Begell House Inc.
Journal of Porous Media
JPM
1091-028X
11
5
2008
Flow and Solute Transport in Saturated Porous Media: 2. Violating the Continuum Hypothesis
421-441
10.1615/JPorMedia.v11.i5.10
Amgad
Salama
Research Associate
Paul J.
Van Geel
Civil and Environmental Engineering Department, Carleton University, Ottawa K1S 5B6, Canada
Several reasons may be invoked that could result in the inappropriateness of assuming the continuum approach when dealing with transport phenomena in porous media. Probably the most serious of these may be the violation of the length scale constraints. In an attempt to explore this, experimental and numerical investigations were conducted to study the significance of violating the length scale constraints when modeling transport phenomena in porous media based on the continuum approach. Initially, a porous system was constructed that complied with all length scale constraints such that it may be safe to assume the medium as a continuum. Then, in successive experimental setups, the system was allowed to violate the length scale constraints in one of its regions, and the behavior of the system in each case was analyzed. It was found that in situations when the length scale constraints are violated, it may not generally be appropriate to model the system using the macroscopic properties. Moreover, the experiments showed that for the cases under study, when the length scale characterizing the domain was not very much larger than the size of the representative elementary volume, REV (i.e., violating the second length scale constraint), significant variations were observed between measurements and simulation, assuming the continuum approach. As the system's size continued to diminish to be in the order of the size of the REV (i.e., violating the first length scale constraint), a surprisingly better match was observed. It was concluded that the boundary effects become significant as the length scale characterizing the domain gets smaller. However, further decrease in length scale incorporates mixing processes that compensate for the effects of the boundary region.
Numerical Modeling of the Gas-Oil Gravity Drainage Process in Stratified and Fractured Porous Media
443-456
10.1615/JPorMedia.v11.i5.20
Moein
Nabipour
Chemical and Petroleum Engineering Department, Islamic Azad University, Marvdasht Branch, Marvdasht, Iran
M. M.
Zerafat
School of Chemical and Petroleum Engineering, Shiraz University, Shiraz, Iran
Shahab
Ayatollahi
Department of Chemical and Petroleum Engineering, Sharif University of Technology, Tehran, Iran
The saturation profiles in homogeneous and nonhomogeneous layered porous media have been analyzed, and the oil recovery rates as well as the ultimate recovery have been calculated. A two-phase flow model is set up and solved numerically to produce the oil saturation profile and estimate the rate of oil recovery in layered porous medium under the gas-oil gravity drainage process. The model was further extended to model very high permeability layers stacked in between two dense layers to simulate horizontally fractured media. This numerical scheme reveals the importance of capillary pressure in the vicinity of the different layers for the calculation of the saturation profile. Oil entrapment in the matrix on top of the more permeable layers is responsible for the low oil recovery efficiency from fractured reservoirs under gravity drainage. Several different tests, including the use of a single high-permeability layer, a single low-permeability layer, and a low on top of a high and high on top of a low permeable stratum, are performed using the proposed technique, qualitatively.
Heat Transfer between Two Vertical Parallel Walls Partially Filled with a Porous Medium: Use of a Brinkman-Extended Darcy Model
457-466
10.1615/JPorMedia.v11.i5.30
Rama Subba Reddy
Gorla
Department of Mechanical Engineering, Cleveland State University, Cleveland, OH, 44115 USA; Department of Mechanical Engineering, University of Akron, Akron, Ohio 44325, USA; Department of Mechanical & Civil Engineering, Purdue University Northwest, Westville, IN 46391, USA
An analysis has been presented for the fully developed heat transfer to a viscous incompressible fluid between two vertical parallel walls partially filled with porous matrix and partially with a clear fluid invoking vertical interface. The momentum transfer in the porous medium is described by the Brinkman-extended Darcy model, and the two regions are coupled by equating the velocity and shear stress at the interface. Perturbation technique is used to solve the governing nonlinear equations. It is observed that for large values of Darcy number, the effects of Brinkman terms is on the entire porous domain, while for small values of Darcy number, its effect is confined in the vicinity of the interface only. The effects of the parameters governing the velocity and temperature distributions are presented graphically, while the numerical values of skin friction, rate of heat transfer, and flux of flow are presented in tables, followed by a discussion.
A Note on Oscillatory Flow of a Third Grade Fluid in a Porous Medium
467-473
10.1615/JPorMedia.v11.i5.40
F.
Shahzad
College of Aeronautical Engineering, National University of Sciences and Technology, PAF Academy, Risalpur 24090, Pakistan
Saleem
Ashgar
Department of Mathematical Sciences, COMSATS Institute of Information Technology, Islamabad, Pakistan
Here a numerical solution is determined for the oscillatory flow of a third grade fluid in a porous medium. A modified Darcy's law has been used in the present analysis. The influence of emerging parameters on the velocity is properly discussed.
Effect of an Endoscope on the Peristaltic Transport through a Porous Medium
477-486
10.1615/JPorMedia.v11.i5.50
Nasir
Ali
Department of Mathematics and Statistics, International Islamic University, Islamabad 44000, Pakistan
Ambreen
Afsar
Department of Mathematics, Quaid-i-Azam University, 45320 Islamabad, Pakistan
This article deals with the influence of an endoscope and magnetic field on the peristaltic flow of a viscous fluid through a porous medium. The mathematical model considers a magnetohydrodynamic fluid through a gap between concentric uniform tubes such that the inner tube is rigid and the outer tube has a sinusoidal wave traveling down its wall. The analysis has been carried out under the assumption of long wavelength and low Reynolds number. Analytic solutions are obtained for the velocity components and pressure gradient. The influence of sundry parameters is seen on the pressure rise per wavelength, friction forces on the inner and outer tubes, and axial pressure gradient.
Time Varying Flow of a Power Law Fluid in a Porous Medium between Parallel Porous Plates with Heat Transfer under an Exponential Decaying Pressure Gradient
487-495
10.1615/JPorMedia.v11.i5.60
Hazem Ali
Attia
Department of Mathematics, College of Science, Al-Qasseem University, P.O. Box 237, Buraidah 81999, Kingdom of Saudi Arabia; On leave from: Department of Engineering Mathematics and physics, Faculty of Engineering, El-Fayoum University, El-Fayoum, Egypt
The time-varying flow in a porous medium of a viscous incompressible non-Newtonian power law fluid between two parallel horizontal porous plates is studied with heat transfer under an exponential decaying pressure gradient. A uniform suction and injection through the surface of the plates is applied. The two plates are kept at different but constant temperatures, while the viscous dissipation is taken into consideration. Numerical solutions for the governing nonlinear momentum and energy equations are obtained using finite difference approximations. The effect of the porosity of the medium, the parameter describing the non-Newtonian behavior, and the velocity of suction and injection on both the velocity and temperature distributions as well as the dissipation terms are examined.
A New Dimensionless Friction Factor for Porous Media
497-506
10.1615/JPorMedia.v11.i5.70
Peter
Ohirhian
UNIVERSITY OF BENIN
A new dimensionless parameter for expressing the ability of a porous material to transmit fluids through its interconnected pores is suggested. The new parameter is developed from the modification of the Hagen-Poiseuille and Darcy-Weisbach equations used for the flow of fluids in pipes. The modification is based on the assumption that a pipe is equivalent to an isotropic porous medium of circular cross section, in which the porosity is 100%. With this assumption, the new dimensionless transmission factor can be related to the porosity of the material. Experimentation has shown that the suggestion here is valid. The equipment used and the results of the experiment are also presented in this article.