Suitability of 2D modelling to evaluate flow properties in 3D porous media

<p>Limitations stemming from the employment of 2D models to investigate the properties of 3D flows in porous media are generally overlooked. In this study, the extent to which 2D modelling can be employed for the representation of genuinely 3D flows in porous media is quantified. To this scope, Representative Elementary Volume (REV) sizes of 2D and 3D media sharing the same porosity are compared. The spatial stationarity of several Quantities of Interest (QoIs) namely, porosity, permeability, mean and variance of velocity, is numerically evaluated. In order to extend conclusions to transport phenomena, the analysis of the velocity variance, which is closely associated to the hydrodynamic dispersion process, is included. Porous media adopted in this study are composed by spheres and disks in 3D and 2D domains respectively, where both 2D and 3D geometries are characterized by random locations. Specifically, for 3D random packings creation, a sphere packing generator program is used. Pore scale flow is simulated by means of the Lattice Boltzmann Model (LBM): the LBM is employed as a numerical flow solver to reproduce the Darcy's experiment through the aforementioned domains. The LBM represents a powerful tool to model flow in porous media and it is able to accurately predict flow paths, permeability and hydraulic conductivity. Hydraulic QoIs are analysed at steady state conditions. To this purpose, the flow velocity field is used to inspect stationarity. The quantitative approaches adopted in the REV assessment procedure allow one to determine the residual variability of the quantity associated to the REV and consequently the level of accuracy that the modeller wants to achieve with respect to the QoIs. Such criteria show that REV estimations through 2D models are much larger than their 3D counterparts. In conclusion, pore scale LBM simulations highlight that the 2D approach leads to inconsistent results, due to the profound difference between 2D and 3D porous flows.</p>

MODELING OF POROUS MEDIA BY THE LATTICE BOLTZMANN METHOD

The principles of modeling heat and mass transfer and hydrodynamics of flows in porous media using the lattices Boltzmann method are considered. The methodology for implementing the Darcy law for the lattices Boltzmann method is shown. In contrast to traditional numerical schemes based on discretization of continuous medium equations, the lattices Boltzmann method is based on microscopic models and mesoscopic kinetic equations. The fundamental idea of the lattices Boltzmann method is to build such simplified kinetic models that include the existing physics of microscopic or mesoscopic processes so that the macroscopic averaged properties correspond to the required macroscopic equations. The main premise of using this simplified method is that the macroscopic dynamics of a fluid is the result of the collective behavior of many microscopic particles of the system. There are two approaches to modeling porous media using the lattices Boltzmann method. The first of them consists in modeling the spatial structure of the simulated system. Therefore, no additional factors need to be considered. The second approach is that the integrated characteristics of the porous medium (Darcy and Forheimer laws) are used to take into account the effect of porosity on the flow. The purpose of this paper is to show the realization of the linear law of hydrodynamic drag (Darcy) in porous media for the lattices Boltzmann method. Usually, the main goal of direct modeling is to determine the integral characteristics of a porous medium. The work considers the flow of fluid through a porous channel, which is formed between two flat walls. A method for implementing the Darcy law in the lattices Boltzmann method is shown. This work will help to simulate the heat transfer and hydrodynamics of flows in porous media without the use of commercial packages.