Layer Of Porous Medium Research Articles

Onset of surface-tension-driven convection in superposed layers of fluid and saturated porous medium

The onset of surface-tension-driven convection is studied in a two-layer system comprising an incompressible fluid-saturated porous layer over which lies a layer of the same fluid. The lower rigid surface of the porous layer is either perfectly heat conducting or insulating, while the upper heat insulating fluid boundary is free and at which the surface tension effects are allowed for. At the contact surface between the fluid-saturated porous medium and the adjacent bulk fluid, both Beavers-Joseph and the Jones conditions are employed. The resulting eigenvalue problem is solved exactly. Besides, analytical expression for the critical Marangoni number is obtained for insulating boundaries by using regular perturbation technique. The effect of variation of different physical parameters on the onset of Marangoni convection is investigated in detail. It is found that the parameter ζ , the ratio of the thickness of the fluid layer to that of the porous layer, has a profound effect on the stability of the system.

The Effect of Heterogeneity on In-Situ Combustion: Propagation of Combustion Fronts in Layered Porous Media

Summary In-situ combustion is a potential method for the recovery of heavy oil. The effect of reservoir heterogeneity, a ubiquitous feature of oil reservoirs, on in-situ combustion has not been systematically addressed in prior studies, however. In this paper, we present analytical models for filtration combustion, namely the combustion of a stationary solid fuel, in the specific case where the reservoir consists of two layers of different permeability and thickness, separated by nearly impermeable shales. We investigate the conditions for the propagation of steady combustion fronts as a function of some key parameters, including the permeability-thickness contrast R between the layers, the thickness ratio η, and the external heat loss coefficient h. We find that heterogeneity acts in two distinct ways: It reduces the temperature of the leading front in the high-permeability layer in all cases, and uncouples the propagation of the fronts in the two layers if R is smaller than a critical value Rc. The first effect may lead to low-temperature oxidation conditions, and therefore to the effective extinction of the front in the high-permeability layer. The second leads to a reduced sweep efficiency (and early breakthrough). However, if R exceeds the critical value, the fronts in the two layers travel coherently (with the same speed). This coherence is identified for the first time. The resulting thermal coupling greatly retards the front in the more permeable layer, and accelerates only slightly that in the less permeable one, until the two fronts reach a common velocity. We study the effects of R, the heat loss rate, and the ratio of thickness η. The coupling is aided by moderate heat losses (small h), and smaller η, which affect the critical value Rc.Asinthe homogeneous case, at sufficiently high heat loss rates, steady front propagation cannot be sustained and the combustion process becomes extinct. The work is useful for the understanding of the viability of in-situ combustion process in heterogeneous layered reservoirs and the effect of a number of injection, combustion, and reservoir parameters.

Investigation of the magnetic fluid mass transfer in porous media

Introduction. Variety of physical effects of the mass transfer process in porous media can be described by the equations of irreversible thermodynamics [1]. It is possible to employ the Onsagers assumption of linear dependence of the mass flow on corresponding force gradients at small deviation from the equilibrium state. Some phenomenological laws exist, which linearly describe the irreversible physical processes. If two or more of these phenomena take place simultaneously, they overlay and cause new effects. By substitution of dissolved substance molar mass with the mass of colloidal particle, it is possible to describe the transfer processes with the same molecular–kinetic equations as those of molecular solutions. The magnetic fluid is identified as a binary solution and the thermodynamics of irreversible processes is employed to describe the mass transfer processes in porous media in this investigation. The changes in composition and structure in the boundary layers of porous media affect not only the flow velocity but cause some additional effects: capillary osmosis – a mass flow under the influence of diluted substance gradient∇C, thermoosmosis – a flow under the influence of temperature gradient ∇T , electroosmosis – a flow under the influence of electric field gradient ∇E. These effects may be expressed separately or as associated phenomena of filtration flow. This is the reason why the mass transfer processes in porous media must be solved taking into account the combined action of all gradients. Consequently, it is necessary to take into account the mass fluxes of different components of the solution as well as the flux of energy and the electric charge.

Application of the heterogeneous (HG) blankets for controlling the base structure vibration levels

This work presents an extensive analysis of the properties of the heterogeneous blankets (HGs) and their effectiveness in controlling the vibration of the base structures. The HG blankets act as a distributed vibration absorbers consisting of mass inhomogeneities inside a layer of porous media (acoustic foam). To asses the effectiveness of these HG blankets in controlling the vibration of the base structure (plate), detailed finite element (FE) models of the foam, the HG blanket, and the plate have been developed. The foam has been dicretized using the eight node hexahedral elements. The HG blanket model consists of the foam model with point masses attached to the nodes of the elements. The structural (plate) domain is discretized using four node rectangular plate elements. Each of the FE models has been individually validated by comparing the numerical results with their respective analytical and experimental results. The structural and the HG blanket FE models were then combined into a larger FE model comprised of a base plate with the HG treatment on its surface. The results from this numerical model have shown that there is a significant reduction in the vibration levels of the base plate due to the HG treatment on it.

Developing fluid flow and heat transfer in a channel partially filled with porous medium

A three-dimensional computational model is developed to analyze fluid flow in a channel partially filled with porous medium. In order to understand the developing fluid flow and heat transfer mechanisms inside the channel partially filled with porous medium, the conventional Navier–Stokes equations for gas channel, and volume-averaged Navier–Stokes equations for porous medium layer are adopted individually in this study. Conservation of mass, momentum and energy equations are solved numerically in a coupled gas and porous media domain along a channel using the vorticity–velocity method with power law scheme. Detailed development of axial velocity, secondary flow and temperature field at various axial positions in the entrance region are presented. The friction factor and Nusselt number are presented as a function of axial position, and the effects of the size of porous media inside the channel partially filled with porous medium are also analyzed in the present study.

Steady filmwise condensation with suction on a finite-size horizontal flat plate embedded in a porous medium based on Brinkman and Darcy models

The steady filmwise condensation outside a finite-size horizontal plate covered with a thick porous medium layer is investigated numerically by boundary layer approximations and Brinkman model. The fourth-order Runge–Kutta scheme and shooting method are employed to solve numerically the nonlinear ordinary differential equation. The results are presented in terms of the dimensionless average Nusselt number Nu ¯ and the dimensionless condensate thickness δ L ∗ ¯ . It is shown from the results presented that the Nusselt number increases with increasing suction parameter and it is also the function of various parameters, such as Darcy number, Da, Jacob number, Ja, Prandtl number, Pr, modified Rayleigh number for a porous medium, Ra, and permeability parameter, λ 0 . It is also shown that the boundary effect plays an important role for the condensation heat transfer rate in a porous medium.

High‐Permeability Layers for Remediation of Ground Water; Go Wide, Not Deep

A nitrate-reactive porous media layer comprising wood particles with very high hydraulic conductivity (K approximately 1 cm/s) was used to successfully treat nitrate in a shallow sand-and-gravel aquifer in southern Ontario. Nitrate concentrations of 1.3 to 14 mg/L as N in the aquifer were attenuated to <0.5 mg/L as N in the reactive layer. Borehole dilution testing indicated that ground water velocities in the reactive layer, although variable, averaged five times higher than in the surrounding aquifer, suggesting that the layer was capturing ground water flow from deeper in the aquifer. The use of high-K reactive media opens up the possibility of installing permeable reactive barriers as horizontal layers in the shallow water table zone that do not necessarily have to penetrate the full depth of a contaminant plume to be effective. Model simulations show that the depth of capture of a high-K layer increases as the layer width in the direction of flow increases. Shallower emplacement could decrease barrier costs at some sites.

Analysis of surface roughness effects on heat transfer in micro-conduits

Modern heat rejection systems, such as micro-heat sinks, are attractive because of their potential for high performance at small size and low weight. However, the impact of microscale effects on heat transfer have to be considered and quantitatively analyzed in order to gain physical insight and accurate Nusselt number data. The relative surface roughness (SR) was selected as a key microscale parameter, represented by a porous medium layer (PML) model. Assuming steady laminar fully developed liquid flow in microchannels and microtubes, the SR effects in terms of PML thermal conductivity ratio and Darcy number on the dimemsionless temperature profile and Nusselt number were analyzed. In summary, the PML characteristics, especially the SR-number and conductivity ratio k m/ k f, greatly affect the heat transfer performance where the Nusselt number can be either higher or lower than the conventional value. The PML influence is less pronounced in microtubes than in parallel-plate microchannels.

Multiple-event study of bioretention for treatment of urban storm water runoff

Bioretention is a novel best management practice for urban storm water, employed to minimize the impact of urban runoff during storm events. Bioretention consists of porous media layers that can remove pollutants from infiltrating runoff via mechanisms that include adsorption, precipitation, and filtration. However, the effectiveness of bioretention in treating repetitive inputs of runoff has not been investigated. In this study, a bioretention test column was set up and experiments proceeded once every week for a total of 12 tests. Through all 12 repetitions, the infiltration rate remained constant (0.35 cm/min). All 12 tests demonstrated excellent removal efficiency for TSS, oil/grease, and lead (99%). For total phosphorus, the removal efficiency was about 47% the system removal efficiency ranged from 2.3% to 23%. Effluent nitrate concentration became higher than the influent concentration during the first 28 days and removal efficiency ranged from 9% to 20% afterward. Some degree of denitrification was apparently proceeding in the bioretention system. Overall, the top mulch layer filtered most of TSS in the runoff and prevented the bioretention media from clogging during 12 repetitions. Runoff quality was improved by the bioretention column.

Analysis of hydrodynamic conditions in adjacent free and heterogeneous porous flow domains

The existence of a free-flow domain (e.g. a liquid layer) adjacent to a porous medium is a common occurrence in many environmental and petroleum engineering problems. The porous media may often contain various forms of heterogeneity, e.g. layers, fractures, micro-scale lenses, etc. These heterogeneities affect the pressure distribution within the porous domain. This may influence the hydrodynamic conditions at the free–porous domain interface and, hence, the combined flow behaviour. Under steady-state conditions, the heterogeneities are known to have negligible effects on the coupled flow behaviour. However, the significance of the heterogeneity effects on coupled free and porous flow under transient conditions is not certain. In this study, numerical simulations have been carried out to investigate the effects of heterogeneous (layered) porous media on the hydrodynamics conditions in determining the behaviour of combined free and porous regimes. Heterogeneity in the porous media is introduced by defining a domain composed of two layers of porous media with different values of intrinsic permeability. The coupling of the governing equations of motion in free and porous domains has been achieved through the well-known Beavers and Joseph interfacial condition. Of special interest in this work are porous domains with flow-through ends. They represent the general class of problems where large physical domains are truncated to smaller sections for ease of mathematical analysis. However, this causes a practical difficulty in modelling such systems. This is because the information on flow behaviour, i.e. boundary conditions at the truncated sections, is usually not available. Use of artificial boundary conditions to solve these problems effectively implies the imposition of conditions that do not necessarily match with the solutions required for the interior of the domain. This difficulty is resolved in this study by employing ‘stress-free boundary conditions’ at the open ends of the domains, which have been shown to provide accurate results by a number of previous workers. Copyright © 2005 John Wiley & Sons, Ltd.

Flow through a Tube with an Annual Porous Medium Layer

In this study, the boundary conditions necessary for continuum numerical modeling of flow involving a porous-medium-free-fluid interface are examined. In a region within the free flow adjacent to a porous medium interface, the momentum dispersion persists due to the extension of the spatial velocity fluctuation into the free flow. Consequently, at elevated flow rates, the viscous response to flow of the fluid in the region adjacent to a porous medium has to be modified due to the presence of such spatial velocity fluctuations caused by the porous medium. This influence decays exponentially and extends several pore sizes into the free fluid. Experimental and numerical studies have shown that, at moderately high flow rates, the pressure drop through a porous bed is a quadratic function of the flow discharge rate. For flow through a straight tube containing no porous structures, the pressure drop is linearly related to the flow discharge rate in the laminar regime. However, experimental observation shows that when fluid flows through a tube with an annular porous medium ring, the qualitative trend of the pressure drop is similar to flow through a porous medium. This behavior confirms our expectations on the existence of momentum dispersion. An exponential decay model is proposed to account for the momentum dispersion variation.

Effects of lubricant additives on the performance of hydrodynamically lubricated journal bearings

A non-Newtonian rheological model to investigate theoretically the effects of lubricant additives on the steady state performance of hydrodynamically lubricated finite journal bearings is introduced. In this model, the non-Newtonian behavior resulting from blending the lubricant with polymer additives is simulated by Stokes couple stress fluid model. The formed boundary layer at the bearing surface is described through the use of a hypothetical porous medium layer that adheres to the bearing surface. The Brinkman-extended Darcy equations are utilized to model the flow in the porous region. A stress jump boundary condition is applied at the porous media/fluid film interface. A modified form of the Reynolds equation is derived and solved numerically using a finite difference scheme. The effects of bearing geometry, and non-Newtonian behavior of the lubricant on the steady-state performance characteristics such as pressure distribution, load carrying capacity, side leakage flow, and coefficient of friction are presented and discussed. The results showed that lubricant additives significantly increase the load carrying capacity and reduce both the coefficient of friction and the side leakage as compared to the Newtonian lubricants.

Transient Forced Convection in an Isothermal Fluid-Saturated Porous-Medium Layer: Effective Permeability and Boundary Layer Thickness

Transient Forced Convection in an Isothermal Fluid-Saturated Porous-Medium Layer: Effective Permeability and Boundary Layer Thickness

Propagation of Transient Acoustic Waves in Layered Porous Media: Fractional Equations for the Scattering Operators

Acoustic waves scattering from a rigid air-saturated porous medium is studied in the time domain. The medium is one dimensional and its physical parameters are depth dependent, i.e., the medium is layered. The loss and dispersion properties of the medium are due to the fluid-structure interaction induced by wave propagation. They are modeled by generalized susceptibility functions which express the memory effects in the propagation process. The wave equation is then a fractional telegraphist’s equation. The two relevant quantities are the scattering operators—transmission and reflection operators—which give the scattered fields from the incident wave. They are obtained from Volterra equations which are fractional equations for the scattering operators.

Sound field of a baffled sound source covered by an anisotropic rigid-porous material

A theoretical approach for the sound field of a piston sound source covered by a finite thickness layer of anisotropic rigid-porous material is presented. The formulation is an extension of the method worked out by Amedin et al. [Sound field of a baffled piston source covered by a porous medium layer. J Acoust Soc Am 1995;98(3):1757]. First, in the present study the sound field of a point source is described by cylindrical waves. Then, with the proper boundary conditions, the sound pressure radiated from a piston source covered by a layer of anisotropic porous material can be calculated. The effects of frequency and bulk density of material on the sound propagation in an anisotropic porous material are studied. Finally, the effect of anisotropy is discussed.

Film condensation on a finite-size horizontal wavy plate bounded by a homogenous porous layer

Steady filmwise condensation on a finite-size horizontal wavy plate which covers a homogeneous porous medium layer filled with a dry saturated vapor has been investigated by boundary layer approximations. The dimensionless average Nusselt number Nu ¯ and dimensionless liquid film thickness on the wavy surface are evaluated as a function of seven parameters: Darcy number Da, Jacob number Ja, the wave number n, Prandtl number Pr, modified Rayleigh number Ra, suction parameter S w and the wave amplitude α. It is shown that the condensation heat transfer coefficient can be enhanced by increasing the contact area of the condensate, which corresponds to increasing values of the wave number and amplitude of the wavy surface, and when suction exists at the condensate surface.

Roof cooling effect with humid porous medium

A method of laying a layer of humid porous medium on roof to gain free cooling effect by passive water evaporation is proposed. Numeric model for simulating cooling effect is built with the help of experimental results of physical properties for humid porous medium, which shows advantage over analytical solutions because of the supposition of constant physical properties in the latter. Through the comparison between simulated and experimental results, the model is validated. And the method of evaporation cooling effect with humid porous medium on the roof is tested to be feasible.

The Onset of Bioconvection in a Horizontal Porous-Medium Layer

In this note the problem of the onset of bioconvection in a horizontal layer occupied by a saturated porous medium is analyzed. Gyrotactic effects are incorporated in the analysis. The Darcy flow model is employed, and it is assumed that the bioconvection Peclet number is not greater than unity. Critical values of the bioconvection Rayleigh number and the corresponding critical Rayleigh number are obtained for various values of the bioconvection Peclet number, the gyrotaxis number and the cell eccentricity.

2D analytical model of a direct methanol fuel cell

Analytical model is a valuable tool for understanding the effect of basic parameters on fuel cell performance. In this paper, two-dimensional (2D) full cell model of the direct methanol fuel cell was developed to describe not only electrochemical reactions on the anode and cathode electrodes, but also transport phenomena in fuel cell. Those phenomena included methanol crossover, diffusion of reactants in porous media layers, fluid flow in reactants distributor, etc. The analytical solution of the model was derived. The theoretical prediction of the analytical solution was in agreement with the experimental data. The 2D analytical model provided acceptable accuracy to predict the performance of direct methanol fuel cells. With the aid of the analytical solution, it was found that the methanol concentration decreases almost linearly along the flow direction in the anode channel. Methanol concentration distribution in the anode catalyst layer showed similar variation. The performance of fuel cell at high current density will benefit from enhancing mass transfer of the methanol from the anode channel to the catalyst layer.

Computational Analysis of Wall Roughness Effects for Liquid Flow in Micro-Conduits

Fluid flow in microchannels or microtubes may differ in terms of wall frictional effects, and hence flow rates, when compared to macrochannels. Focusing on steady laminar fully developed flow of a liquid in different micro-conduits, relative surface roughness is captured in terms of a porous medium layer (PML) model. The new approach allows the evaluation of microfluidics variables as a function of PML characteristics, i.e., layer thickness and porosity, uncertainties in measuring hydraulic diameters as well as the inlet Reynolds number. Specifically, realistic values for the PML Darcy number, relative surface roughness, and actual flow area are taken into account to match observed friction factors in micro-conduits. The model predictions compared well with measured data sets for systems with significant relative roughness values. Although other surface effects may have influenced the experimental results as well, surface roughness is found to affect the friction factor and hence the flow parameters in relatively rough channels, e.g., those which are made of aluminum or stainless steel by way of micro-cutting processes.