Begell House
Journal of Porous Media
Journal of Porous Media
1091-028X
15
12
2012
STOKES'S FIRST PROBLEM FOR A ROTATING SISKO FLUID WITH POROUS SPACE
In this paper the unsteady flow of a Sisko fluid induced by a suddenly moved infinitely long plate is investigated in a rotating frame. The fluid occupying the porous half-space is electrically conducting in the presence of a time-varying magnetic field. Conservation laws of mass and momentum are utilized in the derivation of the differential equation. The modified Darcy's law is employed in the problem development. The governing nonlinear problem is solved numerically. The effects of various parameters of interest on the velocity profiles are shown explicitly.
Tasawar
Hayat
Department of Mathematics, Quaid-I-Azam University 45320, Islamabad 44000, Pakistan; Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Faculty of Science,
King Abdulaziz University, Jeddah 21589, Saudi Arabia
Shirley
Abelman
University of the Witwatersrand, Johannesburg
Charis
Harley
Centrefor Differential Equations, Continuum Mechanics and Applications, School of Computational and Applied Mathematics, University of the Witwatersrand, Johannesburg Private Bag 3, Wits 2050, South Africa
Awatif A.
Hendi
Department of Physics, Faculty of Sciences, King Saud University, P. O. Box 1846, Riyadh 11321, Saudi Arabia
1079-1091
STABILITY AND WIDTH OF REACTION FRONTS IN 3-D POROUS MEDIA
Transport of reactive fluids in porous media may form reaction fronts−narrow zones where the reaction takes place. We derive approximate solutions for the change in concentration and porosity across the front zone. These solutions are used to derive a condition for reaction fronts to be narrow. Reaction fronts tend to be unstable, and they often show a fingered growth into the porous medium. A criterion for the stability of sharp reaction fronts in a 3-D homogeneous porous medium is derived using linear stability analysis. The criterion gives that a perturbation of a flat reaction front of any wavelength becomes unstable if the permeability behind the front increases. The front instability grows faster for short wavelengths than for long wavelengths. Similarly, the perturbations of the front will die out if the permeability behind the front decreases, and short-wavelength perturbations will die out faster than long-wavelength perturbations. Front stability and the stability criterion are demonstrated with numerical examples where the fronts are narrow but not sharp.
Magnus
Wangen
Institute for Energy Technology, P.O. Box 40, N-2027 Kjeller, Norway
1093-1103
SLOW STEADY ROTATION OF A POROUS SPHERE IN A SPHERICAL CONTAINER
The problem of steady rotation of a porous sphere located at the center of a spherical container has been investigated. The flow in the spherical container is governed by the Stokes equations. The flow within the porous sphere is governed by the Brinkman equation. The boundary conditions used at the interface are the stress jump condition for tangential stresses, continuity of the normal stresses, and velocity components. The torque experienced by the porous spherical particle is obtained. The wall correction factor is calculated. The special cases of rotation of a porous sphere and a solid sphere in an unbounded medium are obtained from the present analysis. The variations of torque and wall correction factor are studied with respect to permeability, separation parameter, and stress jump coefficient.
D.
Srinivasacharya
Department of Mathematics, National Institute of Technology, Warangal-506 004, Telangana, India
M. Krishna
Prasad
Department of Mathematics, National Institute of Technology, Warangal 506 004, A.P., India
1105-1110
EXPERIMENTAL INVESTIGATION OF WETTABILITY EFFECT AND DRAINAGE RATE ON TERTIARY OIL RECOVERY FROM FRACTURED MEDIA
Vertical displacement of oil by gas is one of the most efficient methods for oil recovery from naturally fractured reservoirs. Unlike the homogeneous media, the ultimate oil recovery by gravity drainage in fractured media is more dependent on the production rate. Hence finding the optimum production rate for more oil recovery with respect to the properties of media seems to be essential. In this work, unconsolidated packed models of cylindrical geometry surrounded by fractures were utilized to perform a series of flow visualization experiments during which the contribution of different parameters such as the extent of matrix wettability and the withdrawal rate were studied. In addition, mutual effects of wettability and production rate on tertiary oil recovery efficiency through controlled and free fall gravity drainage processes were also investigated. Experimental results obtained from tertiary gravity drainage experiments demonstrated that just before gas breakthrough, lower withdrawal rates facilitate the tertiary oil recovery under the film flow mechanism, which leads to a higher ultimate recovery factor. However, after gas breakthrough, monitoring oil recovery by gravity drainage showed that higher production rates recovered more oil. Furthermore, under tertiary recovery processes in low-production cases, oil-wet systems achieved higher recovery factors, while at high withdrawal rates, more oil was recovered for 50% oil-wet media.
P.
Maroufi
EOR Research Center, School of Chemical and Petroleum Engineering, Shiraz University, Shiraz 713451719, Iran
H.
Rahmanifard
EOR Research Center, School of Chemical and Petroleum Engineering, Shiraz University, Shiraz 713451719, Iran
H. K.
Al-Hadrami
Department of Petroleum and Chemical Engineering, Sultan Qaboos University, Muscat Oman
M.
Escrochi
EOR Research Center, School of Chemical and Petroleum Engineering, Shiraz University, Shiraz 713451719, Iran
Shahab
Ayatollahi
Department of Chemical and Petroleum Engineering, Sharif University of Technology, Tehran, Iran
A.
Jahanmiri
School of Chemical and Petroleum Engineering, Shiraz University, Shiraz 713451719, Iran
1111-1123
FLOW OF A VISCOUS FLUID THROUGH DIFFERENT POROUS STRUCTURES EMBEDDED IN POROUS MEDIUM
The flow of a viscous fluid through different structures embedded in a porous medium has been discussed by many mathematicians. Here the concept of fluid motion through porous structures embedded in a porous medium has been introduced. The motivation of this paper is to discuss the flow of a viscous fluid past a porous circular cylinder and porous sphere embedded in a porous medium. The Brinkman model is used for discussing the motion of fluid in porous media and matching conditions suggested by Williams have been taken for both structures. The streamlines are plotted and the drag on the porous sphere as well as the cylinder has been found. It is observed that in the case of the sphere as well as inside the cylinder the drag increases sharply with the decrease of the permeability of the embedding medium, but outside the cylinder the drag increases with the decrease of the porous material of the cylinder. Results obtained in this analysis are compared with the results obtained by applying Ochoa Tapia and Whitaker matching conditions at the interface.
Parul
Saxena
Department of Mathematics and Astronomy, University of Lucknow, Lucknow, Uttar Pradesh
226007, India
Lokendra
Kumar
Department of Mathematics, Jaypee Institute of Information Technology, A-10, Sec. 62, Noida-201307, Uttar Pradesh, India
1125-1135
AN ANALYTICAL STRESS-STRAIN MODEL FOR OPEN-CELL METAL FOAM
The main objective of the present investigation is to develop an analytical stress-strain model to quantitatively describe the stress-strain behavior of open-cell metal foam. Based on solid mechanics, an analytical stress-strain model is developed. This new stress-strain model involves two main parameters: relative density and plastic Poisson's ratio. As a key characteristic of metal foam, relative density directly takes effect on the uniaxial stress-strain behavior of metal foam and the uniaxial stress of metal foam increases with increasing relative density. Plastic Poisson's ratio is measured as a function of uniaxial compressive plastic strain and its value is neither 0 nor 0.5. Corresponding uniaxial compression tests of metal foams were conducted and numerical simulations were also carried out. The results indicate that this analytical stress-strain model of metal foam is in good agreement with both the experimental validations and the numerical simulations. This work provides useful information for understanding the deformation mechanism of open-cell metal foam.
Yishi
Su
ILaboratory of Mechanical System and Simultaneous Engineering, P2MN, ICD, University of Technology of Troyes, UMR CNRS STMR 6279,12 Rue Marie Curie, 10010, Troyes, France
Gong
Xiaolu
Laboratory of Mechanical System and Simultaneous Engineering, P2MN, ICD, University of Technology of Troyes, UMR CNRS STMR 6279,12 Rue Marie Curie, 10010, Troyes, France
1137-1145
EFFECT OF ROTATION ON THE ONSET OF CONVECTION IN WALTERS'S (MODEL B' ) FLUID HEATED FROM BELOW IN A DARCY-BRINKMAN POROUS MEDIUM
In this article, the effect of rotation on the onset of convection in Walters's (Model B') elasticoviscous fluid heated from below in a porous medium is considered. For the porous medium, the Brinkman model is employed. By applying normal mode analysis method, the dispersion relation has been derived and solved analytically. It is observed that the medium permeability, rotation, gravity field, and viscoelasticity introduce oscillatory modes. For stationary convection, the rotation has a stabilizing effect, whereas Darcy number and medium permeability have a destabilizing/stabilizing effect on the system under certain conditions.
G. C.
Rana
Department of Mathematics, Government College Hamirpur, Himachal Pradesh, India
S. K.
Kango
Department of Mathematics, Govt. College, Haripur-177 103, District Kullu Himachal Pradesh, India
Sanjeev
Kumar
Department of Mathematics, Govt. P. G. College, Mandi 175 001, Himachal Pradesh, India
1149-1153
LIE GROUP ANALYSIS OF RADIATION NATURAL CONVECTION FLOW OVER AN INCLINED SURFACE IN A POROUS MEDIUM WITH INTERNAL HEAT GENERATION
Lie group analysis is performed to study the heat transfer characteristics of the radiation natural convection flow of a heat generating fluid over a semi-infinite inclined surface embedded in a porous medium. The governing partial differential equations are transformed into a system of ordinary differential equations using scaling symmetries. The resulting system is solved numerically using a fourth-order Runge−Kutta method with the shooting technique. It is found that both the velocity and temperature increase significantly when the value of the heat generation parameter increases. The velocity increases and the temperature decreases with the increase in the porosity parameter. The thermal and momentum boundary layer thicknesses decrease when increasing the conduction−radiation parameter The local Nusselt number increases with the porosity and conduction−radiation parameter.
M.
Bhuvaneswari
School of Mechanical Engineering, Sungkyunkwan University, Suwon 440-746, South Korea
Sivanandam
Sivasankaran
King Abdulaziz University
Youn J.
Kim
School of Mechanical Engineering, Sungkyunkwan University, Suwon 440-746, South Korea
1155-1164