A novel reservoir simulation model based on physics informed neural networks

Surrogate models are widely used for reservoir simulations in the petroleum industry to improve computational efficiency. However, the traditional surrogate model mainly relies on the data collected from production wells (e.g., well bottom pressure data and well production data) and ignores the physical mechanism of underground fluid flow; therefore, the surrogate model will be invalid in the case of insufficient data samples. In response to these challenges, a Hard-Soft physics informed neural network (HS-PINN) was proposed to simulate pressure fluctuations around producing wells without relying on any labeled data, where two coupled fully connected neural networks were comprised to control the Hard and Soft constraint conditions. Specifically, in the “Soft Constraint” condition, we employ a modified Lorentz function to incorporate underground flow theory and permeability fields into the loss function. Meanwhile, in the “Hard Constraint” condition, we incorporate an enforcement function in the “output layer” to ensure the network outputs satisfy the boundary and initial conditions. To demonstrate the HS-PINN model's robustness and accuracy abilities, we tested it for single and multi-well production in both noisy low-fidelity and high-fidelity geologic reservoir environments, and the HS-PINN prediction errors were less than 1% in both cases compared to simulation results by the commercial software “COMSOL.” Additionally, we assessed the impacts of varying well interference intensities, adjustments in collocation points counts within the control equations, and diverse geological characteristics on model performance to validate the generalization and stability of HS-PINN. Moreover, the HS-PINN-based surrogate model significantly improves the efficiency of uncertainty quantification tasks compared to simulation-based approaches, requiring only 8% of the computational time. The deep-learning surrogate models developed in this work offer a novel and efficient approach for simulating reservoir development.