1-D modeling of radionuclide transport via heterogeneous geological formations for arbitrary length decay chains using numerical inversion of Laplace transforms

We present the Laplace-transformed analytical solution (LTAS) to the one-dimensional radionuclide transport equation for an arbitrary length decay-chain through an arbitrary combination of multiply fractured and porous transport segments subject to an arbitrary time-dependent release mode at the entrance point to the series of transport segments. The LTAS may be numerically inverted to obtain the time-dependent concentration of the radionuclides of interest at an arbitrary down gradient location. For a special case, where the source function is defined as the band release with a single radionuclide without precursors, the Laplace inverse transformation could be performed analytically, yielding a closed-form analytical solution. A computer code, TTBX, has been developed by implementing the LTAS, and benchmarked against the closed-form analytical solution. Numerical examples are presented to demonstrate the utility of these solutions and the importance of increased fidelity in the transport pathway for reliable performance assessment for the geological disposal of spent nuclear fuels. © 2013 Elsevier Ltd. All rights reserved

Chemical transport in a fissured rock: Verification of a numerical model

Numerical models for simulating chemical transport in fissured rocks constitute powerful tools for evaluating the acceptability of geological nuclear waste repositories. Due to the very long-term, high toxicity of some nuclear waste products, the models are required to predict, in certain cases, the spatial and temporal distribution of chemical concentration less than 0.001% of the concentration released from the repository. Whether numerical models can provide such accuracies is a major question addressed in the present work. To this end, we have verified a numerical model, TRUMP, which solves the advective diffusion equation in general three dimensions with or without decay and source terms. The method is based on an integrated finite-difference approach. The model was verified against known analytic solution of the one-dimensional advection-diffusion problem as well as the problem of advection-diffusion in a system of parallel fractures separated by spherical particles. The studies show that as long as the magnitude of advectance is equal to or less than that of conductance for the closed surface bounding any volume element in the region (that is, numerical Peclet number <2), the numerical method can indeed match the analytic solution within errors of ±10{sup -3} % or less. The realistic input parameters used in the sample calculations suggest that such a range of Peclet numbers is indeed likely to characterize deep groundwater systems in granitic and ancient argillaceous systems. Thus TRUMP in its present form does provide a viable tool for use in nuclear waste evaluation studies. A sensitivity analysis based on the analytic solution suggests that the errors in prediction introduced due to uncertainties in input parameters is likely to be larger than the computational inaccuracies introduced by the numerical model. Currently, a disadvantage in the TRUMP model is that the iterative method of solving the set of simultaneous equations is rather slow when time constants vary widely over the flow region. Although the iterative solution may be very desirable for large three-dimensional problems in order to minimize computer storage, it seems desirable to use a direct solver technique in conjunction with the mixed explicit-implicit approach whenever possible. work in this direction is in progress