Gas-membrane equilibrium

The gas-membrane equilibrium is basically somewhat different if the membrane is made of a metal or an alloy and the gas is diatomic. We have already noted that a diatomic gas such as N2, H2 or O2 dissolves in a molten metal according to Sievert s law, i.e. the mole fraction of the gas (in the atomic state) in the molten metal is proportional to the square root of the gas partial pressure. The same equilibrium behavior, relation (3.3.70), is also observed between a gas and a solid metallic membrane. It is therefore necessary to assume that the gas is present in the atomic state while developing any relation for membrane transport of diatomic gases. 

The similarities between the Langmuir gas-solid isotherm for a pure gas or a mixture and the Langmuir component of gas-membrane equilibrium in equation (3.3.81) or (3.3.82a) should be obvious. 

In these systems, the interface between two phases is located at the high-throughput membrane porous matrix level. Physicochemical, structural and geometrical properties of porous meso- and microporous membranes are exploited to facilitate mass transfer between two contacting immiscible phases, e.g., gas-liquid, vapor-liquid, liquid-liquid, liquid-supercritical fluid, etc., without dispersing one phase in the other (except for membrane emulsification, where two phases are contacted and then dispersed drop by drop one into another under precise controlled conditions). Separation depends primarily on phase equilibrium. Membrane-based absorbers and strippers, extractors and back extractors, supported gas membrane-based processes and osmotic distillation are examples of such processes that have already been in some cases commercialized. Membrane distillation, membrane... 

Fig. 2. (a) comparison of CO2 gas adsorption equilibrium isotherm curve of a-AlaOs support and CMS at 2931 (b) equilibrium isotherm curve of MTES unssuport at 313K (b) CO2 stepwise uptake curve of top layer of membrane(TPABr sol) at 293K. 

The pore size distribution or its mean value of a porous inorganic membrane can be assessed by a number of physical methods. These include microscopic techniques, bubble pressure and gas transport methods, mercury porosimetry, liquid-vapor equilibrium methods (such as nitrogen adsorption/desorption), gas-liquid equilibrium methods (such as permporometry), liquid-solid equilibrium methods (thcrmoporometry) and molecular probe methods. These methods will be briefly surveyed as follows. 

The gas-liquid permporometry combines the controlled stepwise blocking of membrane pores by capillary condensation of a vapor, present as a component of a gas mixture, with the simultaneous measurement of the free diffusive transport of the gas through the open pores of the membrane. The condensable gas can be any vapor provided it has a reasonable vapor pressure and does not react with the membrane. Methanol, ethanol, cyclohexane and carbon tetrachloride have been used as the condensable gas for inorganic membranes. The noncondensable gas can be any gas that is inert relative to the membrane. Helium and oxygen have been used. It has been established that the vapor pressure of a liquid depends on the radius of curvature of its surface. When a liquid is contained in a capillary tube, this dependence is described by the Kelvin equation, Eq. (4-4). This equation which governs the gas-liquid equilibrium of a capillary condensate applies here with the usual assumption of a=0 ... 

In another study by Nishiyama et al. [53], the Vapour-phase Transport method was applied on alumina supports. No permeation of 1,3,5-triisopropylbenzene (kinetic diameter 0.85 nm) could be observed through the 10 pm thick membrane. Mordenite has parallel channels with an elliptical pore dimension of 0.65 x 0.7 nm. Pervaporation of benzene-p-xylene (molar ratio 0.86) at 22°C resulted in a separation factor of 164 (total flux 1.19 10" mol.m s ). The theoretical value based on the gas-liquid equilibrium amounts to 11.3. Apparently, the mordenite-based membrane shows high selectivity for aromatic hydrocarbons. 

Consider a cylinder, such as that shown in Fig 19, containing a quantity of gas in equilibrium with a solution of the gas The vapour pressure of the solvent is supposed to be negligible as compared with that of the gas The solution is separated from the undissolved gas by the membrane be, which only permits the gas to pass through but not the solvent, say water The walls ab and cd are in contact yvith pure solvent and are permeable to the solvent but impermeable to the solute (dissolved gas) The system being in equilibrium, let us suppose that p is the pressure of the gas (in the gas phase), v is the molecular volume or volume of r gram-mole of the gas at pressurep, and similarly let P be the osmotic pressure and V the molecular volume of the solute, 1 e dissolved gas in equilibnum with the gas at p The concentration of... 

Thus, the presence of the inflection point in the calibration E-pO plots is a distinctive feature of the work on the gas membrane oxygen electrode in high-temperature ionic melts. More exactly, there are two linear sections, with slopes corresponding to values of z equal to 1 and 2. This result, noted at first in our paper [233], showed that the electrode process at the gas membrane oxygen electrode was essentially dependent not on peculiarities of the assumed potential-determining process with the participation of the given Lux base (as was considered before), but on the equilibrium concentration of oxide ion created by dissociation of this base in the ionic melt. 

POLYMER MEMBRANES. The transport of gases through dense (nonporous) polymer membranes occurs by a solution-diffusion mechanism. The gas dissolves in the polymer at the high-pressure side of the membranes, diffuses through the polymer phase, and desorbs or evaporates at the low-pressure side. The rate of mass transfer depends on the concentration gradient in the membrane, which is proportional to the pressure gradient across the membrane if the solubility is proportional to the pressure. Typical gradients for a binary mixture are shown in Fig. 26.2. Henry s law is assumed to apply for each gas, and equilibrium is assumed... 

As shown in Figure 9.1 for a nonporous membrane, there is a solute concentration discontinuity at both gas-membrane interfaces. Solute partial pressure pjQ is that in the feed gas just adjacent to the upstream membrane surface, whereas clQ is the solute concentration in the membrane just adjacent to the upstream surface. The two are related by a thermodynamic equilibrium described by Henry s law, which is most conveniently written for membrane applications as... 

The effect of increasing temperature is twofold an increase in the rate of reaction gives faster response time and a shift in the equilibrium value due to variations in the equilibrium constant. Electrochemical sensors of the gas-permeable membrane type (ammonia and carbon dioxide) lead to an additional effect, since the gas membrane and the features of the diffusion are sensitive to temperature variations. Despite the above considerations, a classical bell-shaped curve is almost always obtained when recording the response of the probe as function of temperature. Room temperature, or 25°C (controlled to + 0.2°C is recommended), is often employed when using an electrochemical probe, although when using a gas permeable membrane control to +0.1°C is required. 

First, it is important to understand when the system will reach equiUhrium and then express this condition mathematically. Given that N2 is the only gas that can pass through the membrane, equilibrium will be reached when the pressure of N2 in compartment I (in this case equal to the total pressure of the compartment I) is equal to the partial pressure of N2 in compartment n. We will assume that the direction of N2 movement will be from compartment I to compartment II. If we get a minus sign in the amount of N2 through compartment II, it will imply that the direction is on the other side. 

Kikuchi described a natural gas membrane reactor, which had been developed and operated on a larger scale by Tokyo Gas and Mitsubishi Heavy Industries supplying PEM fuel cells with hydrogen [524]. It was composed of a central burner surrounded by a catalyst bed filled with a commercial nicdcel catalyst. Into the catalyst bed 24 supported palladium membrane tubes were inserted. The membranes had been prepared by electroless plating and were 20-pm thick. Steam was used as a sweep gas for the permeate. The reactor carried 14.5 kg of catalyst. It was operated at 6.2-bar pressure, S/C ratio 2.4 and a 550 °C reaction temperature. The conversion of the natural gas was close to 100%, while the equilibrium conversion was only 30% under the operating conditions used. The retenate composition was 6 vol.% hydrogen, 1 vol.% carbon monoxide, 91 vol.% carbon dioxide and 2 vol.% methane. 

Surprisingly, the temperature does not have a great effect on the equilibrium constant for the reaction of Ag and ethylene. All of the equilibrium constants shown in Tables V and VI are of the same magnitude. In contrast, a temperature increase from 5 to 35 "C enhances the ethylene diffusion coefficients by a factor of 3 to 4. Diffusion coefficients for the Ag -ethylene complex also increase by a factor of 2 to 3 over the same temperature range. This implies that the transport mechanism at low partial pressure of gas is controlled by gas solubility. More likely, a low concentration of gas at the gas-membrane interface limits the amount of gas adsorbed into a membrane. 

There are well-established methods for the characterization of membranes such as microscopic, bubble point, mercury porosimetry, liquid vapor equilibrium, gas-liquid equilibrium and liquid- solid equilibrium method. 

The deduction adopted is due to M. Planck (Thermodynamik, 3 Aufl., Kap. 5), and depends fundamentally on the separation of the gas mixture, resulting from continuous evaporation of the solution, into its constituents by means of semipermeable membranes. Another method, depending on such a separation applied directly to the solution, i.e., an osmotic process, is due to van t Hoff, who arrived at the laws of equilibrium in dilute solution from the standpoint of osmotic pressure. The applications of the law of mass-action belong to treatises on chemical statics (cf. Mel lor, Chemical Statics and Dynamics) we shall here consider only one or two cases which serve to illustrate some fundamental aspects of the theory. 

Furthermore, the application of the SOD membrane in a FT reaction has been investigated. The advantages of water removal in a FT reaction are threefold (i) reduction of H20-promoted catalyst deactivation, (ii) increased reactor productivity, and (iii) displaced water gas shift (WGS) equilibrium to enhance the conversion of CO2 to hydrocarbons [53]. Khajavi etal. report a mixture of H2O/H2 separation factors 10000 and water fluxes of 2.3 kg m h under... 

Gas-sensing electrodes. A gas-sensing electrode consists of a combination electrode that is normally used to detect a gas in its solution by immersion. The sensor contains the inner sensing element, usually a glass electrode or another ISE, and around this a layer of a 0.1 Af electrolyte, surrounded by a gas-permeable membrane. On immersion of the sensor this membrane contacts the solution of the gas which diffuses through it until an overall equilibrium is established, i.e., the partial pressure of the gas attains an equilibrium between sample solution and membrane and between membrane and sensor electrolyte. For a better understanding of the interaction between this electrolyte and the... 

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