A physics-informed convolutional neural network (PICNN) is proposed to simulate two-phase flow in porous media with time-varying well controls. While most PICNNs in the existing literature worked on parameter-to-state mapping, our proposed network parameterizes the solutions with time-varying controls to establish a control-to-state regression. Firstly, a finite volume scheme is adopted to discretize flow equations and formulate a loss function that respects mass conservation laws. Neumann boundary conditions are seamlessly incorporated into the semi-discretized equations so no additional loss term is needed. The network architecture comprises two parallel U-Net structures, with network inputs being well controls and outputs being the system states (e.g., oil pressure and water saturation). To capture the time-dependent relationship between inputs and outputs, the network is well designed to mimic discretized state-space equations. We train the network progressively for every time step, enabling it to simultaneously predict oil pressure and water saturation at each timestep. After training the network for one timestep, we leverage transfer learning techniques to expedite the training process for a subsequent time step. The proposed model is used to simulate oil–water porous flow scenarios with varying reservoir model dimensionality, and aspects including computation efficiency and accuracy are compared against corresponding numerical approaches. The comparison with numerical methods demonstrates that a PICNN is highly efficient yet preserves decent accuracy.

Summary: Reservoir simulations for CO2 sequestration are computationally expensive because they rely on being run for large timescales. Shortened, cheaper simulation timelines prevent the observation of gas leakages that might occur over a longer duration. In the statistics community, the exclusion of these leakages is called censorship. We propose a fast simulator surrogate that captures these potentially unobservable long-term risks. The crux of our approach is survival analysis, a branch of statistics tailored to handle censored data. Our proposed framework begins by sampling scenarios with varied injection and production rates from a number of geological and flow uncertainty realizations. The potentially censored time to gas leakage is recorded for each simulated scenario. We then leverage a variety of survival analysis methods, ranging from Kaplan-Meier to random survival forests, to create a computationally cheap, and highly interpretable, simulator surrogate. The surrogate can predict the risk of CO2 leakage in new scenarios for significantly shorter simulations than usual in carbon sequestration studies, or no new simulations at all. This eases the computational burden of centuries-long, expensive simulations. To validate our methodology, we constructed an exploratory case study with a shortened monitoring window. The proposed framework is implemented within a compositional simulation model where CO2 is injected into a saline aquifer. To assess the risk of leakage and caprock integrity, we simulated scenarios where we inject CO2 for permanent storage using four injector wells, while five producer wells are used for pressure maintenance. This model is run for 2,000 days under varied permeability realizations to monitor CO2 breakthrough from the production wells. We then infer the occurrence of leakage in new scenarios and compare these results to full simulations via appropriate statistical metrics such as hypothesis testing, metrics tailored for the censored data context, and common prediction metrics. Initial results show that the proposed method predicts time to gas leakage with good accuracy without the need for any new simulations at all. To the best of the authors’ knowledge, this is the first paper to approach the broader reservoir engineering for carbon capture area with survival analysis, a clear fit due to the presence of censored data coming from shortened simulations. Our unique, novel framework yields a simulator surrogate built with techniques never before seen in this context. Also, we fill the gap other approaches leave open by focusing on interpretability, a model quality that is paramount to decision-making under high uncertainty.

Injecting greenhouse gas into deep underground reservoirs for permanent storage can inadvertently lead to fault reactivation, caprock fracturing and greenhouse gas leakage when the injection-induced stress exceeds the critical threshold. Extraction of pre-existing fluids at various stages of injection process, referred as pressure management, can mitigate associated risks and lessen environmental impact. However, identifying optimal pressure management strategies typically requires thousands of full-order simulations due to the need for function evaluations, making the process computationally prohibitive. This paper introduces a novel surrogate model-based reinforcement learning method for devising optimal pressure management strategies for geological CO2 sequestration efficiently. Our approach comprises two steps. Firstly, a surrogate model is developed through the embed to control method, which employs an encoder-transition-decoder structure to learn latent dynamics. Leveraging this proxy model, reinforcement learning is utilized to find an optimal strategy that maximizes economic benefits while satisfying various control constraints. The reinforcement learning agent receives the latent state space representation and immediate reward tailored for CO2 sequestration and choose real-time controls which are subject to predefined engineering constraints in order to maximize the long-term cumulative rewards. To demonstrate its effectiveness, this framework is applied to a compositional simulation model where CO2 is injected into saline aquifer. The results reveal that our surrogate model-based reinforcement learning approach significantly optimizes CO2 sequestration strategies, leading to notable economic gains compared to baseline scenarios.