Analytical Solutions for Multidimensional Transport of a Four-Member Radionuclide Decay Chain in Ground Water

摘要

Analytical solutions based on the Laplace and Fourier transformation techniques are presented for the two- and three-dimensional space-time-dependent convective-dispersive transport of a four-member radionuclide decay chain in homogeneous porous media. The longitudinal dispersion-free solution is also reported. The computation was executed using the MASCOT model on a VAX/VMS-Version 4.1. The solutions are designed for an unbounded medium flow field assumed to be semi-infinite in the direction normal to the source, and infinite orthogonal to the source, with a variety of boundary conditions (single or multiple finite line source or a Gaussian distributed source in the two-dimensional case; single or multiple patch source or bivariate normally distributed source in the three-dimensional case). Radionuclide release modes of the constant and nuclide-dependent type are taken into account. An optimization of the convergence of the integration required by these solutions is achieved after operating a transformation of the infinite interval into the sum of two finite ones. The efficiency of two quadrature formulas (Gauss-Legendre and a fourth-order Newton-Cotes based on an iterative approach) was investigated. Solution accuracy was verified against available one- and two-dimensional analytical solutions. 15 refs. (ERA citation 12:028368)