Permeance and Permeability

FIGURE 10.2 Schematic diagram of a permeation test facility. 

Consequently, for single component gases, which are nondissociated during the process, and a linear pressure drop across the porous media, this transport process follows Darcy law [16,19]  

Selectivity, often represented as the permeance ratio of two gases, is the capability of the membrane to separate a given gas mixture into its components [7], Selectivity is a measure of the membrane 

The Physical Chemistry of Materials Energy and Environmental Applications 

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The flux, and hence the permeance and permeability, can be defined on the basis of volume, mass or molar flowrates. The accurate prediction of permeabilities is generally not possible and experimental values must be used. Permeability generally increases with increasing temperature. Taking a ratio of two permeabilities defines an ideal separation factor or selectivity awhich is defined as ... 

Since the permeance and permeability are always different from zero, no permeation is equivalent to zero permeation driving force, which occurs when the species partial pressures on both membrane sides are equal to each other. It must be noted that the equilibrium conversion of an MR is independent of the permeation law that expresses the penetrant velocity through the membrane materials. 

Figures 10.4 and 10.5 show the experimental results of C02 permeation in some of these membranes [18]. In Table 10.1, the permeance and permeability experimental results are reported [18]. In Table 10.2, the estimated pore diameters of the membranes are reported [18].

Water containing urea at a bulk phase concentration of c, = 0.008 kmol/m is flowing on one side of a membrane. The bulk phase concentration of urea on the other side of the membrane is Cj = 0.002 kmol/m The diffusivity of urea in the membrane is D = 2.5 x 10" m /s and the membrane thickness is L = 4 x 10" m. The equilibrium distribution coefficient on either side of the membrane is K= 1.4. The mass transfer coefficients are k, = 3 x lO m/s and kj = 2 x 10 m/s. Calculate the flux of urea through the membrane, the permeance and permeability, and the concentrations of urea at the film interface with the membrane and on the membrane surface on both sides. 

The permeances and permeabilities are calculated from equations equivalent to 18.5 and 18.6, written in terms of Henry s constants ... 

For dense membranes it is more complicated, since the materials property itself can be pressure dependent, and the flux gets various pressure dependences depending on defect structure. It is therefore common to use the terms permeance and permeability for the flux including the actual pressures involved. Permeance is then the same as flux, typically given in area specific values like flux density, with units like mol s cm 2. Permeability is used for the materials specific - thickness independent - flux density obtained by multiplying by the membrane thickness, and with units of typically mol s cm or mL min cm . ... 

Alternatively, the permeance and permeability of a dense membrane can be expressed as a coefficient of flux density per unit pressure to a power depending on defect model (for instance, from the examples we have seen in Section 1.4, /i, A, 0, - /2, and - A). We will see examples of several ways of using these units... 

Fig. 2 Permeance and permeability ratio as a funetion of reeiproeal temperature of M-1 (Si/Al = oc) and M-2 (Si/Al = 20). (View this art in color at www.dekker.com.)...

More information on P, S, and D of water vapor of PLA and some conventional petroleum-based polymers at 23°C is summarized in Table 12.5. Table 12.6 provides data for water vapor permeance and permeability at 25 and 38°C. PLA has lower water vapor barrier properties than equivalent petroleum-based polymers, and it can be included in the group of low-barrier polymers following the classification of Salame and Steingiser [40]. In this classification, a high-barrier polymer has a water vapor permeation of not more than... 

Gas-Transmission Rate n (GTR) The quantity of a given gas passing through a unit area of the parallel surfaces of a plastic film in unit time under the conditions of the test. These conditions, including temperature and partial pressure of the gas on both sides of the film, must be stated. The SI unit of GTR is mol/(m s) but others, some of them involving mixed metric and English units, are still in common use. See ASTM (www.astm.org) for standard method of gas-transmission rate. See also Permeance and Permeability. 

The permeability of dense membranes is low because of the absence of pores, but the permeance of Component i in Equation 10.20 can be high if SM is very small, even though the permeability is low. Thickness of the permselective layer is typically in the range 0.1 to 10 tm for gas separations. The porous support is much thicker than this and typically more than 100 tm. When large differences in PM exist among species, both high permeance and high selectivity can be achieved in asymmetric membranes. 

Both of these methods may be used to calculate permeability, permeance, and water vapor transmission rate (WVTR). ASTM C 355, formerly used for rigid foams, has been discontinued and replaced by ASTM E 96. 

Covers water vapor transmission rate (WVTR), water vapor permeance, and water vapor permeability. 

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. 

It is common practice to define the permeance, and the permeability, Pm as follows ... 

The permeance (or permeability) and the permeation diffusivity are properties relating to component i and the particular membrane type. 

Assume that the GTR of oxygen through a 1-mil PE film, GTR = 3.5 x 10" g/h m, when the partial pressure difference through the film Ap is 30 mm Hg. Calculate the permeance and the permeability coefficient. 

You have the following permeation information about a flexible plastic structure WVTR (obtained at 100°F, 95% RH) =1.2 g/day, area = 100 in, thickness = 3 mil. Calculate, in SI units WVTR, permeance R, thickness-normalized flow N, and permeability coefficient P. Use SI units kg, sec. Pa, m. 

The ASTM standards adopt definitions that are consistent w ith the equivalent definitions for gas transmission. Water vapor transmission rate is the mass transfer rate of water vapor per unit area (g nr 24h). Permeance is the ratio of the water vapor transmission rate to the difference in vapor pressure between the surfaces of the test piece measured in mm of mercury this unit is known as the metric perm (g nr 24h mmHg). This is equivalent to the gas transmission rate. Permeability is the product of the permeance and the thickness of the test piece, assuming that the permeance is inversely proportional to thickness for homogeneous materials this unit is known as the perm-centimetre (g cm nr 24h mmHg). Since the adoption of SI units, the water vapor permeability may also be expressed in the units of microgram meter per newton hour (pgm N h or pgm m Pa h ). 

The two most important characteristics of inorganic membranes are permeance and separation factor. Permeance is a measure of the gas flow rate per unit area per unit pressure difference. A more fundamental unit is permeability, which is the permeance multiplied by the thickness of the membrane. In most cases, the thickness of the membrane is not known very accurately and so permeance is a more practical unit. 

Permeability The proportionality constant in the general equation for mass transport of a penetrant across the barrier, i.e., the product of permeance and thickness. 

The most commonly investigated performance characteristics of gas separation membranes are flux, permeability coefficient/permeance and selectivity. The flux is the amount (mass or moles) of gas that permeates through the membrane per unit time and unit surface area the permeability coefficient is the quantitative expression of a specific measure of gas moving through a membrane and the selectivity is the separating ability of a given membrane (Ockwig and Nenoff, 2007). 

The overall ability of a core to carry flux also depends on its size and shape, and its cross-sectional area. This is described by a quantity called permeance. The basic relationship of permeance to permeability in a core is defined in Eq. (10.2), where P is the permeance, p is the permeability of the material, A is the cross-sectional area of the core, and Z is the mean length of the flux path in the core. This equation assumes uniform flux distribution in the core and constant permeability inside the core. It does not take into account the variations in the length of the flux path from the inside of the core to the outside. The reciprocal of permeance is reluctance... 

Terms other than permeability (Equation 12.6), such as permeant transmission rate, permeance, and thickness normalized flow, can be used to describe the steady-state permeation of molecules through the polymer films [2]. Permeant transmission rate is the amount of permeant passing through a plane of unit area normal to the direction of the flow during unit time (Equation 12.8). The term permeance is used when differences in partial pressure between both sides of the material are also taken into account (Equation 12.9), whereas thickness normalized flow considers material thickness but not difference in partial pressure (Equation 12.10). 

Figure 39.5 Permeance versus permeability representations for O2 transport within membranes based on single- and dual-phase Co-containing perovskites (PVK-Co and PVK-DF-Co), single- and dual-phase Co-free perovskites (PVK-Co-free and PVK-DF-Co) and...

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