Membranes Transport Models

Transport Models. Many mechanistic and mathematical models have been proposed to describe reverse osmosis membranes. Some of these descriptions rely on relatively simple concepts others are far more complex and require sophisticated solution techniques. Models that adequately describe the performance of RO membranes are important to the design of RO processes. Models that predict separation characteristics also minimize the number of experiments that must be performed to describe a particular system. Excellent reviews of membrane transport models and mechanisms are available (9,14,25-29). 

Membrane transport models, 22 638-639 Membrane units, for acid gas removal, 22 377... 

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... 

Tu S.-C., Ravindran V., Den W., and Pirbazari M., Predictive membrane transport model for nanofiltration processes in water treatment, AIChE Journal 47(6) 2001 1346-1362. 

Generalized Formalism A generalized membrane transport model, in the form of the black box models discussed earlier, can be considered in order to compare alternative mechanisms of water backflow in gradients of chemical potential, activity or concentration of water. Each of these gradients can be expressed by a gradient in w. The equation of net water flow is, thus,... 

Often, as in Figure 4.3b, the conductivity is measured as a function of the activity of the solvent with which the membrane is equilibrated. In order to relate these measurements to the actual water content, one can use experimentally determined sorption isotherms as shown in Figure 4.4 for Nafion and a sulfonated polyaromatic membrane. The sorption isotherms will be revisited in more detail to discuss their critical role in membrane transport models [21]. 

The results of the last three sections can now be combined to yield the Binary Friction Membrane Transport Model (BFM2) which, after reinserting the dimensions, can be written as... 

While the focus of the model performance assessment was on Nafion 1100 equivalent weight (EW), the binary friction membrane transport model is quite general and should be applicable to other PFSA membranes. This is supported by preliminary results in applying the model to Dow membranes and membrane C, whereby rational changes in a single model parameter based on physical considerations of structural differences from Nafion yield conductivity predictions that are in good agreement with experimental measurements [61]. 

Membrane-transport models Kedem, Katachalsky, Lonsdale, Merten, Pusch, Sourirajan 1960-1970... 

An extensive hterature is devoted to the physics of water channels formation and to the mechanism of proton and water transport in membranes. In this section, we give a brief overview relevant to the analytical modelling of fuel cells. A detailed review of phenomenological membrane transport models is given in (Weber and Newman, 2007). Atomistic modelling and experiments on proton transport in membranes are reviewed in (Kreuer et al., 2004). Recent advances in mesoscopic membrane modelling are discussed in (Promislow and Wetton, 2009). The reader is referred to these works for a detailed discussion of the transport processes in polymer membranes. 

Combined solution-diffusion film theory models have been presented already in several publications on aqueous systems however, either 100% rejection of the solute is assumed or detailed experimental flux and rejection results are required in order to find parameters by nonlinear parameter estimation (Murthy and Gupta, 1997). Consequently, it is difficult to apply these models for predictive purposes. Peeva et al. (2004) presented the first consideration of concentration polarization in OSN. They coupled the solution-diffusion membrane transport model, Eq. (16.4), with film theory to describe flux and rejection of toluene/ docosane and tolune/TOABr binary mixtures. This approach was able to integrate concentration polarization and nonideal solution behavior into OSN design models and predict fluxes over a wide range of solvent mixtures from a limited data set of the pure solvent fluxes. The only parameters to be estimated, other than physical properties, are the mass transfer coefficients, which may be measured, and the permeabUilies, which may... 

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