The coupling effects of the matrix thickness and Peclet number on the late time transport tailing in the fracture-matrix systems

Abstract

Solute transport process in fractured rocks is central to many engineering applications. However, how matrix diffusion affects non-Fickian transport behavior, which is typically characterized by the late time tailing in breakthrough curves and residence time distributions, remains underexplored, especially considering the coupling effects of the finite matrix thickness (h) and transport regimes quantified by Peclet number (Pe). In this work, the fluid flow and solute transport were simulated by directly solving the Navier-Stokes equations and advection-diffusion equation in a two-dimensional fracture-matrix system considering matrix diffusion. In total, eighty cases considering variations of h and Pe were conducted to investigate the impacts of h and Pe on the late time solute tailing characterized by the exponent (n) in the power law function. Numerical results demonstrate that n decreases with an increase of h and Pe, where n eventually reduces to 1.5 that is a theoretical value for an infinite matrix domain. Moreover, the relationship between n and (h, Pe) is established via a polynomial function, which is further validated by the three-dimensional heterogeneous fracture-matrix system. The newly-established function can be used to accurately assess the power law tailing process given the knowledge of measurable h and Pe.