Mass transfer interparticle

EFFECT OF INTERPARTICLE MASS TRANSFER ON CATALYTIC SELECTIVITY... 

In contrast to chemical and petrochemical reactors, biochemical reactors invariably contain aqueous phase at low pressures. This aqueous phase generally controls the overall interparticle mass-transfer rate and provides four different types of resistances to the overall mass-transfer rate (Moo-Young, 1986) ... 

In fluid-solid systems the interparticle gradients - between the external surface of the particle and the adjacent bulk fluid phase - may be more serious, because the effective thermal conductivity of the fluid may be much lower than that of the particle. For the interparticle situation the heat transfer resistances, in general, are more serious than the interparticle mass transfer effects they may become important if reaction rates and reaction heats are high and flow rates are low. Hie usual experimental test for interparticle effects is to check the influence of the flow rate on the conversion while maintaining constant the space velocity or residence time in the reactor. This should be done over a wide range of flow rates and the conversion should be measured very accurately. 

An alternative strategy for fast liquid chromatography uses short columns packed with small particles operated at high flow rates and often elevated temperatures to separate simple mixtures under conditions were resolution is compromised but still adequate for identification purposes [252-258]. Small diameter particles provide larger plate numbers by virtue of their relatively small interparticle mass transfer resistance combined with a shallow increase in the reduced plate height as the reduced mobile... 

Packed bed reactor The use of immobilized enzymes in packed bed reactors, by virtue of their similarity to chromatographic systems, has been particularly widely accepted. The size of the reactor can be determined by the volume of support necessary for complete conversion of substrate to product. The kinetic situation in a packed reactor with immobilized enzyme(s) is, however, rather more complex. For a low enzyme activity per unit mass of carrier, the interparticle mass transfer is unimportant. When higher carrier specific activities are prepared on... 

Figure 5. Influence of various parameters on the region of parametric sensitivity reaction order n (A), heat transfer (B), activation energy y (C), inlet temperature 6 (E), Lewis number Le (E), interparticle mass transfer resistance Ag, [from Morbidelli and Varma (1987)].

Yadav and Kulkami (2000) have studied the esterification of lactic acid with isopropanol in presence of various ion exchange resin catalysts (Indion-130, Amberlyst-36, Amberlyst-15, Amberlite-120, Dowex 50W, Filtrol-44, 20% DTPA/K-10 and 20% DTPA/Filtrol-44) A theoretical kinetic model was developed for evaluation of this slurry reaction. The effects of various parameters on the rate of reaction were evaluated. The reaction was found to be kinetically controlled and there were no intraparticle as well as interparticle mass transfer limitations on the rate of reactions. 

The concentration profile outside the catalyst particle is controlled by the principles of convective mass transfer (or in a packed bed, interparticle mass transfer). Although the details of convective transport are beyond the scope of this course, it is... 

The performance of adsorption processes results in general from the combined effects of thermodynamic and rate factors. It is convenient to consider first thermodynamic factors. These determine the process performance in a limit where the system behaves ideally i.e. without mass transfer and kinetic limitations and with the fluid phase in perfect piston flow. Rate factors determine the efficiency of the real process in relation to the ideal process performance. Rate factors include heat-and mass-transfer limitations, reaction kinetic limitations, and hydro-dynamic dispersion resulting from the velocity distribution across the bed and from mixing and diffusion in the interparticle void space. 

In practice, of course, it is rare that the catalytic reactor employed for a particular process operates isothermally. More often than not, heat is generated by exothermic reactions (or absorbed by endothermic reactions) within the reactor. Consequently, it is necessary to consider what effect non-isothermal conditions have on catalytic selectivity. The influence which the simultaneous transfer of heat and mass has on the selectivity of catalytic reactions can be assessed from a mathematical model in which diffusion and chemical reactions of each component within the porous catalyst are represented by differential equations and in which heat released or absorbed by reaction is described by a heat balance equation. The boundary conditions ascribed to the problem depend on whether interparticle heat and mass transfer are considered important. To illustrate how the model is constructed, the case of two concurrent first-order reactions is considered. As pointed out in the last section, if conditions were isothermal, selectivity would not be affected by any change in diffusivity within the catalyst pellet. However, non-isothermal conditions do affect selectivity even when both competing reactions are of the same kinetic order. The conservation equations for each component are described by... 

Some additional complexity arises from the possibility of different adsorption sites and the presence of pores, which reflect in nonideal adsorption isotherms and mass-transfer problems. The mass transport can be relatively slow in pores and interparticle spaces [13], as it is the case of P25, for which, in suspension, there are particles ranging from 0.2 to 2 p,m, formed by 30-nrn-sizcd primary particles. In such spaces, the diffusion coefficient is comparable to liquid diffusion in zeolites. 

While the multiple steady-state phenomena may be, at least qualitatively, explained in terms of a simple one-step kinetic mechanism and interactions of the intraphase and interparticle heat and mass transfer (thermokinetic model), there is no acceptable explanation for the periodic activity (12). Since the values of the Lewis number are at least by a factor of 10 lower than those necessary to produce undamped oscillations, there is no doubt that the instability cannot be viewed in terms of mutual... 

The importance of adsorbent non-isothermality during the measurement of sorption kinetics has been recognized in recent years. Several mathematical models to describe the non-isothermal sorption kinetics have been formulated [1-9]. Of particular interest are the models describing the uptake during a differential sorption test because they provide relatively simple analytical solutions for data analysis [6-9]. These models assume that mass transfer can be described by the Fickian diffusion model and heat transfer from the solid is controlled by a film resistance outside the adsorbent particle. Diffusion of adsorbed molecules inside the adsorbent and gas diffusion in the interparticle voids have been considered as the controlling mechanism for mass transfer. 

The role of the pressure gradient may be shown in the momentum equation of a gas-solid mixture. Consider a steady pipe flow without mass transfer and with negligible interparticle collisions. From Eq. (5.170), the momentum equations for the gas and particle phases can be given by... 

If the plug flow assumption holds and the reactor truly behaves in a differential manner, a plot of Xgg Vs. W/Fgg should be linear with the slope equal to the reaction rate. However, as is evident from Figure 1, slight curvature persists in each plot. Typical calculations revealed that intra and interparticle heat and mass transfer problems should not exist at the operating conditions. The reaction rates, therefore, were obtained by evaluating the slope of each curve at the origin and as such can be called initial rates of reaction, Rq. 

The assumptions made in the model of random fluxes are valid for homogeneous high-dispersed systems. Inside large particles, directions of fluxes of heat and mass transfer cannot change randomly. However, in the case of systems with large particles the model of system with random fluxes is applicable to the interparticle zones and the particle s surface, whereas fluxes inside the particles should be described as regular. 

Since electroosmotic flow can exist in both the interparticle and intraparticle spaces, numerous studies have focused on the existence of intraparticle flow in CEC. Several groups have investigated the existence of electroosmotic flow in wide-pore materials [41-44], A model was developed to estimate the extent of perfusive flow in CEC packed with macroporous particles [41] by employing the Rice and Whitehead relationship. Results showed the presence of intraparticle EOF in large-pore packings (> 1000 A) at buffer concentrations as low as 1.0 mM. Additional parameters had been investigated [43,44] to control intraparticle flow by the application of pressure to electro-driven flow. Enhancement in mass transfer processes was obtained at low pore flow velocities under the application of pressure. The authors pointed out that macroporous particles could be used as an alternative to very small particles, as smaller particles were difficult to pack uniformly into capillary columns. 

From the above it follows that in most practical situations a model, that takes into account only an intraparticle mass and an interparticle heat transfer resistance will give good results. However, in experimental laboratory reactors, which usually operate at low gas flow rates, this may not be true. In the above criteria the heat and mass transfer coefficients for interparticle transport also have to be known. These were amply discussed in Section 4.2. 

Excellent interparticle and interphase heat and mass transfer... 

TTIf the annular baskets are used, the interparticle heat- and mass-transfer resistances, as well as the imraparlide heat- and mass-lransfer effects, may be large unless the reactor is highly agitated. 

Comparison of the porous structure of different columns was discussed in Section 3.2 here we emphasize that with a packed column the ratio of particle size to the average interparticle pores (space) is on the level of 3-3.5 while with monolithic columns trough-pores are on the level of 6000 A and silica material is only about 1 u thick, which makes this ratio 0.5-0.2 or about 10 times smaller, thus significantly decreasing the time needed for analyte molecules to diffuse into the mesoporous space for the interaction with main surface. This allows for much faster flow rates without the loss of the dynamic equilibrium conditions (otherwise known as the slow mass transfer term (C) in the Van Deemter equation). 

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