Interphase mass transfer coefficient

Figure 4.58 Interphase mass-transfer coefficient obtained for a reaction engineering model [94. Reactor model...

Finally, in general, the models are less sensitive to the assumed gas-mixing status in the emulsion phase, i.e. complete mixing or plug flow, than to the expressions used to determine the interphase mass transfer coefficient (Grace, 1984). 

Figure 5.2 Interphase mass transfer coefficient obtained from reaction engineering model (by courtesy of Elsevier) [22].

The value of kC02 is 20 s 1 (or 7200 h ) at room temperature [73]. The value of kia, the interphase mass transfer coefficient, for our system must be estimated based on literature reports of mass transfer rates in relatively similar systems. Although the estimate of k a obtained below is highly uncertain, it is orders of magnitude less than kC02 but very much larger (hence, less ratedetermining) than kf. 

Normally, the intrinsic chemical rate is an exponential function of temperature, according to the Arrhenius law, whereas the mass transfer rate is less strongly influenced by a temperature change. The m-traparticlc effective diffusivity Dc is proportional to T1/2 when molecular diffusion dominates, and proportional to T1/2 for the case of governing Knudsen diffusion. The interphase mass transfer coefficient A r ex-... 

Estimate the external resistance to mass transfer by invoking continuity of the normal component of intrapellet fluxes at the gas/porous-solid interface. Then use interphase mass transfer coefficients within the gas-phase boundary layer surrounding the pellets to evaluate interfacial molar fluxes. 

The interphase mass transfer coefficient of reactant A (i.e., a,mtc), in the gas-phase boundary layer external to porous solid pellets, scales as Sc for flow adjacent to high-shear no-slip interfaces, where the Schmidt number (i.e., Sc) is based on ordinary molecular diffusion. In the creeping flow regime, / a,mtc is calculated from the following Sherwood number correlation for interphase mass transfer around solid spheres (see equation 11-121 and Table 12-1) ... 

Stining speed Interphase mass transfer coefficient, specific interfacial area, uniformity of phase dispersion, emulsification Conversion n/i ratio [1, 2, 5, 6]... 

Interphase mass transfer coefficient Molar mass for component i Average molar mass Partial pressure for component i Pre-exponentional factor for permeation of Pd membrane Radial coordinate Universal gas constant ( = 8.3145)... 

Even less is known about the liquid-solid transfer in bubble columns. Ghosh [83] has recently studied the liquid-solid mass transfer by monitoring the rate of dissolution of benzoic acid pellets suspended in a bubble column. He elucidated the effect of gas velocity (air), axial position of pellet and the types of sparger. Figure 8 shows the effect of gas velocity on the interphase mass transfer coefficient (k ) in a 1% aqueous CMC solution when the solute particles are positioned at various heights from the distributor. Within the narrow range of conditions, he found that the type and details of the sparger did not exert any influence on the value of the mass transfer coefficient. He presented his results in terms of Stanton number. 

Application of the same analogy between mass transfer and heat transfer to channel shapes other than the square introduces errors in the estimation of the interphase mass transfer coefficients, which range approximately within 20%, depending on the reaction kinetics and on the channel geometry. On the other... 

Kc interphase mass transfer coefficient per unit bubble volume s-i... 

Values for the interphase mass transfer coefficient kgA can be calculated from y rcorrelations (see Chapter 3). Specific correlations for fluidized beds can be found in Perry [1984]. 

The model species, total mass, momentum, and energy continuity equations are similar to those presented in Section 13.7 on fluidized bed reactors. Constant values of the gas and liquid phase densities, viscosities, and diffusivities were assumed, as well as constant values of the interphase mass transfer coefficient and the reaction rate coefficient. The interphase momentum transfer was modelled in terms of the Eotvos number as in Clift et al. [1978]. The Reynolds-Averaged Navier-Stokes approach was taken and a standard Computational Fluid Dynamics solver was used. In the continuous liquid phase, turbulence, that is, fluctuations in the flow field at the micro-scale, was accounted for using a standard single phase k-e model (see Chapter 12). Its applicability has been considered in detail by Sokolichin and Eigenberger [1999]. No turbulence model was used for the dispersed gas phase. Meso-scale fluctuations around the statistically stationary state occur and were explicitly calculated. This requires a transient simulation and sufficiently fine spatial and temporal grids. 

When the foregoing statement is expressed in a equation, it becomes /P = 1/Pl + l/ m> where P, Pl and P are the total mass transfer coefficient, interphase mass transfer coefficient, and permeation coefficient of the membrane, respectively. Their reciprocals are the total resistance 1/P, interphase resistance 1/Pl> and membrane resistance /Pm- When both sides are fluid, then there will be one more interphase, and the equation becomes 1/P = 1/Pl + 1/Pm + V- l- The unit of the permeation coefficient is cm (STP) cm/cm s cmHg when it is expressed by the partial pressure difference (mol/cm s cmHg), but it is cm/s if it is expressed by concentration difference (mol/cm ). 

Physical transport processes can play an especially important role in heterogeneous catalysis. Besides film diffusion on the gas/hquid boundary, there can also be diffusion of the reactants (products) through a boundary layer to (from) the external surface of the sohd material, as well as through the porous interior to (for reactants) or from (for products) the active catalyst sites. Fleat and mass transfer processes influence the observed catalytic rates. For instance, as discussed previously, the intrinsic rates of catalytic processes follow the Arrhenius law, while mass transfer hinders such pronounced dependence, decreasing the apparent activation energy. The intraparticle and interphase mass transfer coefficients display a lower temperature dependence as visualized in Fig. 10.2 and discussed later. 

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