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

Abstract

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.

Keywords:

• fracture
• Langmuir non-linear sorption
• rock matrix
• spatial moments
• effective solute velocity and dispersion