Bulk mass transfer

Steps 2 and 6 are both pore diffusion processes with apparent activation energies between 2 and 10 kcal/mol. This apparent activation energy is stated to be about 1/2 that of the chemical rate activation energy. The concentration of reactants decreases from the outer perimeter towards the center of the catalyst particle for Step 2. In this case some of the interior of the catalyst is being utilized but not fully. Therefore the effectiveness factor is greater than zero but considerably less than one. These reactions are moderately influenced by temperature but to a greater extent than bulk mass transfer. 

Because of the significant differences in temperature dependence the kinetically limited reactions can be distinguished from pore diffusion that in turn can be differentiated from bulk mass transfer. This is shown in Fig. 7.2 in... 

Fig. 7.2. Conversion of a reactant vs. temperature.The concentration of reactants [R] within the porous catalyst structure. Concentration of R is (a) uniform for kinetic control, (b) decreasing within the catalyst for pore diffusion control, and (c) zero immediately at the surface of the catalyst for bulk mass transfer.

The linear velocity (LV) or superficial velocity is an important engineering term because it relates to pressure drop and turbulence. This parameter is often increased in fixed bed reactors to enhance bulk mass transfer and heat transfer. 

The plot of In ( ) versus T 1 gives a straight line with a slope equal to —E/R and intercept the absolute rate constant kQ as shown in Fig. 7.6. The lowest slope represents reactions controlled by bulk mass transfer, and the largest is... 

This result may be explained by a combination of intraparticle diffusion and bulk mass transfer processes. As material is extracted from the exposed areas of the seed, the solvent must travel further through the pores to reach the solute. Also, as the entrance portion of the bed becomes depleted of soluble components, the effective bed length decreases until the residence time is insufficient to achieve equilibrium. Similar effects were observed in seed oil extraction by Fattori (1) and Taniguchi et al. (9). 

Peclet number (mass transfer) Pe Re Sc = VL D Dimensionless independent mass transfer coefficient (ratio of bulk mass transfer to diffusive mass transfer) Mass transfer... 

In interfacial contact reactors, a selectively wetted porous membrane is used to maintain an organic-aqueous interface in the plane of the membrane, while allowing for interfacial contact between the substrate and the biocatalyst (Fig. 3). Bulk mass transfer limitation, common in conventional heterogeneous emulsion systems, could thus be reduced [125]. Once more, the two liquid phases acted as a reservoir for substrates and/or products. To keep the interface in the plane of the membrane, a slight positive pressure in the non-wetting phase was needed [126,127]. 

All these reactions required some heat or temperature on the catalyst surface for the reaction to occur. When the automobile first starts, both the engine and the catalyst are cold. After startup, the heat of combustion is transferred from the engine and the exhaust piping begins to heat up. Finally, a temperature is reached within the catalyst that initiates the catalytic reactions. This light-off temperature and the concurrent reaction rate are kinetically controlled, that is, depends on the chemistry of the catalyst, since the transport reactions are fast. Typically, the CO (and H2) reaction begins first, followed by the HC and NO reaction. Upon further heating, the chemical reaction rates become fast and the overall conversions are controlled by pore diffusion and/or bulk mass transfer. 

Peclet (Pe) = LU -TT Bulk mass transfer/diffusive Stokes (Stk) = Stopping distance/... 

As has been shown by Uchida and Wen [l38] six different asymptotic cases of mass transfer interfering with instantaneous chemical reaction can be distinguished (Figure 20 a and b). In cases la to Ic the dissolution of the solids in the film at the G-L interface can be neglected relative to the dissolution in the bulk. Mass transfer of A then is in series with the dissolution process. The criterion under which this assumption is valid orginally was derived by Ramachandran and Sharma [l36] ... 

FIG. 22 The dependence of the bulk mass transfer rate on particle radius a for the rotating disk calculated numerically from Eq. (160) (T = 293 K, apparent densities of the particle Ap curve 1, 0.6 kg/dcm curve 2, 0.3 kg/dcm curve 3, 0 curve 4, —0.3 kg/dcm curve 5, —0.6 kg/dcm (the minus sign denotes the gravity force acting opposite the interface). The dashed line denotes the limiting value calculated from Eq. (162) (Stokes law), and the dashed-dotted line represents the results calculated from Eq. (161) (the interception governed flux). (From Ref 37.)... 

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