Advancing graph-based algorithms for predicting flow and transport in fractured rock

Viswanathan, Hari S.; Hyman, Jeffrey De'Haven; Karra, Satish; O'Malley, Daniel; Srinivasan, Shriram; Hagberg, Aric Arild; Srinivasan, Gowri

doi:10.1029/2017WR022368

Title: Advancing graph-based algorithms for predicting flow and transport in fractured rock

Journal Article · Tue Jul 31 00:00:00 EDT 2018 · Water Resources Research

DOI:https://doi.org/10.1029/2017WR022368· OSTI ID:1463552

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

Discrete fracture network (DFN) models are a powerful alternative to continuum models for subsurface flow and transport simulations because they explicitly include fracture geometry and network topology, thereby allowing for better characterization of the latter's influence on flow and transport through fractured media. Recent advances in high performance computing have opened the door for flow and transport simulations in large explicit three-dimensional DFN, but this increase in model fidelity and system size comes at a huge computational cost because of the large number of mesh elements required to represent thousands of fractures (with sizes that can range several orders of magnitude, from mm to km). In most subsurface applications, fracture characteristics are only known statistically and numerous realizations are needed to bound uncertainty in flow and transport in the system, thereby exacerbating the computational burden. blackGraphs provide a simple and elegant way to characterize, query, and interrogate fracture network connectivity. We propose a DFN model reduction framework where various graph-representations are used in conjunction with high-fidelity DFN simulations to increase computational efficiency while retaining accuracy of key quantities of interest. The appropriate choice of a graph-representation, namely, which attributes of the DFN are to be represented as nodes and which ones as edges connecting those nodes, depends on the relevant scientific questions. We demonstrate that the proposed DFN model reduction framework provides an efficient means for DFN modeling through both system reduction of the DFN using graph-based properties and combining DFN and graph-based flow and transport simulations.

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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:: 1463552

Report Number(s):: LA-UR-17-30945

Journal Information:: Water Resources Research, Vol. 54, Issue 9; ISSN 0043-1397

Publisher:: American Geophysical Union (AGU)Copyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 34 works

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References (54)

Groundwater remediation using the information gap decision theory: GROUNDWATER REMEDIATION USING THE INFO-GAP DECISION THEORY O'Malley, D.; Vesselinov, V. V. Water Resources Research, Vol. 50, Issue 1 https://doi.org/10.1002/2013WR014718	journal	January 2014
A Parallel Solver for Large Scale DFN Flow Simulations Berrone, Stefano; Pieraccini, Sandra; Scialò, Stefano SIAM Journal on Scientific Computing, Vol. 37, Issue 3 https://doi.org/10.1137/140984014	journal	January 2015
Topology of fracture networks Andresen, Christian André; Hansen, Alex; Le Goc, Romain Frontiers in Physics, Vol. 1 https://doi.org/10.3389/fphy.2013.00007	journal	January 2013
Topological impact of constrained fracture growth Hope, Sigmund Mongstad; Davy, Philippe; Maillot, Julien Frontiers in Physics, Vol. 3 https://doi.org/10.3389/fphy.2015.00075	journal	September 2015
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
A PDE-Constrained Optimization Formulation for Discrete Fracture Network Flows Berrone, Stefano; Pieraccini, Sandra; Scialò, Stefano SIAM Journal on Scientific Computing, Vol. 35, Issue 2 https://doi.org/10.1137/120865884	journal	January 2013
A descriptive study of fracture networks in rocks using complex network metrics Santiago, Elizabeth; Velasco-Hernández, Jorge X.; Romero-Salcedo, Manuel Computers & Geosciences, Vol. 88 https://doi.org/10.1016/j.cageo.2015.12.021	journal	March 2016
A variable aperture fracture network model for flow and transport in fractured rocks Nordqvist, A. Wille; Tsang, Y. W.; Tsang, C. F. Water Resources Research, Vol. 28, Issue 6 https://doi.org/10.1029/92WR00216	journal	June 1992
Transport behavior in three-dimensional fracture intersections: TRANSPORT IN THREE-DIMENSIONAL FRACTURE INTERSECTIONS Park, Young-Jin; Lee, Kang-Kun; Kosakowski, Georg Water Resources Research, Vol. 39, Issue 8 https://doi.org/10.1029/2002WR001801	journal	August 2003
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
Derivation of equivalent pipe network analogues for three-dimensional discrete fracture networks by the boundary element method Dershowitz, W. S.; Fidelibus, C. Water Resources Research, Vol. 35, Issue 9 https://doi.org/10.1029/1999WR900118	journal	September 1999
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
Connectivity, permeability, and channeling in randomly distributed and kinematically defined discrete fracture network models: PERMEABILITY OF DISCRETE FRACTURE NETWORK Maillot, J.; Davy, P.; Le Goc, R. Water Resources Research, Vol. 52, Issue 11 https://doi.org/10.1002/2016WR018973	journal	November 2016
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 methodology for the characterization of flow conductivity through the identification of communities in samples of fractured rocks Santiago, Elizabeth; Velasco-Hernández, Jorge X.; Romero-Salcedo, Manuel Expert Systems with Applications, Vol. 41, Issue 3 https://doi.org/10.1016/j.eswa.2013.08.011	journal	February 2014
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
Large-scale inverse model analyses employing fast randomized data reduction: INVERSE MODELING WITH DATA REDUCTION Lin, Youzuo; Le, Ellen B.; O'Malley, Daniel Water Resources Research, Vol. 53, Issue 8 https://doi.org/10.1002/2016WR020299	journal	August 2017
Efficient Monte Carlo With Graph‐Based Subsurface Flow and Transport Models O'Malley, D.; Karra, S.; Hyman, J. D. Water Resources Research, Vol. 54, Issue 5 https://doi.org/10.1029/2017WR022073	journal	May 2018
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
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
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
Uncertainty in Prediction of Radionuclide Gas Migration from Underground Nuclear Explosions Jordan, Amy B.; Stauffer, Philip H.; Zyvoloski, George A. Vadose Zone Journal, Vol. 13, Issue 10 https://doi.org/10.2136/vzj2014.06.0070	journal	January 2014
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
Hydraulic properties of two-dimensional random fracture networks following a power law length distribution: 2. Permeability of networks based on lognormal distribution of apertures de Dreuzy, Jean-Raynald; Davy, Philippe; Bour, Olivier Water Resources Research, Vol. 37, Issue 8 https://doi.org/10.1029/2001WR900010	journal	August 2001
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
Dispersion and Mixing in Three‐Dimensional Discrete Fracture Networks: Nonlinear Interplay Between Structural and Hydraulic Heterogeneity Hyman, J. D.; Jiménez‐Martínez, J. Water Resources Research, Vol. 54, Issue 5 https://doi.org/10.1029/2018WR022585	journal	May 2018
Optimal Model Management for Multifidelity Monte Carlo Estimation Peherstorfer, Benjamin; Willcox, Karen; Gunzburger, Max SIAM Journal on Scientific Computing, Vol. 38, Issue 5 https://doi.org/10.1137/15M1046472	journal	January 2016
Inclusion of Topological Measurements into Analytic Estimates of Effective Permeability in Fractured Media: FRACTURE PERMEABILITY FROM TOPOLOGY Saevik, P. N.; Nixon, C. W. Water Resources Research, Vol. 53, Issue 11 https://doi.org/10.1002/2017WR020943	journal	November 2017
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
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
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
PFLOTRAN User Manual: A Massively Parallel Reactive Flow and Transport Model for Describing Surface and Subsurface Processes Lichtner, Peter; Hammond, Glenn; Lu, Chuan https://doi.org/10.2172/1168703	report	January 2015
A quasi steady state method for solving transient Darcy flow in complex 3D fractured networks Nœtinger, B.; Jarrige, N. Journal of Computational Physics, Vol. 231, Issue 1 https://doi.org/10.1016/j.jcp.2011.08.015	journal	January 2012
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
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
A lattice-gas and lattice Boltzmann study of mixing at continuous fracture Junctions: Importance of boundary conditions Stockman, Harlan W.; Li, Chunhong; Wilson, John L. Geophysical Research Letters, Vol. 24, Issue 12 https://doi.org/10.1029/97GL51471	journal	June 1997
Predictions of first passage times in sparse discrete fracture networks using graph-based reductions Hyman, Jeffrey D.; Hagberg, Aric; Srinivasan, Gowri Physical Review E, Vol. 96, Issue 1 https://doi.org/10.1103/PhysRevE.96.013304	journal	July 2017
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: FRACTURE SIZE AND TRANSMISSIVITY CORRELATIONS Hyman, J. D.; Aldrich, G.; Viswanathan, H. Water Resources Research, Vol. 52, Issue 8 https://doi.org/10.1002/2016WR018806	journal	August 2016
Connectivity metrics based on the path of smallest resistance Tyukhova, Alina R.; Willmann, Matthias Advances in Water Resources, Vol. 88 https://doi.org/10.1016/j.advwatres.2015.11.014	journal	February 2016
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
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
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
Minimum Hydraulic Resistance and Least Resistance Path in Heterogeneous Porous Media: MINIMUM HYDRAULIC RESISTANCE Rizzo, Calogero B.; de Barros, Felipe P. J. Water Resources Research, Vol. 53, Issue 10 https://doi.org/10.1002/2017WR020418	journal	October 2017
Understanding hydraulic fracturing: a multi-scale problem Hyman, J. D.; Jiménez-Martínez, J.; Viswanathan, H. S. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 374, Issue 2078 https://doi.org/10.1098/rsta.2015.0426	journal	October 2016
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 Combined Probabilistic/Nonprobabilistic Decision Analysis for Contaminant Remediation O'Malley, D.; Vesselinov, V. V. SIAM/ASA Journal on Uncertainty Quantification, Vol. 2, Issue 1 https://doi.org/10.1137/140965132	journal	January 2014
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
Modeling flow and transport in fracture networks using graphs Karra, S.; O'Malley, D.; Hyman, J. D. Physical Review E, Vol. 97, Issue 3 https://doi.org/10.1103/PhysRevE.97.033304	journal	March 2018
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
Modeling flow and transport in fracture networks using graphs Karra, S.; O'Malley, D.; Hyman, J. D. arXiv https://doi.org/10.48550/arxiv.1708.08556	text	January 2017

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