Phase permeability

When a two- or higher-phase system is used with two or more phases permeable to the solute of interest and when interactions between the phases is possible, it would be necessary to apply the principle of local mass equilibrium [427] in order to derive a single effective diffusion coefficient that will be used in a one-equation model for the transport. Extensive justification of the principle of local thermdl equilibrium has been presented by Whitaker [425,432]. If the transport is in series rather than in parallel, assuming local equilibrium with equilibrium partition coefficients equal to unity, the effective diffusion coefficient is... 

Effect of Rock Permeability. The effect of rock permeability has been investigated by comparison of mobility measurements made with Baker dolomite and Berea sandstone. Mobility measurements carried out with Rock Creek sandstone (from the Big Injun formation in Roane County, W.Va) is also reported. Rock Creek sandstone has a permeability of 14.8 md. A direct comparison was made with Berea sandstone and Baker dolomite measured with 0.1% AEGS. As mentioned in an earlier section, the permeability of Baker dolomite (a quarried carbonate rock of rather uniform texture with microscopic vugs distributed throughout) was 6.09 md, and of Berea sandstone was 305 md. The single phase permeabilities were measured with 1% brine solution. 

Relative permeability is defined as the ratio between the permeability for a phase at a given saturation level to the total (or single-phase) permeability of the studied material. This parameter is important when the two-phase flow inside a diffusion layer is investigated. Darcy s law (Equation 4.4) can be extended to two-phase flow in porous media [213] ... 

From Equation (6.6), it is immediately clear, that by decreasing the pore size, only the surface dilTusion contribution is increased [third term on the right-hand side of Equation (6.6)], due to the increased surface area. It should be noted here that the additivity of surface permeability and gas phase permeability is still a matter of debate, since it is very difficult to determine the surface permeability alone. The experimentally measured surface permeability will always include a contribution due to gas phase permeability. 

Surface diffusion has been extensively studied in literature. An overview of experimental data is given in Table 6.1. Okazaki, Tamon and Toei (1981), for example, measured the transport of propane through Vycor glass with a pore radius of 3.5 nm at 303 K and variable pressure (see Table 6.1). The corrected gas phase permeability was 0.69 m -m/m -h-bar, while the surface permeability was 0.55 m -m/m -h-bar, and so almost as large as the gas phase permeability (Table 6.1). It is clear from Table 6.1, that the effects of surface diffusion, especially at moderate temperatures, can be pronounced. At higher temperatures, adsorption decreases and it can be expected that surface diffusion will become less pronounced. 

Table 6.1. Surface Diffusion Data for Several Membrane/Gas Combinations f o,f s the Corrected Gas Phase Permeability x y/MT), the Corrected Surface...

The buccal permeability of the non-steroidal antiinflammatory drug, diclofenac sodium, has been evaluated in a dog model. The dog was selected because of the similarity of its buccal mucosa to that of man. Analysis of the buccal data indicated that diclofenac sodium permeability followed an essentially zero-order kinetic process with a minimal lag phase. Permeability of the drug was estimated to be 3 mg/cm2.h but significant differences were observed between animals. The absorption rate with the transbuccal delivery device decreased with time whereas the corresponding rate with a saturated solution was constant. This difference was attributed to the time dependency of drug delivery from the device and was modeled on the basis of release from a membrane-dispersed monolith combined with constant buccal permeability. The predictions of the model showed excellent agreement with the experimental data. 

This ratio of dispersed phase (foam) and non-dispersed phase permeabilities indicates that the decrease in permeability of a foam relative to a non-dispersed phase is due largely to (1) the decrease in the fraction of pores occupied by flowing gas, (fc/f ), and (2) the low value of V q/Ui, In addition, we find the ratio of permeabilities increases with displacement rate when n < 1. 

Diffractometer (Model PW 1710), using CuKa radiation. A thin film ( lnun) of 1.5 by 1.5 cm square sample was used for X-ray studies. Both water and gas phase permeability measurements were done with a machined 1 cm diameter thin sample ( limn). The molecular wei t distribution was obtauned using a gel permeation chromatograph (Waters) with a styragel column and using tetrahydrofuran as the solvent. Attenuated total reflectance (ATR) and KBr pellet techniques were used for FTIR. Solid state NMR was done on precipitated powdered samples. A Rayonet RPR-100 reactor at 35 C was used for UV irradiation of the samples. 

Polymerization of styrene in microemulsions has produced porous solid materials with interesting morphology and thermal properties. The morphology, porosity and thermal properties are affected by the type and concentration of surfactant and cosurfactant. The polymers obtained from anionic microemulsions exhibit Tg higher than normal polystyrene, whereas the polymers from nonionic microemulsions exhibit a lower Tg. This is due to the role of electrostatic interactions between the SDS ions and polystyrene. Transport properties of the polymers obtained from microemulsions were also determine. Gas phase permeability and diffusion coefficients of different gases in the polymers are reported. The polymers exhibit some ionic conductivity. 

Two-Phase Region. The two-phase flow and heat transfer are given by the continuity equations for the i and g phases, the momentum equations (Eqs. 9.76 and 9.77), and the energy equation (Eq. 9.80). The two-phase region is assumed to be isothermal by neglecting the effect of the curvature (i.e., saturation) on the thermodynamic equilibrium state. This is justifiable, except for the very small pores (large pc). For the steady-state flow considered here, we have (for the assumed isotropic phase permeabilities)... 

If intrinsic permeability decreases strongly (maximum of 4 orders of magnitude near the drift) due to volumetric deformation induced by compression, the dried zone becomes elongated horizontally but it is flattened in the vertical direction. The volume of the dried zone is smaller than in the case of constant permeability so the drying due to vapor flow is less efficient. This can be due to the lower gas phase permeability. 

In the Abino-Ukrainsk oil field the average well spacing is 100 m, oil viscosity is 4,(XX) centipoise, and the thickness of the producing horizon is 10 m. The phase permeability for oil is... 

Use of hot water is accompanied by high rates of capillary soaking. Therefore, hot water tends to move ahead of the main displacement front of the crude where it gives rise to a zone of two-phase mixture. These processes reduce the phase permeability for crude oil in the area of water-oil contact, and at the same time, they create additional capillary forces that resist the movement of the main displacement front. The effectiveness of oil displacement is somewhat reduced by comparison with steam. 

Field practice shows that during bed ignition, at frrst both the rate of oil displacement from the bottomhole zone of the injection well and the receptivity of the well to air quickly rise. However, once the combustion front is formed, the receptivity of the injection well to air drops sharply (Fig. 52). This phenomenon is caused by "liquid barrier" to air flow. This blocking forms in the zone immediately ahead of the burning front and it acts to reduce the phase permeability to air entering the bed from the injection well. 

A membrane is phase permeable or semipermeable, consisting of polymer, ceramic, or metal, which restricts the mobility of certain compounds. The membrane (barrier) controls the relative rate of mass transport of various compounds through it and then, as in all separations, leads to a free product of certain compounds and a second concentrated product in these compounds. The performance of a membrane is... 

There are only a few reported studies that examine mechanical degradation and review the effect of compression of gas-diffusion layers on the performance of fuel cells [133-135]. Lee and Merida [133] characterized some GDL properties after 300 h. of compression at constant temperature in an ex situ test and found that the dry gas-phase permeabilities remained roughly constant. 

Before commencing two-phase flow operations, single-phase permeability determinations were made at several flow rates, using brine in the water-wet sample, and Soltrol-oil in the samples that had been treated with Dri-Film. In every case, first the drainage relative permeability curves were determined. The first steady-state point was obtained typically at a wetting fluid/non-wetting fluid flow rate ratio of about 10. The filter velocities used... 

Due to the extensive research that has been conducted in the area of foam application in enhanced oil recovery, simulation of foam behaviour has become more feasible. Several methods of foam simulation have been developed population balance models [16, 17], fractional flow models [IS, 19], and models that alter the gas phase permeabilities [20, 21], Although the population balance models treat the foam generation mechanisms in a detailed fashion, they may be impractical to apply on large field scale simulations. Both the fractional flow model and the models that alter the gas phase permeabilities rely on history matching experimental data. The fractional flow model provides insight into onedimensional foam flow, but it may be more difficult to apply in three-dimensional situations. In the following section, the application of relative permeability alterations to model foam flow is investigated. 

Maloney, D. Brinkmeyer, A. Three Phase Permeabilities and Other Characteristics of 260-mD Fired Rerea, NIPER-581, U.S. Dept, of Energy Bartlesville, OK, 1992. 

Table 2.2 Pressure-Independence for Liquid-Phase Permeability and Selectivity...

HDPE is a very good insulator and is therefore widely used for wire and cable encapsulation. Polymer density and molecular weight affect electrical properties very little. HDPE is only slightly permeable to organic compoimds, both in liquid and gas phases. Permeability to water and inorganic gases is also low. 

Since the dominant feature of packings of spheroidal particles is the constrictions between the tetrahedral cavities formed by the Alumina microspheres, a more realistic model is required, based on the random sphere packing models. Such models are obviously more complex. Conversely, they permit a more realistic representation of the pore space among the spheroidal particles. A preliminary model has been reported for sorption [47] and relative permeability Pr [48]. A more realistic model of the sorption and permeability at different porosities is under development, aiming at predicting the sorption and the condensed phase permeabilities, given the porosity and the spheroidal particle size distribution. 

Investigations of liquid cells containing an organic phase permeable to all ions present were initiated by Nernst and Riesenfeld [28-32]. In such systems it is necessary to distinguish concentration cells and chemical galvanic cells. 

In oases where the dense phase permeability remains constant at its minimum fluidisation value, the amount of gas flowing in this phase will in all oases be less than that predicted by the usually formulated two-phase theory. This will generally affect reactor performance adversely although the effect will usually be small. The reason for this is that bubbles reduce the cross-sectional area available for interstitial flow and gas expansion causes a net transfer to the bubble phase. 

With fine powders such as fluidised catalysts the dense phase permeability does in fact increase with gas velocity and the above corrections become negligible in many oases. In a chemical reactor the degree of conversion then becomes importantly dependent on the proportion of gas that flows interstitially but is dominated by the rate of exchange between the two phases. 

Figure 5.21. Selective reduction in the aqueous-phase permeability by treatment with HPAM. Test sequence (1) relative perm to brine at residual oil-kei (2) relative perm to oil at residual brine-koi (3) flush with brine-kei (4) polymer injected (5) relative perm to brine at residual oil-kap (6) relative perm to oil at residual brine-kop (from White et aL, 1973).

The two most commonly measured rock properties are porosity, (f), and absolute (single-phase) permeability, k. The porosity (or voidage) is the fraction of the bulk volume of the porous sample that is occupied by pore or void spaces. For different types of porous media, the porosity can vary from nearly zero (e.g. certain volcanic rocks) to almost unity (e.g. insulators). The porosity can be measured using a variety of methods, which are described by Dullien (1979). 

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