A greyscale volumetric lattice Boltzmann method for upscaling pore-scale two-phase flow

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 porescale 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.