Anomalous transport in disordered fracture networks: Spatial Markov model for dispersion with variable injection modes

Kang, Peter K.; Dentz, Marco; Le Borgne, Tanguy; Lee, Seunghak; Juanes, Ruben

doi:10.1016/j.advwatres.2017.03.024

Title: Anomalous transport in disordered fracture networks: Spatial Markov model for dispersion with variable injection modes

Journal Article · Mon Apr 03 00:00:00 EDT 2017 · Advances in Water Resources

DOI:https://doi.org/10.1016/j.advwatres.2017.03.024· OSTI ID:1533487

Kang, Peter K. ^[1]; Dentz, Marco ^[2]; Le Borgne, Tanguy ^[3]; Lee, Seunghak ^[4]; Juanes, Ruben ^[5]

Korea Institute of Science and Technology (KIST), Seoul (Korea, Republic of); Massachusetts Institute of Technology (MIT), Cambridge, MA (United States)
Spanish National Research Council (CSIC), Barcelona (Spain)
University of Rennes (France)
Korea Institute of Science and Technology (KIST), Seoul (Korea, Republic of)
Massachusetts Institute of Technology (MIT), Cambridge, MA (United States)

Here we investigate tracer transport on random discrete fracture networks that are characterized by the statistics of the fracture geometry and hydraulic conductivity. While it is well known that tracer transport through fractured media can be anomalous and particle injection modes can have major impact on dispersion, the incorporation of injection modes into effective transport modeling has remained an open issue. The fundamental reason behind this challenge is that—even if the Eulerian fluid velocity is steady—the Lagrangian velocity distribution experienced by tracer particles evolves with time from its initial distribution, which is dictated by the injection mode, to a stationary velocity distribution. We quantify this evolution by a Markov model for particle velocities that are equidistantly sampled along trajectories. This stochastic approach allows for the systematic incorporation of the initial velocity distribution and quantifies the interplay between velocity distribution and spatial and temporal correlation. The proposed spatial Markov model is characterized by the initial velocity distribution, which is determined by the particle injection mode, the stationary Lagrangian velocity distribution, which is derived from the Eulerian velocity distribution, and the spatial velocity correlation length, which is related to the characteristic fracture length. This effective model leads to a time-domain random walk for the evolution of particle positions and velocities, whose joint distribution follows a Boltzmann equation. Finally, we demonstrate that the proposed model can successfully predict anomalous transport through discrete fracture networks with different levels of heterogeneity and arbitrary tracer injection modes.

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Research Organization:: Univ. of Texas, Austin, TX (United States); Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)

Sponsoring Organization:: USDOE Office of Science (SC); Korea Institute of Science and Technology (KIST); MIT International Science and Technology Initiatives (MITSI); European Research Council (ERC)

Grant/Contract Number:: SC0009286

OSTI ID:: 1533487

Alternate ID(s):: OSTI ID: 1550459

Journal Information:: Advances in Water Resources, Vol. 106, Issue C; ISSN 0309-1708

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 54 works

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