Size-invariant 3D generation from a single 2D rock image

Abstract

The characterization of 3D structures in porous media is crucial for predicting physical properties in many industries, such as CO2 capture and storage, hydrology, oil & gas. In contrast to the expensive and time-consuming acquisition of 3D images, 2D imaging can provide cheap and fast data. However, the reconstruction of a 3D image from a single 2D image is a complex non-deterministic inverse problem. Several statistical and deep learning-based algorithms have been introduced in the past, however, most of them fail to generalize structures and textures for different types of rocks, in addition to being time-consuming and only able to generate relatively small images (

voxels cube).

In this work, we propose a size-invariant multi-step 3D generation workflow from a single 2D image using a combination of Vector-Quantized Variational AutoEncoder(VQ-VAE), size-invariant Generative Adversarial Networks(GAN), and Image Transformer. The proposed workflow tackles several major challenges in the generation of 3D images since it is designed to not only satisfy the large size constraint (

voxels cube) but also to generate statistically representative pore structures. The combination of these different generative techniques allows us to overcome the scalability, stability, and complexity associated with GAN approaches.

We trained the proposed workflow using several types of rocks with different physical properties, sizes, and resolutions. To validate our methodology, we have generated several large-size 3D rock images and compare them to real 3D images in terms of physical properties (porosity, permeability, and Euler characteristic).