Membrane contactors mass transfer coefficients

When a species is transferred from a phase to another phase by means of a membrane contactor, the mass-transport resistances involved are those offered by the two phases and that of the membrane (see Figure 20.5). The overall mass-transfer coefficient will, therefore, depend on the mass-transfer coefficient of the two phases and of the membrane. 

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 ... 

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... 

For mass transfer across the hollow-fiber membrane contactors described in Example 2.14, the overall mass-transfer coefficient based on the liquid concentrations, Kf, is given by (Yang and Cussler, 1986)... 

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] ... 

Profiles in which this latter profile can be found are electrodialysis, per/aporation, gas separation, dialysis, diffusion dialysis, facilitated transport or carrier mediated transport and membrane contactors. The extent of the boundary layer resistance varies from process to process and even for a specific process it is quite a lot dependent on application. Table Vn.2 summarises the causes and consequences of concentration polarisation in various membrane processes. The effect of concentration polarisation is very severe in microfiltration and ultrafiltration both because the fluxes (J) are high and the mass transfer coefficients k (= EV8) are low as a result of the low diffusion coefficients of macromolecuiar solutes and of small particles, colloids and emulsions. Thus, the diffusion coefficients of macromolecules are of the order of lO ° to 10 m /s or less. The effect is less severe in reverse osmosis both because the flux is lower and the mass transfer coefficient is higher. The diffusion coefficients of low molecular weight solutes are roughly of the order of 10 m /s. In gas separation and pervaporation the effect of concentration polarisation is low or can be neglected. The flux is low and the mass transfer coefficient high in gas separation (the diffusion coefficients of gas molecules are of the... 

Concentration polarisation is not generally severe in dialysis and diffusion dialysis because of the low fluxes involved (lower than in reverse osmosis) and also because the mass transfer coefficient of the low molecular solutes encountered is of the same order of magnitude as in reverse osmosis. In carrier mediated processes and in membrane contactors the effect of concentration polarization may become moderate mainly due to the flux through the membrane. Finally, the effect of concentration polarisation may become ver severe in electrodialysis. In the following sections concentration polarization will be described more in detail. In some module configurations such as plate-and-frame and spiral wound spacer materials are used in the feed compartment (see chapter VIII). These spacers effect the mass transfer coefficient and can be considered as turbulence promoters. 

Mass Transfer in Gas-Liquid Systems As in conventional contactors, mass transfer rates in membrane contactors for gas-liquid systems are generally described by means of an overall mass transfer coefficient, K, and the gas-liquid interfacial area per unit device volume, a. The overall mass transfer coefficient based on the liquid phase for any species i, Ku, is usually described via the principle of the following resistances in series liquid film resistance (1 /fe,/), membrane resistance (//,/, > ), and the gas film resistance (//,/ kig) for the gas-filled membrane pore case in series leading to the overall resistance (1 /Ku) ... 

Mass Ti ansfer The rate of mass transfer in a liquid-liquid extraction system implemented in a nondispersive membrane contactor is analyzed in the manner followed in conventional contactor analysis. The overall organic phase-based mass transfer coefficient Kio of a species i being extracted (or back extracted) from an aqueous solution into a solvent wetting the pores of a hydrophobic membrane is described via the resistances-in-series model ... 

The effects of chemical reactions are exemplified by the data for ammonia adsorption in water summarized in Fig. 17.0-1. The overall mass transfer coefficient, in cm/sec, is based on a liquid side driving force given in mol/cm. The specific values shown are for a hollow-fiber membrane contactor, though similar values would be obtained in a packed tower or other more conventional apparatus. 

As organic and aqueous phases are macroscopically separated by the membrane, HFM offer several hydrodynamic advantages over other contactors, such as the absence of flooding and entrainment, or the reduction of feed consumption (160, 161). The flowsheets tested in HFM were similar to those developed for centrifugal contactor tests. Computer codes based on equilibrium (162) and kinetics data, diffusion coefficients (in both phases and in the membrane pores), and a hydrodynamic description of the module, were established to calculate transient and steady-state effluent concentrations. It was demonstrated that, by selecting appropriate flow rates (as mass transfer is mainly controlled by diffusion), very high DFs (DI A 11 = 20,000 and DFrm = 830) could be achieved. Am(III) and Cm(III) back-extraction efficiency was up to 99.87%. 

Various parameters in Equation 31.17 have been defined earlier. Danesi et al. [92] described a simple correlation between permeability coefficient in FSSLM and HFSLM configuration. At very large values of ( ) (as compared to 1), Equation 31.17 is transformed into the one used for FSSLM by Danesi et al. [92]. Hence, the smaller the value of ( ), the higher will be the negative value of the left-hand side of Equation 31.17, which suggests the higher rate of mass transfer. Later on, D Elia et al. [93] considered the resistance in series model where they have studied the mass transport across hollow-fiber contactors in NDSX mode. They showed that the overall mass transfer resistance is equal to the sum of individual mass transfer resistances across the aqueous boundary layer and membrane phase. Mathematically, it can be written as follows ... 

Table 2.7 Values for mass transfer and resistance coefficients estimated for a typical G-L membrane contactor device equipped by a composite membrane with dense top layer...

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