A stochastic modeling framework for radionuclide migration from deep geological repositories considering spatial variability

Abstract

Considering the influence of uncertainties on radionuclide migration from deep geological repositories (DGR) is of great significance for safety assessment. However, stochastic modeling for DGR safety assessment remains challenging due to the high computational requirements of handling large regional scale models with multiphysics coupling, high-dimensional random inputs, and long simulated durations. This article introduces an efficient numerical framework to tackle this set of challenges. Specifically, the proposed framework relies on three key components, including efficient solutions of stochastic Darcy equations, propagation of stochastic quantities, and efficient solutions of stochastic mass transport equations. Unknown stochastic solutions are approximated by summing a series of products involving random variables and deterministic components. Alternating iterative algorithms are then proposed to decouple the original stochastic problems into deterministic equations for the spatial components, one-dimensional stochastic algebraic equations for the random variables, and one-dimensional ordinary differential equations for the temporal components. These deterministic equations can be solved efficiently using existing solvers, allowing the handling of large-scale problems. The one-dimensional stochastic algebraic equations can be solved efficiently using a sampling strategy, allowing the handling of high-dimensional stochastic state spaces. The one-dimensional ordinary differential equations can be solved cheaply and further accelerated using a time-parallel algorithm, allowing the handling of long simulated time scales. Furthermore, a similar solution approximation and iterative algorithm are also used to propagate stochastic quantities from stochastic Darcy flow to stochastic mass transport. Numerical examples with up to 122 random variables and a simulated duration of one million years demonstrate the promising performance of the proposed framework. The numerical results demonstrate that the developed stochastic framework achieves accuracy comparable to Monte Carlo simulations while significantly improving computational efficiency by two orders of magnitude. Moreover, the evolutionary probability density functions obtained from our stochastic simulations indicate that the proposed framework could potentially serve as an efficient and robust tool for DGR risk assessment.