Mass transfer coefficients membranes, separation

By combining Eqs. (21.1-14) and (21.1-18), fractional extraction can be obtained as a function of kavAulQF for different ratios of feed to dialysate flow rate. These relationships are shown in Fig. 21.1-6. The separation factor aJ in a dialytic process can be considered to be the ratio of the fractional masses of two solutes removed from their common feed stream, under a given set of operating conditions. By applying Eq. (21.1-16) to each solute, we can see that is equal to the ratio of the fractional extractions of the two solutes. Thus, Fig. 21.1-6 can be used to estimate the relative separation of two solutes from a knowledge of their overall mass transfer coefficients, membrane area, and feed and dialysate flow rates. 

The flux rate is obtained from the slope of the receptor chamber solute concentration versus time plot. The mass transfer coefficient, hh is equal to PA, where A is the surface area of the membrane separating the two subcompartments. 

In analogous manner, residue curve maps of the reactive membrane separation process can be predicted. First, a diagonal [/e]-matrix is considered with xcc = 5 and xbb = 1 - that is, the undesired byproduct C permeates preferentially through the membrane, while A and B are assumed to have the same mass transfer coefficients. Figure 4.28(a) illustrates the effect of the membrane at nonreactive conditions. The trajectories move from pure C to pure A, while in nonreactive distillation (Fig. 4.27(a)) they move from pure B to pure A. Thus, by application of a C-selective membrane, the C vertex becomes an unstable node, while the B vertex becomes a saddle point This is due to the fact that the membrane changes the effective volatilities (i.e., the products xn a/a) of the reaction system such that xcc a. ca > xbbO-ba-... 

As demonstrated by means of residue curve analysis, selective mass transfer through a membrane has a significant effect on the location of the singular points of a batch reactive separation process. The singular points are shifted, and thereby the topology of the residue curve maps can change dramatically. Depending on the structure of the matrix of effective membrane mass transfer coefficients, the attainable product compositions are shifted to a desired or to an undesired direction. 

A two-compartment cell was adopted to avoid the reduction of produced persulfate in the cathode and an ion-selective membrane, Nation N117/H+, separated the two compartments of the cell. A circular BDD anode was used and a cathode with the same surface (S = 63 cm2) was used. Two thermostatted tanks maintained the temperature of both solutions constant, while the recirculation of the solutions in the cell by two pumps assured a constant mass-transfer coefficient in the anodic and cathodic region during the test (km = 2.0 x 10-5 ms-1). The characteristic time of the direct oxidation was calculated in this series of tests = l.lOh), with the previous relationship (9.9). 

Mass transfer resistance in a continuous-contact separation device is the inverse of the mass transfer coefficient. In membrane contactors, the total resistance could be expressed as three resistances in series. These include the individual resistances in each flowing phase and the membrane resistance (Figure 2.4). For a liquid-gas contact system Equation 2.2 could be written for each diffusing species ... 

In selective separation of hydrocarbons from their mixtures with air or from their aqueous solutions, it makes sense to use membranes based on rubbery polymers, whose permeability increases with the decrease in glass transition point. Permselectivity of rubbery polymers is dominated by the sorption component, which increases with condensability of the hydrocarbon penetrant. Higher activity of the component being separated in the feed mixture results in plasticization of the membrane and can make it swell. This can produce a non-monotonic dependance of selective properties of the membrane on activity of the component being separated. As a rule, permselectivity for mixtures of penetrants is significantly lower than their ideal values. Negative values of sorption heat of easily condensable hydrocarbons can result in existence of non-monotonic temperature dependencies of mass transfer coefficients. 

Although the second approach can be considered a simplification of the first many systems have been satisfactorily described, and it is often preferred due to its mathematical simphcity. Studies on mass transfer through aqueous-organic interfaces immobilized at the pore mouths of a microporous membrane have shown that for a HF device, the overall mass transfer coefficient obtained can be related to the individual phase mass transfer coefficients and the membrane resistance using simple film theory. However, many authors considered that this separation controlling, overall mass transfer resistance was dominated by the resistance of the membrane. This is because the permeability of the membrane is low and because the membrane is thick [4,19,20,23,52,53]. On the other hand, other authors reported for different systems and conditions that the kinetic control of... 

Next, a mathematical model that allows description of the separation and concentration of the components of a metallic mixture will be detailed the principal assumptions of the model are (1) convective mass transfer dominates diffusive mass transfer in the fluid flowing inside the HFs, (2) the resistance in the membrane dominates the overall mass transport resistance, therefore the overall mass transfer coefficient was set equal to the mass transfer coefficient across the membrane, and (3) chemical reactions between ionic species are sufficiently fast to ignore the contribution of the chemical reaction rates. Thus, the reacting species are present in equilibrium concentration at the interface everywhere [31,32,58,59]. For systems working under nonsteady state, it is also necessary to describe the change in the solute concentration with time both in the modules and in the reservoir tanks. The reservoir tanks will be modeled as ideal stirred tanks. 

The mass-transfer efficiencies of various MHF contactors have been studied by many researchers. Dahuron and Cussler [AlChE 34(1), pp. 130-136 (1988)] developed a membrane mass-transfer coefficient model (k ) Yang and Cussler [AIChE /., 32(11), pp. 1910-1916 (1986)] developed a shell-side mass-transfer coefficient model (ks) for flow directed radially into the fibers and Prasad and Sirkar [AIChE /., 34(2), pp. 177-188 (1988)] developed a tube-side mass-transfer coefficient model (k,). Additional studies have been published by Prasad and Sirkar [ Membrane-Based Solvent Extraction, in Membrane Handbook, Ho and Sirkar, eds. (Chapman Hall, 1992)] by Reed, Semmens, and Cussler [ Membrane Contactors, Membrane Separations Technology Principle. and Applications, Noble and Stern, eds. (Elsevier, 1995)] by Qin and Cabral [MChE 43(8), pp. 1975-1988 (1997)] by Baudot, Floury, and Smorenburg [AIChE ]., 47(8), pp. 1780-1793 (2001)] by GonzSlez-Munoz et al. [/. Memhane Sci., 213(1-2), pp. 181-193 (2003) and J. Membrane Sci., 255(1-2), pp. 133-140 (2005)] by Saikia, Dutta, and Dass [/. Membrane Sci., 225(1-2), pp. 1-13 (2003)] by Bocquet et al. [AIChE... 

Where K a is the mass transfer coefficient, C is the VOC concentration in the solvent in equilibrium with the vapor phase, C is the actual solvent VOC concentration, and J is the flux of the VOC. Raising the temperature will cause C to approach zero. For the dilute VOC in the solvent, small values of C cause the flux to approach zero and separation does not occur. By using membranes with their large area to volume ratio, the mass transfer coefficient can be increased by an order of magnitude or more compare to a conventional packed column (33). This increase in area will enhance flux despite small values of C, thus making the separation more feasible. The VLE data needed to evaluate the MASX/MADS process are currently being collected. It is expected that this process wiU perform well. 

Equation (21.50) has been used to predict the internal mass-transfer resistance for separation processes using hollow-fiber membranes. The recommended equation for heat transfer, Eq. (12,23), has an empirical coefficient of 2.0, and this higher... 

FLOW OUTSIDE TUBES PARALLEL TO AXIS. Some membrane separators have bundles of hollow fibers in a shell-and-tube arrangement with liquid or gas flowing parallel to the tube axis on the outside of the tubes. The external flow passages are irregular in shape and not uniform, since the fibers are not held in position as are the tubes in a heat exchanger. Empirical correlations for the external mass-transfer coefficient have been proposed using an equivalent diameter to calculate the Reynolds number. For a bundle of fibers with diameter d packed in a shell with c void fraction, the equivalent diameter is... 

The Fine Porous Model as presented by Xu and Spencer (1997), describes equilibrium and non-equilibrium factors of rejection. Only coupling between solvent and solute is taken into account, and no solute-solute coupling is permitted. Equilibrium parameters dominated separation, and these are described by the reflection coefficient (J in equation (3.28), where kii is the solute mass transfer coefficient in the membrane. 

Also, the diffusion boundary layer resistances on either side of the membrane filter in membrane transport processes have been extensively examined [125,126], Most of these studies deal with cases wherein solute diffuses across a membrane filter separating two aqueous phases with different concentrations. However, the individual film mass transfer coefficients in both liquid phases are unavailable. 

Mass transfer occurs only by diffusion across the immobilized phase in the pores. The direction of mass transfer of any molecular species depends on the concentration driving force maintained across the membrane for that species. The presence of the stationary phase in the membrane pore creates an extra diffusional mass-transfer resistance [6], However, it can be shown that in many cases, the membrane resistance is negligible and that in most cases, the highly active mass-transfer area created inside a membrane contactor more than compensates for any additional mass-transfer resistance [15,16], Mass-transfer resistance in a continuous-contact separation device is the inverse of the mass-transfer coefficient. In membrane contactors, the total resistance could be expressed as three resistances in series. These include the individual resistances in each flowing phase and the membrane resistance. For a liquid-gas contact system. Equation 4.2 could be written for each diffusing species [6] ... 

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