Effect of fluid velocity on matrix diffusion in a coupled fracture-matrix system

N. Natarajan[1] and G. Suresh Kumar[2]

[1] EWRE Division, Civil Engineering Department, Indian Institute of Technology, Madras, Chennai-36.
[2] Department of Ocean Engineering, Indian Institute of Technology, Madras, Chennai-36
[1] Corresponding author; itsrajan2002@yahoo.co.in
The study of flow and transport processes in rock fractures has received increased attention because of its importance to underground natural - resource recovery, waste storage, and environmental remediation. Modeling of flow in the fractured media is quite different from the porous media because of the distinct heterogeneity in the fracture matrix-coupled system. To understand the movement of contaminants in the fractured media, a simple conceptual model of a single fracture categorized as dual porosity has been considered for this study. Some of the factors, which play an important role in the modeling, are fracture aperture, matrix porosity, and the matrix diffusion coefficient, as they are involved in the coupling term. The fracture aperture plays an important role in the coupling action between the fracture and the rock-matrix as it affects the flux transfer, technically referred to as matrix diffusion. Initially the velocity of the fluid and the solute remains the same but as time progresses the velocity of the solute retards and this has a significant impact on the matrix diffusion. The mathematical expression for coupling fracture and rock-matrix has no specific term accounting for the fluid velocity implying that the fluid velocity has negligible effect on the flux transfer. This work focuses on bringing out the significance of the fluid velocity and its impact on matrix diffusion as there is direct correlation between the flux transfer and the residence time of the solutes. A constant continuous source is considered at the fracture inlet. The coupled equations are numerically solved using an implicit finite difference scheme. A geometrically varying cell width has been considered in the direction perpendicular to the fracture to capture the water transfer into the rock. Results suggest that a very low fluid velocity increases the residence time of the contaminant and enhanced matrix diffusion is observed. This results in significant absorption of the contaminants into the rock-matrix.
KEYWORDS: Velocity of the solute, Matrix diffusion, Residence time, Dual- porosity, Fluid velocity

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