We develop a proxy model based on deep learning methods to accelerate the simulations of oil reservoirs-by three orders of magnitudecompared to industry-strength physics-based PDE solvers. This paper describes a new architectural approach to this task, accompanied by a thorough experimental evaluation on a publicly available reservoir model. We demonstrate that in a practical setting a speedup of more than 2000X can be achieved with an average sequence error of about 10% relative to the oil-field simulator. The proxy model is contrasted with a high-quality physics-based acceleration baseline and is shown to outperform it by several orders of magnitude. We believe the outcomes presented here are extremely promising and offer a valuable benchmark for continuing research in oil field development optimization. Due to its domain-agnostic architecture, the presented approach can be extended to many applications beyond the field of oil and gas exploration.

Optimization of real-world black-box functions defined over purely categorical variables is an active area of research. In particular, optimization and design of biological sequences with specific functional or structural properties have a profound impact in medicine, materials science, and biotechnology. Standalone search algorithms, such as simulated annealing (SA) and Monte Carlo tree search (MCTS), are typically used for such optimization problems. In order to improve the performance and sample efficiency of such algorithms, we propose to use existing methods in conjunction with a surrogate model for the black-box evaluations over purely categorical variables. To this end, we present two different representations, a group-theoretic Fourier expansion and an abridged one-hot encoded Boolean Fourier expansion. To learn such representations, we consider two different settings to update our surrogate model. First, we utilize an adversarial online regression setting where Fourier characters of each representation are considered as experts and their respective coefficients are updated via an exponential weight update rule each time the black box is evaluated. Second, we consider a Bayesian setting where queries are selected via Thompson sampling and the posterior is updated via a sparse Bayesian regression model (over our proposed representation) with a regularized horseshoe prior. Numerical experiments over synthetic benchmarks as well as real-world RNA sequence optimization and design problems demonstrate the representational power of the proposed methods, which achieve competitive or superior performance compared to state-of-the-art counterparts, while improving the computation cost and/or sample efficiency, substantially.

The Thamama group of reservoirs consist of porous carbonates laminated with tight carbonates, with pronounced lateral heterogeneities in porosity, permeability, and reservoir thickness. The main objective of our study was mapping variations and reservoir quality prediction away from well control. As the reservoirs were thin and beyond seismic resolution, it was vital that the facies and porosity be mapped in high resolution, with a high predictability, for successful placement of horizontal wells for future development of the field. We established a unified workflow of geostatistical inversion and rock physics to characterize the reservoirs. Geostatistical inversion was run in static models that were converted from depth to time domain. A robust two-way velocity model was built to map the depth grid and its zones on the time seismic data. This ensured correct placement of the predicted high-resolution elastic attributes in the depth static model. Rock physics modeling and Bayesian classification were used to convert the elastic properties into porosity and lithology (static rock-type (SRT)), which were validated in blind wells and used to rank the multiple realizations. In the geostatistical pre-stack inversion, the elastic property prediction was constrained by the seismic data and controlled by variograms, probability distributions and a guide model. The deterministic inversion was used as a guide or prior model and served as a laterally varying mean. Initially, unconstrained inversion was tested by keeping all wells as blind and the predictions were optimized by updating the input parameters. The stochastic inversion results were also frequency filtered in several frequency bands, to understand the impact of seismic data and variograms on the prediction. Finally, 30 wells were used as input, to generate 80 realizations of P-impedance, S-impedance, Vp/Vs, and density. After converting back to depth, 30 additional blind wells were used to validate the predicted porosity, with a high correlation of more than 0.8. The realizations were ranked based on the porosity predictability in blind wells combined with the pore volume histograms. Realizations with high predictability and close to the P10, P50 and P90 cases (of pore volume) were selected for further use. Based on the rock physics analysis, the predicted lithology classes were associated with the geological rock-types (SRT) for incorporation in the static model. The study presents an innovative approach to successfully integrate geostatistical inversion and rock physics with static modeling. This workflow will generate seismically constrained high-resolution reservoir properties for thin reservoirs, such as porosity and lithology, which are seamlessly mapped in the depth domain for optimized development of the field. It will also account for the uncertainties in the reservoir model through the generation of multiple equiprobable realizations or scenarios.