Nonlinear relative stability analysis of some Nigerian geological formations as radioactive wastes repository

Abstract

This work determines the relative capabilities of some geological formations in Nigeria as radioactive wastes repository. Reaction term of the advection-diffusion-reaction transport in porous media was reworked to address nonlinear radioactive decay and sorption. Lyapunov’s indirect method identified three critical points. A stable attractor at the origin, flanked by two symetric saddles. Phase Potraits show that Caesium and Strontium are well stabilized in sandstone, consolidated clay and limestone. In shale, the focus at the origin indicates weak stability for the two radionuclides. However, for Plutonium, the origin is consisitently a weak node. Hence, its dynamics/disappearance rate is very slow. At half-lifes, breakthrough curves in 200cm radius of host soils show that Strontium and Caesium are best contained in sandstone and consolidated clay. However, they deeply infilterate limestone. Similarly, a fifth of Plutonium’s reposed concentration completely infiltrated the simulation aperture. Hence, Plutonium should not be reposed in natural formations.

Keywords: radionuclides activity, infiltration rate, relative stability, fixed points, geological formation