Abstract A model combining the efficiency of the pore-network (PN) models and the accuracy of the lattice Boltzmann Method (LBM) is proposed. We introduce a multi-scale approach based on a decomposition of the granular assembly into small subsets. A tetrahedrization is considered to describe the pore space and extract the subsets. Hydrostatic properties such as entry capillary pressure, liquid morphology and capillary pressure - degree of saturation relationship are evaluated for each pore throat (subset) of the granular system. This information is incorporated into the pore-network model to reproduce the macro-scale effects during a primary drainage. The hybrid method is able to reproduce accurately the capillary pressure - volume relationship and the motion of the interface during the drainage process. The results obtained with the hybrid method evidence the capability of the method to investigate complex phenomena. Additionally, the combination of PN and LBM leads to a significant gain in terms of computation resources. Finally, the results obtained with a fully resolved LBM and the hybrid model help us validate the accuracy of pore-scale methods based on approximations (MS-P and Incircle methods).

中文翻译：

---

基于孔隙网络方法和格子 Boltzmann 方法的部分饱和介质混合多尺度模型

摘要 提出了一种将孔隙网络（PN）模型的效率与格子玻尔兹曼方法（LBM）的精度相结合的模型。我们引入了一种基于将粒度组件分解为小子集的多尺度方法。考虑使用四面体化来描述孔隙空间并提取子集。对于颗粒系统的每个孔喉（子集），评估流体静力学特性，例如入口毛细管压力、液体形态和毛细管压力 - 饱和度关系。该信息被纳入孔隙网络模型，以重现初级排水过程中的宏观效应。混合方法能够准确再现排水过程中的毛细管压力-体积关系和界面的运动。使用混合方法获得的结果证明了该方法研究复杂现象的能力。此外，PN 和 LBM 的组合导致计算资源方面的显着增益。最后，使用完全解析的 LBM 和混合模型获得的结果帮助我们验证基于近似值的孔隙尺度方法（MS-P 和 Incircle 方法）的准确性。