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Open Access Publications from the University of California

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


A regional scale transport model is introduced that is applicable to non-stationary 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 equal size to that found valid for continuum approximation of flow. In the large-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-conductivity based on its underlying fracture network. To account for channeled transport larger than the block scale, several alternatives in sampling algorithm 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 advective-dispersive equation to determine an effective macroscale dispersion coefficient. 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.

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