Reconstruction of three-dimensional porous media using generative adversarial neural networks (1704.03225v1)

Abstract: To evaluate the variability of multi-phase flow properties of porous media at the pore scale, it is necessary to acquire a number of representative samples of the void-solid structure. While modern x-ray computer tomography has made it possible to extract three-dimensional images of the pore space, assessment of the variability in the inherent material properties is often experimentally not feasible. We present a novel method to reconstruct the solid-void structure of porous media by applying a generative neural network that allows an implicit description of the probability distribution represented by three-dimensional image datasets. We show, by using an adversarial learning approach for neural networks, that this method of unsupervised learning is able to generate representative samples of porous media that honor their statistics. We successfully compare measures of pore morphology, such as the Euler characteristic, two-point statistics and directional single-phase permeability of synthetic realizations with the calculated properties of a bead pack, Berea sandstone, and Ketton limestone. Results show that GANs can be used to reconstruct high-resolution three-dimensional images of porous media at different scales that are representative of the morphology of the images used to train the neural network. The fully convolutional nature of the trained neural network allows the generation of large samples while maintaining computational efficiency. Compared to classical stochastic methods of image reconstruction, the implicit representation of the learned data distribution can be stored and reused to generate multiple realizations of the pore structure very rapidly.

• The paper demonstrates that GANs accurately reconstruct 3D porous media models by replicating pore-scale properties and statistical measures.
• It details a methodology using CNN-based generator and discriminator networks to model varied porous structures from beadpack to sandstone.
• The results indicate that GANs provide an efficient, scalable alternative to traditional methods for simulating complex flow and connectivity in porous media.

Insights on "Reconstruction of three-dimensional porous media using generative adversarial neural networks"

This paper addresses the application of Generative Adversarial Networks (GANs) to reconstruct three-dimensional (3D) porous media. The capacity to accurately model the variability of pore-scale properties is crucial for predicting multi-phase flow characteristics, especially in applications such as carbon capture and storage. Despite advancements in imaging techniques like x-ray computed tomography, limitations remain due to the cost and complexity of acquiring high-resolution images that represent larger pore structures.

Overview of Methodology

The authors propose a methodology leveraging GANs to generate synthetic samples of porous media. GANs consist of two core components: a generator and a discriminator, each represented by convolutional neural networks (CNNs). During training, the generator aims to produce realistic samples mimicking the training data distribution, while the discriminator attempts to distinguish these generated samples from real samples. Through adversarial training, the generator learns to simulate samples that closely resemble real-world data.

For evaluating their approach, the authors use 3D binary representations of different porous media, namely a beadpack, Berea sandstone, and oolitic Ketton limestone. The GAN model was trained to generate samples that capture statistical properties such as the two-point correlation function, Minkowski functionals, and single-phase permeability.

Numerical and Statistical Results

The paper illustrates that the GAN-generated models closely match the pore morphology and statistical characteristics of the training datasets. For instance, the generated samples effectively capture the directional and radial covariance and the Minkowski measures (porosity, specific surface area, and Euler characteristic), indicating successful modeling of the pore network connectivity and surface interactions crucial for fluid flow.

Bidi-borate statistics and visual comparison with the training dataset affirm the validity of generated structures. Single-phase flow simulations further demonstrate that the generated 3D samples capture equivalent permeability features, thereby preserving essential flow properties.

Implications and Future Directions

The application of GANs presents an efficient alternative to classical modeling techniques such as stochastic and Boolean models, primarily due to their implicit representation capability and computational efficiency in generating large, high-resolution 3D structures. This paves the way for robust stochastic modeling, which is both scalable and readily applicable to a variety of porous media, including those that exhibit non-stationarity.

In practice, these advancements mitigate the challenges associated with limited empirical data, allowing for variability assessments in key parameters like porosity and permeability without physical experimentation. The authors note challenges in stable GAN training processes and propose examining various network architectures and configurations in future research.

The implications extend into broader applications such as enhancing reservoir simulations, improving predictions in geoscientific models, and facilitating informed decision-making in subsurface exploration and development. Additionally, integration with multi-scale datasets, utilizing cutting-edge network architectures, and refining stabilization techniques in adversarial training could further optimize the utility of GANs in the field of porous media reconstruction.

In summary, this paper establishes a foundation for the application of GANs to porous media reconstruction, highlighting their potential to revolutionize stochastic modeling by leveraging learned probabilistic representations to simulate realistic 3D structures efficiently.