1. Introduction

Durability is commonly considered to be the most important attribute of nuclear waste forms (WF) [1, 2, 3]. A great deal of effort has been devoted to creating durable waste forms, ranging from borosilicate glasses to crystalline mineral analogues [4, 5], with the assumption that a slow waste form dissolution rate is the most effective means of limiting the release of radionuclides (RN) from a repository to the human accessible environment. This assumption is based on an untested premise that the kinetic dissolution of a primary waste form is the rate-limiting step for radionuclide release. In this short communication, we demonstrate that this may not be the case in an actual repository environment. Once in contact with incoming water, a primary waste form in a repository will eventually degrade into various more stable alteration products (or secondary waste forms). We show that the long-term rate at which radionuclides are released from a repository will be controlled by the solubilities of the alteration products rather than by the dissolution rates of the primary waste forms. Therefore, current requirements for waste form development need to be re-evaluated.

2. Results

Long-term performance assessments (PA) of a geologic repository generally model the degradation of a waste form as a kinetic process, whereas alteration products are assumed to be in chemical equilibrium with the contacting water [6]. Such treatment is referred to as the partial equilibrium approach, which assumes no supersaturation in the system. This approach has been invoked by the IAEA [7] and has been used to assess long-term waste isolation in a geologic repository [8, 9]. This approach seems appropriate, if we look at the dissolution and alteration of natural materials in subsurface environments. We have calculated mineral-saturation indices for groundwater samples collected from Columbia Basin [10], which indicate that a majority of water samples are close to equilibrium with calcite and cristobalite, with little or no oversaturation with other low temperature minerals. This is probably due to the presence of a large number of nucleation and growth sites on mineral surfaces in a rock-weathering system, which effectively lowers the saturation degree for secondary mineral precipitation. As shown in Figure 1, calcium release due to basalt weathering can be very well predicted (within one log unit) by assuming calcite to be the solubility-controlling mineral for dissolved calcium. A similar observation can be made on uranium ore deposits. For example, Lu et al. [11] describes the oxidation of uraninite from a uranium ore deposit in China and the formation of secondary solubility-controlling uranyl-bearing solids.

Based on the assumption of partial equilibrium, in an actual repository environment, waste degradation and radionuclide release can be divided into three stages (Figure 2): Stage I, in which the dissolved concentration of the radionuclide has not reached its solubility limit; Stage II, in which the radionuclide concentration has reached its solubility limit and continues to maintain equilibrium with a solubility-controlling secondary phase; and Stage III, in which the dissolved radionuclide concentration drops rapidly to zero due to the disappearance of both the primary waste form and the solubility-controlling secondary phase. The actual release mode of a radionuclide depends on how fast the repository system can reach Stage II, which is controlled by three factors: (1) the rate of radionuclide release from the waste form, (2) the rate at which water flows through the repository, and (3) the radionuclide’s solubility under repository conditions.

In Stage I, the concentration of a specific radionuclide in a disposal system can be modeled as follows:

$${V_T}\varphi \frac{{dc}}{{dt}} = - \frac{\alpha }{{{m_w}}}\frac{{dM}}{{dt}} - vc\begin{array}{*{20}{c}} {}&{}&{} \end{array}{\rm{for}}\begin{array}{*{20}{c}} {} \end{array}c < {c_{eq}}$$

(1)

$$\frac{{dM}}{{dt}} = - M \cdot A \cdot R$$

(2)

where V_T is the total volume a disposal system (dm³); φ is the porosity in the disposal system after waste emplacement; c is the dissolved concentration of a radionuclide of interest (mol·L⁻¹); t is the time since disposal (s); α is the waste loading factor (g_RN·g_WF⁻¹); m_w is the molecular weight of the radionuclide (g_RN·mol⁻¹); M is the total mass of a waste form in the disposal system (g_eq); v is the rate of water flow percolating through the disposal system (L·s⁻¹); c_w is the solubility of the radionuclide (mol/L); A is the specific surface area of waste form (m²·g_WF⁻¹); and R is the surface-normalized dissolution rate of the waste form (g_WF·m⁻²·s⁻¹). R depends on various factors such as the chemical affinity for waste form dissolution and the coating of alteration products. For simplicity, we assume that the effect of those factors is captured by wide ranges of variability in dissolution rates reported in the literature. In Equation (1), we ignore the concentration change due to radioactive decay. This simplification does not change the overall conclusion drawn in this paper, especially for long-lived radionuclides in which we are interested. Also here we use term “radionuclide” interchangeably with “radioelement” when we refer to “radionuclide solubility”.

Solving Equation (2) and plugging the solution into Equation (1), we obtain:

$${V_T}\varphi \frac{{dc}}{{dt}} = - \frac{{\alpha AR{M_0}}}{{{m_w}}}{e^{ - A \cdot R \cdot t}} - vc$$

(3)

The initial mass of waste form M₀ is M₀ = ρ(1 - φ)V_T, where ρ is the density of waste form (g_WF·m⁻³). Equation (3) can be scaled into:

$$\frac{{du}}{{d\tau }} = {e^{ - \beta \tau }} - \gamma u$$ for u < 1

(4)

with

$$\tau = \frac{t}{T} T = \frac{{c{}_{eq}{m_w}\varphi }}{{\alpha AR\rho (1 - \varphi )}} \beta = \frac{{{c_{eq}}{m_w}\varphi }}{{\alpha \rho (1 - \varphi )}}$$

$$u = \frac{c}{{{c_{eq}}}} \gamma = \frac{{{c_{eq}}{m_w}\varphi }}{{\alpha AR\rho (1 - \varphi )}}\frac{1}{{{T_r}}} {T_r} = \frac{{{V_T}\varphi }}{v}$$

(5)

Parameter T represents a typical time scale for the variation of dissolved radionuclide concentration, over which du/dτ is on the order of 1; T_γ characterizes the residence time water inside the disposal room. For typical parameter values given in Table 1, β < 10^-4, and thus Equation (4) can be simplified to:

$$\frac{{du}}{{d\tau }} = {e^{ - \beta \tau }} - \gamma u$$ for u < 1.

(6)

The small value of β is a characteristic of subsurface systems with high solid/water ratios [12].

For a solubility control of radionuclide release, it is required that γ < 1; that is,

$${T_r} > \frac{{{c_{eq}}{m_w}\varphi }}{{\alpha AR\rho (1 - \varphi )}}$$

(7)

This ensures that the rate of radionuclide dissolution into the solution exceeds the rate of radionuclide transport away from the system by water advection. By solving Equation (6) and then setting u = 1, the time for a dissolved radionuclide to reach its solubility limit (T₁) can be calculated as follows:

$${T_1} = - \frac{T}{\gamma }\ln (1 - \gamma ) = - {T_r}\ln \left[ {1 - \frac{{{c_{eq}}{m_w}\varphi }}{{\alpha AR(1 - \varphi )\rho {T_r}}}} \right]$$

(8)

As indicated in Figure 3, with increasing the residence time of water in the disposal system or increasing dissolution rate of the primary waste form, the concentration of the radionuclide will change from being kinetically controlled to being solubility-controlled. The residence time depends on the actual water flow rate and the total pore volume of the disposal system. An actual disposal system can be a waste container or a waste panel. In the Yucca Mountain repository, radioactive wastes will be container in steel/alloy packages, and each waste package, with a total internal volume of ~15 m³ 9 can be considered as a separate disposal system (note that ignoring the WP and assuming the tunnel immediately surrounding the waste effectively increases the value of pore volume and the corresponding value of T_r). Choosing a typical flow rate in the range 0.1-100 L/year/waste package [13], we estimate the minimum water residence time to be ~60 years. Similarly, for the Waste Isolation Pilot Plant (WIPP), a disposal system can be defined as an individual waste panel, each with the pore volume of 0.3-1.0x10⁴ m³ (Helton et al. , 1998). The maximum rate of water flow through boreholes during a human intrusion scenario is estimated to be ~5.5 m³/year [14]. The minimum water residence time in the WIPP is thus estimated to be ~ 5,000 year. Therefore, as shown in Figure 3, in an actual repository environment, even for the most durable waste forms, the radionuclide release from the near-field of a repository will likely be controlled by the solubility limit of the radionuclide.

For a given repository environment, the time for a radionuclide to reach its solubility limit is determined by the dissolution rate of the waste form that hosts the radionuclide. We have compiled dissolution rates for various waste forms. As shown in Figure 4, for all waste forms considered, the time for a radionuclide to reach its solubility limit is generally less than 300 years. Compared with a typical repository regulatory time (T_reg) (10⁴-10⁶ years), this transient time is negligible. Therefore, the accumulative release of a specific radionuclide can be approximated by:

$${\rm{Total release }} = \int_0^{{{\rm{T}}_{{\rm{reg}}}}} {{\rm{c}} \cdot vdt} \approx \int_{{T_1}}^{{\rm{min(}}{{\rm{T}}_{\rm{2}}}{\rm{, }}{{\rm{T}}_{{\rm{reg}}}})} {{{\rm{c}}_{{\rm{eq}}}}vdt} .$$

(9)

As indicated in Equation (9), there are two ways to reduce the total radionuclide release. One way is to reduce the water flow rate v with an engineered physical barrier, for example, encapsulate a waste form with a low-permeability clay layer [15] (see Table 1). The problem with an engineered barrier is that it is difficult to demonstrate the long-term integrity of barrier over a regulatory time period. The other way, which we believe will be more effective in reducing radionuclide release, is to chemically condition waste forms or repository environments to minimize radionuclide solubility.

The concept of conditioning repository environments can be best demonstrated with the Waste Isolation Pilot Plant (WIPP) [16], which is located in a salt bed in southern New Mexico and designed by U. S. Department of Energy for permanent disposal of defense-related transuranic wastes. WIPP wastes contain a large quantity of organic materials and various nutrients. Thus, there is a concern about the potential impact of microbial CO₂ generation on actinide solubilities. To mitigate this effect, a sufficient amount of MgO will be added to the repository with the backfill. Hydrated MgO will react with CO₂ to form magnesite:

Mg(OH)2 + CO2 → MgCO3 + H2O.

(10)

Reaction (10) will buffer CO₂ fugacity at ~ 10^-7 atm. This low CO₂ fugacity implies that Reaction (10) will remove practically all CO₂ from both gaseous and liquid phases in the repository. A thermodynamic equilibrium calculation using the EQ3/6 code shows that the addition of MgO will buffer pH around 10 for WIPP brines [16]. Under these chemical conditions, actinide solubilities become minimal (Figure 5).

As shown in Figure 5, by appropriately conditioning the near-field environments the dissolved concentration of a radionuclide can be reduced by orders of magnitude. The chemical composition of a waste form can strongly affect the near-field chemistry of a repository, and so an appropriate choice of waste form composition can be an important aspect of overall chemical conditioning. In this sense, amorphous materials may have an advantage over crystalline materials, although the former are generally less “durable” than the latter. Amorphous materials such as glasses have considerable flexibility in incorporating various chemical components. It is known that many radionuclides, especially actinides, can form sparingly soluble phosphates within the glass corrosion layers [17, 18] or as alteration products in uranium deposits [11]. Phosphate has also been used for immobilization of heavy metals in soils and sediments [19, 20]. Therefore, it may be desirable to formulate a high-level waste (HLW) glass by adjusting its phosphate content or even to employ a phosphate glass [21] to minimize radionuclide solubility during glass degradation.

For a given repository environment, dissolved concentrations of some radionuclides may never become solubility-limited, and their releases are generally limited by the dissolution rate of the primary waste form. Clearly, long-term durability of a waste form — especially one that contains a substantial inventory of such potentially mobile radionuclides — is a crucial aspect in limiting radionuclide releases; we are not suggesting otherwise. On the other hand, the proposed chemical conditioning concept may allow us to design waste forms or backfill materials that include chemical components that can precipitate low-solubility radionuclide-bearing solids that would otherwise not be stable. For example, iodine-129, which is considered a highly mobile radionuclide in nearly all repository environments, can potentially form insoluble solids in either a reducing or an oxidizing environment, provided that appropriate chemical components (such as Cu⁺) are added to the host waste form or backfill materials.

Radiation damage has been a concern for the long-term performance of a waste form [2]. The existing studies in this area have been exclusively focused on primary waste forms [29, 30, 31]. Our analysis, however, suggests that the future focus of these studies be shifted to evaluating the potential effect of radiation damage on the stabilities of secondary mineral phases that will directly control dissolved radionuclide concentrations.

3. Conclusion

In summary, due to high solid/water ratios and slow groundwater percolation rates, the concentrations of radionuclides dissolved in water flowing through a repository are expected to reach solubility control by radionuclide-bearing alteration products well within typical regulatory timeframes. Consequently, total release of radionuclides will become insensitive to the dissolution rates of primary waste forms. Our analysis suggests that future waste-form development should be increasingly focused on conditioning waste forms or repository environments to minimize radionuclide solubility, rather than on striving for marginal improvements to the durability of primary waste forms.

Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U. S. Department of Energy’s National Nuclear Security Administration under contract DE-AC04-94AL85000.

All authors declare no conflicts of interest in this paper.