Dynamic Pore‐Scale Model of Drainage in Granular Porous Media: The Pore‐Unit Assembly Method

Abstract

Dynamics of drainage is analyzed for packings of spheres, using numerical experiments. For this purpose, a dynamic pore‐scale model was developed to simulate water flow during drainage. The pore space inside a packing of spheres was extracted using regular triangulation, resulting in an assembly of grain‐based tetrahedra. Then, pore units were constructed by identifying and merging tetrahedra that belong to the same pore, resulting in an assembly of pore units. Each pore unit was approximated by a volume‐equivalent regular shape (e.g., cube and octahedron), for which a local capillary pressure‐saturation relationship was obtained. To simulate unsaturated flow, a pore‐scale version of IMPES (implicit pressure solver and explicit saturation update) was employed in order to calculate pressure and saturation distributions as a function of time for the assembly of pore units. To test the dynamic model, it was used on a packing of spheres to reproduce the corresponding measured quasi‐static capillary pressure‐saturation curve for a sand packing. Calculations were done for a packing of spheres with the same grain size distribution and porosity as the sand. We obtained good agreement, which confirmed the ability of the dynamic code to accurately describe drainage under low flow rates. Simulations of dynamic drainage revealed that drainage occurred in the form of finger‐like infiltration of air into the pore space, caused by heterogeneities in the pore structure. During the finger‐like infiltration, the pressure difference between air and water was found to be significantly higher than the capillary pressure. Furthermore, we tested the effects of the averaging, boundary conditions, domain size, and viscosity on the dynamic flow behavior. Finally, the dynamic coefficient was determined and compared to experimental data.

Wettability Effects on Primary Drainage Mechanisms and NAPL Distribution: A Pore‐Scale Study

“…The pore-network extraction algorithm (Thompson et al, 2008) defined pore bodies similarly to the common definition of largest inscribed sphere in a pore space region (Scheidegger, 1958) but, additionally, employed a burn algorithm to associate pore voxels outside of each inscribed sphere to a pore body. The result is that the pores generated by this extraction algorithm are similar to pore units (e.g., Sweijen et al, 2016;Sweijen et al, 2017;Sweijen et al, 2018) as each identified pore body encompasses the entire pore volume between a set of grains as opposed to the pore volume encompassed by the largest 10.1029/2019WR025381 inscribed sphere. Throats are also defined in a similar manner to pore units as the facet area between two pore bodies and contain no volume.…”

Pore-Scale CO2 Displacement Simulation Based on the Three Fluid Phase Lattice Boltzmann Method

“…Alternatively, with the rapid development of computational software, several numerical and analytical methods have been proposed to simulate the multiphase flow in porous media. − Among these methods, the lattice Boltzmann method (LBM), a pore-scale numerical method based on the kinetic Boltzmann equation, has shown immense potential for investigating the microscale mechanism of the multiphase flow phenomenon. − Eshraghi et al reported that the LBM model could be used in the simulation of dendritic solidification with 36 billion grid points, and the parallel efficiency was almost 100% using 1000–4068 CPU cores. Li et al reported that the three-dimensional (3D) multiphase LBM simulation cases (model size: 512 × 256 × 256) could achieve a parallel efficiency of approximately 60% with 400K CPU cores using a hybrid, heterogeneous, multiple data programming model.…”

Transient Two-Phase Flow in Porous Media: A Literature Review and Engineering Application in Geotechnics

“…Joekar-Niasar and Hassanizadeh [150] studied dynamic capillary flow in angular pore network using DPNM and gave the same conclusion as Karadimitriou, Hassanizadeh, Joekar-Niasar and Kleingeld [51] that proposed constitutive surface (P c -S w -A nw ) exists for non-equilibrium drainage and imbibition but the difference between dynamic surface and static surface increases with both viscous forces and capillary number increase. Later, Sweijen, et al [219] upgraded the angular DPNM to the tetrahedra DPNM using the Discrete Element Method (DEM). Then, they carried out the DPNM simulation through the genuine tetrahedra pore unit formed by an assembly of granular particles.…”

“…Then, they carried out the DPNM simulation through the genuine tetrahedra pore unit formed by an assembly of granular particles. The same as Joekar-Niasar and Hassanizadeh [150], Sweijen, Hassanizadeh, Chareyre and Zhuang [219] also applied the static capillarity into pore-scale modelling and more focused on generating macroscale dynamic effects by regional heterogeneity. Finally, they concluded that regional heterogeneity-induced fingering flow formed dynamic capillarity effects in macroscale.…”