Modeling the Spread of Radioactive Contaminant in Fractured Aquifers Surrounded by Porous Rocks

This research examines the spread of radioactive contaminant by mass transfer through fractures and aquifers in subsurface porous rock. This is a topic of consideration for nuclear power plant and nuclear waste repository design, where radioactive waste must be isolated from the environment and especially groundwater sources. By solving a system of fractional differential equations that model the radioactive contaminant transport in the fractured aquifer and surrounding porous rocks for the steady-state case, the long-time equilibrium situation to determine the maximum possible zones of contamination is determined. The model used accounts for the physical processes of diffusion, dispersion, and advection due to fluid flow, in addition to intrinsic properties of the system, such as rock porosity, radioactive half-life of the contaminant, and anomalous fracture patterns in the rock. Due to prior experimental and theoretical results, which validates that fluid flow and mass transport in fracture patterns with fractal geometry are better modeled by fractional derivatives, this work utilizes these fractional-order terms to model the mass transport in the aquifer and porous rocks. The solutions can then be used to model contaminant spread and decay, and to examine contamination zones in various real-world conditions to help outline safety procedures and guidelines for disaster prevention.