Selectivity Sherwood number

Traditionally, an average Sherwood number has been determined for different catalytic fixed-bed reactors assuming constant concentration or constant flux on the catalyst surface. In reality, the boundary condition on the surface has neither a constant concentration nor a constant flux. In addition, the Sh-number will vary locally around the catalyst particles and in time since mass transfer depends on both flow and concentration boundary layers. When external mass transfer becomes important at a high reaction rate, the concentration on the particle surface varies and affects both the reaction rate and selectivity, and consequently, the traditional models fail to predict this outcome. 

In Table 1.4, the characteristic time-scales for selected operations are listed. The rate constants for surface and volume reactions are denoted by and respectively. Furthermore, the Sherwood number Sh, a dimensionless mass-transfer coefficient and the analogue of the Nusselt number, appears in one of the expressions for the reaction time-scale. The last column highlights the dependence of z p on the channel diameter d. Apparently, the scale dependence of different operations varies from dy f to (d ). Owing to these different dependences, some op-... 

In the. cnnvective-diffusion-contiolled region, the rate should be independent of the value of A/kT. Selecting arbitrary values for the Peclet number and aspect ratio, the Sherwood number is first calculated for A/kT = 0. Then the value of the ratio A/kT Is gradually increased,... 

Pg pressure inside the gas plug pi pressure in the liquid at the interface AP pressure drop q volumetric flow rate r radial coordinate reaction rate Tc radius at chaimel comer Ri principal radius of curvature Ri principal radius of curvature Re Reynolds number S selectivity Sc Schmidt number Sh Sherwood number SR slurry reactor STYv space lime yield t time... 

Mass transfer rates attainable In menbrane separation devices, such as gas permeators or dlalyzers, can be limited by solute transport through the menbrane. The addition Into the menbrane of a mobile carrier species, which reacts rapidly and reversibly with the solute of Interest, can Increase the membrane s solute permeability and selectivity by carrier-facilitated transport. Mass separation is analyzed for the case of fully developed, one-dimensional, laminar flow of a Newtonian fluid in a parallel-plate separation device with reactive menbranes. The effect of the diffusion and reaction parameters on the separation is investigated. The advantage of using a carrier-facilitated membrane process is shown to depend on the wall Sherwood number, tfrien the wall Sherwood nunber Is below ten, the presence of a carrier-facilitated membrane system is desirable to Improve solute separation. 

In many cases of practical interest, the membrane s mass transfer resistance is significant, i.e., the wall Sherwood number is small, leading to relatively low mass transfer rates of the solute. The diffusive flux of the permeate through the membrane can be increased by introducing a carrier species into the membrane. The augmentation of the flux of a solute by a mobile carrier species, which reacts reversibly with the solute, is known as carrier-facilitated transport (25). The use of carrier-facilitated transport in industrial membrane separation processes is of considerable interest because of the increased mass transfer rates for the solute of interest and the improved selectivity over other solutes (26). 

Solution. The identical procedure as is demonstrated in Example 1 can be used to evaluate Shbed at different yb. The results are shown in Fig. 10 where, as expected, a higher yb will generate a higher Sherwood number. The results in Fig. 10 clearly indicate that, in addition to bubble size, the selection of yb is also essential in the estimation of the particle-gas mass transfer coeffficient based on Eq. (61) proposed by Kunii and Levenspiel (1991). 

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