Desorption with mass transfer resistance

Earlier studies of intracrystalline diffusion in zeolites were carried out almost exclusively by direct measurement of sorption rates but the limitations imposed by the intrusion of heat transfer and extra-crystalline mass transfer resistances were not always fully recognized. As a result the reported diffu-sivities showed many obvious inconsistencies such as differences in diffusivity between adsorption and desorption measurements(l-3), diffusivities which vary with fractional uptake (4) and large discrepancies between the values measured in different laboratories for apparently similar systems. More recently other experimental techniques have been applied, including chromatography and NMR methods. The latter have proved especially useful and have allowed the microdynamic behaviour of a number of important systems to be elucidated in considerable detail. In this paper the advantages and limitations of some of the common experimental techniques are considered and the results of studies of diffusion in A, X and Y zeolites, which have been the subject of several detailed investigations, are briefly reviewed. 

In many industrial reactions, the overall rate of reaction is limited by the rate of mass transfer of reactants and products between the bulk fluid and the catalytic surface. In the rate laws and cztalytic reaction steps (i.e., dilfusion, adsorption, surface reaction, desorption, and diffusion) presented in Chapter 10, we neglected the effects of mass transfer on the overall rate of reaction. In this chapter and the next we discuss the effects of diffusion (mass transfer) resistance on the overall reaction rate in processes that include both chemical reaction and mass transfer. The two types of diffusion resistance on which we focus attention are (1) external resistance diffusion of the reactants or products between the bulk fluid and the external smface of the catalyst, and (2) internal resistance diffusion of the reactants or products from the external pellet sm-face (pore mouth) to the interior of the pellet. In this chapter we focus on external resistance and in Chapter 12 we describe models for internal diffusional resistance with chemical reaction. After a brief presentation of the fundamentals of diffusion, including Pick s first law, we discuss representative correlations of mass transfer rates in terms of mass transfer coefficients for catalyst beds in which the external resistance is limiting. Qualitative observations will bd made about the effects of fluid flow rate, pellet size, and pressure drop on reactor performance. 

Section 6.2 shows how they are placed within the model equations. Based on the assumptions for these models it follows that all plant effects as well as axial dispersion, void fraction and mass transfer resistance are independent of the adsorption/ desorption within the column. Modeling always results in a virtual image of the real world, i.e. in reality the parameters might be influenced by adsorption, but with a reliable model this is of minor importance. 

The relatively considerable influence of the pressure on the diffusion coefficients has a major consequence when chromatography is carried out imder very high pressures, in the range of 0.5 to several kbar [24]. The mass transfer resistances are all direct functions of the diffusivity, except the adsorption/desorption kinetics (see Sections 5.2 and 5.2.7 for the case of surface diffusion). Accordingly, the efficiency of colimms packed with very fine particles dp of the order of 1 jim) decreases rapidly with increasing velocity, far more rapidly than anticipated from the small particle diameter. Since it seems highly improbable that this range of pressure will ever be used in preparative HPLC, there will be no elaboration here on the reasons for this fact. 

From the mechanism it can be seen that material is added to or depleted from the gas phase by adsorption/desorption with the exception of hydrogen which is assumed to be consumed directly from the gas phase. In formulating a theoretical model for the system it was assumed that the adsorption/desorption kinetics played an important role in the dynamics of the periodic operation and these kinetics were incorporated into the dynamic equations. Furthermore, it was assumed that there was neither bulk nor pore diffusional heat and mass transfer resistances, that the reactor was isothermal (both in the bulk gas phase and locally) and that the flow pattern in the reactor could be approximated by plug flow. Most of the above assumptions (i.e. plug flow, bulk isothermal conditions, no pore diffusion limitations) could be... 

Thus, when deahng with gas transfer in aerobic fermentors, it is important to consider only the resistance at the gas-liquid interface, usually at the surface of gas bubbles. As the solubihty of oxygen in water is relatively low (cf. Section 6.2 and Table 6.1), we can neglect the gas-phase resistance when dealing with oxygen absorption into the aqueous media, and consider only the liquid film mass transfer coefficient Aj and the volumetric coefficient k a, which are practically equal to and K a, respectively. Although carbon dioxide is considerably more soluble in water than oxygen, we can also consider that the liquid film resistance will control the rate of carbon dioxide desorption from the aqueous media. 

In the cases above, a two-parameter model well represents the data. A model with more parameters would be more flexible, but by using a partition constant, K, or a desorption rate constant ka and k, , for the mass-transfer coefficients, the data are well described (see Figs. 3.4-15 and 3.4-13). While K would be a value experimentally determined, kp can be estimated from eqn. (3.4-97) with the external mass-transfer coefficient, km, estimated from the correlation of Stiiber et al. [25] or from that of Tan et al. [27], and the effective diffusivity from the Wakao Smith model [36], Typical values of kp obtained by fitting the data of Tan and Liou are shown in Fig. 3.4-16. As expected, they are below the usual mass-transfer correlations, because internal resistance diminishes the global mass transfer coefficient. These data correspond to the regeneration of spent activated carbon loaded with ethyl acetate, using high-pressure carbon dioxide, published by Tan and Liou [45]. 

If the rate constants for the sorption-desorption processes are small equilibrium between phases need not be achieved instantaneously. This effect is often called resistance-to-mass transfer, and thus transport of solute from one phase to another can be assumed diffusional in nature. As the solute migrates through the column it is sorbed from the mobile phase into the stationary phase. Flow is through the void volume of the solid particles with the result that the solute molecules diffuse through the interstices to reach surface of stationary phase. Likewise, the solute has to diffuse from the interior of the stationary phase to get back into the mobile phase. 

A porous adsorbent in contact with a fluid phase offers at least two and often three distinct resistances to mass transfer external film resistance and intraparticle diffusional resistance. When the pore size distribution has a well-defined bimodal form, the latter may be divided into macropore and micropore diffusional resistances, Depending on the particular system and the conditions, any one of these resistances may be dominant, or the overall rate of mass transfer may be determined by the combined effects of more than one resistance. The magnitude of the intraparlicle diffusional resistances, or any surface resistance to mass transfer, can be conveniently determined by measuring the adsorption or desorption rate, under controlled conditions, in a batch system. 

Particle Size and Desorption Rates. Bench-scale reactor studies of the desorption of toluene from single, 2- to 6-mm porous clay partides (14) showed desorption times that increased with the square of the particle radius, suggesting that diffusion controls the rate desorption. Parallel experiments performed in a small, pilot-scale rotary kiln at 300°C showed no effect of day partide size for diameters ranging from 0.4 to 7 mm. Additional single-partide studies with temperature profiles controlled to match those in the pilot-scale kiln had desorption times that were a factor of 2—3 shorter for the range of sizes studied (15). Hence, at the conditions examined, intrapartide mass transfer controlled the rate of desorption when single particles were involved and interpartide mass transfer controlled in a bed of particles in a rotary kiln. These results apply to full-scale kilns. As particle size is increased, intraparticle resistances to heat and mass transfer eventually begin to dominate. 

The comparison between the extract mass during the extraction (10 %) and the desorption (1.25 %) shows us that other effects than solubility are more crucial in the desorption process. The butylacetate regeneration is better than xylene regeneration zeolithe is saturated by a mixture composed with butyl acetate (50 %) and xylenes isomeres (30 %), the extracts composition is butyl acetate (60-65 %) and xylenes isomers (35-40 %). The equilibrium thermodynamic and adsorption data could help us to explain these results. To increase the C02 flow rate (Figure 3) contribute to decrease the desorption time but the lowest flow rate does not permit to desorbe completely zeolithe this is suggestive of a film transfer resistance at lower flow rates. 

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