Decay-Series Disequilibrium Study of In Situ Long-Term Radionuclide Transport in Water-Rock Systems
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(1)
where A (=AC; A is the decay constant and C the concentration) is the nuclide activity in groundwater (dpm L-1), with superscriptp referring to its radioactive parent; kp is the precipitation rate constant (y-1); Q, Pd, and Pr are the rates (atoms L-I y-l) of supply by water flow, dissolution, and a recoil, respectively; and Rf is the retardation factor, expressed as: 217
Mat. Res. Soc. Symp. Proc. Vol. 608 © 2000 Materials Research Society
(2)
Rf=I+K=I+ ki k2+(
where K is a dimensionless distribution coefficient between the sorbed and dissolved pools for the radionuclide that has k, and k2 as its sorption and desorption rate constants (y-l), respectively. The model assumes that (1) first-order kinetics govern the processes of sorption-desorption and dissolution-precipitation of radionuclides (It can be shown that dissolution is reduced to zeroth order for a constant radionuclide concentration in the solid pool) and (2) ca-recoil input from the sorbed and dissolved pools to the solid pool is negligible. Implicit in assumption (1) is a linear sorption isotherm for the range of concentrations of the nuclides of interests. For Rf to be independent of nuclide concentrations, it is also assumed that decay of radionuclides on the rock surface (the sorbed pool) releases all daughter nuclides into the dissolved pool. The validity of these assumptions has been assessed by Ku et al. [3] and Murphy [4]. In this paper, the model is applied to characterize the nuclide transport in groundwaters at the Idaho National Engineering and Environmental Laboratory (INEEL), Idaho (Fig. 1). Range
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N Mud Lake
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RfTh228 for most of the samples suggests that the desorption rate constant of Th must be comparable to or smaller than the decay constant of 228Th (0.363 y-'). From eqn. (2), we estimated the sorption and desorption rate constants (kI and k 2 ) of Th to range from 0.12 to 4.1 min-1 and 0.1 to 2.5 y-1 , respectively Whereas the sorption rates of Th and Ra are comparable, the desorption of Th is about two orders slower than that of Ra. U isotopes: Because of the long half lives of 238U and 234U, their Rf values are expected to be the same and estimated to be mostly in the range of 102-103, much smaller than those for Ra and Th isotopes. However, even in this oxygenated, bicarbonate-rich groundwater of INEEL, U is moderately retarded by aquifer solids. This should serve as a cautionary note to using U isotopes as a conservative tracer for groundwater dating or mixing studies.
Since most aquifers have porosities < 0.3 and rock densities - 2.8 g cm-3 , the in-situ distribution coefficients (Kd) of radionuclides are estimated to be at least an order of magnitude smaller than the values of Rf (= K)[1], i.e., they are on the order of 105 for Th, 103 for Ra and 102 for U. Because Rf is site-dependent, the radionuclide migration in water-rock systems can be better understood from the in-situ Kd, rather than from the laboratory-derived Kd. Dissolution and Precipitation Dissolution and precipitation exhibit large spatial
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