Instability Of Plane Poiseuille Flow In A Fluid-Porous System

The instability of Poiseuille flow in a fluid-porous system is investigated. The system consists of a fluid layer overlying porous media and is subjected to a horizontal plane Poiseuille flow. We use Brinkman's model instead of Darcy's law to describe the porous layer. The eigenvalue problem is solved by means of a Chebyshev collocation method. We study the influence of the depth ratio (d) over cap and the Darcy number delta on the instability of the system. We compare systematically the instability of Brinkman's model with the results of Darcy's model. Our results show that no satisfactory agreement between Brinkman's model and Darcy's model is obtained for the instability of a fluid-porous system. We also examine the instability of Darcy's model. A particular comparison with early work is made. We find that a multivalued region may present in the (k, Re) plane, which was neglected in previous work. Here k is the dimensionless wavenumber and Re is the Reynolds number. (C) 2008 American Institute of Physics. [DOI: 10.1063/1.3000643]

Wave propagation and the frequency domain Green's functions in viscoelastic Biot/squirt (BISQ) media

In this paper, we examine the characteristics of elastic wave propagation in viscoelastic porous media, which contain simultaneously both the Biot-flow and the squirt-flow mechanisms (BISQ). The frequency-domain Green's functions for viscoelastic BISQ media are then derived based on the classic potential function methods. Our numerical results show that S-waves are only affected by viscoelasticity, but not by squirt-flows. However, the phase velocity and attenuation of fast P-waves are seriously influenced by both viscoelasticity and squirt-flows; and there exist two peaks in the attenuation-frequency variations of fast P-waves. In the low-frequency range, the squirt-flow characteristic length, not viscoelasticity, affects the phase velocity of slow P-waves, whereas it is opposite in the high-frequency range. As to the contribution of potential functions of two types of compressional waves to the Green's function, the squirt-flow length has a small effect, and the effects of viscoelastic parameter are mainly in the higher frequency range. Crown Copyright (C) 2006 Published by Elsevier Ltd. All rights reserved.

Effects of contact resistance on thermal-conductivity of composite media with a periodic structure

The thermal conductivity of periodic composite media with spherical or cylindrical inclusions embedded in a homogeneous matrix is discussed. Using Green functions, we show that the Rayleigh identity can be generalized to deal with thermal properties ot these systems. A new calculating method for effective conductivity of composite media is proposed. Useful formulae for effective thermal conductivity are derived, and meanings of contact resistance in engineering problems are explained.

Thermal-conductivity of periodic composite media with spherical inclusions

The thermal conductivity of periodic composite media with spherical inclusions embedded in a homogeneous matrix is discussed. Using Green's function, we show that the Rayleigh identity can be generalized to deal with the thermal properties of these systems. A technique for calculating effective thermal conductivities is proposed. Systems with cubic symmetries (including simple cubic, body centered cubic and face centered cubic symmetry) are investigated in detail, and useful formulae for evaluating effective thermal conductivities are derived.

Instabilities of a liquid film flowing down an inclined porous plane

The problem of a film flowing down an inclined porous layer is considered. The fully developed basic flow is driven by gravitation. A careful linear instability analysis is carried out. We use Darcy's law to describe the porous layer and solve the coupling equations of the fluid and the porous medium rather than the decoupled equations of the one-sided model used in previous works. The eigenvalue problem is solved by means of a Chebyshev collocation method. We compare the instability of the two-sided model with the results of the one-sided model. The result reveals a porous mode instability which is completely neglected in previous works. For a falling film on an inclined porous plane there are three instability modes, i.e., the surface mode, the shear mode, and the porous mode. We also study the influences of the depth ratio d, the Darcy number delta, and the Beavers-Joseph coefficient alpha(BJ) on the instability of the system.

I. Stokes flow past a thin screen. II. Viscous flows past porous bodies of finite size

Part I

The slow, viscous flow past a thin screen is analyzed based on Stokes equations. The problem is reduced to an associated electric potential problem as introduced by Roscoe. Alternatively, the problem is formulated in terms of a Stokeslet distribution, which turns out to be equivalent to the first approach.

Special interest is directed towards the solution of the Stokes flow past a circular annulus. A "Stokeslet" formulation is used in this analysis. The problem is finally reduced to solving a Fredholm integral equation of the second kind. Numerical data for the drag coefficient and the mean velocity through the hole of the annulus are obtained.

Stokes flow past a circular screen with numerous holes is also attempted by assuming a set of approximate boundary conditions. An "electric potential" formulation is used, and the problem is also reduced to solving a Fredholm integral equation of the second kind. Drag coefficient and mean velocity through the screen are computed.

Part II

The purpose of this investigation is to formulate correctly a set of boundary conditions to be prescribed at the interface between a viscous flow region and a porous medium so that the problem of a viscous flow past a porous body can be solved.

General macroscopic equations of motion for flow through porous media are first derived by averaging Stokes equations over a volume element of the medium. These equations, including viscous stresses for the description, are more general than Darcy's law. They reduce to Darcy's law when the Darcy number becomes extremely small.

The interface boundary conditions of the first kind are then formulated with respect to the general macroscopic equations applied within the porous region. An application of such equations and boundary conditions to a Poiseuille shear flow problem demonstrates that there usually exists a thin interface layer immediately inside the porous medium in which the tangential velocity varies exponentially and Darcy's law does not apply.

With Darcy's law assumed within the porous region, interface boundary conditions of the second kind are established which relate the flow variables across the interface layer. The primary feature is a jump condition on the tangential velocity, which is found to be directly proportional to the normal gradient of the tangential velocity immediately outside the porous medium. This is in agreement with the experimental results of Beavers, et al.

The derived boundary conditions are applied in the solutions of two other problems: (1) Viscous flow between a rotating solid cylinder and a stationary porous cylinder, and (2) Stokes flow past a porous sphere.

Study on the Dissociation Behavior of Gas Hydrate in Porous Sediment Based on Fractal Theory

The dissociation process of gas hydrate was regarded as a gas-solid reaction without solid production layer when the temperature was above the zero centigrade. Based on the shrinking core model and the fractal theory, a fractional dimension dynamical model for gas hydrate dissociation in porous sediment was established. The new approach of evaluating the fractal dimension of the porous media was also presented. The fractional dimension dynamical model for gas hydrate dissociation was examined with the previous experimental data of methane hydrate and carbon dioxide hydrate dissociations, respectively. The calculated results indicate that the fractal dimensions of porous media acquired with this method agree well with the previous study. With the absolute average deviation (AAD) below 10%, the present model provided satisfactory predictions for the dissociation process of methane hydrate and carbon dioxide hydrate.

Fluid flow control with transformation media.

We introduce a new concept for the manipulation of fluid flow around three-dimensional bodies. Inspired by transformation optics, the concept is based on a mathematical idea of coordinate transformations and physically implemented with anisotropic porous media permeable to the flow of fluids. In two situations-for an impermeable object placed either in a free-flowing fluid or in a fluid-filled porous medium-we show that the object can be coated with an inhomogeneous, anisotropic permeable medium, such as to preserve the flow that would have existed in the absence of the object. The proposed fluid flow cloak eliminates downstream wake and compensates viscous drag, hinting at the possibility of novel propulsion techniques.

Heat and mass transfer in two-phase porous materials under intensive microwave heating

Computational results for the intensive microwave heating of porous materials are presented in this work. A multi-phase porous media model has been developed to predict the heating mechanism. Combined finite difference time-domain and finite volume methods were used to solve equations that describe the electromagnetic field and heat and mass transfer in porous media. The coupling between the two schemes is through a change in dielectric properties which were assumed to be dependent both on temperature and moisture content. The model was able to reflect the evolution of both temperature and moisture fields as well as energy penetration as the moisture in the porous medium evaporates. Moisture movement results from internal pressure gradients produced by the internal heating and phase change.

A new computational approach to microwave heating of two-phase porous materials

Computational results for the microwave heating of a porous material are presented in this paper. Combined finite difference time domain and finite volume methods were used to solve equations that describe the electromagnetic field and heat and mass transfer in porous media. The coupling between the two schemes is through a change in dielectric properties which were assumed to be dependent on both temperature and moisture content. The model was able to reflect the evolution of both temperature and moisture fields as well as energy penetration as the moisture in the porous medium evaporates. Moisture movement results from internal pressure gradients produced by the internal heating and phase change.

Modelagem analítica e experimental da filtração em meios porosos

Deep bed filtration occurs in several industrial and environmental processes like water filtration and soil contamination. In petroleum industry, deep bed filtration occurs near to injection wells during water injection, causing injectivity reduction. It also takes place during well drilling, sand production control, produced water disposal in aquifers, etc. The particle capture in porous media can be caused by different physical mechanisms (size exclusion, electrical forces, bridging, gravity, etc). A statistical model for filtration in porous media is proposed and analytical solutions for suspended and retained particles are derived. The model, which incorporates particle retention probability, is compared with the classical deep bed filtration model allowing a physical interpretation of the filtration coefficients. Comparison of the obtained analytical solutions for the proposed model with the classical model solutions allows concluding that the larger the particle capture probability, the larger the discrepancy between the proposed and the classical models

Modelo Estocástico para bloqueio de poros e redução de permeabilidade

Modeling transport of particulate suspensions in porous media is essential for understanding various processes of industrial and scientific interest. During these processes, particles are retained due to mechanisms like size exclusion (straining), adsorption, sedimentation and diffusion. In this thesis, a mathematical model is proposed and analytical solutions are obtained. The obtained analytic solutions for the proposed model, which takes pore and particle size distributions into account, were applied to predict the particle retention, pore blocking and permeability reduction during dead-end microfiltration in membranes. Various scenarios, considering different particle and pore size distributions were studied. The obtained results showed that pore blocking and permeability reduction are highly influenced by the initial pore and particle size distributions. This feature was observed even when different initial pore and particle size distributions with the same average pore size and injected particle size were considered. Finally, a mathematical model for predicting equivalent permeability in porous media during particle retention (and pore blocking) is proposed and the obtained solutions were applied to study permeability decline in different scenarios

Modelagem matemática para o transporte de partículas sujeitas a múltiplos mecanismos de retenção

Discrepancies between classical model predictions and experimental data for deep bed filtration have been reported by various authors. In order to understand these discrepancies, an analytic continuum model for deep bed filtration is proposed. In this model, a filter coefficient is attributed to each distinct retention mechanism (straining, diffusion, gravity interception, etc.). It was shown that these coefficients generally cannot be merged into an effective filter coefficient, as considered in the classical model. Furthermore, the derived analytic solutions for the proposed model were applied for fitting experimental data, and a very good agreement between experimental data and proposed model predictions were obtained. Comparison of the obtained results with empirical correlations allowed identifying the dominant retention mechanisms. In addition, it was shown that the larger the ratio of particle to pore sizes, the more intensive the straining mechanism and the larger the discrepancies between experimental data and classical model predictions. The classical model and proposed model were compared via statistical analysis. The obtained p values allow concluding that the proposed model should be preferred especially when straining plays an important role. In addition, deep bed filtration with finite retention capacity was studied. This work also involves the study of filtration of particles through porous media with a finite capacity of filtration. It was observed, in this case, that is necessary to consider changes in the boundary conditions through time evolution. It was obtained a solution for such a model using different functions of filtration coefficients. Besides that, it was shown how to build a solution for any filtration coefficient. It was seen that, even considering the same filtration coefficient, the classic model and the one here propposed, show different predictions for the concentration of particles retained in the porous media and for the suspended particles at the exit of the media

Remoção de óleo da água de produção por flotação em coluna utilizando tensoativos de origem vegetal

In the petroleum industry, water is always present in the reservoir formation together with petroleum and natural gas and this fact provokes the production of water with petroleum, resulting in a great environmental impact. Several methods can be applied for treatment of oily waters, such as: gravitational vases, granulated media filtration systems, flotation process, centrifugation process and the use of hydrocyclones, which can also be used in a combined way. However, the flotation process has showed a great efficiency as compared with other methods, because these methods do not remove great part of the emulsified oil. In this work was investigated the use of surfactants derived from vegetable oils, OSS and OGS, as collectors, using the flotation process in a glass column with a porous plate filter in its base for the input of the gaseous steam. For this purpose, oil/water emulsions were prepared using mechanical stirring, with concentrations around 300 ppm. The air flow rate was set at 700 cm3/min and the porous plate filter used for the generation of the air bubbles has pore size varying from 16 to 40 Pm. The column operated at constant volume (1500mL). A new methodology has been developed to collect the samples, where, instead of collecting the water phase, it was collected the oil phase removed by the process in the top of the flotation column. It has been observed that it is necessary to find an optimum surfactant concentration to achieve enhanced removal efficiency. Being for OSS 1.275 mmol/L and for OGS 0.840 mmol/L, with removal efficiencies of 93% and 99%, respectively, using synthetic solutions. For the produced water, the removal in these concentrations was 75% for OSS and 65% for OGS. It is possible to remove oil from water in a flotation process using surfactants of high HLB, fact that is against the own definition of HLB (Hydrophile-Lipophile Balance). The interfacial tension is an important factor in the oil removal process using a flotation process, because it has direct interference in the coalescence of the oil drops. The spreading of the oil of the air bubble should be considered in the process, and for the optimum surfactant concentrations it reached a maximum value. The removal kinetics for the flotation process using surfactants in the optimum concentration has been adjusted according to a first order model, for synthetic water as for the produced water.