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.