Mass external fluid film diffusion

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... 

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

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 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... 

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. 

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). 

Mass film diffusion of reactant from bulk fluid to external surface of catalyst... 

Many events occur in the MTZ during adsorption which render the analysis complex. First, one or more adsorbates transfer from the fluid bulk by convection or diffusion across the fluid film which is external to the solid surface. Secondly, these adsorbates penetrate the particle by Maxwell, Knudsen and surface diffusion mechanisms (see Chapter 4), and adsorb onto the internal surface where the heat of adsorption is released. Heat may then be transferred to the adsorbent, to the flowing process fluid, and, via the vessel wall, to the surrounding environment. Heat and mass transfer may occur in the MTZ by bulk and diffusive flows in both the radial and axial directions. An additional complexity is that the flow through a packed bed may not be uniform across its entire cross-sectional area. This may be because of channelling of fluid at the wall or because of temperature gradients created when the heat of adsorption is released. 

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. 

Heterogeneous catalytic reactions in supercritical solvents Obviously, a solid catalyzed reaction takes place only on the active sites of the porous catalyst with the implication of some mass and heat transport steps prior to and after the reaction. The first step is the diffusion of the reactants through the film surrounding the catalyst particle to the external surface of the catalyst, followed by diffusion of the reactants into the catalyst pore to the active site in the pores. These steps are limited by the dif-fusivity and viscosity of the reactants. In the case of a supercritical fluid phase reaction, the diffusivity is higher than the liquid diffusivity, viscosity is less than the liquid viscosity and therefore, the rate of transfer to the active site will be higher. After the adsorption, reaction and desorption steps, the products have to diffuse out of the pore, and again... 

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