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Analysis of a ,model for contaminant transport in fracture media in the presence of colloid
(1995) Chrysikopoulos Constantinos; Χρυσικοπουλος Κωνσταντινος; Assem Abdel-Salam
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.
Analytical solutions for one-dimensional colloid transport in saturated fractures
(1994) Chrysikopoulos Constantinos; Χρυσικοπουλος Κωνσταντινος; Assem Abdel-Salam
Closed-form analytical solutions for colloid transport in single rock fractures with and without colloid penetration into the rock matrix are derived for constant concentration as well as constant flux boundary conditions. A single fracture is idealized as two semi-infinite parallel plates. It is assumed that colloidal particles undergo irreversible deposition onto fracture surfaces and may penetrate into the rock matrix, and deposit irreversibly onto rock matrix solid surfaces. The solutions are obtained by taking Laplace transforms to the governing transport equations and boundary conditions with respect to time and space. For the case of no colloid penetration into the rock matrix, the solutions are expressed in terms of exponentials and complimentary error functions; whereas, for the case of colloid penetration into the rock matrix, the solutions are expressed in terms of convolution integrals and modified Bessel functions. The impact of the model parameters on colloid transport is examined. The results from several simulations indicate that liquid-phase as well as deposited colloid concentrations in the fracture are sensitive to the fracture surface deposition coefficient, the fracture aperture, and the Brownian diffusion coefficient for colloidal particles penetrating the rock matrix. Furthermore, it is shown that the differences between the two boundary conditions investigated are minimized at dominant advective transport conditions. The constant concentration condition overestimates liquid-phase colloid concentrations, whereas the constant flux condition leads to conservation of mass.
Modeling colloid transport and deposition in saturated fractures
(1997) Chrysikopoulos Constantinos; Χρυσικοπουλος Κωνσταντινος; Assem Abdel-Salam
A model is developed to describe the transport of colloids in a saturated fracture with a spatially variable aperture, accounting for colloid deposition onto fracture surfaces under various physicochemical conditions. The fracture plane is partitioned into unit elements with different apertures generated stochastically from a log-normal distribution. The model also accounts for colloid size exclusion from fracture elements with small apertures. Both equilibrium and kinetic colloid deposition onto fracture surfaces are investigated. Colloid surface exclusion is incorporated in the dynamics of kinetic deposition. The impact of deposited colloids on further colloid deposition is described by either a linear or a non-linear blocking function. The resulting system of governing partial differential equations is solved numerically using the fully implicit finite difference method. Model simulations illustrate the presence of preferential colloid transport in the fracture plane. It is shown that size exclusion increases the dispersion of colloids and leads to earlier breakthrough, especially for large-size particles. Furthermore, it is demonstrated that surface exclusion enhances colloid transport, and the assumption of clean-bed media may underestimate liquid-phase colloid concentrations.
Modeling of colloid and colloid-facilitated contaminant transport in a two-dimensional fracture with spatially variable aperture
(1995) Chrysikopoulos Constantinos; Χρυσικοπουλος Κωνσταντινος; Assem Abdel-Salam
Mathematical models are developed for two-dimensional transient transport of colloids, and cotransport of contaminant/colloids in a fracture-rock matrix system with spatially variable fracture aperture. The aperture in the fracture plane is considered as a lognormally distributed random variable with spatial fluctuations described by an exponential autocovariance function. Colloids are envisioned to irreversibly deposit onto fracture surfaces without penetrating the rock matrix; whereas, the contaminant is assumed to decay, sorb onto fracture surfaces and onto colloidal particles, as well as to diffuse into the rock matrix. The governing stochastic transport equations are solved numerically for each realization of the aperture fluctuations by a fully implicit finite difference scheme. Emphasis is given on the effects of variable aperture on colloid and colloid-facilitated contaminant transport. Simulated breakthrough curves of ensemble averages of several realizations show enhanced colloid transport and more pronounced fingering when colloids are subject to size exclusion from regions of small aperture size. Moreover, it is shown that an increase in the fracture aperture fluctuations leads to faster transport and increases dispersion. For the case of contaminant/colloids cotransport it is shown, for the conditions considered in this work, that colloids enhance contaminant mobility and increase contaminant dispersion.
Unsaturated flow in a quasi-three-dimensional fractured medium with spatially variable aperture
(1996) Chrysikopoulos Constantinos; Χρυσικοπουλος Κωνσταντινος; Assem Abdel-Salam
Transient moisture flow in a variably saturated quasi-three-dimensional fracture-rock matrix system is investigated. The fracture is assumed to possess a spatially variable aperture in its two-dimensional plane, whereas the rock matrix is treated as a two-dimensional homogeneous and tight porous medium. The aperture fluctuations in the fracture plane are described stochastically. Moisture exchange between the fracture and the rock matrix is accounted for via an advective coupling term that governs the transfer of moisture at the fracture-matrix interface and takes into account the effect of a fracturesurface coating material. Although the variable aperture fracture is two-dimensional, the coupling term between the fracture and the rock matrix accounts for the threedimensional nature of the physical system. The stochastic nonlinear set of partial differential equations is solved numerically by the Galerkin finite element method in conjunction with the Picard iterative scheme and an automatic time step marching. Simulations are performed to investigate phenomena which have been ignored in previous studies. It is demonstrated that, for the case of no moisture exchange with the rock matrix, the moisture follows preferential flow paths within the fracture plane and exhibits pronounced fingering effects. Furthermore, it is shown that the larger the fracture aperture fluctuations the more extended the moisture flow in the fracture. In addition, for the case where there exists moisture exchange with the rock matrix, the movement of the moisture front is considerably reduced, whereas fracture-surface coatings tend to slow down moisture absorption by the rock matrix.

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