Convective Instability in Porous Media, Volume II

A special issue of Fluids (ISSN 2311-5521).

Deadline for manuscript submissions: closed (1 December 2020) | Viewed by 26696

Special Issue Editors


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Guest Editor
Department of Mechanical Engineering, University of Bath, Bath BA2 7AY, UK
Interests: convection; porous media; instability; numerical simulation; asymptotic analysis; non-Newtonian fluids
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Guest Editor
Department of Industrial Engineering, Alma Mater Studiorum Università di Bologna, Viale Risorgimento 2, 40136 Bologna, Italy
Interests: stability analysis of convection flows in porous media; convection and instability of dissipative and non-Newtonian fluid flows; new features for the instability of shear flows.
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

The first Special Issue on convective instability in porous medium contained 14 papers covering a wide variety of topics under that general title. The issue included two excellent review articles and 12 papers that dealt with bidispersive effects, unsteady forcing effects, local thermal non-equilibrium, rotation, precipitation, viscoelastic fluids, ferrofluids, and more. To this end, the various authors employed linear theory, weakly nonlinear theory, strongly nonlinear simulations of various kinds, and theory for the absolute/convective instability transition theory. Given the success of that Special Issue, it has been decided to create a second edition, and papers are invited for this. The original Special Issue information remains applicable and it is reproduced below.

Many practical problems involving porous media in engineering, geophysics, and CO2 sequestration involve the simulation of what might be termed convection in a very wide sense. Such instabilities are always brought about by nonuniform buoyancy forces due to density changes, which, in turn, have arisen because of variations in the temperature and/or chemical composition of the fluid, or by miscible or immiscible displacements of heavier fluids by lighter fluids. The aim of this Special Issue is to collect together a wide variety of papers that have, as their unifying theme, the onset and subsequent development of convective instability. We intend there to be a strong emphasis on the methodology of solution, for reasons of pedagogy, for both analytical and numerical methods. Papers that involve those variants of Darcy’s law for which there is no formal support (i.e., REV averaging or experimental validation), will not feature in this Issue. Numerical accuracy will be of paramount importance.

Dr. D. Andrew Rees
Prof. Dr. Antonio Barletta
Guest Editors

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Keywords

  • porous media
  • instability
  • numerical simulation
  • Darcy–Bénard convection
  • boundary layers
  • fingering
  • bifurcations

Published Papers (8 papers)

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Research

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14 pages, 9871 KiB  
Article
Modeling Immiscible Fluid Displacement in a Porous Medium Using Lattice Boltzmann Method
by Magzhan Atykhan, Bagdagul Kabdenova (Dauyeshova), Ernesto Monaco and Luis R. Rojas-Solórzano
Fluids 2021, 6(2), 89; https://doi.org/10.3390/fluids6020089 - 22 Feb 2021
Cited by 4 | Viewed by 2174
Abstract
The numerical investigation of the interpenetrating flow dynamics of a gas injected into a homogeneous porous media saturated with liquid is presented. The analysis is undertaken as a function of the inlet velocity, liquid–gas viscosity ratio (D) and physical properties of the porous [...] Read more.
The numerical investigation of the interpenetrating flow dynamics of a gas injected into a homogeneous porous media saturated with liquid is presented. The analysis is undertaken as a function of the inlet velocity, liquid–gas viscosity ratio (D) and physical properties of the porous medium, such as porous geometry and surface wettability. The study aims to improve understanding of the interaction between the physical parameters involved in complex multiphase flow in porous media (e.g., CO2 sequestration in aquifers). The numerical simulation of a gaseous phase being introduced through a 2D porous medium constructed using seven staggered columns of either circular- or square-shaped micro-obstacles mimicking the solid walls of the pores is performed using the multiphase Lattice Boltzmann Method (LBM). The gas–liquid fingering phenomenon is triggered by a small geometrical asymmetry deliberately introduced in the first column of obstacles. Our study shows that the amount of gas penetration into the porous medium depends on surface wettability and on a set of parameters such as capillary number (Ca), liquid–gas viscosity ratio (D), pore geometry and surface wettability. The results demonstrate that increasing the capillary number and the surface wettability leads to an increase in the effective gas penetration rate, disregarding porous medium configuration, while increasing the viscosity ratio decreases the penetration rate, again disregarding porous medium configuration. Full article
(This article belongs to the Special Issue Convective Instability in Porous Media, Volume II)
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10 pages, 411 KiB  
Article
Instability of Vertical Throughflows in Porous Media under the Action of a Magnetic Field
by Florinda Capone, Roberta De Luca and Maurizio Gentile
Fluids 2019, 4(4), 191; https://doi.org/10.3390/fluids4040191 - 01 Nov 2019
Cited by 4 | Viewed by 1921
Abstract
The instability of a vertical fluid motion (throughflow) in a binary mixture saturating a horizontal porous layer, uniformly heated from below, uniformly salted from below by one salt and permeated by an imposed uniform magnetic field H , normal to the layer, is [...] Read more.
The instability of a vertical fluid motion (throughflow) in a binary mixture saturating a horizontal porous layer, uniformly heated from below, uniformly salted from below by one salt and permeated by an imposed uniform magnetic field H , normal to the layer, is analyzed. By employing the order-1 Galerkin weighted residuals method, the critical Rayleigh numbers for the onset of steady or oscillatory instability, have been determined. Full article
(This article belongs to the Special Issue Convective Instability in Porous Media, Volume II)
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18 pages, 5457 KiB  
Article
Unstable Density-Driven Flow in Fractured Porous Media: The Fractured Elder Problem
by Paiman Shafabakhsh, Marwan Fahs, Behzad Ataie-Ashtiani and Craig T. Simmons
Fluids 2019, 4(3), 168; https://doi.org/10.3390/fluids4030168 - 09 Sep 2019
Cited by 8 | Viewed by 3464
Abstract
The Elder problem is one of the well-known examples of an unstable density-driven flow (DDF) and solute transport in porous media. The goal of this research is to investigate the influence of fracture networks on this benchmark problem due to the great importance [...] Read more.
The Elder problem is one of the well-known examples of an unstable density-driven flow (DDF) and solute transport in porous media. The goal of this research is to investigate the influence of fracture networks on this benchmark problem due to the great importance of the fractured heterogeneity effect on unstable DDF. For this aim, the fractured Elder problem is solved using COMSOL Multiphysics, which is a finite element method simulator. Uniform and orthogonal fracture networks are embedded to analyze free convective flow and development of unstable salt plumes. The results indicate that the mesh sensitivity of the fractured Elder problem is greater than the homogeneous case. Furthermore, it has been shown that in the fractured cases, the onset of instability and free convection occur with lower critical Rayleigh number, which means that fracture networks have a destabilizing effect. Also, we examined the structural properties of fracture networks that control convective flow patterns, and the simulation results show that the strength of convection and instability at the beginning of the intrusion is proportional to the aperture size of the fractures. Moreover, the increase of the fracture’s density leads different modes of transient convective modes, until a specific fracture density after which the transient convective modes become similar to the homogenous case. Full article
(This article belongs to the Special Issue Convective Instability in Porous Media, Volume II)
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10 pages, 2608 KiB  
Article
Three-Dimensional Interaction of Viscous Fingering and Gravitational Segregation in Porous Media
by Tetsuya Suekane, Tomotaka Koe and Pablo Marin Barbancho
Fluids 2019, 4(3), 130; https://doi.org/10.3390/fluids4030130 - 12 Jul 2019
Cited by 12 | Viewed by 4661
Abstract
Viscous fingering is fluid dynamics instability induced on the displacement front when a less viscous fluid (LVF) displaces a more viscous fluid (MVF), thereby reducing the displacement efficiency. The displacement of a denser fluid by a less dense fluid produces a gravitational tongue. [...] Read more.
Viscous fingering is fluid dynamics instability induced on the displacement front when a less viscous fluid (LVF) displaces a more viscous fluid (MVF), thereby reducing the displacement efficiency. The displacement of a denser fluid by a less dense fluid produces a gravitational tongue. This gravitational segregation also reduces the displacement efficiency. In this study, the three-dimensional structure of the fingering pattern at the viscous fingering to gravitational segregation boundary was examined using X-ray microtomography on a packed bed of particles. At low gravity numbers, viscous fingering resembled that without gravity characterized by nonlinear interaction including tip-splitting, shielding, and coalescence. At intermediate gravity numbers, viscous fingering is associated with the gravitational tongue due to segregation. At high gravity numbers, a clear gravitational tongue penetrates from the inlet to the outlet. Consequently, the concentration near the injection point decreases and exhibits a flat profile in the flow direction. The displacement efficiency decreases with increasing gravity number, with the highest value achieved without gravity but depends on many factors, including the viscosity ratio and Péclet number. Full article
(This article belongs to the Special Issue Convective Instability in Porous Media, Volume II)
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16 pages, 1575 KiB  
Article
On Moderate-Rayleigh-Number Convection in an Inclined Porous Layer
by Baole Wen and Gregory P. Chini
Fluids 2019, 4(2), 101; https://doi.org/10.3390/fluids4020101 - 31 May 2019
Cited by 11 | Viewed by 3576
Abstract
We investigate the flow structure and dynamics of moderate-Rayleigh-number ( R a ) thermal convection in a two-dimensional inclined porous layer. High-resolution numerical simulations confirm the emergence of O ( 1 ) aspect-ratio large-scale convective rolls, with one ‘natural’ roll rotating in the [...] Read more.
We investigate the flow structure and dynamics of moderate-Rayleigh-number ( R a ) thermal convection in a two-dimensional inclined porous layer. High-resolution numerical simulations confirm the emergence of O ( 1 ) aspect-ratio large-scale convective rolls, with one ‘natural’ roll rotating in the counterclockwise direction and one ‘antinatural’ roll rotating in the clockwise direction. As the inclination angle ϕ is increased, the background mean shear flow intensifies the natural-roll motion, while suppressing the antinatural-roll motion. Our numerical simulations also reveal—for the first time in single-species porous medium convection—the existence of spatially-localized convective states at large ϕ , which we suggest are enabled by subcritical instability of the base state at sufficiently large inclination angles. To better understand the physics of inclined porous medium convection at different ϕ , we numerically compute steady convective solutions using Newton iteration and then perform secondary stability analysis of these nonlinear states using Floquet theory. Our analysis indicates that the inclination of the porous layer stabilizes the boundary layers of the natural roll, but intensifies the boundary-layer instability of the antinatural roll. These results facilitate physical understanding of the large-scale cellular flows observed in the numerical simulations at different values of ϕ . Full article
(This article belongs to the Special Issue Convective Instability in Porous Media, Volume II)
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13 pages, 5039 KiB  
Article
Inertial Effects on Dynamics of Immiscible Viscous Fingering in Homogenous Porous Media
by Shahid Rabbani, Hamid Abderrahmane and Mohamed Sassi
Fluids 2019, 4(2), 79; https://doi.org/10.3390/fluids4020079 - 21 Apr 2019
Cited by 11 | Viewed by 3481
Abstract
We present a comparative study of the onset and propagation dynamics of the fingering phenomenon in uniform porous media with a radial configuration. With the help of the Finite Element Method (FEM)-based 2D simulations and image processing techniques, we investigate finger morphology, growth [...] Read more.
We present a comparative study of the onset and propagation dynamics of the fingering phenomenon in uniform porous media with a radial configuration. With the help of the Finite Element Method (FEM)-based 2D simulations and image processing techniques, we investigate finger morphology, growth rate, interfacial length, finger length and the number of fingers which are affected due to inertial forces and convective acceleration in a two-phase porous media flow. We considered a modified Darcy’s law with inertial force coupled with convective acceleration and investigate their impact on interfacial instability with different velocity-viscosity combinations. Interestingly, the consequences of inertial corrections become significant with changes in viscosity at high Reynolds numbers. Due to the intrinsic bifurcation nature of inertial forces in the radial flow geometry, finger morphology is changed mostly at high viscosity ratios. We find that the effects of inertia and convective acceleration are markedly significant at relatively high Reynolds numbers while the interfacial length and the number of fingers—which are important parameters for Enhanced Oil Recovery (EOR)—are most affected by the neglecting of these forces. Moreover, at high Reynolds numbers, the rate of growth of fingering instabilities and the fractal number tend to deviate from that for Darcy’s law. Full article
(This article belongs to the Special Issue Convective Instability in Porous Media, Volume II)
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18 pages, 1014 KiB  
Article
Onset of Convection in an Inclined Anisotropic Porous Layer with Internal Heat Generation
by Leiv Storesletten and D. Andrew S. Rees
Fluids 2019, 4(2), 75; https://doi.org/10.3390/fluids4020075 - 16 Apr 2019
Cited by 28 | Viewed by 2779
Abstract
The onset of convection in an inclined porous layer which is heated internally by a uniform distribution of heat sources is considered. We investigate the combined effects of inclination, anisotropy and internal heat generation on the linear instability of the basic parallel flow. [...] Read more.
The onset of convection in an inclined porous layer which is heated internally by a uniform distribution of heat sources is considered. We investigate the combined effects of inclination, anisotropy and internal heat generation on the linear instability of the basic parallel flow. When the Rayleigh number is sufficiently large, instability occurs and a convective motion is set up. It turns out that the preferred motion at convection onset depends quite strongly on the anisotropy ratio, ξ , and the inclination angle. When ξ < 1 the preferred motion is in the form of longitudinal rolls for all inclinations. When ξ > 1 transverse rolls are preferred for small inclinations but, at high inclinations, longitudinal rolls are preferred. At intermediate inclinations the preferred roll orientation varies smoothly between these two extremes. Full article
(This article belongs to the Special Issue Convective Instability in Porous Media, Volume II)
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Review

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30 pages, 6678 KiB  
Review
Instability and Convection in Rotating Porous Media: A Review
by Peter Vadasz
Fluids 2019, 4(3), 147; https://doi.org/10.3390/fluids4030147 - 01 Aug 2019
Cited by 27 | Viewed by 3920
Abstract
A review on instability and consequent natural convection in rotating porous media is presented. Taylor-Proudman columns and geostrophic flows exist in rotating porous media just the same as in pure fluids. The latter leads to a tendency towards two-dimensionality. Natural convection resulting from [...] Read more.
A review on instability and consequent natural convection in rotating porous media is presented. Taylor-Proudman columns and geostrophic flows exist in rotating porous media just the same as in pure fluids. The latter leads to a tendency towards two-dimensionality. Natural convection resulting from density gradients in a gravity field as well as natural convection induced by density gradients due to the centripetal acceleration are being considered. The former is the result of gravity-induced buoyancy, the latter is due to centripetally-induced buoyancy. The effect of Coriolis acceleration is also discussed. Linear stability analysis as well as weak nonlinear solutions are being derived and presented. Full article
(This article belongs to the Special Issue Convective Instability in Porous Media, Volume II)
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