Abstract Solving image-based pore-scale flow and transport in porous materials is a mainstream of fundamental and industrial research to reveal the pertinent physics in the field of hydrogeology, reservoir engineering, paper and filter engineering. This research discipline requires tremendous integration of multidisciplinary research areas of image processing, computational fluid modelling, and high-performance computing. The key challenge in pore-scale multi-phase flow simulation is the overwhelming computational expense. In this paper, we develop a new computational method that integrates GPU-accelerated volumetric lattice Boltzmann method (VLBM) with an upscaling scheme to solve the pore-scale two-phase flow at the centimetre-level length scales. The lattice Boltzmann concept is employed to solve both the level-set equation for image segmentation and governing equations for multi-phase flow dynamics. The signed distance field solved from the level set equation is used to calculate the void volume ratio of each lattice cell, resulting in a seamless connection between image segmentation and computational fluid dynamics. The pore-scale porous materials upscaling is carried out through the average void volume ratio of the neighbouring cells. The algorithm is rigorously tested in three cases: contact angle test for droplets between two plates, co-current flow in a cylindrical tube, and the two-phase flow in a sandstone sample. For the sandstone sample, the porosity, void space topology, relative permeability and preferential flow channels are well retained after 8-times upscaling, while the computational time is dramatically decreased.

中文翻译：

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一种用于放大孔隙尺度两相流的灰度体积格子玻尔兹曼方法

摘要 解决多孔材料中基于图像的孔隙尺度流动和输运是基础和工业研究的主流，以揭示水文地质、储层工程、造纸和过滤工程领域的相关物理。该研究学科需要图像处理、计算流体建模和高性能计算等多学科研究领域的巨大整合。孔隙尺度多相流模拟的主要挑战是巨大的计算费用。在本文中，我们开发了一种新的计算方法，该方法将 GPU 加速的体积晶格玻尔兹曼方法 (VLBM) 与放大方案相结合，以解决厘米级长度尺度的孔隙尺度两相流。采用格子 Boltzmann 概念来求解用于图像分割的水平集方程和用于多相流动力学的控制方程。从水平集方程求解的带符号距离场用于计算每个晶格单元的空隙体积比，从而实现图像分割和计算流体动力学之间的无缝连接。孔尺度多孔材料的放大是通过相邻单元的平均空隙体积比进行的。该算法在三种情况下进行了严格测试：两块板之间的液滴接触角测试、圆柱管中的并流和砂岩样品中的两相流。对于砂岩样品，孔隙度、空隙空间拓扑结构、相对渗透率和优先流道在 8 倍放大后得到很好的保留，