested by three gas pressures under flexible boundary or rigid boundary conditions. Specifications of the tests conducted on the bentonite were shown in Table 2.

Table 2

Specifications of the tests conducted on GMZ bentonite specimens.
Specimen	Boundary condition	Dry density (g/cm³)	Water content of powder (%)	Initial saturation of specimen (%)	Gas pressure (MPa)
A-1	Flexible (confining pressure of 9 MPa)	1.5	11.10	38.18	1.03
A-2			11.10	38.18	2.19
A-3			11.10	38.18	4.20
B-1			18.29	62.43	1.17
B-2			18.29	62.43	2.13
B-3			18.29	62.43	4.10
C-1			23.03	79.38	1.17
C-2			23.03	79.38	2.17
C-3			23.03	79.38	4.15
D-1	Rigid	1.5	11.10	38.18	0.97
D-2			11.10	38.18	2.03
D-3			11.10	38.18	4.06
E-1			18.29	62.43	1.12
E-2			18.29	62.43	2.06
E-3			18.29	62.43	4.05
F-1			23.03	79.38	1.12
F-2			23.03	79.38	2.10
F-3			23.03	79.38	4.14

Here: the specimens with initial saturations of 38.18, 62.43 and 79.38% were expressed as S38, S62 and S79, respectively.

2.4 Determination of diffusion coefficients

According to the Fick’s law, for a given temperature and gas pressure, with the data obtained by the two-chamber tests, the gas diffusion coefficient D can be calculated by the following equations.

$$D=\frac{{\ln \left( {{{{C_0}} \mathord{\left/ {\vphantom {{{C_0}} {{C_i}}}} \right. \kern-0pt} {{C_i}}}} \right)}}{{\left( {{t_i} - {t_0}} \right)}} \cdot \frac{L}{{A\left( {{1 \mathord{\left/ {\vphantom {1 {{V_1}}}} \right. \kern-0pt} {{V_1}}}+{1 \mathord{\left/ {\vphantom {1 {{V_2}}}} \right. \kern-0pt} {{V_2}}}} \right)}}$$

$${C_i}={C_{Li}} - {C_{Ri}}$$

$$\frac{1}{E}=\frac{L}{{A\left( {{1 \mathord{\left/ {\vphantom {1 {{V_1}+{1 \mathord{\left/ {\vphantom {1 {{V_2}}}} \right. \kern-0pt} {{V_2}}}}}} \right. \kern-0pt} {{V_1}+{1 \mathord{\left/ {\vphantom {1 {{V_2}}}} \right. \kern-0pt} {{V_2}}}}}} \right)}}$$

Therefore,

$$\ln \left( {{{{C_0}} \mathord{\left/ {\vphantom {{{C_0}} {{C_i}}}} \right. \kern-0pt} {{C_i}}}} \right)=D \cdot E \cdot \left( {{t_i} - {t_0}} \right)$$

where, C_Li is the percentage of the helium gas concentrations in the He diffusion compartment at time t_i (%); C_Ri is the percentage of the helium gas concentrations in the N₂ diffusion compartment at time t_i (%); C₀ is the difference of the percentage of the helium gas concentrations in the two compartments at the initial time t₀ (%); C_i is the difference of the percentage of the helium gas concentrations in the two diffusion compartments at time t_i (%). V₁ and V₂ are the total volume of the two diffusion compartments and the stainless-steel pipe connected to the two compartments (cm³), respectively; L is the specimen length (cm); A is the specimen cross-sectional area (cm²). Clearly, relationship between ln(C₀/C_i) ~ (t_i-t₀) in Eq. (5) is a straight line with a slope of S (D×E), which can be obtained by the least-squares fitting. Then, with the slope S, diffusion coefficient D can be obtained.

In this work, as the length L and the cross-sectional area A of the specimen are known, the volume of the two diffusion compartments can be calculated with V₁ (42.26 cm³) and V₂ (41.34 cm³) for the flexible boundary test and V₁ (41.48 cm³) and V₂ (42.39 cm³) for the rigid boundary test, respectively.

2.5 Mercury intrusion porosimetry (MIP) test

After the diffusion test, the specimen was removed from the apparatus and cut into small cubes with an edge length of about 10 mm. Then, the clay cubes were immediately frozen with liquid nitrogen and dried in vacuum for more than 48 hours at -61.3 ℃ in order to keep their micro-structure unchanged (Delage and Lefebvre 1984). Finally, the MIP test was performed on the freeze-dried specimens by a mercury porosimeter.

According to the Washburn equation (Purcell 1949), the injection pressure p can be calculated with the pore diameter d of the equivalent capillary column, namely:

$$p= - \frac{{4{T_S}\cos \theta }}{{{d_n}}}$$

where, T_S is the surface tension of mercury (0.48 N/m); θ is mercury-soil contact angle (140°).

In this work, with the mercury injection pressure being continuously increased from 3.45 kPa to 227.45 MPa, the pore diameter detected correspondingly changed from 5.48 nm to 363 µm.

3.1 Gas diffusion under flexible boundary conditions

For the specimens with an initial saturation of 38.18, 62.43 and 79.38% tested with a gas pressure of 1, 2 and 4 MPa under flexible boundary conditions (with a confining pressure of 9 MPa), the measured helium gas concentration evolutions in the N₂ compartment were presented in Fig. 2. Curves in Fig. 2 show that in the initial stage, the helium gas concentration nonlinearly increased from 0 and followed by an approximately linear increase with time. Comparison shows that no significant difference could be observed between the helium gas concentration curves for the specimens with an initial saturation of 38.18 (S38) and 62.43% (S62) tested under a same gas pressure. However, the helium gas concentration curves for the specimen with an initial saturation of 79.38% (S79) were obviously different from that of the former two and increased in a very gentle and an approximately linear way.

Results of the gas diffusion tests performed on the compacted GMZ bentonite specimens under flexible boundary conditions were summarized in Table 3.

Table 3

Results of the gas diffusion tests conducted on the GMZ bentonite specimens under flexible boundary conditions.
Specimen	Boundary condition	Dry density (g/cm³)	Water content of powder (%)	Initial saturation of specimen (%)	Gas pressure (MPa)	Diffusion coefficient (m²/s)
A-1	Flexible (confining pressure of 9 MPa)	1.5	11.10	38.18	1.03	9.58E-11
A-2			11.10	38.18	2.19	4.90E-11
A-3			11.10	38.18	4.20	2.65E-11
B-1			18.29	62.43	1.17	8.27E-11
B-2			18.29	62.43	2.13	4.43E-11
B-3			18.29	62.43	4.10	2.20E-11
C-1			23.03	79.38	1.17	2.37E-12
C-2			23.03	79.38	2.17	2.18E-12
C-3			23.03	79.38	4.15	1.95E-12

3.2 Gas diffusion under rigid boundary conditions

Evolutions of the helium gas concentration detected in the N₂ diffusion compartment for the specimens with different initial saturations tested under different gas pressures and rigid boundary conditions were presented in Fig. 3. In the initial stage, the concentration of helium gas in the N₂ diffusion compartment gradually increased in a nonlinear way, which was followed by an approximating linear increase with time.

Curves in Fig. 3 show that significant differences can be identified from the diffusion test results of the rigid specimens to that of the flexible boundary specimens. Meanwhile, for the same gas pressure, no obvious difference can be detected among the helium gas concentration growth curves of the rigid specimens with three initial saturations of 38.18, 62.43 and 79.38%.

Results of the gas diffusion tests performed on the compacted GMZ bentonite specimens under rigid boundary conditions were shown in Table 4.

Table 4

Results of the gas diffusion teats conducted on the GMZ bentonite specimens under rigid boundary conditions.
Specimen	Boundary condition	Dry density (g/cm³)	Water content of powder (%)	Initial saturation of specimen (%)	Gas pressure (MPa)	Diffusion coefficient (m²/s)
D-1	Rigid	1.5	11.10	38.18	0.97	1.30E-10
D-2			11.10	38.18	2.03	9.27E-11
D-3			11.10	38.18	4.06	5.36E-11
E-1			18.29	62.43	1.12	1.51E-10
E-2			18.29	62.43	2.06	1.08E-10
E-3			18.29	62.43	4.05	6.25E-11
F-1			23.03	79.38	1.12	1.77E-10
F-2			23.03	79.38	2.10	1.25E-10
F-3			23.03	79.38	4.14	7.91E-11

4.1 Effects of gas pressure on gas diffusion

With the helium gas diffusion coefficients of the specimens tested (Tables 3 and 4), relationships between the helium gas diffusion coefficient and gas pressure can be established in Fig. 4. Results show that regardless of the constraint conditions, the diffusion coefficient decreases with increasing gas pressure. For the flexible boundary tests, as the gas pressure increased from 1 to 4 MPa, the helium gas diffusion coefficient of the specimens tested with an initial saturation of 38.18, 62.43 and 79.38% decreased from 9.58E-11, 8.27E-11 and 2.37E-12 m²/s to 2.65E-11, 2.20E-11 and 1.95E-12 m²/s, respectively. For the rigid boundary tests, similar variation patterns also could be observed. As the gas pressure changed from 1 to 4 MPa, the helium gas diffusion coefficient of the specimen with an initial saturation of 38.18, 62.43 and 79.38% decreased from 1.30E-10, 1.51E-10 and 1.77E-10 m²/s to 5.36E-11, 6.25E-11 and 7.91E-11 m²/s, respectively. These observations reveal that the diffusion properties of the helium gas were influenced by gas pressure. In fact, gas diffusion of the compacted bentonite is not only affected by basic properties of the bentonite, but also by that of the gas. Kim et al. (2016) and Zhong et al. (2019) also confirmed that under the same conditions, the gas diffusion coefficient was directly influenced by the gas properties.

Actually, the mean free path of the gas molecules is the average distance when the molecules collide with each other. It can be expressed as (Civan 2010):

$$\lambda =\frac{{{\kappa _B}T}}{{\sqrt 2 \pi \delta _{M}^{2}{p_m}}}=\frac{\mu }{{{p_m}}}\sqrt {\frac{{\pi RT}}{{2{M_g}}}}$$

Where, κ_B is the Boltzmann constant (J/K), µ is gas viscosity (Pa·s), R is the universal gas constant (J/(mol·K)), M_g is the molar mass of the gas (kg/mol), δ_M is the molecular collision diameter (nm), T is the absolute temperature (K), and p_m is the gas pressure in the media (Pa).

Eq. (7) indicates that the mean free path of the gas molecules depends on temperature, gas type and gas pressures. Different gases have their own collision diameters. An increase in gas pressure or a decrease in temperature would induce a decrease in the mean free path. For the helium gas tested in this work, at a constant temperature 20°C, the mean free path was affected by the gas pressure. According to literature, the helium gas collision diameter is 0.26 nm (Sinha et al. 2013). With the Boltzmann's constant 1.38E-23 J/K and temperature 293.15 K, relationship between the gas pressure and the mean free path of the helium gas could be calculated and presented in Fig. 5. Results show that the mean free path of helium gas decreased with increasing gas pressure, with a mean free path λ of 13.73, 6.86 and 3.43 nm for a gas pressure of 1, 2 and 4 MPa, respectively. As the gas pressure increased, the mean free path of gas molecules rapidly decreased first, then followed by a reduction on the decreasing rate until gas pressure increased to 6 MPa. Then, as the gas pressure continued to increase, the mean free path gradually getting stable.

Explanations to the observations mentioned above could be that in an unsaturated porous media, the diffusion of gas molecules could mainly occur in the connected pores, which were not completely occupied by porewater (Wen and Wang 2018). In these pores, the increases in gas pressure caused decreases of the mean free path (Javadpour et al. 2007), indicating that the average distance traveled by the gas molecules while collided with each other became shorter and the gas diffusion coefficient calculated according to the gas dynamics decreased (Qian et al. 2023). In other words, when the gas molecules advanced the same distance, the probability of collision with each other increased greatly, resulting in a lower diffusion efficiency and eventually a decrease in the macroscopic diffusion coefficient.

4.2 Effects of initial saturation on gas diffusion

With the test results obtained in this work, evolutions of the helium gas diffusion coefficient with initial saturation for the specimens tested under different constraint conditions could be obtained and presented in Fig. 6.

Curves in Fig. 6 show that in the flexible boundary tests, for a given gas pressure, the helium gas diffusion coefficient decreased with increases of the initial saturation of the compacted bentonite specimen. That is to say, as the initial saturation increased from 38.18 to 79.38%, for a gas pressure of 1, 2 and 4 MPa, the helium gas diffusion coefficient decreased from 9.58E-11, 4.90E-11 and 2.65E-11 m²/s to 2.37E-12, 2.18E-12 and 1.95E-12 m²/s, respectively.

More interestingly, this decreasing process depends on saturation degree. As the initial saturation increased, the diffusion coefficient slowly decreased first, then followed by a sharp decrease in decreasing rate.

Specifically, in the low saturation stage (from 38.18 to 62.43%), the diffusion coefficient decreased slowly by 10–18% under different gas pressures. However, in the relatively high saturation stage (from 62.43 to 79.38%), the diffusion coefficient rapidly decreased to a level of 10^− 12 m²/s as the specimen approached to be saturated.

Explanations to these observations could be that the specimens compacted by the bentonite powder with different water contents have different pore structures and connectivity, exhibiting different diffusion behaviors during gas diffusion in the specimens being further compacted by the confining pressure.

For the flexible boundary tests, as the initial saturation of the specimen slowly increased from a relatively low value, the proportion of the pore space occupied by the porewater increased and the thickness of the water film on the pore wall also gradually increased, even though the specimen has larger pore size due to the higher degree of hydration of the bentonite powder. Meanwhile, due to the confining pressure, the specimen was compacted and the higher the initial saturation, the greater the volume change (Fig. 7). Consequently, connectivity of the empty pore becomes worse (Currie 1983; Zhang and Yu 2016), leading to decrease trend of the gas diffusion efficiency. More importantly, this degradation process depends on saturation. Macroscopically, as a specimen is far from its fully saturated state, the helium gas diffusion coefficient slowly decreases. However, for the specimen with an initial saturation of 79.38%, the diffusion coefficient significantly decreases with increasing saturation.

For the specimens before and after experienced the flexible boundary tests, the saturations were measured and presented in Fig. 8. Results show that saturation of the specimen became larger after experienced the test, due to the confining pressure. That is to say, after experienced the test, the saturation of the specimens with an initial saturation of 38.18 and 62.43% increased to 48.35 and 80.55%, respectively. However, as initial saturation increased from 79.38–97.79%, the specimen approached an almost completely saturated state. Consequently, the helium gas diffusion gradually changed from the molecular diffusion in the empty pore space to the diffusion of the dissolved gas in pore water, while the diffusion efficiency of gas molecules dissolved in water is much lower than that of gas diffusion in gas phase (Sato et al. 2001).

For the rigid boundary tests, the helium gas diffusion coefficient increased slowly with increasing initial saturation (Fig. 6b). That is to say, as the initial saturation increased from 38.18 to 79.38%, the helium gas diffusion coefficient of the specimen tested at a gas pressure of 1, 2 and 4 MPa increased from 1.30E-10, 9.27E-11 and 5.35E-11 m²/s to 1.77E-10, 1.25E-10 and 7.91E-11 m²/s, respectively. This result is different from that obtained through the flexible boundary tests.

Firstly, these observations could be explained by the microstructural differences in the specimens, which were compacted by the bentonite powder having different water contents. For the rigid boundary tests in this work, as water content of the bentonite powder increased, the macro-pores diameter in the compacted specimen increased. The measured pore size distributions in Fig. 9 and the cumulative injection curves in Fig. 10 also illustrate that the specimens compacted by the bentonite powder with different water contents had different pore structures after experienced the rigid boundary diffusion tests. This conslusion was confirmed by the related studies about the impacts of the specimen preparation procedures on the micro-structures of compacted bentonite in literature (Matusewicz et al. 2016).

Meanwhile, diffusivity is closely related to pore diameters. According to the descriptions in Section 1, the “Fick diffusion” and “transition diffusion” can be divided according to the Knudsen number 0.1, in this work, which corresponds to the pore diameter 137 nm calculated by using Eqs. (1) and (7). Interestingly, with this pore diameter of 137 nm, the pore size distribution curves (Fig. 9) for all the three bentonite specimens with different saturations can be divided into two parts, including the intra-aggregate pores (micro-pores) having a diameter less than 137 nm, and the inter-aggregate pores (macro-pores) having a diameter larger than 137 nm. Therefore, in the micro-pores, “transition diffusion” is dominated, while in the macro-pores, “Fick diffusion” plays an important role (Feng et al. 2019; Wang et al. 2017). Meanwhile, curves in Figs. 9 and 10 also show that as the initial saturation degree of the specimen increased from 38.18 to 79.38%, the total volume of the macro-pores decreased, while the micro-pore size almost did not change.

In fact, according to Mou and Chen (2019), for a given pore, diffusion flux ${J_F}$ of “Fick diffusion” can be expressed as follows:

$${J_F}=\frac{{\pi {p_m}}}{{128\mu }}\frac{{d_{n}^{4}}}{L}$$

Where, p_m is the gas pressure in the medium (Pa). µ is gas viscosity (Pa·s), d_n is the pore diameter (nm), and L is the characteristic length of diffusion (m).

According to Eq. (8), the Fick diffusion flux increases with increasing pore diameter. At the same time, based on Fick’s law, the diffusion coefficient is positively correlated with the diffusion flux (Shackelford and Moore 2013). Therefore, as the initial saturation degree of the specimen increased from 38.18 to 79.38%, the diameter of the macro-pores accordingly increased to facilitate Fick diffusion.

In fact, in unsaturated porous geomaterials, the total diffusion in macro-pore was composed of the molecular diffusion and the diffusion of dissolved gas in the pore liquid (Fig. 11). The diffusion coefficients of the two diffusion mechanisms could often be several orders of magnitude different, with molecular diffusion being much larger than the diffusion of dissolved gas (Yuan et al. 2014).

In this work, for the rigid boundary tests, compared to the micro-pores, the macro-pores size increased with increasing initial saturation, promoting the molecular diffusion dominated by “Fick diffusion”. Meanwhile, as initial saturation increases, the proportion of dissolved diffusion also increased with the increase of the space occupied by the pore water, leading to the decrease of the total amount of gas molecules diffused in the specimen. However, the decrease of the diffusion flux induced by increasing proportion of the dissolved diffusion due to decreases of macro-pores failed to offset the increase of the diffusion coefficient caused by the increase of the large pore diameter. Consequently, the helium diffusion coefficient increased with the increase of the initial saturation.

In this work, self-designed test apparatuses were developed and gas diffusion tests were conducted on GMZ bentonite specimens using the two-chamber method. Effects of boundary conditions, initial saturations and gas pressures on the gas diffusion coefficient of GMZ bentonite were investigated. Main conclusions can be drawn as follows.

With increasing gas pressure, the diffusion coefficient decreased. Explanations could be that gas pressure was inversely proportional to the gas mean free path for molecular diffusions. An increase in gas pressure led to a rapid reduction in the mean free path, resulting in decreasing diffusion efficiency and, macroscopically, a lower gas diffusion coefficient.

The gas diffusion coefficient of the flexible specimens decreased with increasing initial saturations. Furthermore, the decreasing rate depends on saturation with a much higher value in the higher saturation stage (from 62.43 to 79.38%). Explanations could be that the compaction induced by the confining pressure caused increases of compressive strain and saturation for the specimen with a higher initial saturation, resulting a poor connectivity of the effective pores. Consequently, the molecular diffusion in the empty pores was gradually changed to diffusion of dissolved gas in pore water with a decreasing diffusion coefficient.

Conversely, the gas diffusion coefficient of the rigid specimens increased slowly with increasing initial saturations. These observations could be explained by difference of pore structure of the specimens compacted by the bentonite powder with different water contents. MIP results show that specimens with higher initial saturations had larger pore diameter of the macro-pores. The macro-pores are a decisive parameter for gas diffusion in porous media, and the larger pore diameter leads to an increase of diffusion coefficient.

Author Contribution

Yuheng Ji and Puhuai LU wrote the main manuscript text；Weimin YE supervised the work;Qiong Wang and Yonggui Chen conducted the test and results analyzed.

Acknowledgements

The financial supports from the National Nature Science Foundation of China (42030714, 42125701) and the National Key R&D Program of China (2019YFC1509900) are greatly acknowledged.

Alonso EE, Romero E, Hoffmann C, García-Escudero E (2005) Expansive bentonite-sand mixtures in cyclic controlled-suction drying and wetting. Eng Geol 81:213-226. https://doi.org/10.1016/j.enggeo.2005.06.009
Civan F (2010) Effective Correlation of Apparent Gas Permeability in Tight Porous Media. Transp Porous Media 82:375-384. https://doi.org/10.1007/s11242-009-9432-z
Cui LY, Masum SA, Ye WM, Thomas HR (2022) Investigation on gas migration behaviours in saturated compacted bentonite under rigid boundary conditions. Acta Geotech 17:2517-2531. https://doi.org/10.1007/s11440-021-01424-1
Cui LY, Ye WM, Wang Q, Chen YG, Chen B, Cui YJ (2019) Investigation on gas migration in saturated bentonite using the residual capillary pressure technique with consideration of temperature. Process Saf Environ 125:269-278. https://doi.org/10.1016/j.psep.2019.03.036
Cui LY, Ye WM, Wang Q, Chen YG, Chen B, Cui YJ (2020) Insights into Determination of Gas Breakthrough in Saturated Compacted Gaomiaozi Bentonite. J Mater Civ Eng 32. https://doi.org/10.1061/(ASCE)MT.1943-5533.0003206
Cui LY, Ye WM, Wang Q, Chen YG, Cui YJ (2023) A model for describing advective and diffusive gas transport through initially saturated bentonite with consideration of temperature. Eng Geol 323:107215. https://doi.org/10.1016/j.enggeo.2023.107215
Currie JA (1983) Gas diffusion through soil crumbs: the effects of wetting and swelling. J Soil Sci 34:217-232. https://doi.org/10.1111/j.1365-2389.1983.tb01029.x
Delage P, Lefebvre G (1984) Study of the structure of a sensitive Champlain clay and of its evolution during consolidation. Can Geotech J 21:21-35. https://doi.org/10.1139/t84-003
Feng SY, Wang HQ, Cui Y, Ye YJ, Li XY, Xie D, He ZZ, Yang R (2019) Monte Carlo method for determining radon diffusion coefficients in porous media. Radiat Meas 126. https://doi.org/10.1016/j.radmeas.2019.106130
Graham CC, Harrington JF, Sellin P (2016) Gas migration in pre-compacted bentonite under elevated pore-water pressure conditions. Appl Clay Sci 132:353-365. https://doi.org/10.1016/j.clay.2016.06.029
Horseman ST, Harrington JF, Sellin P (1999) Gas migration in clay barriers. Eng Geol 54:139-149. https://doi.org/10.1016/S0013-7952(99)00069-1
Jacops E, Maes N, Bruggeman C, Grade A (2015) Measuring diffusion coefficients of dissolved He and Ar in three potential clay host formations: Boom Clay, Callovo-Oxfordian Clay and Opalinus Clay. the 6th conference on Clays in natural and engineered barriers for radioactive waste confinement, 1 edn, Brussels, Belgium. pp 349-360
Jacops E, Volckaert G, Maes N, Weetjens E, Govaerts J (2013) Determination of gas diffusion coefficients in saturated porous media: He and CH4 diffusion in Boom Clay. Appled Clay Science 83-84:217-223. https://doi.org/10.1016/j.clay.2013.08.047
Javadpour F, Fisher D, Unsworth M (2007) Nanoscale Gas Flow in Shale Gas Sediments. J Can Pet Technol 46:55-61. https://doi.org/10.2118/07-10-06
Kim C, Jang H, Lee Y, Lee J (2016) Diffusion characteristics of nanoscale gas flow in shale matrix from Haenam basin, Korea. Environ Earth Sci 75:350. https://doi.org/10.1007/s12665-016-5267-4
Kim D, Jeon S, Kim SO, Wang S, Lee M (2023) Review for Mechanisms of Gas Generation and Properties of Gas Migration in SNF (Spent Nuclear Fuel) Repository Site. Econ Environ Geol 56:167-183. https://doi.org/10.9719/EEG.2023.56.2.167
Li B, Ren JG, Liu JB, Liu GF, Lv RS, Song ZM (2019) Diffusion and Migration Law of Gaseous Methane in Coals of Different Metamorphic Degrees. Int J Heat Technol 37:1019-1030. https://doi.org/10.18280/ijht.370411
Liu JF, Song Y, Skoczylas F, Liu J (2016) Gas migration through water-saturated bentonite-sand mixtures, COx argillite, and their interfaces. Can Geotech J 53:60-71. https://doi.org/10.1139/cgj-2014-0412
Marschall P, Horseman S, Gimmi T (2005) Characterisation of gas transport properties of the Opalinus Clay, a potential host rock formation for radioactive waste disposal. Oil & Gas Science and Technology - Revue d'IFP Energies nouvelles 60:121-139. https://doi.org/10.2516/ogst:2005008
Marsh AI, Williams LG, Lawrence JA (2021) The important role and performance of engineered barriers in a UK geological disposal facility for higher activity radioactive waste. Prog Nucl Energy 137. https://doi.org/10.1016/j.pnucene.2021.103736
Matusewicz M, Pulkkanen VM, Olin M (2016) Influence of sample preparation on MX-80 bentonite microstructure. Clay Miner 51:189-195. https://doi.org/10.1180/claymin.2015.051.2.06
Mou XZ, Chen ZQ (2019) Mathematical model for effective gas diffusion coefficient in multi-scale fractal porous media. J Southeast U: Nat Sci Ed 49:520-526 (in Chinese). https://doi.org/10.3969/j.issn.1001-0505.2019.03.017
Ohazuruike L, Lee KJ (2023) A comprehensive review on clay swelling and illitization of smectite in natural subsurface formations and engineered barrier systems. Nucl Eng Technol 55:1495-1506. https://doi.org/10.1016/j.net.2023.01.007
Ortiz L, Volckaert G, Mallants D (2002) Gas generation and migration in Boom Clay, a potential host rock formation for nuclear waste storage. Eng Geol 64:287-296. https://doi.org/10.1016/S0013-7952(01)00107-7
Owusu JP, Karalis K, Prasianakis NI, Churakov SV (2023) Diffusion and Gas Flow Dynamics in Partially Saturated Smectites. J Phys Chem C 127:14425-14438. https://doi.org/10.1021/acs.jpcc.3c02264
Purcell WR (1949) Capillary Pressures - Their Measurement Using Mercury and the Calculation of Permeability Therefrom. J Pet Technol 1:39-48. https://doi.org/10.2118/949039-g
Qian RS, Zhang YS, Zhang Y, Fu CQ, Liu C, Yang L, Liu GJ (2023) Various gas transport properties in concrete considering transporting mechanisms and testing methods-A review. Constr Build Mater 389:131636. https://doi.org/10.1016/j.conbuildmat.2023.131636
Rouf MA, Bouazza A, Singh RM, Gates WP, Rowe RK (2016) Gas flow unified measurement system for sequential measurement of gas diffusion and gas permeability of partially hydrated geosynthetic clay liners. Can Geotech J 53:1000-1012. https://doi.org/10.1139/cgj-2015-0123
Sato S, Otsuka T, Kuroda Y, Higashihara T, Ohashi H (2001) Diffusion of Helium in Water-Saturated, Compacted Sodium Montmorillonite. J Nucl Sci Technol 38:577-580. https://doi.org/10.1080/18811248.2001.9715069
Seiphoori A, Ferrari A, Laloui L (2014) Water retention behaviour and microstructural evolution of MX-80 bentonite during wetting and drying cycles. Geotechnique 64:721-734. https://doi.org/10.1680/geot.14.P.017
Sercombe J, Vidal R, Gallé C, Adenot F (2007) Experimental study of gas diffusion in cement paste. Cem Concr Res 37:579-588. https://doi.org/10.1016/j.cemconres.2006.12.003
Shackelford CD, Moore SM (2013) Fickian diffusion of radionuclides for engineered containment barriers: Diffusion coefficients, porosities, and complicating issues. Eng Geol 152:133-147. https://doi.org/10.1016/j.enggeo.2012.10.014
Sinha S, Braun EM, Determan MD, Passey QR, Leonardi SA, Boros JA, Wood AC, Zirkle T, Kudva RA (2013) Steady-State Permeability Measurements on Intact Shale Samples at Reservoir Conditions-Effect of Stress, Temperature, Pressure, and Type of Gas. SPE Middle East Oil and Gas Show and Conference, Manama, Bahrain
Strangfeld C (2021) Quantification of the Knudsen Effect on the Effective Gas Diffusion Coefficient in Partially Saturated Pore Distributions. Adv Eng Mater 23. https://doi.org/10.1002/adem.202100106
Sun J, Liu DH, Zhu X, Huang WJ, Chen L (2021) Experimental investigation on shale gas transport characteristics in nanopores under high temperature and high pressure. Int J Oil Gas Coal T 26:302-325. https://doi.org/10.1504/IJOGCT.2021.113137
Tawara Y, Hazart A, Mori K, Tada K, Shimura T, Sato S, Yamamoto S, Asano H, Namiki K (2012) Extended two-phase flow model with mechanical capability to simulate gas migration in bentonite. the 5th Conference on Clays in Natural and Engineered Barriers for Radioactive Waste Confinement, Montpellier, FRANCE. pp 545-562
Wang JJ, Yuan QW, Dong MZ, Cai JC, Yu L (2017) Experimental investigation of gas mass transport and diffusion coefficients in porous media with nanopores. Int J Heat Mass Transfer 115:566-579. https://doi.org/10.1016/j.ijheatmasstransfer.2017.08.057
Wen Y, Wang YH (2018) Determination of oxygen diffusion coefficients of compacted asphalt mixtures. Constr Build Mater 160:385-398. https://doi.org/10.1016/j.conbuildmat.2017.11.073
Wen ZJ (2006) Physical Property of China's Buffer Material for High-level Radioactive Waste Repositories. Chinese Journal of Rock Mechanics and Engineering 25:794-800. https://doi.org/1000-6915(2006)04-0794-07
Ye WM, Cui YJ, Qian LX, Chen B (2009) An experimental study of the water transfer through confined compacted GMZ bentonite. Eng Geol 108:169-176. https://doi.org/10.1016/j.enggeo.2009.08.003
Ye WM, Xu L, Chen B, Chen YG, Ye B, Cui YJ (2014) An approach based on two-phase flow phenomenon for modeling gas migration in saturated compacted bentonite. Eng Geol 169:124-132. https://doi.org/10.1016/j.enggeo.2013.12.001
Yuan WN, Pan ZJ, Li X, Yang YX, Zhao CX, Connell LD, Li SD, He JM (2014) Experimental study and modelling of methane adsorption and diffusion in shale. Fuel 117:509-519. https://doi.org/10.1016/j.fuel.2013.09.046
Zhang C, Yu QC (2016) The effect of water saturation on methane breakthrough pressure: An experimental study on the Carboniferous shales from the eastern Qaidam Basin, China. J Hydrol 543:832-848. https://doi.org/10.1016/j.jhydrol.2016.11.003
Zhong Y, She JP, Zhang H, Kuru E, Yang B, Kuang JC (2019) Experimental and numerical analyses of apparent gas diffusion coefficient in gas shales. Fuel 258. https://doi.org/10.1016/j.fuel.2019.116123

No competing interests reported.

Download PDF

Editorial decision: Revision requested
25 May, 2024
Reviews received at journal
19 May, 2024
Reviews received at journal
01 May, 2024
Reviewers agreed at journal
18 Apr, 2024
Reviewers agreed at journal
05 Apr, 2024
Reviewers agreed at journal
05 Apr, 2024
Reviewers invited by journal
05 Apr, 2024
Editor assigned by journal
06 Mar, 2024
Submission checks completed at journal
04 Mar, 2024
First submitted to journal
27 Feb, 2024

You are reading this latest preprint version

Gas diffusion property of compacted GMZ bentonite with consideration of saturation and gas pressure

Status:

Version 1

Abstract

Figures

1. Introduction

2. Experimental investigation

2.1 Materials and specimen preparation

2.2 Test apparatus

1) The flexible boundary gas diffusion test

2) The rigid boundary gas diffusion test

2.3 Test procedures

2.4 Determination of diffusion coefficients

2.5 Mercury intrusion porosimetry (MIP) test

3. Results

3.1 Gas diffusion under flexible boundary conditions

3.2 Gas diffusion under rigid boundary conditions

4. Discussion

4.1 Effects of gas pressure on gas diffusion

4.2 Effects of initial saturation on gas diffusion

5. Conclusions

Declarations

Author Contribution

References

Additional Declarations

Status:

Version 1