Free porous media

The primary factor controlling how much gas is in the form of discontinuous bubbles is the lamellae stability. As lamellae rupture, the bubble size or texture increases. Indeed, if bubble coalescence is very rapid, then most all of the gas phase will be continuous and the effectiveness of foam as a mobility-control fluid will be lost. This paper addresses the fundamental mechanisms underlying foam stability in oil-free porous media. 

The most important conclusion from the core-flood experiments is that the selected surfactants produced effective nitrogen-based foams at extreme conditions of salinity and hardness in oil-free porous media under reservoir conditions (2). 

Many hydrocarbon-miscible floods are run in reservoirs containing brines of extremely high salinity and hardness. Surfactants that may be used for mobility control foams at such conditions are commercially available. The effectiveness of foams generated with these surfactants was illustrated by way of representative mobility reductions factors measured in oil-free porous media. 

The following mechanisms are usually major contributors to surfactant loss in an oil-free porous medium ... 

To the extent that dispersion in an inertia free porous medium flow arises from a nonuniform velocity distribution, its physical basis is the same as that of Taylor dispersion within a capillary. Data on solute dispersions in such flows show the long-time behavior to be Gaussian, as in capillaries. The Taylor dispersion equation for circular capillaries (Eq. 4.6.30) has therefore been applied empirically as a model equation to characterize the dispersion process in chromatographic separations in packed beds and porous media, with the mean velocity identified with the interstitial velocity. In so doing it is implicitly assumed that the mean interstitial velocity and flow pattern is independent of the flow rate, a condition that would, for example, not prevail when inertial effects become important. 

At the present time there exist no flux relations wich a completely sound cheoretical basis, capable of describing transport in porous media over the whole range of pressures or pore sizes. All involve empiricism to a greater or less degree, or are based on a physically unrealistic representation of the structure of the porous medium. Existing models fall into two main classes in the first the medium is modeled as a network of interconnected capillaries, while in the second it is represented by an assembly of stationary obstacles dispersed in the gas on a molecular scale. The first type of model is closely related to the physical structure of the medium, but its development is hampered by the lack of a solution to the problem of transport in a capillary whose diameter is comparable to mean free path lengths in the gas mixture. The second type of model is more tenuously related to the real medium but more tractable theoretically. 

The Stefan-Maxwell equations have been presented for the case of a gas in the absence of a porous medium. However, in a porous medium whose pores are all wide compared with mean free path lengths it is reasonable to guess that the fluxes will still satisfy relations of the Stefan-Maxwell form since intermolecular collisions still dominate molecule-wall collisions. 

Knudseci s very careful experiments on a long uniform capillary show that N L/ Pj -p ) passes through a marked minimum when plotted as a function of (P +P2)/2, at a value of the mean pressure such that the capillary diameter and the mean free path length are comparable. At higher values of the mean pressure, N L/(pj " 2 rises linearly, as in the case of a porous medium. 

In order to simplify the situation, we assume that our porous sample under investigation covers the bottom of an open straight-walled can and fills it to a height d (Figure 1). Such a sample will exhibit the same areal exhalation rate as a free semi-infinite sample of thickness 2d, as long as the walls and the bottom of the can are impermeable and non-absorbant for radon. A one-dimensional analysis of the diffusion of radon from the sample is perfectly adequate under these conditions. To idealize the conditions a bit further we assume that diffusion is the only transport mechanism of radon out from the sample, and that this diffusive transport is governed by Fick s first law. Fick s law applied to a porous medium says that the areal exhalation rate is proportional to the (radon) concentration gradient in the pores at the sample-air interface... 

Within the subsurface zone, two hquid phase regions can be defined. One region, containing water near the solid surfaces, is considered the most important surface reaction zone. This near solid phase water, which is affected by the sohd phase properties, controls the diffusion of the mobile fraction of the solute adsorbed on the solid phase. The second region constimtes the free water zone, which governs liquid and chemical flow in the porous medium. 

Dj is the mass diffusion coefficient, and cgas is the total molar concentration of the gas mixture. Although Equations (3.9a) and (3.9b) can be used for a free-path gas (e.g. gas channel), when a gas is moving within a porous media (i.e. electrode), Equation (3.9) may not be the most appropriate. Different constitutive laws can be employed for describing the diffusive flux within a porous medium. The choice of the most appropriate law depends on the operating conditions and the porous media properties, as further explained in Section 3.3.2. 

Abstract When subjected to a mechanical loading, the solid phase of a saturated porous medium undergoes a dissolution due to strain-stress concentration effects along the fluid-solid interface. Through a micromechanical analysis, the mechanical affinity is shown to be the driving force of the local dissolution. For cracked porous media, the elastic free energy is a dominant component of this driving force. This allows to predict dissolution-induced creep in such materials. 

An example of heat transfer through a porous medium is heat transfer through a layer of granular insulating material. This material will be saturated with air, i.e., the space between the granules of insulating material is entirely filled with air, and this air will flow through the insulation material as a result of the temperature difference imposed on the material, i.e., there will be a free convective flow in the porous material. Even when a fibrous insulation is used, the flow in the insulation can be... 

Cheng, P. and Minkowycz, W.J., Free Convection About a Vertical Rat Plate Embedded in a Porous Medium with Application to Heat Transfer from a Dike . J. Geophs. Res., Vol. 82, pp. 2040-2044, 1977. 

Naylor, D. and Oosthuizen, P.H., Free Convection in a Horizontal Enclosure Partly Filled with a Porous Medium . J of Thermophysics and Heat Transfer, Vol. 9, No. 4, pp. 797-800, 1995. 

Oosthuizen, P.H. and Paul. J.T., "Free Convective Flow in a Cavity Filled with a Vertically Layered Porous Medium . Satural Convection in Porous Media, ASME HTD-Vol. 56. AIAA/ASME 4th Thermophysics and Heat Trans. Conf., Am. Soc. Mech. Eng., New York, 1986, pp. 75-84. 

Elder, J.W., Steady Free Convection in a Porous Medium Heated from Below , J. Fluid Mech., Vol. 27, pp. 29-48. 1967. 

Nakayama, A., A Unified Theory for Non-Darcy Free, Forced, and Mixed Convection Problems Associated with a Horizontal Line Heat Source in a Porous Medium , J. Heat Transfer, Vol. 116, pp. 508-513, 1994. 

Knudsen coefficient — The term relates to a particular type of mass transfer of gases through the pores of a specific porous medium. The gas transport characteristics depends on the ratio of the mean free path for the gas molecule, A, to the pore diameter, dpore, which is called the Knudsen number, Kn (Kn = -7 —). 

Gas mobility depends on the permeability of the porous medium. In the presence of foam gas mobility is the mobility of the continuous gas phase through the free channels and the mobility of the confined gas along with the liquid. Formally the relative permeability of each phase (liquid or gas) can be expressed by Darcy s equation. 

Free-molecule or Knudsen flow (Kn 1). The molecules are transported within the porous structure without intermolecular collisions however, the molecules do collide with the pore walls. Collisions between molecules can be ignored compared to collisions of molecules with the walls of the porous medium or tube. 

The basic law governing viscous flow of pure fluid through a porous medium with pores much larger than the mean free path is that of Darcy [13]. This law states that the rate of flow is directly proportional to the pressure gradient causing the flow. In terms of mole flow rate Darcy s law can be written as... 

Filtration is the separation of a partioulate phase (solid or liquid) and a oontinuous phase (liquid or gaseous) by using a porous medium. Most often, filtration involves solid-liquid systems and is intended to either provide a solid-free liquid or isolate a solid from its mother liquor. 

The conducting properties of a liquid in a porous medium can provide information on the pore geometry and the pore surface area [17]. Indeed, both the motion of free carriers and the polarization of the pore interfaces contribute to the total conductivity. Polymer foams are three-dimensional solids with an ultramacropore network, through which ionic species can migrate depending on the network structure. Based on previous works on water-saturated rocks and glasses, we have extracted information about the three-dimensional structure of the freeze-dried foams from the dielectric response. Let be d and the dielectric constant and the conductivity, respectively. Dielectric properties are usually expressed by the frequency-dependent real and imaginary components of the complex dielectric permittivity ... 

Groundwater. The uppermost part of the earth s rocks constitutes a porous medium in which water is stored and through which it moves. Up to a certain level, these rocks are saturated with water that is free to flow laterally under the influence of gravity. Subsurface water in this saturated zone is groundwater, and the uppermost part of the zone is the water table. The chemistry of the groundwater is influenced by the composition of the aquifer and by the chemical and biological events occurriog in the infiltration. 

Effect of Porous Medium Characteristics. Several characteristics of the porous medium, including the average pore size, pore size distribution, and the wettability of the porous medium, can influence the flow of W/O emulsions. Very little information is available on these issues. The role of wettability is intuitively obvious. A water-wet medium would be more conducive to capture of the water droplets at pore walls. This capture facilitates formation of a free-water phase. An oil-wet medium, on the other... 

Gas relative permeability, Pk, is defined as the permeability of a fluid through a porous medium partially blocked by a second fluid, normalized by the permeability when the pore space is free of this second fluid. This property diminishes at the percolation threshold , at which a significant portion of the pores are still conducting but they do not form a continuous path along the flow direction. It is obvious that only the network model, can provide a satisfactory analysis of the percolation threshold problem. Nicholson et al. [3] introduced a simple network model, and applied it on gas relative permeability [4]. For the gas relative permeability, an explicit approximate analytical relation between the relative permeability and the two network parameters, namely z and the first four moments of, f(r), has been developed, based on the Effective Medium Approximation (EMA) [5]. If a porous... 

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