Abstract
Physics-informed neural networks (PINNs) are an efficient technique for incorporating physics law in models based on neural networks (NNs). In this paper, we propose a local refinement physics-informed convolutional neural network (LR-PICNN) to solve the seepage equation in closed boundary reservoirs. LR-PICNN employs a local refinement method to enhance focus on the region containing the well. First, the finite volume (FV) method is used to discretize the seepage equation on the global reservoir domain and on the local domain around the well to construct the loss functions respectively. Second, the boundary between the global and local domains are used as boundary conditions to couple the two systems. Finally, two loss functions are added to train the CNN to solve the seepage equation in autoregressive way and coupled without any labeled data. Experimental results show that LR-PICNN can more accurately solve seepage flow equation. Due to the coupling of solving equations and that LR-PICNN focuses on the behaviors of the well, compared to physics-informed Deep Convolutional neural network (PIDCNN) under the same well grid size, LR-PICNN has a faster solving speed that is at least 8 times faster, higher solution accuracy for BHP that is at least twice as high, and more stable solution, which could be used in numerical well testing.
Published Version
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