Digital rock reconstruction with user-defined properties using conditional generative adversarial networks

Uncertainty is ubiquitous with flow in subsurface rocks because of their inherent heterogeneity and lack of in-situ measurements. To complete uncertainty analysis in a multi-scale manner, it is a prerequisite to provide sufficient rock samples. Even though the advent of digital rock technology offers opportunities to reproduce rocks, it still cannot be utilized to provide massive samples due to its high cost, thus leading to the development of diversified mathematical methods. Among them, two-point statistics (TPS) and multi-point statistics (MPS) are commonly utilized, which feature incorporating low-order and high-order statistical information, respectively. Recently, generative adversarial networks (GANs) are becoming increasingly popular since they can reproduce training images with excellent visual and consequent geologic realism. However, standard GANs can only incorporate information from data, while leaving no interface for user-defined properties, and thus may limit the diversity of reconstructed samples. In this study, we propose conditional GANs for digital rock reconstruction, aiming to reproduce samples not only similar to the real training data, but also satisfying user-specified properties. In fact, the proposed framework can realize the targets of MPS and TPS simultaneously by incorporating high-order information directly from rock images with the GANs scheme, while preserving low-order counterparts through conditioning. We conduct three reconstruction experiments, and the results demonstrate that rock type, rock porosity, and correlation length can be successfully conditioned to affect the reconstructed rock images. Furthermore, in contrast to existing GANs, the proposed conditioning enables learning of multiple rock types simultaneously, and thus invisibly saves the computational cost.

[1]  Dongxiao Zhang,et al.  Multiscale pore structure and its effect on gas transport in organic‐rich shale , 2017 .

[2]  Sunetra Sarkar,et al.  Reconstruction of Porous Media Using Karhunen-Loève Expansion , 2013 .

[3]  Deniz Ertas,et al.  Pore Architecture and Connectivity in Gas Shale , 2015 .

[4]  Jung-Woo Ha,et al.  StarGAN: Unified Generative Adversarial Networks for Multi-domain Image-to-Image Translation , 2017, 2018 IEEE/CVF Conference on Computer Vision and Pattern Recognition.

[5]  Léon Bottou,et al.  Wasserstein GAN , 2017, ArXiv.

[6]  Martin J. Blunt,et al.  Reconstruction of three-dimensional porous media using generative adversarial neural networks , 2017, Physical review. E.

[7]  Jichun Wu,et al.  Predictive Assessment of Groundwater Flow Uncertainty in Multiscale Porous Media by Using Truncated Power Variogram Model , 2018, Transport in Porous Media.

[8]  E. Paleologos,et al.  Stochastic Methods for Flow in Porous Media, Coping With Uncertainties , 2003 .

[9]  Peyman Mostaghimi,et al.  Boosting Resolution and Recovering Texture of 2D and 3D Micro‐CT Images with Deep Learning , 2019, Water Resources Research.

[10]  Martin J. Blunt,et al.  Coupled generative adversarial and auto-encoder neural networks to reconstruct three-dimensional multi-scale porous media , 2020 .

[11]  Aldo Fiori,et al.  Transport in Porous Media , 2008 .

[12]  Dongxiao Zhang,et al.  Efficient uncertainty quantification for permeability of three-dimensional porous media through image analysis and pore-scale simulations. , 2020, Physical review. E.

[13]  Pierre M. Adler,et al.  Flow in simulated porous media , 1990 .

[14]  Aaron C. Courville,et al.  Improved Training of Wasserstein GANs , 2017, NIPS.

[15]  Christopher Burgess,et al.  beta-VAE: Learning Basic Visual Concepts with a Constrained Variational Framework , 2016, ICLR 2016.

[16]  Clayton V. Deutsch,et al.  Geostatistical Reservoir Modeling , 2002 .

[17]  D. Xiu,et al.  Uncertainty quantification on the macroscopic properties of heterogeneous porous media , 2018, Physical Review E.

[18]  G. Mariéthoz,et al.  Multiple-point Geostatistics: Stochastic Modeling with Training Images , 2014 .

[19]  M. Sahimi,et al.  Cross-correlation function for accurate reconstruction of heterogeneous media. , 2013, Physical Review Letters.

[20]  Gregoire Mariethoz,et al.  The Direct Sampling method to perform multiple‐point geostatistical simulations , 2010 .

[21]  S. Bakke,et al.  Process Based Reconstruction of Sandstones and Prediction of Transport Properties , 2002 .

[22]  Natalia Gimelshein,et al.  PyTorch: An Imperative Style, High-Performance Deep Learning Library , 2019, NeurIPS.

[23]  M. Blunt,et al.  Pore space reconstruction using multiple-point statistics , 2005 .

[24]  Ted Chang,et al.  Introduction to Geostatistics: Applications in Hydrogeology , 2001, Technometrics.

[25]  Raul Tempone,et al.  On the predictivity of pore-scale simulations: Estimating uncertainties with multilevel Monte Carlo , 2016 .

[26]  J. Quiblier.  A new three-dimensional modeling technique for studying porous media , 1984 .

[27]  Vincent Dumoulin,et al.  Deconvolution and Checkerboard Artifacts , 2016 .

[28]  Roger B. Grosse,et al.  Isolating Sources of Disentanglement in Variational Autoencoders , 2018, NeurIPS.

[29]  Soumith Chintala,et al.  Unsupervised Representation Learning with Deep Convolutional Generative Adversarial Networks , 2015, ICLR.

[30]  Dinggang Shen,et al.  Medical Image Synthesis with Deep Convolutional Adversarial Networks , 2018, IEEE Transactions on Biomedical Engineering.

[31]  Peyman Mostaghimi,et al.  Enhancing Resolution of Digital Rock Images with Super Resolution Convolutional Neural Networks , 2019, Journal of Petroleum Science and Engineering.

[32]  Timo Aila,et al.  A Style-Based Generator Architecture for Generative Adversarial Networks , 2018, 2019 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR).

[33]  Mian Lin,et al.  A hybrid method for reconstruction of three-dimensional heterogeneous porous media from two-dimensional images , 2019, Journal of Asian Earth Sciences.

[34]  Dongxiao Zhang,et al.  On stochastic modeling of flow in multimodal heterogeneous formations , 2002 .

[35]  Yang Li,et al.  An end-to-end three-dimensional reconstruction framework of porous media from a single two-dimensional image based on deep learning , 2020 .

[36]  Pieter Abbeel,et al.  InfoGAN: Interpretable Representation Learning by Information Maximizing Generative Adversarial Nets , 2016, NIPS.

[37]  Simon Osindero,et al.  Conditional Generative Adversarial Nets , 2014, ArXiv.

[38]  Martin J. Blunt,et al.  Stochastic Reconstruction of an Oolitic Limestone by Generative Adversarial Networks , 2017, Transport in Porous Media.

[39]  Xianghui Xiao,et al.  An Integrated Method for Upscaling Pore-Network Characterization and Permeability Estimation: Example from the Mississippian Barnett Shale , 2015, Transport in Porous Media.

[40]  M. Sahimi,et al.  Three-Dimensional Stochastic Characterization of Shale SEM Images , 2015, Transport in Porous Media.

[41]  Peter Xiaoping Liu,et al.  Deep learning for face image synthesis and semantic manipulations: a review and future perspectives , 2020, Artificial Intelligence Review.

[42]  Guigang Zhang,et al.  Deep Learning , 2016, Int. J. Semantic Comput..

[43]  David M. Loveless,et al.  Nanometer‐scale characterization of microscopic pores in shale kerogen by image analysis and pore‐scale modeling , 2013 .

[44]  R. Hilfer,et al.  Stochastic multiscale model for carbonate rocks. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[45]  Stefan Zaefferer,et al.  Anisotropic distribution of the micro residual stresses in lath martensite revealed by FIB ring-core milling technique , 2018 .

[46]  Yang Jiao,et al.  Direct extraction of spatial correlation functions from limited x-ray tomography data for microstructural quantification , 2018, Materials Characterization.

[47]  D. Rajan.  Probability, Random Variables, and Stochastic Processes , 2017 .

[48]  Sebastien Strebelle,et al.  Conditional Simulation of Complex Geological Structures Using Multiple-Point Statistics , 2002 .

[49]  Shiguang Shan,et al.  AttGAN: Facial Attribute Editing by Only Changing What You Want , 2017, IEEE Transactions on Image Processing.

[50]  Wing Kam Liu,et al.  Computational microstructure characterization and reconstruction: Review of the state-of-the-art techniques , 2018, Progress in Materials Science.