Convection In Porous Medium Research Articles

Vigorous convection in porous media.

The problem of convection in a fluid-saturated porous medium is reviewed with a focus on 'vigorous' convective flow, when the driving buoyancy forces are large relative to any dissipative forces in the system. This limit of strong convection is applicable in numerous settings in geophysics and beyond, including geothermal circulation, thermohaline mixing in the subsurface and heat transport through the lithosphere. Its manifestations range from 'black smoker' chimneys at mid-ocean ridges to salt-desert patterns to astrological plumes, and it has received a great deal of recent attention because of its important role in the long-term stability of geologically sequestered CO2. In this review, the basic mathematical framework for convection in porous media governed by Darcy's Law is outlined, and its validity and limitations discussed. The main focus of the review is split between 'two-sided' and 'one-sided' systems: the former mimics the classical Rayleigh-Bénard set-up of a cell heated from below and cooled from above, allowing for detailed examination of convective dynamics and fluxes; the latter involves convection from one boundary only, which evolves in time through a series of regimes. Both set-ups are reviewed, accounting for theoretical, numerical and experimental studies in each case, and studies that incorporate additional physical effects are discussed. Future research in this area and various associated modelling challenges are also discussed.

Analysis of transport processes in a reacting flow of hybrid nanofluid around a bluff-body embedded in porous media using artificial neural network and particle swarm optimization

This paper investigates heat and mass transfer in a hybrid nanofluid flow impinging upon a cylindrical bluff-body embedded in porous media and featuring homogenous and heterogeneous chemical reactions. The analysis includes mixed convection and local thermal non-equilibrium in the porous medium as well as Soret and Dufour effects. Assuming single-phase mixture, a laminar flow of Al2O3-Cu-water (Aluminium oxide-Copper-water) hybrid nanofluid is considered and coupled transport processes are simulated computationally. Due to the significant complexity of this problem, containing a large number of variables, conventional approaches to parametric study struggle to provide meaningful outcomes. As a remedy, the simulation data are fed into an artificial neural network to estimate the target responses. This shows that the volume fraction of nanoparticles, interfacial area of the porous medium and mixed convection parameter, are of primary importance. It is also observed that small variation in the volume fraction of nanoparticles can considerably alter the response of thermal and solutal domains. Further, it is shown that the parameters affecting the thermal process can modify the problem chemically. In particular, raising the volume fraction of nanoparticles enhances the production of chemical species. Furthermore, particle swarm optimization is applied to predict correlations for Nusselt and Sherwood numbers through a systematic identification of the most influential parameters. The current study clearly demonstrates the advantages of using the estimator algorithms to understand and predict the behaviours of complex thermo-chemical and solutal systems.

On the unsteady forced convection in porous media subject to inlet flow disturbances-A pore-scale analysis

Heat convection response of a porous medium to the harmonic disturbances in the inlet flow is investigated in a configuration consisting of several obstacles. Navier Stokes and energy equations are solved computationally and the average Nusselt number around the obstacles is favourably compared against the existing empirical data. The Nusselt number fluctuations are then examined, revealing that the dynamical relations between the inlet flow fluctuations as the input and those of Nusselt number as the output, can be nonlinear. The extent of encountered nonlinearity is determined quantitatively through introduction of a measure of nonlinearity. It is shown that increases in the pore-scale Reynolds number can strengthen the nonlinearity. However, this is not a global trend and further increases in Reynolds number may push the system dynamics back to linear. Application of the concept of transfer function to the identified linear cases reveals that the frequency response of the Nusselt number closely resembles a classical low-pass filter. Further, through a statistical analysis, it is shown that thermal response of the porous medium is strongly dominated by those of the first few obstacles. This highlights the importance of taking pore-scale approach in the dynamical problems that involve heat convection in porous media.

Forced Convection in Porous Media Using Al2O3 and TiO2 Nanofluids in Differing Base Fluids

The following work presents a numerical evaluation of the use of TiO2 and Al2O3 nanofluids operating with ethylene glycol and water as base fluids—as well as an experimental evaluation of Al2O3-water nanofluid. Both numerical and experimental systems were tested and operated under various flow and heat transfer conditions, including four flow rates and three heat fluxes. When compared, the numerical schemes and experimental results showed deviation of under two degrees Celsius. This led the authors to conclude that the numerical scheme accurately reflected the experimental conditions. When all combinations of mixtures were compared numerically, it was found that ethylene glycol provided the highest average Nusselt number, while water offered significantly lower pumping requirements. When comparing nanoparticles, it was found that, in a carrying-fluid of water, TiO2 had superior performance by approximately one percent.

From Rayleigh–Bénard convection to porous-media convection: how porosity affects heat transfer and flow structure

We perform a numerical study of the heat transfer and flow structure of Rayleigh-B\'enard (RB) convection in (in most cases regular) porous media, which are comprised of circular, solid obstacles located on a square lattice. This study is focused on the role of porosity $\phi$ in the flow properties during the transition process from the traditional RB convection with $\phi=1$ (so no obstacles included) to Darcy-type porous-media convection with $\phi$ approaching 0. Simulations are carried out in a cell with unity aspect ratio, for the Rayleigh number $Ra$ from $10^5$ to $10^{10}$ and varying porosities $\phi$, at a fixed Prandtl number $Pr=4.3$, and we restrict ourselves to the two dimensional case. For fixed $Ra$, the Nusselt number $Nu$ is found to vary non-monotonously as a function of $\phi$; namely, with decreasing $\phi$, it first increases, before it decreases for $\phi$ approaching 0. The non-monotonous behaviour of $Nu(\phi)$ originates from two competing effects of the porous structure on the heat transfer. On the one hand, the flow coherence is enhanced in the porous media, which is beneficial for the heat transfer. On the other hand, the convection is slowed down by the enhanced resistance due to the porous structure, leading to heat transfer reduction. For fixed $\phi$, depending on $Ra$, two different heat transfer regimes are identified, with different effective power-law behaviours of $Nu$ vs $Ra$, namely, a steep one for low $Ra$ when viscosity dominates, and the standard classical one for large $Ra$. The scaling crossover occurs when the thermal boundary layer thickness and the pore scale are comparable. The influences of the porous structure on the temperature and velocity fluctuations, convective heat flux, and energy dissipation rates are analysed, further demonstrating the competing effects of the porous structure to enhance or reduce the heat transfer.

Dynamics of Convective Thermal Explosion in Porous Media

In this paper, we study complex dynamics of the interaction between natural convection and thermal explosion in porous media. This process is modeled with the nonlinear heat equation coupled with the nonstationary Darcy equation under the Boussinesq approximation for a fluid-saturated porous medium in a rectangular domain. Numerical simulations with the Radial Basis Functions Method (RBFM) reveal complex dynamics of solutions and transitions to chaos after a sequence of period doubling bifurcations. Several periodic windows alternate with chaotic regimes due to intermittence or crisis. After the last chaotic regime, a final periodic solution precedes transition to thermal explosion.

Effects of pore scale on the macroscopic properties of natural convection in porous media

Natural convection in porous media is a fundamental process for the long-term storage of CO2 in deep saline aquifers. Typically, details of mass transfer in porous media are inferred from the numerical solution of the volume-averaged Darcy–Oberbeck–Boussinesq (DOB) equations, even though these equations do not account for the microscopic properties of a porous medium. According to the DOB equations, natural convection in a porous medium is uniquely determined by the Rayleigh number. However, in contrast with experiments, DOB simulations yield a linear scaling of the Sherwood number with the Rayleigh number ( $Ra$ ) for high values of $Ra$ ( $Ra\gg 1300$ ). Here, we perform direct numerical simulations (DNS), fully resolving the flow field within the pores. We show that the boundary layer thickness is determined by the pore size instead of the Rayleigh number, as previously assumed. The mega- and proto-plume sizes increase with the pore size. Our DNS results exhibit a nonlinear scaling of the Sherwood number at high porosity, and for the same Rayleigh number, higher Sherwood numbers are predicted by DNS at lower porosities. It can be concluded that the scaling of the Sherwood number depends on the porosity and the pore-scale parameters, which is consistent with experimental studies.

A pore-scale assessment of the dynamic response of forced convection in porous media to inlet flow modulations

An increasing number of technologies require prediction of unsteady forced convection in porous media when the inlet flow is unsteady. To gain further insight into this problem, the unsteady equations of continuity, Navier Stokes and energy are solved within the pores formed by several cylindrical flow obstacles. The system is modulated by sine waves superimposed on the inlet flow velocity, and the spatio-temporal responses of the flow and temperature fields are calculated. The results are then utilised to assess the linearity of the thermal response represented by the Nusselt number on the obstacles. It is shown that for linear cases, a transfer function can be devised for predicting the dynamic response of the Nusselt number. It is further argued that such a transfer function can be approximated by a classic low-pass filter which resembles the average response of the individual obstacles. This indicates that there exists a frequency threshold above which the thermal system is essentially insensitive to flow modulations. The results also show that changes in Reynolds number and porosity of the medium can push the dynamic response of the system towards non-linearity. Yet, there appears to be no monotonic change in the linearity of the response with respect to the Reynolds number and porosity. In general, it is found that for low Reynolds numbers, the dynamics of heat convection can be predicted decently by taking a transfer function approach. The findings of this study can enable further understanding of unsteady forced convection in porous media subject to time-varying inlet flows.

Mathematical Modeling of Fluid Flow and Heat Transfer in Petroleum Industries and Geothermal Applications

This Special Issue of Energies is dedicated to all aspects of fluid flow and heat transfer in geothermal applications, including the ground heat exchanger, conduction, and convection in porous media [...]

The Effect of Throughflow on Weakly Nonlinear Convection in a Viscoelastic Saturated Porous Medium

In this paper we have investigated the effect of throughflow on thermal convection in a viscoelastic fluid saturated porous media. The governing equations are modelled in the presence of throughflow. These equations are made dimensionless and the obtained nonlinear problem solved numerically. There are two types of throughflow effects on thermal instability inflow and outflow investigated by finite amplitude analysis. This finite amplitude equation is obtained using the complex Ginzburg-Landau amplitude equation (CGLE) for a weak nonlinear oscillatory convection. The heat transport analysis is given by complex Ginzburg-Landau amplitude equation (CGLE). The numerical results indicate that due to the non-uniform throughflow there is instability at the bottom plate and influence the heat transfer in the system. The vertical throughflow is having both stable and unstable modes depending on flow direction. The nature of viscoelastic fluid is having both effects either stabilize or destabilize. Further, it is found that the nonlinear throughflow effects have dual role on heat transport. The solutions of the present problem are obtained numerically by using Runge-Kutta fourth order method.

An experimental study of density-driven convection of fluid pairs with viscosity contrast in porous media

CO2 dissolution in saline water during aquifer sequestration causes natural convection because of the density difference between CO2-saturated brine and native brine. In this study, the convective fingers behavior during convection in porous media was visualized by magnetic resonance imaging (MRI). Four kinds of miscible fluid pairs were used as the equivalents of CO2-saturated brine and native brine. Images of finger development were obtained. There are two types of convective fingers that form vertically symmetrical shapes: downward fingers of the dense fluid and upward fingers of the light fluid. The typical stages of natural convection, finger appearance, finger propagation, new finger generation, and finger coalescence were observed in this study. We analyzed the effects of viscosity contrast variation on convective onset. It was found that the viscosity contrast affects not only the convection time but also the finger growth velocity. The dimensionless mass transfer coefficient is characterized by the Sherwood number. The Sherwood number has a power law relationship with the Rayleigh number, with the exponent being larger than 1 for fluid pairs with apparent viscosity contrast. Experimental results showed that a higher viscosity contrast of the fluid pair causes a viscosity increase in the transition zone, resulting in lower mobility of the fluids and retarding convective mixing. For fluid pairs with similar densities, a high viscosity contrast is not conducive to efficient mass transfer in the density-driven convection process.

Terrestrial shallow water hydrothermal outflow characterized from out of space

We investigate the potential of satellite imagery to map and monitor the activity of shallow-water hydrothermal systems, which are often found around volcanic islands. For this study, we used publicly available data and proprietary WorldView-2 satellites images, with spectral bands that can penetrate up to water depths of 30 m. Shallow water hydrothermal sites are visible on satellite imagery, primarily with publicly available data, demonstrating the potential of satellite imagery to study and monitor shallow water hydrothermal activity. We focus our work on volcanic islands, showing intense near-shore, shallow-water hydrothermal activity, and distinct styles of hydrothermal venting. Satellite imagery constrains regional outflow geometry and the temporal variability or stability of these systems. Milos Island shows hydrothermal outflow associated with reflective mineral precipitates and/or bacterial mats, which are stable over time (2010–2014). These outflows locally define polygonal patterns likely associated with hydrothermal convection in porous media. In Kueishantao Island individual hydrothermal plumes charged with particles are visible at the sea surface, and display great variability in intensity and distribution of plume sources (2002–2019). Worldwide we have identified ~15 shallow water hydrothermal sites with satellite imagery, that are similar to either the Milos system (e.g., Vulcano and Panarea, Italy), or the Kueishantao system (numerous sites in Pacific volcanic islands). This study demonstrates that satellite imagery can be used to map and monitor different types of shallow-water hydrothermal systems, at regional scale, and monitor their evolution. Satellite data provide not only regional and temporal information on these systems, unavailable to date, but also the regional context for follow-up in situ field data and observations (e.g., instrumental monitoring, sampling, observations and mapping with divers or AUVs) to understand both the nature and dynamics of these systems, and ultimately the associated fluxes.

Two- and Three-Dimensional Absolute Instabilities in a Porous Medium with Inclined Temperature Gradient and Vertical Throughflow

A linear stability analysis for the onset of mixed convection in a saturated porous medium through an absolute instability of both two- and three-dimensional disturbances is performed. Relevant control parameters associated with the inclined temperature gradient and the vertical throughflow are the vertical and horizontal Rayleigh numbers, $$R_{\mathrm{v}}$$ and $$R_{\mathrm{h}}$$, and the vertical Peclet number, $$Q_{\mathrm{v}}$$, respectively. This work extends previous studies on the very same problem in two fronts. For two-dimensional disturbances, the present results do not agree with the literature for a few of the parametric conditions reported. This is caused by the collision of the convectively unstable downstream propagating branch with multiple upstream propagating branches, which generates several saddle points and, hence, makes the identification of the correct pinching point more difficult. In other words, literature results are all saddle points but not always pinching points. For three-dimensional disturbances, this issue is not present and the current results agree with the literature. On the other hand, due to the inherent difficulties associated with a three-dimensional absolute instability analysis, literature results have only been able to report the group velocities at the onset of convective instability. When their real parts are zero, transition occurs directly from stable to absolutely unstable. Otherwise, transition occurs from stable to convectively unstable first and nothing can be said about the onset of absolute instability. In this work, a novel technique recently developed by the authors allowed the identification of the onset of absolute instability under all parametric conditions investigated in the literature, extending earlier results. Doing so confirmed the dichotomy already observed in these earlier studies, i.e., the onset of absolute instability for two- and three-dimensional longitudinal modes indeed differs.

Numerical solution and Taguchi experimental method for variable viscosity and non-Newtonian fluids effects on heat and mass transfer by natural convection in porous media

Numerical solution and Taguchi experimental method for variable viscosity and non-Newtonian fluids effects on heat and mass transfer by natural convection in porous media

Numerical solution and Taguchi experimental method for variable viscosity and non-Newtonian fluids effects on heat and mass transfer by natural convection in porous media

In this article, both numerical solution and Taguchi method are presented to study the variable viscosity and non-Newtonian fluids effects on coupled heat and mass transfer by free convection over a vertical permeable plate in porous media. The surface temperature, concentration of the plate, and blowing/suction velocity are uniform. The viscosity of the fluid varies inversely as a linear function of the temperature. The partial differential equations are transformed into non-similar equations and solved by Keller box method. Numerical results of the local Nusselt number and local Sherwood number are expressed in the five parameters: 1) blowing/suction parameter ξ; 2) the power-law index of non-Newtonian fluid n; 3) buoyancy ratio N; 4) Lewis number Le; 5) viscosity-variation parameter θr. The best value for confirming the maximum of the local Nusselt (Sherwood) number by the Taguchi method is 6.6328 (10.3056).

Some Results About a Boundary Value Problem on Mixed Convection

The purpose of this paper is to study the autonomous third order non linear differential equation f’’’ + ff’’ + g(f’) = 0 on [0, +∞[ with g(x) = βx(x − 1) and β > 1, subject to the boundary conditions f(0) = a ∈ R, f’(0) = b < 0 and f’(t) → λ ∈ {0, 1} as t → +∞. This problem arises when looking for similarity solutions to problems of boundary-layer theory in some contexts of fluids mechanics, as mixed convection in porous medium or flow adjacent to a stretching wall. Our goal, here is to investigate by a direct approach this boundary value problem as completely as possible, say study existence or non-existence and uniqueness solutions and the sign of this solutions according to the value of the real parameter β.

UNCERTAINTY QUANTIFICATION FOR NATURAL CONVECTION IN RANDOM POROUS MEDIA WITH INTRUSIVE POLYNOMIAL CHAOS EXPANSION

The paper presents a framework for the construction of a stochastic projection method for the natural convection in random porous media under the local thermal nonequilibrium conditions. In this approach, the input stochastic field (porosity) is represented by the Karhunen−Loeve expansion and the output fields (e.g., velocity, pressure, fluid phase temperature, and solid phase temperature) are expressed by the polynomial chaos expansion. Using the spectral decomposition, the stochastic problem in random porous media is reformulated to a set of deterministic problems to be solved for each polynomial chaos. A stochastic projection method is implemented to obtain the chaos coefficients in the corresponding deterministic governing equations and the statistics of the numerical solution is obtained. The prediction results are compared against results obtained using a Monte Carlo method. Excellent agreement between these results indicates the efficiency and accuracy of the proposed method.

Impact of Low- or High-Permeability Inclusion on Free Convection in a Porous Medium

Density-driven free convection in porous media is highly affected by large-scale heterogeneity, typical of which are low- or high-permeability inclusions imbedded in homogeneous porous media. In this research, we applied the modified Elder problem to investigate the impact of low- or high-permeability inclusions on the migration of a dense, unstable salt plume. Sensitivity analyses were conducted in terms of the permeability contrast, the effective area (the area of the inclusion beneath the source zone), and the distance of the inclusion from the source zone, all of which were found to play a significant role in controlling the total mass flux released from the source into the media. Results show that (1) a high-permeability inclusion has stronger effects than low-permeability inclusion, due to significantly unbalanced solute distributions caused by accelerated solute transport, (2) the inclusion with a larger effective area has more potential to influence free convection, (3) free convection is more sensitive to the low-/high-permeability inclusion vertically closer to the source zone, and (4) free convection is more susceptible to the low-permeability inclusion horizontally closer to the source zone. For high-permeability inclusions, the inclusion horizontally closer to the source zone influences the transport process more significantly at the early stage, and conversely, the inclusion far from the source zone has a later impact. The results obtained could offer significant implications for understanding unstable density-driven flow and solute transport in porous media with structured heterogeneity.

Study of the Effect of Thermal Dispersion on Internal Natural Convection in Porous Media Using Fourier Series

Natural convection in a porous enclosure in the presence of thermal dispersion is investigated. The Fourier–Galerkin (FG) spectral element method is adapted to solve the coupled equations of Darcy’s flow and heat transfer with a full velocity-dependent dispersion tensor, employing the stream function formulation. A sound implementation of the FG method is developed to obtain accurate solutions within affordable computational costs. In the spectral space, the stream function is expressed analytically in terms of temperature, and the spectral system is solved using temperature as the primary unknown. The FG method is compared to finite element solutions obtained using an in-house code (TRACES), OpenGeoSys and COMSOL Multiphysics®. These comparisons show the high accuracy of the FG solution which avoids numerical artifacts related to time and spatial discretization. Several examples having different dispersion coefficients and Rayleigh numbers are tested to analyze the solution behavior and to gain physical insight into the thermal dispersion processes. The effect of thermal dispersion coefficients on heat transfer and convective flow in a porous square cavity has not been investigated previously. Here, taking advantage of the developed FG solution, a detailed parameter sensitivity analysis is carried out to address this gap. In the presence of thermal dispersion, the Rayleigh number mainly affects the convective velocity and the heat flux to the domain. At high Rayleigh numbers, the temperature distribution is mainly controlled by the longitudinal dispersion coefficient. Longitudinal dispersion flux is important along the adiabatic walls while transverse dispersion dominates the heat flux toward the isothermal walls. Correlations between the average Nusselt number and dispersion coefficients are derived for three Rayleigh number regimes.

Convective dissolution in porous media: experimental investigation in Hele‐Shaw cell

AbstractThe process of solutal convection in porous media is here studied experimentally in a Hele‐Shaw cell. Motivated by the carbon sequestration process, potassium permanganate and water are used to mimic the dissolution of carbon dioxide in brine in underground geological formations. An optical method is used to accurately reconstruct the solute concentration. In this work, we examine the influence of different calibration conditions on the measurement of the solute dissolution rate and we provide indications to improve the accuracy of the technique.