(312g) Velocity Distribution for Flow in Porous Media

Flow through porous media has been important in many fields and applications such as contaminant transport in aquifers, drug delivery in tissues, chemical reactions in packed bed reactors or surfactant travel in enhanced oil recovery. The transport in such processes is dominated by the fluid velocity in the pore space. Predicting the velocity distribution in porous media is especially significant in fixed bed reactors. Regions of very high or very low velocities may create ‘hot spots’ that lead to catalyst deactivation and reduce the efficiency of catalysts.

In this work, we investigated the three-dimensional velocity distributions of flow through the open space of porous media consisting of sphere packings and scaffolds with different configurations. The sphere packings were simple cubic (SC), body-centered cubic (BCC), face-centered cubic (FCC), randomly packed mono-disperse spheres, randomly packed bi-disperse spheres and tri-disperse sphere packing. Moreover, flow through a fiber scaffold in two different directions and flow through foam scaffolds are examined. Our intention was to find a common form of a statistical distribution that fitted the velocity distribution in various types of porous media. The flow of water through these porous media configurations was simulated by the Lattice Boltzmann method (LBM), which was carefully validated with analytical solutions [1]-[4]. Moreover, the velocity distribution of the flow through randomly packed spheres was validated against experimental results [5]. The velocity fields gained from the LBM method were normalized by the mean pore velocity and the probability density function (pdf) that resulted in each case was calculated. In addition, Kolgomorov-Smirnov (KS) goodness-of-fit tests were utilized to examine whether the velocity distributions followed any well-known forms of pdfs. These tests were performed on the software EASYFIT version 5.6. As a result, the Weibull distribution was found to well describe the distribution of dimensionless velocity magnitude in the examined porous types. However, velocity distributions in SC, BCC and FCC were represented by three different Weibull equations. On the contrary, there was one Weibull form could fit the velocity distributions in the remaining geometries. This observation relates to the differences in pore size distributions, which were analyzed by two methods including watershed methods and maximal ball techniques. The pore size distributions in the structured geometries (SC, BCC and FCC) shown by both methods appeared to be intermittent (i.e., discrete) while the rest were continuous.

It is therefore possible to predict a-priori the distribution of fluid velocities in a typical porous medium when one knows the mean pore velocity and utilizes a Weibull probability density function.

REFERENCES

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[2] R. S. Voronov, S. B. VanGordon, V. I. Sikavitsas, and D. V. Papavassiliou, “Efficient Lagrangian scalar tracking method for reactive local mass transport simulation through porous media,” Int. J. Numer. Methods Fluids, vol. 67, no. 4, pp. 501–517, Oct. 2011, doi: 10.1002/fld.2369.

[3] N. H. Pham, R. S. Voronov, N. R. Tummala, and D. V. Papavassiliou, “Bulk stress distributions in the pore space of sphere-packed beds under Darcy flow conditions,” Phys. Rev. E - Stat. Nonlinear, Soft Matter Phys., vol. 89, no. 3, pp. 1–13, 2014, doi: 10.1103/PhysRevE.89.033016.

[4] V. Nguyen, V. and D.V. Papavassiliou, “Hydrodynamic Dispersion in Porous Media and the Significance of Lagrangian Time and Space Scales,” Fluids, vol 5, no 22, Art 79, (21 pages) 2020; doi: 10.3390/fluids5020079

[5] M. Souzy, H. Lhuissier, Y. Méheust, T. Le Borgne, and B. Metzger, “Velocity distributions, dispersion and stretching in three-dimensional porous media,” J. Fluid Mech., 2020, doi: 10.1017/jfm.2020.113.