Fractional-Derivative Models for Non-Fickian Transport in a Single Fracture, Parallel Fractures, and Discrete Fracture Networks

Abstract:

Analytical solutions describing Fickian diffusion of contaminants in a single fracture or parallel set of fractures with diffusional mass exchange across the fracture-matrix interface are well known. These solutions do not address observations of non-Fickian transport in natural fractures due to within-fracture flow channeling and the presence of stagnant zones. This study expands upon the classical work by Tang et al. (1981, Adv. Water Resour.) by deriving general solutions for anomalous transport in a single fracture described by fractional-derivative models. Non-Fickian diffusive jumps for solute particles along the fracture and time nonlocal mass exchange across the fracture-matrix interface are both considered. Model and solution applications and extensions for discrete parallel fractures and large-scale, irregular fracture matrix systems will be presented, as well as the impact of the orders of fractional derivative on transport dynamics.