Semi-analytical Solution for the Contaminant Transport in Fractured Porous Media with Mobile-Immobile Method

Abstract:

With the consideration of advection, dispersion, adsorption and first order decay in the fracture and rock matrix in a single fracture model, a new semi-analytical solution is derived using the Mobile-Immobile Method. It can be used to estimate the concentration at any location at any time precisely within the fracture and rock matrix. Most fractures found underground are filled with the conglomerate, sand, clay and other kinds of possible porous media. The existence of those filling ingredients leads to the isolated pore space within the fracture, which is also called immobile zone. Certain assumptions have be made: the diffusion is the only way that the contamination travels from the fracture to the matrix as the large permeability difference between them; the diffusive transport is dominant in the rock matrix while the advective-dispersive transport plays the major role in the fracture. Experimental data have been collected from literatures to compare the performance of this semi-analytical solution from the classical analytical solution. The comparison shows that the semi-analytical solution simulates it better when the mobile zone percentage is limited. Also, the effects of matrix diffusion, dispersivity and Darcy velocity in the fracture, fracture aperture, first order mass transfer rate and mobile zone percentage on solute transport are demonstrated through the sensitivity analysis, concentration profiles and breakthrough curves. By modifying the boundary conditions and adding an advection term in the rock matrix governing equation, this model can be extended to a two-layer solute transport model.