A Study on Long-Term Retardation Effect of Integrated Buffer Materials Based on Bentonite on Uranium

Abstract

Buffer material has been shown to be effective over the long term for radionuclide diffusion retardation and is used as the final artificial barrier of the multi-barrier system in the high-level waste disposal repository. The method of disposal raises the possibility of radionuclides escaping and returning to the biosphere when ground water enters the natural geological barrier, risking the repository’s long-term stability and safety. Bentonite was chosen as the basic material in the integrated buffer material due to its low permeability, high swelling, and self-healing ability. Meanwhile, attapulgite served as an auxiliary, and pyrite served as a mineral additive. The buffer material B₇AP was created by combining three materials, namely bentonite, attapulgite, and pyrite, with a mass ratio of 63:27:10. The diffusion of uranium in samples with a dry density of 1.70 g/cm³ was studied using a constant source diffusion experiment. The results showed that the B₇AP buffer material had a good uranium retardation effect, with an apparent diffusion coefficient of 4.07 × 10⁻¹² m²/s. In addition, using the theory of porous media contaminant migration, a simplified convection-dispersion-adsorption equation for uranium migration on integrated buffer material B₇AP was established. MATLAB software was used to simulate time scales, seepage velocity, apparent diffusion coefficient, and retardation factor. The current study provides scientific evidence for improving retardation performance, screening, and optimizing the formula design of radioactive waste repository buffer materials.

1. Introduction

The widespread use of nuclear technology in national defense, industry, agriculture, healthcare, and scientific research is linked to a nuclear fuel cycle, which includes the “beginning” (uranium mining, extraction, refining, conversion, enrichment, and fabrication of spherical fuel, etc.), “intermediate links” (the radionuclides produced by fission during the reactor’s operational process), and the “end” (treatment and disposal of spent fuels and radioactive waste). Particularly toward the end of the 1980s, China’s nuclear industry began to adjust to this cycle on a large scale in terms of scientific research and production capacity. Early military nuclear facilities were extended or suspended, and many of them were decommissioned with large amounts of high-level radioactive waste. These high-level radioactive wastes exist mainly as two forms; one refers to the waste liquid from the disposal of nuclear fuel, and the other refers to the waste from the vitrification of liquid high-level radioactive nuclear waste. Their fission products usually consist of ⁹⁰Sr and ¹³⁷Cs, unrecovered Pu and U, and most of the transuranic elements [1,2,3]. Unlike waste from other industrial sectors, radioactive waste, particularly high-level waste, is distinguished by high radioactivity and toxicity, a long half-life period, a high heat emission, and disposal difficulties. It will pose a serious threat to the environment and human health once it enters the biosphere. As a result, the problem of how to dispose of these radioactive wastes in the long run and isolate them from our environment is difficult in the nuclear industry’s sustainable development.

Deep geological disposal is currently the only accepted and feasible method for the safe disposal of high-level radioactive waste [4,5,6]. Deep geological disposal is a effective strategy in which high-level radioactive waste is solidified and then buried deep underground. The “multi-barrier” system is the basis of the concept of “high level radioactive waste repository”, from inside to outside, which needs to be built before deep geological disposal. From inside to outside, the “multi-barrier” systems include: waste packaging (a glass matrix) → a stainless-steel canister → buffer material → surrounding host rock. The waste packaging is contained within a stainless-steel canister, and the overpack is surrounded and supported by a buffer material within a cavity in the host rock. The waste packaging and buffer material are buried 300–1000 m underground, with natural rock mass acting as a geological barrier. It can be seen that deep geological disposal of high-level radioactive waste aims to solidify and retard the nuclide through the use of multiple barriers. It is a systematic project of deposit repository that protects humans and the environment over a time scale of 1000~10,000 years. As a filling material between the waste canister and the host rock, the buffer material is the most important encapsulating device for retardation and prevention of migration of radionuclides to the groundwater environment, and also is the last engineering barrier to prevent nuclides from entering the biosphere. As a result, the buffer material is critical to the safety of a nuclear waste repository. After conducting numerous relevant experimental studies and comparative analyses, Pusch [7] concluded that bentonite with montmorillonite as the main component is the best buffer material for deep geological disposal of high-level radioactive waste.

However, while pure bentonite meets the basic requirements of adsorption and impermeability for the geological disposal of high-level radioactive waste, it cannot overcome the low thermal conductivity of pure bentonite and un-even compaction caused by agglomeration after humidification. To address this issue, various studies have been conducted by adding quartz sand, graphite, zeolite, kaolin, and other materials to the main material of bentonite [8,9], with the most common method being to supplement 10%–30% of quartz sand. However, the overall water-blocking performance and adsorption of the mixed sand-bentonite buffer material were lower when compared to pure bentonite [10,11,12,13,14,15,16,17,18,19,20]. Our preliminary studies revealed that the permeability, swelling, compacting behavior, and thermal conductivity of the integrated buffer material containing 63%–72% bentonite from Xinjiang province of China (abbreviated as B), 18%–27% attapulgite from Mingguang district in Anhui province of China (abbreviated as A), and 10% pyrite from Jiangyou district in Sichuan province (abbreviated as P) met the engineering performance requirements of artificial geochemical barriers in high-level radioactive waste disposal repositories [21,22]. The long-term retardation effect of B₇AP (the mass ratio of B:A:P equals 63:27:10) on uranium was studied in this paper by studying the adsorption, the migration and diffusion of the nuclide in the integrated buffer material. A radionuclide retardation model was developed, and the effects of different time scales, retardation coefficients, diffusion coefficients, and seepage velocity on the migration of uranium in the integrated buffer material were predicted using MATLAB numerical simulation software. The current study has a high reference value for better understanding retardation performance and buffer material optimization, which is critical for the long-term security of deep geological disposal of high-level radioactive waste.

2. Materials and Methods

2.1. Materials

All chemicals used in the experiments were purchased as analytical purity and used without further purification. In all experiments, Milli-Q water was used. U (VI) stock solution was made by dissolving weighed amounts of uranyl nitrate in Milli-Q water. The concentrations of U (VI) were determined using an ultraviolet pulse trace uranium analyzer (WGJ-III, China). The integrated buffer materials contained substrate minerals, auxiliary minerals, and mineral additive.

Substrate minerals: natural sodium bentonite (Altay, Xinjiang, China) is a mineral composed of layered hydrous aluminosilicate. It is mainly composed of montmorillonite, and α-cristobalite, feldspar, limonite, illite as the secondary components. Montmorillonite content is 76.67%.

Auxiliary minerals: attapulgite (Mingguang, Anhui, China) is a kind of layered-chain structure clay mineral of hydro-rich magnesium aluminum silicate with special fiber structure, large specific surface, permanent negative charge and multiple adsorption centres its surface. The main mineral composition is attapulgite, followed by montmorillonite, opal, dolomite, calcite, and a small amount of quartz and chlorite.

Mineral additive: pyrite (FeS₂, Jiangyou, Sichuan, China) contains a high concentration of pyrite as well as small amounts of quartz and dolomite. Pyrite is the most common and stable sulphide mineral in nature, with reductive Fe²⁺ and S₂²⁻. Furthermore, S₂²⁻ is more reductive than Fe²⁺. Pyrite can inhibit the migration of multivalent nuclides that are easily transportable via adsorption and restoration [23,24,25,26,27,28]. As a result, pyrite, as an additive to the integrated buffer material, can both create a restoring environment for the disposal repository’s near field and improve the buffer material’s thermal conductivity.

After drying at 105 °C for 4 h, the minerals were ground to 200 meshes and sealed for later use.

2.2. Constant Source Diffusion Experimental Procedure

The radionuclide uranium diffusion experiments were conducted using a small self-designed and processed constant source diffusion experimental device (Figure 1). The volume of the original liquid pool is V₁ = 710 cm³, and the volume of the sampling pool is V₂ = 110 cm³. Bentonite, attapulgite, and pyrite with a hydro content of 15% and a mass ratio of 63:27:10 were mixed and moistened for 48 h before being placed on a pressure test machine. The load was gradually applied to 50 MPa at a rate of 2 kN/s and then saturated for 10 min. The obtained sample was a buffer material diffuser with diameter of Φ = 50 mm, thickness of h = 5 mm and dry density of ρ_d = 1.70 g/cm³ (dry density is the ratio of solid particles to the total volume of the material when there is no water in the material void). This was installed between the source liquid pool and the sampling pool. To prevent the sample from cracking in water, a 400-mesh stainless steel web was attached to both sides of the sample, and the fixing bolts were tightened after installation. After filling the original liquid pool with distilled water, a vacuum pump was used to vacuum the diffusion sheet on the sampling poolside, and the vacuum was turned off when the water on the sampling poolside began to ooze steadily. The original liquid pool’s distilled water was poured out, and a radionuclide uranium solution (75 mg/L) was added. The pH of the solution was brought back to neutral. The diffusion pool was adjusted to leverage with the same liquid level on both sides while the sampling pool was filled with distilled water and tightly sealed. At regular intervals, 1.0 mL of the solution from the sampling pool was drawn. To avoid the interference of the liquid height gap on both sides after sampling, the same volume of distilled water was quickly added to the sampling pool. A single-dimensional diffusion equation (Equation (1)) was obtained using Diffusion Theory, Fick’s Second Law, and Constant Source Diffusion Method Boundary Conditions. The C/C₀-t relationship curve was drawn according to the concentration of radionuclide solution in the sampling pool at different time points, then the values of De and α can be obtained from the slope k and intercept tg of the straight line segment in the C/C₀-t curve, and the values of De and α are calculated using Equations (2) and (3) [21,22].

$$\frac{C(L,t)}{C_0}=\frac{A{D}_{e}t}{LV}-\frac{\alpha AL}{6V}$$

(1)

$$k=\frac{A{D}_e}{LV}$$

(2)

$$t_g=\frac{L^2}{6D_a}$$

(3)

where D_a (m² × s⁻¹) is the apparent diffusion coefficient and calculated from D_a = D_e/α, α is the capacity factor of diffusion sheet and calculated from α = e + ρ_dK_d, De (m²/s) is the internal diffusion coefficient independent of distance x, K_d (mL/g) is the adsorption partition coefficient, e is the void ratio, ρ_d (g/cm³) is the sample dry density, V (m³) is the volume of sampling pool, A (m²) is the diffusion cross-sectional area, L (m) is the thickness of diffusion sheet, C₀ (mg/L) is the concentration of nuclides in the original liquid pool, t (s) is the breakthrough time.

2.3. Evaluation of Long-Term Retardation Effect of B₇AP Integrated Buffer Material to U

If the deposit canister breaks in the multi-barrier design of deep geological repositories, the buffer materials can prevent or slow radionuclide migration to the host rock and the biosphere. As a consequence, it is critical to investigate the retardation characteristics of radionuclides in buffer material for the long-term safety of deep geological repositories for high-level radioactive waste.

As a result, an understanding of the processes affecting radionuclide migration in compacted buffer materials (such as compacted bentonite) is critical for assessing the safety of geological disposal of high-level radioactive waste (HLW). The migration of radionuclides in compacted buffer materials, in particular, can be influenced by two important processes that occur on the buffer materials: sorption and diffusion. Many studies have been conducted on the sorption and diffusion of radionuclides in compacted bentonite or other types of buffer materials [29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51]. The majority of the diffusion tests were carried out using the in-diffusion, through-diffusion, back-to-back diffusion, reservoir-depletion method, capillary method, or flow-through migration, and were primarily concerned with the effect of dry density, sand ratio, solution concentration, ionic strength, pH, humic acid, or temperature on the apparent diffusion coefficient. The apparent diffusion coefficient D_a is a direct measure of radionuclide mobility in the compacted bentonite buffer, and distribution coefficients (K_d values) and effective or pore diffusivities (D_e or D_p) are typically required as input parameters of the respective transport codes used for performance evaluation calculations. The migration of radionuclide in buffer materials is commonly described by the well-developed convection–dispersion migration model, which is based on Fick’s second law and the mass conservation equation for the solute. Wang [52,53] investigated the effect of dispersion coefficient, distribution coefficient, and pore water velocity on the migration of Eu(III) in compacted bentonite. Zhou [16] demonstrated the migration of Eu(III) in compacted bentonite–sand mixtures with varying sand ratios. However, Wang [35,38,52,54] discovered that the K_d values of radionuclides in compacted and powdered bentonite differ due to differences in bulk density. The K_d values in compacted bentonite derived from capillary experiments are approximately half to one-third that in powdered bentonite derived from batch experiments, and the K_d values derived from batch experiments cannot be used directly to predict radionuclide migration because the value is greater than that in compacted bentonite. Furthermore, the dispersion coefficient (D) is also an important parameter in determining radionuclide migration in compacted buffer materials. Because of the extremely long time spans required for measuring sorbing radionuclides to reach steady state, effective diffusivities (D_e) are frequently used to characterize D and are often derived from measured apparent diffusion coefficient (D_a) or through analogue considerations.

Therefore, the values of the apparent diffusion coefficient, retardation factor, and capacity factor were calculated using the aforementioned constant source experiment and formula, which provided the simulation parameters of the migration process for the convection-diffusion migration model. The long-term security of deep geological disposal of high-level radioactive waste is generally measured on a time scale ranging from 1000 to 10,000 years. So, it is crucial to establish a migration retardation model of radionuclide in buffer materials and to predict the radionuclide process in buffer materials [55]. On this basis, the relationship between migration distance and migration time, retardation factor, apparent diffusion coefficient, and seepage velocity is analyzed to serve as a guide for the design of buffer backfill materials.

The establishment of a migration model of radionuclides in buffer material requires the following assumptions: (1) the buffer material is the homogeneous isotropic material; (2) the adsorption processes of radionuclides on the buffer material are linear isotherm; (3) the buffer material has reached the state of water saturation before the nuclear waste tank corroded or destroyed, and the structure is stable; (4) the migration of the fluid in the buffer material fits the law of Darcy; (5) the radionuclides in the migration process of buffer materials do not destroy the mass of radionuclides due to chemical reaction, and follow the mass conservation; (6) except for the radionuclides leached from the condensates of high-level radioactive waste, there are no other sources. Hence, the concentration of radionuclides in the solid and liquid forms has reached the balance.

The model of ‘‘multi-barrier’’ systems for deep geological disposal of high-level radioactive waste shows that the system is projected longitudinally along the central axis of the engineering barrier system (EBS) to the facade, and the condensates of high-level radioactive waste are surrounded by the buffer material. The migration of radionuclides in the buffer material is analogous to the diffusion of a constant source in the endeavor. The migration of radionuclides in the x-direction has been considered. The radionuclides moved out of the disposal repository at the one-dimensional level in the buffer material. When x = 0, the concentration of released radionuclides was C₀ (as is shown in Figure 2).

According to the transport equation of general pollutants in porous medium [57], the migration and diffusion of radionuclides in buffer material are affected by the interaction between radionuclides and buffer material as well as groundwater hydrodynamics. Therefore, the radionuclides migration mode is a coupling of the radionuclides adsorption and the groundwater hydrodynamics. Therefore, in order to develop a nuclide migration retardation model, the solute convection, hydrodynamic dispersion, radionuclide adsorption, and decay must be considered [50,58]. The radionuclide migration in buffer material is described by the convection-dispersion-adsorption-decay Equation (4):

$$R_d\frac{\partial c}{\partial t}=D_x\frac{{\partial }^{2}c}{\partial x^2}+D_y\frac{{\partial }^{2}c}{\partial y^2}+D_z\frac{{\partial }^{2}c}{\partial z^2}-v_x\frac{\partial c}{\partial x}-v_y\frac{\partial c}{\partial y}-v_z\frac{\partial c}{\partial z}-\lambda R_{d}c$$

(4)

where R_d is the retardation factor; λ = ln2/t is the decay constant of the radionuclides; D is the diffusion coefficient of radionuclides in the buffer material. When the flow velocity is small, D is approach to the apparent diffusion coefficient D_a, m²/a; c is the concentration of radionuclides at any time and any place in the buffer material, mg/L; v is the flow velocity of groundwater in the buffer material, m/a; where v = kI, k is the saturated infiltration coefficient of the compacted buffer material, m/a; I is the hydraulic gradient, which is dimensionless; t is the time during which the nuclide migrates in the buffer material.

Because of the long half-life of uranium (λ = 4.51 × 10⁹ years) [59], the convection-dispersion-adsorption-decay equation of radionuclide migration in the buffer material is simplified by ignoring radionuclide decay. That is, the x-direction migration of radionuclides in saturated buffer material can be depicted in the one-dimensional migration equation to more precisely estimate radionuclide migration. The simplified uranium migration retardation model is shown in Equation (5) [50,53]:

$$R_d\frac{\partial c}{\partial t}=D\frac{{\partial }^{2}c}{\partial x^2}-v\frac{\partial c}{\partial x}$$

(5)

Then, the Equation (5) is performed by the Laplace transform and the inverse transform according to the initial and boundary conditions in the Equation (6) [58,60,61], and the analytical solution of uranium transport equation is shown in Equation (7) [16,52,53,62]:

$$\begin{array}{l}c(x\ge 0,t=0)=0\\ c(x=0,t>0)=c_0\\ c(x=\infty ,t>0)=0\end{array}$$

(6)

$$\stackrel{-}{c}(x,t)=\frac{c(x,t)}{c_0}=\frac{1}{2}\left[erfc\left(\frac{x-\frac{vt}{R_d}}{2\sqrt{\frac{D_{a}t}{R_d}}}\right)+\exp \left(\frac{vx}{D_a}\right)erfc\left(\frac{x+\frac{vt}{R_d}}{2\sqrt{\frac{D_{a}t}{R_d}}}\right)\right]$$

(7)

In this equation, $\stackrel{-}{c}(x,t)=\frac{c(x,t)}{c_0}$ is the ratio of the radionuclides concentration to the initial concentration at any time and any cross section, which is the relative concentration; x is the distance from the radionuclides pollution, m; c₀ is the concentration of the radionuclides pollutant, mg/L. $R_d=1+\frac{(1-n){\rho }_d{K}_d}{n}=1+\frac{{\rho }_d{K}_d}{e}=\frac{\alpha }{e}$ is the retardation factor to buffer materials, which is dimensionless. ρ_d is the dry density of the compacted buffer material, g/cm³. n is the effective porosity of the compacted buffer material; e is the effective void ratio of the e-compacted buffer material; α is the capacity factor of the buffer material; K_d is the partition coefficient of the radionuclides in the buffer material, mL/g; erfc(x) is the residual error function.

In order to more intuitively show the migration behavior of radionuclide uranium in the integrated buffer material, MATLAB software was used to simulate and analyze the migration behavior of radionuclide in the buffer materials. MATLAB is a high-performance scientific computing software produced by MathWorks. It is not only an intuitive and efficient computer language, but also a scientific computing platform, which can provide important mathematical and graphical tools for data analysis and visualization, algorithm and application development. Moreover, users only need to simply list mathematical expressions, and the results can be displayed numerically and graphically. Therefore, the radionuclide uranium migration in buffer material is described by Equation (7) of the analytical solution of uranium transport equation, and by writing the source code of uranium migration in the command window of MATLAB software, the migration distance of uranium can be intuitively displayed for buffer materials under the conditions of different time scales. The software can also simulated and analyze the influence of different retardation coefficients, diffusion coefficients and percolation speeds on the degree of uranium migration. The results provide technical methods and a scientific basis for the study of uranium migration and the design of buffer materials. The source code for the numerical simulation of nuclide uranium migration in the MATLAB software is detailed in Appendix A.

3. Results and Discussion

3.1. Migration and Diffusion Characteristics of Uranium in Integrated Buffer Material (B₇AP)

According to the constant source diffusion method, the concentration changes of nuclide solution in the sampling pool at different time points were analyzed. The migration -diffusion curves of radionuclide in buffer materials were obtained by plotting the relative concentration (C/C₀) against time (t) (as shown in Figure 3a), and the intercept t_g and slope k are obtained by extending the straight section of the diffusion curve to the time axis (as shown in Figure 3b). The diffusion parameters of radionuclides such as D_e, D_a and α in buffer materials can be obtained using Equations (1) and (2). As shown in

Table 1. Diffusion experimental results of uranium on B₇AP integrated buffer material.

Sample	Nuclide	C0/(mg·L−1)	ρd/(g·cm−3)	k/d−1	tg/d	De/(m2·s−1)	α	Da/(m2·s−1)
B7AP	uranium	75	1.70	0.0014	11.86	4.54 × 10−12	1.116	4.1 × 10−12

, the apparent diffusion coefficient of B₇AP integrated buffer was 4.07 × 10⁻¹² m²/s when the concentration of uranium is 75 mg/L and the dry density of B₇AP integrated buffer is 1.70 g/cm³ by using the constant source diffusion experimental device.

Muurinen [63] used the diffusion pool method to determine the apparent diffusion coefficient of uranium in US MX-80 sodium bentonite with a dry density of 0.6–1.6 g/cm³, and the results confirmed that the D_a value ranged from 8.4 × 10⁻¹³ to 4.8 × 10⁻¹² m²/s. Idemitsu [64] used a back-to-back diffusion method to investigate the migration and diffusion of uranium in Japanese Kunigel Vl compacted sodium bentonite with a dry density of 0.8–2.0 g/cm³. Under oxidation conditions, the D_a value was in the range 10⁻¹²~10⁻¹³ m²/s. García-Gutiérrez [65] demonstrated that the apparent diffusion coefficient of uranium in Spanish FEBEX bentonite with a dry density of 1.65 g/cm³ was 4 × 10⁻¹⁴ m²/s < D_a < 1 × 10⁻¹³ m²/s using the constant source diffusion pool method. Korichi [66] used a constant source diffusion experiment to investigate the migration and diffusion of uranium in Algerian bentonite and NaCl activated bentonite. The results showed that when the dry density of compacted samples was 1.4, 1.8, and 2.4 g/cm³, the apparent diffusion coefficient varied from 1.1 × 10⁻¹² m²/s < D_a < 5.5 × 10⁻¹² m²/s and 3.6 × 10⁻¹³ m²/s < D_a < 8.3 × 10⁻¹³ m²/s. According to Bai [67], the D_a values of uranium diffusing in silt/clay mixtures ranged from 1.60 to 1.70 × 10⁻¹⁰ m²/s, based on the second law of Fick and the concentration profiles of uranium obtained by diffusion tests with non-stationary mode. Due to the similar ionic radius and properties, the chemical behavior of REEs resembles that of radionuclides, and some REEs have been used as chemical analogues of radio-nuclides. Kasar [44] used the out-diffusion method to determine the D_a of Eu(III) in smectite rich natural clay, and the D_a value of ¹⁵⁴Eu in the smectite rich natural clay at dry density 1.6 g/cm³ was found to be 1.23 (±0.15) × 10⁻¹³ m²/s. Wang [35] used the ‘in-diffusion’ method to study the diffusion behavior of Eu(III) in compacted MX-80 bentonite, and the results showed that the D_a values of Eu(III) on the compacted bentonite decreased from 2.8 × 10⁻¹² m²/s to about 1.0 × 10⁻¹² m²/s when the Eu(III) concentration decreased from 10⁻³ mol/L to about 10⁻⁷ mol/L, and the compacted MX-80 bentonite with dry density of 1.00 g/cm³ and 1.15 g/cm³. García-Gutiérrez [42] applied the ‘‘instantaneous planar source’’ method to obtain the estimation apparent diffusion coefficient of ¹⁵²Eu in compacted FEBEX bentonite. The result showed that the ranges of D_a values obtained from these experiments in the FEBEX clay compacted at 1.65 g/cm³ were (0.8–2.5) × 10⁻¹⁴ m²/s for Eu. Chen [20,45] observed the diffusion coefficients of La³⁺ at different dry densities and pH levels. Results showed that the apparent diffusion coefficients of La³⁺ decreased as the dry density (1.3–1.7 g/cm³) and the pH (3.6–8.9) of GMZ bentonite increased, and the D_a varied from 2 × 10⁻¹² m²/s to 16 × 10⁻¹² m²/s.

Our previous research [21,22] compared the adsorption properties of Xinjiang bentonite (B), Xinjiang zeolite (Z), Anhui Mingguang attapulgite (A), and Sichuan Jiangyou pyrite (P) for uranium. On this basis, four types of mixture buffer materials (B-Z, B-Z-P, B-A, and B-A-P) were prepared using Xinjiang bentonite as the principal material, zeolite and attapulgite as auxiliary materials, and pyrite as an additive, and the adsorption performance and diffusion characteristics of uranium in the mixture buffer materials were compared and analyzed. The results showed that the adsorption performance of B-A-P type mixture buffer materials for radionuclide uranium was superior to pure bentonite and the other three types of integrated buffer materials (B-Z, B-Z-P, B-A). Furthermore, uranium in B₇AP mixture buffer materials (the mass ratio of B:A:P equals 63:27:10) had the lowest apparent diffusion coefficient D_a = 4.07 × 10⁻¹² m²/s. In conclusion, comparing the studies of other researchers on the apparent diffusion coefficient of uranium in mixed buffer materials, it can be concluded that B₇AP has a better barrier effect on uranium than pure bentonite and other types of buffer materials, and can be one of the alternatives of buffer materials for deep geological disposal of high-level radioactive waste.

3.2. Prediction of Uranium Migration Degree in Integrated Buffer Material (B₇AP) of Different Time Scales, Retardation Factors, Diffusion Coefficients and Seepage Velocity

Based on the experimental results of B₇AP integrated buffer material diffusion presented in Section 3.1 and the saturated infiltration coefficient of B₇AP integrated buffer material obtained by experimental research on the permeability of the buffer material from our previous research [21,22,68,69,70,71], the migration retardation numerical simulation parameters of uranium in the B₇AP buffer material are presented in

Table 2. Diffusion coefficient of uranium in integrated buffer material (B₇AP).

Sample	Nuclide	C0/(mg·L−1)	ρd/(g·cm−3)	v/(m·a−1)	k/(m·s−1)	e	Da (m2·a−1)	α	Rd
B7AP	Uranium	75	1.70	3.15 × 10−5	1.0 × 10−12	0.32	1.29 × 10−4	1.116	3.49

. In addition, the analytical solution (Equation (7)) is derived from the simplified radionuclide migration retardation model (Equation (5)). The uranium migration in the buffer material was numerically simulated using MATLAB. Meanwhile, the migration of uranium through different time scales, retardation factors, diffusion coefficients, and seepage velocity after pollutant release was studied, and the results provided a scientific foundation for the design of buffer materials for high-level waste repositories.

3.2.1. Prediction of Uranium Migration Degree in Integrated Buffer Material (B₇AP) of Different Time Scales

In order to determine the migration distance of uranium in the B₇AP integrated buffer material after the release of pollutants in 100 a, 300 a, 1000 a, 5000 a and 10,000 a (years), the diffusion of uranium in the B₇AP integrated buffer material was simulated numerically using the migration parameters listed in Table 2, and the results are presented in Figure 4 As shown, the migration distances of uranium in B₇AP integrated buffer material are 0.25 m, 0.8 m, and 3.0 m after 100 a, 1000 a, and 10,000 a, respectively. Therefore, if the thickness of the B₇AP integrated buffer material is set to 0.8 m, uranium will almost certainly not migrate out of the buffer material within 1000 a. Since high level waste is a unique type of waste, the high level radioactive waste disposal repository must not be invalidated within 10,000 a. When the thickness of the B₇AP integrated buffer material is set to 3.0 m, the high-level radioactive waste disposal repository can operate effectively without migration into the groundwater from the surrounding rock. Wang [36] simulated and analyzed the migration distance of uranium in the MX-80 bentonite of compacted dry density (ρ_d = 1.0 g/cm³) and apparent diffusion coefficient (D_a = 1.7 × 10⁻¹² m²/s) at different time scales (100 a, 1000 a, 10,000 a and 100,000 a). The results showed that uranium migrated 0.66 m after 100 a, 2.1 m after 1000 a, 6.6 m after 10,000 a, and 21 m after 100,000 a. Moreover, several diffusion tests have been performed to investigate the effect of dry density on radionuclide diffusion [20,31,42,72]. Dry density is one of the important factors influencing the diffusion behavior of radionuclides in compacted bentonite [32,73]. Lee et al. [31] performed through-diffusion tests on Sr-90 in a local Korean bentonite and reported that its apparent diffusion coefficients (D_a) decreased from 1.41 × 10⁻¹² to 1.2 × 10⁻¹² m²/s with increase in dry density from 1.0 to 1.7 g/cm³. Wu et al. [72] investigated the diffusion behavior of Se(IV) and Re(VII) in GaoMiaoZi (GMZ) bentonite using the through diffusion method and found that the D_a values of HSeO³⁻ and ReO⁴⁻ were (7.8–0.7) × 10⁻¹¹ m²/s and (19–2.1) × 10⁻¹¹ m²/s, respectively, at dry density ranging from 1.3 to 1.8 g/cm³. Chen [20] carried out diffusion experiments of La(III) in compacted GaoMiaoZi (GMZ) bentonite by using the indiffusion method, and the experimental results shown that a general trend of decreasing D_a values with increasing dry density of compacted bentonite can be noted; when dry density increases from 1.3 to 1.7 g/cm³, the D_a value for La(III) decreases from 1.58 × 10⁻¹¹ m²/s to 2.7 × 10⁻¹² m²/s. In comparison, the B₇AP integrated buffer material still has good blocking properties for uranium, inhibiting its migration behavior and reducing the ability of uranium to migrate and release in the environment.

3.2.2. Simulation of the Effect of Seepage Velocity on Uranium Migration

With the passage of time and the effect of groundwater seepage, the buffer material gradually reaches saturation. If the overpack fails, radionuclides are released and come into contact with groundwater, where they migrate to the surrounding rock and biosphere. A buffer material with high impermeability can effectively prevent radionuclide migration into the environment. Thus, the saturation permeability of buffer material is an important indicator of the buffer material’s barrier function. The IAEA recommended that the permeability coefficients of the compact buffer material used in deep geological disposal of radioactive waste should be less than 1 × 10⁻¹⁰ m/s [74]. Therefore, as the seepage velocity has a direct influence on the migration of radionuclide in the buffer material, it is necessary to explore the sensitivity of uranium migration to the seepage velocity in the buffer material.

With B₇AP as the object, simulation analysis was made under different seepage velocity conditions (v₁ = 3.15 × 10⁻⁶ m/a, v₂ = 3.15 × 10⁻⁵ m/a, v₃ = 6.30 × 10⁻⁵ m/a, v₄ = 3.15 × 10⁻⁴ m/a, v₅ = 6.30 × 10⁻⁴ m/a, v₆ = 3.15 × 10⁻³ m/a, v₇ = 6.30 × 10⁻³ m/a). The numerical simulation parameters were as follows: retardation factor R_d = 3.49, apparent diffusion coefficient D_a = 1.29 × 10⁻⁴ m/a, and migration time t = 1000 a to 10,000 a. As shown in the simulation results (Figure 5 and Figure 6), when the seepage velocity is (v) ≤ 10⁻⁴ m/a, the migration distance curves 1, 2, 3, 4, and 5 are relatively close to each other, and the migration distance of uranium in B₇AP varies little with the increase or decrease of the seepage velocity over time scales of 1000 a and 10,000 a (Figure 5 and Figure 6). A buffer material thickness of 1.0 m can ensure that uranium does not enter the repository’s surrounding rock after 1000 a. If the buffer material thickness is set to 4.0 m, the uranium can be effectively blocked in the buffer material for 10,000 a. When the percolation velocity v ≥ 10⁻³ m/a, the distance between migration curves 6 and 7 gradually increases, and the migration distance of uranium in the B₇AP increases exponentially as the percolation velocity increases on the 1000 a and 10,000 a time scales. To ensure that uranium does not migrate into the surrounding rock groundwater of the repository, the effect of seepage velocity on migration distance must be taken into account when determining the thickness of the buffer material, so as to prevent the diffusion of nuclide into the surrounding rock groundwater due to insufficient buffer material thickness. As a result, when the seepage velocity v is ≤10⁻⁴ m/a, the uranium migration degree is less sensitive, while when the seepage velocity is v ≥ 10⁻³ m/a, the uranium migration degree is more sensitive to the seepage velocity and the response speed is fast. Therefore, in the screening study of buffer materials, it is of little significance to improve the retardation of buffer material only from the perspective of reducing the permeability coefficient of buffer material, because the saturation permeability coefficient of buffer material k ≤ 10⁻¹¹ m/s can meet the demand of impermeability.

3.2.3. Simulation Analysis of the Uranium Migration Affected by Apparent Diffusion Coefficient

The apparent diffusion coefficient is one of the most important parameters to evaluate radionuclide migration behavior in buffer material [39], and it can be used to analyze the response characteristics of uranium migration in buffer material. The migration degree of uranium in buffer material B₇AP was investigated using various simulated apparent diffusion coefficients (D_a1 = 1.29 × 10⁻⁵ m²/a; D_a2 = 1.29 × 10⁻⁴ m²/a; D_a3 = 2.58 × 10⁻⁴ m²/a; D_a4 = 1.29 × 10⁻³ m²/a; D_a5 = 2.58 × 10⁻³ m²/a). The numerical simulation parameters were as follows: retardation factor R_d = 3.49, seepage velocity v = 3.15 × 10⁻⁵ m/a, and migration time t = 1000 a to 10,000 a.

According to the simulation results (Figure 7 and Figure 8), the migration distance of uranium in the buffer material increased as the apparent diffusion coefficient increased. When the apparent coefficient D_a was increased by one order of magnitude, 5 times, and 2 times, the migration distance of uranium in the buffer material increased by about 3 times, 2 times, and 1.5 times, respectively. The results showed that the apparent diffusion coefficient change had a large influence on the degree of nuclide migration, and the migration degree of nuclides in the buffer material responded quickly to the apparent diffusion coefficient change. Based on the effect of seepage velocity, the apparent diffusion coefficient is one of the important factors influencing the degree of nuclide migration, which is consistent with the conclusion from Zhou [16] and Wang [22] that the apparent diffusion coefficient is the major factor influencing the migration behavior of nuclides in geological medium. As a result, the effect of apparent diffusion coefficient on uranium migration should be fully considered in buffer material formulation screening and thickness setting. Furthermore, it is preferable to improve uranium retardation by lowering the apparent diffusion coefficient of uranium in the buffer material rather than lowering the permeability coefficient of the buffer material.

3.2.4. Simulation Analysis of the Uranium Migration Affected by the Retardation Factor

The buffer material acts as a reactive barrier to radionuclide immobilization in the process of radionuclide migration with groundwater in the disposal repository. As a result, radionuclide travels at a slower rate than groundwater, and the retardation factor is a quantitative parameter used to characterize the radionuclide retardation ability of buffer materials to radionuclide. The response characteristics of uranium in buffer materials at different retardation factors were analyzed as the different retardation effects of the buffer material to the nuclides, and the correlation between retarding factors and uranium migration degree was also discovered.

The different migration degrees of uranium in buffer materials B₇AP with different retardation factors (R_d) were simulated and analyzed (R_d1 = 1.00, R_d2 = 1.75, R_d3 = 3.49, R_d4 = 6.98 and R_d5 = 13.96). The parameters were set as follows respectively, D_a = 1.29 × 10⁻⁴ m²/a, percolation velocity v = 3.15 × 10⁻⁵ m/a, migration time t = 1000 a and 10,000 a.

As shown by the numerical simulation results (Figure 9 and Figure 10), the migration of uranium in the buffer material decreased as the retardation factor increased. The migration distance of nuclides uranium in the buffer materials shrank by 1.5 times when the retardation factor R_d was increased by twofold, indicating that the retardation factor was an important factor influencing nuclide migration. Similarly, when compared to the effect of seepage velocity on radionuclide migration degree, the retardation factor has a significant effect on radionuclide uranium migration degree in the buffer material. Similar retardation effects in buffer material have been reported. For example, Xie [75] used the PHREEQC-II to simulate the influence of retardation factor on nuclide migration distance in compacted sodium bentonite and shallow groundwater, and Wang [22] used MATLAB software to analyze the long-term retardation performance of integrated buffer material B₇AP on simulated nuclide strontium under different retardation factors.

4. Conclusions

The constant source diffusion experiment was used in the study to analyze the diffusion of the buffer material B₇AP, and the apparent diffusion coefficient was 4.07 × 10⁻¹² m²/s. Furthermore, Liu [76] and Wang [21] investigated that the equilibrium adsorption capacity of BAP type integrated buffer material and pure bentonite from Xinjiang for uranium was 24 mg/g and 19.6 mg/g, respectively, which indicating that B₇AP has better retardation performance than pure bentonite from Xinjiang. The convection-dispersion-sorption-decay equation was developed based on the theory of porous-media pollutant migration, solute convection and hydrodynamic dispersion of groundwater, as well as nuclide adsorption and decay. In the absence of nuclide decay, the convection-dispersion-sorption-decay equation of uranium migrating in the buffer material was simplified to a one-dimensional migrating and retarding equation to the x direction of nuclides in saturated buffer materials, allowing a more precise estimate of nuclide migration. According to the one-dimensional numerical model of nuclides migrating and retarding the buffer material, and the analytical solution obtained from the Laplace Transform, this research used MATLAB to simulate the effects on nuclides migration distance imposed by different time scales, seepage velocity, apparent diffusion coefficients and retardation factors after pollutants release. The results showed that when the seepage velocity was v ≤ 10⁻⁴ m/a, the major factors restricting the uranium migration were apparent diffusion coefficients and retardation factors. The migration distance of uranium increased with the apparent diffusion coefficient, and was decreased by increased retardation factors. When the seepage velocity is v ≥ 10⁻³ m/a, the effects of apparent diffusion coefficients, retardation factors and seepage velocity on uranium migrating in B₇AP should all be considered. As a result, the research findings can be used to improve the retardation effect, select appropriate materials, and optimize the design and ingredients of the buffer material.