Begell House
Journal of Porous Media
Journal of Porous Media
1091-028X
1
1
1998
Foreword
It is our pleasure to present this first issue of the Journal of Porous Media to researchers in Science, Engineering, and Industry. Our hope is that the variety and depth of the field will be reflected in the Journal articles. It has long been felt that the diversity and common underlying principles of porous media research needed a journal of their own. This publication will span the territory that is covered by papers currently spread over many journals. As time progresses this Journal can become the main forum for many topics. Another advantage of this publication will be the stimulus that it can give to research through review articles and industrial interactions, in addition to specific research papers. This Journal will also bring together researchers in conferences, thereby giving a unique identity to the Porous Media field.
The Journal of Porous Media is fortunate to have a highly distinguished Editorial Board whose members are leaders in the mainstream of research. The procedure for submitting an article and the scope of this Journal are outlined within its pages. The Journal of Porous Media will publish original full-length research papers (and technical notes) in a wide variety of areas of porous media studies: for example, Mathematical Modeling, Numerical and Experimental Techniques; Industrial and Environmental Heat and Mass Transfer; Conduction, Convection, Radiation; Particle Transport and Capillary Effects, Reactive Flows, Deformable Porous Media, and Mechanics of the Porous Substrate. Emphasis will be given to manuscripts that present novel findings pertinent to the previously mentioned areas. This Journal will also consider publication of state-of-the-art reviews. Manuscripts applying only known methods to previously solved problems or providing results in the absence of scientific motivation or application will not be accepted. Submitted articles should contribute to the understanding of specific scientific problems or to solution techniques that are useful in applications. Papers that link theory with computational practice to provide insight into the processes are welcome.
An historical note regarding the events and in-depth discussions leading to the establishment of the Journal: in October 1994, the Institute of Industrial Mathematical Sciences (IIMS) at the University of Manitoba organized a Conference on Porous Media and the Environment in Winnipeg, Canada with the University of New Brunswick. This in turn led to the International Conference on Porous Media and its Applications in Science, Engineering, and Industry Meeting being held in June 1996 in Hawaii. The latter meeting was organized by IIMS and the Engineering Foundation with the cooperation of The Ohio State University.
iii
Capillary Effects and Multiphase Flow in Porous Media
Against a background of the topologies of the immiscible fluids in porous media, a few recent advances in multiphase flow involving capillarity have been briefly reviewed. 1) Measurement and interpretation of hydrodynamic coupling in cocurrent two-phase flow: In steady flow, in the absence of a saturation gradient, coupling of a purely kinematic character can exist in low permeability media at low wetting fluid saturations when the wetting phase, of a lower viscosity than the nonwetting phase, is continuous only on the pore walls in the form of thick films. As a result of this lubricating effect, the flow of the nonwetting phase is increased, whereas the flow of the wetting phase is unaffected. In the presence of a saturation gradient, however, significant viscous coupling between two fluids of the same viscosity has been measured in experiments in a sand pack where the pressure gradient in one of the two fluids was kept zero, while the other fluid was pumped at a constant rate. 2) General representation of the evolution of saturation profiles in waterfloods in different porous media in terms of two scaling parameters: The viscosity ratio and the ratio of viscous-to-capillary forces CA = Q/Q0 (Q is the constant injection rate of water in the water flood and Q0 is the rate of spontaneous imbibition of water into the same system at zero time). 3) Imbibition of blobs of nonspreading oil (negative spreading coefficient) in film form over thick water films present in the edges and/or grooves of pore walls: Oil blobs that are surrounded by water and trapped by capillary forces spread, after draining the bulk of the water, on the surface of the remaining thick water films (i) if the spreading coefficient is positive by the known laws of spreading and (ii) by capillary forces if the spreading coefficient is negative. The conditions controlling the second kind of spreading (ii) have been quantified by using classical Gibbs-free energy treatment and the predictions have been verified by experiment.
F. A. L.
Dullien
Porous Media Research Institute, Department of Chemical Engineering, University of Waterloo, Ontario N2L3G1, Canada
1-29
Heat Transfer at the Boundary Between a Porous Medium and a Homogeneous Fluid: The One-Equation Model
The heat transfer condition at the boundary between a porous medium (the ω region) and a homogeneous fluid {the η region) is developed as a flux jump condition based on the "nonlocal form" of the volume-averaged thermal energy equation that is valid within the "boundary region." Away from the boundary region, we impose the condition of "local thermal equilibrium" so that the nonlocal form simplifies to the classic one-equation model for thermal energy transport. The derived jump condition for the energy flux contains terms representing the accumulation, conduction, and convection of "excess surface thermal energy," in addition to an "excess nonequilibrium thermal source" that results from the potential failure of local thermal equilibrium in the boundary region. When the transport of excess surface thermal energy is negligible, the analysis indicates that the jump condition reduces to
nωη · Κω* · ∇ (T)ω = nωη · kβ(T)η + Φs, at the ω−η boundary
Because local thermal equilibrium will fail in the boundary region before it fails in the homogeneous region of the porous medium, the nonequilibrium thermal source, Φs represents an important term in the transition from a one-equation model to a two-equation model.
J Alberto
Ochoa-Tapia
Departamento de I.P.H., Universidad Autonoma Metropolitana-Iztapalapa, Av. San Rafael Atlixco 186, Col. Vicentina, 09340, Mexico, D.F., Mexico
Stephen
Whitaker
Department of Chemical Engineering and Material Science, University of California, Davis, California, USA
31-46
Numerical Modeling of Turbulent Flow in Porous Media Using a Spatially Periodic Array
Turbulent flowfields within a spatially periodic array were calculated numerically using a finite difference method with a low Reynolds number, two-equation model of turbulence. Exploiting periodic boundary conditions, only a one-structural unit was taken as a calculation domain to simulate a porous medium of regular arrangement in an infinite space. Extensive numerical calculations were carried out for a wide range of Reynolds numbers, to elucidate hydrodynamic behaviors of turbulent flow (post-Forchheimer flow) in porous media. The microscopic numerical results thus obtained at a pore scale were processed to extract the macroscopic hydrodynamic characteristics in terms of the volume-averaged quantities. The macroscopic pressure and flow rate relationship, determined purely from a theoretical basis, has been examined against the existing semiempirical laws, namely, Forchheimer-extended Darcy's law. Thus, departure from Darcy's law resulting from combined nonlinear effects of both porous inertia and turbulence on the macroscopic pressure drop has been investigated numerically and correlated with the porosity and Reynolds number.
Fujio
Kuwahara
Department of Mechanical Engineering, Shizuoka University, 3-5-1 Johoku, Hamamatsu, 432-8561 Japan
Y.
Kameyama
Department of Mechanical Engineering, Shizuoka University, 3-5-1 Johoku, Hamamatsu 432, Japan
S.
Yamashita
Department of Mechanical Engineering, Shizuoka University, 3-5-1 Johoku, Hamamatsu 432, Japan
Akira
Nakayama
Department of Mechanical Engineering, Shizuoka University, 3-5-1 Johoku, Naka-ku, Hamamatsu, 432-8561, Japan; Wuhan Polytechnic University, Wuhan, Hubei 430023, China
47-55
Convection Induced by Inclined Gradients in a Shallow Porous Medium Layer
A review is made of recent convection studies in a shallow layer of a saturated porous medium, induced by applied thermal and/or solutal gradients. This problem is likely to be paradigmatic for convection induced by such gradients in more general geometries. A horizontal gradient induces a "Hadley circulation," which can be superimposed on any existing forced convection flow. The stability of the combined basic flow depends on the horizontal and vertical components of the inclined gradients. Above a certain vertical gradient value an additional cellular flow is superimposed on the basic flow. The nature of the additional cellular flow (e.g., stationary or oscillatory horizontal rolls whose axes are perpendicular to the vertical gradient and aligned with or perpendicular to the horizontal gradient), depends on the parameters involved.
Jose
Lage
Southern Methodist University
57-69
Review of Porous Media Enhanced Vapor-Phase Diffusion Mechanisms, Models, and Data—Does Enhanced Vapor-Phase Diffusion Exist?
A review of mechanisms, models, and data relevant to the postulated phenomenon of enhanced vapor-phase diffusion in porous media is presented. Information is obtained from literature spanning two different disciplines (soil science and engineering) to gain a diverse perspective on this topic. Findings indicate that while enhanced vapor diffusion tends to correct the discrepancies observed between past theory and experiments, no direct evidence exists to support the postulated processes causing enhanced vapor diffusion. Numerical modeling analyses of experiments representative of the two disciplines are presented in this paper to assess the sensitivity of different systems to enhanced vapor diffusion. Pore-scale modeling is also performed to evaluate the relative significance of enhanced vapor diffusion mechanisms when compared to Fickian diffusion. The results demonstrate the need for additional experiments so that more discerning analyses can be performed.
Stephen W.
Webb
Geohydrology Department, Sandia National Laboratories, Albuquerque, New Mexico 87185-1324, USA
Clifford K.
Ho
Geohydrology Department, Sandia National Laboratories, Albuquerque, New Mexico, 87185-1324, USA
71-92
Experimental Evidence for Permeability Minima at Low-Velocity Gas Flow Through Naturally Formed Porous Media
The objective of this paper is to describe and discuss experiments that document the presence of minima in the permeability to nitrogen gas for a number of rock samples at fluid velocities of 0.3−0.8 × 10−3 m/s, and mean pressures up to 0.4 MPa. The k-minima are interpreted as occurring in a transitional flow regime, in which, as fluid velocities decrease, the contribution of viscous or Poiseuille flow is progressively exceeded and ultimately replaced by "molecular streaming" or Knudsen flow. These are the first reported experiments known to the authors that are specifically designed to test the effects of low flow rates on the gas permeability of natural samples. The test samples are sandstones and limestones, displaying a broad range of porosities (0.12−0.30) and gas permeabilities (1.5−1600 × 10−3 μm2). For every sample, a k-minimum can be found at each of three mean pressures, but the three minima correspond to a single, "critical" fluid velocity. Fluid velocities as low and lower than those tested are common, if not predominant, under natural and induced subsurface conditions. The experimental results indicate that the widely accepted Klinkenberg correction for gas "slippage," based on the mean pressure-dependence of slip flow, is not applicable at these low fluid velocities. Instead, fluid velocity is proposed as a critical parameter controlling the onset of subviscous flow mechanisms.
Rudi
Meyer
Department of Geology and Geophysics, The University of Calgary, 2500 University Drive N.W., Calgary, Alberta T2N 1N4, Canada
Federico F.
Krause
Department of Geology and Geophysics, The University of Calgary, 2500 University Drive N.W., Calgary, Alberta T2N 1N4, Canada
93-106
Onset of a Double-Diffusive Convective Regime in a Rectangular Porous Cavity
The onset of a double-diffusive convective regime in a rectangular cavity filled with a porous medium saturated by a binary fluid is studied. The two vertical walls are kept at different but uniform temperatures and concentrations, while the horizontal walls are impermeable and adiabatic. When the ratio of the resulting solutal and thermal buoyancy forces is equal to (−1), an equilibrium solution corresponding to a purely diffusive regime is obtained. We demonstrate that this regime is linearly stable until a critical thermal Rayleigh number, Rac, depending on the cell aspect ratio, A, and the Lewis number, Le. For a square cavity we obtained Rac|Le − 1| = 184.06, and for an infinite vertical layer the critical parameters are found to follow Rac|Le − 1| = 105.33 and kc = 2.51. These analytical results are in good agreement with numerical direct simulations. It is thus found that the bifurcation that corresponds to the onset of convection is a transcritical type for A = 1. The structures of the subcritical and supercritical steady solutions, at several values of the Lewis number and for a square cavity, have been studied numerically. The double-diffusive convective regime taking place when the equilibrium regime loses its stability is also described.
Marie-Catherine
Charrier-Mojtabi
Laboratoire PHASE E.A. 3028, Université Paul Sabatier, France
Mohammad
Karimi-Fard
Institut de Mécanique des Fluides, UMR CNRS-INP-UPS №5502, Avenue du Professeur Camille Soula, F 31400 Toulouse, France
Mejdi
Azaiez
IMFT, UMR CNRS/INP/UPS N°5502, UFR MIG, Université Paul Sabatier, 118r oute de Narbonne, 31062, Toulouse Cedex, France
Abdelkader
Mojtabi
Institut de Mécanique des Fluides, UMR CNRS-INP-UPS №5502, Université Paul Sabatier, Avenue du Professeur Camille Soula, F 31400 Toulouse, France
107-121