Permeation transport models

Fig. 19.3 The solution-diffusion transport model in pervaporation. a Solution of compounds from the feed phase into the membrane surface, b Diffusion across the membrane barrier, c Desorption from the membrane permeate (downstream) side into the permeate phase...

Implications of the Dual-Mode Sorption and Transport Models for Mixed Gas Permeation... 

Whereas the dual sorption and transport model described above unifies independent dilatometric, sorption and transport experiments characterizing the glassy state, an alternate model offered recently by Raucher and Sefcik provides an empirical and fundamentally contradictory fit of sorption, diffusion and single component permeation data in terms of parameters with ambiguous physical meanings (28), The detailed exposition of the dual mode model and the demonstration of the physical significance and consistency of the various equilibrium and transport parameters in the model in the present paper provide a back drop for several brief comments presented in the Appendix regarding the model of Raucher and Sefcik,... 

Figure 2.5 Pressure driven permeation of a one-component solution through a membrane according to the solution-diffusion transport model...

Several authors have already developed methodologies for the simulation of hybrid distillation-pervaporation processes. Short-cut methods were developed by Moganti et al. [95] and Stephan et al. [96]. Due to simplifications such as the use of constant relative volatility, one-phase sidestreams, perfect mixing on feed and permeate sides of the membrane, and simple membrane transport models, the results obtained should only be considered qualitative in nature. Verhoef et al. [97] used a quantitative approach for simulation, based on simplified calculations in Aspen Plus/Excel VBA. Hommerich and Rautenbach [98] describe the design and optimization of combined pervaporation-distillation processes, incorporating a user-written routine for pervaporation into the Aspen Plus simulation software. This is an improvement over most approaches with respect to accuracy, although the membrane model itself is still quite... 

The constitutive equations of transport in porous media comprise both physical properties of components and pairs of components and simplifying assumptions about the geometrical characteristics of the porous medium. Two advanced effective-scale (i.e., space-averaged) models are commonly applied for description of combined bulk diffusion, Knudsen diffusion and permeation transport of multicomponent gas mixtures—Mean Transport-Pore Model (MTPM)—and Dusty Gas Model (DGM) cf. Mason and Malinauskas (1983), Schneider and Gelbin (1984), and Krishna and Wesseling (1997). The molar flux intensity of the z th component A) is the sum of the diffusion Nc- and permeation N contributions,... 

The predicted effect of du mode sorption on the time lag and permeability vras derived by Paul using the total immobilization transport model and experimentally verified by Paul and Kemp using molecular sieves embedded in a silicone mbber. This was an excellent model system which fulfilled the postulate of complete inunobilization of the Langmuirian mode penetrant. The possibility that gas molecules sorbed in the Langmuirian mode may not necessarily be completely immobilized in glassy polymers was first raised by Petropoulos in 1970 Equations were developed and the possibility of these being used to check the assumption of immobilization by sorption and permeation data were described. The relaxation of the... 

The models most frequently used to describe the concentration dependence of diffusion and permeability coefficients of gases and vapors, including hydrocarbons, are transport model of dual-mode sorption (which is usually used to describe diffusion and permeation in polymer glasses) as well as its various modifications molecular models analyzing the relation of diffusion coefficients to the movement of penetrant molecules and the effect of intermolecular forces on these processes and free volume models describing the relation of diffusion coefficients and fractional free volume of the system. Molecular models and free volume models are commonly used to describe diffusion in rubbery polymers. However, some versions of these models that fall into both classification groups have been used for both mbbery and glassy polymers. These are the models by Pace-Datyner and Duda-Vrentas [7,29,30]. 

The Mean Transport Pore Model (MTPM) described diffusion and permeation the model (represented as a boundary value problem for a set of ordinary differential equations) are based on Maxwell-Stefan diffusion equation and Weber permeation law. Parameters of MTPM are material constants of the porous solid and, thus, do not dependent on conditions under which the transport proeesses take place. 

Today two models are available for description of combined (diffusion and permeation) transport of multicomponent gas mixtures the Mean Transport-Pore Model (MTPM)[21,22] and the Dusty Gas Model (DGM)[23,24]. Both models enable in future to connect multicomponent process simultaneously with process as catalytic reaction, gas-solid reaction or adsorption to porous medium. These models are based on the modified Stefan-Maxwell description of multicomponent diffusion in pores and on Darcy (DGM) or Weber (MTPM) equation for permeation. For mass transport due to composition differences (i.e. pure diffusion) both models are represented by an identical set of differential equation with two parameters (transport parameters) which characterise the pore structure. Because both models drastically simplify the real pore structure the transport parameters have to be determined experimentally. 

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 combined procedure described above, which uses only sorption and steady state permeation data, specifies all five of the sorption and transport model parameters without requiring reference to the independently measured time lags. Comparison of theoretically predicted time lags with the experimentally measured values provides a rigorous test of the internal consistency of the transport and sorption data as well as a check of the applicability of the partial immobilization model for description of the transient processes. 

As in all compartmental models with more than one compartment, the central compartment (compartment 1) always contains the systemic circulation, and additionally contains aU tissues that can be taken to reach equilibrium instantly with the systemic circulation. Drug distribution can never truly be instantaneous, as it cannot occur faster than the perfusion and permeation transport to the tissues. However, instantaneous distribution to the tissues in compartment 1 provides a reasonable approximation as long as these tissues approach equilibrium with plasma in a time period that is small compared to the elimination half-life. The assumption of instantaneous distribution throughout the central compartment also implies that the volume of distribution of this compartment (Fi) is a constant. 

Tu S.-C., Ravindran V, Badtiyha B.N., Pirbazari M. (1997), A membrane transport model for predicting permeate flux in nanofiltration processes, Proc. AWWA Membrane Technology Conference, New Orleans, Feb. 97, 487-498. 

Oxygen permeation fluxes oxygen exchange and transport models suffer from not considering that the membrane is a polycrystal material in which grain boundaries have different properties than bulk grain. 

Machado, D. R., Hasson, R., and Semiat, R. (2000) Effect of solvent properties on permeate flow through nanofiltration membranes Part II. Transport model. Journal of Membrane Science 166, 63-69. 

In many instances polymers are in contact with liquids that penetrate their stmcture. This process is usually accelerated when the Uquid has a plasticizing effect on polymer. The permeation of a solvent through a pervaporation membrane is a special case of such a situation. Figure 11.2 shows a schematic transport model of a mixture of methanol, MeOH, and methyl tert-butyl ether, MTBE, through cellulose triacetate pervaporation membrane. " ... 

NUMERICAL SOLUTION OF THE PERMEATION, SORPTION, AND DESORPTION RATE CURVES INCORPORATING THE DUAL-MODE SORPTION AND TRANSPORT MODEL... 

Numerical solutions were applied to the dual-mode sorption and transport model for gas permeation, sorption, and desorption rate curves allowing for mobility of the Langmuir component. Satisfactory agreement is obtained between integral diffusion coefficient from sorption and desorption rate curves and apparent diffusion coefficient from permeation rate curves (time-lag method). These rate curves were also compared to the curves predicted by Fickian-type diffusion equations. 

---