  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 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.
Furthermore, in contrast to existing GANs, the proposed conditioning enables
learning of multiple rock types simultaneously, and thus invisibly saves
computational cost.
