Contaminant transport in a fracture with spatially variable aperture in the presence of monodisperse and polydisperse colloids

Abstract

A quasi-three-dimensional particle tracking model is developed to characterize the spatial and temporal effects of advection, molecular diffusion, Taylor dispersion, fracture wall deposition, matrix diffusion, and co-transport processes on two discrete plumes (suspended monodisperse or polydisperse colloids and dissolved contaminants) flowing through a variable aperture fracture situated in a porous medium. Contaminants travel by advection and diffusion and may sorb onto fracture walls and colloid particles, as well as diffuse into and sorb onto the surrounding porous rock matrix. A kinetic isotherm describes contaminant sorption onto colloids and sorbed contaminants assume the unique transport properties of colloids. Sorption of the contaminants that have diffused into the matrix is governed by a first-order kinetic reaction. Colloids travel by advection and diffusion and may attach onto fracture walls; however, they do not penetrate the rock matrix. A probabilistic form of the Boltzmann law describes filtration of both colloids and contaminants on fracture walls. Ensemble-averaged breakthrough curves of many fracture realizations are used to compare arrival times of colloid and contaminant plumes at the fracture outlet. Results show that the presence of colloids enhances contaminant transport (decreased residence times) while matrix diffusion and sorption onto fracture walls retard the transport of contaminants. Model simulations with the polydisperse colloids show increased effects of cotransport processes.

Colloid dispersion in a uniform-aperture fracture

“…Molecular diffusion of dissolved species (e.g., chloride) is significantly larger than that of colloids such that D Taylor will sufficiently approximate the dispersion process in these experiments (less than a 20% increase from D to D Taylor is realized); however, for colloids, this is not true and D eff more accurately describes the dispersive process (D Taylor is orders of magnitude larger than D). A well-developed particle-tracking algorithm is used to simulate the movement of colloids through the Plexiglas fractures [15,[26][27][28][29]. The model is fit to normalized concentration data on a logarithmic scale to emphasize the tails of the breakthrough curves where the effects of dispersion are captured.…”

Influence of aperture field heterogeneity and anisotropy on dispersion regimes and dispersivity in single fractures

“…[11] The RWPT technique has been applied in numerous studies to investigate contaminant transport in fractured media [e.g., Moreno et al, 1988;Detwiler et al, 2000;Chrysikopoulos and James, 2003;James et al, 2005]. In vector form, the RWPT equation is given by [Tompson and Gelhar, 1990] …”

“…The particles are then distributed on the basis of the local volumetric flow rate and velocity vectors as detailed by James et al [2005]. The RWPT model parameters are listed in Table 2.…”

“…Fifty realizations for each set of aperture field statistics (m b , s b , and AR) were generated by changing the seed number supplied to the random field generator. The random noise present in the stochastic simulations was smoothed out using ensemble averages of the breakthrough curves generated by each of the 50 aperture field realizations [James et al, 2005]. [Reimus, 1995].…”

“…It was assumed that the aperture field is symmetric about the center plane of the fracture. Upon calculation of the two-dimensional flow field, a parabolic velocity profile was imposed across the fracture and the quasi-three-dimensional RWPT equations were employed to simulate the transport process [James et al, 2005]:…”