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

Hyman, Jeffrey De'Haven; Aldrich, Garrett Allen; Viswanathan, Hari S.; Makedonska, Nataliia; Karra, Satish

doi:10.1002/2016WR018806

Title: 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

Journal Article · Mon Aug 01 00:00:00 EDT 2016 · Water Resources Research

DOI:https://doi.org/10.1002/2016WR018806· OSTI ID:1321775

Hyman, Jeffrey De'Haven ^[1]; Aldrich, Garrett Allen ^[2]; Viswanathan, Hari S. ^[1]; Makedonska, Nataliia ^[1]; Karra, Satish ^[1]

Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Univ. of California, Davis, CA (United States); Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

We characterize how different fracture size-transmissivity relationships influence flow and transport simulations through sparse three-dimensional discrete fracture networks. Although it is generally accepted that there is a positive correlation between a fracture's size and its transmissivity/aperture, the functional form of that relationship remains a matter of debate. Relationships that assume perfect correlation, semicorrelation, and noncorrelation between the two have been proposed. To study the impact that adopting one of these relationships has on transport properties, we generate multiple sparse fracture networks composed of circular fractures whose radii follow a truncated power law distribution. The distribution of transmissivities are selected so that the mean transmissivity of the fracture networks are the same and the distributions of aperture and transmissivity in models that include a stochastic term are also the same. We observe that adopting a correlation between a fracture size and its transmissivity leads to earlier breakthrough times and higher effective permeability when compared to networks where no correlation is used. While fracture network geometry plays the principal role in determining where transport occurs within the network, the relationship between size and transmissivity controls the flow speed. Lastly, these observations indicate DFN modelers should be aware that breakthrough times and effective permeabilities can be strongly influenced by such a relationship in addition to fracture and network statistics.

View Accepted Manuscript (DOE)

Cite

Export

Save

Research Organization:: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)

Sponsoring Organization:: USDOE Laboratory Directed Research and Development (LDRD) Program

Grant/Contract Number:: AC52-06NA25396

OSTI ID:: 1321775

Report Number(s):: LA-UR-16-20525

Journal Information:: Water Resources Research, Journal Name: Water Resources Research; ISSN 0043-1397

Publisher:: American Geophysical Union (AGU)Copyright Statement

Country of Publication:: United States

Language:: English

Citation Metrics:

Cited by: 87 works

Citation information provided by
Web of Science

References (59)

Incorporating spatial distribution into stochastic modelling of fractures: multifractals and Levy-stable statistics Belfield, William C. Journal of Structural Geology, Vol. 20, Issue 4 https://doi.org/10.1016/S0191-8141(97)00118-1	journal	April 1998
Cubic law with aperture-length correlation: implications for network scale fluid flow Klimczak, Christian; Schultz, Richard A.; Parashar, Rishi Hydrogeology Journal, Vol. 18, Issue 4 https://doi.org/10.1007/s10040-009-0572-6	journal	February 2010
Transport of reactive tracers in rock fractures Cvetkovic, V.; Selroos, J. O.; Cheng, H. Journal of Fluid Mechanics, Vol. 378 https://doi.org/10.1017/S0022112098003450	journal	January 1999
Evaluation of cubic law based models describing single-phase flow through a rough-walled fracture: EVALUATION OF CUBIC LAW BASED MODELS Konzuk, Julie S.; Kueper, Bernard H. Water Resources Research, Vol. 40, Issue 2 https://doi.org/10.1029/2003WR002356	journal	February 2004
Stochastic fractal-based models of heterogeneity in subsurface hydrology: Origins, applications, limitations, and future research questions Molz, Fred J. Reviews of Geophysics, Vol. 42, Issue 1 https://doi.org/10.1029/2003RG000126	journal	January 2004
Hydraulic conductivity of rock fractures Zimmerman, RobertW.; Bodvarsson, GudmundurS. Transport in Porous Media, Vol. 23, Issue 1 https://doi.org/10.1007/BF00145263	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 Hyman, J. D.; Painter, S. L.; Viswanathan, H. Water Resources Research, Vol. 51, Issue 9 https://doi.org/10.1002/2015WR017151	journal	September 2015
Influence of Fracture Connectivity and Characterization Level on the Uncertainty of the Equivalent Permeability in Statistically Conceptualized Fracture Networks Ji, Sung-Hoon; Park, Young-Jin; Lee, Kang-Kun Transport in Porous Media, Vol. 87, Issue 2 https://doi.org/10.1007/s11242-010-9690-9	journal	December 2010
Three-dimensional control-volume distributed multi-point flux approximation coupled with a lower-dimensional surface fracture model Ahmed, Raheel; Edwards, Michael G.; Lamine, Sadok Journal of Computational Physics, Vol. 303 https://doi.org/10.1016/j.jcp.2015.10.001	journal	December 2015
dfnWorks: A discrete fracture network framework for modeling subsurface flow and transport Hyman, Jeffrey D.; Karra, Satish; Makedonska, Nataliia Computers & Geosciences, Vol. 84 https://doi.org/10.1016/j.cageo.2015.08.001	journal	November 2015
A New Approach to Simulating Flow in Discrete Fracture Networks with an Optimized Mesh Mustapha, Hussein; Mustapha, Kassem SIAM Journal on Scientific Computing, Vol. 29, Issue 4 https://doi.org/10.1137/060653482	journal	January 2007
Trends, prospects and challenges in quantifying flow and transport through fractured rocks Neuman, Shlomo P. Hydrogeology Journal, Vol. 13, Issue 1 https://doi.org/10.1007/s10040-004-0397-2	journal	February 2005
A Connectivity Index for Discrete Fracture Networks Xu, C.; Dowd, P. A.; Mardia, K. V. Mathematical Geology, Vol. 38, Issue 5 https://doi.org/10.1007/s11004-006-9029-9	journal	November 2006
Conforming Delaunay Triangulation of Stochastically Generated Three Dimensional Discrete Fracture Networks: A Feature Rejection Algorithm for Meshing Strategy Hyman, Jeffrey D.; Gable, Carl W.; Painter, Scott L. SIAM Journal on Scientific Computing, Vol. 36, Issue 4 https://doi.org/10.1137/130942541	journal	January 2014
Power-law velocity distributions in fracture networks: Numerical evidence and implications for tracer transport: POWER-LAW VELOCITY DISTRIBUTIONS IN FRACTURE NETWORKS Painter, Scott; Cvetkovic, Vladimir; Selroos, Jan-Olof Geophysical Research Letters, Vol. 29, Issue 14 https://doi.org/10.1029/2002GL014960	journal	July 2002
Anomalous transport on regular fracture networks: Impact of conductivity heterogeneity and mixing at fracture intersections Kang, Peter K.; Dentz, Marco; Le Borgne, Tanguy Physical Review E, Vol. 92, Issue 2 https://doi.org/10.1103/PhysRevE.92.022148	journal	August 2015
Permeability of a random array of fractures of widely varying apertures Charlaix, Elisabeth; Guyon, Etienne; Roux, Stephane Transport in Porous Media, Vol. 2, Issue 1 https://doi.org/10.1007/BF00208535	journal	February 1987
Effects of simplifying fracture network representation on inert chemical migration in fracture-controlled aquifers: EFFECTS OF FRACTURE NETWORK SIMPLIFICATION Wellman, Tristan P.; Shapiro, Allen M.; Hill, Mary C. Water Resources Research, Vol. 45, Issue 1 https://doi.org/10.1029/2008WR007025	journal	January 2009
Application of the discrete fracture network concept with field data: Possibilities of model calibration and validation Dverstorp, Björn; Andersson, Johan Water Resources Research, Vol. 25, Issue 3 https://doi.org/10.1029/WR025i003p00540	journal	March 1989
Characterizing flow and transport in fractured geological media: A review Berkowitz, Brian Advances in Water Resources, Vol. 25, Issue 8-12 https://doi.org/10.1016/S0309-1708(02)00042-8	journal	August 2002
A methodology to constrain the parameters of a hydrogeological discrete fracture network model for sparsely fractured crystalline rock, exemplified by data from the proposed high-level nuclear waste repository site at Forsmark, Sweden Follin, Sven; Hartley, Lee; Rhén, Ingvar Hydrogeology Journal, Vol. 22, Issue 2 https://doi.org/10.1007/s10040-013-1080-2	journal	December 2013
Fracture networks and fluid transport in active fault zones Gudmundsson, Agust; Berg, Silje S.; Lyslo, Kellfrid B. Journal of Structural Geology, Vol. 23, Issue 2-3 https://doi.org/10.1016/S0191-8141(00)00100-0	journal	February 2001
Flow Simulation in Three-Dimensional Discrete Fracture Networks Erhel, Jocelyne; de Dreuzy, Jean-Raynald; Poirriez, Baptiste SIAM Journal on Scientific Computing, Vol. 31, Issue 4 https://doi.org/10.1137/080729244	journal	January 2009
Non-universal scaling of fracture length and opening displacement Hatton, C. G.; Main, I. G.; Meredith, P. G. Nature, Vol. 367, Issue 6459 https://doi.org/10.1038/367160a0	journal	January 1994
Solute transport and retention in three-dimensional fracture networks: TRANSPORT IN FRACTURE NETWORKS Cvetkovic, Vladimir; Frampton, Andrew Water Resources Research, Vol. 48, Issue 2 https://doi.org/10.1029/2011WR011086	journal	February 2012
A new stochastic particle-tracking approach for fractured sedimentary formations: FRACTURE-MATRIX PARTICLE TRACKING Willmann, M.; Lanyon, G. W.; Marschall, P. Water Resources Research, Vol. 49, Issue 1 https://doi.org/10.1029/2012WR012191	journal	January 2013
Stochastic simulation of radionuclide migration in discretely fractured rock near the Äspö Hard Rock Laboratory: RETENTION IN FRACTURE NETWORKS Cvetkovic, V.; Painter, S.; Outters, N. Water Resources Research, Vol. 40, Issue 2 https://doi.org/10.1029/2003WR002655	journal	February 2004
Inference of field-scale fracture transmissivities in crystalline rock using flow log measurements: TRANSMISSIVITY INFERENCE FROM FLOW LOGS Frampton, A.; Cvetkovic, V. Water Resources Research, Vol. 46, Issue 11 https://doi.org/10.1029/2009WR008367	journal	November 2010
Effective permeability of fractured porous media with power-law distribution of fracture sizes Bogdanov, I. I.; Mourzenko, V. V.; Thovert, J. -F. Physical Review E, Vol. 76, Issue 3 https://doi.org/10.1103/PhysRevE.76.036309	journal	September 2007
Relation between vein length and aperture Vermilye, Jan M.; Scholz, Christopher H. Journal of Structural Geology, Vol. 17, Issue 3 https://doi.org/10.1016/0191-8141(94)00058-8	journal	March 1995
Hydraulic properties of fractured rock masses with correlated fracture length and aperture Baghbanan, Alireza; Jing, Lanru International Journal of Rock Mechanics and Mining Sciences, Vol. 44, Issue 5 https://doi.org/10.1016/j.ijrmms.2006.11.001	journal	July 2007
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 Joyce, Steven; Hartley, Lee; Applegate, David Hydrogeology Journal, Vol. 22, Issue 6 https://doi.org/10.1007/s10040-014-1165-6	journal	July 2014
Hydraulic properties of two-dimensional random fracture networks following power law distributions of length and aperture: PERMEABILITY OF HETEROGENEOUS FRACTURE NETWORKS de Dreuzy, J. -R.; Davy, P.; Bour, O. Water Resources Research, Vol. 38, Issue 12 https://doi.org/10.1029/2001WR001009	journal	December 2002
Effect of mechanical interactions on the scaling of fracture length and aperture Renshaw, C. E.; Park, J. C. Nature, Vol. 386, Issue 6624 https://doi.org/10.1038/386482a0	journal	April 1997
The tempered one-sided stable density: a universal model for hydrological transport? Cvetkovic, Vladimir Environmental Research Letters, Vol. 6, Issue 3 https://doi.org/10.1088/1748-9326/6/3/034008	journal	July 2011
A mixed hybrid Mortar method for solving flow in discrete fracture networks Pichot, G.; Erhel, J.; de Dreuzy, J. R. Applicable Analysis, Vol. 89, Issue 10 https://doi.org/10.1080/00036811.2010.495333	journal	October 2010
Structure, flow, and generalized conductivity scaling in fracture networks Margolin, Gennady; Berkowitz, Brian; Scher, Harvey Water Resources Research, Vol. 34, Issue 9 https://doi.org/10.1029/98WR01648	journal	September 1998
Particle tracking approach for transport in three-dimensional discrete fracture networks: Particle tracking in 3-D DFNs Makedonska, Nataliia; Painter, Scott L.; Bui, Quan M. Computational Geosciences, Vol. 19, Issue 5 https://doi.org/10.1007/s10596-015-9525-4	journal	September 2015
Upscaling discrete fracture network simulations: An alternative to continuum transport models: UPSCALING FRACTURE NETWORK SIMULATIONS Painter, S.; Cvetkovic, V. Water Resources Research, Vol. 41, Issue 2 https://doi.org/10.1029/2004WR003682	journal	February 2005
Validity of Cubic Law for fluid flow in a deformable rock fracture Witherspoon, P. A.; Wang, J. S. Y.; Iwai, K. Water Resources Research, Vol. 16, Issue 6 https://doi.org/10.1029/WR016i006p01016	journal	December 1980
Evaluating the effect of internal aperture variability on transport in kilometer scale discrete fracture networks Makedonska, Nataliia; Hyman, Jeffrey D.; Karra, Satish Advances in Water Resources, Vol. 94 https://doi.org/10.1016/j.advwatres.2016.06.010	journal	August 2016
Dynamics of Fluids and Transport in Fractured Rock Faybishenko, Boris; Witherspoon, Paul A.; Gale, John Geophysical Monograph Series https://doi.org/10.1029/GM162	book	January 2005
Analysis and Visualization of Discrete Fracture Networks Using a Flow Topology Graph Aldrich, Garrett; Hyman, Jeffrey D.; Karra, Satish IEEE Transactions on Visualization and Computer Graphics, Vol. 23, Issue 8 https://doi.org/10.1109/TVCG.2016.2582174	journal	August 2017
Connectivity of random fault networks following a power law fault length distribution Bour, Olivier; Davy, Philippe Water Resources Research, Vol. 33, Issue 7 https://doi.org/10.1029/96WR00433	journal	July 1997
Effect of advective flow in fractures and matrix diffusion on natural gas production Karra, Satish; Makedonska, Nataliia; Viswanathan, Hari S. Water Resources Research, Vol. 51, Issue 10 https://doi.org/10.1002/2014WR016829	journal	October 2015
Significance of injection modes and heterogeneity on spatial and temporal dispersion of advecting particles in two-dimensional discrete fracture networks Frampton, A.; Cvetkovic, V. Advances in Water Resources, Vol. 32, Issue 5 https://doi.org/10.1016/j.advwatres.2008.07.010	journal	May 2009
Scaling Relations for the Lengths and Widths of Fractures Walmann, T.; Malthe-Sørenssen, A.; Feder, J. Physical Review Letters, Vol. 77, Issue 27 https://doi.org/10.1103/PhysRevLett.77.5393	journal	December 1996
A Generalized Mixed Hybrid Mortar Method for Solving Flow in Stochastic Discrete Fracture Networks Pichot, G.; Erhel, J.; de Dreuzy, J. -R. SIAM Journal on Scientific Computing, Vol. 34, Issue 1 https://doi.org/10.1137/100804383	journal	January 2012
Hydrodynamic control of tracer retention in heterogeneous rock fractures: HYDRODYNAMIC CONTROL OF RETENTION IN FRACTURES Cheng, H.; Cvetkovic, V.; Selroos, J. O. Water Resources Research, Vol. 39, Issue 5 https://doi.org/10.1029/2002WR001354	journal	May 2003
Control-volume distributed multi-point flux approximation coupled with a lower-dimensional fracture model Ahmed, R.; Edwards, M. G.; Lamine, S. Journal of Computational Physics, Vol. 284 https://doi.org/10.1016/j.jcp.2014.12.047	journal	March 2015
Effect of pressure and stress on water transport in intact and fractured gabbro and granite Trimmer, D.; Bonner, B.; Heard, H. C. Journal of Geophysical Research, Vol. 85, Issue B12 https://doi.org/10.1029/JB085iB12p07059	journal	January 1980
Scaling of fracture systems in geological media Bonnet, E.; Bour, O.; Odling, N. E. Reviews of Geophysics, Vol. 39, Issue 3 https://doi.org/10.1029/1999RG000074	journal	August 2001
Influence of spatial correlation of fracture centers on the permeability of two-dimensional fracture networks following a power law length distribution: FRACTURE CORRELATION AND PERMEABILITY de Dreuzy, Jean-Raynald; Darcel, Caroline; Davy, Philippe Water Resources Research, Vol. 40, Issue 1 https://doi.org/10.1029/2003WR002260	journal	January 2004
A new particle-tracking approach to simulating transport in heterogeneous fractured porous media: A NEW PARTICLE-TRACKING APPROACH Roubinet, Delphine; Liu, Hui-Hai; de Dreuzy, Jean-Raynald Water Resources Research, Vol. 46, Issue 11 https://doi.org/10.1029/2010WR009371	journal	November 2010
Pathline tracing on fully unstructured control-volume grids Painter, S. L.; Gable, C. W.; Kelkar, S. Computational Geosciences, Vol. 16, Issue 4 https://doi.org/10.1007/s10596-012-9307-1	journal	July 2012
Influence of fracture scale heterogeneity on the flow properties of three-dimensional discrete fracture networks (DFN): 3D FRACTURE NETWORK PERMEABILITY de Dreuzy, J. -R.; Méheust, Y.; Pichot, G. Journal of Geophysical Research: Solid Earth, Vol. 117, Issue B11 https://doi.org/10.1029/2012JB009461	journal	November 2012
Numerical and analytical modeling of advective travel times in realistic three-dimensional fracture networks: MODELING OF ADVECTIVE TRAVEL TIMES Frampton, A.; Cvetkovic, V. Water Resources Research, Vol. 47, Issue 2 https://doi.org/10.1029/2010WR009290	journal	February 2011
Stereological analysis of fractures in the Roselend tunnel and permeability determination: STEREOLOGY IN THE ROSELEND TUNNEL Patriarche, Delphine; Pili, Eric; Adler, Pierre Michel Water Resources Research, Vol. 43, Issue 9 https://doi.org/10.1029/2006WR005471	journal	September 2007
Simulation of the von mises fisher distribution Wood, Andrew T. A. Communications in Statistics - Simulation and Computation, Vol. 23, Issue 1 https://doi.org/10.1080/03610919408813161	journal	January 1994

Cited By (13)

Machine learning for graph-based representations of three-dimensional discrete fracture networks Valera, Manuel; Guo, Zhengyang; Kelly, Priscilla Computational Geosciences, Vol. 22, Issue 3 https://doi.org/10.1007/s10596-018-9720-1	journal	January 2018
Robust system size reduction of discrete fracture networks: a multi-fidelity method that preserves transport characteristics Srinivasan, Shriram; Hyman, Jeffrey; Karra, Satish Computational Geosciences, Vol. 22, Issue 6 https://doi.org/10.1007/s10596-018-9770-4	journal	September 2018
Model reduction for fractured porous media: a machine learning approach for identifying main flow pathways Srinivasan, Shriram; Karra, Satish; Hyman, Jeffrey Computational Geosciences, Vol. 23, Issue 3 https://doi.org/10.1007/s10596-019-9811-7	journal	March 2019
Characterizing the Impact of Fractured Caprock Heterogeneity on Supercritical CO$$_2$$ Injection Hyman, Jeffrey D.; Jiménez-Martínez, Joaquin; Gable, Carl W. Transport in Porous Media, Vol. 131, Issue 3 https://doi.org/10.1007/s11242-019-01372-1	journal	November 2019
Prediction of water inflow into underground excavations in fractured rocks using a 3D discrete fracture network (DFN) model Karimzade, E.; Sharifzadeh, M.; Zarei, H. R. Arabian Journal of Geosciences, Vol. 10, Issue 9 https://doi.org/10.1007/s12517-017-2987-z	journal	May 2017
An efficient karst fracture seepage path construction algorithm based on a generalized disk model Rui, Xiaoping; Yu, Tian Arabian Journal of Geosciences, Vol. 12, Issue 8 https://doi.org/10.1007/s12517-019-4412-2	journal	April 2019
Tectonic Controls on Taupo Volcanic Zone Geothermal Expression: Insights From Te Mihi, Wairakei Geothermal Field McNamara, D. D.; Milicich, S. D.; Massiot, C. Tectonics, Vol. 38, Issue 8 https://doi.org/10.1029/2018tc005296	journal	August 2019
Advective Transport in Discrete Fracture Networks With Connected and Disconnected Textures Representing Internal Aperture Variability Frampton, A.; Hyman, J. D.; Zou, L. Water Resources Research, Vol. 55, Issue 7 https://doi.org/10.1029/2018wr024322	journal	July 2019
U‐Th Dating of Syntectonic Calcite Veins Reveals the Dynamic Nature of Fracture Cementation and Healing in Faults Williams, Randolph T.; Mozley, Peter S.; Sharp, Warren D. Geophysical Research Letters, Vol. 46, Issue 22 https://doi.org/10.1029/2019gl085403	journal	November 2019
Quantifying Topological Uncertainty in Fractured Systems using Graph Theory and Machine Learning Srinivasan, Gowri; Hyman, Jeffrey D.; Osthus, David A. Scientific Reports, Vol. 8, Issue 1 https://doi.org/10.1038/s41598-018-30117-1	journal	August 2018
Particle-Based Workflow for Modeling Uncertainty of Reactive Transport in 3D Discrete Fracture Networks Vu, Phuong Thanh; Ni, Chuen-Fa; Li, Wei-Ci Water, Vol. 11, Issue 12 https://doi.org/10.3390/w11122502	journal	November 2019
U-Th Dating of Syntectonic Calcite Veins Reveals the Dynamic Nature of Fracture Cementation and Healing in Faults Williams, Randolph; Mozley, Peter; Sharp, Warren https://doi.org/10.5194/egusphere-egu2020-12447	posted_content	May 2020
Machine learning for graph-based representations of three-dimensional discrete fracture networks Valera, Manuel; Guo, Zhengyang; Kelly, Priscilla arXiv https://doi.org/10.48550/arxiv.1705.09866	text	January 2017

Similar Records

Robust system size reduction of discrete fracture networks: a multi-fidelity method that preserves transport characteristics

Journal Article · Mon Sep 17 00:00:00 EDT 2018 · Computational Geosciences · OSTI ID:1321775

Srinivasan, Shriram; Hyman, Jeffrey De'Haven; Karra, Satish; +3 more

Predictions of first passage times in sparse discrete fracture networks using graph-based reductions

Journal Article · Mon Jul 10 00:00:00 EDT 2017 · Physical Review E · OSTI ID:1321775

Hyman, Jeffrey De'Haven; Hagberg, Aric Arild; Mohd-Yusof, Jamaludin; +2 more

Development of Upscaling Techniques and Construction of Calibrated Models for Fractured Rocks Using Discrete Fracture Network Approaches

Technical Report · Thu Nov 14 00:00:00 EST 2019 · OSTI ID:1321775

Parashar, Rishi; Pham, Hai V.; Sund, Nicole L.

Related Subjects

58 GEOSCIENCES
Earth Sciences

Title: 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

Citation Formats

References (59)

Cited By (13)

Similar Records

Related Subjects