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

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.Comment: 21 pages, 20 figure

Rapid seismic domain transfer: Seismic velocity inversion and modeling using deep generative neural networks

Traditional physics-based approaches to infer sub-surface properties such as full-waveform inversion or reflectivity inversion are time-consuming and computationally expensive. We present a deep-learning technique that eliminates the need for these computationally complex methods by posing the problem as one of domain transfer. Our solution is based on a deep convolutional generative adversarial network and dramatically reduces computation time. Training based on two different types of synthetic data produced a neural network that generates realistic velocity models when applied to a real dataset. The system's ability to generalize means it is robust against the inherent occurrence of velocity errors and artifacts in both training and test datasets.Comment: Extended abstract submitted to EAGE 2018, 5 pages, 3 figure

Reservoir modeling and inversion using generative adversarial network priors

Determining the spatial distribution of geological heterogeneities and their petrophysical properties is key to successful hydrocarbon production and carbon capture and storage. Due to the sparse nature of direct observations of the earth’s interior from borehole data, most inferences about the interior structure of the earth and its properties have to be made by indirect observation such as seismic reflection or dynamic data. Determining these property distributions from indirect observations requires solving an ill-posed inverse problem which can be defined as a Bayesian inference problem where we seek to obtain the posterior distribution of the subsurface properties given the observed data. Recently, deep generative modeling has enabled multi-modal probability distributions of large three-dimensional natural images to be represented. Generative Adversarial Networks (GANs) are deep generative models that learn a representation of the probability distribution implicitly defined by a set of training images using two competing neural networks. This thesis introduces GANs as probabilistic models of geological features and petrophysical properties at the reservoir scale and images of porous media at the pore-scale. A GAN can be trained to represent pore-scale micro-CT images of segmented and grayscale porous media. After training, the GAN generator is used to sample large high-fidelity realizations that follow the same statistical and physical properties as represented in the training images. Using GANs as a probabilistic generative model allows them to be incorporated in a Bayesian inversion workflow. Based on a synthetic test-case, two inverse problems were considered: inversion of acoustic properties from seismic observations and reservoir history matching of a two-phase flow problem at the reservoir-scale. In both cases, the posterior distribution of the petrophysical property distributions was obtained using approximate Bayesian inference over the latent variables. The samples obtained from the posterior match the observed seismic or production data, and can be conditioned to direct observations at wells. This approach of deep stochastic inversion based on deep generative models such as GANs opens new opportunities for geological modeling and solving ill-posed inverse problems.Open Acces