Continuous Time Random Walk Analysis of Solute Transport

8 9 The objective of this work is to discuss solute transport phenomena in fractured porous 10 media, where the macroscopic transport of contaminants in the highly permeable inter11 connected fractures can be strongly affected by solute exchange with the porous rock 12 matrix. We are interested in a wide range of rock types, with matrix hydraulic 13 conductivities varying from almost impermeable (e.g., granites) to somewhat permeable 14 (e.g., porous sandstones). In the first case, molecular diffusion is the only transport 15 process causing the transfer of contaminants between the fractures and the matrix blocks. 16 In the second case, additional solute transfer occurs as a result of a combination of 17 advective and dispersive transport mechanisms, with considerable impact on the 18 macroscopic transport behavior. We start our study by conducting numerical tracer 19 experiments employing a discrete (microscopic) representation of fractures and matrix. 20 Using the discrete simulations as a surrogate for the “correct” transport behavior, we then 21 evaluate the accuracy of macroscopic (continuum) approaches in comparison with the 22 discrete results. However, instead of using dual-continuum models, which are quite often 23 used to account for this type of heterogeneity, we develop a macroscopic model based on 24 the Continuous Time Random Walk (CTRW) framework, which characterizes the 25 interaction between the fractured and porous rock domains by using a probability 26 distribution function of residence times. A parametric study of how CTRW parameters 27 evolve is presented, describing transport as a function of the hydraulic conductivity ratio 28 between fractured and porous domains. 29 30 Introduction 31 32 The internal heterogeneity of fractured porous formations is a significant obstacle to the 33 prediction of solute transport processes (Berkowitz, 2002). The macroscopic transport of 34 contaminants in such systems is mainly carried out in high-permeable, interconnected 35 fractures, but most of the capacity for storing a pollutant is provided by the low36 permeability porous matrix. Because of the much slower transport in the matrix, steep 37 concentration gradients may occur between the fractures and the porous blocks, giving 38 rise to a local disequilibrium. The terms “macroscopic” and “local” or “microscopic” are 39 used in this paper to define different scales of interest. The macroscopic scale 40 incorporates a large number of individual fractures and matrix blocks, e.g., between a 41 contaminant source and a monitoring well. In contrast, the local (microscopic) scale is on 42 the order of single fractures and single matrix blocks. The local disequilibrium situation 43 with regard to the solute concentrations in fractures and matrix can lead to significant 44 solute transfer at the fracture/matrix interfaces. This local transfer can strongly influence 45 the macroscopic solute transport in a fractured porous formation, and thus needs to be 46 accounted for in numerical models (Berkowitz, 2002). 47 48 Generally, the numerical simulation of flow and transport processes in fractured porous 49 media can be performed with discrete models or continuum models (e.g., Berkowitz, 5