Characterizing the Influence of Fracture Density on Network Scale Transport

T. S. is supported by the National Science Foundation Graduate Research Fellowship under Grant DGE‐1841556. D. B. was supported by the US Army Research Office under Contract/Grant W911NF‐18‐1‐0338 and by the National Science Foundation under award CBET‐1803989. Los Alamos National Laboratory is operated by Triad National Security, LLC, for the National Nuclear Security Administration of U.S. Department of Energy (Contract 89233218CNA000001). J. D. H. acknowledges support from the LANL LDRD program office Grant 20180621ECR and DOE's Office of Science Basic Energy SciencesE3W1: LA‐UR‐19‐27671. M. D. acknowledges funding from the European Research Council under the European Union's Seventh Framework Programme (FP7/2007‐2013)/ ERC Grant Agreement 617511 (MHetScale). DFNWORKS and and simulation data can be obtained at GitHub (https://github.com/lanl/dfnWorks and https://github.com/tjsherman24/FractureNetworkDensity, respectively).

[1]  Tanguy Le Borgne,et al.  Spatial Markov processes for modeling Lagrangian particle dynamics in heterogeneous porous media. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[2]  S Pacala,et al.  Stabilization Wedges: Solving the Climate Problem for the Next 50 Years with Current Technologies , 2004, Science.

[3]  Kamini Singha,et al.  Parameterizing the Spatial Markov Model From Breakthrough Curve Data Alone: PARAMETERIZING SMM FROM BTC DATA , 2017 .

[4]  Tanguy Le Borgne,et al.  Lagrangian statistical model for transport in highly heterogeneous velocity fields. , 2008, Physical review letters.

[5]  J. Thovert,et al.  Effective permeability of fractured porous media with power-law distribution of fracture sizes. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[6]  Caroline Darcel,et al.  Connectivity, permeability, and channeling in randomly distributed and kinematically defined discrete fracture network models , 2016 .

[7]  Jeffrey D. Hyman,et al.  Conforming Delaunay Triangulation of Stochastically Generated Three Dimensional Discrete Fracture Networks: A Feature Rejection Algorithm for Meshing Strategy , 2014, SIAM J. Sci. Comput..

[8]  Alexandre M Tartakovsky,et al.  Flow intermittency, dispersion, and correlated continuous time random walks in porous media. , 2013, Physical review letters.

[9]  P. Davy,et al.  Percolation parameter and percolation-threshold estimates for three-dimensional random ellipses with widely scattered distributions of eccentricity and size , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[10]  M E J Newman.  Assortative mixing in networks. , 2002, Physical review letters.

[11]  Mary C. Hill,et al.  Effects of simplifying fracture network representation on inert chemical migration in fracture‐controlled aquifers , 2009 .

[12]  Georg Kosakowski,et al.  Transport behavior in three‐dimensional fracture intersections , 2003 .

[13]  Olivier Bour,et al.  On the connectivity of three‐dimensional fault networks , 1998 .

[14]  M. Dentz,et al.  Impact of velocity correlation and distribution on transport in fractured media: Field evidence and theoretical model , 2015 .

[15]  Arash Massoudieh,et al.  A spatial Markov model for the evolution of the joint distribution of groundwater age, arrival time, and velocity in heterogeneous media , 2017 .

[16]  Ruben Juanes,et al.  Pore‐scale intermittent velocity structure underpinning anomalous transport through 3‐D porous media , 2014 .

[17]  E Morgenroth,et al.  Pore‐Scale Hydrodynamics in a Progressively Bioclogged Three‐Dimensional Porous Medium: 3‐D Particle Tracking Experiments and Stochastic Transport Modeling , 2018, Water resources research.

[18]  Ruben Juanes,et al.  Anomalous transport on regular fracture networks: Impact of conductivity heterogeneity and mixing at fracture intersections. , 2015, Physical review. E, Statistical, nonlinear, and soft matter physics.

[19]  Carl W. Gable,et al.  Pathline tracing on fully unstructured control-volume grids , 2012, Computational Geosciences.

[20]  Kamini Singha,et al.  Predicting Downstream Concentration Histories From Upstream Data in Column Experiments , 2018, Water Resources Research.

[21]  N. Odling,et al.  Scaling of fracture systems in geological media , 2001 .

[22]  Satish Karra,et al.  PFLOTRAN User Manual A Massively Parallel Reactive Flow and Transport Model for Describing Surface and Subsurface Processes , 2015 .

[23]  M. Becker,et al.  Tracer transport in fractured crystalline rock: Evidence of nondiffusive breakthrough tailing , 2000 .

[24]  A. Zuber,et al.  On the physical meaning of the dispersion equation and its solutions for different initial and boundary conditions , 1978 .

[25]  M. Dentz,et al.  Modeling non‐Fickian transport in geological formations as a continuous time random walk , 2006 .

[26]  Jean-Raynald de Dreuzy,et al.  Influence of spatial correlation of fracture centers on the permeability of two‐dimensional fracture networks following a power law length distribution , 2004 .

[27]  Philippe Gouze,et al.  Stochastic Dynamics of Lagrangian Pore‐Scale Velocities in Three‐Dimensional Porous Media , 2019, Water Resources Research.

[28]  Brian Berkowitz,et al.  ANOMALOUS TRANSPORT IN RANDOM FRACTURE NETWORKS , 1997 .

[29]  Marco Dentz,et al.  Anomalous dispersion in correlated porous media: a coupled continuous time random walk approach , 2017, 1707.05560.

[30]  M. Newman,et al.  Mixing patterns in networks. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[31]  Satish Karra,et al.  Evaluating the effect of internal aperture variability on transport in kilometer scale discrete fracture networks , 2016 .

[32]  Satish Karra,et al.  Fracture size and transmissivity correlations: Implications for transport simulations in sparse three‐dimensional discrete fracture networks following a truncated power law distribution of fracture size , 2016 .

[33]  Antti I. Koponen,et al.  Tortuous flow in porous media. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[34]  M. Dentz,et al.  Intermittent Lagrangian velocities and accelerations in three-dimensional porous medium flow. , 2015, Physical review. E, Statistical, nonlinear, and soft matter physics.

[35]  Philippe Gouze,et al.  Upscaling of Anomalous Pore-Scale Dispersion , 2019, Transport in Porous Media.

[36]  Vladimir Cvetkovic,et al.  Inference of field‐scale fracture transmissivities in crystalline rock using flow log measurements , 2010 .

[37]  J. Thovert,et al.  Percolation of three-dimensional fracture networks with power-law size distribution. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[38]  Olivier Bour,et al.  Hydraulic properties of two‐dimensional random fracture networks following power law distributions of length and aperture , 2002 .

[39]  Satish Karra,et al.  Influence of injection mode on transport properties in kilometer‐scale three‐dimensional discrete fracture networks , 2015 .

[40]  Scott L. Painter,et al.  Upscaling discrete fracture network simulations: An alternative to continuum transport models , 2005 .

[41]  Ruben Juanes,et al.  Anomalous transport in disordered fracture networks: Spatial Markov model for dispersion with variable injection modes , 2017, 1704.02762.

[42]  A. Wood.  Simulation of the von mises fisher distribution , 1994 .

[43]  Daniel R. Lester,et al.  Continuous Time Random Walks for the Evolution of Lagrangian Velocities , 2016, 1608.02208.

[44]  S. Ab.  Model summary report for the safety assessment SR-Site , 2011 .

[45]  Ruben Juanes,et al.  Spatial Markov model of anomalous transport through random lattice networks. , 2011, Physical review letters.

[46]  Pierre M. Adler,et al.  Geometry and topology of fracture systems , 1997 .

[47]  Peter Jackson,et al.  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 , 2014, Hydrogeology Journal.

[48]  Marco Dentz,et al.  Upscaling and Prediction of Lagrangian Velocity Dynamics in Heterogeneous Porous Media , 2019, Water Resources Research.

[49]  M. Dentz,et al.  Distribution- versus correlation-induced anomalous transport in quenched random velocity fields. , 2010, Physical review letters.

[50]  H. S. Viswanathan,et al.  Understanding hydraulic fracturing: a multi-scale problem , 2016, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[51]  Ruben Juanes,et al.  Stress‐Induced Anomalous Transport in Natural Fracture Networks , 2019, Water Resources Research.

[52]  Brian Berkowitz,et al.  PERCOLATION THEORY AND ITS APPLICATION TO GROUNDWATER HYDROLOGY , 1993 .

[53]  M. Sahimi,et al.  Tortuosity in Porous Media: A Critical Review , 2013 .

[54]  M. Dentz,et al.  Linking Structural and Transport Properties in Three‐Dimensional Fracture Networks , 2019, Journal of Geophysical Research: Solid Earth.

[55]  Olivier Bour,et al.  Connectivity of random fault networks following a power law fault length distribution , 1997 .

[56]  Tanguy Le Borgne,et al.  Modeling preasymptotic transport in flows with significant inertial and trapping effects – The importance of velocity correlations and a spatial Markov model , 2014 .

[57]  Ruben Juanes,et al.  Emergence of Anomalous Transport in Stressed Rough Fractures , 2015 .

[58]  M. Sahini,et al.  Applications of Percolation Theory , 2023, Applied Mathematical Sciences.

[59]  G. Marsily,et al.  Modeling fracture flow with a stochastic discrete fracture network: calibration and validation: 1. The flow model , 1990 .

[60]  Significance of injection modes and heterogeneity on spatial and temporal dispersion of advecting particles in two-dimensional discrete fracture networks , 2009 .

[61]  Satish Karra,et al.  dfnWorks: A discrete fracture network framework for modeling subsurface flow and transport , 2015, Comput. Geosci..

[62]  Enrico Barbier,et al.  Geothermal energy technology and current status: an overview , 2002 .

[63]  Jeffrey D. Hyman,et al.  Identifying Backbones in Three-Dimensional Discrete Fracture Networks: A Bipartite Graph-Based Approach , 2018, Multiscale Model. Simul..

[64]  Géraldine Pichot,et al.  Influence of fracture scale heterogeneity on the flow properties of three-dimensional discrete fracture networks (DFN) , 2012 .

[65]  Nataliia Makedonska,et al.  Characterizing the impact of particle behavior at fracture intersections in three-dimensional discrete fracture networks. , 2019, Physical review. E.

[66]  M. Willmann,et al.  Stochastic dynamics of intermittent pore‐scale particle motion in three‐dimensional porous media: Experiments and theory , 2017 .

[67]  Jean-Raynald de Dreuzy,et al.  Random Walk Methods for Modeling Hydrodynamic Transport in Porous and Fractured Media from Pore to Reservoir Scale , 2016, Transport in Porous Media.

[68]  Allen M. Shapiro,et al.  Interpreting tracer breakthrough tailing from different forced‐gradient tracer experiment configurations in fractured bedrock , 2002 .

[69]  J. Hyman,et al.  Advective Transport in Discrete Fracture Networks With Connected and Disconnected Textures Representing Internal Aperture Variability , 2019, Water Resources Research.

[70]  Satish Karra,et al.  Particle tracking approach for transport in three-dimensional discrete fracture networks , 2015, Computational Geosciences.

[71]  G. Porta,et al.  A double-continuum transport model for segregated porous media: Derivation and sensitivity analysis-driven calibration , 2019, Advances in Water Resources.