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A mechanistic model describing a dynamic mass balance between the production and consumption of silicic acid was coupled to a near-field mass transport model to predict the dissolution kinetics of a high-level waste glass in a deep geologic repository. The effects of interactions between an iron overpack and the glass are described by a time-dependent precipitation reaction for a ferrous silicate mineral. The kinetic model is used to transform radionuclide concentration-versus-reaction progress values, predicted from a geochemical reaction path computer code, to concentration-versus-time values that are used to calculate the rate of radionuclide release by diffusive mass transfer to the surrounding host rock. The model provides for both solubility-limited and kinetically limited release; the rate-controlling mechanism is dependent on the predicted glass/groundwater chemistry.
Part of a strategy for evaluating the compliance of geologic repositories with Federal regulations is a modeling approach that would provide realistic release estimates for a particular configuration of the engineered-barrier system. The objective is to avoid worst-case bounding assumptions that are physically impossible or excessively conservative and to obtain probabilitistic estimates of (1) the penetration time for metal barriers and (2) radionuclide-release rates for individually simulated waste packages after penetration has occurred. The conceptual model described in this paper will assume that release rates are explicitly related to such time-dependent processes as mass transfer, dissolution and precipitation, radionuclide decay, and variations in the geochemical environment. The conceptual model will take into account the reduction in the rates of waste-form dissolution and metal corrosion due to a buildup of chemical reaction products. The sorptive properties of the metal-barrier corrosion products in proximity to the waste form surface will also be included. Cumulative releases from the engineered-barrier system will be calculated by summing the releases from a probabilistically generated population of individual waste packages.
Results of a previous paper (Liebetrau (1977a)) are extended to higher dimensions. An estimator V∗(t1, t2) of the variance function V(t1, t2) of a two-dimensional process is defined, and its first- and second-moment structure is given assuming the process to be Poisson. Members of a class of estimators of the form where and for 0 < α i < 1, are shown to converge weakly to a non-stationary Gaussian process. Similar results hold when the t′i are taken to be constants, when V is replaced by a suitable estimator and when the dimensionality of the underlying Poisson process is greater than two.
The second-moment structure of an estimator V*(t) of the variance-time curve V(t) of a weakly stationary point process is obtained in the case where the process is Poisson. This result is used to establish the weak convergence of a class of estimators of the form Tβ(V*(tTα) – V(tTα)), 0 < α < 1, to a non-stationary Gaussian process. Similar results are shown to hold when α = 0 and in the case where V(tTα) is replaced by a suitable estimator.