Abstract
Numerical simulation studies of water–rock interaction mechanisms and pore-scale multiphase flow properties often require high computational efficiency and realistic geometries to enable a fast and accurate description of hydrodynamic behavior. In this paper, we have chosen to use deep learning models to achieve these requirements, firstly by using encoder structures to refine the image segmentation of void-solid structures on complex geometries of scanning electron microscopy (SEM) images of porous media through few-shot learning (FSL), not only obtaining an accuracy of 0.97, but also reducing the amount of annotation work. We then focus on pore-scale three-dimensional (3D) structural reconstruction using the unpaired image-to-image translation method, optimizing the cycle-consistent adversarial network (cycle-GAN) model via sliced Wasserstein distance (SWD) to transfer marine sedimentary sandstone features to the initial image, and the geometric stochastic reconstruction problems are transformed into optimization problems. Subsequently, the computational efficiency was improved by a factor of 21 by implementing the lattice Boltzmann simulation method (LBM) accelerated by GPU through compute-unified device architecture (CUDA). The flow field distribution and absolute permeability of the extracted 2D samples and the reconstructed 3D porous media structure were simulated. The results showed that our method could rapidly and accurately reconstruct the 3D structures of a given feature, ensuring statistical equivalence between the 3D reconstructed structures and 2D samples. We solve the problem of extrapolation-based 3D reconstruction of porous media and significantly reduce the time spent on structure extraction and numerical calculations.
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References
Adler, P.M., Thovert, J.-F.: Fractures and Fracture Networks. Kluwer Academic, Dordrecht (1999)
Barzegar, F., Masihi, M., Tabar, M.A.: A rigorous algebraic-analytical method for pore network extraction from micro-tomography images. J. Hydrol. 590, 125561 (2020). https://doi.org/10.1016/j.jhydrol.2020.125561
Bauer, M., Kostler, H., Rude, U.: lbmpy: Automatic code generation for efficient parallel lattice Boltzmann methods. J. Comput. Sci. 49, 101269 (2021). https://doi.org/10.1016/j.jocs.2020.101269
Berrone, S., Hyman, J.D., Pieraccini, S.: Multilevel Monte Carlo predictions of first passage times in three-dimensional discrete fracture networks: a graph-based approach. Water Resour. Res. 56(6), e2019WR026493 (2020). https://doi.org/10.1029/2019WR026493
Blunt, M.J., Jackson, M.D., Piri, M., Valvatne, P.H.: Detailed physics, predictive capabilities and macroscopic consequences for pore-network models of multiphase flow. Adv. Water Resour. 25(8–12), 1069–1089 (2002). https://doi.org/10.1016/S0309-1708(02)00049-0
Buslaev, A., Iglovikov, V.I., Khvedchenya, E., Parinov, A., Druzhinin, M., Kalinin, A.A.: Albumentations: fast and flexible image augmentations. Information 11(2), 125 (2020). https://doi.org/10.3390/info11020125
Chan, S., Elsheikh, A.: Parametrization and generation of geological models with generative adversarial networks. (2017). https://doi.org/10.48550/ar**v.1708.01810
Chaurasia, A., Culurciello, E.: Linknet: Exploiting encoder representations for efficient semantic segmentation, pp. 1–4, IEEE (2017).
Chen, L.-C., Papandreou, G., Schroff, F., Adam, H.: Rethinking atrous convolution for semantic image segmentation. ar**v preprint ar**v:1706.05587 (2017).
Chen, L.-C., Zhu, Y., Papandreou, G., Schroff, F., Adam, H.: Encoder-decoder with atrous separable convolution for semantic image segmentation, pp. 801–818 (2018).
Chen, L., Zhang, L., Kang, Q.J., Viswanathan, H.S., Yao, J., Tao, W.Q.: Nanoscale simulation of shale transport properties using the lattice Boltzmann method: permeability and diffusivity. Sci. Rep. 5, 8089 (2015). https://doi.org/10.1038/srep08089
Davahli, M.R., Fiok, K., Karwowski, W., Aljuaid, A.M., Taiar, R.: Predicting the dynamics of the COVID-19 pandemic in the United States using graph theory-based neural networks. Int. J. Env. Res. Public Health 18(7), 3834 (2021). https://doi.org/10.3390/ijerph18073834
de Vries, E.T., Raoof, A., van Genuchten, M.T.: Multiscale modelling of dual-porosity porous media; a computational pore-scale study for flow and solute transport. Adv. Water Resour. 105, 82–95 (2017). https://doi.org/10.1016/j.advwatres.2017.04.013
Dorafshan, S., Thomas, R.J., Maguire, M.: Comparison of deep convolutional neural networks and edge detectors for image-based crack detection in concrete. Constr. Build. Mater. 186, 1031–1045 (2018). https://doi.org/10.1016/j.conbuildmat.2018.08.011
Fang, F., Li, L.Y., Gu, Y., Zhu, H.Y., Lim, J.H.: A novel hybrid approach for crack detection. Pattern Recogn. 107, 107474 (2020). https://doi.org/10.1016/j.patcog.2020.107474
Fenwick, D.H., Blunt, M.J.: Three-dimensional modeling of three phase imbibition and drainage. Adv. Water Resour. 21(2), 121–143 (1998). https://doi.org/10.1016/S0309-1708(96)00037-1
Ghallab, A.: Simulation of cracking in high concrete gravity dam using the extended finite elements by ABAQUS. Am. J. Mech. Appl. 8(1), 7–15 (2020). https://doi.org/10.11648/j.ajma.20200801.12
Goodfellow, I., Pouget-Abadie, J., Mirza, M., Xu, B., Warde-Farley, D., Ozair, S., Courville, A., Bengio, Y.: Generative adversarial nets. Adv. Neural. Inf. Process. Syst. 27, 2672–2680 (2014)
Gu, L.X., Wang, N., Tang, X., Changela, H.G.: Application of FIB-SEM techniques for the advanced characterization of earth and planetary materials. Scanning 2020, 1–15 (2020). https://doi.org/10.1155/2020/8406917
Hilpert, M., Miller, C.T.: Pore-morphology-based simulation of drainage in totally wetting porous media. Adv. Water Resour. 24(3–4), 243–255 (2001). https://doi.org/10.1016/S0309-1708(00)00056-7
Ho, M., Seif, M., McDaniel, S., Leclaire, S., Reggio, M., Trépanier, J.-Y., Beck, M., Martin, A. AIAA Scitech 2021 Forum, American Institute of Aeronautics and Astronautics. (2021)
Jaganathan, S., Tafreshi, H.V., Pourdeyhimi, B.: A realistic approach for modeling permeability of fibrous media: 3-D imaging coupled with CFD simulation. Chem. Eng. Sci. 63(1), 244–252 (2008). https://doi.org/10.1016/j.ces.2007.09.020
Ji, A.K., Xue, X.L., Wang, Y.N., Luo, X.W., Xue, W.R.: An integrated approach to automatic pixel-level crack detection and quantification of asphalt pavement. Autom. Constr. 114, 103176 (2020). https://doi.org/10.1016/j.autcon.2020.103176
Ju, Y., Zheng, J.T., Epstein, M., Sudak, L., Wang, J.B., Zhao, X.: 3D numerical reconstruction of well-connected porous structure of rock using fractal algorithms. Comput. Methods Appl. Mech. Eng. 279, 212–226 (2014). https://doi.org/10.1016/j.cma.2014.06.035
Keehm, Y., Mukerji, T., Nur, A.: Permeability prediction from thin sections: 3D reconstruction and Lattice-Boltzmann flow simulation. Geophys. Res. Lett. 31(4), 1–4 (2004). https://doi.org/10.1029/2003GL018761
Kim, T., Cha, M., Kim, H., Lee, J.K., Kim, J.: Learning to discover cross-domain relations with generative adversarial networks. PR Mach. Learn. Res. 70 (2017).
Laloy, E., Herault, R., Jacques, D., Linde, N.: Training-image based geostatistical inversion using a spatial generative adversarial neural network. Water Resour. Res. 54(1), 381–406 (2018). https://doi.org/10.1002/2017wr022148
Laloy, E., Herault, R., Lee, J., Jacques, D., Linde, N.: Inversion using a new low-dimensional representation of complex binary geological media based on a deep neural network. Adv. Water Resour. 110, 387–405 (2017). https://doi.org/10.1016/j.advwatres.2017.09.029
Latham, S., Varslot, T. and Sheppard, A.: Image registration: enhancing and calibrating X-ray micro-CT imaging. (2008).
Lei, Y.: Reconstruction and analysis of tight sandstone digital rock combined with X-ray CT scanning and multiple-point geostatistics algorithm. Math. Probl. Eng. 2020, 1–10 (2020). https://doi.org/10.1155/2020/9476060
Leu, L., Berg, S., Enzmann, F., Armstrong, R.T., Kersten, M.: Fast X-ray micro-tomography of multiphase flow in berea sandstone: a sensitivity study on image processing. Transp. Porous Med. 105(2), 451–469 (2014). https://doi.org/10.1007/s11242-014-0378-4
Lin, T.-Y., Dollár, P., Girshick, R., He, K., Hariharan, B., Belongie, S.: Feature pyramid networks for object detection, pp. 2117–2125 (2017).
Liu, Y.M., Durlofsky, L.J.: 3D CNN-PCA: A deep-learning-based parameterization for complex geomodels. Comput. Geosci. 148, 104676 (2021). https://doi.org/10.1016/j.cageo.2020.104676
Lu, J., Gong, P., Ye, J. and Zhang, C.: Learning from very few samples: a survey. (2020)
Ma, K., Zhang, J.H., Zhou, Z., Xu, N.W.: Comprehensive analysis of the surrounding rock mass stability in the underground caverns of **** I hydropower station in Southwest China. Tunnel. Undergr. Space Technol. 104, 103525 (2020). https://doi.org/10.1016/j.tust.2020.103525
Marcato, A., Boccardo, G., Marchisio, D.L.: A computational workflow to study particle transport in porous media: coupling CFD and deep learning. Comput.-Aid. Chem. En. 48, 1753–1758 (2020). https://doi.org/10.1016/B978-0-12-823377-1.50294-9
McGlade, C., Speirs, J., Sorrell, S.: Methods of estimating shale gas resources: comparison, evaluation and implications. Energy 59, 116–125 (2013). https://doi.org/10.1016/j.energy.2013.05.031
Molaeimanesh, G.R., Akbari, M.H.: Agglomerate modeling of cathode catalyst layer of a PEM fuel cell by the lattice Boltzmann method. Int. J. Hydrogen Energy 40(15), 5169–5185 (2015). https://doi.org/10.1016/j.ijhydene.2015.02.097
Mora, P., Morra, G., Yuen, D.A.: A concise python implementation of the lattice Boltzmann method on HPC for geo-fluid flow. Geophys. J. Int. 220(1), 682–702 (2020). https://doi.org/10.1093/gji/ggz423
Mosser, L., Dubrule, O., Blunt, M.: Conditioning of three-dimensional generative adversarial networks for pore and reservoir-scale models. (2018a).
Mosser, L., Dubrule, O., Blunt, M.J.: Reconstruction of three-dimensional porous media using generative adversarial neural networks. Phys. Rev. E 96(4), 043309 (2017). https://doi.org/10.1103/PhysRevE.96.043309
Mosser, L., Dubrule, O., Blunt, M.J.: Stochastic reconstruction of an oolitic limestone by generative adversarial networks. Transport. Porous Med. 125(1), 81–103 (2018b). https://doi.org/10.1007/s11242-018-1039-9
Mostaghimi, P., Blunt, M.J., Bijeljic, B.: Computations of absolute permeability on micro-CT images. Math. Geosci. 45(1), 103–125 (2013). https://doi.org/10.1007/s11004-012-9431-4
Nan, N., Wang, J.: FIB-SEM three-dimensional tomography for characterization of carbon-based materials. Adv. Mater. Sci. Eng. 2019, 8680715 (2019). https://doi.org/10.1155/2019/8680715
Nie, B.S., Liu, X.F., Yang, L.L., Meng, J.Q., Li, X.C.: Pore structure characterization of different rank coals using gas adsorption and scanning electron microscopy. Fuel 158, 908–917 (2015). https://doi.org/10.1016/j.fuel.2015.06.050
Niu, Y., Mostaghimi, P., Shabaninejad, M., Swietojanski, P., Armstrong, R.T.: Digital rock segmentation for petrophysical analysis with reduced user bias using convolutional neural networks. Water Resour. Res. 56(2), e2019WR026597 (2020a). https://doi.org/10.1029/2019WR026597
Niu, Y.F., Mostaghimi, P., Shabaninejad, M., Swietojanski, P., Armstrong, R.T.: Digital rock segmentation for petrophysical analysis with reduced user bias using convolutional neural networks. Water Resour. Res. 56(2), e2019WR26597 (2020b). https://doi.org/10.1029/2019WR026597
O.Ghaffari, H.: Fracture networks: analysis with graph theory, LBM and FEM. CoRR arxiv:1107.4918 (2011).
Okabe, H., Blunt, M.J.: Prediction of permeability for porous media reconstructed using multiple-point statistics. Phys. Rev. E 70(6), 066135 (2004). https://doi.org/10.1103/PhysRevE.70.066135
Rabbani, A., Ayatollahi, S.: Comparing three image processing algorithms to estimate the grain-size distribution of porous rocks from binary 2D images and sensitivity analysis of the grain overlap** degree. Spl. Topics Rev. Porous Media 6, 71–89 (2015). https://doi.org/10.1615/SpecialTopicsRevPorousMedia.v6.i1.60
Rabbani, A., Babaei, M.: Hybrid pore-network and lattice-Boltzmann permeability modelling accelerated by machine learning. Adv. Water Resour. 126, 116–128 (2019). https://doi.org/10.1016/j.advwatres.2019.02.012
Rabbani, A., Jamshidi, S., Salehi, S.: An automated simple algorithm for realistic pore network extraction from micro-tomography images. J. Petrol. Sci. Eng. 123, 164–171 (2014). https://doi.org/10.1016/j.petrol.2014.08.020
Radford, A., Metz, L., Chintala, S.: Unsupervised representation learning with deep convolutional generative adversarial networks. Computer Science (2015).
Rahman, M.A., Wang, Y.: Optimizing intersection-over-union in deep neural networks for image segmentation. In: Bebis, G., Boyle, R., Parvin, B., Koracin, D., Porikli, F., Skaff, S., Entezari, A., Min, J., Iwai, D., Sadagic, A., Scheidegger, C., Isenberg, T. (eds), pp. 234–244, Springer International Publishing, Cham (2016)
Ronneberger, O., Fischer, P., Brox, T. 2015 U-net: convolutional networks for biomedical image segmentation, pp. 234–241, Springer.
Shabaninejad, M., Middleton, J., Latham, S., Fogden, A.: Pore-scale analysis of residual oil in a reservoir sandstone and its dependence on water flood salinity, oil composition, and local mineralogy. Energy Fuels 31, 13232 (2017). https://doi.org/10.1021/acs.energyfuels.7b01978
Shlomi, J., Battaglia, P., Vlimant, J.-R.: Graph neural networks in particle physics. Mach. Learn. Sci. Technol. 2(2), 021001 (2021). https://doi.org/10.1088/2632-2153/abbf9a
Siracusano, G., La Corte, A., Tomasello, R., Lamonaca, F., Scuro, C., Garesci, F., Carpentieri, M., Finocchio, G.:Automatic crack detection and classification by exploiting statistical event descriptors for Deep Learning. (2019)
Sudakov, O., Burnaev, E., Koroteev, D.: Driving digital rock towards machine learning: predicting permeability with gradient boosting and deep neural networks. Comput. Geosci. 127, 91–98 (2019). https://doi.org/10.1016/j.cageo.2019.02.002
Tang, M., Liu, Y.M., Durlofsky, L.J.: Deep-learning-based surrogate flow modeling and geological parameterization for data assimilation in 3D subsurface flow. Comput. Methods Appl. Mech. Eng. 376, 113636 (2021). https://doi.org/10.1016/j.cma.2020.113636
Tauzin, B., Pham, T.S., Tkalcic, H.: Receiver functions from seismic interferometry: a practical guide. Geophys. J. Int. 217(1), 1–24 (2019). https://doi.org/10.1093/gji/ggz002
Tyukhova, A.R., Kinzelbach, W., Willmann, M.: Delineation of connectivity structures in 2-D heterogeneous hydraulic conductivity fields. Water Resour. Res. 51(7), 5846–5854 (2015). https://doi.org/10.1002/2014wr015283
Tyukhova, A.R., Willmann, M.: Connectivity metrics based on the path of smallest resistance. Adv. Water Resour. 88, 14–20 (2016). https://doi.org/10.1016/j.advwatres.2015.11.014
Varfolomeev, I., Yakimchuk, I., Safonov, I.: An application of deep neural networks for segmentation of microtomographic images of rock samples. Computers 8(4), 72 (2019). https://doi.org/10.3390/computers8040072
Wang, H., Yang, G.G., Li, S.A., Shen, Q.W., Liao, J.D., Jiang, Z.H., Espinoza-Andaluz, M., Su, F.M., Pan, X.X.: Numerical study on permeability of gas diffusion layer with porosity gradient using lattice Boltzmann method. Int. J. Hydrogen Energ 46(42), 22107–22121 (2021). https://doi.org/10.1016/j.ijhydene.2021.04.039
Wang, Y.D., Chung, T., Armstrong, R., Mostaghimi, P.: ML-LBM: Machine learning aided flow simulation in porous media. (2020)
**ong, Q.R., Baychev, T.G., Jivkov, A.P.: Review of pore network modelling of porous media: experimental characterisations, network constructions and applications to reactive transport. J. Contam. Hydrol. 192, 101–117 (2016). https://doi.org/10.1016/j.jconhyd.2016.07.002
Yeh, R.A., Chen, C., Lim, T.Y., Schwing, A.G., Hasegawa-Johnson, M., Do, M.N.: Semantic image inpainting with deep generative models. Proc. CVPR IEEE, 6882–6890 (2017). https://doi.org/10.1109/Cvpr.2017.728
Yi, Z.L., Zhang, H., Tan, P., Gong, M.L.: DualGAN: Unsupervised dual learning for image-to-image translation. IEEE Int. Conf. Comp. Vis., 2868–2876 (2017). https://doi.org/10.1109/Iccv.2017.310
Yin, Z.X., **a, K.W., He, Z.P., Zhang, J.N., Wang, S.J., Zu, B.K.: Unpaired image denoising via Wasserstein GAN in low-dose CT image with multi-perceptual loss and fidelity loss. Symmetry 13(1), 126 (2021). https://doi.org/10.3390/sym13010126
Yu, S., Zhang, K., **ao, C., Huang, J.Z., Li, M.J., Onizuka, M.: HSGAN: Reducing mode collapse in GANs by the latent code distance of homogeneous samples. Comput. vis. Image Underst. 214, 103314 (2022). https://doi.org/10.1016/j.cviu.2021.103314
Zhang, G., He, H., Katabi, D.: Circuit-GNN: Graph neural networks for distributed circuit design. International Conference on Machine Learning, Vol 97 97 (2019).
Zhang, M., Zhang, J., Lu, Z., **ang, T., Ding, M., Huang, S.: IEPT: Instance-level and episode-level pretext tasks for few-shot learning. International Conference on Learning Representations (2021).
Zhao, S., Cui, J., Sheng, Y., Dong, Y., Liang, X., Chang, E., Xu, Y.: Large scale image completion via co-modulated generative adversarial networks. (2021)
Zhao, Y.X., Peng, L., Liu, S.M., Cao, B., Sun, Y.F., Hou, B.F.: Pore structure characterization of shales using synchrotron SAXS and NMR cryoporometry. Mar. Petrol. Geol. 102, 116–125 (2019). https://doi.org/10.1016/j.marpetgeo.2018.12.041
Zhao, Y.X., Sun, Y.F., Liu, S.M., Chen, Z.W., Yuan, L.: Pore structure characterization of coal by synchrotron radiation nano-CT. Fuel 215, 102–110 (2018). https://doi.org/10.1016/j.fuel.2017.11.014
Zhou, Z., Siddiquee, M.M.R., Tajbakhsh, N., Liang, J.: Deep learning in medical image analysis and multimodal learning for clinical decision support, pp. 3–11, Springer. (2018)
Zhu, J.Y., Park, T., Isola, P., Efros, A.A.: Unpaired image-to-image translation using cycle-consistent adversarial networks. IEEE Int. Conf. Comp. Vis. 2242–2251 (2017). https://doi.org/10.3390/sym13010126
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This work was supported by the National Natural Science Foundation of China (Grant nos. 52090081, 52079068), and the State Key Laboratory of Hydroscience and Hydraulic Engineering (Grant no. 2021-KY-04).
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Wang, M., Wang, E., Liu, X. et al. Sliced Wasserstein Distance-Guided Three-Dimensional Porous Media Reconstruction Based on Cycle-Consistent Adversarial Network and Few-Shot Learning. Transp Porous Med (2024). https://doi.org/10.1007/s11242-024-02099-4
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DOI: https://doi.org/10.1007/s11242-024-02099-4