Anomalous transport in disordered fracture networks: Spatial Markov model for dispersion with variable injection modes
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...
| Main Authors: | , , , , |
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| Other Authors: | |
| Format: | Article |
| Language: | en_US |
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Elsevier BV
2020
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| Online Access: | https://hdl.handle.net/1721.1/123817 |
| _version_ | 1811072720673177600 |
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| author | Kang, Peter Kyungchul Dentz, Marco Le Borgne, Tanguy Lee, Seunghak Juanes, Ruben |
| author2 | Massachusetts Institute of Technology. Department of Civil and Environmental Engineering |
| author_facet | Massachusetts Institute of Technology. Department of Civil and Environmental Engineering Kang, Peter Kyungchul Dentz, Marco Le Borgne, Tanguy Lee, Seunghak Juanes, Ruben |
| author_sort | Kang, Peter Kyungchul |
| collection | MIT |
| description | 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. Keywords: Discrete fracture networks; Injection modes; Anomalous transport; Stochastic modeling; Lagrangian velocity; Time domain random walks; Continuous time random walks; Spatial Markov model |
| first_indexed | 2024-09-23T09:10:57Z |
| format | Article |
| id | mit-1721.1/123817 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T09:10:57Z |
| publishDate | 2020 |
| publisher | Elsevier BV |
| record_format | dspace |
| spelling | mit-1721.1/1238172022-09-30T13:58:06Z Anomalous transport in disordered fracture networks: Spatial Markov model for dispersion with variable injection modes Kang, Peter Kyungchul Dentz, Marco Le Borgne, Tanguy Lee, Seunghak Juanes, Ruben Massachusetts Institute of Technology. Department of Civil and Environmental Engineering Ruben Juanes 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. Keywords: Discrete fracture networks; Injection modes; Anomalous transport; Stochastic modeling; Lagrangian velocity; Time domain random walks; Continuous time random walks; Spatial Markov model United States. Department of Energy (Grant DE-SC0009286) 2020-02-14T19:15:10Z 2020-02-14T19:15:10Z 2017-08 2017-03 Article http://purl.org/eprint/type/JournalArticle 0309-1708 https://hdl.handle.net/1721.1/123817 Kang, Peter K. et al. "Anomalous transport in disordered fracture networks: Spatial Markov model for dispersion with variable injection modes." Advances in Water Resources 106 (August 2017): 80-94 © 2017 Elsevier en_US http://dx.doi.org/10.1016/j.advwatres.2017.03.024 Advances in Water Resources Creative Commons Attribution-NonCommercial-NoDerivs License http://creativecommons.org/licenses/by-nc-nd/4.0/ application/pdf Elsevier BV Prof. Juanes via Elizabeth Soergel |
| spellingShingle | Kang, Peter Kyungchul Dentz, Marco Le Borgne, Tanguy Lee, Seunghak Juanes, Ruben 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 |
| title_full | Anomalous transport in disordered fracture networks: Spatial Markov model for dispersion with variable injection modes |
| title_fullStr | Anomalous transport in disordered fracture networks: Spatial Markov model for dispersion with variable injection modes |
| title_full_unstemmed | Anomalous transport in disordered fracture networks: Spatial Markov model for dispersion with variable injection modes |
| title_short | Anomalous transport in disordered fracture networks: Spatial Markov model for dispersion with variable injection modes |
| title_sort | anomalous transport in disordered fracture networks spatial markov model for dispersion with variable injection modes |
| url | https://hdl.handle.net/1721.1/123817 |
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