Matrix Diffusion in Fractured Media: New Insights Into Power Law Scaling of Breakthrough Curves

doi:10.1029/2019GL085454

Title: Matrix Diffusion in Fractured Media: New Insights Into Power Law Scaling of Breakthrough Curves

Abstract

Here, we develop a theoretical model for power law tailing behavior of transport in fractured rock based on the relative dominance of the decay rate of the advective travel time distribution, modeled using a Pareto distribution (with tail decaying as ~ time^-(1+α)), versus matrix diffusion, modeled using a Lévy distribution. The theory predicts that when the advective travel time distribution decays sufficiently slowly (α<1), the late-time decay rate of the breakthrough curve is -(1+α/2) rather than the classical -3/2. Yet, if α>1, the -3/2 decay rate is recovered. For weak matrix diffusion or short advective first breakthrough times, we identify an early-time regime where the breakthrough curve follows the Pareto distribution, before transitioning to the late-time decay rate. The theoretical predictions are validated against particle tracking simulations in the three-dimensional discrete fracture network simulator dfnWorks, where matrix diffusion is incorporated using a time domain random walk.

Authors:

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Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Johns Hopkins Univ., Baltimore, MD (United States)

Publication Date:: 2019-11-03

Research Org.:: Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

Sponsoring Org.:: USDOE National Nuclear Security Administration (NNSA)

OSTI Identifier:: 1581275

Alternate Identifier(s):: OSTI ID: 1576828

Report Number(s):: LA-UR-19-23625
Journal ID: ISSN 0094-8276

Grant/Contract Number:: 89233218CNA000001; AC52-06NA25396; 20180621ECR; 20170103DR; 20170508DR

Resource Type:: Accepted Manuscript

Journal Name:: Geophysical Research Letters

Additional Journal Information:: Journal Volume: 46; Journal Issue: 23; Journal ID: ISSN 0094-8276

Publisher:: American Geophysical Union

Country of Publication:: United States

Language:: English

Subject:: 58 GEOSCIENCES; Earth Sciences; Energy Sciences

Citation Formats


                    Hyman, Jeffrey D., Rajaram, Harihar, Srinivasan, Shriram, Makedonska, Nataliia, Karra, Satish, Viswanathan, Hari, and Srinivasan, Gowri. Matrix Diffusion in Fractured Media: New Insights Into Power Law Scaling of Breakthrough Curves.  United States: N. p., 2019. 
        Web.  doi:10.1029/2019GL085454.

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                    Hyman, Jeffrey D., Rajaram, Harihar, Srinivasan, Shriram, Makedonska, Nataliia, Karra, Satish, Viswanathan, Hari, & Srinivasan, Gowri. Matrix Diffusion in Fractured Media: New Insights Into Power Law Scaling of Breakthrough Curves.  United States.  doi:10.1029/2019GL085454.

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                    Hyman, Jeffrey D., Rajaram, Harihar, Srinivasan, Shriram, Makedonska, Nataliia, Karra, Satish, Viswanathan, Hari, and Srinivasan, Gowri. Sun .  
        "Matrix Diffusion in Fractured Media: New Insights Into Power Law Scaling of Breakthrough Curves".  United States.  doi:10.1029/2019GL085454.  https://www.osti.gov/servlets/purl/1581275.

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@article{osti_1581275,

  title        = {Matrix Diffusion in Fractured Media: New Insights Into Power Law Scaling of Breakthrough Curves},

  author       = {Hyman, Jeffrey D. and Rajaram, Harihar and Srinivasan, Shriram and Makedonska, Nataliia and Karra, Satish and Viswanathan, Hari and Srinivasan, Gowri},

  abstractNote = {Here, we develop a theoretical model for power law tailing behavior of transport in fractured rock based on the relative dominance of the decay rate of the advective travel time distribution, modeled using a Pareto distribution (with tail decaying as ~ time-(1+α)), versus matrix diffusion, modeled using a Lévy distribution. The theory predicts that when the advective travel time distribution decays sufficiently slowly (α<1), the late-time decay rate of the breakthrough curve is -(1+α/2) rather than the classical -3/2. Yet, if α>1, the -3/2 decay rate is recovered. For weak matrix diffusion or short advective first breakthrough times, we identify an early-time regime where the breakthrough curve follows the Pareto distribution, before transitioning to the late-time decay rate. The theoretical predictions are validated against particle tracking simulations in the three-dimensional discrete fracture network simulator dfnWorks, where matrix diffusion is incorporated using a time domain random walk.},

  doi          = {10.1029/2019GL085454},

  journal      = {Geophysical Research Letters},

  number       = 23,

  volume       = 46,

  place        = {United States},

  year         = {2019},

  month        = {11}

}

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DOI: 10.1029/2019GL085454

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Similar Records

Title: Matrix Diffusion in Fractured Media: New Insights Into Power Law Scaling of Breakthrough Curves

Abstract

Citation Formats

Transport of reactive tracers in rock fractures journal, January 1999

Interpretation of tracer tests performed in fractured rock of the Lange Bramke basin, Germany journal, January 1999

Field-scale effective matrix diffusion coefficient for fractured rock: Results from literature survey journal, August 2007

Tracer experiments in fractured rocks: Matrix diffusion and the validity of models journal, August 1993

Emergence of anomalous transport in stressed rough fractures journal, November 2016

Hydraulic conductivity of rock fractures journal, April 1996

Influence of injection mode on transport properties in kilometer-scale three-dimensional discrete fracture networks: INFLUENCE OF INJECTION MODE IN 3-D DFNs journal, September 2015

Navier-Stokes flow and transport simulations using real fractures shows heavy tailing due to eddies journal, January 2007

Fickian dispersion is anomalous journal, December 2015

Interpreting tracer breakthrough tailing from different forced-gradient tracer experiment configurations in fractured bedrock: TRACER EXPERIMENTS IN FRACTURED BEDROCK journal, January 2003

Upscaling and Prediction of Lagrangian Velocity Dynamics in Heterogeneous Porous Media journal, May 2019

On the theory of tracer experiments in fissured rocks with a porous matrix journal, July 1985

dfnWorks: A discrete fracture network framework for modeling subsurface flow and transport journal, November 2015

Linking Structural and Transport Properties in Three‐Dimensional Fracture Networks journal, February 2019

Trends, prospects and challenges in quantifying flow and transport through fractured rocks journal, February 2005

Contaminant transport in fractured porous media: Analytical solution for a single fracture journal, June 1981

Solute transport through fractured media: 1. The effect of matrix diffusion journal, August 1980

Conforming Delaunay Triangulation of Stochastically Generated Three Dimensional Discrete Fracture Networks: A Feature Rejection Algorithm for Meshing Strategy journal, January 2014

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

Power-law velocity distributions in fracture networks: Numerical evidence and implications for tracer transport: POWER-LAW VELOCITY DISTRIBUTIONS IN FRACTURE NETWORKS journal, July 2002

Time domain random walk method to simulate transport by advection-dispersion and matrix diffusion in fracture networks journal, November 2001

On the physical meaning of the dispersion equation and its solutions for different initial and boundary conditions journal, January 1978

Particle-tracking simulations of anomalous transport in hierarchically fractured rocks journal, January 2013

Time domain particle tracking methods for simulating transport with retention and first-order transformation: TIME DOMAIN PARTICLE TRACKING journal, January 2008

On the late-time behavior of tracer test breakthrough curves journal, December 2000

Tracer tests in a fractured dolomite: 1. Experimental design and observed tracer recoveries journal, May 2001

The state of the art in monitoring and verification—Ten years on journal, September 2015

Multi-Scale Characterization of Fractured Rocks Used as a Means for the Realistic Simulation of Pollutant Migration Pathways in Contaminated Sites: A Case Study journal, October 2004

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

Non-Fickian mass transport in fractured porous media journal, February 2011

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

Advective Transport in Discrete Fracture Networks With Connected and Disconnected Textures Representing Internal Aperture Variability journal, July 2019

Dispersion and Mixing in Three‐Dimensional Discrete Fracture Networks: Nonlinear Interplay Between Structural and Hydraulic Heterogeneity journal, May 2018

Study of alternative tracer tests in characterizing transport in fractured rocks journal, June 1995

Dissolution of non-aqueous-phase liquids and aqueous-phase contaminant transport in discretely-fractured porous media journal, June 1996

Multi-scale groundwater flow modeling during temperate climate conditions for the safety assessment of the proposed high-level nuclear waste repository site at Forsmark, Sweden journal, July 2014

The Behavior of Dense, Nonaqueous Phase Liquids in Fractured Clay and Rock journal, September 1991

Particle tracking approach for transport in three-dimensional discrete fracture networks: Particle tracking in 3-D DFNs journal, September 2015

Evaluating the effect of internal aperture variability on transport in kilometer scale discrete fracture networks journal, August 2016

Perspective on theories of non-Fickian transport in heterogeneous media journal, May 2009

Stress‐Induced Anomalous Transport in Natural Fracture Networks journal, May 2019

Shale gas and non-aqueous fracturing fluids: Opportunities and challenges for supercritical CO2 journal, June 2015

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

Effect of advective flow in fractures and matrix diffusion on natural gas production journal, October 2015

Significance of injection modes and heterogeneity on spatial and temporal dispersion of advecting particles in two-dimensional discrete fracture networks journal, May 2009

Testing and parameterizing a conceptual model for solute transport in a fractured granite using multiple tracers in a forced-gradient test: MULTIPLE TRACER TESTING IN FRACTURED ROCK journal, December 2003

Simulation of solute transport in discrete fracture networks using the time domain random walk method journal, March 2003

The Grimsel (Switzerland) migration experiment: integrating field experiments, laboratory investigations and modelling journal, February 1996

Understanding hydraulic fracturing: a multi-scale problem journal, October 2016

Diffusion and trapping in heterogeneous media: An inhomogeneous continuous time random walk approach journal, December 2012

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

Trapping zones: The effect of fracture roughness on the directional anisotropy of fluid flow and colloid transport in a single fracture journal, January 2006

Upscaling solute transport in naturally fractured porous media with the continuous time random walk method: UPSCALING TRANSPORT IN FRACTURED ROCK WITH CTRW journal, December 2010

Anomalous transport in disordered fracture networks: Spatial Markov model for dispersion with variable injection modes journal, August 2017

An interpretation of potential scale dependence of the effective matrix diffusion coefficient journal, February 2007

Diffusion in the rock matrix: An important factor in radionuclide retardation? journal, August 1980

Quantifying diffusive mass transfer in fractured shale bedrock journal, July 1999

Influence of fracture scale heterogeneity on the flow properties of three-dimensional discrete fracture networks (DFN): 3D FRACTURE NETWORK PERMEABILITY journal, November 2012

Channeling with diffusion into stagnant water and into a matrix in series: CHANNELING WITH DIFFUSION INTO MATRIX IN SERIES journal, November 2006

On Characterization of Anomalous Dispersion in Porous and Fractured Media journal, June 1995

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

A borehole temperature during drilling in a fractured rock formation journal, January 2005

Solute transport in variable-aperture fractures: An investigation of the relative importance of Taylor dispersion and macrodispersion journal, July 2000

Characterizing the impact of particle behavior at fracture intersections in three-dimensional discrete fracture networks journal, January 2019

Upscaled discrete fracture matrix model (UDFM): an octree-refined continuum representation of fractured porous media journal, December 2019

Transport of reactive tracers in rock fractures
journal, January 1999

Interpretation of tracer tests performed in fractured rock of the Lange Bramke basin, Germany
journal, January 1999

Field-scale effective matrix diffusion coefficient for fractured rock: Results from literature survey
journal, August 2007

Tracer experiments in fractured rocks: Matrix diffusion and the validity of models
journal, August 1993

Emergence of anomalous transport in stressed rough fractures
journal, November 2016

Hydraulic conductivity of rock fractures
journal, April 1996

Influence of injection mode on transport properties in kilometer-scale three-dimensional discrete fracture networks: INFLUENCE OF INJECTION MODE IN 3-D DFNs
journal, September 2015

Navier-Stokes flow and transport simulations using real fractures shows heavy tailing due to eddies
journal, January 2007

Fickian dispersion is anomalous
journal, December 2015

Interpreting tracer breakthrough tailing from different forced-gradient tracer experiment configurations in fractured bedrock: TRACER EXPERIMENTS IN FRACTURED BEDROCK
journal, January 2003

Upscaling and Prediction of Lagrangian Velocity Dynamics in Heterogeneous Porous Media
journal, May 2019

On the theory of tracer experiments in fissured rocks with a porous matrix
journal, July 1985

dfnWorks: A discrete fracture network framework for modeling subsurface flow and transport
journal, November 2015

Linking Structural and Transport Properties in Three‐Dimensional Fracture Networks
journal, February 2019

Trends, prospects and challenges in quantifying flow and transport through fractured rocks
journal, February 2005

Contaminant transport in fractured porous media: Analytical solution for a single fracture
journal, June 1981

Solute transport through fractured media: 1. The effect of matrix diffusion
journal, August 1980

Conforming Delaunay Triangulation of Stochastically Generated Three Dimensional Discrete Fracture Networks: A Feature Rejection Algorithm for Meshing Strategy
journal, January 2014

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

Power-law velocity distributions in fracture networks: Numerical evidence and implications for tracer transport: POWER-LAW VELOCITY DISTRIBUTIONS IN FRACTURE NETWORKS
journal, July 2002

Time domain random walk method to simulate transport by advection-dispersion and matrix diffusion in fracture networks
journal, November 2001

On the physical meaning of the dispersion equation and its solutions for different initial and boundary conditions
journal, January 1978

Particle-tracking simulations of anomalous transport in hierarchically fractured rocks
journal, January 2013

Time domain particle tracking methods for simulating transport with retention and first-order transformation: TIME DOMAIN PARTICLE TRACKING
journal, January 2008

On the late-time behavior of tracer test breakthrough curves
journal, December 2000

Tracer tests in a fractured dolomite: 1. Experimental design and observed tracer recoveries
journal, May 2001

The state of the art in monitoring and verification—Ten years on
journal, September 2015

Multi-Scale Characterization of Fractured Rocks Used as a Means for the Realistic Simulation of Pollutant Migration Pathways in Contaminated Sites: A Case Study
journal, October 2004

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

Non-Fickian mass transport in fractured porous media
journal, February 2011

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

Advective Transport in Discrete Fracture Networks With Connected and Disconnected Textures Representing Internal Aperture Variability
journal, July 2019

Dispersion and Mixing in Three‐Dimensional Discrete Fracture Networks: Nonlinear Interplay Between Structural and Hydraulic Heterogeneity
journal, May 2018

Study of alternative tracer tests in characterizing transport in fractured rocks
journal, June 1995

Dissolution of non-aqueous-phase liquids and aqueous-phase contaminant transport in discretely-fractured porous media
journal, June 1996

Multi-scale groundwater flow modeling during temperate climate conditions for the safety assessment of the proposed high-level nuclear waste repository site at Forsmark, Sweden
journal, July 2014

The Behavior of Dense, Nonaqueous Phase Liquids in Fractured Clay and Rock
journal, September 1991

Particle tracking approach for transport in three-dimensional discrete fracture networks: Particle tracking in 3-D DFNs
journal, September 2015

Evaluating the effect of internal aperture variability on transport in kilometer scale discrete fracture networks
journal, August 2016

Perspective on theories of non-Fickian transport in heterogeneous media
journal, May 2009

Stress‐Induced Anomalous Transport in Natural Fracture Networks
journal, May 2019

Shale gas and non-aqueous fracturing fluids: Opportunities and challenges for supercritical CO2
journal, June 2015

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

Effect of advective flow in fractures and matrix diffusion on natural gas production
journal, October 2015

Significance of injection modes and heterogeneity on spatial and temporal dispersion of advecting particles in two-dimensional discrete fracture networks
journal, May 2009

Testing and parameterizing a conceptual model for solute transport in a fractured granite using multiple tracers in a forced-gradient test: MULTIPLE TRACER TESTING IN FRACTURED ROCK
journal, December 2003

Simulation of solute transport in discrete fracture networks using the time domain random walk method
journal, March 2003

The Grimsel (Switzerland) migration experiment: integrating field experiments, laboratory investigations and modelling
journal, February 1996

Understanding hydraulic fracturing: a multi-scale problem
journal, October 2016

Diffusion and trapping in heterogeneous media: An inhomogeneous continuous time random walk approach
journal, December 2012

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

Trapping zones: The effect of fracture roughness on the directional anisotropy of fluid flow and colloid transport in a single fracture
journal, January 2006

Upscaling solute transport in naturally fractured porous media with the continuous time random walk method: UPSCALING TRANSPORT IN FRACTURED ROCK WITH CTRW
journal, December 2010

Anomalous transport in disordered fracture networks: Spatial Markov model for dispersion with variable injection modes
journal, August 2017

An interpretation of potential scale dependence of the effective matrix diffusion coefficient
journal, February 2007

Diffusion in the rock matrix: An important factor in radionuclide retardation?
journal, August 1980

Quantifying diffusive mass transfer in fractured shale bedrock
journal, July 1999

Influence of fracture scale heterogeneity on the flow properties of three-dimensional discrete fracture networks (DFN): 3D FRACTURE NETWORK PERMEABILITY
journal, November 2012

Channeling with diffusion into stagnant water and into a matrix in series: CHANNELING WITH DIFFUSION INTO MATRIX IN SERIES
journal, November 2006

On Characterization of Anomalous Dispersion in Porous and Fractured Media
journal, June 1995

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

A borehole temperature during drilling in a fractured rock formation
journal, January 2005

Solute transport in variable-aperture fractures: An investigation of the relative importance of Taylor dispersion and macrodispersion
journal, July 2000

Characterizing the impact of particle behavior at fracture intersections in three-dimensional discrete fracture networks
journal, January 2019

Upscaled discrete fracture matrix model (UDFM): an octree-refined continuum representation of fractured porous media
journal, December 2019