Lattice Boltzmann Simulations of the Klinkenberg Effect in Porous Media
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The numerical simulation of lattice Boltzmann method (LBM) is one of the most efficient methods to investigate the complex porous media structure, particularly the Klinkenberg effect. It is very useful to deal with the related complex boundary problems.The problems of gas flow through porous media are studied by using the lattice Boltzmann methods. Comparison between the numerical simulation results and the experimental results is carried out. It is shown that the lattice Boltzmamn method is one of the most efficient methods to simulate the problems of gas flow through complex porous media.Keywords:
Lattice Boltzmann methods
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Summary Digital images of porous media often include features approaching the image resolution length scale. The behavior of numerical methods at low resolution is therefore important even for well‐resolved systems. We study the behavior of the Shan‐Chen (SC) and Rothman‐Keller (RK) multicomponent lattice‐Boltzmann models in situations where the fluid‐fluid interfacial radius of curvature and/or the feature size of the medium approaches the discrete unit size of the computational grid. Various simple, small‐scale test geometries are considered, and a drainage test is also performed in a Bentheimer sandstone sample. We find that both RK and SC models show very high ultimate limits: in ideal conditions the models can simulate static fluid configuration with acceptable accuracy in tubes as small as three lattice units across for RK model (six lattice units for SC model) and with an interfacial radius of curvature of two lattice units for RK and SC models. However, the stability of the models is affected when operating in these extreme discrete limits: in certain circumstances the models exhibit behaviors ranging from loss of accuracy to numerical instability. We discuss the circumstances where these behaviors occur and the ramifications for larger‐scale fluid displacement simulations in porous media, along with strategies to mitigate the most severe effects. Overall we find that the RK model, with modern enhancements, exhibits fewer instabilities and is more suitable for systems of low fluid‐fluid miscibility. The shortcomings of the SC model seem to arise predominantly from the high, strongly pressure‐dependent miscibility of the two fluid components.
Lattice Boltzmann methods
Complex fluid
Length scale
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In this paper, the lattice Boltzmann method, a mesoscale numerical tool based on particle distribution function is used to simulate thermal fluid flow in porous media. The key point is to combine the simplest four and nine lattice velocity model to represent the temperature and density distribution functions respectively. A wide range of Rayleigh numbers and material's porosity was applied to study their effects on the thermal fluid flow in the enclosure. The numerical experiments demonstrated excellent agreements when the computed results were compared with those predicted by the finite element solution to the Brinkmann-Forccheimer equation and the conventional lattice Boltzmann scheme. This indicates the applicability of the present approach in the realistic simulation of thermal fluid flow in porous media.
Lattice Boltzmann methods
Boltzmann relation
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Lattice Boltzmann methods
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Lattice Boltzmann methods
Boltzmann relation
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Lattice Boltzmann methods
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Lattice Boltzmann methods
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The lattice Boltzmann method (LBM) is adopted to simulate natural convection in porous media at the representative elementary volume (REV) scale. The influence of porous media is considered by including the porosity into the equilibrium distribution function and by adding a force term to the evolution equation. The temperature field is simulated by a simplified thermal energy distribution function which neglects the compression work done by the pressure and the viscous heat dissipation. A comprehensive parametric study of natural convective flows is carried out for various values of Rayleigh number (Ra), of Darcy number (Da), and of porosity (ε). The results of the LBM indicate that the average Nusselt number (Nu) increases with the fluid Rayleigh number, the Darcy number, or the porosity of the medium. The comparison with those of earlier studies shows good quantitative agreement for the whole range of Darcy and Rayleigh numbers. It is reasonably concluded that the lattice Boltzmann method may have applicability to simulate natural convection in porous media.
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Abstract The lattice Boltzmann method is a relatively new simulation technique of computational fluid dynamic class. Its several advantages such as dealing with complex boundary and incorporating of microscopic interaction make it an alternative and promising numerical scheme for simulating fluid flow in porous media. Three lattice Boltzmann equation models are introduced and used for calculating permeability of a 2D porous media. Analytical solutions of Poiseuille flow between infinite parallel plates is used for validating lattice Boltzmann equation models. In the numerical simulations the effects of grid resolution and viscosity on the predicted permeability are checked.
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Hagen–Poiseuille equation
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A lattice Boltzmann description of fluid flow in heterogeneous porous media is presented which is intended for modeling flow processes which occur in liquid composite molding applications. The lattice Boltzmann method is equivalent to solving a hybrid method of the Stokes and Brinkman equations, with the Brinkman equation being implemented to model flow through porous structures, while the Stokes equation is applied to the open regions outside the porous structures. The Brinkman equation is recovered through a modification of the particle equilibrium distribution function, which reduces the magnitude of momentum at specified lattice sites, while leaving the direction of momentum unchanged. As a test of the new lattice Boltzmann model, steady transverse flow (saturated) through a square array of porous cylinders of elliptical cross section is investigated. Cell permeabilities obtained from the lattice Boltzmann simulations are in excellent agreement with a lubrication model, validating the lattice Boltzmann formulation of the Stokes and Brinkman equations.
Lattice Boltzmann methods
Boltzmann relation
Microscale chemistry
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