A regional‐scale particle‐tracking method for nonstationary fractured media

Abstract

[1] A regional-scale transport model is introduced that is applicable to nonstationary and statistically inhomogeneous fractured media, provided that hydraulic flow, but not necessarily solute transport, can be approximated by equivalent continuum properties at some block scale. Upscaled flow and transport block properties are transferred from multiple fracture network realizations to a regional model with grid elements of size equal to that found valid for continuum approximation of flow. In the regional-scale model, flow is solved in a stochastic continuum framework, whereas the transport calculations employ a random walk procedure. Block-wise transit times are sampled from distributions linked to each block based on its underlying fracture network. To account for channeled transport larger than the block scale, several alternative sampling algorithms are introduced and compared. The most reasonable alternative incorporates a spatial persistence length in sampling the particle transit times; this tracer transport persistence length is related to interblock channeling, and is quantified by the number N of blocks. The approach is demonstrated for a set of field data, and the obtained regional-scale particle breakthroughs are analyzed. These are fitted to the one-dimensional advectivedispersive equation to determine an effective macroscale dispersion coefficient for the regional scale. An interesting finding is that this macroscale dispersion coefficient is found to be a linear function of the transport persistence, N, with a slope equal to a representative mean block-scale dispersion coefficient and a constant that incorporates background dispersion arising from the regional heterogeneous conductivity field.Citation: Ö hman, J., A. Niemi, and C.-F. Tsang (2005), A regional-scale particle-tracking method for nonstationary fractured media, Water Resour. Res., 41, W03016,

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

“…For example, analyses show that the effective matrix diffusion coefficient may be scale dependent [40], permeability and porosity changes with support scale and spatial resolution [41], and apparent dispersivity in fractures varies with the scale of observation (in time and space) [7]. The extensive upscaling experiments conducted by Öhman et al [42] and Odén et al [43] further reveal that the standard continuum model cannot capture the dynamics of tracer transport through regional-scale, nonstationary fractured media.…”

A new approach to account for fracture aperture variability when modeling solute transport in fracture networks

“…In our case, data from Sellafield, England, are used (Table 2). These were previously analyzed by € Ohman and Niemi [2003], € Ohman et al [2005], and Od en et al [2008], but without considering the effect of FWS. The blocks containing the fracture network are chosen to be cubic with each side of 7.5 m length.…”

“…Both the flow and the particle transport are simulated using the matrix and fracture interaction code (MAFIC) [Miller et al, 1999]. More details concerning the generation of the fracture networks and simulations without the effect of heterogeneity within the fracture plane, and thereby a variable FWS, can be found in the work of € Ohman and Niemi [2003] and € Ohman et al [2005].…”

“…In section 4 the results of the fracture network simulations are presented for three different scenarios of the fracture networks and the effect of accounting for the variable FWS analyzed. The results can, in principle, be used to further upscale transport from block to regional scale by the method presented by € Ohman et al [2005].…”

“…However, the computational weight has strongly limited the scale where such detailed modeling can be done. There are also hybrid methods where several approaches are combined [e.g., Cacas et al, 1990;Niemi et al, 2000;€ Ohman et al, 2005;Svensson et al, 2010], and they often include calculating block-scale properties with a fracture network model and then using these block-scale values in a stochastic continuum model at the larger scale.…”