Numerical Study on the Effect of Fracture Characteristics on Flow and Solute Transport in a Fractured Medium

Abstract

This study simulates the effect of fracture characteristics on permeability, average linear velocity, breakthrough time, and megascopic dispersivity of a fractured medium. The authors use a power law for fracture length distribution and a fractional Brownian motion for hydraulic fracture aperture spatial distribution, which can be characterized by a and H , respectively. A new finite difference model is developed for solute transport that considers advection, adsorption, first-order decay, and scale-dependent dispersivity of a single fracture using a numerical dispersion term caused by finite difference approximation. The ranges of 1 . 4 h a h 2 . 2 and 0 . 1 h H h 0 . 9 are considered. The results show that the permeability is not very affected by a , but increases slightly with increasing H . The average linear velocity decreases with increasing a , but increases with increasing H . Both the breakthrough time and the megascopic dispersivity increase as a becomes larger, but decrease as H becomes larger. Finally, the megascopic dispersivity is proportional to the linear size of a medium by the power of i , which increases from approximately 0.65 to 0.85 with increasing a , which shows the analogy of the fractured medium to a highly heterogeneous porous medium.