Empirical Indicators for Screening Three-Tier Retardation of Decay Chain Radionuclides in Sequential Triple-Continuum Fractured Media

Abstract Using a solubility-controlled Th-230–Ra-226 decay-pair transport model in GoldSim, dimensionless screening diagnostics are developed for fractured rock in which retardation proceeds through three successive tiers: deposited-colloid coating, fracture skin, and rock matrix. Two empirical indicators are proposed: the cascade number N c , quantifying the competition between skin diffusive uptake and fracture advection, and the decay-diffusion number N d , quantifying the competition between Th-230 decay and Ra-226 back-diffusion from the matrix. Systematic parameter sweeps over pore diffusion coefficient, flow rate, coating and Ra-226 distribution coefficients, and skin thickness across 31 simulations are used to evaluate these diagnostics against model outputs. N c captures a multi-order-of-magnitude transition in Th-230 outlet flux from advection-dominated to diffusion-bridge-dominated behaviour, while N d independently governs the Ra-226 secondary peak flux via the matrix retardation factor. The coating distribution coefficient exhibits a threshold response, functioning as an activation switch that determines whether the Th-230 residence time at the fracture wall is sufficient for the diffusion bridge to operate. A sequence sensitivity index evaluated at midstream shows that two fracture-segment arrangements can produce nearly identical outlet fluxes yet diverge considerably at interior observation points, indicating that outlet-based assessments may obscure fundamentally different internal risk distributions. Together, these diagnostics provide a rapid screening tool for performance assessment to determine, before committing to full simulations, whether the three-tier cascade, sequence effects, and midstream monitoring warrant explicit consideration under site-specific conditions. Article Highlights Two dimensionless indicators rapidly screen whether a three-tier retardation cascade matters for a given site. Colloid-coating sorption acts as an on/off switch, not a gradual modifier, for daughter–nuclide generation. Outlet monitoring alone can mask large internal flux differences caused by fracture-segment ordering.