ADVANCED NUCLEAR FUEL CYCLE FOR IMPROVED RADIOACTIVE WASTE MANAGEMENT

Transcription

1 ADVANCED NUCLEAR FUEL CYCLE FOR IMPROVED RADIOACTIVE WASTE MANAGEMENT Joonhong Ahn Department of Nuclear Engineering University of California, Berkeley Berkeley, California, Introduction and Scope of the Study Over the last generation, radioactive waste management has been conducted in a reactive manner. Engineering measures, such as spent fuel storage, final disposal, partitioning and transmutation, are planned or being performed after wastes have been generated and accumulated in significant amounts. If the utilization of nuclear power is to be expanded in the next generation, however, proactive measures should be taken in waste management. The current nuclear power capacity in the US is anticipated to decline sharply by 2030 (Fig. 1)[1]. Now could be a once-in-thirty-year opportunity to reconsider how the nuclear power system should be. The current study has been made, based on the following observations. First, a future nuclear power system is not likely to be accepted by the public if it generates as much radioactive waste as the current system does. For an enduring nuclear fuel cycle to be accepted by the public, a clear vision should be presented of the quantity and the toxicity of wastes arising from the enduring system, the number of repositories needed, and so on. These should be significantly smaller than those needed by the current system to support a long-term commitment to nuclear fission. Second, concern over proliferation and weaponsusable nuclear material will increase as more countries have nuclear power systems, as radiation barriers decline in spent fuel, and as the number of waste-storage locations increases. More countries, especially those countries recognized as Newly Industrialized Economies in Asia, are likely to increase Figure 1 Projected US Nuclear generating capacity [1] nuclear power capacity in the future, because carbon dioxide emission must be limited while making economic growth. Recycle methods that permit safeguards termination on resulting high-level waste provide the best method to control proliferation risk from long-term use of fission energy, but require systematic life-cycle study. In the past, nuclear-fuel-cycle concepts were proposed mainly aiming at better materials utilization or electricity production. Proposed partitioning-and-transmutation (P/T) systems have been designed to maximize the rate of transmutation of problematic long-lived nuclides. Analyses of the impact of P/T systems on the performance of a geologic repository have also been done by estimating the mass of radionuclides lost as waste from the P/T systems. But, partly because many previous studies for geologic-repository-performance assessment indicate that effects of P/T systems are not justifiable for their high costs and modest improvement of the radiological safety [2,3], feedback from the repository performance studies to the design or optimization of the whole P/T system has rarely been considered. The repository performance can be assessed by many aspects, such as safety, cost, simplicity in regulations, and so on. In this paper, three quantities are considered as measures for the repository safety. The first is the impact on the public health by released radionuclides. Radionuclides are released

2 from the repository into the surrounding rock, eventually reaching human beings. The radiological safety can be quantified by evaluating when and how much radioactivities would be taken by human beings. The second is criticality safety. Energy release due to sustained fission chain reactions by thermally fissile materials (TFMs) disposed of in a geologic repository could occur if chemical and hydrogeological processes reconfigure TFMs into a configuration, where the effective neutron multiplication factor k eff exceeds unity. Rock and water slow (moderate) fast neutrons to thermal velocities by collisions with light nuclei, facilitating fission of the TFMs such as 235 U, 233 U and 239 Pu. Reconfiguration of fissile materials could occur by transport and accumulation of fissile materials from multiple failed canisters [4,5,6]. Thus, transport and accumulation of fissile nuclides in the host rock need to be quantitatively modeled. The third is proliferation resistance [7]. In countries that are signatories of the Nuclear Nonproliferation Treaty (NPT), waste materials from safeguarded civilian facilities must remain under safeguards unless they meet international safeguards termination (IST) criteria [8]. To qualify for IST, nuclear material contained in the waste must be consumed or diluted in such a way that it is no longer usable for any nuclear activity relevant from the view point of safeguards, or has become practicably irrecoverable [9]. Otherwise, permanent safeguard monitoring may be required for a repository, which will result in long-term burden and risk on future generations. Thus, the mass of fissile materials in the repository needs to be quantified because the more fissile materials remain in the repository, the more attractive the repository is for the recovery of such materials for weapons production. Recently, we have performed a mass flow analysis and a repository-performance-assessment study for the Accelerator-driven Transmutation of Waste (ATW) system, conceived of by the team of Los Alamos National Laboratory (LANL)[10]. By the mass flow analysis, we have estimated the mass of individual radionuclides that will be destined for the geologic repository, as well as the mass of each radionuclide transmuted per passage through the reactor. With the obtained mass of waste, we have estimated the radiological impact of the geologic disposal of the waste by mass transport analysis. We have established quantitative relationships among the performance of the transmuter performance, waste loss, and the repository performance. The transmuter design can be modified for improvement of the repository performance. Mass Flow in ATW System Spent fuel from light-water reactors (LWR) contains uranium, plutonium, other actinides, and long-lived fission products that require the long-term isolation. The ATW system [10] has been proposed for separation and transmutation of long-lived actinides and fission products in the spent fuel from commercial LWR. It aims at avoiding the safety assessment required for the proposed Yucca Mountain Repository (YMR) [11] for an unprecedented long time period (ten thousand years or longer) by converting long-lived radionuclides in spent fuel into short-lived species. Because the ATW system generates wastes, that require a geologic repository for the disposal, the extent to which the ATW system can reduce the difficulty of geologic disposal of spent nuclear fuel is determined by comparing the performance of YMR for the case of direct disposal of spent fuel with that for the case of ATW waste disposal. Mathematical models are established for the radiological hazard at the boundary of the accessible environment (5 km distant from the repository) and the mass (or inventory) existing in the repository. For both models, the mass of each radionuclide to be placed initially in the repository is the key information. Therefore, a model is established to quantify the mass of each radionuclide that comes out of the ATW system as waste. We call this the mass flow model of the ATW system. Thus, the present analysis has been performed by establishing (1) the mass flow model, (2) the inventory model, and (3) the radiological hazard model. As a measure for the radiological impact of the repository, the radiological hazard of a radionuclide is defined in this study as the ratio of the radioactivity per year [Bq/yr] of a particular radionuclide arriving at the accessible environment boundary to the annual limit on intake for oral ingestion [Bq/yr] of that radionuclide given in 10CFR20 [12]. The mass of fissile materials existing in the repository, which is obtained by the inventory model, is used as a measure for the criticality safety and the proliferation resistance. The differences between the repository performance by LWR spent fuel disposal and that by the disposal of waste from ATW are presented in terms of the radiological hazard at the boundary of the accessible environment and the radionuclide inventory in the repository. The observations obtained by such comparison give insights for optimization and improvement of the ATW concept.

3 Mass Flow Model for ATW The ATW system is divided into four parts [10]: the reprocessing of LWR spent fuel, the fabrication of ATW transmutation assembly (TA), the burner, and the partitioning of spent TA (Fig. 2). Radioactive wastes are generated at each of these parts. The mass of each radionuclide coming out of ATW as waste is the basis for the repository performance assessment for the ATW system, and can be obtained by the following mass flow analysis. Approximately 63,000 ton of LWR spent fuel and 7,000 ton of defense HLW are considered to be disposed of in YMR. In the ATW concept, the LWR spent fuel is first reprocessed. In the reprocessing part, uranium and fission products except for iodine and technetium are removed from the spent fuel. The spent fuel pins are chopped, and the oxide fuel is separated from zircaloy cladding. The oxide fuel is sent to the reduction process, where the oxide fuel is converted to metal. The metal including virtually all uranium, transuranic elements, and fission products, will be the anode of the electro-refining process. The separated cladding material is used as the source of zirconium, which is the base-matrix material for the ATW target assembly. The off-gas released by the decladding process is collected, stored in a metal container, and eventually sent to the repository. In the electrorefining process of Spent fuel ATW Burner Spent TA Chopping Spent Fuel Decladding the reprocessing, the metal from the direct Direct Oxide Reduction reduction process is Anode Polishing Electrorefining Electrorefining U Storage Electrowinning TA Fabrication Electrowinning R P Reprocessing Reductive Extraction Partitioning YMR Figure 2 ATW treatment system [10] placed in the anode. Virtually pure uranium is collected on the cathode. In the molten salt, most of the actinides and the rare earth elements as well as a small fraction of uranium are included. This molten salt is sent to the next stage, the electro-winning process. The anode shrinks as the electro-refining process proceeds. A batch electrorefining process is stopped after a certain time period. The anode still containing small fractions of uranium, actinides and rare earth elements is polished to reduce the discharge of the actinides and the rare earth as waste. The actinides and the rare earth recovered by the anode polishing are returned to the electro-refining process. The uranium recovered in the cathode of the electro-refining and the anode polishing stages is stored. In the current ATW concept, the recovered uranium is sent to a lowlevel waste repository(this would not be permitted under the current US regulations, though.). The anode after polishing is regarded as radioactive waste from the ATW system by LANL [10]. At the electro-winning process, the molten salt from the electro-refining process is further separated into three parts. On the cathode, uranium is concentrated. The recovered uranium is also sent to the uranium storage. On the anode, the actinide elements are extracted with small fractions of uranium and the rare earth elements. This is the feed material for the ATW target assembly fabrication. In the molten salt, most of the rare earth fission products is included. The molten salt is sent to the reductive extraction process, where the fission products are removed from the molten salt. The cleaned-up molten salt is re-utilized in the electro-refining process. The removed fission products are solidified, stored, and eventually disposed of in YMR. The material from the electro-winning process is fabricated into an alloy fuel. Small fuel pellets are fabricated, which are assembled into a fuel rod. Such mechanical processes as grinding or cutting are likely to be required, which generate wastes, to keep accuracy in dimensions of pellets and rods. In the burner, the target assembly is exposed to neutrons. Some actinides undergo fission, generating fission products, while others become heavier species by neutron absorption. After some residence time in the burner, the target assembly (TA) is discharged from the burner, and stored for cooling. In the discharged TA, there are still actinides that have not fissioned. Therefore, the spent TA is sent to the partitioning part, where remaining actinides are separated from fission product elements. The partitioning starts with chopping of the irradiated TA into small sections. The used cladding

4 is sent to storage. The off-gas released by chopping is collected and stored. The alloy fuel is processed at the electro-refining process to remove fission products. On the cathode, most of the actinides are collected with small fractions of uranium and fission products. This is sent to the target assembly fabrication. In the molten salt, still considerable amount of uranium, actinides, and the rare earths are included. Therefore, the molten salt is sent to the electro-winning process for further recovery of the actinides, the rare earths and uranium. The anode contains most of uranium and very small fractions of the actinides and the rare earths. This is regarded as waste from the ATW process [10]. At the electro-winning process in the partitioning part, the rare earths remaining in molten salt are sent to the reductive extraction process. Cleaned-up molten salt is re-utilized in the electro-refining process. The rare earths are solidified, stored, and eventually sent to the repository. The recovered actinides with small fractions of uranium and the rare earths in the cathode are sent to the target assembly fabrication. The total mass of the materials returned to the TA fabrication from the partitioning side is smaller than the mass of the target before burning it in the burner because fission products are removed by partitioning. Also, some fractions of actinides are lost as waste from the processes in the partitioning part. The mass deficit is made up by the feed materials coming from the electro-winning of the reprocessing. Based on the aforementioned material flow in the ATW system, we determine the mass of each radionuclide that comes out of the ATW system as waste, which is disposed of in the repository. 1 Figure 3 α a α U Reprocessing δ α Spent Fuel Decladding d α Direct Oxide Reduction o Anode Electrorefining α r Polishing γ β aγr β r a ε r α U Storage Electrowinning w 1 α 1 ATW Burner TAA α1 α 2 Figure 4 Waste fractions from the reprocessing part. Subscript i is omitted. n Partitioning α 1 Recycling g Fractions of radionuclide coming out of the ATW process as waste (α's are waste fractions. δ is the fraction transmuted. They are defined for each radionuclide. Subscript i for radionuclide is omitted). Figure 3 is applied for each radionuclide. A unit mass of a radionuclide is considered as input to the reprocessing part, consisting of the decladding, the oxide reduction, the electrorefining, the electrowinning, and the anode polishing. It is assumed that all the spent fuel is reprocessed once at the same time. It is assumed that the mass fraction, α 1,i, of radionuclide i comes out from the reprocessing part. The fraction, 1 α 1,i, is sent to the TA fabrication. This is the starting material for recycling. The fraction, α 1,i, is determined by the detailed mass flow consideration in the reprocessing part. Figure 4 shows the breakdown of the fraction, α 1,i. The fraction, α di,, is assumed to be lost as waste by the spent fuel decladding. This fraction represents the loss of radionuclide i as such forms as fine particles generated by chopping or inclusions in the cladding material. At the direct oxide reduction process, the fraction, α oi,, is assumed to be lost as waste. The fraction, (1Ð α di, )(1Ð α oi, ) is input to the electro-refining process. The output from the electro-refining is assumed to be divided into four fractions: the fraction, γ ri,, included in the anode and sent to the anode polishing, the fraction, β ri,, included in the cathode and sent to the uranium storage, the fraction, ε ri,, included in the molten salt and sent to the electro-winning process, and the loss, α ri,, as waste. Therefore, these four fractions satisfy α + β + γ + ε =1. (1) ri, ri, ri, ri, α 3

5 At the anode polishing, the fraction, γ ai,, is recovered and sent to the electro-winning process. The fraction, β ai,, is included in the recovered uranium as impurity. The fraction, α ai,, is lost as waste. Therefore, the relation, αai, + βai, + γ ai, =1, (2) is satisfied. The electro-winning process receives a fraction, (1Ð α di, )(1Ð α oi, ) ε ri,, from the electro-refining, and a fraction, (1Ð α di, )(1Ð α oi, ) γ ri, γ ai,, from the anode polishing. At the electro-winning process, a fraction, α wi,, is lost as waste. A fraction, β wi,, is included as impurity in the uranium recovered in the cathode. Thus, the total waste fraction, α 1,i, from the entire reprocessing process is obtained by summing the aforementioned waste losses as α1, i = αdi, + 1 αdi, αoi, 1 αdi, 1 αoi, αri, βri, γ ri, βai, εri, βwi, γ, iαai, εri, αwi, ( ) + ( )( )( ) (3) The mass fraction, 1 Ð α 1,i, is sent from the reprocessing part to the TA fabrication part, and the first cycle starts. In the TA fabrication part, the fraction, α 2,i, is assumed to be lost as waste. Thus, for the first cycle, the fraction, (1 Ð α 1,i )(1 Ð α 2,i ), is fabricated into a TA, and installed in the burner. At the burner, it is assumed that the mass fraction, δ i, of radionuclide i becomes some other species (or, is transmuted). The spent TA after the first-time irradiation in the burner contains radionuclide i with the mass fraction of (1 Ð α 1,i )(1 Ð α 2,i )(1 Ð δ i ). The spent TA is sent to the partitioning γ r Spent TA Chopping Electrorefining β r Electrowinning 1 α 3 α c α r α w Figure 5 Waste fractions from the partitioning part. Subscript i is omitted. part. It is assumed that the fraction, α 3,i, is lost as waste from the entire partitioning process. From the partitioning part, the fraction, (1 Ð α 1,i )(1 Ð α 2,i )(1 Ðδ i )(1 Ð α 3,i ) is returned to the target fabrication for the second cycle. The detail of the partitioning process is depicted in Fig. 5. At the spent TA chopping, the fraction, α ci,, is lost as waste. Then, the fraction, 1 Ð α ci,, is sent to the electro-refining process. The fraction, (1 Ð α ci, ) α ri,, is lost as waste from the electrorefining process. The fraction, β ri,, is included in the molten salt, and sent to the electro-winning process. The fraction, γ ri,, is included in the cathode of the electro-refining process, and sent to the target fabrication. The mass fraction lost as waste from the entire partitioning process is obtained by summing the losses from the TA chopping, the electro-refining, and the electro-winning, as α3, i = αc, i + ( 1 αc, i) ( αr, i + βr, iαw, i)) (4) The first cycle starts with the mass fraction, 1 Ð α 1,i, of radionuclide i coming from the reprocessing part to the TA fabrication part, and ends in the fraction (1 Ðα 1,i )(1 Ðα 2,i )(1 Ð δ i )(1 Ðα 3,i ) from the partitioning part. The waste fraction, f 1, i, occurring in the first cycle is obtained by summing the waste fraction, (1 Ð α 1,i ) α 2,i, from the target fabrication, and the fraction, (1 Ðα 1,i )(1 Ð α 2,i )(1 Ð δ i ) α 3,i, from the partitioning as ( ) + ( )( )( ) f 1, i = 1 1, i 2, i 1 1, i 1 2, i 1 i 3, i α α α α δ α. (5) The second cycle starts with the mass fraction, (1 Ð α 1,i )(1 Ð α 2,i )(1 Ðδ i )(1 Ð α 3,i ), inherited from the first cycle. The fraction of waste at the TA fabrication is obtained as (1 Ðα 1,i )(1 Ð α 2,i )(1 Ðδ i )(1 Ð α 3,i ) α 2,i. After the transmutation in the burner, the fraction, (1 Ðα 1,i )(1 Ðα 2,i ) 2 (1 Ðδ i ) 2 (1 Ðα 3,i )

6 remains in the target. At the partitioning, the fraction, (1 Ðα 1,i )(1 Ð α 2,i ) 2 (1 Ð δ i ) 2 (1 Ðα 3,i ) α 3,i is lost as waste. Thus, for the second cycle, the waste fraction, f2, i, is obtained as 2 2 f2, i = ( 1 α1, i) ( 1 α2, i) ( 1 δi) ( 1 α3, i) α2, i + ( 1 α1, i) ( 1 α2, i) ( 1 δi) ( 1 α3, i) α 3, i.(6) In general, for the k-th cycle, the waste fraction, f ki,, is written as the sum of the waste fraction from the target fabrication part and the fraction from the partitioning part as k k k k k k f ki, = (, i )(, i ) 1 ( i ) 1 (, i ) , i + ( 1, i) ( 1, i) ( 1 i ) ( 1, i ) 1 α1 α2 δ α3 α2 α1 α2 δ α3 α 3,i for k ³ 1. (7) The total fraction, F ni,, lost as waste at the end of the n-th cycle is obtained by summing f ki, from k = 1 to n and the waste fraction, α 1,i, from the reprocessing part, as F n 1 ( ){ + ( )( ) } ( 1 α ) ( 1 δ ) ( 1 α ) 1 ( 1 α2, i) ( 1 δi) ( 1 α3, i) = α + f = α + 1 α α 1 α 1 δ α ni, 1, i ki, 1, i 1, i 2, i 2, i i 3, i k = 1 n n n 2, i i 3, i The total fraction, F ni,, increases with the number, n, of recyclings, approaching the upper bound, F, i, by taking n to infinity, as i i i i F = + α2, + ( 1 α2, )( 1 δ ) α3,, i α1, i ( 1 α1, i ). (9) 1 ( 1 α2, i)( 1 δi)( 1 α3, i) ( SF If the mass of radionuclide i in the spent fuel initially available is M ) i [mol], then the mass of ( SF) radionuclide i in the waste from the ATW system destined to the repository is written as Mi F, i. This mass is considered the mass of the radionuclide initially placed in the repository. Note that radioactive decay during the ATW process operation is neglected in the aforementioned formulation. Considering that the operation period is approximately half a century, which is significantly shorter than the half-lives of most actinides considered in this analysis, this assumption is reasonable. However, for 238 Pu and 241 Pu, whose half-lives are 87 and 14 years respectively, radioactive decay should be taken into account in future analyses. Also to determine the waste fractions from ATW for short-lived fission products, especially for 90 Sr and 137 Cs (half-lives about 30 years), two major heat generators, more detailed analyses are required. Models for Repository Performance Assessment Mass of radionuclides in the repository The mass of a radionuclide existing in the repository changes with time due to radioactive decay and release to the surrounding geologic formation after failure of waste canisters. In this section, we conservatively overestimate the mass by neglecting the release to the surrounding geologic medium. With overestimated mass of actinides in the repository, the repository criticality safety and the attractiveness of the repository as the source of fissile materials are estimated conservatively. The preliminary calculations based on the model that includes the loss by radionuclide release from the repository show, however, that the cumulative radionuclide mass release from the repository to the surrounding geologic formation is small compared to the mass that decays within the repository, for most actinide radionuclides [13]. If the radionuclides initially placed in the repository are assumed to be kept in the repository, the change of the mass with time is governed by the Bateman equations [14]: dmi() t = λimi() t + λi 1 Mi 1 (), t t > 0, i = 12,,..., λ 0 = 0, (10) dt where λ i is the radioactive decay constant [yr Ð1 ] of radionuclide i, M i [mol] the mass of radionuclide i existing in the repository, subject to the initial conditions, Mi( 0) = Mi o, i = 1, 2,.... (11) The mass of radionuclide i existing initially in the repository, M o i [mol], is expressed as Mi o ( Mi SF ) = F, i. (12) The analytical solution to this mathematical problem is readily obtained [14]. Radiological hazard at boundary of accessible environment (8)

7 ( SF) The mass, Mi F, i, of radionuclide i coming out of the ATW system as waste is to be placed in ( SF) the repository. It is assumed that the mass, Mi F, i, is placed in the repository immediately after it is generated, and that all the ATW waste is placed in the repository at the same time. The mass of ( SF) radionuclide i in one canister is assumed Mi F, i N, where N is the number of waste canisters. We assume that all the canisters fail, i.e., start to release radionuclides into groundwater, at the same time. Waste canisters are assumed to be placed in a two-dimensional array fashion in the repository area. If d is the distance between neighboring canisters, the repository footprint per canister is d 2. In YMR, waste canisters are initially placed in open excavated tunnels. We assume that the tunnels are filled by rubble of the host rock (i.e., tuff) by the time the canisters fail. We assume that the rubble filling the tunnels is regarded as a homogeneous porous medium, where radionuclides released from failed canisters are transported by molecular diffusion. The YMR is located above the water table [11]. The water flow through the repository is vertical, whereas it is horizontal below the water table. The tuffaceous rock in Yucca Mountain contains many fractures of various sizes. Fractures are considered to be main conduits for groundwater flow. We assume that there is a path between each canister and the boundary of the accessible environment, which is considered 5 km distant from the repository in the EPA regulation (40CFR191 [15]). It is assumed that water flows through fractures steadily in a liquid column with a constant velocity v, and that water in the pores of the rock matrix is stationary. To simplify the analysis, a parallel planar fracture of aperture 2b and width d times n is assumed to be the path connecting one canister to the accessible environment boundary [5,16]. With the distance, d, between neighboring canisters, and the spacing, 2a, of fractures, the number, n, of fractures intersecting the repository footprint per canister is calculated as n = d 2 a. Actual paths between individual canisters and the boundary of the accessible environment are tortuous. Actual travel distance between individual canisters and the accessible environment boundary is greater than the straight-line distance between two points. The planar-fracture assumption is, therefore, conservative for the evaluation of the mass flux at some distance away from the source point because it always gives shorter travel times resulting in less radioactive decay loss during the transport. Materials released from the waste form are assumed to be transported through fractures by advection as solutes, and to diffuse into the rock matrix by molecular diffusion. As the pores in the rock matrix are partially filled with water, diffusion in the rock matrix is assumed to occur only through the interconnected water phase in the pores. The fraction of the pore spaces filled with water, i.e., the water saturation is assumed S. The solutes in the pores of the rock matrix are in sorption equilibrium with the solid phase of the rock, resulting in retardation of radionuclide transport. For some radionuclides such as plutonium, transport in a colloidal form as well as in a solute form can be considered. In Yucca Mountain conditions, colloids with positive surface charge would be expected to attach to tuff with negative surface charge. According to the numerical results obtained based on a simplified colloid-facilitated transport model for plutonium [5], most plutonium decays while it exists in the waste form, and the transport distance of most colloids is relatively short (less than 50 m). Therefore, in this study, we assume that materials released from the waste form are all transported as solutes. The radionuclide transport equations for the solute concentrations Ck (,)[mol/m3 z t ] of radionuclide k in the water in the fracture and C kp ( y, t; z) in the pore water of the rock matrix are given in [16]. Here k = 1, 2, É, i. The velocity v [m/yr] and the longitudinal hydrodynamic dispersion coefficient D L [m 2 /yr] are assumed to be constant with time and uniform in the fracture and common for all radionuclides, since the hydrodynamic dispersion is determined mainly by the geometry of the contaminant transport paths. Molecular diffusion of radionuclides from water flowing in the fractures into the pores of the rock matrix is an important retardation mechanism. For sorption equilibrium in the porous rock, we define the capacity factor α ek ( ) for radionuclide k of element e as ( ) αek ( ) = Sεp + ρp 1 Sεp Kdp, (13) where ρ p [kg/m 3 e ] and ε p are the density and porosity of the porous rock matrix, and K dp [m 3 /kg] the sorption distribution coefficient of element e for the rock matrix. Subscript e(k) indicates that the k-th member nuclide in a decay chain is an isotope of element e. The saturation of the rock matrix, S, is included to account for the partial saturation of the geologic medium in the Yucca Mountain. The retardation coefficient, R ek ( ), for advection and longitudinal dispersion in the fracture is defined as e

8 ( ) f f Kdf Rek ( ) = + ρ 1 ε 1, (14) ε f e where ρ f and ε f are the density and the porosity of the material filling the fractures. K df [m 3 /kg] is the sorption distribution coefficient of element e for the material filling the fractures. The rubble-rock region between the waste solid and the surrounding rock formation is simplified as a single uniform porous medium. We assume that radionuclides are transported only by molecular diffusion through the stationary water in the pores of the region around a waste canister filled with rubbles of the host rock. The retardation coefficient, K e(k), for diffusion in the rubble rock region is defined as: e Kd Kek ( ) = + ρ( 1 ε) 1 (15) ε, where ρ [kg/m 3 e ] and ε are the density and the porosity of the rubble rock, respectively, and K d [m 3 /kg], a constant sorption distribution coefficient. In [16], the diffusive mass flux of radionuclide k at the interface between the rubble-rock region and the surrounding host rock was obtained based on the concentration profile in the water phase in the rubble-rock region obtained by analytically solving diffusion equations that take into account retardation of diffusion by sorption and a multiple-member decay chain. This is the source term for the transport in the fractures to the accessible environment boundary. On the waste-form surface, if the solubility of element e is so low that all the radionuclides of element e released by the alteration of the waste form cannot dissolve into the water phase, then precipitate of element e will occur. The concentration of element e at the interface between waste form and the rubble region is limited by its elemental solubility until the moment when the precipitate disappears. If there are multiple isotopes, then a precipitate of element e is assumed to consist of its isotopes, and the concentration of each isotope at the interface between waste form and the rubble rock region will be a fraction of the elemental solubility. The fraction is assumed to be equal to the ratio of total mass of the isotope released to that of all the isotopes of element e, from a waste form by alteration. If it is found that no precipitate occurs, then for the boundary condition at the interface a mass flux of radionuclide k is assumed to be equal to its congruent release rate from the waste form. The congruent release is assumed to continue for the leach time of the waste solid, TL [yr], which is the time period between the beginning and the end of the waste form alteration. The analytical solution for the concentrations Ck (,) z t [mol/m3 ] of radionuclide k in the fracture are available for the mathematical problem described above [16]. The radiological hazard, Hk ( L, t ), for radionuclide k at the observation point L [m] distant from the waste canister is expressed as L vc L t D C k k (, ) ε fs f [Bq/yr] z z L Hk ( L, t) = = (16) ALIk [Bq/yr] where ALI k is the annual limit on intake for ingestion of radionuclide k, given in 10CFR20 [12]. A computer code was readily developed based on the analytical solutions [16]. The numerical results for the total radiological hazard (the sum of hazards of all radionuclides at the point L m away from the repository) based on (16) will be presented for the following cases: (1) the direct disposal of the LWR spent fuel, and (2) the disposal of wastes from the operation of the ATW system starting with the same amount of LWR spent fuel. Input data LWR Spent Fuels e Table 1 Assumed Spent Fuel Canister Parameters Values [11] Diameter 1.52m Length 4.91m Mass of spent fuel 8.2 MTU Total number of canisters 7640 The total mass of LWR spent fuel to be disposed of in the proposed YMR is approximately 63,000 metric tons (MT). Waste packages have the characteristics given in Table 1. The total number of waste canisters is given in

9 [11]. The mass (8.2 MTU) of one canister for disposal is obtained by dividing the total mass (62,829 MTU) assumed in [11] by the total number of canisters (7,640). Masses and half-lives of radionuclides in the spent fuel are summarized in Table 2. These values have been obtained and utilized in the previous performance assessment for the YMR [11]. The fourth column in Table 2 is obtained by multiplying the value in the third column by 63,000 MTU. The values in the fourth column are the total masses of radionuclides included in 63,000 MTU of the LWR spent fuel. The fifth column is obtained by dividing the value in the fourth column by the total number, 7640, of the canisters. The values for 246 Cm, 242m Am, 238 Pu, and 244 Cm are not shown. These masses are lumped with those of their daughters due to their short half-lives (less than 100 yr) or negligibly small inventories. Table 2 Radionuclide Inventories in LWR Spent Fuel. Isotope Half life Inventory [9] Inventory, Inventory, M (years) (Ci/MTU) ( SF M i SF) / N ALI (Bq/yr) i (mol) (mol/canister) [10] Cm E E E E+08 Pu E E E E E+04 Am242m 1.520E E E E+06 Pu E E E E+06 U E E E E E+05 U E E E E E+05 Th E E E E E+05 Ra E E E E E+04 Cm E E E E+06 Am E E E E E+04 Pu E E E E E+04 U E E E E E+05 Pa E E E E E+08 Ac E E E E E+03 Cm E E E E E+04 Pu E E E E E+06 Am E E E E E+04 Np E E E E E+04 U E E E E E+05 Th E E E E E+04 Cm E E E E+05 Pu E E E E E+04 U E E E E E+05 Cs E E E E E+07 I E E E E E+05 Sn E E E E E+07 Pd E E E E E+09 Tc E E E E E+08 Mo E E E E E+08 Nb E E E E E+07 Zr E E E E E+07 Se E E E E E+07 Ni E E E E E+08 Cl E E E E E+07 C E E E E E+07 ATW System Parameters The fractions, δ, transmuted by the burner per passage are given in Table 3 [10]. We assume that the values in Table 3 are applied for all passages through the burner. Because actual values can be strongly dependent on the designs and neutronics of the burner core, determination of these values will be the major task for future design studies for ATW.

10 Table 3 Fractions Transmuted per Passage Through the Burner [10] Element Values Element Values Element Values U Pu Cm Np Am Cm Pu Am Cm Pu Am Cm Pu Cm Tc Pu Cm In Table 4, fractions lost as waste from the recycling system of ATW are shown. Here two different cases are assumed: minimum and realistic waste losses. The Òminimum waste lossó case is the one assumed in the report by the LANL [10]. In this case, mass losses are assumed to occur only at the anodes of electro-refining in the reprocessing and in the partitioning. No mass is assumed to be lost as waste from other processes in the reprocessing and the partitioning. No waste generation is assumed at the TA fabrication stage. The anode from the electro-refining of the reprocessing, which contains 0.37% of actinide processed, is to be polished to reduce the actinide mass lost as waste. 99.7% of actinide in the anode is recovered by the anode polishing, and returned to the electro-refining process. Thus, the polished anode is considered to contain 0.3% of 0.37% of the mass processed at the electro-refining. The mass fraction, α 1, is calculated as 1.1E-5. At the partitioning stage, 9.47 ppm of the mass processed by the electrorefining is assumed to be included in the anode, which is regarded as waste. Approximately 7% of actinide is included in the molten salt phase, and is transferred to the electrowinning process. It is assumed in [10] that all actinides are recovered by the electrowinning process, and are transferred to the TA fabrication stage. In the Òrealistic waste loss caseó, in addition to the waste loss at the anode polishing process and the electrorefining in the partitioning assumed for the minimum waste loss case, 0.3% of mass is arbitrarily assumed to be lost as waste at other processes, based on previous experiences for EBR-II* spent fuel treatment[17]. Table 4 Spent fuel reprocessing Transmutation assembly fabrication Partitioning Fractions Lost as Waste per Passage Through the Material Recycle Process ATW waste treatment Symbol Waste loss rate Minimum Realistic Spent fuel decladding α d Direct oxide reduction α o Waste α r Electrorefining Impurity in U storage β r To anode polishing γ r 3.7E-3 3.7E-3 To electrowinning ε r Waste α a Anode polishing Impurity in U storage β a To electrowinning γ a Electrowinning Waste α w Impurity in U storage β w Total α 1 1.1E Total α Chopping c Electrorefining Waste α r 9.47E E-6 To electrowinning β r Electrowinning α w Total α E

11 Repository Performance Parameters In Table 5, the input data for the radionuclide transport calculations are summarized. The cylindrical waste canister and buffer region are transformed to spheres with the same surface areas. The surface area of the cylindrical waste canister is obtained from [11]. Based on the radius of the excavated disposal drift and the spacing between two adjacent canisters [11], the surface area of the rubble-rock region is determined. In [5], the water flow velocity through the vertical parallel fractures is assumed 40 m/yr. This value is used for the evaluation of the radiological hazard at the location 200 m below the repository Table 5 Input Data for Radionuclide Transport Analysis Parameters Values Surface are of waste form 28.3m 2 [11] Surface area of buffer 726 m 2 [11] Distance between waste forms 30m [11] Equivalent radius of spherical waste form, r 1 1.5m Equivalent radius of buffer (crushed tuff), r 2 7.6m Leach time of waste form 100,000 yr [5,11] Matrix rock (tuff) porosity 0.1 [11] Saturation of the host rock matrix pores, S [11] Buffer (crushed tuff) porosity 0.3 Matrix rock and buffer density 2.2 g/cm 3 Dispersion coefficient 1.0 m 2 /yr Water velocity 10 or 40 m/yr [5,11] Diffusion coefficient in matrix rock 2.05E-4 m 2 /yr Diffusion coefficient in buffer 3.15E-3 m 2 /yr Retardation in the fracture 1 Fracture spacing, 2a 1m [11] Fracture aperture, 2b 1.8E-4m [11] Number of fractures intersecting repository 2,000 Repository dimension, L R 2000m horizon, where the water table is considered to be located. The water flow is considered to be horizontal below the water table, and is assumed slower than the vertical flow in the unsaturated region. Within the transport over 5 km, both the vertical transport through the unsaturated region and the horizontal transport through the saturated region are included. In this preliminary calculation, a single value of 10 m/yr is used for the evaluation of the hazard at the location 5 km away from the repository. The retardation due to the sorption on to the fracture surfaces is conservatively neglected. The spacing and the aperture of the fractures are taken from the previous study [5]. The hazard has been evaluated numerically for two different geologic conditions: ÒmobileÓ and ÒimmobileÓ. A medium for which the upper-bound values of the ranges given in [11] are assigned for radionuclide solubilities, and the lower-bound values of the ranges are assigned for sorption retardation coefficients, is referred to as a ÒmobileÓ medium. A medium with the lower-bound values for solubilities and the upper-bound values for sorption retardation coefficients is referred to as an ÒimmobileÓ medium. In Table 6, values are shown, which are determined from the ranges reported in previous performance assessments [11][18]. For the rubble-rock region, the same value for the sorption distribution coefficient is used for the retardation coefficient in the buffer (15) and for the capacity factor in the rock matrix (13). Table 6 Data for Radionuclide Transport in Geologic Formations (Upper row:òimmobileó case, Lower row: ÒmobileÓ case). Element Cm, Am, Ac Pu Solubility (mol/m 3 ) Sorption distribution coefficient (cm 3 /kg) Retardation coefficient in rubbles, K e(k) Capacity factor in rock, α ek ( ) 1.E E E+02 1.E E E+03 1.E E E+01

12 1.E E E+02 Np 1.E E-02 1.E E E+02 U 1.E E-02 1.E E E+01 Pa 1.E E-02 1.E E E+02 Th 1.E E E+02 1.E E E+03 Ra 1.E E E+02 1.E E E+04 Cs ÐÐÐ E E E E+03 I, Tc, Cl ÐÐÐ E E-02 Sn 1.E E E+01 1.E E E+02 Pd, Mo ÐÐÐ E E E E+02 Nb 1.E E E+02 1.E E E+03 Zr 1.E E E+02 1.E E E+03 Se ÐÐÐ E E E+01 Ni 1.E E-02 1.E E E+03 C ÐÐÐ E E E E+02 Numerical Results Total Mass of ATW Waste The total mass of ATW waste is estimated approximately 21,000MT after transmutation of 63,000 MTU [11]. More than two-thirds of 21,000 MT is due to the cladding and hardware of the target assembly. In the present analysis, only the mass flow of actinides and Tc-99 is considered. Other materials such as fission products except for 129 I and 99 Tc, and structural materials in LWR spent fuel, are not considered. For 99 Tc, the mass flow analysis has been performed in the same way as for actinides, based on the model shown above. For 129 I, it is assumed that its mass in the LWR spent fuel is reduced by a factor of 15 by the ATW system [10] for all the cases, without performing the mass flow analysis. In Table 7, the total waste fraction, F, i, defined by (9), is shown for two cases: ÒminimumÓ and ÒrealisticÓ in the second and third columns. For those radionuclides whose fraction, δ, transmuted is zero, such as 246 Cm, 245 Cm, and 243 Cm, the total waste fraction is obtained unity for both minimum and realistic cases. This means that all the masses originally included in the LWR spent fuel will be transferred to the waste stream. For those radionuclides with δ greater than zero, the total fraction, F, i, becomes less than unity. F, i is smaller for the minimum waste case than that for the realistic case. In the fourth and fifth columns, the mass of radionuclide i in the waste from the ATW system ( destined to the repository, Mi SF ) F, i is tabulated. The mass, M i ( SF), initially included in the LWR spent fuel is given in the fourth column of Table 2. In the sixth and seventh columns, the mass of a radionuclide per canister is shown, which is obtained by dividing the values in the fourth and fifth columns by the number of canisters. The number of canisters for wastes generated by ATW is estimated by assuming that 9 MT of waste is contained in one canister. With the total mass of waste (21,000 MT), 2,300 canisters are assumed for ATW waste

13 Mass (kg) 10 7 LWR spent fuel Figure 6 ATW+U, realistic and minimum ATW, realistic ATW, minimum Time (year) Masses of thermally fissile actinides. disposal. The values for 246 Cm, 244 Cm and 243 Cm are not given in the table. These masses are lumped with those of their daughters to simplify the decay chains. For example, the mass of 246 Cm is lumped with that of 242 Pu. For the mass flow analysis, only the radionuclides shown in Table 7 have been considered. Mass flow for other radionuclides, such as most fission products, has not been considered because they are assumed to be removed from the LWR spent fuel by the reprocessing and from the spent TA by the partitioning. Because their contribution to the radiological hazard is negligibly small, except for those of 129 I and 99 Tc, comparison between the hazard from the whole LWR spent fuel with that from ATW waste resulting from those radionuclides shown in this table is still meaningful. Uranium isotopes are also omitted from this consideration because by the assumption made by LANL [10] uranium is assumed to be removed from the LWR spent fuel and sent to a low-level waste repository. However, as we observe later, the recovered uranium has considerable radiological impact. Table 7 Radionuclides Data and Results of ATW Mass Flow Analysis. Total waste fraction, Inventory (mol) ( SF) Mi F, i / N F ( SF) Isotope, i Mi F, i (mol/canister) Minimum Realistic Minimum Realistic Minimum Realistic Cm E E E E+01 Pu E E E E E E+00 Cm E E E E+01 Am E E E E E E-01 Pu E E E E E E+01 Cm E E E E E E-01 Pu E E E E E E+00 Am E E E E E E+00 Np E E E E E E+00 Cm E E E E+03 Pu E E E E E E+01 I E E E E E E+00 Tc E E E E E E+01 Radionuclides in LWR Spent Fuel and ATW Waste Masses of major TFMs ( 235 U, 233 U, and 239 Pu) are depicted in Fig. 6. The masses of TFMs can be used as a measure for the criticality safety of the repository [4,5,6]. The repository with LWR spent fuel contains about 1000 MT of TFMs. This can be reduced to 10 MT by ATW with the realistic waste loss, and to 10 kg with the minimum waste loss. With 10 kg, the possibility of criticality accident can be completely eliminated. For the realistic waste loss case, the judgement is more complex. The fraction of TFMs in the total actinide mass is as high as 40% at early times. The fraction of fissile actinides in LWR spent fuel is 1.7% initially and decreases continuously. From the viewpoint of the attractiveness to the proliferator, the ATW waste seems to have a clear advantage over the LWR spent fuel because of the significantly reduced mass of TFMs. In Fig. 6, we also observe the effect of the uranium recovered from the LWR spent fuel in case that it is disposed of in the YMR together with the wastes from the ATW operation. By combining the

14 ATW waste with the recovered uranium, the total mass of uranium to be disposed of in YMR becomes comparable to that included in LWR spent fuel. Although, the total mass of TFMs other than 235 U is reduced significantly by the ATW system, there are negligible differences among three cases due to dominant 235 U in the recovered uranium. By dilution with the recovered uranium and by the transmutation of TFMs and their precursors, the mass fraction of TFMs in the repository is reduced significantly, which implies that the possibility of criticality accident in and around the repository becomes negligibly small. Comparisons of Total Radiological Hazard LWR In Fig.7, the hazard at the 5 km location from 2292 canisters of ATW waste is compared with that from 7640 canisters of LWR spent fuel, disposed of in YMR for the mobile and immobile medium cases. The main contributor to the total hazard from all LWR spent fuel canisters in the repository observed at the 5 km location in the mobile medium is 237 Np, whereas main contributors in the immobile medium are 129 I and 99 Tc. The difference between the mobile and immobile cases is about 350-fold. At the 5-km point, practically no hazard is observed until 50,000 years regardless of the medium assumption. This is because, even for non-sorbing 129 I and 99 Tc, radionuclide migration through fractured media can be retarded significantly due to the diffusion of radionuclides from fractures into surrounding rock matrix [19]. If the 10,000-year time frame is the major concern for the repository safety as is specified by the EPA regulation [15], the repository already comprises with the regulation. ATW Waste without Recovered Uranium It is claimed by the ATW concept that by the ATW (1) the hazard of the waste will be reduced significantly, (2) the length of time for the repository safety assessment can be reduced significantly, and (3) the uncertainties due to the heterogeneous geologic formations can be reduced. Hereafter, we observe these points. For the total hazard of ATW with realistic waste losses, the main contributor in the mobile medium is 237 Np, whereas in the immobile medium, the main hazard comes from 129 I and 99 Tc. At the 5 km location, the difference between the mobile and immobile cases is about 150-fold. The total hazard is smaller for the ATW realistic waste loss case than that for the LWR spent fuel, by a factor of 35 for the mobile medium, and by a factor of 15 for the immobile medium. For the length of time frame for repository safety assessment, it is observed that nothing has changed due to ATW. The hazard rises at about 50,000 year at the 5km location Mobile Medium 10 6 LWR 10 7 Immobile Medium 10 6 Hazard ATW, Realistic ATW, Minimum Hazard ATW, Realistic or ATW+U, Realistic ATW, Minimum or ATW+U, Minimum LWR Time, year Time, year Figure 7 Comparison of hazard from 2292 canisters of ATW waste with that from 7640 canisters of LWR spent fuel, disposed of in YMR surrounded. For the immobile medium, the same graph is obtained regardless of 7285 canisters of recovered uranium. For the reduction of the uncertainties, it is observed that the difference between the mobile and immobile for the ATW realistic case is about 150 fold, whereas the difference for the LWR spent fuel