Interparticle mass transfer rates

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... 

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 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. 

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. 

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. 

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). 

Therefore, Giddings [67] has demonstrated that nonequilibrium effects resulting from the finite rate of mass transfer kinetics can be treated as a contribution to the axial dispersion, itself the result of axial molecular diffusion, the tortuosity of the packing, the anastomosis of the network of interparticle channels where the stream of mobile phase flows, and the nonhomogeneity of the coliunn packing. The axial diffusion and column tortuosity account for the B term of the classical Knox equation ... 

The rates of polymerization and particle growth, and the development of the MWD and CCD depend on the temperature and concentration of monomers and chains transfer agent inside the growing polymer particles. In order to do so, the rates of mass transfer from the continuous phase, through the boundary around the particle (interparticle) and then through the particle (intraparticle), and of heat transfer in the other direction need to be predicted simultaneously. Problems combining reaction kinetics, mass and heat transfer phenomena are classical ones in chemical engineering. 

D13. We wish to use the local equilibrium model to estimate reasonable flow rates for the separation of dextran and fructose using an SMB. The isotherms are linear and both q and c are in g L. The linear equilibrium constants are dextran, 0.23 and fructose, 0.69. The interparticle void fraction = 0.4 and the intraparticle void fraction = 0.0. The columns are 40.0 cm in diameter. We want a feed flow rate of 1.0 L/min. The feed has 50.0 of each component. The desorbent is water and the adsorbent is silica gel. The columns are each 60.0 cm long. The limped parameter mass transfer coefficients using fluid concentration differences as the driving force are 2.84 l/min for both dextran and fructose. Operation is isothermal. Use multiplier values (see notation in Figure 18-14i of M] = 0.97, M2 = 0.99, M3 = 1.01, and M4 = 1.03. Determine the flow rates of desorbent, dextran product, fructose product, and recycle rate and find the ratio D/F. 

The concept of criteria for exclusion of interparticle mass and heat transfer effects is the following. Since during a reaction non-zero gradients of concentration and/or of temperature always exist in the fixed bed reactor (albeit sometimes they are very small), a somewhat arbitrary assumption has to be made about the maximum deviation up to which the reaction can be considered not to be influenced by axial and radial mass and heat transport phenomena. The maximum deviation commonly used is 5%, for example, of the reaction rate compared to the zero-gradient rate or of the reactor length compared to the length of an ideal PFR. 

In the simplest case of a fixed bed of adsorbent particles, the following mass transport processes are considered axial dispersion in the interparticle fluid phase, fluid-to-particle mass transfer, intrapaitide diffusion, and a first-order, reversible adsorption in the interior of the particle. The last step corresponds to a linear adsorption isotherm with a finite adsorption rate. This assumption includes the case of inflnitdy fast adsorption rate. 

In 0.1 wt% slurries, the average interparticle distance is so small that the measured rate of TCE conversion is much less than the potential mass transfer limit [117]. In contrast, with the catalyst immobilized on walls of tubes of several mm diameter, mass transfer influence may exist, and has been demonstrated with data for salicylic acid conversion in a coiled tube [68,116]. A clear variation of reaction rate with flow rate exists, and an analysis [117] suggested that the data are very strongly mass transfer influenced. A similar influence of fluid flow rate on the first order rate constant has been noted in chlorophenol degradation on photocatalyst-coated glass beads [36]. 

The calculated values of temperature and ammonia concentration in the bulk gas and at the catalyst external surface are reported in Table 6.7 for the first catalyst bed of Fig. 6.2 in both axial and radial centrifugal flow. Since radial flow converters are usually filled with smaller-size catalyst particles than the catalyst considered here, from this point of view they are equivalent to axial converters, which are always filled with large-size catalysts to contain pressure drops. It also appears that the effects of mass and heat transfer at the external surface of the catalyst particle are oppositely directed so that they partly compensate for each other. We may conclude that in industrial converters their combined influence on the reaction rate is negligible compared to the inaccuracies inherent in the experimental determination of the intrinsic activity of the catalyst. In any case, interparticle phenomena can be readily incorporated as boundary conditions in the intraparticle problem ... 

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