Reservoir modeling and inversion using generative adversarial network priors

Abstract

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.