Dual-mode-transport model

The discussion directly following Eq (6) provides a simple, physically reasonable explanation for the preceding observations of marked concentration dependence of Deff(C) at relatively low concentrations. Clearly, at some point, the assumption of concentration independence of Dp and in Eq (6) will fail however, for our work with "conditioned" polymers at CO2 pressures below 300 psi, such effects appear to be negligible. Due to the concave shape of the sorption isotherm, even at a CO2 pressure of 10 atm, there will still be less than one CO2 molecule per twenty PET repeat units at 35°C. Stern (26) has described a generalized form of the dual mode transport model that permits handling situations in which non-constancy of Dp and Dh manifest themselves. It is reasonable to assume that the next generation of gas separation membrane polymers will be even more resistant to plasticization than polysulfone, and cellulose acetate, so the assumption of constancy of these transport parameters will be even more firmly justified. 

Based on the dual-mode transport model, calculate the pure component and mixtures permeability of CO2 and CH4 using a polysulfone membrane. The gas pressure is 10 atm for each component. 

For the separation of gas mixtures (permanent gases and/or condensable vapors) where the feed and permeate streams are both gas phase, the driving force across the membrane is the partial pressure difference. The membrane is typically a dense film and the transport mechanism is sorption-diffusion. The dual-mode transport model is typically used with polymer materials that are below their glass transition temperature. 

The permeability of the selective layer to each penetrant obeys the dual-mode transport model. 

Composition-Dependent Permeability. There are some experimental data 8"19 indicatiug the existence of competition between penetrants in accordance with the postulations of the generalized dual-mode transport model [Eq. (20.6-40)]. It is of interest to examine the magnitude or this competition effect on the overall performance of an actual separator. This is illustrated in Tables 20.6-5 and 20.6-6. Equation... 

The dual-mode-transport model is mathematically described in Eq. (9-16). 

Simple Dual-Mode Transport Models. As a direct extension of the dualmode sorption model, it is convenient to treat pure-gas permeability as the siun of two terms, which are characteristic of the two sorbed penetrant populations. Petropoulos first developed such an expression in terms of the chemical potential gradient of the sorbed gas (100). For the case where there is a vacuum downstream and a pressure pa2 of component A upstream, the following expression results ... 

The extension of this model to mixed-gases is considerably more difficult than the extension of the simple dual-mode transport models. To include gas mixtures, the Barrer model must be modified to accurately describe the fraction of filled Langmuir sorption sites when more than one gas species is present in the pol5mier. To account for the presence of a second gas, the flux expressions can be rewritten using the following definition for the fraction of filled holes ... 

It is most likely that the prediction of the permeability of gas mixtures containing CO2 could be improved by accoimting for the effects of C02-induced plasticization on transport parameters. This could be tested best at higher CO2 pressures where such effects should be significant and, in fact, would correspond to conditions of practical importance in enhanced oil recovery operations where CO2 and CH4 must be separated at pressures as high as 6.9 MPa (1000 psia) and with CO2 contents above 50%. The dual-mode transport model of Petropoulos has recently been extended to accoimt for the effects of plasticization in both pure- and mixed-gas environments (110). 

Advanced Dual-Mode Transport Models. To account for the effect of nearby gas molecules on the ability of a given gas molecule to find sites into which it might jump, Barrer proposed and developed a model that adopts a somewhat... 

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