A fractional derivative model for nuclides transport in heterogeneous fractured media

Abstract

Nuclide transport in fractured media involves the advection, dispersion, adsorption, etc. The dispersion and adsorption properties of the rock matrix have spatial variability, which results in an anomalous transport of nuclides. In this study, a time-fractional advection-diffusion equation (t-FADE) model is utilized to capture the sub-diffusion transport behavior with heavy-tail property, including the breakthrough curves (BTCs) of uranium and thorium transport in granite plates. Moreover, hydrodynamic dispersion of tritiated water, strontium and cesium in granite fractures are also studied. The results indicate that BTCs of nuclides transport in the granite fractures are unimodal and asymmetric. The decrease of the fractional order α reflects the stronger sub-diffusion. Furthermore, small initial velocity enhances sub-diffusion effect of nuclides and lengthens the breakout time of BTCs, which results in obvious heavy-tail phenomena. The analysis results demonstrate that the t-FADE model can accurately describe sub-diffusion behavior of nuclides transport. At last, the advantages of the t-FADE model in prediction and remediation of nuclides contamination are put forward.

Keywords: Anomalous transport; Fractional derivative model; Fractured media; Nuclide.