Abstract
Random reconstruction of three-dimensional (3D) digital rocks from two-dimensional (2D) slices is crucial for elucidating the microstructure of rocks and its effects on pore-scale flow in terms of numerical modeling, since massive samples are usually required to handle intrinsic uncertainties. Despite remarkable advances achieved by traditional process-based methods, statistical approaches and recently famous deep learning-based models, few works have focused on producing several kinds of rocks with one trained model and allowing the reconstructed samples to approximately satisfy certain given properties, such as porosity. To fill this gap, we propose a new framework with deep learning, named RockGPT, which is composed of VQ-VAE and conditional GPT, to synthesize 3D samples based on a single 2D slice from the perspective of video generation. The VQ-VAE is utilized to compress high-dimensional input video, i.e., the sequence of continuous rock slices, to discrete latent codes and reconstruct them. In order to obtain diverse reconstructions, the discrete latent codes are modeled using conditional GPT in an autoregressive manner, while incorporating conditional information from a given slice, rock type, and porosity. We conduct two experiments on five kinds of rocks, and the results demonstrate that RockGPT can produce different kinds of rocks with a single model, and the porosities of reconstructed samples can distribute around specified targets with a narrow range. In a broader sense, through leveraging the proposed conditioning scheme, RockGPT constitutes an effective way to build a general model to produce multiple kinds of rocks simultaneously that also satisfy user-defined properties.
Article PDF
Similar content being viewed by others
Explore related subjects
Find the latest articles, discoveries, and news in related topics.Avoid common mistakes on your manuscript.
References
Chen, C., Hu, D., Westacott, D., Loveless, D.: Nanometer-scale characterization of microscopic pores in shale kerogen by image analysis and pore-scale modeling. Geochem. Geophys. Geosyst. 14(10), 4066–4075 (2013). https://doi.org/10.1002/ggge.20254
Bostanabad, R., Zhang, Y., Li, X., Kearney, T., Brinson, L.C., Apley, D.W., Liu, W.K., Chen, W.: Computational microstructure characterization and reconstruction: review of the state-of-the-art techniques. Prog. Mater. Sci. 95, 1–41 (2018). https://doi.org/10.1016/j.pmatsci.2018.01.005
Li, H., Singh, S., Chawla, N., Jiao, Y.: Direct extraction of spatial correlation functions from limited x-ray tomography data for microstructural quantification. Mater. Charact. 140, 265–274 (2018). https://doi.org/10.1016/j.matchar.2018.04.020
Archie, F., Mughal, M.Z., Sebastiani, M., Bemporad, E., Zaefferer, S.: Anisotropic distribution of the micro residual stresses in lath martensite revealed by FIB ring-core milling technique. Acta Mater. 150, 327–338 (2018). https://doi.org/10.1016/j.actamat.2018.03.030
Tahmasebi, P., Javadpour, F., Sahimi, M.: Three-dimensional stochastic characterization of shale SEM images. Transp. Porous Media. 110(3), 521–531 (2015). https://doi.org/10.1007/s11242-015-0570-1
Peng, S., Yang, J., Xiao, X., Loucks, B., Ruppel, S.C., Zhang, T.: An integrated method for upscaling pore-network characterization and permeability estimation: example from the Mississippian Barnett shale. Transp. Porous Media. 109(2), 359–376 (2015). https://doi.org/10.1007/s11242-015-0523-8
Wu, T., Li, X., Zhao, J., Zhang, D.: Multiscale pore structure and its effect on gas transport in organic-rich shale. Water Resour. Res. 53(7), 5438–5450 (2017). https://doi.org/10.1002/2017WR020780
King Jr., H.E., Eberle, A.P., Walters, C.C., Kliewer, C.E., Ertas, D., Huynh, C.: Pore architecture and connectivity in gas shale. Energy Fuel. 29(3), 1375–1390 (2015). https://doi.org/10.1021/ef502402e
Latief, F., Biswal, B., Fauzi, U., Hilfer, R.: Continuum reconstruction of the pore scale microstructure for Fontainebleau sandstone. Physica A: Statis Mech Appli. 389(8), 1607–1618 (2010). https://doi.org/10.1016/j.physa.2009.12.006
Bakke, S., Øren, P.: 3-D pore-scale modelling of sandstones and flow simulations in the pore networks. SPE J. 2(02), 136–149 (1997). https://doi.org/10.2118/35479-PA
Quiblier, J.A.: A new three-dimensional modeling technique for studying porous media. J. Colloid Interface Sci. 98(1), 84–102 (1984). https://doi.org/10.1016/0021-9797(84)90481-8
Adler, P.M., Jacquin, C.G., Quiblier, J.A.: Flow in simulated porous media. Int. J. Multiphase Flow. 16(4), 691–712 (1990). https://doi.org/10.1016/0301-9322(90)90025-E
Guardiano, F.B., Srivastava, R.M.: Multivariate geostatistics: beyond bivariate moments, 133-144. Springer. (1993)
Strebelle, S.: Conditional simulation of complex geological structures using multiple-point statistics. Math. Geol. 34(1), 1–21 (2002). https://doi.org/10.1023/A:1014009426274
Tahmasebi, P., Hezarkhani, A., Sahimi, M.: Multiple-point geostatistical modeling based on the cross-correlation functions. Comput. Geosci. 16(3), 779–797 (2012). https://doi.org/10.1007/s10596-012-9287-1
Tahmasebi, P., Sahimi, M., Caers, J.: MS-CCSIM: accelerating pattern-based geostatistical simulation of categorical variables using a multi-scale search in Fourier space. Comput. Geosci. 67, 75–88 (2014). https://doi.org/10.1016/j.cageo.2014.03.009
Tahmasebi, P., Sahimi, M.: Enhancing multiple-point geostatistical modeling: 1. Graph theory and pattern adjustment. Water Resour. Res. 52(3), 2074–2098 (2016). https://doi.org/10.1002/2015WR017807
Tahmasebi, P., Sahimi, M.: Enhancing multiple-point geostatistical modeling: 2. Iterative simulation and multiple distance function. Water Resour. Res. 52(3), 2099–2122 (2016). https://doi.org/10.1002/2015WR017807
Gao, M., He, X., Teng, Q., Zuo, C., Chen, D.: Reconstruction of three-dimensional porous media from a single two-dimensional image using three-step sampling. Phys. Rev. E. 91(1), 13308 (2015). https://doi.org/10.1103/PhysRevE.91.013308
Goodfellow, I., Pouget-Abadie, J., Mirza, M., Xu, B., Warde-Farley, D., Ozair, S., Courville, A., Bengio, Y.: Generative adversarial nets. Advances in neural information processing systems, 20142672–2680. (2014)
Kingma, D.P., Welling, M.: Auto-encoding variational bayes. arXiv preprint arXiv:1312.6114 (2013)
Mosser, L., Dubrule, O., Blunt, M.J.: Reconstruction of three-dimensional porous media using generative adversarial neural networks. Phys. Rev. E. 96(4), 43309 (2017). https://doi.org/10.1103/PhysRevE.96.043309
Shams, R., Masihi, M., Boozarjomehry, R.B., Blunt, M.J.: Coupled generative adversarial and auto-encoder neural networks to reconstruct three-dimensional multi-scale porous media. J. Pet. Sci. Eng. 186, 106794 (2020). https://doi.org/10.1016/j.petrol.2019.106794
Zhang, F., Teng, Q., Chen, H., He, X., Dong, X.: Slice-to-voxel stochastic reconstructions on porous media with hybrid deep generative model. Comput. Mater. Sci. 186, 110018 (2021). https://doi.org/10.1016/j.commatsci.2020.110018
Feng, J., Teng, Q., Li, B., He, X., Chen, H., Li, Y.: An end-to-end three-dimensional reconstruction framework of porous media from a single two-dimensional image based on deep learning. Comput. Methods Appl. Mech. Eng. 368, 113043 (2020). https://doi.org/10.1016/j.cma.2020.113043
Anderson, T.I., Guan, K.M., Vega, B., Aryana, S.A., Kovscek, A.R.: RockFlow: fast generation of synthetic source rock images using generative flow models. Energies. 13(24), 6571 (2020). https://doi.org/10.3390/en13246571
You, N., Li, Y.E., Cheng, A.: 3D carbonate digital rock reconstruction using progressive growing GAN. J. Geophys. Res. Solid Earth. 126(5), (2021). https://doi.org/10.1029/2021JB021687
Karras, T., Aila, T., Laine, S., Lehtinen, J.: Progressive growing of gans for improved quality, stability, and variation. arXiv preprint arXiv:1710.10196 (2017)
Kench, S., Cooper, S.J.: Generating three-dimensional structures from a two-dimensional slice with generative adversarial network-based dimensionality expansion. Nat. Mach. Intell. 3(4), 299–305 (2021). https://doi.org/10.1038/s42256-021-00322-1
Yan, W., Zhang, Y., Abbeel, P., Srinivas, A.: VideoGPT: video generation using VQ-VAE and transformers. arXiv preprint arXiv:2104.10157 (2021)
Oord, A.V.D., Vinyals, O., Kavukcuoglu, K.: Neural discrete representation learning. arXiv preprint arXiv:1711.00937 (2017)
Chen, M., Radford, A., Child, R., Wu, J., Jun, H., Luan, D., Sutskever, I.: Generative pretraining from pixels. Proceedings of the 37th International Conference on Machine Learning, 2020. PMLR, p 1691–1703. (2020)
Goodfellow, I.: Nips 2016 tutorial: Generative adversarial networks. arXiv preprint arXiv:1701.00160 (2016)
Oord, A.V.D., Kalchbrenner, N., Vinyals, O., Espeholt, L., Graves, A., Kavukcuoglu, K.: Conditional image generation with pixelcnn decoders. arXiv preprint arXiv:1606.05328 (2016)
Vaswani, A., Shazeer, N., Parmar, N., Uszkoreit, J., Jones, L., Gomez, A.N., Kaiser, A., Polosukhin, I.: Attention is all you need. Advances in neural information processing systems, 5998–6008. (2017)
Radford, A., Narasimhan, K., Salimans, T., Sutskever, I.: Improving Language Understanding by Generative Pre-Training (2018)
Fan, Z., Gong, Y., Liu, D., Wei, Z., Wang, S., Jiao, J., Duan, N., Zhang, R., Huang, X.: Mask attention networks: rethinking and strengthen transformer. arXiv preprint arXiv:2103.13597 (2021)
Raffel, C., Shazeer, N., Roberts, A., Lee, K., Narang, S., Matena, M., Zhou, Y., Li, W., Liu, P.J.: Exploring the limits of transfer learning with a unified text-to-text transformer. arXiv preprint arXiv:1910.10683 (2019)
Jiang, Y., Chang, S., Wang, Z.: Transgan: Two transformers can make one strong gan. arXiv preprint arXiv:2102.07074 (2021)
Dosovitskiy, A., Beyer, L., Kolesnikov, A., Weissenborn, D., Zhai, X., Unterthiner, T., Dehghani, M., Minderer, M., Heigold, G., Gelly, S.: An image is worth 16x16 words: Transformers for image recognition at scale. arXiv preprint arXiv:2010.11929 (2020)
Chen, X., Wu, Y., Wang, Z., Liu, S., Li, J.: Developing real-time streaming transformer transducer for speech recognition on large-scale datasetICASSP 2021–2021 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), 2021. IEEE, p 5904–5908. (2021)
Ihm, H.R., Lee, J.Y., Choi, B.J., Cheon, S.J., Kim, N.S.: Reformer-TTS: neural speech synthesis with reformer network. INTERSPEECH, 2012–2016. (2020)
Ba, J.L., Kiros, J.R., Hinton, G.E.: Layer normalization. arXiv preprint arXiv:1607.06450 (2016)
He, K., Zhang, X., Ren, S., Sun, J.: Deep residual learning for image recognition. Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, 2016770–778. (2016)
Zheng, Q., Zhang, D.: Digital rock reconstruction with user-defined properties using conditional generative adversarial networks. Transp. Porous Media. (2022). https://doi.org/10.1007/s11242-021-01728-6
Neumann, R., Andreeta, M., Lucas-Oliveira, E.: 11 Sandstones: raw, filtered and segmented data. Digital Rocks Portal, http://www.digitalrocksportal.org/projects/317. (2020)
Moon, C., Andrew, M.: Intergranular pore structures in sandstones. Digital Rocks Portal, https://www.digitalrocksportal.org/projects/222. (2019)
Muljadi, B.P.: Estaillade carbonate. Digital Rocks Portal, http://www.digitalrocksportal.org/projects/10. (2015)
Raeini, A.Q., Bijeljic, B., Blunt, M.J.: Generalized network modeling: network extraction as a coarse-scale discretization of the void space of porous media. Phys. Rev. E. 96(1), 13312 (2017). https://doi.org/10.1103/PhysRevE.96.013312
Mohammadmoradi, P.: A Multiscale sandy microstructure. Digital Rocks Portal, http://www.digitalrocksportal.org/projects/92. (2017)
Kingma, D.P., Ba, J.: Adam: A method for stochastic optimization. arXiv preprint arXiv:1412.6980 (2014)
Unterthiner, T., van Steenkiste, S., Kurach, K., Marinier, R., Michalski, M., Gelly, S.: Towards accurate generative models of video: A new metric & challenges. arXiv preprint arXiv:1812.01717 (2018)
Domander, R., Felder, A.A., Doube, M.: BoneJ2-refactoring established research software. Wellcome Open Research, 47(6), 1076–1079 (2021). https://doi.org/10.12688/wellcomeopenres.16619.2
Schindelin, J., Arganda-Carreras, I., Frise, E., Kaynig, V., Longair, M., Pietzsch, T., Preibisch, S., Rueden, C., Saalfeld, S., Schmid, B.: Fiji: an open-source platform for biological-image analysis. Nat. Methods. 9(7), 676–682 (2012). https://doi.org/10.1038/nmeth.2019
Hajizadeh, A., Safekordi, A., Farhadpour, F.A.: A multiple-point statistics algorithm for 3D pore space reconstruction from 2D images. Adv. Water Resour. 34(10), 1256–1267 (2011). https://doi.org/10.1016/j.advwatres.2011.06.003
Eshghinejadfard, A., Daróczy, L., Janiga, G., Thévenin, D.: Calculation of the permeability in porous media using the lattice Boltzmann method. Int. J. Heat Fluid Flow. 62, 93–103 (2016). https://doi.org/10.1016/j.ijheatfluidflow.2016.05.010
Zhang, D.: Stochastic methods for flow in porous media: coping with uncertainties. Elsevier. (2001)
Child, R., Gray, S., Radford, A., Sutskever, I.: Generating long sequences with sparse transformers. arXiv preprint arXiv:1904.10509 (2019)
Ho, J., Kalchbrenner, N., Weissenborn, D., Salimans, T.: Axial attention in multidimensional transformers. arXiv preprint arXiv:1912.12180 (2019)
Acknowledgments
This work is partially funded by the Shenzhen Key Laboratory of Natural Gas Hydrates (Grant No. ZDSYS20200421111201738), the SUSTech - Qingdao New Energy Technology Research Institute, and the China Postdoctoral Science Foundation (Grant No. 2020 M682830). The data of this work is available at https://doi.org/10.6084/m9.figshare.16545663.v1.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
About this article
Cite this article
Zheng, Q., Zhang, D. RockGPT: reconstructing three-dimensional digital rocks from single two-dimensional slice with deep learning. Comput Geosci 26, 677–696 (2022). https://doi.org/10.1007/s10596-022-10144-8
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10596-022-10144-8