Considerations of Autocatalytic Criticality of Fissile Materials in Geologic Repositories

Research Preprint (to appear in Nuclear Technology)

W.E. Kastenberg, P.F. Peterson, J. Ahn, J. Burch, G. Casher, P. Chambré, E. Greenspan, D.R. Olander, J. Vujic
Department of Nuclear Engineering
University of California
Berkeley, CA 94720-1730

B. Bessinger, N.G.W. Cook, F.M. Doyle, B. Hilbert
Department of Materials Science and Mineral Engineering
University of California
Berkeley, CA 94720-1760

April 4, 1996

Abstract

We systematically assess potential routes to autocatalytic criticality in geologic repositories. If HEU or 239Pu are transported and deposited in concentrations similar to natural uranium ore, criticality can, in principle, occur. For some hypothesized critical configurations, removal of a small fraction of pore water provides a positive feedback mechanism which can lead to supercriticality. Rock heating and homogenization for these configurations can also increase reactivity significantly. At Yucca Mountain, it is highly unlikely that these configurations can occur; Pu transport would occur primarily as colloids and deposit over short distances. HEU solute can move large distances in the Yucca Mountain setting; its ability to precipitate into critical configurations is unlikely, due to a lack of active reducing agents. Appropriate engineering of the waste form and the repository can reduce any remaining probability of criticality.

Introduction

We have systematically analyzed scenarios, postulated by C.D. Bowman and F. Venneri, for large energy releases from fissile materials buried in geologic repositories [1]. Energy release could, in principal, occur if chemical and hydrologic processes reconfigure fissile material into a critical or supercritical configuration, where on average one or more of the neutrons released by fission of a nucleus go on to cause another fission. For a supercritical system, the effective neutron multiplication factor keff exceeds 1 and the fission power climbs with time as

(1)

where the inverse period or "time eigenvalue" is approximately equal to the instantaneous reactivity

(2)

divided by the effective neutron generation time . In all supercritical systems, the energy release eventually terminates after negative feedback mechanisms force to become negative.
In these scenarios, the most likely critical configurations consist of a moderating material such as rock or water interspersed with fissile material. The rock slows (moderates) fast neutrons to thermal velocities by collisions with light nuclei, facilitating fission of the thermally fissile isotopes uranium-235 and plutonium-239. Original emplacements of fissile material in repositories will be made subcritical (keff < 1) by design, incorporating neutron absorbing materials and by controlling the quantity and geometry of fissile material in each canister.

The United States is considering four classes of materials for potential geologic disposal. Because of significant differences in the quantities and environmental transport behavior of the thermally fissile materials (TFM) 235U and 239Pu, the potential routes to criticality differ for each nuclide. The disposal of commercial spent fuel, with typical effective enrichments (235U and 239Pu) around 2%, and vitrified military high-level reprocessing wastes containing trace quantities of plutonium and uranium, have been studied for more than 20 years. Recently, the U.S. Department of Energy has also initiated studies of the geologic disposal of 50,000 kg or more of separated excess weapons plutonium, that may be immobilized in glass or ceramic (2), and 210,000 kg, or more, of highly enriched uranium (HEU) from research and naval reactors [3].

In this paper we address the following two questions, "Are there realizable geometric and material configurations of thermally fissile material and moist rock which are critical and can exhibit positive feedback?" and, "In the Yucca Mountain geologic, hydrologic and geochemical setting, can these configurations occur?" To help answer these questions, we present an event tree, a summary and selected cases from our detailed criticality analyses and considerations of TFM release and transport. These will be described below.

AUTOCATALYTIC CRITICALITY EVENT TREE

We found that seven events would be required to cause autocatalytic criticality with rapid energy release, sufficient to vent radioactivity above ground. For a given scenario and waste form, if engineered or natural features prevent any of the seven events from occurring, venting of radioactivity becomes impossible.

First, the waste package must degrade before significant quantities of TFM undergo radioactive decay. For scenarios involving 239Pu the time scale for degradation is limited by the 24,400-year half life. For scenarios involving HEU spent fuel (and weapons-grade plutonium that has decayed to HEU), the main time constraint comes from regulatory requirements, because 235U has a 700-million-year half life.

Second, chemical processes must separate neutron absorbing poisons such as boron and 238U from the TFM. Third, hydrologic processes must transport the TFM, either dispersing it into moderating material around the original waste emplacement, or carrying it away from multiple emplacements. Fourth, a sufficient quantity of TFM must be available and transported. Fifth, the TFM must be re-deposited in a critical configuration. Sixth, upon reaching criticality, some mechanism must provide positive reactivity feedback as the system heats. Seventh, the dynamic response of the system must keep the neutron multiplication factor keff above unity until sufficient energy has been released to cause venting of radioactivity to the atmosphere. Without venting to the atmosphere, the primary effect of criticality is to generate additional fission products below the repository.

Figure 1 shows an event tree constructed for the four nuclear material types now considered for geologic disposal. In this paper, we divided scenarios into three subsets. The first subset consists of scenarios at the original waste emplacement location (paths 2-5-10-14 and 3-7-12-14). The second subset involves transport of HEU in solution to the far field (1-8-13). The third subset involves transport of plutonium in colloid form away from emplacements (2-4-9-13, 3-6-11-13). Though improbable to varying degrees, these scenarios should be considered during detailed design of any repository containing fissile materials.

Fig. 1 Autocatalytic event tree.

Undermoderated Criticality at a Waste Emplacement

Bowman and Venneri [1] proposed a scenario for undermoderated (dry) autocatalytic criticality occurring at the original emplacement of weapons plutonium immobilized in borosilicate glass, in intimate contact with surrounding fractured rock. The scenario required that the stronger neutron absorbers leach from the glass before significant 239Pu decay occurs, leaving plutonium behind. Subsequently the resulting undermoderated configuration was assumed to be driven critical by dispersion of the plutonium into surrounding rock, effectively adding more moderator to the initially undermoderated system and increasing reactivity. They then postulated that vaporized plutonium would vent through fractures in the surrounding dry rock, providing a positive reactivity feedback mechanism.

While previous reviews have confirmed the neutronics calculations performed by Bowman and Venneri, none have supported their estimates of high probability for the formation of critical deposits or for significant release of energy [4-7]. Without detailed calculations, we take no position on whether dry undermoderated systems might experience positive reactivity feedback, but note that such mechanisms appear speculative for the following reasons.

Large quantities of TFM are required to achieve criticality under dry conditions. Sanchez et al. 8 calculated the minimum 239Pu critical mass for reflected homogeneous spheres with various moderators: pure water requires 0.49 kg of 239Pu; pure silicon dioxide requires 35.1 kg of 239Pu; and tuff rock requires 85.6 kg of 239Pu. A typical 125-ton steel multipurpose canister for commercial spent fuel would contain around 60 kg of 239Pu and 40 kg of 240Pu. Considering realistic moderating materials, heterogeneity, and non-spherical geometry, this mass is insufficient to support dry criticality. Furthermore, if necessary, waste-form designs can incorporate neutron absorbers with solubilities comparable to plutonium, providing long-term criticality control.

Overmoderated Criticality

Bowman and Venneri also proposed scenarios for overmoderated (wet) autocatalytic criticality [1]. Water absorbs neutrons more effectively than many types of rock (including tuff). Hence, in a geologic setting, a system is overmoderated when the neutron-absorbing effect of water exceeds its moderating contribution, so that water expulsion from rock pores increases reactivity. Overmoderated criticality in a geologic setting was recognized in the 1970s, but generated less interest then because no plans existed to dispose of HEU and it was difficult to postulate credible chemical mechanisms to separate plutonium from the large quantities of neutron-absorbing 238U in commercial spent fuel [9, 10].

Achievement of overmoderated criticality at a waste emplacement would require the addition of water followed by the removal of other neutron absorbers. It is best prevented by the use of neutron absorbers with lower solubility than the TFM.

For scenarios involving transport of TFM away from emplacements, the potential quantity of TFM is greater than the inventory in a single canister. We were unable to entirely eliminate two potential mechanisms that may deposit critical configurations of TFM from single or multiple emplacements. In this paper we address these two mechanisms: the potential for transport of HEU in solution in ground water, with precipitation in the far field; and the transport of plutonium-bearing colloids, with deposition away from multiple emplacements.

Only two of the potential waste forms can yield HEU: HEU spent fuel; and weapons-grade plutonium immobilized in glass or ceramic, after the 239Pu decays to 235U. Natural uranium ore deposits provide evidence for the configurations HEU might take, if it were to precipitate below a repository. For example, in the Peña Blanca uranium deposit in Mexico, pitchblende (UO2+x) is found in fault zones in fractured tuff as coatings, veinlets, stringers and disseminations. In deposits of this type, average uranium weight fractions can be 0.3 percent, reaching 10 percent locally [11]. Figure 2 shows that these concentrations would be sufficient to reach criticality in infinite, homogeneous systems (kinf = 1) for uranium with enrichment greater than roughly 4%. For finite systems, neutron leakage increases the critical concentration of HEU somewhat.

Heterogeneity can greatly increase the critical concentration of HEU. For HEU deposited in parallel fractures spaced at 20 cm rather than homogeneously, Figure 2 shows that the critical concentration doubles or quadruples depending on water content. Though the geometry of HEU in actual deposits could differ, such deposits would likely become critical at concentrations between the heterogeneous and homogeneous cases shown in Figure 2. Increasing water content in the rock matrix, like heterogeneity, increases the critical concentration of HEU.

Fig. 2 Average uranium density required to achieve criticality, kinf = 1, in tuff rock (2.2 g/cc). Homogeneous mixtures require lower concentrations, ( - 0.1, - 0.2 g/cm^3 H2O). Heterogeneous UO2+x coatings in parallel fractures spaced at 20 cm require more ( - 0.1, - 0.2 g/cm^3 H2O). (*Approximate enrichment, diluted primarily with U-236.)

Figure 3 illustrates why deposition of critical heterogeneous configurations of HEU could be a significant concern. The curves show that for higher enrichments, removing all of the water from the rock matrix would take the calculated neutron multiplication factor kinf above 1.3. If the energy release begins to melt rock, mixing of rock and TFM can occur. Based on this static calculation and neglecting other feedback mechanisms, complete mixing and homogenization would give kinf above 1.5. Plutonium deposited in rock fractures exhibits similar criticality behavior to HEU deposits.

Fig. 3 Effect of 100% water expulsion for systems with initial water contents of - 0.1 and - 0.2 g/cm^3 H2O, and effect of homogenization for systems with water contents - 0.1 and - 0.2 g/cm^3 H2O, on the neutron multiplication factor of an initially critical (kinf = 1), wet, heterogeneous rock/water/U-235/U-238 system with 20 cm fracture spacing.

STATIC NEUTRONIC ANALYSIS FOR HETEROGENEOUS ACCUMULATIONS OF TFM AWAY FROM EMPLACEMENTS

Among the major criticisms of the Bowman and Venneri analysis are the assumptions of homogeneous (rather than heterogeneous) mixtures, use of pure SiO2 rather than real tuff rock, and the use of 239Pu rather than the inclusion of even isotopes such as 240Pu. For the neutronics analysis presented here, geohydrologic transport processes were assumed to carry TFM from multiple canisters and deposit it in rock fractures as shown in Figure 4a. This heterogeneous arrangement is more consistent with the fractures encountered in common geologic media. Static calculations were performed for plutonium dioxide and uranium dioxide at different enrichments. Though many geologic media can serve as moderators, the rock considered here is real tuff (Table 1) rather than pure SiO2.

Table 1 - Reference Topopah Spring rhyolite tuff composition, density = 2.2 g/cm^3.

Here we report on a limited subset of the cases we considered. Six reactivity-feedback mechanisms were studied independently: water removal, TFM-temperature increase, rock-temperature increase, homogenization of TFM and rock, buildup of fission and transmutation products, and expansion. Two code systems were used: the BONAMI-NITAWL- XSDRN (1-D Sn) modules of SCALE 4.2 with a 27-group cross section library [12], and MCNP, a 3-D Monte Carlo code [13].

We selected two reference configurations to illustrate the magnitude of different reactivity feedback mechanisms:

(1) An infinite lattice of parallel fractures, 1 mm wide and 200 mm apart, having a thin layer of TFM uniformly deposited on the surfaces of the fractures (Fig. 4a). The TFM thickness was adjusted between 0 and 0.2 mm to give kinf = 1. As noted above this geometry is typical of repository conditions.

(2) A spherical "core" (Fig. 4b) consisting of the homogenized lattice (Fig. 4a). A 2-m radius reference case is presented here for illustration, choosen from several radii considered in this study . To give keff = 1, this 2-m "core" contains 254 kg of 239Pu, and is surrounded by 1.2-m of rock (essentially an infinitely thick neutron reflector).

Fig. 4 Schematic of a) parallel fracture lattice used for infinite system kinf and finite keff calculations, and b) the spherical finite system.

Figures 5 and 6 illustrate the effect of water removal. If fracture water flow deposits 239Pu on the fracture surfaces and brings k to about 1, when the fractures dry, k drops slightly below 1 (Fig. 6). As a drying front propagates into the rock (Fig. 5), the neutron multiplication factor k increases. The effect of even isotopes such as 240Pu on the feedback from drying is relatively small. In the finite system, drying less than 30 mm of the rock brings k back to 1. Uranium-rock-water systems have similar behavior with even smaller effects of even isotopes such as 238U on the feedback from drying. Thus drying would provide the most likely mechanism to initiate a chain reaction.

Fig. 5 Schematic of drying front propagating from fracture into rock.

Fig. 6 Effect of drying on neutron multiplication k and inverse period in the reference infinite and finite heterogeneous systems, containing pure Pu-239 and, initially, 0.1 g/cm3 pore water.

Fission-generated heat would accelerate the drying process. In the finite system the effect of drying on k is substantially smaller, because water removal increases the neutron leakage probability from the core. Sufficiently small systems have no positive feedback. Figure 6 also provides curves for the inverse period . After removal of a fraction of the water from the rock sufficient to make the system prompt-critical, the fission power can ramp rapidly over a time period well under a second.

The TFM temperature will increase significantly should a prompt critical state be established. If the amount of 239Pu equals or is greater than 99% in TFM, the reactivity insertion is slightly positive due to the increase in the effective 239Pu cross-section from resonance (Doppler) broadening. However, with more than 1% 240Pu the Doppler effect on reactivity is negative. In the case of uranium systems, the reactivity insertion is slightly positieve only for systems with pure 235U. However, for fuel temperatures above 50,000 K the uranium systems with even 25% of 238U show the positive reactivity trend due to the Doppler effect.

Heat conduction and direct volumetric heating would increase the rock temperature, increasing the average neutron energy and expanding the rock. For relatively pure 239Pu this neutron spectrum hardening can have a significant positive reactivity feedback, as Fig. 7 illustrates for infinite lattice systems. This positive reactivity feedback is attributed to the effect of the pronounced 0.3 eV resonance of 239Pu: as the spectrum hardens with the increase in temperature, there is an increase in the ratio of the average absorption cross-sections of 239Pu to the average absorption cross-section of hydrogen and the rock constituents. Heterogeneous systems of 235U also have positive reactivity feedback, even though 235U lacks a strong low-energy resonance. The positive temperature feedback becomes significantly stronger as the rock water content increases. If the system is well thermalized when at room temperature, spectrum hardening will reduce the effective absorption cross-section of the fissile material, i.e., reduce the thickness of the HEU layer as measured in unites of mean-free-path for absorption. The net outcome is a reduction in the self-shielding of the HEU layer and, hence, an increase in the ratio of absorptions in the HEU layer to absorptions in the rock (plus water) layer. All the homogeneous HEU systems have a negative temperature coefficient of reactivity, regardless of the amount of water in the rock. The even isotopes 240Pu and 238U reduce reactivity feedback due to temperature change.

Fig. 7 Effect of heating of rock moderator on neutron multiplication kinf in heterogeneous critical systems with pure Pu-239 , Pu-239 with 6% Pu-240 , pure U-235 , and U-235 with 25% U-238 (fuel temperature remains constant). Open symbols indicate the corresponding homogeneous systems.

Once the rock temperature becomes sufficiently high for the rock to start melting, homogenization becomes a potentially significant mechanism for reactivity insertion. Figures 8 and 9 show the effect of homogenization in terms of the change in k and as TFM mixes with rock, layer by layer, for both the infinite lattice and finite system. With full homogenization, power doubling occurs within less than 1 msec (0.693/).

Fig. 8 Schematic of homogenization front propagating from fracture into rock

Fig. 9 Effect of homogenization on neutron multiplication k and inverse period in the reference infinite and finite heterogeneous systems containing pure Pu-239 and 0.1 g/cm^3 pore water.

Expansion increases neutron leakage and provides the primary mechanism for bringing keff below one, quenching the chain reaction. Figure 10 shows that the fully homogenized 2-m radius reference system (right side, Fig. 9) becomes subcritical when expanded to a 3.7 m radius with a uniform core density.

Fig. 10 Effect of uniform expansion on neutron multiplication k and inverse period a in the reference homogenized finite spherical system containing pure Pu-239 and 0.1 g/cm^3 pore water.

Additional mechanisms influence the TFM-rock-water system neutronics, although to a lesser degree. The buildup of fission products (i.e. 135Xe) and other neutron absorbers (i.e. 240Pu) plays a negligible role. The presence of additional neutron absorbing material in the rock, impurities in water (i.e. B, Cl), increased fracture spacing, and nonspherical core geometries increase the critical TFM mass. However, if sufficient TFM is available, these effects also increase the potential reactivity insertion. Positive feedback from pore water removal disappears if the rock neutron absorber concentration becomes sufficiently large. A nonuniform distribution of TFM, peaking toward the center of the core, can decrease the critical TFM mass. Additional subcritical TFM-rock-water configurations near a critical system may increase the energy release.

DYNAMIC RESPONSE OF OVERMODERATED, HETEROGENEOUS ROCK/WATER/TFM SYSTEMS

If TFM deposits away from multiple emplacements, criticality could be approached in two ways. First, TFM deposition may continue until the critical concentration is reached. Alternatively, an initially subcritical deposit of TFM may become critical upon drying. For instance, HEU precipitated below the water table could become critical if the water table drops, as might occur with ground-water pumping.

Should a heterogeneous, overmoderated TFM system reach criticality, the initial response will depend on the relative magnitude of the various reactivity feedback mechanisms. Initial slow heating will expel water. Due to low rock permeability, the time scales for water expulsion will be of the order of seconds to hours for length scales of millimeters to several centimeters. For typical saturated conditions, a slow 70°C temperature increase can expel 3.5% of the rock matrix water, because the water thermal expansion coefficient exceeds the rock thermal-expansion coefficient by over an order of magnitude. For unsaturated conditions, vapor pressure gradients generated by temperature gradients will drive vapor transport, by diffusion at lower temperatures and increasingly by advection as the temperature approaches boiling. Although some negative feedback mechanisms may slow the power rise, such as rock thermal expansion or opening of fractures by steam pressure, water expulsion (and reactivity insertion) can continue due to the temperature gradients.

The prompt energy released by TFM-fission partitions with approximately 93.3% from fission fragment energy deposited locally, while 2.8% from neutron kinetic energy and 3.9% from prompt gamma radiation deposits through the rock mass.

With TFM deposited as coatings in rock fractures, the TFM is thermally well coupled to the rock and can bring the rock fracture surfaces to the rock melt temperature. For tuff, the rock melt temperature depends on water content, ranging from 950°C for dry tuff to 720°C for fully saturated tuff [14].

As rock melts, some mixing of TFM and rock can occur. As noted above, the reactivity increase from mixing will be substantial. Figure 10 indicates that considerable expansion can be required to return a fully homogenized system to subcriticality. Such expansion can only be driven by vaporization of rock and TFM. Rayleigh-Taylor instability will make it difficult for the vaporized material to drive dense molten rock outward; rather the vaporized material could be expected to preferentially finger into, and mix with, molten rock as the system expands.

Modeling the coupled hydrodynamic and neutronic response of heterogeneous configurations was beyond the scope of the present work. For a given system the magnitude of the energy release, however, can be bounded by assuming instantaneous homogenization (likely a highly conservative assumption). Using a LLNL code, the coupled momentum, energy, mass, and neutronics equations were solved for the reference 2-m radius spherical system. With the large instantaneous reactivity insertion from homogenization (Fig. 7), the power began to ramp rapidly at 5.8 msec. The system became subcritical at 6.8 msec, upon reaching a core radius of 3.1 m. The calculated energy release, 0.32 kilo-tonne (1.3x1012 J), likely bounds the release possible for this idealized configuration (254 kg of 239Pu in tuff with 0.1 g/cm3 water) with slower reactivity insertion rates. Scaling rules used at the Nevada Test Site (NTS) indicate that the repository overburden is sufficiently deep to contain this energy release. For deposits close to repository tunnels, the potential for venting will depend on the backfill system employed in the tunnels.

RELEASE, TRANSPORT, AND DEPOSITION OF PU AND HEU

Three distinct aqueous processes would be involved in forming actinide deposits from repository emplacements: release from the waste form; transport in solution or suspension through the void volumes in the rock; and localized deposition from solution. These processes would have to be driven by water flowing through the repository from surface precipitation.

At Yucca Mountain, waste would likely be emplaced horizontally in mined drifts in massive metal canisters, located in unsaturated, highly-fractured welded tuff, a minimum of 200 m below the mountain surface and 300 m above the water table. The average vertical water infiltration rate is currently about 10-3 m3/yr-m2 (1 mm/yr), but is likely to rise by an order of magnitude during future pluvial periods [16]. The present flow rate is equivalent to a few drops of water per hour per square meter of repository area. The flow distribution through the repository may be nonuniform as a result of the thermal perturbation from waste decay heat and fast-path flow through fractures. Regardless, on purely geometric grounds, only a fraction f < ~0.1 of this vertical influx would contact waste. The rest would either pass through the rock between drifts, fall in the air gap between waste and canister, or filter through canister debris. Engineered barriers such as graded backfill can provide additional protection against water ingress.

Based on typical fracture-augmented surface-to-mass ratios (0.01 - 0.02 m^2/kg) and the rough mean of numerous estimates of the "long-term" glass alteration rate (~ 0.002 g/m^2-d) [17], the lifetime of a glass log is ~10^5 years. The longevity of ceramic UO2 waste forms such as spent fuel, estimated by solubility-limited dissolution kinetics, is at least as long. As the glass or ceramic degrades, U and Pu would be released from the pristine waste form. Because of their low solubilities in water, they tend to remain on the waste surface as precipitates, most likely the dioxide for Pu, and for uranium, one or more of the numerous solid phases that U(VI) naturally forms.

Plutonium behavior

The true solubility of PuO2 in water is almost certainly less than 10 ppb by weight 18, but because of the propensity of Pu to form colloidal particles, or more likely to be sorbed onto colloids formed from degradation of the waste form and canister, the apparent solubility can approach 1 ppm [19]. These suspensions are not very stable, as evidenced by the following: i) when formed by degradation of Pu-containing glass, the solution concentration of Pu decreases with standing with a half-life of ~ 50 days 19; ii) the sorption coefficient of Pu on tuff of ~ 200 l/kg rock [3], which, though not giving concentrations sufficient for criticality, is still very large and probably reflects mainly removal of colloidal species; iii) almost all static or flow leach experiments involving Pu report the propensity of this element to adhere to experimental structures. In a repository setting, the most likely physical states of released Pu are: 1) mineralization on the altered glass surface; this form is easily spalled by water flow or even drying out [19]; 2) particulates collecting on the drift bottom mixed with much larger amounts of rock rubble and iron oxides from the canister; and 3) in fractures within meters of emplacement.

Pu deposited in fractures can potentially form a critical configuration. However, the expected short range of migration, either because of colloid filtration or sorption on rock, means that such deposits would originate from one or at most a few emplacements. Because each emplacement would probably contain ~60 kg of 239Pu, much of which decays to soluble uranium before complete waste form degradation occurs, the probability of collecting the necessary critical mass from this limited source is very small. The small range of Pu migration is corroborated inferentially by the nearly complete immobilization of this element in the Oklo natural reactors since their activation two billion years ago [20]. The absence of long-range Pu migration is also supported by detailed diffusion-advection-sorption analysis of transport in a dual porosity system consisting of fractures and matrix porosity [21].

The Pu in colloids will likely be diluted significantly by SiO2 and other species, making it geometrically impossible to deposit critical concentrations in fractures of typical apertures.
Particulate Pu from many emplacements that has collected at the bottom of drifts may be washed by periodic high water flows to a low point in the repository where a critical mass could accumulate. However, the chief role of 239Pu in inducing criticality appears to be to produce more mobile 235U by radioactive decay at the emplacement site.

Uranium behavior

The water chemistry at Yucca Mountain is conducive to high uranium solubility: it is oxidizing, carbonated, and moderately basic. Solubilities calculated from geochemical codes PHREEQE and EQ3/6 range from 10^-9 to 10^-4 M, depending on the solid phase assumed in the analysis [22, 23]. Measured solubilities of UO2 or spent fuel in typical oxidic, carbonated ground water center around 1 ppm by weight (Csat ~ 4x10-6 M) [23, 24], too small for criticality. Colloid formation is less important for uranium than for Pu. Assuming a water infiltration rate I = 10 mm/yr, and solubility-limited release of U from the waste form with a dilution factor of f ~ 0.1, the release rate of U to the tuff underneath the repository is q = f I Csat ~ 10^-6 kgU/m2-yr. The diffusion-advection-sorption analysis with this release rate provides the spatial and temporal distribution of U in the rock, assuming that the fracture surfaces are not sealed [21]. The maximum concentration of sorbed U is 0.235 (1-e) r Kd Csat, where e ~ 0.1 is the porosity and r = 2200 kg/m^3 is the density of the rock. With a U sorption coefficient Kd ~ 10 lit/kg [3], the sorbed concentration is ~ 0.02 kgU/m^3 or a weight fraction of ~ 10^-5, which is too small for a critical assembly, even for pure 235U (Fig. 2).

Whereas diffusion into the matrix would disperse uranium throughout the rock mass, sealing of fracture surfaces by mineral precipitates would permit these flow paths to deliver uranium to deep rock beneath the repository. Were such flow to encounter a zone of rock containing an accessible reducing agent (such as sulfides or other Fe(II) compounds), U(VI) compounds could be reduced to insoluble U(IV) and a pitchblende-like ore body formed. There is evidence that water in the aquifer of Yucca Mountain is, at least in some locations, chemically reducing [25]. Furthermore, the tuff at all elevations contains small amounts of Fe(II), principally as magnetite (Fe3O4) [26]. The mountain-average concentration of this oxide is ~ 0.33 volume percent, which, if all used exclusively to reduce U(VI), could precipitate ~ 10 kgU/m^3.

Despite these suggestions of the potential for uranium reduction, numerous factors indicate that such a process is highly unlikely. First, the usual and most geologically potent reducing agents, pyrite and organic matter, have not been detected at Yucca Mountain. Second, rock minerals containing reduced Fe in Yucca Mountain have survived ~ 2 million years of exposure to oxidizing water, suggesting that the Fe(II) is not accessible. Third, although some of the reducing components in the rock could be exposed by thermomechanical perturbations due to the repository or because of seismic activity, it is very unlikely that the entire charge of newly-accessible Fe(II) could be utilized to reduce U(VI). The concentration of dissolved O2 in Yucca Mountain water above the aquifer is ~ 100 times larger than that of uranium, although kinetic factors may favor uranium reduction over O2 reduction. However, radiolysis of the descending ground water and air by alpha decay of 239Pu produces very potent oxidizing agents (e.g., H2O2 and ) at concentrations comparable to those of uranium. In contrast with the roll-front mechanism responsible for many ancient uranium deposits, Yucca Mountain does not appear to contain sufficient quantities of reducing rock or reduced pore water to overwhelm the strong oxidizing agents expected in the water from the repository, thereby permitting uranium precipitation.

If, despite the above contraindications, a volume of reducing rock in the path of uranium-laden ground water from the repository becomes chemically activated, the time to accumulate a critical mass is Mcrit/qA, where q is the uranium release rate from the repository and A is the projected area of the reducing zone. Taking Mcrit ~ 100 kg 235U, A ~ 10 m^2 and q = 10-6 kgU/m^2-yr, the time to achieve static criticality is ~ 10^7 years. This estimate does not account for "focusing" of the descending water which could occur because the relatively impermeable basal vitrophyre layer below the repository is penetrated only by a small number of fractures. Focusing of the flow reduces the time required to achieve a critical mass, but also reduces the probability that the flow would encounter a zone of active, accessible, reducing rock.

Summary of actinide behavior

The probability of accumulation of a critical mass of Pu or HEU in the Yucca Mountain tuff by the action of geologic processes on glass or ceramic UO2 waste forms is likely very small. Pu is expected to remain close to the emplacement site and to decay to HEU before the waste form matrix is completely degraded. Uranium will eventually be removed from the repository by water, but will be dispersed into the rock by diffusion and sorption at concentrations well below that required for criticality. Conditions for precipitation of uranium into an underground critical mass are improbable in the Yucca Mountain environment.

Any deposition that did occur would likely be nonuniform. For some scenarios a small region could become critical early in the deposition process. If sufficiently small, the deposit would be undermoderated. For example, at 0.2 g/cm^3 water content the transition from overmoderated to undermoderated occurs at a sphere diameter of approximately 0.5 m. Subsequent addition of TFM to an undermoderated critical deposit would cause drying, preventing the creation of an overmoderated deposit exhibiting positive reactivity feedback from water expulsion.

ENGINEERING STRATEGIES

Though the probability of forming critical deposits of TFM at Yucca Mountain appears exceedingly low, engineered systems can further reduce the probability, and may also provide a simpler basis for meeting licensing criteria. Reprocessing to extract fissile material from spent fuel provides an engineered solution to criticality, however we believe that other strategies can also alleviate criticality concerns.

Criticality at Original Waste Emplacement - Insoluble Poisons. Here an engineered strategy is to provide neutron absorbers with lower or comparable solubilities to plutonium and HEU in the waste form.

HEU Precipitation in Far Field - Dilution. Dilution of 239Pu or HEU with depleted uranium (DU), which is 99.7% 238U, is an effective method of preventing criticality. Over 80% of the uranium ever mined exists as the tails of uranium enrichment plants, and is readily available as UF6. This material has no current large-scale use and is essentially free of charge.
To be effective in protecting Pu wastes from criticality, sufficient DU must remain at the emplacement site during the lifetime of 239Pu. In the current design of the Yucca Mountain repository, the air gap between the canister and rock is large enough to accommodate 50MT of DU per meter of tunnel length. With the infiltration rate and uranium solubility used above, the lifetime of this quantity of uranium dioxide is approximately 10^9 years. Thus a much smaller quantity of DU would satisfy the 239Pu lifetime requirement of 10^5 years. The potential of separation of DU from fissile material does not arise with HEU wastes, because both are chemically identical (even metallic HEU spent fuel will first be converted to the stable oxide upon contact with water).

At Yucca Mountain 238UO2 pellets could serve as the gravel in a graded backfill system, discussed below. For other repositories, alternative strategies could be adopted, such as integrating DU directly in glass waste forms.

Pu Colloid Transport Away From Emplacements - Immobilization. Engineered backfill systems can potentially immobilize Pu colloids and allow their decay. Isolated failure of a backfill system could be acceptable, because the Pu release would be limited to a single emplacement.

Capillary barriers formed by the interface between sandy silt and gravel are now under study for use in a graded-backfill system for Yucca Mountain 27, 28. A gravel backfill would be placed below and over horizontal MPC canisters prior to repository closure, after a several-decade retrievability period. Silty sand would be emplaced over the mounded gravel. Recent experiments have shown that recharge water flows up to 6.0 ml/hr/cm2, or fast path fracture flows up to 15 liters/hr, can be directed into the sand, and the water wicks laterally through the sand without causing saturation. This prevents water penetration across the capillary interface into the gravel [29]. By eliminating advection of water to the waste form, this system prevents mobilization of colloids. The performance of such systems has been demonstrated both by human analog structures--burial mounds over 1300 years old 30--and by natural graded-fill analogs--protected pockets in gravel layers under finer-textured soil horizons that have resisted the penetration of liquid-water flow for tens of thousands, and in some cases, hundreds of thousands of years.

SUMMARY

We can conceive of a large number of geometric and material configurations of TFM with rock and water, some of which are critical and have positive feedback. However, at Yucca Mountain it is highly unlikely that Pu will travel large distances as a solute to form these configurations; Pu is more likely to be transported as colloids, and be redeposited close to its original emplacement. Additionally, 239Pu will decay to 235U before most of a glass waste form is leached. It is expected that commercial spent fuel behavior is similar.

Water chemistry at Yucca Mountain is conducive to high uranium solubility, hence 235U can move large distances as a solute. However, at Yucca Mountain, once uranium is in solution it is unlikely to precipitate into these critical configurations due to lack of reducing agents.

Engineering of the waste forms and the repository can further reduce the likelihood of the formation of critical emplacements with positive feedback. Reprocessing of spent fuel to extract fissile material would also eliminate any criticality problems. Other important topics remain to be investigated theoretically, including the minimum size for critical systems with positive reactivity feedback; parametric studies of dynamic response and energy release, particularly for small TFM deposits; and the potential for TFM deposition in repository back-fill material. The composition of Pu pseudo colloids, their mobility in rock fractures, the efficiency of their removal from infiltrating water are topics that must be explored by experiment.

ACKNOWLEDGMENTS

This review was performed under the support of LANL UCDRD funds. We gratefully acknowledge the researchers who provided useful information and input, including C.D. Bowman, D.K. Parsons, W.R. Stratton, and F. Venneri of LANL; T.S. Carman, W. Glassley, and R. Van Konynenburg at LLNL; R.P. Rechard at SNL; J. Apps at LBNL, F.F. Peterson at UNR, and J.L. Conca at WSU.

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NOTES

a The assistance of T. Scott Carman of Lawrence Livermore National Laboratory in performing the calculation is appreciated. The tuff (Table 1), initially at 17°C with 0.1 g/cm^3 water, was modeled with SESAME equation of state 7112. An 8-m thick tuff reflector was assumed.

b At the NTS containment is expected for depths greater than 122 (yield kt)^1/3 m, for fully tamped conditions. For Yucca Mountain, this implies a yield of 4.4 kilo-tonne of explosive equivalent at the minimum repository depth (200 m) and 69 kt at the water table (500 m). Caveats include: an autocatalytic deposit couples energy to surrounding rock differently from nuclear weapons; containment varies with the geologic condition of the overburden; for deposits close to tunnels, back-fill methods affect containment; residual stresses from slow, low-yield events may be less effective in forming a "containment cage" to seal fractures; and rock with lower porosity than tuff may be less effective for containment [15].

For more information, see:

U.C. Berkeley Department of Nuclear Engineering

UCB Center for Nuclear and Toxic Waste Management