scholarly journals MODELING OF POROUS MEDIA BY THE LATTICE BOLTZMANN METHOD

2020 ◽  
Vol 42 (3) ◽  
pp. 23-28
Author(s):  
A.A. Avramenko ◽  
A.I. Tyrinov ◽  
V.E. Domashev ◽  
A.V. Kovalenko
Keyword(s):  
Porous Medium ◽  
Porous Media ◽  
Kinetic Equations ◽  
Darcy Law ◽  
Hydrodynamic Drag ◽  
Flows In Porous Media ◽  
Microscopic Models ◽  
Simulated System ◽  
Integral Characteristics ◽  
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.

scholarly journals Predicting porosity, permeability, and tortuosity of porous media from images by deep learning

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
Krzysztof M. Graczyk ◽  
Maciej Matyka
Keyword(s):  
Neural Networks ◽  
Porous Medium ◽  
Porous Media ◽  
Deep Learning ◽  
Lattice Boltzmann ◽  
Good Accuracy ◽  
Two Dimensional ◽  
Empirical Estimate ◽  
Flow Through ◽  
Boltzmann Method

AbstractConvolutional neural networks (CNN) are utilized to encode the relation between initial configurations of obstacles and three fundamental quantities in porous media: porosity ($$\varphi$$ φ ), permeability (k), and tortuosity (T). The two-dimensional systems with obstacles are considered. The fluid flow through a porous medium is simulated with the lattice Boltzmann method. The analysis has been performed for the systems with $$\varphi \in (0.37,0.99)$$ φ ∈ ( 0.37 , 0.99 ) which covers five orders of magnitude a span for permeability $$k \in (0.78, 2.1\times 10^5)$$ k ∈ ( 0.78 , 2.1 × 10 5 ) and tortuosity $$T \in (1.03,2.74)$$ T ∈ ( 1.03 , 2.74 ) . It is shown that the CNNs can be used to predict the porosity, permeability, and tortuosity with good accuracy. With the usage of the CNN models, the relation between T and $$\varphi$$ φ has been obtained and compared with the empirical estimate.

scholarly journals Numerical Study of Suspension Filtration Model in Porous Medium with Modified Deposition Kinetics

Symmetry ◽  
2020 ◽  
Vol 12 (5) ◽  
pp. 696
Author(s):  
Bekzodjon Fayziev ◽  
Gafurjan Ibragimov ◽  
Bakhtiyor Khuzhayorov ◽  
Idham Arif Alias
Keyword(s):  
Porous Medium ◽  
Porous Media ◽  
Chemical Engineering ◽  
Numerical Study ◽  
Kinetic Equations ◽  
Sufficient Conditions ◽  
Computational Mathematics ◽  
Deposition Kinetics ◽  
Dynamic Factors ◽  
Suspension Filtration

Filtration is one of the most used technologies in chemical engineering. Development of computer technology and computational mathematics made it possible to explore such processes by mathematical modeling and computational methods. The article deals with the study of suspension filtration in a porous medium with modified deposition kinetics. It is suggested that deposition is formed in two types, reversible and irreversible. The model of suspension filtration in porous media consists of the mass balance equation and kinetic equations for each type of deposition. The model includes dynamic factors and multi-stage deposition kinetics. By using the symmetricity of porous media, the higher dimensional cases are reduced to the one-dimensional case. To solve the problem, a stable, effective and simple numerical algorithm is proposed based on the finite difference method. Sufficient conditions for stability of schemes are found. Based on numerical results, influences of dynamic factors on solid particle transport and deposition characteristics are analyzed. It is shown that the dynamic factors mainly affect the profiles of changes in the concentration of deposition of the active zone.

Lattice-Boltzmann Method for Macroscopic Porous Media Modeling

1998 ◽  
Vol 09 (08) ◽  
pp. 1491-1503 ◽  
Author(s):  
David M. Freed
Keyword(s):  
Porous Medium ◽  
Porous Media ◽  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Inertial Effects ◽  
Simulation Region ◽  
Flow Through ◽  
Previous Algorithm ◽  
Validation Tests ◽  
Boltzmann Method

An extension to the basic lattice-BGK algorithm is presented for modeling a simulation region as a porous medium. The method recovers flow through a resistance field with arbitrary values of the resistance tensor components. Corrections to a previous algorithm are identified. Simple validation tests are performed which verify the accuracy of the method, and demonstrate that inertial effects give a deviation from Darcy's law for nominal simulation velocities.

Reassessing the single relaxation time Lattice Boltzmann method for the simulation of Darcy’s flows

2016 ◽  
Vol 27 (04) ◽  
pp. 1650037 ◽  
Author(s):  
Pietro Prestininzi ◽  
Andrea Montessori ◽  
Michele La Rocca ◽  
Sauro Succi
Keyword(s):  
Porous Media ◽  
Relaxation Time ◽  
Lattice Boltzmann Method ◽  
Knudsen Number ◽  
Lattice Boltzmann ◽  
Physical Dependence ◽  
Single Relaxation Time ◽  
Flows In Porous Media ◽  
Percent Accuracy ◽  
Boltzmann Method

It is shown that the single relaxation time (SRT) version of the Lattice Boltzmann (LB) equation permits to compute the permeability of Darcy’s flows in porous media within a few percent accuracy. This stands in contrast with previous claims of inaccuracy, which we relate to the lack of recognition of the physical dependence of the permeability on the Knudsen number.

Thermodynamic Analysis of the Darcy Law

1961 ◽  
Vol 28 (2) ◽  
pp. 208-212 ◽  
Author(s):  
R. G. Mokadam
Keyword(s):  
Porous Medium ◽  
Porous Media ◽  
Fluid Flow ◽  
Gravitational Force ◽  
Equation Of Motion ◽  
Darcy Law ◽  
Navier Stokes ◽  
Proportionality Factor ◽  
Navier Stokes Equation ◽  
Special Case

The Darcy law is used extensively to describe the flow of fluids through porous media. According to this law the fluid flow is linearly dependent upon the pressure gradient and the gravitational force. The proportionality factor is generally known as the permeability of the porous medium. The Darcy law cannot be derived from the Navier-Stokes equation since this equation includes terms which characterize the fluid only. With the help of nonreversible thermodynamics it is possible to develop a general equation of motion of a fluid through a porous body, and obtain the Darcy law as a special case of such an equation.

scholarly journals Modeling Immiscible Fluid Displacement in a Porous Medium Using Lattice Boltzmann Method

Fluids ◽  
2021 ◽  
Vol 6 (2) ◽  
pp. 89
Author(s):  
Magzhan Atykhan ◽  
Bagdagul Kabdenova (Dauyeshova) ◽  
Ernesto Monaco ◽  
Luis R. Rojas-Solórzano
Keyword(s):  
Porous Medium ◽  
Porous Media ◽  
Lattice Boltzmann ◽  
Capillary Number ◽  
Viscosity Ratio ◽  
Penetration Rate ◽  
Surface Wettability ◽  
Gas Viscosity ◽  
Boltzmann Method ◽  
Gas Penetration

The numerical investigation of the interpenetrating flow dynamics of a gas injected into a homogeneous porous media saturated with liquid is presented. The analysis is undertaken as a function of the inlet velocity, liquid–gas viscosity ratio (D) and physical properties of the porous medium, such as porous geometry and surface wettability. The study aims to improve understanding of the interaction between the physical parameters involved in complex multiphase flow in porous media (e.g., CO2 sequestration in aquifers). The numerical simulation of a gaseous phase being introduced through a 2D porous medium constructed using seven staggered columns of either circular- or square-shaped micro-obstacles mimicking the solid walls of the pores is performed using the multiphase Lattice Boltzmann Method (LBM). The gas–liquid fingering phenomenon is triggered by a small geometrical asymmetry deliberately introduced in the first column of obstacles. Our study shows that the amount of gas penetration into the porous medium depends on surface wettability and on a set of parameters such as capillary number (Ca), liquid–gas viscosity ratio (D), pore geometry and surface wettability. The results demonstrate that increasing the capillary number and the surface wettability leads to an increase in the effective gas penetration rate, disregarding porous medium configuration, while increasing the viscosity ratio decreases the penetration rate, again disregarding porous medium configuration.

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