Statistics of highly heterogeneous flow fields confined to three-dimensional random porous media

Abstract

We present a strong relationship between the microstructural characteristics of, and the fluid velocity fields confined to, three-dimensional random porous materials. The relationship is revealed through simultaneously extracting correlation functions R_{uu}(r) of the spatial (Eulerian) velocity fields and microstructural two-point correlation functions S_{2}(r) of the random porous heterogeneous materials. This demonstrates that the effective physical transport properties depend on the characteristics of complex pore structure owing to the relationship between R_{uu}(r) and S_{2}(r) revealed in this study. Further, the mean excess plot was used to investigate the right tail of the streamwise velocity component that was found to obey light-tail distributions. Based on the mean excess plot, a generalized Pareto distribution can be used to approximate the positive streamwise velocity distribution.

Probability density function (PDF) models for particle transport in porous media

“…Similar statistics were found for the distribution of stream-wise Eulerian velocity for 2-dimensional synthetic fibrous media Matyka et al (2016). Jin et al (2016) analysed correlations in medium and flow properties as well as distributions of stream-wise velocities for different 3-dimensional porous media. These authors find similar behaviours for flow and structural correlation functions.…”

Upscaling of Anomalous Pore-Scale Dispersion

“…Meyer and Bijeljic (2016) used a Langevin approach to account for the impact of pore-scale velocity heterogeneity on solute dispersion. Due to their central role for transport upscaling from the pore to the Darcy scale, pore-scale particle velocities and their relation to the flow velocity and porous medium structure have been the subject of recent research (De Anna et al, 2013;Siena et al, 2014;Holzner et al, 2015;Morales et al, 2017;Jin et al, 2016;Matyka et al, 2016;De Anna et al, 2017;Dentz et al, 2018).…”

Velocity distributions, dispersion and stretching in three-dimensional porous media

“…(a). It provides the three velocity components with a higher spatial resolution (d/228) than the most recent numerical simulations performed at the pore scale(Maier et al 1998;Kang et al 2014;Jin et al 2016). …”