Physics-informed neural networks (PINNs) have received great attention as a promising paradigm for forward, inverse, and surrogate modeling of various physical processes with limited or no labeled data. However, PINNs are rarely used to predict two-phase flow in heterogeneous and fractured porous media, which is critical to lots of subsurface applications, due to the significant challenges in their training. In this work, we present an Enriched Physics-Informed Neural Network (E-PINN) to overcome these barriers and realize the simulation of such flow. Specifically, the Embedded Discrete Fracture Model (EDFM) is adopted to explicitly represent fractures, and then the finite volume method (FVM) instead of the Automatic Differentiation (AD) is used to evaluate spatial derivatives and construct the physics-informed loss function, so that the flux continuity between neighboring elements with different properties (e.g. matrix and fracture) can be defined rigorously. Besides, we develop a novel physics-informed neural network (NN) architecture adopting the adjacency-location anchoring, adaptive activation function, skip connection and gated updating to enrich the pressure information and enhance the learning ability of NN. Additionally, the initial and boundary conditions are constrained through a hard approach, which encodes them into network design, to improve the accuracy and efficiency of network training. In order to further reduce the difficulty of training, the Implicit-Pressure Explicit-Saturation (IMPES) scheme is used to calculate pressure and saturation, in which only the pressure needs to be solved by training NN. Finally, the superiority and applicability of E-PINN to complex practical problems is demonstrated through the simulations of immiscible displacement in 2D/3D heterogeneous and fractured reservoirs.

中文翻译：

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非均质和裂隙多孔介质中两相流的物理信息神经网络模拟


物理信息神经网络（PINN）作为一种有前途的范式受到了极大的关注，它可以在有限或无标记数据的情况下对各种物理过程进行正向、逆向和代理建模。然而，PINN 很少用于预测非均质和裂隙多孔介质中的两相流，这对于许多地下应用至关重要，因为它们的训练面临巨大挑战。在这项工作中，我们提出了一种丰富的物理信息神经网络（E-PINN）来克服这些障碍并实现此类流的模拟。具体来说，采用嵌入式离散断裂模型（EDFM）来显式地表示断裂，然后使用有限体积法（FVM）代替自动微分法（AD）来评估空间导数并构造物理信息损失函数，因此可以严格定义具有不同属性（例如基体和断裂）的相邻单元之间的通量连续性。此外，我们开发了一种新颖的物理信息神经网络（NN）架构，采用邻接位置锚定、自适应激活函数、跳跃连接和门控更新来丰富压力信息并增强神经网络的学习能力。此外，通过硬方法约束初始条件和边界条件，将其编码到网络设计中，以提高网络训练的准确性和效率。为了进一步降低训练难度，采用隐式压力显式饱和度（IMPES）方案来计算压力和饱和度，其中仅需要通过训练NN来求解压力。 最后，通过2D/3D非均质和裂缝性油藏非混相驱替模拟，证明了E-PINN对复杂实际问题的优越性和适用性。