N. Natarajan

Numerical modelling and spatial moment analysis of solute transport with Langmuir sorption in a fracture matrix-coupled system

Sorption is one of the key processes that play a major role in the transport of contaminants in fractured porous media. While Freundlich adsorption isotherm has been studied extensively in fractured porous media, limited studies have been conducted using Langmuir sorption. To address this issue, a numerical model is developed for analysing the influence of sorption intensities on velocity, macro-dispersion coefficient and dispersivity using the method of moments. Implicit finite difference numerical technique has been used to solve the coupled non-linear-governing equations. A varying grid is adopted at the fracture and rock matrix interface to capture the mass transfer at the interface. Results suggest that for relatively higher sorption capacities and distribution coefficients, the effective solute velocity as well as the retardation factor clearly becomes a non-linear function of time. The higher magnitude of second spatial moments for the cases of higher sorption capacities and distribution coefficients clearly conveys that there is an excessive mixing of solutes within the fracture resulting from Langmuir sorption with reference to the classical porous medium mixing. Also, the behaviour of effective macro-dispersion coefficient with time is highly complex for higher maximum sorption capacity.

Lower order spatial moments for colloidal transport in a fracture-matrix coupled system

This paper presents an analysis of the lower order spatial moments of colloidal transport in a coupled fracture-matrix system. For this purpose, colloidal transport is numerically modeled to obtain the spatial distribution of concentration profiles along the fracture. Implicit finite-difference numerical technique has been adopted to obtain the colloidal concentration in the fracture. Subsequently, the first and second spatial moments are evaluated using the colloidal concentration. The results suggest that effective velocity of the colloid is retarded by increment in rock matrix porosity, matrix diffusion coefficient, filtration coefficient, reduction of half-fracture aperture, initial colloid velocity, and remobilization coefficient. Significant mixing of colloids occurs in the fracture due to low-fracture aperture, initial colloid velocity, and filtration coefficient.

Numerical modelling of colloidal transport in fractured porous media with double layered fracture-skin

A numerical model is developed for studying the transport of colloids in a coupled fracture-matrix system with double layer fracture-skin. The governing equations describing colloid transport along the fracture and diffusion into fracture-skin layers as well as rock-matrix, normal to the fracture axis are coupled with each other. The coupled non linear equations are solved numerically with fully implicit finite difference method. Sensitivity analysis is performed to investigate the effect of various colloid properties on the colloid concentration in the multiple porosity fractured system. Colloid remobilisation and filtration has been accounted in the model. Results suggest that the inclusion of a second fracture-skin layer has a marginal effect on the transport mechanism of colloids. As colloid velocity increases, the diffusion of colloids into the fracture-skin decreases due to the low residence time available for the colloids. High first layer fracture-skin thickness and porosity enhances the diffusion of colloids from the aqueous phase of the fracture into the skin considerably resulting in low colloidal concentration within the fracture. Variation in the porosity as well as thickness of the second layer of the fracture-skin has negligible effect on the colloidal concentration in the fracture. The colloid transport mechanism in fractured porous media is marginally affected by the multiple porosity system, or in other words additional layers of fracture skin. High filtration coefficient and low remobilisation coefficient result in low colloidal concentration within the fracture.