Begell House
Journal of Porous Media
Journal of Porous Media
1091-028X
12
5
2009
Surface Wave Propagation in a Fluid-Saturated Incompressible Porous Layer Lying between an Empty Porous Elastic Layer and an Empty Elastic Porous Half-Space
Dispersion of Rayleigh-type surface waves, in a model consisting of a poroelastic plate of thickness H of a fluid-saturated incompressible porous material lying between an empty porous elastic layer of thickness h and an empty porous half-space, is analyzed. The frequency equation connecting the phase velocity with wave number is derived. Special cases such as (i) Rayleigh-type surface waves in an incompressible poroelastic layer lying between two empty porous elastic half-spaces; (ii) Rayleigh-type surface waves in an incompressible poroelastic layer lying over an elastic half-space; and (iii) Rayleigh waves propagating along the free surface of a fluid-saturated incompressible porous elastic half-space are investigated. Numerical results with graphical presentations of the variations of phase velocity and attenuation coefficient with wave number are also included.
Rajneesh
Kumar
Department of Mathematics, Kurukshetra University, India
B. S.
Hundal
Department of Mathematics, S. R. Government College for Women, Amritsar, Punjab, India
387-402
Shrinkage/Swelling Behavior of Knitted Fabrics during Relative Humidity Cycles Determined by X-ray Imaging
The 2D deformation of knitted jersey ready-to-wear clothing made of cotton was measured during adsorption and desorption steps. A digital x-ray imaging system was coupled with a climatic chamber to control temperature and relative humidity during the cycle. Images of the samples were recorded at each different equilibrium state of the cycle. Finally, an image correlation process was used to compare the recorded images and to determine the 2D strain. The deformations along course (εcc) and wale (εww) directions and the shear (εwc) were measured for four identical samples. The repeatability of the results shows the reproducibility of the measurement process. These original experimental results establish a clear anisotropic shrinkage and swelling behavior between the wale and course directions. The anisotropic ratio (εcc/εww) rises up to 2 during the adsorption step. Moreover, they enlighten a hysteresis between the adsorption and desorption steps. It denotes the effect of the material's history and it is explained by geometrical considerations of the structure at the microscopic level and the relationship with the manufacturing process. Finally, the shear strain is explained at the microscopic level by electronic microscopy (ESEM) observations that show the fibers' twist dissymmetry between the two wings of the stitch.
N.
Bhouri
LERMAB-UMRINRA 1093, ENGREF 14, rue Girardet, 54042 Nancy Cedex, France; and LESTE, ENIM Avenue IBN ELJAZZAR, 5019 Monastir, Tunisie
Eric
Badel
LERMAB-UMRINRA 1093, ENGREF 14, rue Girardet, 54042 Nancy Cedex, France
Sassi Ben
Nasrallah
Laboratoire d'Études des Systèmes Thermiques et Énergétiques, Ecole Nationale d'Ingénieurs
de Monastir, Monastir 5019 Tunisie
Patrick
Perre
Laboratoire de Genie des Procedes et des Materiaux, Ecole Centrale Paris, CentraleSupelec, campus de Chatenay-Malabry Grande Voie des Vignes F-92 295 Chatenay-Malabry Cedex, Paris, France
403-415
Pore-Scale Model for Reactive Transport and Biomass Growth
Two Lagrangian particle models for biomass growth in porous media were proposed. In the first model, a cellular automata approach was used to model interactions of biomass with a fluid. In the second model, pair-wise particle-particle interactions were used to simulate interactions within the biomass and both biomass-fluid and biomass-soil grain interactions. The biomass growth rate in both models was described by double Monod kinetics. For the set of parameters used in the simulations, both models produced qualitatively similar predictions: (1) biomass grows in the shape of bridges connecting soil grains and oriented in the direction of flow so as to minimize resistance to the fluid flow; (2) the solution containing electron donors and acceptors rapidly becomes depleted as it enters the fractured porous domain; and (3) the biomass growth occurs mainly at the entrance into the fracture. Quantitative predictions, such as total mass of microbes and spatial distribution of microbe concentration, were found to be strongly dependent on the type of model. The model that accounted for the detachment and attachment of the microbes predicted a higher ability of biomass to spread along preferential flow paths and seal off the porous matrix than the model with immobile biomass phase.
Alexandre M.
Tartakovsky
Pacific Northwest National Laboratory, Richland, WA 99352, USA
Timothy D.
Scheibe
Pacific Northwest National Laboratory, Richland, WA 99352, USA
Paul
Meakin
Idaho National Laboratory, Idaho Falls, ID 83415, USA
417-434
Influence of Fracture Tip on Fluid Flow Displacements
Understanding multiphase fluid flow in fractured rocks is essential for designing and optimizing hydrocarbon recovery processes. The fluid flow interactions between the fractures and the matrix have a significant impact on displacement processes. This work focuses on multiphase flow in the presence of a fracture tip. It studies two-phase fluid flow (water-il) displacements in layered Berea sandstones that have been artificially fractured with a single extensional fracture perpendicular to the natural layers. Two experiments were considered in this work. In the first experiment, the fracture was induced at the inlet end of the sample and it spanned the first third of the core. Thus, the diverging flow at the tip of the fracture was studied. In the second experiment, the fracture was induced at the outlet end of the sample and it spanned about one-third of the core. The impact of the fracture tip on fluid flow was studied in both experiments. The temporal and spatial saturation distributions of the two cases were determined using x-ray computed tomography, CT. The 4D-CT experimental data and recovery information were used as the basis for simulation in an effort to determine the interaction of the fracture-matrix environment with multiphase flow. At the tip of the fracture, the two experiments showed different fluid flow patterns.
Abdullah F.
Alajmi
Petroleum Engineering Department, College of Engineering & Petroleum, Kuwait University
Abraham
Grader
Petroleum and Natural Gas Engineering Department, Pennsylvania State University, University Park, 16802, Pennsylvania, USA
435-447
Application of the Homotopy Perturbation Method to Micropolar Flow in a Porous Channel
In this article, the problem of two-dimensional flow of a micropolar fluid in a porous channel is presented, and the homotopy perturbation method (HPM) is employed to compute an approximation to the solution of the system of nonlinear differential equations governing the problem. Comparisons are made between the numerical solution and the results of the HPM. The results reveal that this method is very effective and simple and can be applied to other nonlinear problems.
E.
Mohseni
Department of Mechanical Engineering, University of Wisconsin-Milwaukee, Milwaukee, WI 53201, USA
M.
Esmaeilpour
Department of Mechanical Engineering, Babol University of Technology, Iran
Davood D.
Ganji
Department of Mechanical Engineering, Babol University of Technology, Babol, Iran
451-459
Mathematical Manipulation of the Interface Region of Multilayer Flows
In this paper, an accurate and fast algorithm is proposed to numerically solve for the velocity profile of fluid flow through multilayer porous media. We consider a finite width two-porous-layer problem, where the layers have different permeabilities, which introduces a discontinuity in the permeability at the interface region. At the interface, the continuity of the velocity and shear stress are imposed. The proposed algorithm is based on the nonlinear shooting method and the two-dimensional Newton's method. The accuracy of the proposed algorithm is validated by applying it to examples of known exact solutions. A comparison between the proposed algorithm and a finite difference approach is made, and it shows that the proposed algorithm is more accurate and more efficient.
M. A.
Hajji
Department of Mathematical Sciences, United Arab Emirates University, P.O. Box 17551, A1 Ain, United Arab Emirates
F.
Allan
Department of Mathematical Sciences, United Arab Emirates University, P.O. Box 17551, A1 Ain, United Arab Emirates
461-475
Effects of Variable Properties on Magnetohydrodinamics Unsteady Mixed-Convection in non-Newtonian Fluid with Variable Surface Temperature
A mathematical model will be analyzed numerically in order to study the effects of a variable viscosity and thermal conductivity on unsteady heat and mass transfer in a non-Newtonian power-law fluid flow through a porous medium past a semi-infinite vertical plate with variable surface temperature in the presence of magnetic field and radiation. The fluid viscosity and thermal conductivity are assumed to vary linearly with temperature. The governing nonlinear partial differential equations are transformed into a linear algebraic system utilizing the Chebyshev collocation method in spatial and the Crank-Nicolson method in time. Numerical results for the velocity, temperature, and concentration profiles as well as for the local skin friction, Nusselt number, and Sherwood number are obtained and reported in tabular form and graphically for various parametric conditions to show interesting aspects of the solution.
Nasser S.
Elgazery
Department of Mathematics, Deanship of Educational Services, Qassim University, P. O. Box 6595, Al-Qassim, Buraidah: 51452 Saudi Arabia
Nader Y.
Abd Elazem
Department of Mathematics, Faculty of Education, Ain Shams University, Roxy, Heliopolis, Cairo, Egypt
477-488