History matching under uncertainty of geological scenarios with implicit geological realism control with generative deep learning and graph convolutions

Autoencoders are useful in reservoir modelling because they learn a compact, low-dimensional representation of complex, high-dimensional geological realisations and can then reconstruct and generate new, plausible models from that representation. This provides an efficient parameterisation for assisted history matching, where the inverse problem can be tackled by searching in latent space rather than directly in the full grid/property space. We propose a graph-based variational autoencoder architecture (implemented as a Graph-based Wasserstein Autoencoder) to represent and condition geological models under uncertainty of geological scenarios. The key idea of the graph-based approach is to represent a geological model as a graph so that convolutions operate on connectivity and topology, which can better preserve geological structure than standard lattice/grid-based deep learning when geometries are curvilinear or discontinuous. We also introduce an implicit control of geological realism by incorporating geodesic metrics in latent space, reflecting its non-Euclidean internal geometry and helping guide sampling/optimisation toward dense, well-supported regions associated with realistic prior models. In this opening paper, we demonstrate the approach on a synthetic dataset of 3D channelised reservoirs with two scenarios (single-channel and double-channel realisations) as a proof of concept for the assisted history matching solution via a latent space. Finally, we analyse the learned latent space with Principal Component Analysis, t-distributed Stochastic Neighbour Embedding, and Topological Data Analysis to illustrate how geological variability and scenario structure are organised within the representation. • Utilisation of generative machine learning methods with graph convolutions to describe geological features of different natures in a single parametric space and identification dependencies implicitly. • Consideration the uncertainty of different geological scenarios in the process of history matching through the latent space of decreased dimensionality. • Implicit control of geological realism through the latent space allows for an efficient process of geological model history matching. • Geodesic metrics allows to work effectively in hidden space, increases efficiency and reliability of search and conditioning.