Theoretical-experimental analyses of simple geometry saturated conductivities for a Newtonian fluid

Abstract

The conductivity (K) of porous media represents an important physical parameter in several areas of knowledge. In saturated flow, the saturated conductivity (K 0 ) is the most important parameter of porous system and it is related to the fluid and porous media properties. In order to evaluate the potential of a new tool for measuring K 0 , such as the computational simulation with Boltzmann models for fluid flows, two experiments were carried out using two simplified media: 1) a cylindrical cavity and 2) a cavity having a parallelepiped shape. Both have simple geometries that allow analytical K 0 solutions in order to compare with the experimental and simulated results. Glycerin was used as infiltrate fluid due to its high viscosity that permits laminar flows and the use of Darcy's law to evaluate K 0 . The results demonstrate a good agreement among techniques (experimental, computational, and analytical) of K 0 determination for cavities that present Reynolds number (Re) smaller than one.

Lattice Boltzmann Method for Evaluating Hydraulic Conductivity of Finite Array of Spheres

“…An experimental apparatus tested by Camargo et al [ 8 ] was used for K experimental measurements ( Figure 1(a) ). The steps below were followed to determine K : (a) porous media saturation (acrylic box with a certain sphere arrangement) with glycerin, C 3 H 5 (OH) 3 , (manufactured by Biotec, 99.5% purity); (b) H length measurement (hydraulic load) and L (porous media height); (c) percolated glycerin mass measurement to obtain its volume, where the glycerin density is known; (d) measurement of the necessary time interval for the glycerin to percolate; (e) use of Darcy's Law to calculate conductivity using V = volume of percolated glycerin (cm 3 ), A = cross sectional area of the box containing spheres (cm 2 ), and t = time interval for a given volume of glycerin to percolate (s) [ 16 ]; (f) glycerin viscosity measurement using its flow through a D = 0.27 cm diameter acrylic cylinder and the analytical expression for the cylinder conductivity ν = ( D 2 /32)( g / K cylinder ): g = gravity acceleration (cm s −2 ); (g) K cylinder was measured using the steps (a) to (e).…”

“…One theoretical tool that can be successfully used to predict K is the Lattice Boltzmann method (LBM) [ 8 , 9 ]. The LBM is based on evolution of a relaxation equation for fluid particles distribution function, which is related to density and fluid macroscopic momentum.…”