scholarly journals Enhancement of plume dilution in two‐dimensional and three‐dimensional porous media by flow focusing in high‐permeability inclusions

2015 ◽  
Vol 51 (7) ◽  
pp. 5582-5602 ◽  
Author(s):  
Yu Ye ◽  
Gabriele Chiogna ◽  
Olaf A. Cirpka ◽  
Peter Grathwohl ◽  
Massimo Rolle
Keyword(s):  
Porous Media ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Flow Focusing ◽  
High Permeability

The competition between gravity and flow focusing in two-layered porous media

2013 ◽  
Vol 720 ◽  
pp. 5-14 ◽  
Author(s):  
Herbert E. Huppert ◽  
Jerome A. Neufeld ◽  
Charlotte Strandkvist
Keyword(s):  
Porous Media ◽  
Lower Layer ◽  
Flow Focusing ◽  
High Permeability ◽  
Critical Flux ◽  
Two Fluids ◽  
Input Flux ◽  
Layered Porous Media ◽  
Gravity Driven ◽  
Gravity Driven Flow

AbstractThe gravitationally driven flow of a dense fluid within a two-layered porous media is examined experimentally and theoretically. We find that in systems with two horizontal layers of differing permeability a competition between gravity driven flow and flow focusing along high-permeability routes can lead to two distinct flow regimes. When the lower layer is more permeable than the upper layer, gravity acts along high-permeability pathways and the flow is enhanced in the lower layer. Alternatively, when the upper layer is more permeable than the lower layer, we find that for a sufficiently small input flux the flow is confined to the lower layer. However, above a critical flux fluid preferentially spreads horizontally within the upper layer before ultimately draining back down into the lower layer. This later regime, in which the fluid overrides the low-permeability lower layer, is important because it enhances the mixing of the two fluids. We show that the critical flux which separates these two regimes can be characterized by a simple power law. Finally, we briefly discuss the relevance of this work to the geological sequestration of carbon dioxide and other industrial and natural flows in porous media.

scholarly journals Steady Flux Regime During Convective Mixing in Three-Dimensional Heterogeneous Porous Media

Fluids ◽  
2018 ◽  
Vol 3 (3) ◽  
pp. 58 ◽  
Author(s):  
Christopher Green ◽  
Jonathan Ennis-King
Keyword(s):  
Porous Media ◽  
Three Dimensional ◽  
Heterogeneous Porous Media ◽  
Three Dimensions ◽  
Two Dimensional ◽  
Anisotropic Porous Media ◽  
Initial Flow ◽  
Anisotropic Models ◽  
Convective Mixing ◽  
Heterogeneous Models

Density-driven convective mixing in porous media can be influenced by the spatial heterogeneity of the medium. Previous studies using two-dimensional models have shown that while the initial flow regimes are sensitive to local permeability variation, the later steady flux regime (where the dissolution flux is relatively constant) can be approximated with an equivalent anisotropic porous media, suggesting that it is the average properties of the porous media that affect this regime. This work extends the previous results for two-dimensional porous media to consider convection in three-dimensional porous media. Through the use of massively parallel numerical simulations, we verify that the steady dissolution rate in the models of heterogeneity considered also scales as k v k h in three dimensions, where k v and k h are the vertical and horizontal permeabilities, respectively, providing further evidence that convective mixing in heterogeneous models can be approximated with equivalent anisotropic models.

A NUMERICAL STUDY ON FRACTAL DIMENSIONS OF CURRENT STREAMLINES IN TWO-DIMENSIONAL AND THREE-DIMENSIONAL PORE FRACTAL MODELS OF POROUS MEDIA

Fractals ◽  
2015 ◽  
Vol 23 (01) ◽  
pp. 1540012 ◽  
Author(s):  
WEI WEI ◽  
JIANCHAO CAI ◽  
XIANGYUN HU ◽  
PING FAN ◽  
QI HAN ◽  
...  
Keyword(s):  
Porous Media ◽  
Fractal Dimension ◽  
Numerical Study ◽  
Three Dimensional ◽  
Fractal Dimensions ◽  
Simple Relation ◽  
Two Dimensional ◽  
Random Walker ◽  
Fractal Models ◽  
Novel Method

The fractal dimension of random walker (FDRW) is an important parameter for description of electrical conductivity in porous media. However, it is somewhat empirical in nature to calculate FDRW. In this paper, a simple relation between FDRW and tortuosity fractal dimension (TFD) of current streamlines is derived, and a novel method of computing TFD for different generations of two-dimensional Sierpinski carpet and three-dimensional Sierpinski sponge models is presented through the finite element method, then the FDRW can be accordingly predicted; the proposed relation clearly shows that there exists a linear relation between pore fractal dimension (PFD) and TFD, which may have great potential in analysis of transport properties in fractal porous media.

THREE-DIMENSIONAL APOLLONIAN NETWORKS

2006 ◽  
Vol 17 (08) ◽  
pp. 1219-1226 ◽  
Author(s):  
DANYEL J. B. SOARES ◽  
JOSÉ S. ANDRADE ◽  
HANS J. HERRMANN ◽  
LUCIANO R. da SILVA
Keyword(s):  
Porous Media ◽  
Three Dimensional ◽  
Small World ◽  
Clustering Coefficient ◽  
Force Chains ◽  
Two Dimensional ◽  
Space Filling ◽  
Scale Free ◽  
Wide Range ◽  
Granular Packings

We discuss the three-dimensional Apollonian network introduced by Andrade et al.1 for the two-dimensional case. These networks are simultaneously scale-free, small world, Euclidean, space-filling and matching graphs and have a wide range of applications going from the description of force chains in polydisperse granular packings to the geometry of fully fragmented porous media. Some of the properties of these networks, namely, the connectivity exponent, the clustering coefficient, the shortest path, and vertex betweenness are calculated and found to be particularly rich.

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