Journal
JOURNAL OF COMPUTATIONAL PHYSICS
Volume 477, Issue -, Pages -Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jcp.2023.111919
Keywords
Deep learning; Convolutional neural network; Porous media; Darcy flow; Physics informed
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The physics-informed convolutional neural network (PICNN) is developed for simulating transient two-phase Darcy flows in heterogeneous reservoir models with source/sink terms in the absence of labeled data. The finite volume method (FVM) is used to approximate the PDE residual in the loss function, and a well model is adopted to handle high pressure gradient near sources or sinks. The proposed approach is validated in homogeneous and heterogeneous reservoirs, and its efficiency and accuracy are discussed.
The physics-informed neural network (PINN) is a general deep learning framework for simulating flows with limited or no labeled data. In the current study, we develop a physics-informed convolutional neural network (PICNN) for simulating transient two-phase Darcy flows in heterogeneous reservoir models with source/sink terms in the absence of labeled data, where the finite volume method (FVM) is adopted to approximate the PDE residual in the loss function such that flux continuity between neighboring cells of different properties is defined rigorously, and a well model is adopted to approximate the high pressure gradient near sources or sinks. The implicit-pressure explicit-saturation (IMPES) scheme is employed such that only a single CNN needs to be trained per time step. Dirichlet boundary conditions are not a mandatory requirement for PICNN-based implicit solver but act as labeled data that can help enhance accuracy. The proposed approach is validated in homogeneous and heterogeneous reservoirs and aspects including efficiency and accuracy are discussed. In addition, we demonstrate that the CNN structure can be trained as a data-driven surrogate for two-phase Darcy flows given sufficient labeled samples. (c) 2023 Elsevier Inc. All rights reserved.
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