Migration Rates of Brine Inclusions in Single Crystals of NaCl
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MIGRATION RATES OF BRINE INCLUSIONS IN SINGLE CRYSTALS OF NaCl
I-MING CHOU U.S. Geological Survey,
959 National Center,
Reston, VA
22092
INTRODUCTION Rock-salt deposits have been considered as a possible medium for the permanent storage of high-level radioactive wastes and spent fuel. Brine inclusions present in natural salt can migrate toward the waste if the temperature and the temperature gradients in the vicinity of the radioactive waste are large enough. This migration is due to the dissolution of salt at the hot side of the salt-brine interface, ion diffusion through the brine droplet, and the precipitation of salt at the cold side of the salt brine interface. In order to quantify the problem, the migration rate of these brine inclusions must be estimated under various repository conditions. Several different models of the migration process were reviewed recently(l),(2),(3). Among them, the model presented by Anthony and Cline(4) is considered as being most complete (1),(2), because it accounts for most of the phenomena known to be involved in the migration process. However, application of their model is difficult because of an insufficient data base. The present paper estimates migration rates for all-liquid brine inclusions in single crystals of NaCl by utilizing recent data for brines and the model of Anthony and Cline. The predictions are compared with experimentally measured migration rates. MAXIMUM MIGRATION RATE AS A FUNCTION OF THE SORET COEFFICIENT Derivations of the equation According to the model of Anthony and Cline(4), the migration velocity of brine inclusions in polycrystalline salt, V, represents the summation of four components, such that
V = VT +V V-VK
(1)
where, VT = velocity due to ordinary (concentration gradient) diffusion; V. = velocity due to thermal diffusion (Soret effect); VK = velocity due to kinetics of dissolution and crystallization of salt at the salt brine interface; VI = velocity due to surface tension at grain boundaries. When the discussions are limited to single crystals, VI = 0. By further neglecting interface kinetics, the maximum migration velocity in single crystals of NaCl becomes Vmax. = VT + Va
(2)
Because Soret coefficients (q in °C-I) of salt in brines are not known, the Soret coefficient must be treated as a variable. Then the theoretical expression given by Anthony and Cline reduces to a simple linear equation: Vmax./Gs = a 7 + b,
(3)
where Vmax. = maximum migration velocity (cm/sec); Gs = temperature gradient within the salt (°C/cm); a = -aDCE/Cs; b = cD(OCE/aT)/Cs; and ol= GI/Gs; GI = temperature gradient in the brine droplet (oC/cm); CR = concentration of salt in brine droplet (moles/liter); Cs = concentration of salt in solid salt (moles/liter); D = diffusivity of salt in brine (cm 2/sec); CE = equilibrium
304 TABLE I Values of the temperature gradient magnification factor, values of X/L
a, for various
T(°C) X/L
Fa) 50
1.0 2.0 3.0 4.0
0.33 0.53 0.64 0.70
1.41 1.87 2.28 2.58
100
150
200
1.39 1.81 2.18 2.45
1.37 1.76 2.09 2.
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