Begell House
Journal of Porous Media
Journal of Porous Media
1091-028X
13
5
2010
UPSCALING TRANSPORTOF ADSORBING SOLUTES IN POROUS MEDIA
Adsorption of solutes in porous media is commonly modeled as an equilibrium process. Indeed, one may safely assume that within the pore space, the concentration of adsorbed solute at a point on the grain surface is algebraically related to the concentration in the fluid next to the grain. The same, however, cannot be said about average concentrations. In fact, during solute transport, concentration gradients develop within the pore space, and these could potentially give rise to a scale-dependent adsorption process. The main objective of this research is to develop relationship between pore-scale adsorption coefficient and corresponding upscaled adsorption parameters. Two approaches are used: Theoretical averaging and numerical upscaling. In the averaging approach, equilibrium adsorption is assumed at the pore-scale and solute transport equations are averaged over REV. This leads to explicit expressions for macro-scale adsorption rate constants as a function of micro-scale parameters. In the numerical approach, first we simulate solute transport within a single tube undergoing equilibrium adsorption at the pore wall, and then flux averaged concentration breakthrough curves are obtained. These are used to determine the upscaled adsorption rate constants as functions of pore-scale hydraulic and adsorption parameters. Results of the two approaches agree very well.
Amir
Raoof
Utrecht University, Netherlands
Seyed Majid
Hassanizadeh
Department of Earth Sciences, Utrecht University
395-408
RESISTIVE FORCES QUANTIFICATION IN POLYMERIC SOLUTIONS IN POROUS MEDIA
The objective of this work is to evaluate the flow of polymer solutions through porous media. Flow tests were performed with different polymeric solutions through consolidated inert porous media at large pressure differentials (high deformation rates). Experimental results indicate expressive deviation from Darcy’s law. The next step was to validate alternative expressions for resistive forces that contemplate the effects of the first normal stress difference, as defined by Noll (1958). Based on such expressions, regions of viscosity-governed flows, elasticity-governed flows, and mixed flows were identified.
Martins
Petrobras-Cidade Universitária, Q7-Ilha do Fundão RJ CEP: 21941-598 Brasil
A.
Waldmann
Petrobras-Cidade Universitária, Q7-Ilha do Fundão RJ CEP: 21941-598 Brasil
Giulio
Massarani
In memoriam-Federal University of Rio de Janeiro, Cidade Universitária−Ilha do Fundão Brasil
409-422
FLOW OF SUSPENSIONS IN TWO-DIMENSIONAL POROUS MEDIA WITH MOBILE AND IMMOBILE LIQUID ZONES
In this paper, flow of suspensions in a 2D porous medium is considered. The porous medium consist of two zones, one of them is saturated with a mobile, pure (without any solid particles) liquid and another one is saturated with an immobile liquid. The flow of suspensions occurs with colmatation and suffosion, longitudinal and across diffusion effects and in the immobile liquid zone only, diffusion transport of particles is observed. The problem is numerically solved and the influence of colmatation-suffosion, diffusion, hydrodynamic dispersion effects on filtration and mass transport characteristics is estimated. The fields of relative concentration of particles in both mobile and immobile liquid zones, porosity, permeability, and pressure gradient in the mobile liquid zone are determined for several values of diffusion, dispersion coefficients, and colmatation-suffosion intensity coefficients. Relative current, common, and total mass fluxes of solid particles through the common boundary of the mobile and immobile liquid zones are also determined. It is shown that the presence of immobile liquid zones in porous media considerably alter both the filtration and transport characteristics. Colmatation and suffosion effects in the zone with mobile liquid influence not only the filtration and transport characteristics of this zone, but also the diffusion particle transport from the zone with the mobile liquid into the zone with the immobile liquid. Results can be important in field data interpretation during water flooding in oil reservoirs, wastewater filtration, environment protection, etc.
J. M.
Makhmudov
Complex Research Institute of Regional Problems, Academy of Science of Uzbekistan, Uzbekistan
B. Kh.
Khuzhayorov
Complex Research Institute of Regional Problems, Academy of Science of Uzbekistan, Uzbekistan
423-437
EFFECT OF ELECTRIC LOAD PARAMETER ON UNSTEADY MHD CONVECTIVE FLOW OFVISCOUS IMMISCIBLE LIQUIDS IN A HORIZONTAL CHANNEL: TWO-FLUID MODEL
An analytical study of the two-fluid hydromagnetic unsteady mixed convective flow of viscous, incompressible, electrically conducting, immiscible liquids in a horizontal channel is investigated. Both liquids are considered to have different densities, viscosities, and thermal and electrical conductivities, and occupy equal heights. The transport properties of both liquids are taken to be constant and the bounding channel walls are maintained at constant and equal temperature. A regular perturbation technique is applied to obtain the solutions of velocity field and temperature distribution of both liquids. Expressions for skin frictions and heat transfer rates at the plates are also derived. The effects of various parameters entered into the equations of momentum and energy are evaluated numerically and plotted graphically, while numerical values of variations in skin frictions and heat transfer rates at the plates are presented in tabular form. The results of the study are discussed.
Atul Kumar
Singh
Department of Mathematics, V. S. S. D. College, Kanpur 208002, India
Pratibha
Agnihotri
Department of Mathematics, V. S. S. D. College, Kanpur 208002, India
439-455
ELECTROHYDRODYNAMIC INSTABILITY CONDITIONS FOR TWO SUPERPOSED DIELECTRIC BOUNDED FLUIDS STREAMING WITH FINE DUST INA POROUS MEDIUM
The electrohydrodynamic Kelvin-Helmholtz instability of the plane interface between two uniform superposed dielectric fluids of finite depths permeated with suspended particles through a porous medium is considered under the influence of general applied horizontal or vertical (in the absence and presence of surface charges) electric fields. Applying appropriate boundary conditions, the corresponding dispersion relations are obtained in these cases. Using a novel technique, the stability conditions are derived, separately, and some limiting cases are recovered. The maximum growth rates and corresponding critical dominant wavenumbers are discussed in detail if the two fluids are bounded or not, and also in the absence or presence of surface charges. It is found that the horizontal electric field, porosity of a porous medium, and surface tensions have stabilizing effects, while the vertical electric fields and fluid velocities have destabilizing effects. Also, the fluid viscosities are found to have stabilizing as well as destabilizing effects, and the medium permeability has an opposite effect, while the number densities of suspended particles have no effect on the stability of the considered system.
Mohamed F.
El-Sayed
Department of Mathematics, Faculty of Education, Ain Shams University, Heliopolis (Roxy), Cairo, Egypt; Department of Mathematics, College of Science, Qassim University, P. O. Box 6644, Buraidah 51452, Saudi Arabia
457-473
FLOW ANALYSIS OF NON-NEWTONIAN VISCOELASTIC FLUIDS IN POROUS MEDIA
In this article, a Burgers fluid model is introduced to the seepage flow mechanics to establish the relaxation models of non-Newtonian viscoelastic fluids. The flow characteristics of non-Newtonian viscoelastic fluids through a porous medium are studied using the integral transform. Exact solutions are obtained using Weber transform and Hankel transform. The long-time and short-time asymptotic solutions for an infinite formation are also obtained. The pressure-transient behavior of non-Newtonian viscoelastic fluid flow through an infinite reservoir is studied using the asymptotic solutions. In the initial stage, the more obvious the viscoelastic characteristics of the fluid are, the more distinct are the effects toward the pressure curves. The effects of different outer boundaries on the pressure behavior are also studied. The well-known solutions for a Newtonian fluid as well as those corresponding to a Maxwell fluid, a second-grade fluid, and an Oldroyd-B fluid appear as limiting cases of our solutions.
Dengke
Tong
China University of Petroleum, Shandong, Dongyiing 257061, China
Huiping
Hu
China University of Petroleum, Shandong, Dongyiing 257061, China
477-486
LOCAL NONSIMILARITY SOLUTION ON MHD CONVECTIVE HEAT TRANSFER FLOW PAST A POROUS WEDGEIN THE PRESENCE OF SUCTION/INJECTION
The behavior of the steady convective heat transfer of an electrically conducting fluid flow over a porous wedge with uniform suction or injection was investigated. The wall of the wedge is embedded in a uniform porous medium in order to allow for possible fluid wall suction or injection. The governing boundary layer equations are written into a dimensionless form by similarity transformations. Because of the effect of suction/injection on the wall of the wedge with buoyancy force and variable wall temperature, the flow field is locally nonsimilar. The nonsimilar ordinary differential equations were obtained by means of a local nonsimilarity method. The resulting ordinary differential equations are solved by Runge-Kutta−Gill with a shooting method for finding a skin friction and a rate of heat transfer. The effects of suction/injection, nonuniform wall temperature and buoyancy force parameters on the dimensionless velocity and temperature profiles are shown graphically. Comparisons to previously published works are performed, and excellent agreement between the results is obtained. The conclusion is drawn that the flow field and temperature profiles are significantly influenced by these parameters.
Muhaimin
Centre for Science Studies, Universiti Tun Hussein Onn Malaysia, 86400 Parit Raja, Batu Pahat Johor, Malaysia
Azme B
Khamis
Centre for Science Studies, Universiti Tun Hussein Onn Malaysia, 86400 Parit Raja, Batu Pahat Johor, Malaysia
487-495