External fluid film mass transfer

The limiting cases of the analytical solutions for external fluid-film mass transfer controlling (c —> 0) and solid diffusion controlling -> oo ) are the following ... 

The number of transfer units for each mechanism can be estimated from known parameters and mass transfer correlations (4). For example, for a column with particles 0.01 cm in diameter, a superficial velocity of 0.01 cm/sec, and a solute bulk diffusivity of 7 x 10-7 cm2/sec, the estimated number of transfer units in a packed bed of length L for the four mechanisms, axial dispersion, external fluid film mass transfer, pore diffusion, and solid homogeneous particle diffusion,are... 

Overall heat transfer coefficient Solid film mass transfer coefficient External fluid film mass transfer coefficient Dimensionless Henry constant... 

External Fluid Film Resistance. A particle immersed ia a fluid is always surrounded by a laminar fluid film or boundary layer through which an adsorbiag or desorbiag molecule must diffuse. The thickness of this layer, and therefore the mass transfer resistance, depends on the hydrodynamic conditions. Mass transfer ia packed beds and other common contacting devices has been widely studied. The rate data are normally expressed ia terms of a simple linear rate expression of the form... 

FIGURE 4 Schematic diagram of a biporous adsorbent pellet showing the three resistances to mass transfer (external fluid film, macropore diffusion, and micropore diffusion). R9 pellet radius rc crystal radius. 

The method can be applied to investigate the bidisperse pore structures, which consist of small microporous particles formed into macroporous pellets with a clay binder. In such a structure there are three distinct resistances to mass transfer, associated with diffusion through the external fluid film, the pellet macropores, and the micropores. Haynes and Sarma [24] developed a suitable mathematical model for such a system. 

The external fluid film resistance (the corresponding mass-transfer coefficient ki from equations (3.4.32a,b)) is in series with the intraparticle transport resistance. The flux of a species through a porous/mesoporous/microporous adsorbent particle consists, in general, of simultaneous contributions from the four transport mechanisms described earlier for gas transport in Section 3.1.3.2 (for molecular diffusion, where (Dak/T>ab) 2> 1) ... 

Possibilities for a single resistance include a linear rate expression with a lumped parameter mass transfer coefficient based either on the external fluid film or on a hypothetical solid film, depending on which film is controlling the rate of uptake of adsorbate. A quadratic driving force expression, again with a lumped parameter mass transfer coefficient, may be used instead. Alternatively, intraparticle diffusion, if the dominant form of mass transfer, may be described by the general diffusion equation (Pick s second law) with its appropriate boundary conditions, as described in Chapter 4. 

Mass transfer through the external fluid film, and macropore, micropore and surface diffusion may all need to be accounted for within the particles in order to represent the mechanisms by which components arrive at and leave adsorption sites. In many cases identification of the rate controlling mechanism(s) allows for simplification of the model. To complicate matters, however, the external film coefficient and the intraparticle diffusivities may each depend on composition, temperature and pressure. In addition the external film coefficient is dependent on the local fluid velocity which may change with position and time in the adsorption bed. 

As illustrated ia Figure 6, a porous adsorbent ia contact with a fluid phase offers at least two and often three distinct resistances to mass transfer external film resistance and iatraparticle diffusional resistance. When the pore size distribution has a well-defined bimodal form, the latter may be divided iato macropore and micropore diffusional resistances. Depending on the particular system and the conditions, any one of these resistances maybe dominant or the overall rate of mass transfer may be determined by the combiaed effects of more than one resistance. 

Mass-Transfer Coefficient Denoted by /c, K, and so on, the mass-transfer coefficient is the ratio of the flux to a concentration (or composition) difference. These coefficients generally represent rates of transfer that are much greater than those that occur by diffusion alone, as a result of convection or turbulence at the interface where mass transfer occurs. There exist several principles that relate that coefficient to the diffusivity and other fluid properties and to the intensity of motion and geometry. Examples that are outlined later are the film theoiy, the surface renewal theoiy, and the penetration the-oiy, all of which pertain to ideahzed cases. For many situations of practical interest like investigating the flow inside tubes and over flat surfaces as well as measuring external flowthrough banks of tubes, in fixed beds of particles, and the like, correlations have been developed that follow the same forms as the above theories. Examples of these are provided in the subsequent section on mass-transfer coefficient correlations. 

There are three distinct mass-transfer resistances (1) the external resistance of the fluid film surrounding the pellet, (2) the diffusional resistance of the macropores of the pellet, and (3) the diffusional resistance of the zeolite crystals. The external mass-transfer resistance may be estimated from well-established correlations (4, 5) and is generally negligible for molecular sieve adsorbers so that, under practical operating conditions, the rate of mass transfer is controlled by either macropore diffusion or zeolitic diffusion. In the present analysis we consider only systems in which one or other of these resistances is dominant. If both resistances are of comparable importance the analysis becomes more difficult. 

External mass transfer (1) and kinetic of adsorption (4) are normally very fast in the fluid phase (Guiochon, 1994) (Ruthven, 1984). The speed limiting processes are the film diffusion (2) and transport inside the pore system (3a, 3b). 

Two simple extensions of SCM can be used to describe CIS behavior. The external shell is treated as a separate phase surrounding the pellet (Figure CS6.4) that offers one more step of pure mass transfer resistance with no reaction in addition to the fluid film. Akiti. (2001) used such a model to obtain an approximate fit of the data. 

IRREVERSIBLE ADSORPTION. Irreversible adsorption with a constant mass-transfer coefficient is the simplest case to consider, since the rate of mass transfer is then just proportional to the fluid concentration. A truly constant coefficient is obtained only when all resistance is in the external film, but a moderate internal resistance does not change the breakthrough curve very much. Strongly favorable adsorption gives almost the same results as irreversible adsorption, because the equilibrium concentration in the fluid is practically zero until the solid concentration is over half the saturation value. If the accumulation term for the fluid is neglected, Eqs. (25.6) and (25.7) are combined to give... 

If the hypothesis of an external film is made, it can be assumed that the uptake rate of a species in the spherical particle is proportional to the difference between the concentration of drat species in the fluid phase and at die outer surface of the particle. The external mass transfer is dius given by ... 

The external mass transfer process can be described by the so-called film model as shown in Figure 2.19. According to the film model, a stagnant fluid layer of thickness 5 surrounds the external surface, where the total resistance to mass transfer is located. Accordingly, the concentration profile is confined to this layer. The molar flux of reactant A is proportional to the difference in concentration (the driving... 

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