Multifractal analysis of flow velocity simulated with the lattice model approach in idealized three-dimensional porous media

2007 ◽  
Vol 43 (12) ◽  
Author(s):  
F. J. Jiménez-Hornero ◽  
J. V. Giráldez ◽  
A. M. Laguna
Keyword(s):  
Porous Media ◽  
Flow Velocity ◽  
Lattice Model ◽  
Multifractal Analysis ◽  
Three Dimensional ◽  
Model Approach

MULTIFRACTAL DESCRIPTION OF SIMULATED FLOW VELOCITY IN IDEALISED POROUS MEDIA BY USING THE SANDBOX METHOD

Fractals ◽  
2013 ◽  
Vol 21 (01) ◽  
pp. 1350006 ◽  
Author(s):  
FRANCISCO J. JIMÉNEZ-HORNERO ◽  
ANA B. ARIZA-VILLAVERDE ◽  
EDUARDO GUTIÉRREZ DE RAVÉ
Keyword(s):  
Porous Media ◽  
Flow Velocity ◽  
Extreme Values ◽  
Three Dimensional ◽  
Fractal Dimensions ◽  
Counting Procedure ◽  
Velocity Magnitude ◽  
Box Counting ◽  
Multifractal Spectra ◽  
Few Data

The spatial description of flows in porous media is a main issue due to their influence on processes that take place inside. In addition to descriptive statistics, the multifractal analysis based on the Box-Counting fixed-size method has been used during last decade to study some porous media features. However, this method gives emphasis to domain regions containing few data points that spark the biased assessment of generalized fractal dimensions for negative moment orders. This circumstance is relevant when describing the flow velocity field in idealised three-dimensional porous media. The application of the Sandbox method is explored in this work as an alternative to the Box-Counting procedure for analyzing flow velocity magnitude simulated with the lattice model approach for six media with different porosities. According to the results, simulated flows have multiscaling behaviour. The multifractal spectra obtained with the Sandbox method reveal more heterogeneity as well as the presence of some extreme values in the distribution of high flow velocity magnitudes as porosity decreases. This situation is not so evident for the multifractal spectra estimated with the Box-Counting method. As a consequence, the description of the influence of porous media structure on flow velocity distribution provided by the Sandbox method improves the results obtained with the Box-Counting procedure.

Unsteady and porous media flow of reactive non-Newtonian fluids subjected to buoyancy and suction/injection

2015 ◽  
Vol 25 (7) ◽  
pp. 1682-1704 ◽  
Author(s):  
Tirivanhu Chinyoka ◽  
Daniel Oluwole Makinde
Keyword(s):  
Heat Transfer ◽  
Porous Media ◽  
Boundary Conditions ◽  
Flow Velocity ◽  
Flow System ◽  
Finite Difference Methods ◽  
Porous Media Flow ◽  
Convective Boundary Conditions ◽  
Convective Boundary ◽  
Content Type

Purpose – The purpose of this paper is to examine the unsteady pressure-driven flow of a reactive third-grade non-Newtonian fluid in a channel filled with a porous medium. The flow is subjected to buoyancy, suction/injection asymmetrical and convective boundary conditions. Design/methodology/approach – The authors assume that exothermic chemical reactions take place within the flow system and that the asymmetric convective heat exchange with the ambient at the surfaces follow Newton’s law of cooling. The authors also assume unidirectional suction injection flow of uniform strength across the channel. The flow system is modeled via coupled non-linear partial differential equations derived from conservation laws of physics. The flow velocity and temperature are obtained by solving the governing equations numerically using semi-implicit finite difference methods. Findings – The authors present the results graphically and draw qualitative and quantitative observations and conclusions with respect to various parameters embedded in the problem. In particular the authors make observations regarding the effects of bouyancy, convective boundary conditions, suction/injection, non-Newtonian character and reaction strength on the flow velocity, temperature, wall shear stress and wall heat transfer. Originality/value – The combined fluid dynamical, porous media and heat transfer effects investigated in this paper have to the authors’ knowledge not been studied. Such fluid dynamical problems find important application in petroleum recovery.

Fragmentation of viscous fingers in porous media: A three dimensional video microscopic study

Soft Matter ◽  
2012 ◽  
Vol 8 (21) ◽  
pp. 5791 ◽  
Author(s):  
Prerna Sharma ◽  
P Aswathi ◽  
Anit Sane ◽  
Shankar Ghosh ◽  
Sabyasachi Bhattacharya
Keyword(s):  
Porous Media ◽  
Microscopic Study ◽  
Three Dimensional ◽  
Viscous Fingers

scholarly journals Statistics of highly heterogeneous flow fields confined to three-dimensional random porous media

2016 ◽  
Vol 93 (1) ◽  
Author(s):  
C. Jin ◽  
P. A. Langston ◽  
G. E. Pavlovskaya ◽  
M. R. Hall ◽  
S. P. Rigby
Keyword(s):  
Porous Media ◽  
Three Dimensional ◽  
Flow Fields ◽  
Heterogeneous Flow ◽  
Random Porous Media
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