Fouling, membrane models

J. Siler, "Reverse Osmosis Membranes-Concentration Polarization and Surface Fouling Predictive Models and Experimental Verifications," dissertation. University of Kentucky, Lexington, Ky., 1987. 

The Resistance in Series Model describes the flux of a fouled membrane. This is given in equation (3.4). The resistances Ra>, Ri> and Rc denote the additional resistances which result from the exposure of the membrane to a solution containing particles or solute. Rcp is the resistance due to concentration polarisation, Ri> the internal pore fouling resistance, and Rc the resistance due to external deposition or cake formation. These resistances are usually negligible in RO, where the osmotic pressure effects become more important (Fane (1997)). However, the osmotic pressure can also be incorporated into Rcp. 

Although it is safe to say that NF nowadays can be implemented without problems in many known applications, it is expected that the evolution in NF wUl continue. Some of the expected progresses include modeling of rejection in aqueous solutions, understanding of the performance in organic solvents, prediction and control of fouling, membranes with controlled pore size, possibly in hoUow-fiber configmation, development of hydrophobic ceramic NF membranes, and the optimization of hybrid processes with NF. 

Equation (20-80) requires a mass transfer coefficient k to calculate Cu, and a relation between protein concentration and osmotic pressure. Pure water flux obtained from a plot of flux versus pressure is used to calculate membrane resistance (t ically small). The LMH/psi slope is referred to as the NWP (normal water permeability). The membrane plus fouling resistances are determined after removing the reversible polarization layer through a buffer flush. To illustrate the components of the osmotic flux model. Fig. 20-63 shows flux versus TMP curves corresponding to just the membrane in buffer (Rfouimg = 0, = 0),... 

Green, G and Belfort, G. Desalination 35 (1980) 129. Fouling of ultrafiltration membranes lateral migration and particle trajectory model. 

Model and Preliminary Experiments on Membrane Fouling in Reverse Osmosis... 

As described above, the initial cause of membrane fouling is concentration polarization, which results in deposition of a layer of material on the membrane surface. The phenomenon of concentration polarization is described in detail in Chapter 4. In ultrafiltration, solvent and macromolecular or colloidal solutes are carried towards the membrane surface by the solution permeating the membrane. Solvent molecules permeate the membrane, but the larger solutes accumulate at the membrane surface. Because of their size, the rate at which the rejected solute molecules can diffuse from the membrane surface back to the bulk solution is relatively low. Thus their concentration at the membrane surface is typically 20-50 times higher than the feed solution concentration. These solutes become so concentrated at the membrane surface that a gel layer is formed and becomes a secondary barrier to flow through the membrane. The formation of this gel layer on the membrane surface is illustrated in Figure 6.6. The gel layer model was developed at the Amicon Corporation in the 1960s [8],... 

Concentration polarization can dominate the transmembrane flux in UF, and this can be described by boundary-layer models. Because the fluxes through nonporous barriers are lower than in UF, polarization effects are less important in reverse osmosis (RO), nanofiltration (NF), pervaporation (PV), electrodialysis (ED) or carrier-mediated separation. Interactions between substances in the feed and the membrane surface (adsorption, fouling) may also significantly influence the separation performance fouling is especially strong with aqueous feeds. 

Flux. The film model (Equation 6.6) illustrates that increasing flux has an exponential effect on CP. If we accept that fouling is a consequence of CP the impact of excessive flux is obvious. As a result high flux membranes tend to be short lived and foul unless improved fluid management is able to enhance k. Selection of the appropriate flux and crossflow velocity is a trade-offbetween capital and operating costs (see cost of fouling below). 

Void [52] developed a variety of ballistic deposition models to simulate sedimentation processes. Void used ballistic models to determine deposition densities for spherical particles which traveled via vertical paths and were deposited on horizontal surfaces. Recently, Schmitz et al. [53] used a ballistic aggregation model to describe particle aggregation at the surface of a crossflow microfiltration membrane. Schmitz and co-workers were able to account for interfacial forces empirically, and demonstrated the influence of physical and chemical variables on the resulting morphology of the fouling deposits (such as aggregate density variation with depth, and influence of shear flow and re-entrainment properties on fouling deposit density and porosity). 

P. Bacchin, P. Aimar and V. Sanchez, Model for colloidal fouling of membranes, AIChEJ 41 (1995) 368-376. 

The mechanisms of microfiltration membrane fouling were investigated in wine and model solutions (Vernhet and Moutounet 2002). The sharp decline observed in microfiltration fluxes within the first minutes of the process could not be attributed to adsorption alone. They can be explained by a two step mechanisms involving first interaction of the wine constituents with the membrane, quickly followed by their aggregation at the pore entrance (Vernhet and Moutounet 2002). 

In addition to the Navier-Stokes equations, the convective diffusion or mass balance equations need to be considered. Filtration is included in the simulation by preventing convection or diffusion of the retained species. The porosity of the membrane is assumed to decrease exponentially with time as a result of fouling. Wai and Fumeaux [1990] modeled the filtration of a 0.2 pm membrane with a central transverse filtrate outlet across the membrane support. They performed transient calculations to predict the flux reduction as a function of time due to fouling. Different membrane or membrane reactor designs can be evaluated by CFD with an ever decreasing amount of computational time. 

Passage of bacteria through membrane Analysis of deposits ATR, FTIR, measuring fouling in real time Measuring concentration polarization Mathematical modeling of flux decline... 

A comprehensive difference model was developed by Madireddi et al. [71] to predict membrane fouling in commercial spiral-wound membranes with various spacers. This is a useful paper for experimental studies on the effect of flow channel thickness on flux and fouling. Avlonitis et al. [72] presented an analytical solution for the performance of spiral-wound modules with seawater as the feed. In a key finding they showed that it was necessary to incorporate the concentration and pressure of the feed into the correlation for the mass transfer coefficient. In a similar study, Boudinar et al. [73] developed the following relationship for calculating mass transfer coefficients in channels equipped with a spacer ... 

Bacchin P., Aimar P., and Sanches V., Model of colloidal fouling of membranes. AIChE Journal 41(2) 1995 368-376. 

The concentration polarization model, which is based on the stagnant fihn theory, was developed to describe the back-diffusion phenomenon during filtration of macromolecules. In this model, the rejection of particles gives rise to a thin fouling layer on the membrane surface, overlaid by a concentration polarization layer in which particles diffuse away from the membrane surface, where solute concentration is high, to the bulk phase, where the solute concentration is low [158]. At steady state, convection of particles toward the membrane surface is balanced by diffusion away from the membrane. Thus, integrating the onedimensional convective-diffusion equation across the concentration polarization layer gives... 

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