T.H. Pigford

Analytical Performance Models for Geologic Repositories

This report presents analytical solutions of the dissolution and hydrogeologic transport of radionuclides in geologic repositories. Numerical examples are presented to demonstrate the equations resulting from these analyses. The subjects treated in the present report are: (a) Solubility-limited transport with transverse dispersion (Chapter 2); (b) Transport of a radionuclide chain with nonequilibrium chemical reactions (Chapter 3); (c) Advective transport in a two-dimensional flow field (Chapter 4); (d) Radionuclide.transport in fractured media (Chapter 5); (e) A mathematical model for EPAs analysis of generic repositories (Chapter 6); and (f) Dissolution of radionuclides from solid waste (Chapter 7).

Steady-state and transient radionuclide transport through penetrations in nuclear waste containers

The transport of radionuclides through penetrations in wastes containers is analyzed. Penetrations may result from corrosion or cracks and may occur in the original container material, in degraded or corroded material, or in deposits of corrosion products. In this report we do not consider how these penetrations occur or the characteristics of expected penetrations in waste containers. We are concerned here only with the analytical formulation and solutions of equations to predict rates of mass transfer through penetrations of specified size and geometry. Expressions for the diffusive mass transfer rates through apertures are presented in Chapter 2, and numerical illustrations are presented in Chapter 3. The calculations show that mass transfer through small penetrations in thin-wall containers can be great enough that the penetrated container is no longer an effective barrier for radionuclide release. Use of this theory to calculate mass transfer through thick-wall containers is the subject of a later report. 3 refs., 9 figs.

Intermediate-field transport of contaminants: Multiple areal sources in fractured rock and point sources in porous rock

Abstract The authors show exact analytic solutions for hydrogeologic transport of contaminants from an array of point sources in a waste disposal site, and contaminants released from finite areal sources into a planar fracture. For dispersion from an array of sources, dispersion may be isotropic or anisotropic, and equilibrium sorption and radioactive decay are considered. For contaminant released into a fracture, the solution includes the effects of advection in the fracture, transverse dispersion and surface sorption, as well as diffusion into and sorption in the rock matrix. We illustrate the solutions through numerical and graphical displays of the spatial and temporal distribution of the contaminant. The numerical illustrations show that at a certain distance away from the sources, indicated by a distance parameter, equivalent single-source solutions give acceptable approximations.

Transport of soluble species in backfill and rock

In this report we study the release and transport of soluble species from spent nuclear fuel. By soluble species we mean a fraction of certain fission product species. Our previously developed methods for calculating release rates of solubility-limited species need to be revised for these soluble species. Here we provide methods of calculating release rates of soluble species directly into rock and into backfill and then into rock. Section 2 gives a brief discussion of the physics of fission products dissolution from U0{sub 2} spent fuel. Section 3 presents the mathematics for calculating release rates of soluble species into backfill and then into rock. The calculation of release rates directly into rock is a special case. Section 4 presents numerical illustrations of the analytic results.

Waste-package release rates for site suitability studies

Performance-assessment calculations in support of the site- suitability effort for the Yucca Mountain Project will address radionuclide transport arising from various disruptive scenarios. Here we present release rates of radionuclides from individual waste packages for scenarios involving various postulated forms of water intrusion, including increased infiltration rate as well as rock immediately surrounding an individual waste package becoming saturated with ground water. We examine: (1) effect of increased water infiltration rate on release rates; increases in radionuclide release rates resulting from water filling the annulus between the waste container and the surrounding rock, as well as water saturating the pores and fractures in the rock surrounding the waste package; (3) the effect of flow in fractures in the saturated rock on release rate; and (4) release of radionuclides to the mountain surface resulting from an exploratory borehole shaft intersecting a waste package. The radionuclides considered are Tc-99; I-129; Cs-135; Np- 237; Pu-239,240,242; and Am-241,243. Release rates are calculated for both the wet-drip bathtub and the wet-continuous water-contact modes, as described in the Working Group 2 report, applying equations as published by Sadeghi, et al., [1990] and as extended in the present report.

Transport of gaseous C-14 from a repository in unsaturated rock

The authors predict the transport of gaseous {sup 14}CO{sub 2} from a nuclear waste repository in unsaturated rock using a porous-medium model. This model is justified if the appropriate modified Peclet number, which indicates equilibrium between gas in fractures and liquid in rock pores, is much less than unity. Numerical illustrations are given which are applicable to the proposed repository at Yucca Mountain which is 350 m underground. Maximum predicted concentrations of {sup 14}CO{sub 2} near the ground surface are comparable to the USNRC limit for unrestricted areas. Maximum predicted dose rates above ground are less than 1% of background. Travel times are predicted to be hundreds to thousands of years. For some cases, it is shown that the release rate from the source has negligible effect on concentrations at the ground surface. 15 refs., 10 figs., 1 tab.

Prediction of release rates for a potential waste repository at Yucca Mountain

Nuclear waste may be placed in the potential repository at Yucca Mountain in waste packages. The waste will consist of spent fuel assemblies or consolidated fuel rods, as well as borosilicate glass in steel pour containers, each enclosed in sealed containers. Current design calls for the waste packages to be surrounded by an air gap. Although the waste package is generally not seen as the primary barrier for nuclear waste isolation, it must in fact meet specific regulatory requirements. The US Nuclear Regulatory Commission requires that the release rate of any radionuclide from the engineered barrier system following the containment period shall not exceed one part in 100,000 per year of the inventory of that radionuclide calculated to be present at 1000 years following permanent closure. For low-inventory radionuclides, those that constitute less than 0.1 percent of the calculated total curie inventory at 1000 years, the allowable annual release is a constant value, equal to 10{sup {minus}8} of the total curie inventory in the repository at 1000 years. Therefore it is necessary to calculate release rates for waste packages at Yucca Mountain. We calculate release rates for key radionuclides using analytic solutions presented in a companion report. We consider both wet-drip and moist- continuous water-contact modes. We consider the release three types of species: solubility-limited species, species released congruent with solid-solid alteration of spent-fuel matrix or borosilicate glass, and readily soluble species from the fuel-cladding gap, gas plenum, and readily accessible grain boundaries. In each case we give the release rates of the species as a function of time. 22 refs., 11 figs., 9 tabs.

Brine migration in a salt repository

The possible role of brine migration in radionuclide transport in a nuclear waste repository is studied. Mathematical derivation of the analysis is given, along with numerical illustrations using parameter values typical of a nuclear waste repository. For heat-emitting wastes and the parameters studied here, brine migration in salt is minuscule, of the order of micrometers per year, localized within a few meters from the waste package, and highly transient, fading away within a few years of waste emplacement.

Transient Diffusion of Radionuclides from a Cylindrical Waste Solid into Fractured Porous Rock

This paper presents the numerical results of an analytical study for mass transfer and transport of radionuclides released from a cylindrical waste solid into water-saturated fractured porous rock. The purposes of this study are (1) to predict the diffusive mass flux from a cylindrical waste solid into a planar fracture and the surrounding rock matrix for the low-flow conditions wherein near-field mass transfer is expected to be controlled by molecular diffusion and (2) to investigate the effects of cylindrical geometry and of multidimensional matrix diffusion including diffusion in the directions parallel to the fracture plane. In the paper are presented the derivation of an analytical solution for the time-dependent mass transfer from the cylinder for low-flow conditions and computer-code implementation and numerical results. The problem was first proposed and solved analytically by Chambre. Numerical results are shown for (1) the diffusive mass fluxes from the cylindrical waste solid into the fracture and into the rock matrix, (2) the diffusive mass flux across the rock/fracture interface, and (3) the instantaneous concentration isopleths in the fracture and in the rock matrix. Comparison of the present cylindrical model with previous planar models, wherein contaminant was assumed to be released only into the fracture and diffusion in the rock matrix was assumed to be one-dimensional perpendicular to the fracture plane, shows that the cylindrical model is more conservative than the planar models with respect to the mass transfer from the source into the fracture and with respect to the far-field transport, provided that diffusion is dominant in the fracture. 21 refs., 10 figs., 3 tabs.

Mass transport in salt repositories: Transient diffusion into interbeds

To estimate possible radioactive releases from a waste package to the near-field environment, we analyzed pressure-driven brine migration movement and release rates of low-solubility and readily soluble nuclides by diffusion. A possible pathway for radioactive release in salt repositories in interbeds and we have analyzed the steady-state transport of species through the interbeds in which there is ground-water flow. A more realistic situation is when there is no ground-water flow in the interbeds. Here we use some results previously obtained for transient diffusion of radioactive species from a waste cylinder intersecting a planar fracture in rock to the problem of diffusion from a waste cylinder intersecting an interbed in a salt repository. 5 refs., 8 figs., 3 tabs.