Deep Learning Accelerated Hydraulic-Mechanical Simulation with Prior Smoothness Constraints for Heterogeneous Petroleum Reservoirs

Abstract

Summary Coupled hydraulic-mechanical (HM) reservoir simulation requires tremendous efforts of development and is usually time-consuming. Consequently, the accurate yet fast simulation of poroelastic reservoirs is a challenge to traditional reservoir simulation methods. In this work, we aim to resolve this issue by replacing the geomechanical simulation module with a proxy stress predictor. We have developed a deep learning (DL)-based stress inference module to accelerate geomechanical simulation. The DL is based on convolutional neural network. We have constructed a 2D U-Net network, which takes the pressure, rock properties, and initial and boundary conditions as input and predicts the induced stress fields. We use the upper bound of the gradient of the stress field, which is from the a priori analysis of the mechanical governing equation, as a Lipschitz smoothness constraint. The model is trained with 80,000 pressure–stress pairs and demonstrates accuracy that is greater than 99%. We have augmented the trained network to a hydraulic reservoir simulator to conduct coupled HM simulation. Our results show that the proxy network effectively reduces the computational time of the mechanical module by more than 90% while still maintaining the accuracy of the physical simulator. The smoothness-constrained U-Net demonstrates significantly higher convergence rate and generalization capability. The novelty of this work is that it is arguably the first effort to combine a priori analysis of governing partial differential equations (PDE) with convolutional neural networks.