Data-driven methods have been revolutionizing the way physicists and engineers handle complex and challenging problems even when the physics is not fully understood. However, these models very often lack interpretability. Physics-aware machine learning (ML) techniques have been used to endow proxy models with features closely related to the ones encountered in nature; examples span from material balance to conservation laws. In this study, we proposed a hybrid-based approach that incorporates physical constraints (physics-based) and yet is driven by input/output data (data-driven), leading to fast, reliable, and interpretable reservoir simulation models. To this end, we built on a recently developed deep learning–based reduced-order modeling framework by adding a new step related to information on the input–output behavior (e.g., well rates) of the reservoir and not only the states (e.g., pressure and saturation) matching. A deep-neural network (DNN) architecture is used to predict the state variables evolution after training an autoencoder coupled with a control system approach (Embed to Control—E2C) along with the addition of some physical components (loss functions) to the neural network training procedure. Here, we extend this idea by adding the simulation model output, for example, well bottom-hole pressure and well flow rates, as data to be used in the training procedure. Additionally, we introduce a new architecture to the E2C transition model by adding a new neural network component to handle the connections between state variables and model outputs. By doing this, it is possible to estimate the evolution in time of both the state and output variables simultaneously. Such a non-intrusive data-driven method does not need to have access to the reservoir simulation internal structure, so it can be easily applied to commercial reservoir simulators. The proposed method is applied to an oil–water model with heterogeneous permeability, including four injectors and five producer wells. We used 300 sampled well control sets to train the autoencoder and another set to validate the obtained autoencoder parameters. We show our proxy’s accuracy and robustness by running two different neural network architectures (propositions 2 and 3), and we compare our results with the original E2C framework developed for reservoir simulation.

Oil and gas field development optimization, which involves the determination of the optimal number of wells, their drilling sequence and locations while satisfying operational and economic constraints, represents a challenging computational problem. In this work, we present a deep-reinforcement-learning-based artificial intelligence agent that could provide optimized development plans given a basic description of the reservoir and rock/fluid properties with minimal computational cost. This artificial intelligence agent, comprising of a convolutional neural network, provides a mapping from a given state of the reservoir model, constraints, and economic condition to the optimal decision (drill/do not drill and well location) to be taken in the next stage of the defined sequential field development planning process. The state of the reservoir model is defined using parameters that appear in the governing equations of the two-phase flow (such as well index, transmissibility, fluid mobility, and accumulation, etc.,). A feedback loop training process referred to as deep reinforcement learning is used to train an artificial intelligence agent with such a capability. The training entails millions of flow simulations with varying reservoir model descriptions (structural, rock and fluid properties), operational constraints (maximum liquid production, drilling duration, and water-cut limit), and economic conditions. The parameters that define the reservoir model, operational constraints, and economic conditions are randomly sampled from a defined range of applicability. Several algorithmic treatments are introduced to enhance the training of the artificial intelligence agent. After appropriate training, the artificial intelligence agent provides an optimized field development plan instantly for new scenarios within the defined range of applicability. This approach has advantages over traditional optimization algorithms (e.g., particle swarm optimization, genetic algorithm) that are generally used to find a solution for a specific field development scenario and typically not generalizable to different scenarios. The performance of the artificial intelligence agents for two- and three-dimensional subsurface flow are compared to well-pattern agents. Optimization results using the new procedure are shown to significantly outperform those from the well pattern agents.