Upscaling solute transport in naturally fractured porous media with the continuous time random walk method

Abstract

[1] Solute transport in fractured porous media is typically "non-Fickian"; that is, it is characterized by early breakthrough and long tailing and by nonlinear growth of the Green function-centered second moment. This behavior is due to the effects of (1) multirate diffusion occurring between the highly permeable fracture network and the low-permeability rock matrix, (2) a wide range of advection rates in the fractures and, possibly, the matrix as well, and (3) a range of path lengths. As a consequence, prediction of solute transport processes at the macroscale represents a formidable challenge. Classical dual-porosity (or mobile-immobile) approaches in conjunction with an advection-dispersion equation and macroscopic dispersivity commonly fail to predict breakthrough of fractured porous media accurately. It was recently demonstrated that the continuous time random walk (CTRW) method can be used as a generalized upscaling approach. Here we extend this work and use results from high-resolution finite element-finite volume-based simulations of solute transport in an outcrop analogue of a naturally fractured reservoir to calibrate the CTRW method by extracting a distribution of retention times. This procedure allows us to predict breakthrough at other model locations accurately and to gain significant insight into the nature of the fracture-matrix interaction in naturally fractured porous reservoirs with geologically realistic fracture geometries.

A comprehensive numerical analysis of the hydraulic behavior of a permeable pavement

“…The rock matrix also provides storage capacity because of its significantly larger volume than the fracture system. Typical breakthrough curves for a fractured aquifer are characterized by early breakthrough and long tailing (Geiger et al, 2010). This is due to the fact that the matrix has a delayed response to pressure head changes that occur in the surrounding fractures.…”

Report on THMC Modeling of the Near Field Evolution of a Generic Clay Repository: Model Validation and Demonstration

“…Cortis and Birkholzer (2008) and Geiger et al (2010) have utilized a continuous-time random-walk numerical method to investigate the effects of diffusion and advection in fractured, permeable rock. Transport calculations for a two-dimensional fracture network having a range of fracture and matrix permeabilities were used to identify the parameter ranges over which matrix advection has a significant role or may be neglected.…”

On the reliability of analytical models to predict solute transport in a fracture network

“…In such aquifers, open and wellconnected fractures constitute high permeability pathways and are orders of magnitude more permeable than the rock matrix (Bear and Berkowitz, 1987;Berkowitz, 2002;Bodin et al, 2003;Cherubini, 2008;Cherubini and Pastore, 2011;Geiger et al, 2010;Neuman, 2005).…”