Abstract Lattice Boltzmann method (LBM) and pore network model (PNM) are two types of simulation methods for modelling the fluid flow in porous media at the pore scale. LBM is accurate in representing the pore structures but is computationally expensive, while PNM is very efficient but cannot capture the details of pore structures. In this work, we propose to couple these two methods to simulate two-phase drainage flow in porous media. To describe the throat geometry more accurately, an improved pore network extraction method is proposed based on watershed method, where throat bonds with real throat cross sections are extracted. A multi-relaxation-time color-gradient lattice Boltzmann model is adopted to simulate the flow properties for each throat bond, namely critical entry capillary pressure, capillary pressure – saturation relationship, single-phase conductance and relative conductance – saturation relationship for both phases, which are the input parameters for PNM simulations. To further improve the computational efficiency, five artificial neural network models are developed which relate the five flow properties to the actual shape of throat cross sections, where the shape is characterized by 9 parameters. The database consists of LBM simulations of the flow properties of 1421 throat cross sections extracted from 5 sandstone digital rocks. The trained artificial neural network models show much better performance than the conventional PNM when predicting the flow properties for each throat bond. Finally, the accuracy of the improved PNM coupled with LBM is validated by both the single-phase flow and two-phase drainage flow in a Berea sandstone.

中文翻译：

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孔隙尺度上多孔介质中准静态排水位移的模拟：耦合格子玻尔兹曼方法和孔隙网络模型

摘要 格子玻尔兹曼法（LBM）和孔隙网络模型（PNM）是在孔隙尺度下模拟多孔介质中流体流动的两种模拟方法。LBM 在表示孔隙结构方面是准确的，但计算成本很高，而 PNM 非常有效，但无法捕获孔隙结构的细节。在这项工作中，我们建议将这两种方法结合起来模拟多孔介质中的两相排水流。为了更准确地描述喉道几何形状，提出了一种基于分水岭法的改进的孔隙网络提取方法，提取具有真实喉道横截面的喉道键。采用多弛豫时间颜色梯度格子 Boltzmann 模型来模拟每个喉管键的流动特性，即临界入口毛细管压力、毛细管压力-饱和度关系，单相电导和相对电导 - 两相的饱和关系，这是 PNM 模拟的输入参数。为了进一步提高计算效率，开发了五种人工神经网络模型，将五种流动特性与喉部横截面的实际形状联系起来，其中形状由 9 个参数表征。该数据库包括从 5 个砂岩数字岩石中提取的 1421 个喉道横截面的流动特性的 LBM 模拟。在预测每个喉道粘结的流动特性时，经过训练的人工神经网络模型显示出比传统 PNM 更好的性能。最后，通过 Berea 砂岩中的单相流和两相排水流验证了改进的 PNM 与 LBM 相结合的准确性。