A Temporally Relaxed Theory for Non-equilibrium Multispecies Contaminants Transport in Finite Media with Time-Varying Boundary Conditions

The fate of multispecies contaminants in groundwater is often studied using conventional advection–dispersion equations (ADEs) coupled with first-order decay reactions describing the Fickian and non-Fickian solute transport behavior. This study presents a novel approach for multispecies contaminants transport in heterogeneous porous media that is founded on the temporally relaxed theory of Fick’s Law. The methodology introduces two relaxation times to account for solute particle collisions and attachment, leading to the derivation of new coupled ADEs. The semi-analytical solution is obtained in the Laplace domain after a linear transformation of Clement to address the mathematical complexity of the problem. The model’s simulation results show excellent agreement with semi-analytical models and existing analytical solutions for multispecies contaminants transport in Fickian and non-Fickian transport concepts. Results obtained demonstrated that the effects of time lagging of the temporal and spatial distribution of each species of the decay chain depend on the retardation factor, decay constant as well as input distribution of each member. Additionally, the temporal relaxed theory can quickly assess the risks incurred by drinking groundwater contaminated by radionuclides as shown in the application to \({}^{238}{\text{Pu}}\) the decay chain in a waste deposition site. This innovative approach provides an in-depth understanding of the transport of contaminants from multiple species and its impact on groundwater contamination. The temporal relaxed theory seems promising for more accurately estimating the risks associated with decay chains, such as radionuclides.