Diffusion Capability of Cs-137 in Compacted Soil and Bentonite Under Groundwater-saturated Condition

doi:10.21203/rs.3.rs-3005790/v1

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Diffusion Capability of Cs-137 in Compacted Soil and Bentonite Under Groundwater-saturated Condition

https://doi.org/10.21203/rs.3.rs-3005790/v1

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Several researches have been studied the diffusion coefficient (Da) of radionuclide in soil samples in varies location around the world; however, the effect of cations in groundwater as a medium of saturation for Cs-137 diffusion in soil and bentonite remains to be accomplished. Compacted soil and bentonite layers are utilized in the construction of radioactive waste disposal sites, which serve to prevent the release of Cs-137 from the repository to the unsaturated zone. The samples used were soil from the prospective disposal site in SP4 – Serpong Nuclear Center (SNC) and bentonite taken from Santrijaya, Tasikmalaya. The diffusion coefficient (Da) is used as indicator of Cesium-137 diffusion in the samples. Experimental measurements were conducted on a diffusion column unit that varied in diffusion time and density conditions to determine diffusion coefficients. The samples were cut into slices and analyzed using Multichannel Analyzer (MCA) unit to measure Cs-137 radioactivity. The measurement results were then incorporated into Fick's Law equation to obtain the value of the diffusion coefficient (Da) of Cs-137 in soil and bentonite. The experimental results showed that the diffusion coefficients of samples with groundwater simulation are in the range of 10^− 12 m².s^− 1 for the local soil and bentonite samples, respectively. Compare to the similar experiment that was conducted previously, the results indicated that the groundwater content could slightly impact the increase in the diffusion coefficient value of Cs-137.

near surface disposal facility

Cs-137

groundwater saturation

diffusion coefficient

Many industrial and medical activities in Indonesia currently generate radioactive waste (Bunawas and Syarbaini, 2005; Hermawan, 2010; Gunandjar and Sundari, 2013). The management of radioactive waste in Indonesia is managed by the Directorate of Nuclear Facilities Management – National Research and Innovation Agency (DPFK-BRIN) (Sumarbagiono, 2021). Until now, Indonesia does not have any disposal facility, so that the radioactive waste is stored in the interim storage facility. Hence, the amount of waste stored will continue to increase, requiring larger storage facilities. Therefore, there are plans to build disposal facilities in Indonesia. The first stage in the development of disposal facilities is the determination of a location that suitable for the disposal site. One important factor in the safety aspect view for the disposal site is the retention ability of host rock in the event of a leakage of radionuclide from the disposal facility to the surrounding environment.

Candidate locations for the disposal site have been surveyed in various regions of Indonesia since 1989 until now (Sucipta and Hendra Adhi Pratama, 2014; Syaeful, Sucipta and Sadisun, 2014) and one of the candidates is the Serpong Nuclear Center (SNC). This location was designated by the government (Ekaningrum, 2022) based on the co-location principal, as it is can be a part of the centralized radioactive waste management facility from all over Indonesia. Therefore, it can also reduce the potential burden of transportation costs and in terms of public acceptance, considering that nuclear acceptance in Indonesia is still controversial in some areas (Wijayanti, 2017; Herawati and Sudagung, 2020).

The disposal facility itself has many types depending on the type of nuclear waste stored (IAEA, 2011). The type of disposal planned to be built in SNC is Near Surface Disposal (NSD) (Syaeful, Sucipta and Sadisun, 2014; Ekaningrum, 2022) has been widely used to store low and intermediate level radioactive waste. Cs-137 is a radionuclide that is easily absorbed by the soil material (Koarashi et al., 2019) and the Cs cation is also in Group IA and has the property of being completely soluble in water (EPA, 2023) so if this ion is absorbed by the groundwater and consumed by the surrounding community (for irrigation, agriculture, and drinking), it can increase the risk to public health (Rauwel and Erwan Rauwel, 2019).

For the second aspect, the safety aspect of the disposal site's designer is evaluated by selecting bentonite as one of the layers in the engineered barrier system. Research related to the selection of bentonite is still ongoing because it has different characteristics in each region. The use of bentonite has been widely used in disposal facility. Bentonite is a clay with many smectite mineral contents. The structure of smectite itself is not neutral (electric) so it can attract exchangeable cations such as Na, Ca, or Mg to ensure electro-neutrality (Saiyouri, Tessier and Hicher, 2004) and it has been recognized that 60% of bentonite pores are capable of absorbing water (Laloui, Ferrari and Bosch, 2020) and it swells when exposed to water, making it an excellent sealing material and helps to trap any radionuclides in the unlikely event they were to escape from the container (NWMO, 2015). Bentonite itself consists of two groups, specifically sodium bentonite (swelling bentonite) and calcium bentonite (non-swelling bentonite) (Peinado and Moreno, 2012) and is found in various regions of Indonesia such as Java Island, Sumatra Island, part of Kalimantan Island, and Sulawesi Island (Ruskandi, Siswanto and Widodo, 2020).

This study utilized bentonite from Tasikmalaya, a region in Indonesia. The chemical composition of the Tasikmalaya bentonite and the candidate disposal site soil at SNC composed of Montmorillonite with other phases, where the local soil contain considerable amounts of Kaolinite based on XRF and XRD characterizations (Ekaningrum, 2022). The diffusion rate of Cs-137 in soil and bentonite was identified through mathematical modeling using Fick's second law. This study builds upon previous research conducted by Ekaningrum (2022) which used demineralized water for saturation. Given the potential variation in soil characteristics, such as groundwater content, across different locations, it is possible that the diffusion rate of Cs-137 may differ. Therefore, this study aims to investigate the impact of groundwater from SNC on the vertical position diffusion coefficient of Cs-137, with sample density and time as variables. The results of this research are expected as updated data in the safety assessment program for the development of a radioactive waste disposal site in the SNC disposal site development program.

Materials and characterization

Soil samples were gathered from the SP-4 SNC location, specifically from drill hole DH-2, which was 7 meters depth below the surface. Meanwhile, natural bentonite samples were procured from a mining site in Santrijaya-Tasikmalaya. The saturation conditions used are simulated groundwater of groundwater from the SP-4 SNC site. Radiocesium Cs-137 used was a solution from Specific activity 3.7 MBq/5 ml from Eckert & Ziegler Isotope Production diluted to 10,000 Bq/ml as radioactive solution stock.

Procedure

Samples of local soil and bentonite with varying densities between 1.2 to 1.4 g.cm^− 3 were prepared for a one-dimensional non-steady state diffusion experiment. The experiment involved inserting the soil and bentonite samples into a stainless-steel cylindrical diffusion cell with a volume of 15.4 m³, compacting them according to their respective densities by using the formula ρ = m/V and saturating them with simulated groundwater.

Table 1

Chemical composition in simulated groundwater
Chemical composition	Amount in ppm
NaCl	19
KCl	20
CaCO₃	50
MgCl₂·6H₂O	15
FeCl₃·6H₂O	0.25

The chemical composition for simulated groundwater shown in Table 1 were mixed into demineralization water. A small amount (1000 µL) of Cs-137 tracer solution were then added to the top of the diffusion cell after saturation. The diffusion column unit was made of stainless steel and hosted cylindrical samples of 20 mm in diameter and 50 mm in length. The upper end of the column was covered with a porous metal filter, while filter paper was installed at the bottom end. The samples were then saturated in a desiccator filled with simulated ground to be vacuumed for 2 hours with pressure of 1 atm. After saturation, the top cover of the diffusion column was opened, and the Cs-137 solution was dripped onto the sample. The diffusion experiment was carried out for varying densities at specified times (3, 4, and 6 weeks) and for specified times at varying densities (1.2 to 1.4 g.cm^− 3). After the diffusion time was reached, the sample was sliced into 2 mm segments, and the gamma-activity was measured to analyze Cs-137 directly with a Multichannel Analyzer (MCA) with 20% efficiency at the 662 keV for characteristic gamma peak of the Cs-137. Figure 1 below provides a schematic representation of the diffusion column unit.

Mathematical model and disposal concept

According to Pelleg (Pelleg, 2016), the diffusion process occurs when there is movement of particles or atoms that penetrate a medium due to differences in the concentration gradients. This process is usually irreversible.

$${J}_{x}=-D. \frac{\partial C}{\partial x}$$

The mass flux of diffusion (J) is expressed in kg m^− 2 s^− 1, and it is affected by the diffusion coefficient (D) in free water (m²s^− 1), the concentration (C) in count m³, and the distance of diffusion (x) in meters. Diffusion events typically occur in a transient state where the material concentration and material flux change according to a function of time (O’Hayre, 2015), as illustrated in Fig. 2.

When dealing with radionuclides, the concentration typically diffuses from a higher concentration to a lower concentration. At the initial time (t = 0), the radionuclide concentration at any distance x within the foundation layer (C_xa) is equal to zero. As the radionuclide source with a concentration (C_a=M) is introduced at the boundary (x = a), the diffusion proceeds due to the concentration difference. The alteration in concentration is determined by the disparity between the incoming flux at x_a and the outgoing flux at x, which is represented as J_xa – J_x. The flux difference that takes place at any given moment represents the rate of concentration change, which is denoted as C_x. In the meantime, the flux that exits at x is equal to the sum of the incoming flux at xa and the derivative of J with respect to x. Consequently, the equation can be expressed as ${J}_{x}= {J}_{xa}+ \frac{\partial J}{\partial x}$. This is known as Fick's-II law, which is expressed in Eq. (2).

$\frac{d{C}_{x}}{dt}=- \frac{\partial J}{\partial x} . \varDelta x= \frac{d}{dx}\left[D.\frac{d{C}_{x}}{dx}\right]$ $=\left[D.\frac{{d}^{2}{C}_{x}}{d{x}^{2}}\right]$ (2)

The diffusion coefficient (Da) can be determined by solving Eq. (2) with specific initial and boundary conditions, where:

t = 0, C = C_a = M

t = t₁, C = C_x1

t = t₂, C = C_x2

In a cylindrical system of infinite length, assuming a planar source with a small quantity of soluble substances, the solution of Eq. (2) is expressed in Eq. (3), as derived by Crank (1975).

$$C(x,t)=\frac{M}{2\sqrt{\pi {D}_{a}t}}\text{e}\text{x}\text{p}(-\frac{{x}^{2}}{4{D}_{a}t})$$

The following equation presents the linear version of Eq. (3), which utilizes the variables C for the total concentration of radiocesium in Bq, t for the diffusion time in seconds, x for the distance between the source and the measurement point in meters, and M for the concentration of radiocesium per unit square (Bq m^− 2) (Milligen, B. P., Bons, P. D., Carreras and S´anchez, 2005)

$$\text{l}\text{n}C= -\frac{{x}^{2}}{4{D}_{a}t}+\text{l}\text{n}\left(\frac{M}{\sqrt{4{D}_{a}t}}\right)$$

The slope of equation above is utilized to derive the diffusion coefficient according to the subsequent process,

$$Slope=\frac{1}{4{D}_{a}t}$$

To conduct a precise examination of the diffusivity of radionuclides within the compacted soil and bentonite layers, the diffusion coefficient (Da) was determined via a diffusion column unit constructed from stainless steel. Fick's 2nd Law and vertical diffusion are commonly used to examine the coefficient diffusion Da of Cesium-137 in diffusion columns due to the design of the columns and the properties of the medium being studied. In this case, a diffusion column with a diameter of 2 cm and a height of 5 cm is used, which is thin and tall in shape. The vertical diffusion approach is used for a thin and tall diffusion column because of gravitational forces. It is assumed that vertical transport occurs only due to diffusion and that convection caused by gravitational forces doesn't affect the system. The height being longer than the diameter implies that there is a stable gradient of Cesium-137 concentration in the vertical direction of the column. Consequently, it becomes easier to determine the spatial distribution of Cesium-137 within the medium and study its transport behavior in the vertical direction.

The diagram presented in Fig. 3 depicts the proposed layout of a facility located at SNC. The scenario of radionuclide waste release started when it got out from disposal vault. The waste leak and infiltrating water occur simultaneously that caused the radionuclides to dissolve into the water and migrate vertically to the bottom of NSD facility. If there is no barrier, the fluids will directly be absorbed by unsaturated zone then soaked into aquifer zone that will contaminate water consumption for organism and residents around the disposal facility. With the scenario of adding compacted layers of bentonite and local soil as barriers, it can decelerate the leak until these layers become saturated. Overall, the effectiveness of the engineered barriers to halt the migration of radionuclides relies on various factors including the materials used in constructing the barriers, the density of the barriers, the rate of water intrusion, and the properties of the surrounding environment.

Effect of diffusion time

The diffusion coefficient of cesium-137 is a measure of the rate at which the radioactive isotope moves through a porous medium, such as soil. Several factors can influence the diffusion coefficient of cesium-137, including the density and texture of the soil, as well as the chemical and physical properties of the cesium-137 ions.

Table 2

The values of Da of Cs-137 in soil samples as a function of diffusion time, ρ: 1.4 g.cm^-3
No.	t_diffusion(weeks)	Da (m².s^− 1)
No.	t_diffusion(weeks)	Soil
1.	3	5.29 x 10^− 12
2.	4	5.26 x 10^− 12
3.	6	5.22 x 10^− 12

Our results in Fig. 4 and Table 2 shown that the variation of time does not significantly impact changes in the diffusion coefficient of cesium-137. These results also can be explained by the specific conditions of the system, which involves a planar source with a small amount of soluble substances present in an infinitely long cylindrical system, where the density in the diffusion column is considered to be homogeneous, resulting in a constant velocity of Cs-137 through the diffusion column (Crank, 1975). This phenomenon can also be explained by several factors, including the nature of cesium-137 and the properties of the soil through which it is moving. The isotope of Cesium-137 has a relatively long half-life of 30.2 years (EPA, 2023) can lead the concentration of cesium-137 in the soil remains relatively stable over time, as the rate of decay is relatively slow. As a result, changes in the diffusion coefficient of cesium-137 due to time-dependent factors may not be significant over relatively short periods, such as a few years or even a few decades. Also, cesium-137 is a highly soluble element (EPA, 2023) that is readily absorbed onto soil particles and other surfaces so it may not be as susceptible to changes in the chemical and physical properties of the soil over time, which can help to stabilize its diffusion coefficient.

Table 3

Comparison of Da value of the previous experiment results (Ekaningrum, 2022)
No.	t_diffusion(months)	Da (m².s^− 1)
No.	t_diffusion(months)	Soil
1.	2	3.58 x 10^− 12
2.	4	3.51 x 10^− 12

Some studies have found similar results that the variation of time does not significantly impact changes in the diffusion coefficient of cesium-137, even though the coefficient may slightly decrease over time. It is also supported by other studies that investigated the impact of diffusion time on the diffusion coefficient of cesium-137. Ekaningrum (2022) found that the diffusion coefficient of cesium-137 remained relatively constant over a range of diffusion times in soils and bentonite shown in Table 3. Another study (He et al., 2015) found that when the shift of initial time is considered, the diffusion coefficient will be constant.

The stability of the diffusion coefficient of cesium-137 over varying diffusion times can be attributed to the diffusion process itself. Diffusion is a mass transfer process that is dependent on the concentration gradient of the diffusing substance (Park and Kim, 2000). This study applied Fick's 2nd Law to study the diffusion process because it is a well-established model that describes the diffusion of a solute through a stationary medium. This law and vertical diffusion method are used to examine the coefficient diffusion Da of Cesium-137 in a diffusion column because of the thin and tall design of the column, the stable gradient of Cesium-137 concentration in the vertical direction, and the fundamental mathematical equation that they provide for diffusion in stationary medium. As long as the concentration gradient remains constant over time, the diffusion coefficient will also remain constant. And the temperature also remained stable during the experiment so there is no additional energy. Furthermore, the stability of the diffusion coefficient of cesium-137 over time has important implications for predicting the transport of this radioactive isotope in the environment.

Table 4

Comparison of Da value from other studies
No.	Da soil (m².s^− 1)	Ref.
1.	5.22 x 10^− 12	This experiment
2.	3.5 x 10^− 12	(Ekaningrum, 2022)
3.	2.03 x 10^− 12	(Jagercikova et al., 2015)
4.	~ 10^− 12	(Sato and Hirota, 2019)

As we compare the results with values obtained in different studies in Table 4, (Jagercikova et al., 2015) (Sato & Hirota, 2019) which used soil from Fukushima prefecture and the neighboring areas, all values ranges in order 10^–12, indicating that the soil in SNC has similar ability to impede the release of Cesium-137 to the environment with soils from other country so it can be considered for barrier in disposal facilities. Our comparison of this study in Table 2 with previous study in Table 3 suggests that the diffusion coefficient can be accurately estimated based on measurements made over a relatively short period of time, rather than requiring measurements over a longer period of time.

Effect of material density

The following outcomes depict the evaluation of D_a values in diverse densities, and the experiment was conducted concurrently, specifically for 6 weeks of diffusion duration.

The result shown in Fig. 5 and Fig. 6 showed that the diffusion coefficient of cesium-137 is influenced by the density of the soil and bentonite as mediums through which it is moving. The density of the mediums can impact the rate at which cesium-137 diffuses through the soil and therefore, can affect the overall transport of this radioactive isotope in the environment.

The diffusion coefficient of cesium-137 is dependent on several factors including the size and shape of the pores in the soil, the porosity, and the tortuosity of the soil matrix. The porosity of the soil is defined as the ratio of the volume of voids in the soil to the total volume of the soil (P.K. Jayasree, K Balan, 2021). We found the trend of this study was attributed to the fact that denser soils tend to have smaller pores, which limit the movement of cesium-137 particles through them. As the density of the soil increases, the size and shape of the pores in the soil are altered, resulting in a reduction in the overall porosity of the soil. This reduction in porosity, in turn, leads to a decrease in the diffusion coefficient of cesium-137. This is because the diffusion of cesium-137 is restricted by the smaller pore spaces, which limits the ability of the cesium-137 ions to move freely through the soil matrix. Other aspect is the tortuosity which is a term used to describe the sinuosity and interconnectedness of the pore space as it affects transport processes through porous media (Silva et al., 2022), these factors affect the diffusion coefficient of cesium-137. The denser soils or media tend to have smaller pores and fewer voids, which restrict the movement of particles through them (Chittoori et al., 2016) that makes the diffusion of cesium-137 through denser soils or media is slower than through less dense soils or media.

Table 5

The values of D_a of Cs-137 in the local soil and bentonite samples as a function of sample density, t : 6 weeks
No.	Density (g. cm^− 3)	D_a (m².s^− 1)
No.	Density (g. cm^− 3)	Soil	Bentonite
1.	1.2	6.81 x 10^− 12	2.57 x 10^− 12
2.	1.3	6.21 x 10^− 12	2.1 x 10^− 12
3.	1.4	5.22 x 10^− 12	1.73 x 10^− 12

From diffusion coefficient values in Table 5, it can be observed that the value of D_a decreases as the density of the medium increases. This means that the diffusion rate of particles or molecules through a denser medium is slower compared to a less dense medium. The denser medium contains more particles, which causes more collisions and obstacles for the diffusing particles to overcome. Therefore, the diffusing particles take a longer time to reach their destination, resulting in a lower diffusion coefficient value (Da).

From the Table 5, we also obtained that the diffusion coefficient value of Cesium-137 is on average three times smaller in bentonite samples compared to soil samples. The results of the study suggest that bentonite, a type of clay, is more effective in retaining Cesium-137 than soil. Soil with smaller particle sizes, such as clay, has been found to have lower diffusion coefficients compared to soils with larger particle sizes. The slower diffusion coefficient (Da) of Cs-137 in bentonite compared to soils can be attributed to several factors, such as the presence of exchangeable cations in soils that increase the diffusion coefficient, while the non-swelling nature of bentonite limits the interlayer diffusion of Cs-137. Also, the mineralogical composition of bentonite and soils also affects the diffusion behavior of Cs-137.

Siyal et al. (2005) had shown similar result with soil dry densities 1.24, 1.28 and 1.31 mg/mm³ where they found solute diffused our more rapidly from the small size aggregates as compared to larger aggregates may be because the rate of solute transfer is inversely proportional to square of the aggregate diameter and the effective diffusion coefficient of the solute decreased with increase in dry density of the aggregate may be due to difference in dry density which makes the diffusion paths more tortuous.

Table 6

Comparison of Da value from other studies
No.	Da bentonite (m².s^− 1)	Ref.
1.	1.73 x 10^− 12	This experiment
2.	5 x 10^− 13	(Ekaningrum, 2022)
3.	3.9 x 10^− 13	(Cho, Lee and Kang, 2001)
4.	3.2 x 10^− 11	(Suzuki, Haginuma and Suzuki, 2007)

In Table 6, we can see comparison of our results with different studies where(Cho et al., 2001) used bentonite from Kyungju while(Satoru Suzuki & Suzuki, 2007) used saline water for diffusion of Cesium-137 in their bentonite samples resulting in higher value. It can be seen the saline water can impact the increase of Da value in line with our results we obtained compare to Ekaningrum (2022) that used identical samples.

Figure 7 shows Cesium-173 diffuse easier in soil sample rather than its movement in bentonite when both samples have similar density and diffusion time (1.2 g.cm^-3 and 6 weeks), that can occur because bentonite has a more complex pore structure, which makes it harder for Cesium-137 to diffuse through the material. In contrast, soil has a more open pore structure, which allows for easier diffusion of Cesium-137 and the presence of montmorillonite in bentonite a can facilitate Cs-137 adsorption and reduce its diffusion coefficient.

Impact of groundwater saturation

Our local soil was found to contain high amounts of iron and alumina, while our bentonite samples contained high amounts of iron and calcium. Both materials were composed of Montmorillonite, with the bentonite samples containing a mix of sodium and calcium Montmorillonite. Furthermore, our local soil contained Kaolinite-1A, while the bentonite samples contained silicon oxide. Our results demonstrated that the presence of exchangeable cations, including Na⁺, K⁺, Ca²⁺, Mg²⁺, and Fe²⁺, led to an increase in the diffusion coefficient of cesium-137 in our soil samples.

Table 7

The values of D_a of Cs-137 in the local soil and bentonite samples as a function of sample density
No.	Density (g. cm^− 3)	D_a (m².s^− 1)
No.	Density (g. cm^− 3)	Soil	Bentonite
1.	1.2	6.81 x 10^− 12	2.57 x 10^− 12
2.	1.4	5.22 x 10^− 12	1.73 x 10^− 12

Table 8

Comparison of D_a value of the previous experiment results (Ekaningrum, 2022)
No.	Density (g. cm^− 3)	D_a (m².s^− 1)
No.	Density (g. cm^− 3)	Soil	Bentonite
1.	1.2	5.1 x 10^− 12	5 x 10^− 13
2.	1.4	3.5 x 10^− 12	5 x 10^− 13

Overall, the results obtained in this study have a slightly higher diffusion coefficient value compared to a similar study shown in Table 7 and Table 8. This suggests that the type of saturation media used in the diffusion experiment can indeed affect the diffusion coefficient value. Cesium cation diffusion coefficients have been shown to increase with the presence of other cations. Cations such as Ca, Na, K, Mg, and Fe can affect the soil properties and alter the pore structure, which can affect the diffusion coefficient value of cesium-137. These cations can also interact with the cesium-137 and influence its sorption behavior of Cs-137 in the soil (Sriwahyuni and Setiawan, 2019; Ekaningrum and Setiawan, 2020). However, the presence of these cations in the soil solution can have different effects on the diffusion coefficient (Da) of cesium-137 through soil, depending on their concentrations and chemical properties.

The presence of other ions or salts such as Mg, Na, Li and K also affects the ¹³⁷Cs⁺ adsorption due to the inherent competition between them. Cations like Na⁺ and K⁺ can increase the mobility of cesium-137 in the soil solution, and therefore may increase the effective diffusion coefficient because in the presence of other salts in the aqueous medium such as Na⁺ and K⁺ can cause low sorption efficiency (Rauwel and Erwan Rauwel, 2019). These cations increase the electrical conductivity of the soil solution, which enhances the diffusion of ions through the soil by reducing the electrical resistance of the soil solution. Three main mechanisms governed the ¹³⁷Cs⁺ ion exchange according to them, with the ¹³⁷Cs⁺-K⁺ ion exchanges being predominant, as also stipulated by other research group(Takahashi et al., 2018). For low K⁺ incorporation in the structure, proton exchange between ¹³⁷Cs⁺ and K⁺ ions was evidenced (Rauwel and Erwan Rauwel, 2019).

Additionally, the presence of other cations may also affect the physical properties of the soil, such as its porosity and water content, which can also impact the diffusion coefficient of cesium-137 through soil. Cations like Ca²⁺, Mg²⁺, and Fe³⁺ can form strong complexes with cesium-137, reducing its mobility in the soil solution and decreasing the effective diffusion coefficient. These cations can also compete with cesium-137 for binding sites on soil particles, reducing the overall concentration of available cesium in the soil solution and limiting its diffusion through the soil. We can see the cation exchange plays an important role in the transport of Cs-137 in soil, and that a better understanding of this process is essential for effective soil remediation strategies. However, the impact of other cations on the diffusion coefficient of cesium-137 through soil is complex and is dependent on a number of factors including the concentration and chemical properties of the cations, as well as the physical properties of the soil.

Other study that can support the presence of certain cations may increase diffusion is the case of electrostatic field originating from the surface charges of soil particles exerts a substantial influence on ion adsorption and diffusion in soil (Li et al., 2010; Xiong and Jivkov, 2018) as illustrated in Fig. 8. This effect can occur when charged ions diffuse through a soil matrix that contains other charged ions. Electric double layer (EDL) arises from the screening of the negative surface charge of clay minerals by accumulating cations. The other ions in the soil can help to screen the electrostatic interactions between the diffusing ion and the charged soil particles, reducing the effective attraction or repulsion that would normally slow down or speed up the diffusion process. In this case, the diffusion coefficient of the ion of interest may increase.

As we can also see from Table 5 earlier, the value of Da in our Bentonite is smaller than the ones in soil samples indicating the cation exchange capacity (CEC) of bentonite is much larger than soil. Bentonite is a type of clay that has a very high surface area (Uddin, 2008) and a net negative charge, which allows it to attract and hold positively charged ions in its structure. This high CEC makes bentonite an effective material for various applications including a barrier for nuclear waste disposal while for CEC in soils it may vary in each location. Unfortunately, in this study the CEC measurement has not been carried out so that CEC data of our samples cannot be analyzed and compared between samples.

It is important to consider the influence of other cations in the saturation media when conducting diffusion experiments in soil. This can help in understanding the diffusion behavior of the test substance in a more realistic scenario, where the soil is exposed to various cations that are commonly found in the environment. However, it is important to note that the specific composition of soil and materials used in our study may have contributed to variations in our results compared to previous research. Further investigation into the impact of exchangeable cations on cesium-137 diffusion in different soil types and materials is necessary to fully understand this phenomenon.

In conclusion, the density of the soil or medium through which cesium-137 is moving can have a significant impact on its diffusion coefficient. As the density of the soil or medium increases, the diffusion coefficient of cesium-137 decreases, resulting in slower diffusion through denser soils or media. This relationship between density and diffusion coefficient has been observed in various studies and should be taken into consideration when assessing the transport of cesium-137 through soils and other porous media. In the other hand, the diffusion coefficient of cesium-137 is not significantly impacted by the length of diffusion time in a system with specific conditions, resulting in a constant velocity of Cs-137 through the diffusion column. This may be due to a combination of factors, including the long half-life of cesium-137, the stability of soil properties over time, and the properties of the cesium-137 ions themselves. Also, the addition of groundwater saturation that contains cations is found to impact the diffusion coefficient of cesium-137. The impact of cations on the diffusion coefficient of other ions or molecules can be complex and depend on many factors. As an impact, it increases Cs-137 mobility and its diffusion coefficient competing with other cations for adsorption sites and affecting the soil structure and porosity. By understanding how the presence of other cations can influence the diffusion behavior of cesium-137 can aid in developing more accurate models to predict the migration of this radioactive isotope in the environment.

Data Availability

Not applicable.

Acknowledgments

We would like to thank the Research Center of Nuclear Fuel Cycle and Radioactive Waste Technology - National Research and Innovation Agency of Indonesia for giving us privilege to use the facilitation in the institution during our research experiment so that we are able to finish this study.

Funding

Financial support for this research was provided by the National Research and Innovation Agency of Indonesia (Grant ID: Research Organization for Nuclear Energy FY 2023)

Contributions

Sufi Adzkia Salma: laboratory experiment and writing—original draft preparation; Nurul Efri Ekaningrum: laboratory experiment, mathematical model and methodology; Hendra Adhi Pratama: project administration, visualization, writing—review and editing; Budi Setiawan: conceptualization, laboratory experiment supervisor, methodology, visualization, writing—review and editing. All authors reviewed the manuscript.

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All authors have read, understood, and have complied as applicable with the statement on “Ethical responsibilities of Authors” as found in the Instructions for Authors and are aware that with minor exceptions, no changes can be made to authorship once the paper is submitted.

Ethics approval

Not applicable.

Competing interests

The authors declare no competing interests.

Suplementary Information

Suplementary materials have been submitted.

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Diffusion Capability of Cs-137 in Compacted Soil and Bentonite Under Groundwater-saturated Condition

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