Back diffusion of a Th-230-Ra-226 decay chain in a multilayer fractured-rock matrix with stagnant-zone and skin effects.

This study develops a one-dimensional numerical model to investigate back diffusion of the Th-230-Ra-226 decay chain in fractured crystalline rock with a stagnant water zone, an altered fracture-skin layer, and an intact host-rock matrix. Radionuclide-specific boundary conditions are applied: Th-230 is supplied from the stagnant zone via time-dependent source strength functions (step, exponential, and linear depletion), whereas Ra-226 is constrained to a zero-concentration boundary so that all Ra-226 originates from in situ matrix decay. The finite-difference model, validated against two analytical solutions for layered diffusion with decay, resolves diffusion, sorption, and mass-flux continuity across sharp contrasts in porosity and retardation between skin and host rock. Results show that a thin, high-porosity skin layer stores substantially more Th-230 than a homogeneous matrix and thereby amplifies subsequent back-diffusive fluxes, while source-depletion kinetics exert a first-order control on the onset and magnitude of flux reversal. Exponential depletion prevents Th-230 flux reversal but still drives sustained Ra-226 back diffusion, indicating that weakly sorbing daughters can be released even when the parent remains trapped. Spatial profiles and cumulative mass budgets further reveal Ra-226 hotspots at the skin-host-rock interface and scenarios where the long-term back-diffused mass of Ra-226 exceeds that of Th-230, underscoring the need to account for layered interfaces and decay-chain coupling when assessing contaminant persistence in fractured low-permeability media.