Prediction of Effective Diffusion and Dispersion Coefficients, Considering Different Flow and Heterogeneity Properties of Porous Media

2013 ◽  
Author(s):  
Jalal Abedi ◽  
Apostolos Kantzas ◽  
Saeed Taheri
Keyword(s):  
Porous Media ◽  
Effective Diffusion ◽  
Dispersion Coefficients

scholarly journals Laboratory Determination of Transverse and Longitudinal Dispersion coefficients in Porous Media

1996 ◽  
Vol 38 (1) ◽  
pp. 13-27 ◽  
Author(s):  
Makoto NISHIGAKI ◽  
Teddy SUDINDA ◽  
Y. SASAKI ◽  
M. INOUE ◽  
T. MORIWAKI
Keyword(s):  
Porous Media ◽  
Longitudinal Dispersion ◽  
Dispersion Coefficients ◽  
Laboratory Determination

Diffusion velocity lattice Boltzmann formulation applied to transport in macroscopic porous media

2014 ◽  
Vol 25 (12) ◽  
pp. 1441006 ◽  
Author(s):  
Janez Perko ◽  
Ravi A. Patel
Keyword(s):  
Porous Media ◽  
Diffusion Coefficient ◽  
Lattice Boltzmann ◽  
Diffusion Coefficients ◽  
Effective Diffusion ◽  
Hydrodynamic Dispersion ◽  
Traditional Treatment ◽  
Dissipative Term ◽  
Diffusion Velocity ◽  
Variable Diffusion

This paper describes the application of a single relaxation time (SRT) lattice Boltzmann scheme to the transport in porous media with large spatial variations of diffusion coefficients. Effective diffusion coefficients can vary substantially within porous media because of their dependence on porosity and tortuosity which can span over several orders of magnitude, depending on pore size and connectivity. Moreover, when mass is transported with pore-water in porous media, the hydrodynamic dispersion, which depends on Darcy's velocity, contributes additionally to the usually anisotropic variation of the dissipative term. In contrast to the traditional treatment of spatially variable diffusion coefficient by the variation of a SRT, here the variability is accommodated through the use of diffusion velocity formulation which allows for larger variabilities of diffusion coefficient. The volume averaged properties of mass transport in macroscopic porous media are resolved through the additional source term which is similar to the existing force adjusting methods. The applicability of both the proposed schemes is demonstrated on two examples. The first demonstrates that the method is accurate for the large variation of diffusion coefficients and porosities. The second example introduces mass diffusion in a real, geometrically complex system with spatially contrasting properties.

scholarly journals Mixing-scale dependent dispersion for transport in heterogeneous flows

2015 ◽  
Vol 777 ◽  
pp. 178-195 ◽  
Author(s):  
Marco Dentz ◽  
Felipe P. J. de Barros
Keyword(s):  
Porous Media ◽  
Velocity Fluctuation ◽  
Heterogeneous Porous Media ◽  
Coarse Grained ◽  
Dispersion Effect ◽  
Dispersion Coefficients ◽  
Velocity Fluctuations ◽  
Heterogeneous Flow ◽  
Scalar Dispersion ◽  
The Impact

Dispersion quantifies the impact of subscale velocity fluctuations on the effective movement of particles and the evolution of scalar distributions in heterogeneous flows. Which fluctuation scales are represented by dispersion, and the very meaning of dispersion, depends on the definition of the subscale, or the corresponding coarse-graining scale. We study here the dispersion effect due to velocity fluctuations that are sampled on the homogenization scale of the scalar distribution. This homogenization scale is identified with the mixing scale, the characteristic length below which the scalar is well mixed. It evolves in time as a result of local-scale dispersion and the deformation of material fluid elements in the heterogeneous flow. The fluctuation scales below the mixing scale are equally accessible to all scalar particles, and thus contribute to enhanced scalar dispersion and mixing. We focus here on transport in steady spatially heterogeneous flow fields such as porous media flows. The dispersion effect is measured by mixing-scale dependent dispersion coefficients, which are defined through a filtering operation based on the evolving mixing scale. This renders the coarse-grained velocity as a function of time, which evolves as velocity fluctuation scales are assimilated by the expanding scalar. We study the behaviour of the mixing-scale dependent dispersion coefficients for transport in a random shear flow and in heterogeneous porous media. Using a stochastic modelling framework, we derive explicit expressions for their time behaviour. The dispersion coefficients evolve as the mixing scale scans through the pertinent velocity fluctuation scales, which reflects the fundamental role of the interaction of scalar and velocity fluctuation scales in solute mixing and dispersion.

scholarly journals Mathematical Model for Effective Gas Diffusion Coefficient in Multi-scale Fractal Porous Media

2021 ◽  
Vol 248 ◽  
pp. 01026
Author(s):  
Du Zhehua
Keyword(s):  
Mathematical Model ◽  
Porous Media ◽  
Diffusion Coefficient ◽  
Fractal Dimension ◽  
Fractal Theory ◽  
Effective Diffusion ◽  
Gas Diffusion ◽  
Pore Connectivity ◽  
Multi Scale ◽  
Pore Area

Based on the capillary hypothesis and fractal theory, a mathematical model for calculating the effective gas diffusion coefficient in porous media is established. By using fractal geometry theory, pore area fractal dimension, tortuosity fractal dimension and pore connectivity are introduced to quantitatively characterize the real internal structure in the porous media. An effective gas diffusion coefficient model for the fractal porous media is derived, and the influence of multi-scale porous media microstructure parameters on the effective gas diffusion coefficient is discussed. The results show that effective gas diffusion coefficient approximates to linearly increase with the increase of porosity, the pore area fractal dimension and the effective gas diffusion coefficient is positive correlation, but the tortuosity fractal dimension is negatively related to it. In the case of different porosities, the gas effective diffusion coefficient varies with the change of the pore diameter ratio, the effective gas diffusion coefficient increases with the increase of pore connectivity.

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