Thiele analysis

Fig. 20. Effect of degree of crosslinking (% DVB) of a standard ion exchanger on the diffusivities, Def (cm2 min-1), and the selectivity ratio, S = efs/ efAc ( ef = effective rate coefficient, S = sucrose, Ac = ethyl acetate). Data were obtained by rate measurements and Wheeler—Thiele analysis of simultaneous sucrose and ethyl acetate hydrolysis at 70°C [508],...

The location of a metal sulfide deposit in a catalyst pellet is dependent on the relative rates of reaction and diffusion. The theory describing diffusion and reaction in catalysts was first developed by Thiele (1939) and extended by many others, including Wheeler (1955), Weisz (1962) and Satterfield (1970), and has been discussed in Section IV. Sato et al. (1971) and Tamm et al. (1981) have discussed metal deposit profiles in the context of the Thiele analysis. 

Figure 31. McCabe-Thiele analysis of equilibrium stages for the ethanol-water system.

Like distillation, the McCabe-Thiele analysis is strictly valid only for a binary system. However, only two components are usually present at significant concentrations within each individual section of the coliunn (and, besides, in practice, the SMB process is essentially used to separate binary mixtrues). A preliminary analysis in which each section is considered as a pseudo binary McCabe-Thiele system can therefore provide useful guidance in the design of a multicomponent adsorption system. 

The equilibrium relationship is given. The slope of the operating line is also given. To use the McCabe-Thiele analysis, one point on the operating line is needed. The exit gas composition is 1% of H2S (y = 0.01) and the entering water does not contain any H2S (x = 0). Since the points represent passing streams on one end of the cascade, they represent one point on the operating line. 

Total reflux is similar to minimum reflux in that it is not usually a real condition. In total reflux, all of the overhead vapor is returned to the column as reflux, and all of the liquid is returned as boilup, so that there are no distillate and bottom flows out of the column. At steady-state, this means that the feed stream flowrate is also zero. Total reflux is used in actual columns during start up and also to test their efficiency. Total reflux is useful in a McCabe-Thiele analysis in order to find the minimum number of stages required for a given separation. 

Figure 4.10 McCabe-Thiele analysis for total reflux and minimum number of plates.

The material balances give a slightly different answer than that obtained from the McCabe-Thiele analysis shown in Figure 4.15. The McCabe-Thiele analysis is only an approximate solution, and it may be that the discrepancy comes from the need for more equilibrium data points to obtain a more accurate equilibrium curve. 

Figure 4.19 McCabe-Thiele analysis for a system with a side stream.

Some extraction systems are such that the solvent and diluent phases are almost completely immiscible in each other. Hence, separation yields an extract phase essentially free of diluent and a raffinate phase that is almost pure diluent. This greatly simplifies the characterization of the system. When partial miscibility for an extraction process is very low, the system may be considered immiscible and application of McCabe-Thiele analysis is appropriate. It is important to note that McCabe-Thiele analysis for immiscible extraction applies to a countercurrent cascade. The McCabe-Thiele analysis for immiscible extraction is analogous to the analysis for absorption and stripping processes. Consider the flow scheme shown in Figure 5.23,... 

All extraction systems are partially miscible to some extent, but when partial miscibility is very low, the system may be treated as completely immiscible and McCabe-Thiele analysis is appropriate. 

The McCabe-Thiele analysis can be used to model physical absorption and stripping processes that use equilibrium stages. 

Tphe most effective way to utilize a given quantity of catalytic material - is to deposit it on a layer of porous support. The classical Thiele analysis demonstrated that, for a first order reaction, it is preferable to concentrate the active ingredients in a thin layer to minimize diffusion effects this conclusion remains valid for any positive order kinetics. This diffusion effect causes a decline in reactant concentration toward the interior of a porous catalytic layer, leading to a decline in reaction rate in the interior. When the Thiele modulus is sufficiently large, such as when the reaction rate is fast and when diffusion through a porous layer is slow, only a very thin layer on the exterior is contributing to the reaction rate. 

Fig. 11 Experimental verification of Thiele analysis as applied to intracrystalline diffusion control of catalytic reaction of 2,2-dimethylbutane in H-ZSM-5 catalysts. Open symbols are from Post et al. [68], filled symbols are from Haag et al. [67], duly corrected to adsorbed phase basis. From Post et al. [68]...

This linear relationship between the total pressure, P, and the mole fraction, x, of the most volatile species is a characteristic of Raoult s law, as shown in Figure 7.18a for the benzene-toluene mixture at 90°C. Note that the bubble-point curve (P-x) is linear between the vapor pressures of the pure species (at x, = 0, 1), and the dew-point curve (P-yJ lies below it. When the (x, yi) points are graphed at different pressures, the familiar vapor-liquid equilibrium curve is obtained, as shown in Figure 7.18b. Using McCabe-Thiele analysis, it is shown readily that for any feed composition, there are no limitations to the values of the mole fractions of the distillate and bottoms products from a distillation tower. 

For the carbon molecular sieving catalysts, thoe is clear evidence that the global rate is intonally transport limited. Consistent with this, a reduction of particle size of the Fe/SiOi CMS ca yst increased the global reaction rale by decreasing the diffusion length to the active metal sites. Using first-wder kinetics in the Thiele analysis, to consider the conversion ratios of the intemal-transport limited CMS catalyst particles at modest convositxis, leads to the result ... 

Example 4-4. McCabe-Thiele analysis of open steam heatii ... 

Second, we would like to assume CMO so that we can use the McCabe-Thiele analysis procedure. An easy way to check this assunption is to conpare the latent heats of vaporization per mole rHimmelblau. 1974k... 

---