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Transfer learning-based physics-informed convolutional neural network for simulating flow in porous media with time-varying controls

arXiv 2310.06319 ↗First posted 10 Oct 2023cs.LG cs.CEcited by 4

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Abstract (arXiv)

A physics-informed convolutional neural network is proposed to simulate two phase flow in porous media with time-varying well controls. While most of PICNNs in existing literatures worked on parameter-to-state mapping, our proposed network parameterizes the solution with time-varying controls to establish a control-to-state regression. Firstly, finite volume scheme is adopted to discretize flow equations and formulate 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. 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 timestep, 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 subsequent timestep. The proposed model is used to simulate oil-water porous flow scenarios with varying reservoir gridblocks and aspects including computation efficiency and accuracy are compared against corresponding numerical approaches. The results underscore the potential of PICNN in effectively simulating systems with numerous grid blocks, as computation time does not scale with model dimensionality. We assess the temporal error using 10 different testing controls with variation in magnitude and another 10 with higher alternation frequency with proposed control-to-state architecture. Our observations suggest the need for a more robust and reliable model when dealing with controls that exhibit significant variations in magnitude or frequency.

Key facts. Cited by 4 papers in the map (data through 7 Oct 2026). Builds on 19 of its 38 references that are in the map. First posted on arXiv 10 Oct 2023.

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19 of 38 references.

References · 19

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7 more
  1. 2022Physics-Informed Neural Networks with Adaptive Localized Artificial Viscositycited by 21
  2. 2020Deep-Learning based Inverse Modeling Approaches: A Subsurface Flow Examplecited by 13
  3. 2021A Gradient-based Deep Neural Network Model for Simulating Multiphase Flow in Porous Mediacited by 8
  4. 2022Deep Learning-Accelerated 3D Carbon Storage Reservoir Pressure Forecasting Based on Data Assimilation Using Surface Displacement from InSARcited by 7
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  6. 2023Physics-informed Convolutional Recurrent Surrogate Model for Reservoir Simulation with Well Controlscited by 4
  7. 2023Physics-Informed Localized Learning for Advection-Diffusion-Reaction Systemscited by 2

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