A review of near-field mass transfer in geologic disposal systems

Abstract

N*u4«ld Maw Trantfw 2.0 LOW-SOLUBILITY SPECIES The dissolution rate of waste solids in a geologic repository is a complex function of waste solid geometry, chemical reaction rate, exterior flow field, and chemical environment. Our analysis of dissolution rates is divided into those of low solubility and readily soluble. 2.1 Dissolution from Waste Into Porous Rock with a Solubility Boundary Condition We are concerned with the transfer of a diffusing species from a waste form into porous rock. The governing equation in the most general sense, without accounting for losses, is K-+ vVc = DV 3 c (2.1.1) at where c is the concentration of the species in ground water, v is the ground water velocity, D the diffusion or dispersion coefficient and A" is the species retardation coefficient. The solubility boundary cotidition is c = c, (2.1.2) on the surface of the waste form the concentration is that of the species solubility e, (Figure 2.1), and the other boundary condition is c=0, at infinity (2.1.3) and the initial condition c = 0, < = 0 (2.1.4) We shall be concerned with solving this set of governing equations in various forms throughout the remainder of this paper. 2.1.1 Steady-State Results 2.1.1.1 Diffusive The steady-state form of the equation for for mass transfer by molecular diffusion a low-solubility longlived species, assuming constant saturation concentration c, in the liquid at the waste surface and assuming that the waste solid is surrounded by porous rock, is /=^i (2.1.1.1.1) where / is the fractional dissolution rate of the species, t is the porosity of the rock, D is the diffusion coefficient in pore water, and M is the bulk density of the elemental species in the waste. B is a geometrical factor that can be calculated from the waste-form dimensions. For a spherical waste solid of radius R B=± (2.-1.1.1.2) For a prolate spheroid approximating a cylindrical waste form 3£ * = 6*log[coth(*,/2)]

AREST model description

“…Researchers at UCB (Kang 1990;Pigford et al 1990) have developed a general, time-dependent . model for this fracture scenario.…”

“…An exact analytical equation has been developed for decay chain in-growth (Kang 1990;Pigford et al 1990), although for completely different set of boundary conditions than are considered in AREST. While new release models for evaluating decay chain in-growth are being developed, it is necessary for the currently implemented models in AREST to approximate the effect of decay chain in-growth.…”

Preliminary calculations of release rates of Tc-99, I-129, and Np-237 from spent fuel in a potential repository in tuff

“…Because every unit increase in pH leads to a reduction in UO2 alteration/dissolution rate by a factor of 10, the effect of boiling may be a key process that affects source-term calculations. [Pigford and Lee 1989;Pigford and Chambrd 1988).…”