Pressure dependence, permeability

Conventionally, the sample is initially saturated with one fluid phase, perhaps including the other phase at the irreducible saturation. The second fluid phase is injected at a constant flow rate. The pressure drop and cumulative production are measured. A relatively high flow velocity is used to try to negate capillary pressure effects, so as to simplify the associated estimation problem. However, as relative permeability functions depend on capillary number, these functions should be determined under the conditions characteristic of reservoir or aquifer conditions [33]. Under these conditions, capillary pressure effects are important, and should be included within the mathematical model of the experiment used to obtain property estimates. 

Effective porosity (Ne) is of more importance and, along with permeabihty (the ability of a material to transmit fluids), determines the overall ability of the material to store and transmit fluids or vapors readily. Where porosity is a basic feature of sediments, permeability is dependent upon the effective porosity, the shape and size of the pores, pore interconnectiveness (throats), and properties of the fluid or vapor. Fluid properties include capillary force, viscosity, and pressure gradient. 

The different capillary pressure, saturation, and permeability relationships of the different models can be compared. To do this, the effective permeabilities from some of the different models are plotted as a function of the capillary pressure in Figure 8. In the figure, the capillary pressure at which the effective permeability no longer changes is where the medium is fully saturated. Also, the values of the effective permeability are dependent on the diffusion media being tested. Furthermore, the value of the effective permeability at the right end of the curves corresponds to the saturated permeability, except for the model of Weber and Newman, who use a gas-phase residual saturation. 

Nonlinear, pressure-dependent solubility and permeability in polymers have been observed for over 40 years. Meyer, Gee and their co-workers (5) reported pressure-dependent solubility and diffusion coefficients in rubber-vapor systems. Crank, Park, Long, Barrer, and their co-workers (5) observed pressure-dependent sorption and transport in glassy polymer-vapor systems. Sorption and transport measurements of gases in glassy polymers show that these penetrant-polymer systems do not obey the "ideal sorption and transport eqs. (l)-(5). The observable variables,... 

Nonlinear, pressure-dependent sorption and transport of gases and vapors in glassy polymers have been observed frequently. The effect of pressure on the observable variables, solubility coefficient, permeability coefficient and diffusion timelag, is well documented (1, 2). Previous attempts to explain the pressure-dependent sorption and transport properties in glassy polymers can be classified as concentration-dependent and "dual-mode models. While the former deal mainly with vapor-polymer systems (1) the latter are unique for gas-glassy polymer systems (2). 

Comparing the curves in Fig. 2 shows that representing the permeability versus pressure data by either model provides a satisfactory fit to the data over the pressure range of 1 to 20 atm. However, at pressures less than 1 atm. the two models differ in their prediction regarding the behavior of the permeability-pressure curve [Fig. 2]. While the matrix model predicts a strong apparent pressure dependence of the permeability in this range (solid line), the dual-mode model predicts only a weak dependence (broken line). 

The permeability coefficient depends on the characteristics of the membrane and solute, and can vary considerably for various solutes. For example,/) = 10-21 m/s for sucrose and 10 4 m/s for water in the human red blood cell membrane. Equation (1) may be generalized by including the effect of pressure gradient APm = P(0) - P(L), and we have... 

The particle size and surface area distributions of pharmaceutical powders can be obtained by microcomputerized mercury porosimetry. Mercury porosimetry gives the volume of the pores of a powder, which is penetrated by mercury at each successive pressure the pore volume is converted into a pore size distribution. Two other methods, adsorption and air permeability, are also available that permit direct calculation of surface area. In the adsorption method, the amount of a gas or liquid solute that is adsorbed onto the sample of powder to form a monolayer is a direct function of the surface area of the sample. The air permeability method depends on the fact that the rate at which a gas or liquid permeates a bed of powder is related, among other factors, to the surface area exposed to the permeant. The determination of surface area is well described by the BET (Brunauer, Emmett, and Teller) equation. 

Figure 18 Pressure dependence of the CO2 permeability through a microporous glass membrane. Experimental results are compared to theory of combined gaseous and surface flow. (I Barrer = 3.35 X 10" mol m m Pa -sec". ) (Adapted from Ref. 38.)...

Pressure Dependence of Hydrocarbon Permeability in Rubbery Polymers Effect... 

For the silica aerogel we examined, the permeability and its pressure dependence thus determined is consistent with pore size information gathered independently. Appearance of a crack in the sample could be detected as an apparent 30% jump in the permeability. 

The technique consists in measuring the B (e.g. water) flow rate (/) through a membrane impregnated with A (e.g. isobutanol or mixtures of alcohols and water) as a function of the pressure difference AP. We have to note that it is possible to modify the method from "pressure controlled" to "flow controlled" in order to reduce the test time and increase its flexibility [126]. At a certain minimum pressure the largest pores become permeable, while the smaller pores still remain impermeable. This minimum pressure depends mainly on the type of membrane material (contact angle), type of permeate (surface tension) and pore size. When all pores are filled with B, the liquid flux / through the membrane becomes directly proportional to the pressure. 

A type of pore blocking by one of the components occurs but whether this is capillary condensation is not certain. Asaeda and Du [38] reported values up to a > 100 for water-light-alcohol mixtures at 70-90°C in cilumina-silica membranes. The water permeability is dependent on its concentration in the mixture. At atmospheric pressure and 20% water a typical water permeation vcdue is 1.3x10 m s (= 20 1 H2O (liquid) m" day ). Azeotropic points can be bypassed in this way with an alcohol concentration much higher than the azeotropic concentration. 

T)q)ical data for dense membranes are collected in Table 9.16. A full discussion of these data is outside the scope of this chapter. Using permeation values the reader should be aware of the fact that the pressure dependence of the flux is usually strongly non-linear, but takes the form of a power law with values for the exponent around 0.5. This makes direct comparison on the basis of permeance or permeability not meaningful. Furthermore, the permeation value is limited by surface reactions with a critical thickness varying between 0.1 and 2 mm depending on material and condition. 

Figure 10. Pressure-dependence of permeability rate of asymmetric...

Accurate description of barrier films and complex barrier structures, of course, requires information about the composition and partial pressure dependence of penetrant permeabilities in each of the constituent materials in the barrier structure. As illustrated in Fig. 2 (a-d), depending upon the penetrant and polymer considered, the permeability may be a function of the partial pressure of the penetrant in contact with the barrier layer (15). For gases at low and intermediate pressures, behaviors shown in Fig. 2a-c are most common. The constant permeability in Fig.2a is seen for many fixed gases in rubbery polymers, while the response in Fig. 2b is typical of a simple plasticizing response for a more soluble penetrant in a rubbery polymer. Polyethylene and polypropylene containers are expected to show upwardly inflecting permeability responses like that in Fig. 2b as the penetrant activity in a vapor or liquid phase increases for strongly interacting flavor or aroma components such as d-limonene which are present in fruit juices. 

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