Lattice Boltzmann Modeling of Multicomponent Fluid Flow in Multiscale Porous Media

Resumo

Since its development, the lattice Boltzmann method (LBM) has proven to be an excellent tool for simulating multiphase/multicomponent fluid flows through porous media. Rooted in the kinetic theory of particles, the method effectively models the interactions at fluid interfaces between different phases. The discrete formulation of the lattice Boltzmann method, based on the processes of collision and streaming, enables the straightforward implementation of boundary conditions, making it particularly suitable for representing fluid flow in complex geometries. This capability is crucial for accurately modeling intricate solid structures, such as 3D microtomography images of porous media. Moreover, the LBM framework offers a high degree of parallelization on both CPUs and GPUs, allowing for near-perfect scalability in well-parallelized codes.However, in the LBM literature, the multiphase/multicomponent multiscale approaches (Spaid and Phelan Jr, 1998; McDonald and Turner, 2015; Pereira, 2016; Zalzale et al., 2016; Ning et al., 2019; An et al., 2020; Lautenschlaeger et al., 2022; Liu et al., 2024) usually keep the fluid segregation term within the porous-continuous media (PCM), thereby clearly identifying the immiscible fluid interface. This aspect eliminates the relative permeability resistance and the capillary pressure effects during fluid-fluid displacement, making it solely dependent on absolute permeability. Therefore, the present work proposes a multiscale multicomponent modeling by incorporating the non-linearity of relative permeability resulting from fluid–fluid interactions within the PCM region. To achieve this, the study combines pore-scale immiscible flow, represented by the Navier-Stokes equations, with the Buckley–Leverett equation to describe the non-linear mass balance of the two components. Additionally, the generalized porous continuous Navier-Stokes equation proposed by Nithiarasu et al. (1997) is employed to account for the momentum balance. By integrating these equations, the present work provides a comprehensive framework for modeling the PCM region, effectively capturing both mass and momentum dynamics influenced by non-linear relative permeability (described by Lomeland et al. (2005) correlation) and capillary pressure effects (described by Van Genuchten (1980) correlation).