Digital Rock Reconstruction with User-Defined Properties Using Conditional Generative Adversarial Networks

Abstract

Uncertainty is ubiquitous with multiphase flow in subsurface rocks due to 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 representativeness 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. The randomly reconstructed samples with specified rock type, porosity and correlation length will contribute to the subsequent research on pore-scale multiphase flow and uncertainty quantification.

Predicting 3D Physical Properties From a Single 2D Slice Based on Convolutional Neural Networks: 2D‐Slice‐To‐3D‐Properties for Porous Rocks

“…advantage of the Python library called "porepy.metrics.two_point_correlation" to conveniently implement calculations. In practice, the two-point correlation function can be transformed into a basic variable-the correlation length λ, S pore (d) = exp (−d/λ) (Zheng & Zhang, 2022). However, the S pore (d) of this sample set does not satisfy an exponential relationship but a power law relationship with d. Therefore, this work directly uses two-point correlation function data to analyze the connectivity characteristics of representative volume element (REV) for the 3D sample sets.…”

GANSim‐3D for Conditional Geomodeling: Theory and Field Application

“…Such technique was initially proposed by Jetchev et al. (2016) and has been used in numerous geosciences researches (e.g., Laloy et al., 2018; Zheng & Zhang, 2022). We will use this technique for geomodeling of large‐size reservoirs in Section 6.2.…”

“…This feature is critical in geosciences because: first, it is impossible to train a deep learning model to produce earth models with very large size due to the limitation of training data size and computational resources; and second, practical areas of interest can be of many possible sizes. Such technique was initially proposed by Jetchev et al (2016) and has been used in numerous geosciences researches (e.g., Laloy et al, 2018;Zheng & Zhang, 2022). We will use this technique for geomodeling of large-size reservoirs in Section 6.2.…”

“…As illustrated in Figure S2 in Supporting Information S1, in the generator of GANSim, the concatenation of a random latent vector and a vector of global features is mapped into a feature vector with a fully connected neural network layer, and the following reshape layer further converts the feature vector into multiple channels of 2D feature maps. However, in GANSim-3D, the input latent vector and each global feature are transformed into a 3D data cube, respectively, as in Zheng and Zhang (2022). The original fully-connected and reshape layers are replaced by a 3D convolutional layer, which converts the concatenation of the random latent cube and global feature cubes into multiple channels of 3D feature cubes.…”

“…In recent years, GANs have been combined with geomodeling in different aspects (e.g., Chan & Elsheikh, 2017Dupont et al, 2018;Laloy et al, 2018;Mosser et al, 2020;Nesvold & Mukerji, 2021;Song et al, 2021aSong et al, , 2021bSong et al, , 2022Zhang et al, 2019;Zheng & Zhang, 2022). Like any other approach, unconditional and conditional geomodeling are considered.…”