×

Physics-informed machine learning for backbone identification in discrete fracture networks. (English) Zbl 1439.86009

Summary: The phenomenon of flow-channeling, or the existence of preferential pathways for flow in fracture networks, is well known. Identification of the channels (“backbone”) allows for system reduction and computational efficiency in simulation of flow and transport through fracture networks. However, the purpose of machine learning techniques for backbone identification in fractured media is two-pronged system reduction for computational efficiency in simulation of flow and transport as well as physical insight into the phenomenon of flow channeling. The most critical aspect of this problem is the need to have a truly “physics-informed” technique that respects the constraint of connectivity. We present a method that views a network as a union of connected paths with each path comprising a sequence of fractures. Thus, the fundamental unit of selection becomes a sequence of fractures, classified based on attributes that characterize the sequence. In summary, this method represents a parametrization of the sample space that ensures every selected sample sub-network (which is the union of all selected sequences of fractures) always respects the constraint of connectivity, demonstrating that it is a truly physics-informed method. The algorithm has a user-defined parameter which allows control of the backbone size when using the random forest or logistic regression classifier. Even when the backbones are less than 30% in size (leading to computational savings), the backbones still capture the behavior of the breakthrough curve of the full network. Moreover, there is no need to check for path connectedness in the backbones unlike previous methods since the backbones are guaranteed to be connected.

MSC:

86-08 Computational methods for problems pertaining to geophysics
76S05 Flows in porous media; filtration; seepage
74R10 Brittle fracture
68T05 Learning and adaptive systems in artificial intelligence
62H30 Classification and discrimination; cluster analysis (statistical aspects)
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Bonnet, E.; Bour, O.; Odling, NE; Davy, P.; Main, I.; Cowie, P.; Berkowitz, B., Scaling of fracture systems in geological media, Rev. Geophys., 39, 3, 347 (2001)
[2] Hyman, J.; Jiménez-Martínez, J.; Viswanathan, H.; Carey, J.; Porter, M.; Rougier, E.; Karra, S.; Kang, Q.; Frash, L.; Chen, L.; Lei, Z.; O’Malley, D.; Makedonska, N., Understanding hydraulic fracturing: a multi-scale problem, Philosophical Transactions of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, 374, 2078, 20150426 (2016)
[3] Karra, S.; Makedonska, N.; Viswanathan, HS; Painter, SL; Hyman, JD, Effect of advective flow in fractures and matrix diffusion on natural gas production,, Water Resour. Res., 51, 10, 8646 (2015)
[4] Middleton, R.; Carey, J.; Currier, R.; Hyman, J.; Kang, Q.; Karra, S.; Jiménez-Martínez, J.; Porter, M.; Viswanathan, H., Shale gas and non-aqueous fracturing fluids: opportunities and challenges for supercritical CO2, Appl. Energy, 147, 500 (2015)
[5] National Research Council: Rock fractures and fluid flow: contemporary understanding and applications. National Academy Press (1996)
[6] Neuman, S., Trends, prospects and challenges in quantifying flow and transport through fractured rocks, Hydrogeol. J., 13, 1, 124 (2005)
[7] VanderKwaak, J.; Sudicky, E., Dissolution of non-aqueous-phase liquids and aqueous-phase contaminant transport in discretely-fractured porous media, J. Contam. Hydrol., 23, 1-2, 45 (1996)
[8] Jenkins, C.; Chadwick, A.; Hovorka, SD, The state of the art in monitoring and verification—ten years on, Int. J. Greenh. Gas Control, 40, 312 (2015)
[9] Kueper, BH; McWhorter, DB, The behavior of dense, nonaqueous phase liquids in fractured clay and rock, Ground Water, 29, 5, 716 (1991)
[10] Ng, LWT; Willcox, KE, Multifidelity approaches for optimization under uncertainty, Int. J. Numer. Methods Eng., 100, 746 (2014) · Zbl 1352.74230
[11] Giles, MB, Multilevel Monte Carlo path simulation, Oper. Res., 56, 607 (2008) · Zbl 1167.65316
[12] Berrone, S.; Canuto, C.; Pieraccini, S.; Scialò, S., Uncertainty quantification in discrete fracture network models: Stochastic geometry, Water Resour. Res., 54, 1338 (2018)
[13] O’Malley, D.; Karra, S.; Hyman, JD; Viswanathan, HS; Srinivasan, G., Efficient Monte Carlo with graph-based subsurface flow and transport models, Water Resour. Res., 54, 3758 (2018)
[14] Jackson, CP; Hoch, AR; Todman, S., Self-consistency of a heterogeneous continuum porous medium representation of a fractured medium, Water Resour. Res., 36, 189 (2000)
[15] Painter, S., Cvetkovic, V.: Upscaling discrete fracture network simulations: an alternative to continuum transport models. Water Resources Research 41(2) (2005)
[16] Karimi-Fard, M., Gong, B., Durlofsky, L.J.: Generation of coarse-scale continuum flow models from detailed fracture characterizations. Water Resources Research 42. 10.1029/2006wr005015(2006)
[17] Botros, F.E., Hassan, A.E., Reeves, D.M., Pohll, G.: On mapping fracture networks onto continuum. Water Resources Research 44. 10.1029/2007wr006092 (2008)
[18] Tsang, CF; Neretnieks, I., Flow channeling in heterogeneous fractured rocks, Rev. Geophys., 36, 2, 275 (1998)
[19] Abelin, H.; Birgersson, L.; Moreno, L.; Widén, H.; Ågren, T.; Neretnieks, I., A large-scale flow and tracer experiment in granite: 2. Results and interpretation, Water Resour. Res., 27, 12, 3119 (1991)
[20] Abelin, H., Neretnieks, I., Tunbrant, S., Moreno, L.: Final report of the migration in a single fracture: experimental results and evaluation. Tech. Rep SKB-SP-TR-85-03 (1985)
[21] Hyman, JD; Painter, SL; Viswanathan, H.; Makedonska, N.; Karra, S., Influence of injection mode on transport properties in kilometer-scale three-dimensional discrete fracture networks, Water Resour. Res., 51, 9, 7289 (2015)
[22] Frampton, A., Cvetkovic, V.: Numerical and analytical modeling of advective travel times in realistic three-dimensional fracture networks. Water Resources Research 47(2) (2011)
[23] de Dreuzy, JR; Davy, P.; Bour, O., 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, 8, 2079 (2001)
[24] de Dreuzy, J.R., Méheust, Y., Pichot, G.: Influence of fracture scale heterogeneity on the flow properties of three-dimensional discrete fracture networks. Journal of Geophysical Research-Solid Earth 117 (B11) (2012)
[25] Hyman, J.; Aldrich, G.; Viswanathan, H.; Makedonska, N.; Karra, S., 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, 8, 6472 (2016)
[26] Hyman, JD; Hagberg, A.; Srinivasan, G.; Mohd-Yusof, J.; Viswanathan, H., Predictions of first passage times in sparse discrete fracture networks using graph-based reductions, Phys. Rev. E, 96, 1, 013304 (2017)
[27] Ghaffari, H., Nasseri, M., Young, R.: Fluid flow complexity in fracture networks: analysis with graph theory and lbm. arXiv:1107.4918 (2011)
[28] Andresen, C.A., Hansen, A., Le Goc, R., Davy, P., Hope, S.M.: Topology of fracture networks. Frontiers in physics 1 art (2013)
[29] Santiago, E.; Velasco-Hernández, JX; Romero-salcedo, M., A methodology for the characterization of flow conductivity through the identification of communities in samples of fractured rocks,, Expert Syst. Appl., 41, 3, 811 (2014)
[30] Sævik, PN; Nixon, CW, Inclusion of topological measurements into analytic estimates of effective permeability in fractured media, Water Resour. Res., 53, 11, 9424 (2017)
[31] Hope, SM; Davy, P.; Maillot, J.; Le Goc, R.; Hansen, A., Topological impact of constrained fracture growth, Front. Phys., 3, 75 (2015)
[32] Hyman, J.D., Jiménez-Martínez, J.: Dispersion and mixing in three-dimensional fracture networks: nonlinear interplay between structural and hydraulic heterogeneity. Water Resources Research. 10.1029/2018WR022585 (2018)
[33] Huseby, O.; Thovert, JF; Adler, PM, Geometry and topology of fracture systems, J. Phys. A Math. Gen., 30, 1415 (1997) · Zbl 1001.74593
[34] Aldrich, G.; Hyman, JD; Karra, S.; Gable, CW; Makedonska, N.; Viswanathan, H.; Woodring, J.; Hamann, B., Analysis and visualization of discrete fracture networks using a flow topology graph, IEEE Trans. Vis. Comput. Graph., 23, 8, 1896 (2017)
[35] Karra, S.; O’Malley, D.; Hyman, J.; Viswanathan, H.; Srinivasan, G., Modeling flow and transport in fracture networks using graphs, Phys. Rev. E, 97, 3, 033304 (2018)
[36] Viswanathan, H.S., Hyman, J.D., Karra, S., O’Malley, D., Srinivasan, S., Hagberg, A., Srinivasan, G.: Advancing graph-based algorithms for predicting flow and transport in fractured rock. Water Resources Research. 10.1029/2017WR022368 (2018)
[37] Hyman, JD; Hagberg, A.; Osthus, D.; Srinivasan, S.; Srinivasan, G.; Viswanathan, HS, Identifying backbones in three dimensional discrete fracture networks: a graph-based multi-scale approach, Multiscale Modeling Sim., 16, 4, 5477 (2018)
[38] Dershowitz, W.; Fidelibus, C., Derivation of equivalent pipe network analogues for three-dimensional discrete fracture net works by the boundary element method, Water Resour. Res., 35, 9, 2685 (1999)
[39] Cacas, MC; Ledoux, E.; Marsily, GD; Tillie, B.; Barbreau, A.; Durand, E.; Feuga, B.; Peaudecerf, P., Modeling fracture flow with a stochastic discrete fracture network: calibration and validation: 1. the flow model, Water Resour. Res., 26, 3, 479 (1990)
[40] Srinivasan, G., Hyman, J.D., Osthus, D., Moore, B., O’Malley, D., Karra, S., Rougier, E., Hagberg, A., Hunter, A., Viswanathan, H.: Quantifying topological uncertainty in fractured systems using graph theory and machine learning. Nature Scientific Reports 8 (11665) (2018)
[41] Srinivasan, S., Hyman, J., Karra, S., O’Malley, D., Viswanathan, H., Srinivasan, G.: Robust system size reduction of discrete fracture networks: a multi-fidelity method that preserves transport characteristics. Computational Geosciences. 10.1007/s10596-018-9770-4 (2018) · Zbl 1404.86009
[42] Bergen, KJ; Johnson, PA; de Hoop, MV; Beroza, GC, Machine learning for data-driven discovery in solid earth geoscience, Science, 363, 6433 (2019)
[43] Karpatne, A., Ebert-Uphoff, I., Ravela, S., Babaie, H.A., Kumar, V.: Machine learning for the geosciences: challenges and opportunities. IEEE Transactions on Knowledge and Data Engineering. p. 1. 10.1109/TKDE.2018.2861006 (2018)
[44] Zhang, L.; Zhang, L.; Du, B., Deep learning for remote sensing data: a technical tutorial on the state of the art, IEEE Geoscience and Remote Sensing Magazine, 4, 2, 22 (2016)
[45] Cracknell, MJ; Reading, AM, Geological mapping using remote sensing data: a comparison of five machine learning algorithms, their response to variations in the spatial distribution of training data and the use of explicit spatial information, Comput. Geosci., 63, 22 (2014)
[46] National Oceanic and Atmospheric Administration: National Centers for Environmental Information. www.ncdc.noaa.gov (2018)
[47] World Climate Research Program: Coupled model intercomparison Project. http://cmip-pcmdi.llnl.gov (2018)
[48] Scavuzzo, JM; Trucco, F.; Espinosa, M.; Tauro, CB; Abril, M.; Scavuzzo, CM; Frery, AC, Modeling dengue vector population using remotely sensed data and machine learning, Acta Trop., 185, 167 (2018)
[49] Hengl, T.; de Jesus, JM; Heuvelink, GB; Gonzalez, MR; Kilibarda, M.; Blagotić, A.; Shangguan, W.; Wright, MN; Geng, X.; Bauer-Marschallinger, B., Soilgrids250m: global gridded soil information based on machine learning, PLOS One, 12, 2, E0169748 (2017)
[50] Dev, S.; Wen, B.; Lee, YH; Winkler, S., Ground-based image analysis: a tutorial on machine-learning techniques and applications, IEEE Geoscience and Remote Sensing Magazine, 4, 2, 79 (2016)
[51] Zhang, Z., When doctors meet with alphago: potential application of machine learning to clinical medicine, Ann. Transl. Med., 4, 125 (2016)
[52] Lary, DJ; Alavi, AH; Gandomi, AH; Walker, AL, Machine learning in geosciences and remote sensing, Geosci. Front., 7, 1, 3 (2016)
[53] Griewank, A.; Reich, S.; Roulstone, I.; Stuart, AM, Mathematical and algorithmic aspects of data assimilation in the geosciences, Oberwolfach Reports, 13, 4, 2705 (2017) · Zbl 1390.00096
[54] Ravela, S.: A Symbiotic Framework for coupling Machine Learning and Geosciences in Prediction and Predictability. In: AGU Fall Meeting Abstracts (2017)
[55] Dell’Aversana, P., Ciurlo, B., Colombo, S.: Integrated Geophysics and Machine Learning for Risk Mitigation in Exploration Geosciences. In: 80Th EAGE Conference and Exhibition 2018 (2018)
[56] Karpatne, A.; Atluri, G.; Faghmous, JH; Steinbach, M.; Banerjee, A.; Ganguly, A.; Shekhar, S.; Samatova, N.; Kumar, V., Theory-guided data science: a new paradigm for scientific discovery from data, IEEE Trans. Knowl. Data Eng., 29, 10, 2318 (2017)
[57] Pan, S.; Duraisamy, K., Data-driven discovery of closure models, SIAM J. Appl. Dyn. Syst., 17, 4, 2381 (2018) · Zbl 1411.70023
[58] Valera, M.; Guo, Z.; Kelly, P.; Matz, S.; Cantu, VA; Percus, AG; Hyman, JD; Srinivasan, G.; Viswanathan, HS, Machine learning for graph-based representations of three-dimensional discrete fracture networks, Comput. Geosci., 22, 695 (2018) · Zbl 1405.76059
[59] Srinivasan, S., Karra, S., Hyman, J., Viswanathan, H., Srinivasan, G.: Model reduction for fractured porous media: a machine learning approach for identifying main flow pathways. Computational Geosciences (2018) · Zbl 1419.76508
[60] Hyman, JD; Karra, S.; Makedonska, N.; Gable, CW; Painter, SL; Viswanathan, HS, dfnworks: A discrete fracture network framework for modeling subsurface flow and transport, Comput. Geosci., 84, 10 (2015)
[61] Hyman, JD; Gable, CW; Painter, SL; Makedonska, N., Conforming delaunay triangulation of stochastically generated three dimensional discrete fracture networks: a feature rejection algorithm for meshing strategy, SIAM J. Sci. Comput., 36, 4, A1871 (2014) · Zbl 1305.74082
[62] LaGriT: Los Alamos Grid Toolbox, (LaGriT). http://lagrit.lanl.gov (2013). Last Checked : May 20, 2019
[63] Lichtner, P., Hammond, G., Lu, C., Karra, S., Bisht, G., Andre, B., Mills, R., Kumar, J.: PFLOTRAN user manual: a massively parallel reactive flow and transport model for describing surface and subsurface processes. Tech. rep. (Report No.: LA-UR-15-20403) Los Alamos National Laboratory. 10.2172/1168703 (2015)
[64] Makedonska, N.; Painter, SL; Bui, QM; Gable, CW; Karra, S., Particle tracking approach for transport in three-dimensional discrete fracture networks, Comput. Geosci., 19, 5, 1123 (2015) · Zbl 1391.76735
[65] Painter, SL; Gable, CW; Kelkar, S., Pathline tracing on fully unstructured control-volume grids, Comput. Geosci., 16, 4, 1125 (2012)
[66] Long-term Safety for the Final Repository for Spent Nuclear Fuel at Forsmark. Tech. Rep, SKB TR-11-01 (2011), Stockholm: Swedish Nuclear Fuel and Waste Management Co., Stockholm
[67] Alemanni, A.; Battaglia, M.; Bigi, S.; Borisova, E.; Campana, A.; Loizzo, M.; Lombardi, S., A three dimensional representation of the fracture network of a co2 reservoir analogue (Latera Caldera, Central Italy), Energy Procedia, 4, 3582 (2011)
[68] Boussinesq, J., Mémoire sur l’in uence des frottements dans les mouvements réguliers des fluids, J. Math. Pures. Appl., 13, 377-424, 21 (1868)
[69] Sherman, T.; Hyman, JD; Bolster, D.; Makedonska, N.; Srinivasan, G., Characterizing the impact of particle behavior at fracture intersections in three-dimensional discrete fracture networks, Phys. Rev. E., 99, 013110 (2019)
[70] Yen, JY, Finding the k shortest loopless paths in a network, Manag. Sci., 17, 11, 712 (1971) · Zbl 0218.90063
[71] Brandes, U., A faster algorithm for betweenness centrality, J. Math. Sociol., 25, 2, 163 (2001) · Zbl 1051.91088
[72] Hagberg, A.A., Schult, D.A., Swart, P.: Exploring network structure, dynamics, and function using NetworkX. In: Proceedings of the 7th Python in Science Conferences (SciPy 2008), pp. 11-15 (2008)
[73] Pedregosa, F.; Varoquaux, G.; Gramfort, A.; Michel, V.; Thirion, B.; Grisel, O.; Blondel, M.; Prettenhofer, P.; Weiss, R.; Dubourg, V.; Vanderplas, J.; Passos, A.; Cournapeau, D.; Brucher, M.; Perrot, M.; Duchesnay, E., Scikit-learn: Machine learning in Python, J. Mach. Learn. Res., 12, 2825 (2011) · Zbl 1280.68189
[74] Hosmer, D.W. Jr, Lemeshow, S., Sturdivant, R.X.: Applied logistic regression. vol. 398, Wiley (2013) · Zbl 1276.62050
[75] Cutler, A., Cutler, D.R., Stevens, J.R.: Random Forests. In: Ensemble machine learning, pp. 157-175. Springer (2012)
[76] Grindrod, P.; Impey, M., Channeling and Fickian dispersion in fractal simulated porous media, Water Resour. Res., 29, 12, 4077 (1993)
[77] Ouillon, G.; Castaing, C.; Sornette, D., Hierarchical geometry of faulting, J. Geophys. Res., 101, B3, 5477 (1996)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.