Abstract
Accurately analyzing the flow and transport behavior in a large discrete fracture network is computationally expensive. Fortunately, recent research shows that most of the flow and transport occurs within a small backbone in the network, and identifying the backbone to replace the original network can greatly reduce computational consumption. However, the existing machine learning based methods mainly focus on the features of the fracture itself to evaluate the importance of the fracture, the local structural information of the fracture network is not fully utilized. More importantly, these machine learning methods can neither control the identified backbone’s size nor ensure the backbone’s connectivity. To solve these problems, a deep learning model named multi-aggregator graph neural network (MA-GNN) is proposed for identifying the backbone of discrete fracture networks. Briefly, MA-GNN uses multiple aggregators to aggregate neighbors’ structural features and thus generates an inductive embedding to evaluate the criticality score of each node in the entire fracture network. Then, a greedy algorithm, which can control the backbone’s size and connectivity, is proposed to identify the backbone based on the criticality score. Experimental results demonstrate that the backbone identified by MA-GNN can recover the transport characteristics of the original network, outperforming state-of-the-art baselines. In addition, MA-GNN can identify influential fractures with higher Kendall’s \(\tau \) correlation coefficient and Jaccard similarity coefficient. With the ability of size control, our proposed MA-GNN can provide an effective balance between accuracy and computational efficiency by choosing a suitable backbone size.
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The datasets generated during the current study are available from the corresponding author on reasonable request.
References
Berrone, S., Della Santa, F., Mastropietro, A., Pieraccini, S., Vaccarino, F.: Graph informed deep learning for uncertainty quantification in discrete fracture networks. PROCEEDINGS OF SIMAI 2020+ 21. (2021)
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. Computat. Geosci. 23, 617–629 (2019). https://doi.org/10.1007/s10596-019-9811-7
Wolfsberg, A.: Rock fractures and fluid flow: contemporary understanding and applications. Wiley Online Library (1997)
Frampton, A., Cvetkovic, V.: Numerical and analytical modeling of advective travel times in realistic three-dimensional fracture networks. Water Resour Res. 47(2) (2011) https://doi.org/10.1029/2010WR009290
Hyman, J., Jiménez-Martínez, J., Viswanathan, H.S., Carey, J.W., Porter, M.L., Rougier, E., Karra, S., Kang, Q., Frash, L., Chen, L., et al.: Understanding hydraulic fracturing: a multi-scale problem. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences. 374(2078), 20150426 (2016). https://doi.org/10.1098/rsta.2015.0426
Karra, S., Makedonska, N., Viswanathan, H.S., Painter, S.L., Hyman, J.D.: Effect of advective flow in fractures and matrix diffusion on natural gas production. Water Resour. Res. 51(10), 8646–8657 (2015). https://doi.org/10.1002/2014WR016829
Jenkins, C., Chadwick, A., Hovorka, S.D.: The state of the art in monitoring and verification–ten years on. International Journal of Greenhouse Gas Control. 40, 312–349 (2015). https://doi.org/10.1016/j.ijggc.2015.05.009
Aldrich, G., Hyman, J.D., Karra, S., Gable, C.W., Makedonska, N., Viswanathan, H., Woodring, J., Hamann, B.: Analysis and visualization of discrete fracture networks using a flow topology graph. IEEE transactions on visualization and computer graphics. 23(8), 1896–1909 (2016). https://doi.org/10.1109/TVCG.2016.2582174
Maillot, J., Davy, P., Le Goc, R., Darcel, C., De Dreuzy, J.-R.: Connectivity, permeability, and channeling in randomly distributed and kinematically defined discrete fracture network models. Water Resour. Res. 52(11), 8526–8545 (2016). https://doi.org/10.1002/2016WR018973
Hyman, J.D., 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). https://doi.org/10.1103/PhysRevE.96.013304
Hyman, J.D., Hagberg, A., Osthus, D., Srinivasan, S., Viswanathan, H., Srinivasan, G.: Identifying backbones in three-dimensional discrete fracture networks: A bipartite graph-based approach. Multiscale Modeling & Simulation. 16(4), 1948–1968 (2018). https://doi.org/10.1137/18M1180207
Valera, M., Guo, Z., Kelly, P., Matz, S., Cantu, V.A., Percus, A.G., Hyman, J.D., Srinivasan, G., Viswanathan, H.S.: Machine learning for graph-based representations of three-dimensional discrete fracture networks. Comput. Geosci. 22, 695–710 (2018). https://doi.org/10.1007/s10596-018-9720-1
Wu, Z., Pan, S., Chen, F., Long, G., Zhang, C., Philip, S.Y.: A comprehensive survey on graph neural networks. IEEE Transactions on Neural Networks and Learning Systems. 32(1), 4–24 (2020). https://doi.org/10.1109/TNNLS.2020.2978386
Song, W., Xiao, Z., Wang, Y., Charlin, L., Zhang, M., Tang, J.: Session-based social recommendation via dynamic graph attention networks. In: Proceedings of the Twelfth ACM International Conference on Web Search and Data Mining, pp. 555–563 (2019)
Bastings, J., Titov, I., Aziz, W., Marcheggiani, D., Sima’an, K.: Graph convolutional encoders for syntax-aware neural machine translation. arXiv preprint arXiv:1704.04675. (2017) https://doi.org/10.48550/arXiv.1704.04675
Wang, L., Huang, Y., Hou, Y., Zhang, S., Shan, J.: Graph attention convolution for point cloud semantic segmentation. In: Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pp. 10296–10305 (2019)
Ou, Y., Guo, Q., Xing, J.-L., Liu, J.-G.: Identification of spreading influence nodes via multi-level structural attributes based on the graph convolutional network. Expert Systems with Applications. 203, 117515 (2022). https://doi.org/10.1016/j.eswa.2022.117515
Hamilton, W., Ying, Z., Leskovec, J.: Inductive representation learning on large graphs. Advances in Neural Information Processing Systems. 30 (2017)
Zhao, G., Jia, P., Zhou, A., Zhang, B.: Infgcn: Identifying influential nodes in complex networks with graph convolutional networks. Neurocomputing. 414, 18–26 (2020). https://doi.org/10.1016/j.neucom.2020.07.028
Hyman, J.D., Karra, S., Makedonska, N., Gable, C.W., Painter, S.L., Viswanathan, H.S.: dfnworks: A discrete fracture network framework for modeling subsurface flow and transport. Comput. Geosci. 84, 10–19 (2015). https://doi.org/10.1016/j.cageo.2015.08.001
Bonnet, E., Bour, O., Odling, N.E., Davy, P., Main, I., Cowie, P., Berkowitz, B.: Scaling of fracture systems in geological media. Rev. Geophys. 39(3), 347–383 (2001). https://doi.org/10.1029/1999RG000074
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), 6472–6489 (2016). https://doi.org/10.1002/2016WR018806
Hyman, J.D., Gable, C.W., Painter, S.L., 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), 1871–1894 (2014). https://doi.org/10.1137/130942541
George, D.: Unstructured 3d grid toolbox for modeling and simulation. Technical report, Los Alamos National Lab.(LANL), Los Alamos, NM (United States) (1997)
Lichtner, P.C., Hammond, G.E., 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. Technical report, Los Alamos National Lab.(LANL), Los Alamos, NM (United States); Sandia ... (2015)
Painter, S., Gable, C., Kelkar, S.: Pathline tracing on fully unstructured control-volume grids. Comput. Geosci. 16, 1125–1134 (2012). https://doi.org/10.1007/s10596-012-9307-1
Makedonska, N., Painter, S.L., Bui, Q.M., Gable, C.W., Karra, S.: Particle tracking approach for transport in three-dimensional discrete fracture networks: Particle tracking in 3-d dfns. Computational Geosciences. 19, 1123–1137 (2015). https://doi.org/10.1007/s10596-015-9525-4
Freeman, L.C., et al.: Centrality in social networks: Conceptual clarification. Social network: critical concepts in sociology. Londres: Routledge. 1, 238–263 (2002)
Freeman, L.C.: A set of measures of centrality based on betweenness. Sociometry, 35–41 (1977)
Kitsak, M., Gallos, L.K., Havlin, S., Liljeros, F., Muchnik, L., Stanley, H.E., Makse, H.A.: Identification of influential spreaders in complex networks. Nat. Phys. 6(11), 888–893 (2010). https://doi.org/10.1038/nphys1746
Ullah, A., Wang, B., Sheng, J., Long, J., Khan, N., Sun, Z.: Identifying vital nodes from local and global perspectives in complex networks. Expert Syst. Appl. 186, 115778 (2021). https://doi.org/10.1016/j.eswa.2021.115778
Kendall, M.G.: A new measure of rank correlation. Biometrika. 30(1/2), 81–93 (1938)
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All authors contributed to the study conception and design. Material preparation, data collection and analysis were performed by Jiawei Ye, Xiaobin Rui and Jian Zhang. The first draft of the manuscript was written by Tianji Zheng and Zhixiao Wang commented on previous versions of the manuscript. All authors read and approved the final manuscript.
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Zheng, T., Sun, C., Zhang, J. et al. A multi-aggregator graph neural network for backbone exaction of fracture networks. Comput Geosci (2024). https://doi.org/10.1007/s10596-024-10281-2
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DOI: https://doi.org/10.1007/s10596-024-10281-2