Plain Language Summary
Digital rock physics is an effective approach to characterize pore microstructures and predict effective physical properties of porous medium. However, there is an inherent trade-off between imaging resolution and field of view (FoV) due to the limitations of different imaging techniques: high-resolution data can resolve pore structures up to nano scale but the FoV is not large enough to capture a representative volume element; low-resolution data have larger FoV but cannot capture the fine features. To overcome the trade-off, it is necessary to develop a workflow of multiscale data fusion for the reconstruction of digital rocks with both high-resolution and large FoV. The major challenges are (1) that the high-resolution images are usually limited in number and (2) that the imaging data are typically acquired at different locations of the rock sample, which means that the training samples are unpaired. To address such challenges, we use a style-based generative adversarial network (GAN) to augment the limited high-resolution data and then use a cycle-consistent GAN to integrate the unpaired digital rock data from multiple sources. The proposed method performs well at reconstructing high-resolution rock models that allows more accurate fluid flow simulation at pore-scale and prediction of effective properties.
Introduction
Having a deep understanding of pore-scale processes in porous media is of critical importance for various subsurface applications, such as water resources, oil and gas recovery and carbon dioxide sequestration. The conventional method that takes the physical experiments on core plugs are typically time-consuming and limited by the lab environment. As an alternative approach, digital rock physics (DRP) performs numerical simulations of pore-scale processes of interest directly on digital scans of porous rocks (Keehm et al., 2001 and 2004; Andrä et al., 2013a and 2013b; Blunt et al., 2013; Saxena et al., 2017). It provides a non-destructive means of repeatedly carrying out numerical simulations under different scenarios on the same rock sample. The simulations at pore-scale can then be interpretated to derive macroscopic reservoir properties (e.g., permeability, formation factor, elastic moduli, etc.) and used for sensitivity analysis. A representative elementary volume (REV) of the rock sample with high resolution is an important prerequisite for accurate digital rock physics results. However, in practice, there is an inherent trade-off between field of view (FoV) and image resolution due to the limitation of imaging techniques (Wildenschild et al., 2002; Wildenschild and Sheppard, 2013). Low-resolution imaging cannot resolve micro pores, which often makes the estimated rock properties to be underestimated or overestimated with regards to experimental measurements. On the other hand, the high-resolution image may not capture a REV due to the small FoV.
One way to overcome the trade-off is to integrate imaging data from multiple sources, such as 3-D micro-CT images at the micron scale and 2-D SEM images at the nano scale. Traditional solutions to this challenging problem are mainly stochastic methods based on the spatial statistical information (e.g., two-point correlation functions and multiple-point statistics). Jiao et al. (2007) modeled heterogeneous materials from two-point correlation functions using simulated annealing. Okabe and Blunt (2007) reconstructed 3-D pore space structure by integrating micro-CT images at the micron-scale that resolve large pores with statistically simulated high-resolution images from 2-D thin sections that provides finer-scale features. Mohebi et al. (2009) proposed a statistical method to fuse low-resolution measurements with a high-resolution prior model. Tahmasebi et al. (2015) proposed a multiscale and multiresolution reconstruction method to generate 3-D models of shales using 2-D images.
In recent years, deep learning methods have been developed to alleviate the trade-off between resolution and FoV. Wang et al. (2019) and Da Wang et al. (2019) applied convolutional neural networks (CNN) for micro-CT image enhancement. Da Wang et al. (2020) proposed a generative adversarial network (GAN) to increase the micro-CT image resolution. The above works are based on supervised learning methods that require a large number of paired training data of corresponding low- and high-resolution images. However, in practice, the paired training data are often not available because the sample locations of imaging data are often different. To circumvent this limitation, Niu et al., (2020) proposed a cycle-in-cycle GAN to deal with the unpaired training data for boosting lateral resolution of micro-CT images. You et al. (2021) developed a progressive growing GAN to increase the vertical resolution by combination with the technique of GAN inversion. The deep learning methods are powerful for resolution enhancement of micro-CT images and have high perceptive accuracy compared to traditional interpolation algorithms (e.g., nearest neighborhood and bicubic interpolation). However, previous works mainly focused on the super-resolution problem aiming to increase the resolution of micro-CT images by two or four times. They are useful to make the micro-CT images sharper but cannot resolve pore structures at multiscale or integrate data from different imaging modalities such as micro-CT and SEM images.
The major challenges in multiscale digital rock data fusion are (1) that the high-resolution images are usually limited in number, which would make the model to be easily overfitted and (2) that the digital rock images from multiple sources are typically acquired at different locations of the rock sample, which means that the training samples are unpaired and therefore, supervised methods of machine learning are not applicable. In this letter we propose an innovative method to solve this problem based on deep neural networks. It uses a style-based GAN (Karras et al., 2019; Karras et al., 2020a and 2020b) to augment the limited high-resolution images and then fuses unpaired data at different resolutions by a cycle-consistent GAN (CycleGAN) (Zhu et al., 2017). The disentanglement representation learning of the style-based GAN allows us to generate images with different styles by sampling in different regions of the latent space. With such an advantage, we can train multiple CycleGAN models by feeding training samples with different styles and thus generate multiple high-resolution realizations of the rock that are consistent with the input of low-resolution micro-CT.
Methodology and Data
The proposed workflow of multiscale digital rock data fusion is illustrated in Figure 1. In this study, we have five carbonate samples, most of which exhibit high heterogeneity and anisotropy. Each sample has one high-resolution 2-D SEM image with a size of about 7500×4500 pixels and two or three low-resolution 3-D micro-CT volumes with a size of about 600×600×900 voxels. The resolutions of the micro-CT images range from 1.0 to 2.0 µm, while the resolutions of all SEM images are 0.1 µm. A Style-based GAN is first trained to augment the limited number of SEM images and then a CycleGAN is used to reconstruct high-resolution images from low-resolution micro-CT data.