Continuous time random walk analysis of solute transport in fractured porous media

Abstract

[1] The objective of this work is to discuss solute transport phenomena in fractured porous media, where the macroscopic transport of contaminants in the highly permeable inter-connected fractures can be strongly affected by solute exchange with the porous rock matrix. We are interested in a wide range of rock types, with matrix hydraulic conductivities varying from almost impermeable (e.g., granites) to somewhat permeable (e.g., porous sandstones). In the first case, molecular diffusion is the only transport process causing the transfer of contaminants between the fractures and the matrix blocks. In the second case, additional solute transfer occurs as a result of a combination of advective and dispersive transport mechanisms, with considerable impact on the macroscopic transport behavior. We start our study by conducting numerical tracer experiments employing a discrete (microscopic) representation of fractures and matrix. Using the discrete simulations as a surrogate for the ''correct'' transport behavior, we then evaluate the accuracy of macroscopic (continuum) approaches in comparison with the discrete results. However, instead of using dual-continuum models, which are quite often used to account for this type of heterogeneity, we develop a macroscopic model based on the Continuous Time Random Walk (CTRW) framework, which characterizes the interaction between the fractured and porous rock domains by using a probability distribution function of residence times. A parametric study of how CTRW parameters evolve is presented, describing transport as a function of the hydraulic conductivity ratio between fractured and porous domains.

Shear-Induced Flow Channels in a Single Rock Fracture and Their Effect on Solute Transport

“…Solute transport can be studied using continuous time random walk (Berkowitz and Scher 1997;Noetinger et al 2001;Cortis and Birkholzer 2008), multi-rate mass transfer (Haggerty and Gorelick 1995;Carrera et al 1998), and the advection-dispersion equation (ADE) (Neuman 1984). The ADE can fail to simulate correctly the tailing of solute transport because of the non-Fickian behavior of dispersive transport (Carrera 1993;Berkowitz et al 2006).…”

Simulation of Solute Transport Through Fractured Rock: A Higher-Order Accurate Finite-Element Finite-Volume Method Permitting Large Time Steps

“…3, Berkowitz and Scher 1997). This behaviour cannot be modelled using the classical ADE approach relying on the concept of macro-dispersivity as expressed by a symmetric tensor (Cortis and Birkholzer 2008). However, the tracer profiles observed in models BED3 and FRACS2000 can be modelled using the Continuous-Time Random-Walk Method (CTRW, Berkowitz and Scher 1997;Cortis and Birkholzer 2008).…”

Fractional dynamics of tracer transport in fractured media from local to regional scales

“…Numerical simulations in Cortis and Birkholzer [38] show that the PDF of resident times for solute transport in an idealized formation of DFN (shown in Figure 4a) evolves as a function of the hydraulic conductivity ratio between fractured and porous domains. In particular, if the ratio is large (i.e., the matrix permeability is relatively low), the tracer BTC contains an apparent late-time tail (see DFN 1 in Figure 4b), and the best-fit resident time PDF is heavy tailed; otherwise the BTC and the resident time PDF are thin-tailed (see DFN 2 in Figure 4b).…”

“…As described by Cortis and Birkholzer [38], the CTRW approach characterizes the interaction (i.e., matrix diffusion and/or sorption/desorption) between the fractured and porous rock domains using a probability distribution function (PDF) of residence times. The PDF of residence times efficiently models the delay that solute particles experience when trapped in immobile zones (i.e., low velocity matrix or adsorptive sites located on fracture walls, or absorptive sites within the rock matrix).…”

“…The type of continuum model depends on the relative contribution of porous matrix to flow and transport. Dual-permeability models are often needed for a permeable porous matrix (where flow and transport processes happen in both domains), while dual-porosity models can be used to describe the transfer of solutes into a low-permeability matrix (which acts as a storage domain and is not explicitly represented in the flow model) [e.g., [37,38]]. A hybrid discrete-continuum model has also been developed by combining the DFN and the continuum approach into a fracture continuum where fracture networks or interconnected fracture zones are directly mapped onto a continuum grid, thereby preserving hydraulic and geometric properties of the network [10,39].…”