Begell House
Journal of Porous Media
Journal of Porous Media
1091-028X
5
1
2002
The Importance of Capillary Forces in Waterflooding: An Examination of the Buckley-Leverett Frontal Displacement Theory
In the study described in this article waterflood saturation profiles have been simulated at field injection rates, using the complete fractional flow equation, in models of length ranging from 1 m to 200 m. The profiles change from very gradual in the 1 m model to near piston-like in the 200 m model. It has been demonstrated that neglecting the capillary term from the complete fractional flow equation results in a multiple-valued saturation profile. The simulated profiles indicated that the Buckley-Leverett front is never reached at reservoir oil-water interfacial tensions. Only at very low interfacial tensions does the capillary term become vanishingly small. The behavior observed in waterfloods, according to which the saturation profile becomes steeper at increasing water injection rates, is explained in terms of a capillary model in which there is pressure equilibration between the parallel capillaries of the model. It is shown that, at reservoir interfacial tensions, in this model the water front in the narrower capillary is ahead of the front in the wider capillary and also that the distance between the two fronts decreases at increasing water injection rates, but the front in the wider capillary never advances ahead of the front in the narrower capillary. This capillary model is shown to lead to the complete fractional flow equation of Leverett.
F. A. L.
Dullien
Porous Media Research Institute, Department of Chemical Engineering, University of Waterloo, Ontario N2L3G1, Canada
Mingzhe
Dong
School of Petroleum Engineering, China University of Petroleum (East China), Qingdao
266580, People's Republic of China; Department of Chemical and Petroleum Engineering, University of Calgary, Calgary, AB, T2N 1N4, Canada
16
Multilayer Three-Node Model of Convective Transport Within Cotton Fibrous Medium
The air penetration within a porous clothing system on a moving human is an important physical process that considerably affects the heat and moisture resistance of the textile material. This effect of the coupled convection heat and mass exchange within the clothing system is experimentally investigated and theoretically modeled to predict the fabric regain, the fabric temperature, and the transient exit conditions of air penetrating the void space and the solid fiber. Experiments were conducted inside environmentally controlled chambers to measure the transient moisture uptake of untreated cotton fabric samples as well as the outer fabric temperature using an infrared pyrometer. The moisture uptake was conducted at three different volumetric flow rates of 0.0067, 0.018, and 0.045 m3/s/m2 of fabric area to represent air flow penetrations that could result from vigorous, medium, and slow walking, respectively. The theoretical analysis is based on a three-layer three-node adsorption model of the fibrous medium and air void. In each layer, the outer nodes represents the exposed surface of the "solid yarn" that is in direct contact with the penetrating air in the void space, and the inner node represents the inner portion of the solid yarn and is completely surrounded by the outer node at that layer. The penetrating air multilayer nodes are the links between the inner and outer layers. A set of six coupled differential equations were derived describing time-dependent convective heat and mass transfer between the penetrating air and the solid fiber in terms of relevant transport coefficients at each layer level. The outer heat and mass transfer coefficients were obtained from the single-layer two-node absorption model of Gali et al. (2000). The transport equations were solved numerically, for the regain and fabric nodes temperatures, using an explicit integration by the second-order Adams-Bashforth scheme. The increase in the air temperature predicted by the current model agreed well with the experimentally measured values.
Kamel
Ghali
Beirut Arab University, Engineering College, Beirut, Lebanon
Byron
Jones
Kansas State University, College of Engineering, Manhattan, Kansas 66506-5202
18
Examination of the Thermal Equilibrium Assumption in Periodic Forced Convection in a Porous Channel
The validity of the local thermal equilibrium assumption in the periodic forced convection porous channel flow is investigated analytically. Closed form expressions are presented for the temperatures of the fluid and solid domains and for the criterion that ensures the validity of the local thermal equilibrium assumption. It is found that four dimensionless parameters control the local thermal equilibrium assumption. These parameters are the porous domain void fraction ∈, the volumetric Biot number Bi, the dimensionless frequency ω, and the solid-to-fluid total thermal capacity ratio CR. The criterion that secures the validity of the local thermal equilibrium assumption within 5% error, is found to be...
S.
Kiwan
Mechanical Engineering Department, Jordan University of Science and Technology, lrbid 22110, Jordan
Moh'd Ahmad
Al-Nimr
Jordan University of Science and Technology
6
Non-Darcy Forced Convective Heat Transfer in a Viscoelastic Fluid Flow Over a Nonisothermal Stretching Sheet
In the present article an analysis has been carried out to study the boundary layer flow behavior and heat transfer characteristics of a viscoelastic fluid immersed in a porous medium over a semi-infinite impermeable stretching sheet. The presence of non-Darcy forced convection leads to coupling and high nonlinearity in the boundary value problem. Because of coupling and nonlinearity, the proposed intricate mathematical problem has been solved numerically by employing a fourth-order Runge-Kutta integration scheme and shooting technique for two-unknown initial conditions. Numerical results are analyzed for various values of viscoelastic parameter and inertia parameter. One of the important observations is that the inertia parameter has a significant influence on the flow in reducing the boundary layer velocity and increasing the rate of heat transfer.
K. V.
Prasad
Department of Mathematics, Central College Campus, Bangalore University, Bangalore, India
M. Subhas
Abel
Department of Mathematics, Gulbarga University, Gulbarga, Kamataka, India
Sujit Kumar
Khan
Department of Mathematics, Gulbarga University, Gulbarga, 585 106, Karnataka, India
P. S.
Datti
School of Mathematics, TIFR Centre, Indian Institute of Science Campus, Bangalore, India
8
Evaluation of Steady Flow Through a Six-Lobe Sand Cartridge Filter by the Boundary Perturbation Method
Consolidated sand cartridge filters are used in the oil industry to filter particles from produced water before pumping the water back into the ground for secondary oil recovery. The sand filter is essentially an annulus, but its outer surface is structured into a six-lobed curved geometry that gives it larger surface area for filtration. The larger surface area increases the life of the filter, but the geometry is more difficult to evaluate than the simple cylindrical geometry. The problem addressed in this article is to determine the steady-state pressure profile for radial flow of water through the filter. This pressure profile can then be used to determine the velocity profiles through the filter, and finally determine the flow rate that can be achieved through the filter. For porous media with uniform isotropic permeability, Darcy's law (Darcy, 1856) is used to describe the pressure-velocity relationship. The six-lobed geometry forms a boundary condition that does not coincide with a level surface in cylindrical coordinates. This is not only a basic flow problem of addressing the needs of filtration industry, oil industry, or chemical engineering, but it is also of mathematical interest. The boundary perturbation method (Van Dyke, 1975; Georgescu, 1995) is not widely used to solve partial differential equations, even though the method is well illustrated. The application of the method to model the irregular geometry of the six-lobed cartridge filter is new. When the boundary perturbation method is used to solve a partial differential equation, the resulting solution can be described in a series form. The first term of the solution corresponds to the simple cylindrical annular geometry. The subsequent terms converge to describe the solution for the six-lobed geometry. A third order solution, beyond the annular solution, is sufficiently accurate for calculating the pressure profile, for typical filter designs. The results show that for a given pressure drop, the six-lobed design provides greater flow rates than would be obtained for cylindrical filters of similar size.
H. R.
Patel
Department of Chemical Engineering, The University of Akron, Akron, Ohio 44325-3906
S. I.
Hariharan
Department of Mathematical Sciences, The University of Akron, Akron, Ohio, U.S.A.; and ICOMP, NASA Lewis Research Center, Cleveland, Ohio, U.S.A.
G. G.
Chase
Department of Chemical Engineering, Microscale Physiochemical Engineering Center, The University of Akron, Akron, Ohio 44325-3906
8
Heat and Mass Transfer by Natural Convection from a Vertical Surface to the Stratified Darcian Fluid
The effect of the combined stratification on natural convection about a vertical surface in a porous medium is studied. This article reports a similarity solution and the Von Karman integral method for buoyancy-induced flow and heat and mass and mass flux from the wall is constant. Governing parameters for the problem are the buoyancy ratio N, Lewis number Le, thermal stratification parameter S2 and the solutal stratification parameter S2. Results for Nusselt and Sherwood numbers are presented for wide range of governing parameters, and it is observed that both these physical characteristics increase with S1 and S2.
Virendra
Bansod
Department of Mathematics, Dr. B. A. Technological University, Lonere, India
P.
Singh
Department of Mathematics, Indian Institute of Technology, Kanpur, India
B. V.
Rathishkumar
Institute of Physical and Chemical Research Hirosawa 2-1, Wako-shi, Saitama, 351-0198, Japan; and Department of Mathematics, Indian Institute of Technology, Kanpur, India
10
International Conference on Applications of Porous MediaJerba, Tunisia, June 02-08, 2002
10