Begell House Inc.
Journal of Porous Media
JPM
1091-028X
14
12
2011
USE OF FRACTURE AS A PLANAR SOURCE OF FLOW TO DETERMINE THE EFFECT OF A STAGNANT ZONE ON THE DILUTION OF A FRONT
1047-1057
10.1615/JPorMedia.v14.i12.10
Somenath
Ganguly
Department of Chemical Engineering, Indian Institute of Technology, Kharagpur 721302, West-Bengal, India
fracture
matrix
flow
pressure
diffusion
Transport of solute through fracture is important in several aspects of oil recovery. The presence of a stagnant zone within the fracture as well as the porous matrix affects the transport process significantly, and is investigated here. This paper describes experiments with potassium iodide (KI) as a solute in brine flowing through a fractured slab of Berea sandstone. A step change in concentration at the fracture inlet was tracked at the outlet. A similar experiment was performed in smooth replica of a fracture with saw-cut face of Berea rock forming the wall. The responses were also simulated using theoretical models, accounting for (a) diffusion into the stagnant zone inside the fracture and (b) diffusion into the stagnant zone that, in turn, is open for diffusive transport into the brine in the adjoining matrix. The laboratory model of the fracture used in the experiment allowed for a controlled flow of injected solution into the matrix in addition to flow through the fracture. The control of such flow is a novel approach to establish in the laboratory the flow in a fracture that is entirely surrounded by a porous matrix. The mathematical model developed in this paper suggests that uniform penetration into the matrix throughout the entire length of the fracture requires a thin, wide, and (preferably) low-permeability slab. In one of the experiments with unidirectional flow through the fracture, some of the injected KI solution flowed into the matrix prior to flow through the fracture outlet. The concentrations, recorded at the fracture outlet, provided further insight to the transport of solute when the fluid from the stagnant zones had been dispelled into the matrix. Porous media, beyond a distance equal to a few fracture apertures does not contribute to the dilution of the solution front for the flow velocity and timeframe in this experiment.
HEAT TRANSFER ENHANCEMENTS USING PIN FINS-POROUS-MEDIA SYSTEMS
1059-1075
10.1615/JPorMedia.v14.i12.20
A.-R.A.
Khaled
King Abdulaziz University
conduction
convection
heat transfer
fins
porous media
The present work analyzes heat transfer inside pin fins with cores filled with porous media. Two different systems are considered: a typical fin-porous-medium system (type A) and a joint fin-porous-medium system (type B). The coupled energy equations are solved numerically by an implicit, iterative finite difference scheme. Comparisons between numerical and analytical solutions are performed, and very good agreement is obtained. A new criterion for the validity of local thermal equilibrium assumptions inside the pin fin cores is identified. The numerical results are presented graphically in terms of Darcy number, porosity, thermal conductivity ratio, Biot numbers, relative radii ratio, Peclet number, and aspect ratio. It is found that thermal efficiencies of these systems can be increased significantly by introducing highly convective flows inside the porous cores. However, factors causing increases in external convections are found to decrease the thermal efficiency. Yet the decrease is expected to be higher for ordinary fins. Moreover, thermal efficiencies of type B systems are found to be highly responsive to internal convections, while those of type A systems are less sensitive to internal convections. Finally, the obtained results demonstrate that fins-porous-media systems can be efficient in transferring heat, which can be at no additional cost if the pressure difference across the joined reservoirs is large.
DEPENDENCE OF SINGLE-PHASE AND MULTIPHASE PERMEABILITY ON CAPILLARY PRESSURE: A UNIFIED APPROACH
1077-1086
10.1615/JPorMedia.v14.i12.30
B.
Markicevic
Department of Mechanical Engineering, Kettering University, Flint, Michigan 48504, USA
Ned
Djilali
Institute for Integrated Energy Systems and Department of Mechanical Engineering, University of Victoria, PO Box 1700, Victoria, BC V8W 2Y2, Canada
multiphase flow in porous media
invasion percolation
Katz and Thompson formula
generalized formation factor
capillary pressure and relative permeability unified formulation
We present a formulation to predict simultaneously the porous medium (single-phase) permeability, and the multiphase flow permeability of a non-wetting liquid in the limit of slow flow. The formulation is based on a new set of mixing rules in which weighting coefficients are obtained from the capillary pressure in the breakthrough point. These weights are calculated by mixing the harmonic average capillary pressure of the actual heterogeneous sample and the capillary pressure of a corresponding homogeneous medium. The porous medium (single phase) and the phase permeability are, on the other hand, found using two length scales: the first determined from the capillary pressure in the breakthrough point and the second calculated again using the homogeneous sample. This formulation is successfully validated for a slow drainage using capillary network simulations based on the invasion percolation mechanism with phase trapping. In the numerical simulations, both network heterogeneity and network size are varied. The simulations reveal that with increasing medium heterogeneity, the porous medium permeability (single phase) decreases, whereas for multiphase flow, the mobile phase permeability and the capillary pressure increase. For a sufficiently large domain (network) size, all three parameters are independent of domain size. The analytical mixing rules capture all of these dependencies, and very good agreement between analytical and numerical results is found.
CAPILLARY RISE OF A NON-NEWTONIAN LIQUID INTO A DEFORMABLE POROUS MATERIAL
1087-1102
10.1615/JPorMedia.v14.i12.40
Javed
Siddique
Department of Mathematics, Pennsylvania State University, York Campus, York, Pennsylvania 17403, USA
D. M.
Anderson
Department of Mathematical Sciences, George Mason University, Fairfax, Virginia 22030, USA
mixture theory
non-Newtonian fluid
deformable porous material
capillary rise
In this study we explore the one-dimensional capillary rise of a non-Newtonian, power-law fluid into rigid and deformable porous materials with and without gravity effects. For non-Newtonian flow in rigid porous materials with gravity, an equilibrium height equivalent to that for the classical Newtonian case is reached. However, the evolution toward the equilibrium solution differs between Newtonian and non-Newtonian cases. In the case of deformable porous material where both fluid and solid phases move, we use mixture theory to formulate the problem. Again equilibrium solutions exist and are the same for both Newtonian and non-Newtonian cases. In contrast to capillary rise in rigid porous material there are now two moving boundaries−the fluid height and the solid displacement at the bottom of the deforming porous material. In the absence of gravity effects, the model admits a similarity solution, which we compute numerically. With gravity present, the free boundary problem is solved numerically. In this case, the liquid rises to a finite height and the porous material deforms to a finite depth, following dynamics that depends on power-law index n and power-law consistency index μ;*.
A COMPARATIVE STUDY ON MHD FLOW BY TWO DIFFERENT TRANSFORM METHODS
1105-1113
10.1615/JPorMedia.v14.i12.50
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, P.O. Box 80257, Jeddah 21589, Saudi Arabia
M. Faheem
Afzaal
Imperial College London, University of Birmingham, Department of Mathematics, Quaid-i-Azam University
S.
Asghar
Department of Mathematical Sciences, COMSATS Institute of Information Technology, 30 Islamabad, Pakistan
Awatif A.
Hendi
Department of Physics, Faculty of Sciences, King Saud University, P. O. Box 1846, Riyadh 11321, Saudi Arabia
viscous fluid
Laplace transform
Fourier sine transform
tabulated functions
MHD
porous medium
This study is performed to provide a comparison for magnetohydrodynamic (MHD) flow in steady and transient solutions obtained by Laplace and Fourier sine transform methods. Oscillatory flow in a porous semi-infinite space is considered. Plots for the emerging parameters are presented and analyzed.
PULSATILE FLOW OF A VISCOUS STRATIFIED FLUID OF VARIABLE VISCOSITY BETWEEN PERMEABLE BEDS
1115-1124
10.1615/JPorMedia.v14.i12.60
K.
Avinash
Department of Mathematics, Osmania University, Hyderabad, 500007, India
J. Anand
Rao
Department of Mathematics, Faculty of Science, Osmania University, Hyderabad, 500007,
Telangana State, India
S.
Sreenadh
Department of Mathematics, Sri Venkateswara University, Tirupati, Andhra Pradesh, India-517502
Y. V. K. Ravi
Kumar
Department of Mathematics, Stanley College of Engineering and Technology for Women, Hyderabad, 500001, India
pulsatile flow
stratified fluid
permeable beds
variable viscosity
Pulsatile flow of a viscous stratified fluid of variable viscosity between permeable beds is studied. The flow between permeable beds is governed by Navier-Stokes equations and the flow through permeable beds is governed by Darcy's law. The velocity field is obtained for steady and unsteady cases. The volume flux and fractional increase are also determined and the results are deduced and discussed through graphs.
NEW ANALYTICAL SOLUTION OF STAGNATION POINT FLOW IN A POROUS MEDIUM
1125-1135
10.1615/JPorMedia.v14.i12.70
Mohammad Mehdi
Rashidi
Tongji University
Davood
Ganji (D.D. Ganji)
Babol University
Seyed Majid
Sadri
Mechanical Engineering Department, Engineering Faculty of Bu-Ali Sina University, Hamedan, Iran
differential transform method
Padé approximant
stagnation point flow
porous medium
nonlinear differential equations
In this paper, we propose a reliable algorithm to develop approximate solutions for the problem of the Brinkmann equation governing the two-dimensional stagnation point flow in a porous medium. The governing system of partial differential equations is transformed into an ordinary differential equation. The differential transform method (DTM) is employed to compute an approximation to the solution of the nonlinear differential equation governing the problem in the form of a series with easily computable terms Then, the Padé approximant is applied to the solutions to increase the convergence of a given series. The features of the flow characteristics for different values of the governing parameters are analyzed and discussed. It is shown that the reliability and performance of the DTM is very good in comparison with differential transform method in solving this problem.