Pore-scale statistics of flow and transport through porous media

Abstract

Flow in porous media is known to be largely affected by pore morphology. In this work, we investigate the effects of pore geometry on the transport and spatial correlations of flow through porous media in two distinct pore structures arising from three-dimensional assemblies of overlapping and nonoverlapping spheres. Using high-resolution direct numerical simulations (DNS), we perform Eulerian and Lagrangian analysis of the flow and transport characteristics in porous media. We show that the Eulerian velocity distributions change from nearly exponential to Gaussian distributions as porosity increases. A stretched exponential distribution can be used to represent this behavior for a wide range of porosities. Evolution of Lagrangian velocities is studied for the uniform injection rule. Evaluation of tortuosity and trajectory length distributions of each porous medium shows that the model of overlapping spheres results in higher tortuosity and more skewed trajectory length distributions compared to the model of nonoverlapping spheres. Wider velocity distribution and higher tortuosity for overlapping spheres model give rise to non-Fickian transport while transport in nonoverlapping spheres model is found to be Fickian. Particularly, for overlapping spheres model our analysis of first-passage time distribution shows that the transport is very similar to those observed for sandstone. Finally, using three-dimensional (3D) velocity field obtained by DNS at the pore-scale, we quantitatively show that despite the randomness of pore-space, the spatially fluctuating velocity field and the 3D pore-space distribution are strongly correlated for a range of porous media from relatively homogeneous monodisperse sphere packs to Castlegate sandstone.

Role of Pore-Size Distribution on Effective Rheology of Two-Phase Flow in Porous Media

“…Above studies support the fact that, when up-scaled to a certain pore-network, both Binghum flow and two-phase flow is affected by the pore-size distribution and hence the topology of the of the network. The effect of pore size distribution has been explored extensively in case of a single phase flow where the distribution of local fluid velocity is observed to be affected by the distribution of pore-sizes [38][39][40][41][42]. In the present work we demonstrated how flow equations are affected by the pore-size distribution during a two-phase flow.…”

“…With that, Alim et al (2017) proposed an approach for single phase flow to predict the flow distribution from the geometrical properties of porous media that is based on Kirchhoff 's law for fluid mass conservation coupled with assumptions on the distribution of coordination numbers of pore bodies. There are more studies on the local velocity distribution for single phase flow (Siena et al, 2014;Wu et al, 2016;De Anna et al, 2017;Aramideh et al, 2018;An et al, 2020;Souzy et al, 2020), but detailed study for two-phase flow are lacking. Furthermore, Alim et al (2017) also emphasized that, in addition to the distribution of pore sizes, the local correlations between adjacent pores are necessary to predict the flow distribution.…”

Characterization and upscaling of hydrodynamic transport in heterogeneous dual porosity media

“…However, advective heterogeneity, this means velocity variability in the flowing medium portion, by itself gives rise to anomalous transport ( Bijeljic et al, 2011;De Anna et al, 2013;Kang et al, 2014;Puyguiraud et al, 2019 ). This is why the importance of pore-scale velocity statistics and their relation to the complex medium and heterogeneity structure have been studied in a series of recent experimental and numerical works ( Siena et al, 2014;Matyka et al, 2016;Holzner et al, 2015;De Anna et al, 2017;Alim et al, 2017;Dentz et al, 2018;Aramideh et al, 2018 ).…”

Pressure statistics from the path integral for Darcy flow through random porous media

“…There are two basic methods to simulate such flow through a porous medium [10]. One is to solve the Navier-Stokes equations at the pore level [11]. This method is computationally too intensive for our purposes, because our goal is to simulate the flow in a macroscopic volume that spans many pores.…”