Analysis of a ,model for contaminant transport in fracture media in the presence of colloid

Abstract

A mathematical model has been developed to study the cotransport of contaminants with colloids in saturated rock fractures. The contaminant is assumed to decay, and sorb on to fracture surfaces and on to colloidal particles, as well as to diffuse into the rock matrix; whereas, colloids are envisioned to deposit irreversibly on to fracture surfaces without penetration into the rock matrix. The governing one-dimensional equations describing the contaminant and the colloid transport in the fracture, colloid deposition on to fracture surfaces, and contaminant diffusion into the rock matrix are coupled. This coupling is accomplished by assuming that the amount of contaminant mass captured by colloidal particles in solution and the amount captured by deposited colloids on fracture surfaces are described by modified Freundlich reversible equilibrium sorption relationships, and that mass transport by diffusion into the rock matrix is a first-order process. The contaminant sorption on to fracture surfaces is described by a linear equilibrium sorption isotherm, while the deposition of colloids is incorporated into the model as a first-order process. The resulting coupled contaminant transport non-linear equation is solved numerically with the fully implicit finite difference method. The constant concentration as well as the constant flux boundary conditions have been considered. The impact of the presence of colloids on contaminant transport is examined. According to model simulations the results show that, depending on the conditions of the physical system considered, colloids can increase or decrease the mobility of contaminants.