Begell House Inc.
Journal of Porous Media
JPM
1091-028X
14
5
2011
A FEASIBILITY STUDY OF EMPLOYING SEQUENTIAL FUNCTION SPECIFICATION METHOD FOR ESTIMATION OF TRANSIENT HEAT FLUX IN A NON-THERMAL EQUILIBRIUM POROUS CHANNEL
375-381
10.1615/JPorMedia.v14.i5.10
Mohsen
Nazari
Department of Mechanical Engineering, Shahrood University of Technology, Shahrood, Iran
Farshad
Kowsary
Department of Mechanical Engineering, University College of Engineering, University of Tehran, Tehran 515-14395, Iran
sequential function specification method
porous medium
non-thermal equilibrium
This paper is concerned with the inverse heat transfer between two parallel plates filled with a porous medium under a non-equilibrium condition. One of the difficulties in an inverse problem utilizing a non-thermal equilibrium model in porous media is the fact that it is not clear whether to assign the measured temperatures to a solid or fluid phase. A sequential function specification method (SFSM) is employed to estimate the transient wall heat flux imposed on the porous boundary. Effects of the future temperature data (r parameter) and sensor location on the estimated heat flux have been completely studied in the SFSM. The values of bias and variance errors have been calculated at sensor locations to obtain the optimum temperature measurements. Results show that sensor locations and existing errors in the measured data have important effects on the calculated heat flux; nonetheless, accurate heat flux estimation is quite achievable.
A MODEL FOR PARTICLE DEPOSITION DURING IMPREGNATION OF FIBROUS POROUS MEDIA
383-394
10.1615/JPorMedia.v14.i5.20
Claire
Steggall-Murphy
Department of Mechanical Engineering, University of Delaware; and Center for Composite Materials, University of Delaware, Newark, Delaware 19716, USA
Pavel
Simacek
Department of Mechanical Engineering and Center for Composite Materials, University of
Delaware, Newark, DE 19716
Suresh G.
Advani
Department of Mechanical Engineering and Center for Composite Materials, University of
Delaware, Newark, DE 19716
Amandine
Barthelemy
Department of Mechanical Engineering, University of Delaware; and Center for Composite Materials, University of Delaware, Newark, Delaware 19716, USA
Shridhar
Yarlagadda
Center for Composite Materials, University of Delaware, Newark, Delaware 19716, USA
Shawn
Walsh
Aberdeen Proving Grounds, United States Army Research Laboratory, Aberdeen, Maryland 21005, USA
composite materials
particle impregnation
glass fiber composites
dual scale porous media
suspension flow
Filtration of particles in porous media is used for many applications, including desalination and water treatment, food manufacturing, paper making, and composites processing. In this paper, the deposition of thermoplastic particles is used to deliver matrix material within a composite textile. A constitutive model to describe the filtration behavior within the porous fabric with respect to time is proposed. The model requires characterization of a filtration coefficient that is a function of suspension concentration and shear rate. Experiments with different concentrations and shear rates are designed and conducted to measure the constants needed to characterize the filtration coefficient through regression analysis. The model is then compared with experimental data for a wide range of particle concentrations and fluid velocities. Although there is a difference between the model and the experimental results, the trends of the model are encouraging.
INVESTIGATING ROCK-FACE BOUNDARY EFFECTS ON CAPILLARY PRESSURE AND RELATIVE PERMEABILITY MEASUREMENTS
395-409
10.1615/JPorMedia.v14.i5.30
O. A.
Al-Omair
Department of Petroleum Engineering, Kuwait University, P.O. Box 5969, Safat 13060, Kuwait
S. M.
Al-Mudhhi
Department of Petroleum Engineering, Kuwait University, P.O. Box 5969, Safat 13060, Kuwait
M. M.
Al-Dousari
Department of Petroleum Engineering, Kuwait University, P.O. Box 5969, Safat 13060, Kuwait
capillary pressure
relative permeability
spinning disk
boundary effect
This paper covers the experimental study of water-gas capillary pressure and relative permeability in laboratory scale using the centrifuge spinning disk method to investigate the rock-face boundary effects. The capillary pressure wetting-phase saturation data were first generated using both the centrifuge spinning disk setup and the porous plate setup for the same samples. These measurements are performed to validate the accuracy of the centrifuge spinning disk method. Using the measured capillary pressure data, relative permeability relationships were estimated for each sample by history-matching production and saturation distribution data. The production data was monitored for each disk-shaped rock sample using two different experimental conditions—one by sealing the top and bottom faces of the sample and the other without sealing the rock faces. This is done to investigate the effects of sealing the tested samples on the measured data and ultimately on the relative permeability. Results show that the measured capillary pressure data generated using the spinning disk method are in agreement with the capillary pressure data generated with the porous plate method. Results also showed that the gas and brine relative permeabilities are independent of the rock sealing conditions. The average variation between the two methods used was in the order of 2% with a standard deviation of 2.2%. Capillary pressure data measured using cases with unsealed boundaries were practically a reproduction of capillary pressure data for the same core samples with sealed boundaries. The average variation between these methods was approximately 2.3% with a standard deviation of 2.6%. Capillary pressure and relative permeability are of great importance to petroleum engineers attempting to understand and predict the behavior of various petroleum recovery processes. Accurate determination of relative permeability data is essential for estimating the free water saturation, aiding in evaluating drill-stem and production tests, and estimating the residual saturations. This accuracy of the capillary pressure data and the precession of generated relative permeability data is a consequence of the refinement of the spinning disk setup. The improvement consists of modification of the core holder and adaptation of better lighting conditions. With this procedure, direct determination of capillary pressure saturation data is possible for the equilibrium saturation distribution.
CAPILLARY RISE IN A NON-UNIFORM TUBE
411-422
10.1615/JPorMedia.v14.i5.40
Mohamed El Amine
Ben Amara
Laboratoire d'Etudes des Systemes Thermiques et Energetiques, Ecole Nationale d'Ingenieurs de Monastir, Monastir 5019, Tunisia
Sassi Ben
Nasrallah
Laboratoire d'Études des Systèmes Thermiques et Énergétiques, Ecole Nationale d'Ingénieurs
de Monastir, Monastir 5019 Tunisie
capillary rise
cone capillary
sinusoidal capillary
Lucas-Washburn equation
In this paper we describe the liquid progression in a non-uniform capillary in the case where the inertia effects are considered. The approach is based on the application of Newton’s second law on the liquid column. Numerical solutions are obtained by solving a general differential equation describing the time-dependent rise of the liquid-gas interface. The effect of capillary geometry on the progress of the liquid interface has been investigated in conical and sinusoidal capillaries while varying several parameters, such as cone opening angle α in both converging and diverging tubes and the undulation of a sinusoidal capillary. The influence of inertia and viscosity on the equilibrium height and on the rise dynamics is investigated. The results allow better comprehension of the capillary rise in complex geometry under inertia effects and these might provide further explanation for fluid distribution in modeled porous media.
IMMISCIBLE FLUID DISPLACEMENT IN POROUS MEDIA: EXPERIMENTS AND SIMULATIONS
423-435
10.1615/JPorMedia.v14.i5.50
C. P.
Krishnamoorthy
Department of Chemical Engineering, Indian Institute of Technology Madras, Chennai 600 036, India
Abhijit P.
Deshpande
Department of Chemical Engineering, Indian Institute of Technology Madras, Chennai 600 036, India
S.
Pushpavanam
Department of Chemical Engineering, Indian Institute of Technology Madras, Chennai 600 036, India
pore-network modeling
stable displacement
viscous fingering
In this work, we investigate experimentally as well as numerically a drainage displacement system; i.e., a non-wetting fluid displacing a wetting fluid in a porous medium. Experiments were carried out in a horizontal rectangular channel packed with a monolayer of glass beads. The displacement of a higher viscosity wetting fluid (silicone oil) by a lower viscosity non-wetting fluid (air) is studied. Similarly, the displacement of a lower viscosity wetting fluid (silicone oil) by a higher viscosity non-wetting fluid (glycerol) is also studied. Flow structures, such as viscous fingering and stable displacement, were obtained. The behavior of the flow in the experiments was simulated using a pore network model. The model consists of a network of tubes of equal lengths inclined at 45±. The radius of the tubes is assumed to follow a random distribution to ensure a realistic representation of a porous medium. The pressure distribution across the network is obtained by assuming laminar flow in each tube. The Hagen-Poiseuille equation is used after including the effect of capillary pressure to determine the flow velocity in each tube. The displacement of the interface for each time step is restricted to 2.5−.0% of the tube length and the maximum velocity in the network is used to calculate this time interval. The movement of the interface inside the tube is calculated using a second-order Runge-Kutta method. Once the interface reaches a node, the volume of the fluid entering the neighboring tubes is determined by the pressure drop across them. We have varied the capillary number, Ca (μ;ν/σA), and viscosity ratio, M, and have obtained two different flow regimes, viscous fingering and stable displacement. The residual amount of defending fluid present in the network model is calculated for the two regimes of drainage displacements. It is found that when stable displacement occurs, the system has significantly less amount of defending fluid present for the same duration of time as compared with the case when viscous fingering is exhibited. The fronts of the invading fluid during viscous fingering at different capillary numbers are self-similar with a fractal dimension of 1.3 that matches with the experimental results.
ON THE EFFECTS OF A CUBIC TEMPERATURE PROFILE ON OSCILLATORY RAYLEIGH-BENARD CONVECTION IN A VISCOELASTIC FLUID-FILLED HIGH-POROSITY MEDIUM
437-447
10.1615/JPorMedia.v14.i5.60
Ruwaidiah
Idris
Department of Mathematics, Faculty of Science and Technology, Universiti Malaysia Terengganu, 21030 Kuala Terengganu, Malaysia
Ishak
Hashim
School of Mathematical Sciences & Solar Energy Research Institute, Faculty of Science
& Technology, Universiti Kebangsaan Malaysia 43600 UKM Bangi, Selangor DE, Malaysia
Rayleigh-Benard convection
cubic thermal gradient
viscoelastic fluid
porous medium
This study investigated the instability of Rayleigh-Bénard convection in a horizontal layer of Boussinesq, viscoelastic fluid-filled high-porosity medium under the influence of a cubic temperature profile. A linear stability analysis was performed. A single-term Galerkin technique was used to obtain the critical stability parameter for free-free, free- rigid, and rigid-rigid boundary combinations with conducting temperature conditions. It is shown that the strain retardation time delayed the convection while the stress relaxation time promoted it. The effect of the Darcy number and the Brinkman number on the linear stability of the system is analyzed and presented graphically.
EFFECTS OF PERIODIC PERMEABILITY AND SUCTION VELOCITY ON THREE-DIMENSIONAL FREE CONVECTION FLOWPAST A VERTICAL POROUS PLATE EMBEDDED IN HIGHLY POROUS MEDIUM
451-460
10.1615/JPorMedia.v14.i5.70
Ajay Kumar
Singh
Department of Mathematics, C. L. Jain College, Firozabad-283 203, India
P. P.
Singh
Department of Mathematics, C. L. Jain (P.G.) College, Firozabad 283203, India
N. P.
Singh
Department of Applied Sciences and Humanities, Rama Institute of Engineering and Technology, Mandhan, Kanpur-209217; and Department of Humanities and Applied Science, Amity University, Lucknow 226010, India
three-dimensional
free convection
viscous fluid
porous medium
The present paper deals with analytical solution of three-dimensional (3D) free convection, laminar flow of an incompressible viscous fluid past an infinite, vertical, and porous plate embedded within a highly porous medium. It is assumed that the plate is subjected to a periodic suction velocity normal to the plate in the presence of a temperature-dependent heat sink. The periodicity of the suction velocity, permeability, and heat sink are assumed to be of equal magnitude and wavelength. Approximate solutions for the potential flow, cross flow, and temperature distribution are obtained using perturbation techniques and the results are shown. Expressions for skin-friction due to the main flow and the rate of heat transfer at the plate are derived and discussed and their numerical values for various physical parameters are presented. It is observed that (1) an increase in the Prandtl, Grashof, and Reynolds numbers of permeability increases the velocity of the main flow, while an increase in the suction parameter decreases the main flow; (2) an increase in the suction parameter or Reynolds number decreases the cross flow while an increase in permeability increases the cross flow; and (3) an increase in the Prandtl and Reynolds numbers or the suction decreases the temperature. The results of the some earlier authors are deduced as particular cases of the present study.
STEADY INCOMPRESSIBLE FLOWOF A COUPLE STRESS FLUID IN A POROUS MEDIUM
461-466
10.1615/JPorMedia.v14.i5.80
S.
Islam
Department of Mathematics, COMSATS Institute of Information Technology, Chakshazad Park Road, Islamabad, Pakistan
X. J.
Ran
Department of Basic Sciences, Harbin Institute of Technology Shenzhen, 518055, China
Q. K.
Ghori
Department of Mathematics, COMSATS Institute of Information Technology, 30 H-8/1, Islamabad Pakistan
Abdul Majeed
Siddiqui
Department of Mathematics, Pennsylvania State University, York Campus, 1031 Edgecomb Avenue, York, PA 17403, USA
stream function
exact solution
modified Darcy's law
separation of variables
Two-dimensional steady flow of an incompressible homogenous couple stress fluid through a porous medium is considered. Exact solutions of the nonlinear equations of motion are derived, using canonical transformation and the generalized method of separation of variables. Expressions for the stream function and velocity components are derived in each case.