Figure 3. Microstructure analyses for the real and synthetic SEM samples: (a) porosity; (b) specific surface area; (c) two-point correlation function; (d) two-point correlation length.
Figure 4a and 4b shows the predicted high-resolution images from micro-CT data using the trained CycleGAN. With the generator \(G_{L2H}\)of the trained CycleGAN, the low-resolution micro-CT image with a size of 64×64 can be increased by 16 times to the high-resolution domain with a size of 1024×1024. We can see that the reconstructed images not only keep the geometric structures of the input micro-CT images but also recover the fine details present in the SEM data. The recovered fine microstructural details would be helpful to accurately predict pore-scale fluid flow and effective petrophysical properties. Thanks to the disentanglement of the latent style space learned by the StyleGAN2, we can control the styles of the synthetic SEM images by sampling in different regions of the latent space. As illustrated in the Supporting Information Figure S7, we can train multiple CycleGAN models by feeding training samples with different styles and thus generate multiple high-resolution realizations of the rock that all are consistent with the input of low-resolution micro-CT.
Then, we use the CycleGAN to down-scale the entire 3-D micro-CT volumes. The prediction is performed slice by slice and each slice is divided into patches with a size of 64×64. The vertical resolution of micro-CT is first increased by 16 times by bicubic interpolation to make the reconstructed rock models have same resolution along all three directions. To mitigate the artifacts at boundaries, there is an overlap of 8 pixels between patches. One predicted slice with a larger size of 3584×3584 is shown in the Supporting Information Figure S8. The predicted high-resolution images are close to the true SEM image from the same rock sample in terms of porosity, specific surface area and two-point correlation as illustrated in the Supporting Information Figure S9. Figure 4c and 4d show the pore-scale Stokes flow (the slow, incompressible, viscous steady flow) (Allen, 2021) simulated by the LIR solver of the GeoDict software (Linden et al., 2015) over a sub-cube of micro-CT with a size of 64×64×64 and the reconstructed high-resolution rock, respectively. We can observe more details from the reconstructed high-resolution model and thus have deeper understanding of physical procedures at pore-scale. Figure 4f shows one 3-D realization with a size of 1792×1792×2688 from the micro-CT data with a size of 112×112×168 (Figure 4e). More realizations can be found in the Supporting Information Figure S10. As shown in Table 1, the predicted permeabilities of the reconstructed high-resolution models are more consistent with the permeability from the laboratory core measurement than the prediction from micro-CT data.