Integrated Multi Path Model to Calculate Radionuclide Release From a Repository Using Wavelet Galerkin Method

Abstract

This work represents a WIRS code developed using wavelet Galerkin method to solve radionuclide transport model in near field and far field of a repository for high-level radioactive waste. After overpack failure, radionuclides diffuse through the bentonite buffer material to the water bearing fracture around the repository transport horizontally through this geosphere then transport vertically through the major water conducting fault (MWCF) reach the biosphere. The radionuclides transport barriers considered in this model are engineered barrier system (EBS), geosphere, and MWCF. Hydraulic conductivity of the bentonite is more than three orders of magnitude smaller than that of the surrounding host rock, so the only transport mechanism through EBS is diffusion. In the host rock, the problem is of advection-diffusion type with highly varying parameters from one medium to other due to the variability in length, transmissivity and other transport-relevant properties of the transport paths. Daubechies’ wavelet is used as a basis function to solve the nonlinear partial differential equations arising from the model formulation of the radionuclides transport. Since the scaling functions are compactly supported, only a finite number of the connection coefficients are nonzero. The resultant matrix has a block diagonal structure, which can be inverted easily. We tested our WGM algorithm with several problems to verify the model. The solutions are very accurate with a proper selection of Daubechies’ order and dilation order. The solution is very accurate at the interfaces where the radionuclide concentration exhibits very steep gradients.