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

Title
Anomalous transport in disordered fracture networks: Spatial Markov model for dispersion with variable injection modes
Authors
이승학강경철Marco DentzTanguy Le BorgneRuben Juanes
Keywords
Discrete fracture networks; Injection modes; Anomalous transport; Stochastic modeling; Lagrangian velocity; Time domain random walks; Continuous time random walks; Spatial Markov model
Issue Date
2017-08
Publisher
Advances in water resources
Citation
VOL 106-94
Abstract
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.
URI
http://pubs.kist.re.kr/handle/201004/66578
ISSN
0309-1708
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