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

Abstract

The hydraulic conductivity (K) represents an important hydrophysical parameter in a porous media. K direct measurements, usually demand a lot of work, are expensive and time consuming. Factors such as the media spatial variability, sample size, measurement method, and changes in the sample throughout the experiment directly affect K evaluations. One alternative to K measurement is computer simulation using the Lattice Boltzmann method (LBM), which can help to minimize problems such as changes in the sample structure during experimental measurements. This work presents K experimental and theoretical results (simulated) for three regular finite arrangements of spheres. Experimental measurements were carried out aiming at corroborating the LBM potential to predict K once the smallest relative deviation between experimental and simulated results was 1.4%.

Calibrating Lattice Boltzmann flow simulations and estimating uncertainty in the permeability of complex porous media

“…LB methods are a popular way to simulate fluid flow [1,2,3,4,31] in many areas including material science [15,14], hydrology [11], biology [9] as well as the simulation of oil and gas behaviour in porous rock [32,33,34,35,36]. LB simulations of flow through pore geometries derived from real rocks have been used to estimate effective permeability [37] or relative permeability [38,39], using microporous rocks [40], sandstones [41] (even the same Fontainebleau sandstone that we use in this study [42]) and (typically with more complex porosity) carbonates [39].…”

“…We define the covariance matrices Σ 1 and Σ 2 (the subscripts indicate case number) in Equation (10) to be diagonal matrices containing the entries of Equations (14) and 15respectively on their diagonals, that is Σ 1,ii = 1 6 σ 2…”

“…Such simulations are often used to estimate particular quantities of interest concerning either the fluid flow or the porous medium. Amongst the most interesting flow properties in reservoir engineering (our current area of focus) is the permeability of porous subsurface rocks that contain fluid, and estimating permeability is important in a wide variety of other fields such as biology [5,6,7], medicine [8,9], soil science [10,11] and material science [12,13,14,15].…”

Numerical Simulation on Hydromechanical Coupling in Porous Media Adopting Three-Dimensional Pore-Scale Model

“…Breakthrough in this field can be summarized as two aspects: lattice Boltzmann method (LBM) and finite element method (FEM). In LBM, the discrete form of Boltzmann equation, which is solved over a regular lattice grid, is used to conduct the simulation of fluid flow in the porous media [ 10 , 11 ]. While Navier-Stokes equations are usually adopted in FEM [ 12 ], two-dimensional (2D) [ 13 , 14 ] and three-dimensional (3D) [ 15 – 17 ] pore networks of heterogeneous porous media are used in these simulations.…”