Transport of a Two-Member Decay Chain of Radionuclides through a Discrete Fracture in a Porous Rock Matrix in the Presence of Colloids

Abstract

Many physical and chemical processes dominate the transport of radionuclides in groundwater. Among these processes, the decay chain process of radionuclides was frequently disregarded in previous research. However, the daughter products may travel much farther than their parents along the fracture. Therefore, some models neglecting the effect of the decay chain may underestimate the transport radionuclide concentration in geological media. The transport of radionuclides in groundwater is also controlled by colloidal particles. The radionuclides may be enhanced or retarded by the colloids, according to the mobility of these colloidal particles. This work describes a novel model of the transport of a two-member decay chain of radionuclides through a discrete fracture in a porous rock matrix in the presence of colloids. The model addresses the following processes: (a) advective transport in the fracture, (b) mechanical dispersion and molecular diffusion along the fracture, (c) molecular diffusion from the fracture to the rock matrix, (d) adsorption onto the fracture wall, (e) adsorption in the rock matrix, and (f) radioactive decay. Furthermore, colloids are assumed to be excluded from the matrix pores because of their size. A fully developed concentration profile system with nonreactive colloids is used to understand the effect of colloidal sizes by using hydrodynamic chromatography. The external forces acting on the colloid surface, such as the inertial, the van der Waals attractive force, the double layer force, and the gravitational force are accounted for. The parameters, the average velocity of the colloid, the dispersion coefficient of the colloid, and the distribution coefficient of radionuclides with colloids are modified according to the colloidal size. The transport equations for the parent radionuclides are solved analytically using the Laplace transformation and inversion method. However, for the transformed solution of the daughter products along the fracture, the equations become very complicated in Laplace space. Accordingly, the solutions are obtained numerically by using Durbin’s algorithms. The behaviors of colloids within the fracture are a function of their size, and they may affect the transport of radionuclides because of the large radionuclide adsorption surface of colloids. Thus, various colloid radii are considered to elucidate this size effect.