Semi-analytical modeling of multispecies radionuclide decay chain transport in heterogeneous aquifers using the Temporally Relaxed Theory (TRT).

This study presents a semi-analytical model based on the temporally relaxed theory (TRT) of Fick's Law to simulate non-Fickian transport of a multispecies contaminant decay chain in groundwater. The model introduces two relaxation times per species: the flux lag ( [Formula: see text] ) accounting for solute particle inertial collisions, and the storage lag ( [Formula: see text] ) accounting for sorption and secondary pore water exchange. Spatio-temporally dependent transport coefficients are incorporated via spatial and temporal attenuation parameters, providing a more realistic representation of aquifer heterogeneity. The model considers simultaneous coupling between parent and daughter species in both the dissolved and sorbed phases, with time-dependent contamination sources described by the generalized Bateman equations. The semi-analytical solution is obtained in the Laplace using the linear transformation of Clement and inverted numerically via the Concentrated Matrix Exponential-Smoothing (CME-S) algorithm. Validation against existing semi-analytical and numerical finite volume (NFV) solutions for a four-member radionuclide decay chain shows excellent agreement. A quantitative comparison with fractional ADE, MIM, and RLS models confirms the superior accuracy of TRT for non-Fickian multispecies transport. Sensitivity analysis reveals the distinct roles of the relaxation times: ( [Formula: see text] ) governs the nuclide's response to transport dynamics through inertial effects, while ( [Formula: see text] ) controls mass redistribution between early and late times by delaying solute interaction with the solid phase. The sensitivity of nuclide distribution to the time lags depends on the attenuation parameters and the species position. Application to a dose assessment scenario for hypothetical waste repository demonstrates that neglecting attenuation parameters leads to significant misestimation of the committed effective dose, particularly for mobile daughter products like at far-field locations and late times. This work provides a comprehensive analytical tool that integrates non-Fickian transport, dual-phase coupling, spatio-temporal variability of parameters, and time-dependent sources, thereby improving forecasting and risk management for subsurface contamination arising from multispecies decay chains.