scholarly journals Reply to comment by A. Fiori et al. on “Asymptotic dispersion in 2D heterogeneous porous media determined by parallel numerical simulations”

2008 ◽  
Vol 44 (6) ◽  
Author(s):  
Jean Raynald de Dreuzy ◽  
Anthony Beaudoin ◽  
Jocelyne Erhel
Keyword(s):  
Porous Media ◽  
Numerical Simulations ◽  
Heterogeneous Porous Media ◽  
Asymptotic Dispersion

Miscible rectilinear displacements with gravity override. Part 2. Heterogeneous porous media

2000 ◽  
Vol 420 ◽  
pp. 259-276 ◽  
Author(s):  
EMMANUEL CAMHI ◽  
ECKART MEIBURG ◽  
MICHAEL RUITH
Keyword(s):  
Porous Media ◽  
Velocity Field ◽  
Numerical Simulations ◽  
Correlation Length ◽  
Resonant Interaction ◽  
Heterogeneous Porous Media ◽  
Direct Numerical Simulations ◽  
Buoyant Flows ◽  
Neutrally Buoyant ◽  
Strong Vorticity

The effects of permeability heterogeneities on rectilinear displacements with viscosity contrast and density variations are investigated computationally by means of direct numerical simulations. Physical interpretations are given in terms of mutual interactions among the three vorticity components related to viscous, density and permeability effects. In homogeneous environments the combined effect of the unfavourable viscosity gradient and the potential velocity field generated by the horizontal boundaries was seen to produce a focusing mechanism that resulted in the formation of a strong vorticity layer and the related growth of a dominant gravity tongue (Ruith & Meiburg 2000). The more randomly distributed vorticity associated with the heterogeneities tends to ‘defocus’ this interaction, thereby preventing the formation of the vorticity layer and the gravity tongue. When compared to neutrally buoyant flows, the level of heterogeneity affects the breakthrough recovery quite differently. For moderate heterogeneities, a gravity tongue still forms and leads to early breakthrough, whereas the same result is accomplished for large heterogeneities by channelling. At intermediate levels of heterogeneity, these tendencies partially cancel each other, so that the breakthrough recovery reaches a maximum. Similarly, the dependence of the breakthrough recovery on the correlation length is quite different in displacements with density contrasts compared to neutrally buoyant flows. For neutrally buoyant flows the resonant interaction between viscosity and permeability vorticities typically leads to a minimal recovery at intermediate values of the correlation length. In contrast, displacements with density contrast give rise to a gravity tongue for both very small and very large values of this length, so that the recovery reaches a maximum at intermediate values.

scholarly journals Modeling Longitudinal Dispersion in Variable Porosity Porous Media: Control of Velocity Distribution and Microstructures

2021 ◽  
Vol 3 ◽  
Author(s):  
Philippe Gouze ◽  
Alexandre Puyguiraud ◽  
Thierry Porcher ◽  
Marco Dentz
Keyword(s):  
Porous Media ◽  
Random Walk ◽  
Numerical Simulations ◽  
Dispersion Coefficient ◽  
Flow Distribution ◽  
Flow Speed ◽  
Direct Numerical Simulations ◽  
Hydrodynamic Dispersion ◽  
Geometrical Properties ◽  
Asymptotic Dispersion

Hydrodynamic dispersion process in relation with the geometrical properties of the porous media are studied in two sets of 6 porous media samples of porosity θ ranging from 0.1 to 0.25. These two sets of samples display distinctly different evolutions of the microstructures with porosity but share the same permeability trend with porosity. The methodology combines three approaches. First, numerical experiments are performed to measure pre-asymptotic to asymptotic dispersion from diffusion-controlled to advection-controlled regime using Time-Domain Random Walk solute transport simulations. Second, a porosity-equivalent network of bonds is extracted in order to measure the geometrical properties of the samples. Third, the results of the direct numerical simulations are interpreted as a Continuous Time Random Walk (CTRW) process controlled by the flow speed distribution and correlation. These complementary modeling approaches allow evaluating the relation between the parameters of the conceptual transport process embedded in the CTRW model, the flow field properties and the pore-scale geometrical properties. The results of the direct numerical simulations for all the 12 samples show the same scaling properties of the mean flow distribution, the first passage time distribution and the asymptotic dispersion vs. the Péclet number than those predicted by the CTRW model. It allows predicting the asymptotic dispersion coefficient D* from Pe = 1 to the largest values of Pe expected for laminar flow in natural environments (Pe≈ 4,000). D*∝Pe2−α for Pe≥Pecrit, where α can be inferred from the Eulerian flow distribution and Pecrit depends on porosity. The Eulerian flow distribution is controlled by the distribution of fractions of fluid flowing at each of the pore network nodes and thus is determined mainly by the distribution of the throat radius and the coordination number. The later scales with the number of throats per unit volume independently on the porosity. The asymptotic dispersion coefficient D* decreases when porosity increases for all Péclet values larger than 1 due to the increase with porosity of both α and the flow speed decorrelation length.

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