A probabilistic clustering approach for identifying primary subnetworks of discrete fracture networks with quantified uncertainty. (English) Zbl 1446.60078


60K30 Applications of queueing theory (congestion, allocation, storage, traffic, etc.)
05C90 Applications of graph theory
62H30 Classification and discrimination; cluster analysis (statistical aspects)
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[1] H. Abelin, L. Birgersson, L. Moreno, H. Widén, T. \AAgren, and I. Neretnieks, A large-scale flow and tracer experiment in granite 2: Results and interpretation, Water Resour. Res., 27 (1991), pp. 3119-3135.
[2] H. Abelin, I. Neretnieks, S. Tunbrant, and L. Moreno, Final Report of the Migration in a Single Fracture: Experimental Results and Evaluation, Nat. Genossenschaft für die Lagerung radioaktiver Abfälle, 1985.
[3] G. Aldrich, J. D. Hyman, S. Karra, C. W. Gable, N. Makedonska, H. Viswanathan, J. Woodring, and B. Hamann, Analysis and visualization of discrete fracture networks using a flow topology graph, IEEE Trans. Vis. Comput. Graphics, 23 (2017), pp. 1896-1909.
[4] J. Andersson and B. Dverstorp, Conditional simulations of fluid flow in three-dimensional networks of discrete fractures, Water Resour. Res., 23 (1987), pp. 1876-1886.
[5] C. A. Andresen, A. Hansen, R. Le Goc, P. Davy, and S. M. Hope, Topology of fracture networks, Front. Phys., 1 (2013), 7.
[6] B. Berkowitz and H. Scher, Anomalous transport in random fracture networks, Phys. Rev. Lett., 79 (1997), pp. 4038-4041.
[7] S. Berrone, S. Pieraccini, S. Scialò, and F. Vicini, A parallel solver for large scale DFN flow simulations, SIAM J. Sci. Comput., 37 (2015), pp. C285-C306, https://doi.org/10.1137/140984014. · Zbl 1320.65167
[8] I. Bogdanov, V. Mourzenko, J.-F. Thovert, and P. Adler, Effective permeability of fractured porous media with power-law distribution of fracture sizes, Phys. Rev. E, 76 (2007), 036309.
[9] F. Bonneau, G. Caumon, and P. Renard, Impact of a stochastic sequential initiation of fractures on the spatial correlations and connectivity of discrete fracture networks, J. Geophys. Res. Solid Earth, 121 (2016), pp. 5641-5658.
[10] E. Bonnet, O. Bour, N. E. Odling, P. Davy, I. Main, P. Cowie, and B. Berkowitz, Scaling of fracture systems in geological media, Rev. Geophys., 39 (2001), pp. 347-383.
[11] O. Bour and P. Davy, Connectivity of random fault networks following a power law fault length distribution, Water Resour. Res., 33 (1997), pp. 1567-1583.
[12] M.-C. Cacas, E. Ledoux, G. d. Marsily, B. Tillie, A. Barbreau, E. Durand, B. Feuga, and P. Peaudecerf, Modeling fracture flow with a stochastic discrete fracture network: Calibration and validation 1: The flow model, Water Resour. Res., 26 (1990), pp. 479-489.
[13] P. Davy, R. Le Goc, and C. Darcel, A model of fracture nucleation, growth and arrest, and consequences for fracture density and scaling, J. Geophys. Res. Solid Earth, 118 (2013), pp. 1393-1407.
[14] J.-R. de Dreuzy, C. Darcel, P. Davy, and O. Bour, Influence of spatial correlation of fracture centers on the permeability of two-dimensional fracture networks following a power law length distribution, Water Resour. Res., 40 (2004), W01502.
[15] J.-R. de Dreuzy, P. Davy, and O. Bour, Hydraulic properties of two-dimensional random fracture networks following a power law length distribution \(2\): Permeability of networks based on lognormal distribution of apertures, Water Resour. Res., 37 (2001), pp. 2079-2095.
[16] J.-R. de Dreuzy, P. Davy, and O. Bour, Hydraulic properties of two-dimensional random fracture networks following power law distributions of length and aperture, Water Resour. Res., 38 (2002), pp. 12-1-12-9.
[17] J.-R. de Dreuzy, Y. Méheust, and G. Pichot, Influence of fracture scale heterogeneity on the flow properties of three-dimensional discrete fracture networks (DFN), J. Geophys. Res. Solid Earth, 117 (2012), B11207.
[18] W. Dershowitz and C. Fidelibus, Derivation of equivalent pipe network analogues for three-dimensional discrete fracture networks by the boundary element method, Water Resour. Res., 35 (1999), pp. 2685-2691.
[19] J. Erhel, J.-R. de Dreuzy, and B. Poirriez, Flow simulation in three-dimensional discrete fracture networks, SIAM J. Sci. Comput., 31 (2009), pp. 2688-2705, https://doi.org/10.1137/080729244. · Zbl 1387.65124
[20] S. Follin, L. Hartley, I. Rhén, P. Jackson, S. Joyce, D. Roberts, and B. Swift, 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, Hydrogeol. J., 22 (2014), pp. 313-331.
[21] A. Frampton and V. Cvetkovic, Inference of field-scale fracture transmissivities in crystalline rock using flow log measurements, Water Resour. Res., 46 (2010), W11502.
[22] A. Gelman and D. B. Rubin, Inference from iterative simulation using multiple sequences, Statist. Sci., 7 (1992), pp. 457-472. · Zbl 1386.65060
[23] M. T. Goodrich and R. Tamassia, Data Structures and Algorithms in Java, 2nd ed., John Wiley & Sons, 2008. · Zbl 1059.68022
[24] P. Grindrod and M. Impey, Channeling and Fickian dispersion in fractal simulated porous media, Water Resour. Res., 29 (1993), pp. 4077-4089.
[25] N. Guihéneuf, A. Boisson, O. Bour, B. Dewandel, J. Perrin, A. Dausse, M. Viossanges, S. Chandra, S. Ahmed, and J. Maréchal, Groundwater flows in weathered crystalline rocks: Impact of piezometric variations and depth-dependent fracture connectivity, J. Hydrol., 511 (2014), pp. 320-334.
[26] T. Hadgu, S. Karra, E. Kalinina, N. Makedonska, J. D. Hyman, K. Klise, H. S. Viswanathan, and Y. Wang, A comparative study of discrete fracture network and equivalent continuum models for simulating flow and transport in the far field of a hypothetical nuclear waste repository in crystalline host rock, J. Hydrology, 553 (2017), pp. 59-70.
[27] S. M. Hope, P. Davy, J. Maillot, R. Le Goc, and A. Hansen, Topological impact of constrained fracture growth, Front. Phys., 3 (2015), 75, https://doi.org/10.3389/fphy.2015.00075.
[28] O. Huseby, J. Thovert, and P. Adler, Geometry and topology of fracture systems, J. Phys A, 30 (1997), pp. 1415-1444. · Zbl 1001.74593
[29] O. Huseby, J.-F. Thovert, and P. Adler, Dispersion in three-dimensional fracture networks, Phys. Fluids, 13 (2001), pp. 594-615. · Zbl 1184.76239
[30] J. Hyman, M. Dentz, A. Hagberg, and P. K. Kang, Linking structural and transport properties in three-dimensional fracture networks, J. Geophys. Res. Solid Earth, 124 (2019), pp. 1185-1204.
[31] J. D. Hyman, G. Aldrich, H. Viswanathan, N. Makedonska, and S. Karra, 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, Water Resour. Res., 52 (2016), pp. 6472-6489, https://doi.org/10.1002/2016WR018806.
[32] J. D. Hyman, M. Dentz, A. Hagberg, and P. Kang, Emergence of stable laws for first passage times in three-dimensional random fracture networks, Phys. Rev. Lett., 123 (2019), 248501.
[33] J. D. Hyman, C. W. Gable, S. L. Painter, and N. Makedonska, Conforming Delaunay triangulation of stochastically generated three dimensional discrete fracture networks: A feature rejection algorithm for meshing strategy, SIAM J. Sci. Comput., 36 (2014), pp. A1871-A1894, https://doi.org/10.1137/130942541. · Zbl 1305.74082
[34] J. D. Hyman, A. Hagberg, D. Osthus, S. Srinivasan, H. Viswanathan, and G. Srinivasan, Identifying backbones in three-dimensional discrete fracture networks: A bipartite graph-based approach, Multiscale Model. Simul., 16 (2018), pp. 1948-1968, https://doi.org/10.1137/18M1180207. · Zbl 1457.76165
[35] J. D. Hyman, A. Hagberg, G. Srinivasan, J. Mohd-Yusof, and H. Viswanathan, Predictions of first passage times in sparse discrete fracture networks using graph-based reductions, Phys. Rev. E, 96 (2017), 013304, https://doi.org/10.1103/PhysRevE.96.013304.
[36] J. D. Hyman and J. Jiménez-Martínez, Dispersion and mixing in three-dimensional discrete fracture networks: Nonlinear interplay between structural and hydraulic heterogeneity, Water Resour. Res., 54 (2018), pp. 3243-3258.
[37] J. D. Hyman, J. Jiménez-Martínez, C. W. Gable, P. Stauffer, and R. Pawar, Characterizing the impact of fractured caprock heterogeneity on supercritical \(CO_2\) injection, Transport Porous Media, 131 (2020), pp. 935-955.
[38] J. D. Hyman, J. Jiménez-Martínez, H. Viswanathan, J. Carey, M. Porter, E. Rougier, S. Karra, Q. Kang, L. Frash, L. Chen, D. Lei, Z. O’Malley, and N. Makedonska, Understanding hydraulic fracturing: A multi-scale problem, Phil. Trans. R. Soc. A, 374 (2016), 20150426.
[39] J. D. Hyman, S. Karra, N. Makedonska, C. W. Gable, S. L. Painter, and H. S. Viswanathan, DFNWorks: A discrete fracture network framework for modeling subsurface flow and transport, Comput. Geosci., 84 (2015), pp. 10-19.
[40] J. D. Hyman, S. L. Painter, H. Viswanathan, N. Makedonska, and S. Karra, Influence of injection mode on transport properties in kilometer-scale three-dimensional discrete fracture networks, Water Resour. Res., 51 (2015), pp. 7289-7308.
[41] J. D. Hyman, H. Rajaram, S. Srinivasan, N. Makedonska, S. Karra, H. Viswanathan, and G. Srinivasan, Matrix diffusion in fractured media: New insights into power-law scaling of breakthrough curves, Geophys. Res. Lett., 46 (2019), pp. 13785-13795.
[42] C. Jenkins, A. Chadwick, and S. D. Hovorka, The state of the art in monitoring and verification-ten years on, Int. J. Greenh. Gas. Con., 40 (2015), pp. 312-349.
[43] S. Joyce, L. Hartley, D. Applegate, J. Hoek, and P. Jackson, 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, Hydrogeol. J., 22 (2014), pp. 1233-1249.
[44] S. Karra, D. O’Malley, J. Hyman, H. Viswanathan, and G. Srinivasan, Modeling flow and transport in fracture networks using graphs, Phys. Rev. E, 97 (2018), 033304.
[45] K. Klint, P. Gravesen, A. Rosenbom, C. Laroche, L. Trenty, P. Lethiez, F. Sanchez, L. Molinelli, and C. Tsakiroglou, Multi-scale characterization of fractured rocks used as a means for the realistic simulation of pollutant migration pathways in contaminated sites: A case study, Water Air Soil Poll., 4 (2004), pp. 201-214.
[46] B. H. Kueper and D. B. McWhorter, The behavior of dense, nonaqueous phase liquids in fractured clay and rock, Ground Water, 29 (1991), pp. 716-728.
[47] LaGriT, Los Alamos Grid Toolbox (LaGriT), Los Alamos National Laboratory, http://lagrit.lanl.gov, 2016.
[48] P. Lang, A. Paluszny, and R. Zimmerman, Permeability tensor of three-dimensional fractured porous rock and a comparison to trace map predictions, J. Geophys. Res. Solid Earth, 119 (2014), pp. 6288-6307.
[49] P. Lichtner, G. Hammond, C. Lu, S. Karra, G. Bisht, B. Andre, R. Mills, and J. Kumar, PFLOTRAN User Manual: A Massively Parallel Reactive Flow and Transport Model for Describing Surface and Subsurface Processes, Tech. report LA-UR-15-20403, Los Alamos National Laboratory, 2015.
[50] J. Long, J. Remer, C. Wilson, and P. Witherspoon, Porous media equivalents for networks of discontinuous fractures, Water Resour. Res, 18 (1982), pp. 645-658.
[51] J. Maillot, P. Davy, R. Le Goc, C. Darcel, and J.-R. De Dreuzy, Connectivity, permeability, and channeling in randomly distributed and kinematically defined discrete fracture network models, Water Resour. Res., 52 (2016), pp. 8526-8545.
[52] N. Makedonska, J. D. Hyman, S. Karra, S. L. Painter, C. W. Gable, and H. S. Viswanathan, Evaluating the effect of internal aperture variability on transport in kilometer scale discrete fracture networks, Adv. Water Resour., 94 (2016), pp. 486-497.
[53] N. Makedonska, S. L. Painter, Q. M. Bui, C. W. Gable, and S. Karra, Particle tracking approach for transport in three-dimensional discrete fracture networks, Comput. Geosci., 19 (2015), pp. 1123-1137. · Zbl 1391.76735
[54] R. S. Middleton, R. Gupta, J. D. Hyman, and H. S. Viswanathan, The shale gas revolution: Barriers, sustainability, and emerging opportunities, Appl. Engrg., 199 (2017), pp. 88-95.
[55] National Research Council, Rock Fractures and Fluid Flow: Contemporary Understanding and Applications, National Academy Press, 1996.
[56] S. Neuman, Trends, prospects and challenges in quantifying flow and transport through fractured rocks, Hydrogeol. J., 13 (2005), pp. 124-147.
[57] A. W. Nordqvist, Y. Tsang, C. Tsang, B. Dverstorp, and J. Andersson, A variable aperture fracture network model for flow and transport in fractured rocks, Water Resour. Res., 28 (1992), pp. 1703-1713.
[58] S. L. Painter, C. W. Gable, and S. Kelkar, Pathline tracing on fully unstructured control-volume grids, Comput. Geosci., 16 (2012), pp. 1125-1134.
[59] M. Plummer, RJAGS: Bayesian Graphical Models Using MCMC, R Package Version 4-6, 2016, https://CRAN.R-project.org/package=rjags.
[60] M. Plummer, JAGS Version 4.3.0 User Manual, 2017, http://people.stat.sc.edu/hansont/stat740/jags_user_manual.pdf (accessed: 11-11-2017).
[61] R Core Team, R: A Language and Environment for Statistical Computing, R Foundation for Statistical Computing, Vienna, 2018, https://www.R-project.org/.
[62] A. Rasmuson and I. Neretnieks, Radionuclide transport in fast channels in crystalline rock, Water Resour. Res., 22 (1986), pp. 1247-1256.
[63] J.-O. Selroos, D. D. Walker, A. Ström, B. Gylling, and S. Follin, Comparison of alternative modelling approaches for groundwater flow in fractured rock, J. Hydrol., 257 (2002), pp. 174-188.
[64] G. Srinivasan, J. D. Hyman, D. Osthus, B. Moore, D. O’Malley, S. Karra, E. Rougier, A. Hagberg, A. Hunter, and H. S. Viswanathan, Quantifying topological uncertainty in fractured systems using graph theory and machine learning, Scientific Reports, 8 (2018), 11665.
[65] S. Srinivasan, J. Hyman, S. Karra, D. O’Malley, H. Viswanathan, and G. Srinivasan, Robust system size reduction of discrete fracture networks: A multi-fidelity method that preserves transport characteristics, Comput. Geosci., 22 (2018), pp. 1515-1526. · Zbl 1404.86009
[66] S. Srinivasan, S. Karra, J. D. Hyman, H. S. Viswanathan, and G. Srinivasan, Model reduction for fractured porous media: A machine-learning approach for identifying main flow pathways, Comput. Geosci., 23 (2019), pp. 617-629. · Zbl 1419.76508
[67] C.-F. Tsang and I. Neretnieks, Flow channeling in heterogeneous fractured rocks, Rev. Geophys., 36 (1998), pp. 275-298.
[68] M. Valera, Z. Guo, P. Kelly, S. Matz, V. A. Cantu, A. G. Percus, J. D. Hyman, G. Srinivasan, and H. S. Viswanathan, Machine learning for graph-based representations of three-dimensional discrete fracture networks, Comput. Geosci., 22 (2018), pp. 695-710. · Zbl 1405.76059
[69] J. VanderKwaak and E. Sudicky, Dissolution of non-aqueous-phase liquids and aqueous-phase contaminant transport in discretely-fractured porous media, J. Contam. Hydrol., 23 (1996), pp. 45-68.
[70] H. S. Viswanathan, J. D. Hyman, S. Karra, D. O’Malley, S. Srinivasan, A. Hagberg, and G. Srinivasan, Advancing graph-based algorithms for predicting flow and transport in fractured rock, Water Resour. Res., 54 (2018), pp. 6085-6099.
[71] T. Walmann, A. Malthe-Sørenssen, J. Feder, T. Jøssang, P. Meakin, and H. H. Hardy, Scaling relations for the lengths and widths of fractures, Phys. Rev. Lett., 77 (1996), pp. 5393-5396.
[72] T. P. Wellman, A. M. Shapiro, and M. C. Hill, Effects of simplifying fracture network representation on inert chemical migration in fracture-controlled aquifers, Water Resour. Res., 45 (2009), W01416.
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