Surface , mass-transfer coefficients

Figure 9.10. Characterization of the surface mass transfer coefficients for the tank tests. The 95% confidence interval is included (Shierholz et al., 2006). CB, coarse bubble FB, fine bubble LACSD, Los Angeles County Sanitary District WES, U.S. Army Engineer Waterways Experiment Station.

For gas-solid fluidized beds, Wen and Fane (1982) suggested that the determination of the bed-to-surface mass transfer coefficient can be conducted by using the corresponding heat transfer correlations, replacing the Nusselt number with the Sherwood number, and replacing the Prandtl number by Sc(cpp)/(cpp)/(l — a). Few experimental results on bed-to-surface mass transfer are available, especially for gas-solid fluidized beds operated at relatively high gas velocities. 

Cag ) comes into contact with the surface of concrete(take x = 0 at the surface). (2) Diffusive CO2 (molar concentration, Ca2 diffusion coefficient, Da2 in concrete) feels the mass transfer resistance at the surface of concrete (surface mass transfer coefficient, Kg g), unless the equilibrium Ca2 = al satisfied ( k-ag + ). The retardation effects of finishes on the diffusion of CO2 (thickness,... 

Surface mass transfer coefficient is high enough so that the material moisture content at the surface is in equilibrium with the air drying conditions. 

By analogy, a surface mass transfer coefficient can be defined using the following equation ... 

Correlations for the catalyst surface mass transfer coefficient ksurf and the heat transfer coefficient hsurf are seen in [199] [440]. They are usually... 

Figure 9. Variation of (a) surface mass transfer coefficient and (b) internal diffiisivity with loading for O2 and N2 in BF CMS at 298K. From Sundaram et a/[46].

Detailed studies show that the sorption kinetics are controlled by a combination of surface resistance and internal diffusion although, depending on the particular adsorbent and the conditions, one or other of these resistances may be dominant [44-47]. The uptake curves show a clear transition from surface barrier control in the initial region to diffusion control at long times. The differential diffusivity and the surface mass transfer coefficient both increase strongly with loading much more strongly than is predicted by the thermodynamic correction factor (Eq. 4). The data are correlated by the empirical expressions ... 

KG Surface mass transfer coefficient, kmol/hr/m" solid... 

To model this mass transfer, we have introduced, in addition to the diffusion coefficient D, the surface mass transfer coefficient H representing the above asymptotic sorption-kinetics at contenl/conlainer interface. Both parameters have been determined from sorption tests. Experimental results show that the diffusion coefficient D remains constant, while the surface mass transfer coefficient H increases with amyl acetate concentration and temperature of the solution. 

Neither the penetration nor the surface renewal theory can be used to predict mass transfer coefficients directiy because T and s are not normally known. Each suggests, however, that mass transfer coefficients should vary as the square root of the molecular diffusivity, as opposed to the first power suggested by the film theory. 

The rate of mass transfer,/, is then assumed to be proportional to the concentration differences existing within each phase, the surface area between the phases,, and a coefficient (the gas or Hquid film mass transfer coefficient, k or respectively) which relates the three. Thus... 

The value of the saturation concentration,, is the spatial average of the value determined from a clean water performance test and is not corrected for gas-side oxygen depletion therefore K ji is an apparent value because it is determined on the basis of an uncorrected. A tme volumetric mass transfer coefficient can be evaluated by correcting for the gas-side oxygen depletion. However, for design purposes, can be estimated from the surface saturation concentration and effective saturation depth by... 

To estimate the slumping motion of the kiln bed which periodically exposes a fresh, vapor saturated surface at the bed—freeboard interface must be considered. Based on Pick s second law in a bed of porosity, S, and for an effective diffusion coefficient, the mass-transfer coefficient on the bed side is... 

The drying rate is represented by differential equation (eq. 6) where h is mass transfer coefficient 1/(hcm ) , specific surface area of desiccant beads, cm /g mass of desiccant, g C, concentration by weight of water in the fluid being dried (7, concentration of water at the surface of the desiccant, ie, concentration of water in the fluid that would be in equihbrium with the instantaneous loading on the desiccant, wt-ppm and t — time, h. 

If requited, the drydown can be hastened by increasing desiccant mass, particle surface area, or mass-transfer coefficient. The mass-transfer coefficient can be altered to some extent by the design of the desiccant container. 

A = effective surface area for heat and mass transfer in m L = latent heat of vaporization at in kj/kg k = mass-transfer coefficient in kg/ (sm kPa) t = mean source temperature for all components of heat transfer in K t = Hquid surface temperature in K p = Hquid vapor pressure at in kPa p = partial pressure of vapor in the gas environment in kPa. It is often useful to express this relationship in terms of dry basis moisture change. For vaporization from a layer of material ... 

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. 

Simplified Mass-Transfer Theories In certain simple situations, tne mass-transfer coefficients can be calculated from first principles. The film, penetration, and surface-renewal theories are attempts to extend tnese theoretical calculations to more complex sit-... 

The unknown intermediate concentration C, has been mathematically ehminated from the last term. In this case, r can be solved for explicitly, but that is not always possible with surface rate equations of greater complexity. The mass transfer coefficient /ci is usually obtainable from correlations. When the experimental data are of (C, r) the other constants can be found by linear plotting. 

However, any average drop size is fictitious, and none is completely satisfactory. For example, there is no way in which the high surface and transfer coefficients in small drops can be made avail le to the larger drops. Hence, a process calculation based on a given droplet size describes only what happens to that size and gives at best an approximation to the total mass. 

Overall Mass-Transfer Coejficient Tatterson (op. cit.) and Zlokarnik (op. cit.) have summarized the hterature covering overall mass-transfer coefficients. There is much scatter in the experimental data because the presence of surface-ac tive agents and electrolytes have a significant effect on the mass transfer. The correlation of Van t Riet [Ind. Eng Chem. Process Des. Dev., 18(3), 357 (1979)] is recommended ... 

Because of the complexities encountered with a rigorous treatment of the hydrodynamics around particles in industri contactors, mass transfer to and from the adsorbent is described in terms of a mass-transfer coefficient kf. The flux at the particle surface is ... 

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