Macroscopic Modeling of Turbulent Mass Transport in Heterogeneous Porous Media

2004 ◽  
Author(s):  
Maximilian S. Mesquita ◽  
Marcelo J. S. de Lemos
Keyword(s):  
Porous Media ◽  
Mass Transport ◽  
Transport Model ◽  
Control Volume ◽  
Fluid Phase ◽  
Heterogeneous Porous Media ◽  
Macroscopic Model ◽  
Simple Method ◽  
Macroscopic Modeling ◽  
Flow Equations

In this work, results for a macroscopic mass transport model are presented for a parallel plate channel filled with a fluid saturated heterogeneous porous medium. The numerical methodology herein employed is based on the control volume approach. Turbulence is assumed to exist within the fluid phase. High and low Reynolds k-e models were used to model such non-linear effects. The flow equations at the pore-scale were numerically solved using the SIMPLE method applied to a non-orthogonal boundary-fitted coordinate system. Integrated mass fraction results were compiled leading to correlations for the mass dispersion coefficients in the x and y directions. Application of the macroscopic model using the proposed correlations showed the role of dispersion mechanism in the overall transport in porous media.

Mass Dispersion Coefficients for Turbulent Flow in an Infinite Porous Medium

Volume 1 ◽  
2004 ◽  
Author(s):  
Maximilian S. Mesquita ◽  
Marcelo J. S. de Lemos
Keyword(s):  
Porous Medium ◽  
Control Volume ◽  
Fluid Phase ◽  
Pore Scale ◽  
Simple Method ◽  
Flow Equations ◽  
Mass Dispersion ◽  
Spatially Periodic ◽  
Linear Effects ◽  
Control Volume Approach

In this work, mass dispersion tensors were calculated within an infinite porous medium formed by a spatially periodic array of longitudinally-displaced cylindrical rods. For the sake of simplicity, just one unit-cell, together with periodic boundary conditions for mass and momentum equations, and Neumann conditions for the mass concentration, was used to represent such medium. The numerical methodology herein employed is based on the control volume approach. Turbulence is assumed to exist within the fluid phase. High and low Reynolds k-e models were used to model such non-linear effects. The flow equations at the pore-scale were numerically solved using the SIMPLE method applied to a non-orthogonal boundary-fitted coordinate system. Integrated mass fraction results were compared with existing data in the literature.

A Lagrangian Porous Media Mass Transport Model

1984 ◽  
Vol 20 (3) ◽  
pp. 391-399 ◽  
Author(s):  
N. R. Thomson ◽  
J. F. Sykes ◽  
W. C. Lennox
Keyword(s):  
Porous Media ◽  
Mass Transport ◽  
Transport Model ◽  
Mass Transport Model

Wave propagation in heterogeneous porous media formulated in the frequency-space domain using a discontinuous Galerkin method

Geophysics ◽  
2011 ◽  
Vol 76 (4) ◽  
pp. N13-N28 ◽  
Author(s):  
Bastien Dupuy ◽  
Louis De Barros ◽  
Stephane Garambois ◽  
Jean Virieux
Keyword(s):  
Porous Media ◽  
Wave Propagation ◽  
Galerkin Method ◽  
Frequency Domain ◽  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Method ◽  
Solid Phase ◽  
Numerical Models ◽  
Fluid Phase ◽  
Heterogeneous Porous Media

Biphasic media with a dynamic interaction between fluid and solid phases must be taken into account to accurately describe seismic wave amplitudes in subsurface and reservoir geophysical applications. Consequently, the modeling of the wave propagation in heteregeneous porous media, which includes the frequency-dependent phenomena of the fluid-solid interaction, is considered for 2D geometries. From the Biot-Gassmann theory, we have deduced the discrete linear system in the frequency domain for a discontinuous finite-element method, known as the nodal discontinuous Galerkin method. Solving this system in the frequency domain allows accurate modeling of the Biot wave in the diffusive/propagative regimes, enhancing the importance of frequency effects. Because we had to consider finite numerical models, we implemented perfectly matched layer techniques. We found that waves are efficiently absorbed at the model boundaries, and that the discretization of the medium should follow the same rules as in the elastodynamic case, that is, 10 grids per minimum wavelength for a P0 interpolation order. The grid spreading of the sources, which could be stresses or forces applied on either the solid phase or the fluid phase, did not show any additional difficulties compared to the elastic problem. For a flat interface separating two media, we compared the numerical solution and a semianalytic solution obtained by a reflectivity method in the three regimes where the Biot wave is propagative, diffusive/propagative, and diffusive. In all cases, fluid-solid interactions were reconstructed accurately, proving that attenuation and dispersion of the waves were correctly accounted for. In addition to this validation in layered media, we have explored the capacities of modeling complex wave propagation in a laterally heterogeneous porous medium related to steam injection in a sand reservoir and the seismic response associated to a fluid substitution.

scholarly journals Macroscopic Model for Passive Mass Dispersion in Porous Media Including Knudsen and Diffusive Slip Effects

2021 ◽  
Vol 3 ◽  
Author(s):  
Francisco J. Valdés-Parada ◽  
Didier Lasseux
Keyword(s):  
Boundary Condition ◽  
Porous Media ◽  
Mass Transport ◽  
Gas Flow ◽  
Macroscopic Model ◽  
Type Model ◽  
Pore Scale ◽  
Advective Transport ◽  
Apparent Permeability ◽  
Slip Effects

In this work, a macroscopic model for incompressible and Newtonian gas flow coupled to Fickian and advective transport of a passive solute in rigid and homogeneous porous media is derived. At the pore-scale, both momentum and mass transport phenomena are coupled, not only by the convective mechanism in the mass transport equation, but also in the solid-fluid interfacial boundary condition. This boundary condition is a generalization of the Kramers-Kistemaker slip condition that includes the Knudsen effects. The resulting upscaled model, applicable in the bulk of the porous medium, corresponds to: 1) A Darcy-type model that involves an apparent permeability tensor, complemented by a dispersive term and 2) A macroscopic convection-dispersion equation for the solute, in which both the macroscopic velocity and the total dispersion tensor are influenced by the slip effects taking place at the pore-scale. The use of the model is restricted by the starting assumptions imposed in the governing equations at the pore scale and by the (spatial and temporal) constraints involved in the upscaling process. The different regimes of application of the model, in terms of the Péclet number values, are discussed as well as its extents and limitations. This new model generalizes previous attempts that only include either Knudsen or diffusive slip effects in porous media.

scholarly journals Macroscopic Modeling of In Vivo Drug Transport in Electroporated Tissue

2016 ◽  
Vol 138 (3) ◽  
Author(s):  
Bradley Boyd ◽  
Sid Becker
Keyword(s):  
Electric Field ◽  
Mass Transport ◽  
Drug Transport ◽  
Irreversible Electroporation ◽  
Drug Uptake ◽  
Macroscopic Model ◽  
Uniform Electric Field ◽  
Macroscopic Modeling ◽  
Reversible Electroporation

This study develops a macroscopic model of mass transport in electroporated biological tissue in order to predict the cellular drug uptake. The change in the macroscopic mass transport coefficient is related to the increase in electrical conductivity resulting from the applied electric field. Additionally, the model considers the influences of both irreversible electroporation (IRE) and the transient resealing of the cell membrane associated with reversible electroporation. Two case studies are conducted to illustrate the applicability of this model by comparing transport associated with two electrode arrangements: side-by-side arrangement and the clamp arrangement. The results show increased drug transmission to viable cells is possible using the clamp arrangement due to the more uniform electric field.

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