Fluid Flow Simulation in Random Porous Media at Pore Level Using Lattice Boltzmann Method

Abstract

Fluid flow in two dimensional random porous media is simulated at pore level using the Lattice Boltzmann Method. Random media are constructed by placing identical rectangles with a random distribution and free overlapping. Different domain resolutions are examined and it is shown that the effect of the domain resolution is negligible in the range examined. Simulations clearly indicate, for the same porosity, the permeability of the random porous media is lower than the permeability of the regularly ordered medium; the permeability, independently of the porous media organization, varies exponentially with the porosity. Average tortuosity of the flow is calculated and it is proposed its correlation with the porosity. The effect of the aspect ratio of the randomly placed obstacles on the predicted tortuosity and permeability is studied, and it is found that an increase of the obstacles' aspect ratio (height to width ratio) yields an increase of the tortuosity and consequent decrease of the permeability. The predicted values of the permeability and tortuosity are in close agreement with the data available in the literature.

Open Channel Flow over a Permeable River Bed

“…According to [7] and [8], fluid flow in a porous media shows some of the characteristics of flow in the absence of rigid matrix and in such a flow regime, the inertia and fluid shear stress effects not included in the Darcy model become significant affecting the flow characteristics. Flow in solid media or flow in the absence of a rigid matrix is governed by some fundamental laws based on the conservation of mass, momentum and energy.…”

Analytical tortuosity–porosity correlations for Sierpinski carpet fractal geometries

“…The concept of tortuosity was first introduced by Carman [7] in 1937 as a parameter that describes the average elongation of microscopic fluid flow (particle) pathways in porous media with respect to free flow [8]. In the subsequent and often cited Kozeny-Carman relationship, tortuosity is used to determine the permeability, K, of porous media, as follows [5,6]: where C KC , φ, and S are the Kozeny-Carman constant (shape factor), porosity, and specific surface area, respectively [9]. In the literature, most investigations of tortuosity involve porous media consisting of mono-sized (same-sized) particles, such as the analytical studies by Yun et al [10], Yu & Li [11], and Jian-Long et al [12] or the numerical studies by Koponen et al [6,13] and Matyka et al [14].…”

“…Tortuosity, τ , is a parameter frequently utilized in continuum models during estimates of effective flow and transport properties within porous media [5,6]. The concept of tortuosity was first introduced by Carman [7] in 1937 as a parameter that describes the average elongation of microscopic fluid flow (particle) pathways in porous media with respect to free flow [8].…”

Using cellular automata for porous media simulation

“…A short but complete review of LBM methods implementation for porous material study is given in [5]. Some of them are very sophisticated allowing for permeability prediction and calculating the tortuosity of the flow.…”