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Title: Anomalous transport on regular fracture networks: Impact of conductivity heterogeneity and mixing at fracture intersections

Abstract

We investigate here transport on regular fracture networks that are characterized by heterogeneity in hydraulic conductivity. We discuss the impact of conductivity heterogeneity and mixing within fracture intersections on particle spreading. We show the emergence of non-Fickian transport due to the interplay between the network conductivity heterogeneity and the degree of mixing at nodes. Specifically, lack of mixing at fracture intersections leads to subdiffusive scaling of transverse spreading but has negligible impact on longitudinal spreading. An increase in network conductivity heterogeneity enhances both longitudinal and transverse spreading and leads to non-Fickian transport in longitudinal direction. Based on the observed Lagrangian velocity statistics, we develop an effective stochastic model that incorporates the interplay between Lagrangian velocity correlation and velocity distribution. The model is parameterized with a few physical parameters and is able to capture the full particle transition dynamics.

Authors:
 [1];  [2];  [3];  [4]
  1. Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States); Korea Inst. of Science and Technology, Seoul (Korea, Republic of)
  2. Spanish National Research Council (CSIC), Barcelona (Spain). Inst. of Environmental Assessment and Water Research (IDAEA)
  3. Univ. of Rennes 1 (France). Geosciences Rennes
  4. Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
Publication Date:
Research Org.:
Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States); Spanish National Research Council (CSIC), Barcelona (Spain)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22); European Research Council (ERC)
OSTI Identifier:
1505822
Alternate Identifier(s):
OSTI ID: 1213280
Grant/Contract Number:  
SC0003907; 617511
Resource Type:
Accepted Manuscript
Journal Name:
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
Additional Journal Information:
Journal Volume: 92; Journal Issue: 2; Journal ID: ISSN 1539-3755
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
58 GEOSCIENCES

Citation Formats

Kang, Peter K., Dentz, Marco, Le Borgne, Tanguy, and Juanes, Ruben. Anomalous transport on regular fracture networks: Impact of conductivity heterogeneity and mixing at fracture intersections. United States: N. p., 2015. Web. doi:10.1103/physreve.92.022148.
Kang, Peter K., Dentz, Marco, Le Borgne, Tanguy, & Juanes, Ruben. Anomalous transport on regular fracture networks: Impact of conductivity heterogeneity and mixing at fracture intersections. United States. doi:10.1103/physreve.92.022148.
Kang, Peter K., Dentz, Marco, Le Borgne, Tanguy, and Juanes, Ruben. Fri . "Anomalous transport on regular fracture networks: Impact of conductivity heterogeneity and mixing at fracture intersections". United States. doi:10.1103/physreve.92.022148. https://www.osti.gov/servlets/purl/1505822.
@article{osti_1505822,
title = {Anomalous transport on regular fracture networks: Impact of conductivity heterogeneity and mixing at fracture intersections},
author = {Kang, Peter K. and Dentz, Marco and Le Borgne, Tanguy and Juanes, Ruben},
abstractNote = {We investigate here transport on regular fracture networks that are characterized by heterogeneity in hydraulic conductivity. We discuss the impact of conductivity heterogeneity and mixing within fracture intersections on particle spreading. We show the emergence of non-Fickian transport due to the interplay between the network conductivity heterogeneity and the degree of mixing at nodes. Specifically, lack of mixing at fracture intersections leads to subdiffusive scaling of transverse spreading but has negligible impact on longitudinal spreading. An increase in network conductivity heterogeneity enhances both longitudinal and transverse spreading and leads to non-Fickian transport in longitudinal direction. Based on the observed Lagrangian velocity statistics, we develop an effective stochastic model that incorporates the interplay between Lagrangian velocity correlation and velocity distribution. The model is parameterized with a few physical parameters and is able to capture the full particle transition dynamics.},
doi = {10.1103/physreve.92.022148},
journal = {Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics},
number = 2,
volume = 92,
place = {United States},
year = {2015},
month = {8}
}

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Cited by: 20 works
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Works referenced in this record:

Time behavior of solute transport in heterogeneous media: transition from anomalous to normal transport
journal, February 2004


Representative hydraulic conductivities in saturated groundwater flow
journal, January 2006

  • Sanchez-Vila, Xavier; Guadagnini, Alberto; Carrera, Jesus
  • Reviews of Geophysics, Vol. 44, Issue 3
  • DOI: 10.1029/2005RG000169

Reassessment of the 2010-2011 Haiti cholera outbreak and rainfall-driven multiseason projections
journal, April 2012

  • Rinaldo, A.; Bertuzzo, E.; Mari, L.
  • Proceedings of the National Academy of Sciences, Vol. 109, Issue 17
  • DOI: 10.1073/pnas.1203333109

Experimental Features of Self-Organization in Traffic Flow
journal, October 1998


Anomalous physical transport in complex networks
journal, November 2010


Spatial Fluctuations of Fluid Velocities in Flow through a Three-Dimensional Porous Medium
journal, August 2013


Physical Nature of Bacterial Cytoplasm
journal, March 2006


Discrete fracture network interpretation of field tracer migration in sparsely fractured rock
journal, September 1992

  • Dverstorp, Björn; Andersson, Johan; Nordqvist, Wille
  • Water Resources Research, Vol. 28, Issue 9
  • DOI: 10.1029/92WR01182

Integration of Artificial Recharge and Recovery Systems for Impaired Water Sources in Urban Settings: Overcoming Current Limitations and Engineering Challenges
journal, August 2013

  • Regnery, Julia; Lee, Jonghyun; Kitanidis, Peter
  • Environmental Engineering Science, Vol. 30, Issue 8
  • DOI: 10.1089/ees.2012.0186

Impact of velocity correlation and distribution on transport in fractured media: Field evidence and theoretical model
journal, February 2015

  • Kang, Peter K.; Le Borgne, Tanguy; Dentz, Marco
  • Water Resources Research, Vol. 51, Issue 2
  • DOI: 10.1002/2014WR015799

Lagrangian Statistical Model for Transport in Highly Heterogeneous Velocity Fields
journal, August 2008


Anomalous Fluid Transport in Porous Media Induced by Biofilm Growth
journal, November 2004


Large-scale modeling of reactive solute transport in fracture zones of granitic bedrocks
journal, January 2006


Anomalous transport in correlated velocity fields
journal, January 2010


Quantitative nuclear magnetic resonance measurements of preasymptotic dispersion in flow through porous media
journal, November 2005

  • Scheven, U. M.; Verganelakis, D.; Harris, R.
  • Physics of Fluids, Vol. 17, Issue 11
  • DOI: 10.1063/1.2131871

Dispersive transport of ions in column experiments: An explanation of long-tailed profiles
journal, May 1998

  • Hatano, Y.; Hatano, N.
  • Water Resources Research, Vol. 34, Issue 5
  • DOI: 10.1029/98WR00214

Fractional advection-dispersion equation: A classical mass balance with convolution-Fickian Flux
journal, December 2000

  • Cushman, John H.; Ginn, Tim R.
  • Water Resources Research, Vol. 36, Issue 12
  • DOI: 10.1029/2000WR900261

Multiple-Rate Mass Transfer for Modeling Diffusion and Surface Reactions in Media with Pore-Scale Heterogeneity
journal, June 1995

  • Haggerty, Roy; Gorelick, Steven M.
  • Water Resources Research, Vol. 31, Issue 10
  • DOI: 10.1029/95WR10583

Effective transport dynamics in porous media with heterogeneous retardation properties: EFFECTIVE TRANSPORT DYNAMICS
journal, February 2009

  • Dentz, Marco; Castro, Adolfo
  • Geophysical Research Letters, Vol. 36, Issue 3
  • DOI: 10.1029/2008GL036846

Modeling non-Fickian transport in geological formations as a continuous time random walk
journal, January 2006

  • Berkowitz, Brian; Cortis, Andrea; Dentz, Marco
  • Reviews of Geophysics, Vol. 44, Issue 2
  • DOI: 10.1029/2005RG000178

Lévy flight search patterns of wandering albatrosses
journal, May 1996

  • Viswanathan, G. M.; Afanasyev, V.; Buldyrev, S. V.
  • Nature, Vol. 381, Issue 6581
  • DOI: 10.1038/381413a0

Spatial Markov processes for modeling Lagrangian particle dynamics in heterogeneous porous media
journal, August 2008


Tracer tests in a fractured dolomite: 3. Double-porosity, multiple-rate mass transfer processes in convergent flow tracer tests
journal, May 2001

  • McKenna, Sean A.; Meigs, Lucy C.; Haggerty, Roy
  • Water Resources Research, Vol. 37, Issue 5
  • DOI: 10.1029/2000WR900333

Transport and intersection mixing in random fracture networks with power law length distributions
journal, October 2001

  • Park, Young-Jin; de Dreuzy, Jean-Raynald; Lee, Kang-Kun
  • Water Resources Research, Vol. 37, Issue 10
  • DOI: 10.1029/2000WR000131

Tracer tests in a fractured dolomite: 2. Analysis of mass transfer in single-well injection-withdrawal tests
journal, May 2001

  • Haggerty, Roy; Fleming, Sean W.; Meigs, Lucy C.
  • Water Resources Research, Vol. 37, Issue 5
  • DOI: 10.1029/2000WR900334

Application of a fractional advection-dispersion equation
journal, February 2000

  • Benson, David A.; Wheatcraft, Stephen W.; Meerschaert, Mark M.
  • Water Resources Research, Vol. 36, Issue 6
  • DOI: 10.1029/2000WR900031

Anomalous Transport in “Classical” Soil and Sand Columns
journal, January 2004

  • Cortis, Andrea; Berkowitz, Brian
  • Soil Science Society of America Journal, Vol. 68, Issue 5
  • DOI: 10.2136/sssaj2004.1539

Predictability of anomalous transport on lattice networks with quenched disorder
journal, March 2011


Nonergodic Subdiffusion from Brownian Motion in an Inhomogeneous Medium
journal, April 2014


Non-Fickian transport through two-dimensional rough fractures: Assessment and prediction: NON-FICKIAN TRANSPORT THROUGH 2-D FRACTURES
journal, February 2014

  • Wang, Lichun; Cardenas, M. Bayani
  • Water Resources Research, Vol. 50, Issue 2
  • DOI: 10.1002/2013WR014459

Overview of scientific investigations at Yucca Mountain—the potential repository for high-level nuclear waste
journal, May 1999


Pore-scale intermittent velocity structure underpinning anomalous transport through 3-D porous media
journal, September 2014

  • Kang, Peter K.; de Anna, Pietro; Nunes, Joao P.
  • Geophysical Research Letters, Vol. 41, Issue 17
  • DOI: 10.1002/2014GL061475

Implications of Rate-Limited Mass Transfer for Aquifer Storage and Recovery
journal, July 2008


Anomalous Transport in Random Fracture Networks
journal, November 1997


Distribution- Versus Correlation-Induced Anomalous Transport in Quenched Random Velocity Fields
journal, December 2010


Mass transfer at fracture intersections: An evaluation of mixing models
journal, June 1994

  • Berkowitz, Brian; Naumann, Curt; Smith, Leslie
  • Water Resources Research, Vol. 30, Issue 6
  • DOI: 10.1029/94WR00432

Solute transport in low-heterogeneity sandboxes: The role of correlation length and permeability variance
journal, October 2014


Anomalous transit-time dispersion in amorphous solids
journal, September 1975


Upscaling discrete fracture network simulations: An alternative to continuum transport models: UPSCALING FRACTURE NETWORK SIMULATIONS
journal, February 2005


A lattice-gas and lattice Boltzmann study of mixing at continuous fracture Junctions: Importance of boundary conditions
journal, June 1997

  • Stockman, Harlan W.; Li, Chunhong; Wilson, John L.
  • Geophysical Research Letters, Vol. 24, Issue 12
  • DOI: 10.1029/97GL51471

Spatial Markov Model of Anomalous Transport Through Random Lattice Networks
journal, October 2011


Flow Intermittency, Dispersion, and Correlated Continuous Time Random Walks in Porous Media
journal, May 2013


The origins and the future of microfluidics
journal, July 2006


Continuous time random walks for non-local radial solute transport
journal, August 2015


The random walk's guide to anomalous diffusion: a fractional dynamics approach
journal, December 2000


Signature of Non-Fickian Solute Transport in Complex Heterogeneous Porous Media
journal, November 2011


Anomalous diffusion in disordered media: Statistical mechanisms, models and physical applications
journal, November 1990


Derivation of the Continuous-Time Random-Walk Equation
journal, January 1980


Asymptotic solutions of continuous-time random walks
journal, May 1974

  • Shlesinger, Michael F.
  • Journal of Statistical Physics, Vol. 10, Issue 5
  • DOI: 10.1007/BF01008803

Tracer transport in fractured crystalline rock: Evidence of nondiffusive breakthrough tailing
journal, July 2000

  • Becker, Matthew W.; Shapiro, Allen M.
  • Water Resources Research, Vol. 36, Issue 7
  • DOI: 10.1029/2000WR900080

Large-scale natural gradient tracer test in sand and gravel, Cape Cod, Massachusetts: 2. Analysis of spatial moments for a nonreactive tracer
journal, May 1991

  • Garabedian, Stephen P.; LeBlanc, Dennis R.; Gelhar, Lynn W.
  • Water Resources Research, Vol. 27, Issue 5
  • DOI: 10.1029/91WR00242

Origins of anomalous transport in heterogeneous media: Structural and dynamic controls
journal, February 2014

  • Edery, Yaniv; Guadagnini, Alberto; Scher, Harvey
  • Water Resources Research, Vol. 50, Issue 2
  • DOI: 10.1002/2013WR015111

Optimal design of measures to correct seawater intrusion: MEASURES TO CORRECT SEAWATER INTRUSION
journal, September 2006

  • Abarca, Elena; Vázquez-Suñé, Enric; Carrera, Jesús
  • Water Resources Research, Vol. 42, Issue 9
  • DOI: 10.1029/2005WR004524

On matrix diffusion: formulations, solution methods and qualitative effects
journal, June 1998

  • Carrera, Jesús; Sánchez-Vila, Xavier; Benet, Inmaculada
  • Hydrogeology Journal, Vol. 6, Issue 1
  • DOI: 10.1007/s100400050143