Comprehensive Numerical Study of Fluid Displacement in Homogeneous/Heterogeneous Microstructures with Consideration of Inertial Effects

Direct numerical simulation of flow in porous media plays an increasingly important role in understanding pore-scale flow physics and obtaining constitutive parameters for upscaling, thanks to the improvement of numerical models and increase in computational capability. Inertial effects are largely ignored in such simulations as the bulk Reynolds number is very small. Recent study¹ shows that the inertial effects have significant impact on the process of scCO₂ displacing brine in a heterogeneous micromodel and a real sandstone sample. However, whether the inertial effects play an important role in other fluid systems is unclear.

In this work, we employed a two-dimensional (2D) version of our well demonstrated high-performance lattice Boltzmann code¹ to perform a comprehensive study of fluid displacement in homogeneous/heterogeneous microstructures. By taking advantage of significantly reduced computational cost of 2D simulations and a highly efficient code, we were able to run over 1000 simulations and explore the effects of capillary number, viscosity ratio, contact angle, Ohnesorge number (inertial effects) and homogeneous/heterogeneous geometries, which gives a more comprehensive picture of the fluid displacement in porous media. The simulation results regarding the inertial effects agree well with our previous work¹ in heterogeneous geometries. We found the inertial effects in homogeneous geometries are less significant which also agrees with a previous study in the literature. In addition, when viscosity ratio and large capillary number come into play, the inertial effects show more complicated trends in certain cases compared to our previous study for the scCO₂-brine system. In summary, the work reexamined the role of different dimensionless numbers in multiphase flow in porous media which could provide a better understanding of the fluid displacement process, and the enormous simulation data could be used as training data in developing future fast flow solver based on physics informed machine learning.

1. Chen, Y., Valocchi, A. J., Kang, Q. & Viswanathan, H. S. Inertial Effects During the Process of Supercritical CO2 Displacing Brine in a Sandstone: Lattice Boltzmann Simulations Based on the Continuum-Surface-Force and Geometrical Wetting Models. Water Resour. Res. 55, 11144-11165 (2019).