Mass transfer resistance, absence

Eor a linear system f (c) = if, so the wave velocity becomes independent of concentration and, in the absence of dispersive effects such as mass transfer resistance or axial mixing, a concentration perturbation propagates without changing its shape. The propagation velocity is inversely dependent on the adsorption equiUbrium constant. 

The ratio of the overall rate of reaction to that which would be achieved in the absence of a mass transfer resistance is referred to as the effectiveness factor rj. SCOTT and Dullion(29) describe an apparatus incorporating a diffusion cell in which the effective diffusivity De of a gas in a porous medium may be measured. This approach allows for the combined effects of molecular and Knudsen diffusion, and takes into account the effect of the complex structure of the porous solid, and the influence of tortuosity which affects the path length to be traversed by the molecules. 

Another enzyme that was studied extensively in microreactors to determine kinetic parameters is the model enzyme alkaline phosphatase. Many reports have appeared that differ mainly on the types of enzyme immobilization, such as on glass [413], PDMS [393], beads [414] and in hydrogels [415]. Kerby et al. [414], for example, evaluated the difference between mass-transfer effects and reduced effidendes of the immobilized enzyme in a packed bead glass microreactor. In the absence of mass-transfer resistance, the Michaelis-Menten kinetic parameters were shown to be flow-independent and could be appropriately predicted using low substrate conversion data. 

For a zero-order process, the effectiveness factor (defined as the ratio of the actual consumption of reactant to that which would occur in the absence of mass transfer resistance) is equal to unity whenever the following inequality holds ... 

In the first set of runs In Table I, the H2/CO feed ratio exceeds the consumption ratio, 7/12 m 0.58 In the second It Is less than the consumption ratio. In each case, the H2 partial pressure In the reactor Increased with decreased agitation, as conversion dropped. In the absence of mass transfer resistance this would be expected to Increase the P/0 ratio. The fact that the P/0 ratio In both cases Instead decreased is consistent with the postulate that the H- concentration In the liquid has decreased. The corresponding mass transfer resistance K, back-calculated from equation (8), is given at each stirring speed together with the hydrogen and carbon monoxide liquid-phase concentrations that are estimated by equations (6) and (7). 

Internal and external mass transfer resistances are important factors affecting the catalyst performance. These are determined mainly by the properties of the fluids in the reaction system, the gas-liquid contact area, which is very high for monolith reactors, and the diffusion lengths, which are short in monoliths. The monolith reactor is expected to provide apparent reaction rates near those of intrinsic kinetics due to its simplicity and the absence of diffusional limitations. The high mass transfer rates obtained in the monolith reactors result in higher catalyst utilization and possibly improved selectivity. 

FIG. 7-13 Concentration profiles with reaction control ( = 1, in absence of gas particle mass-transfer resistance. [From Wen, oncat-alytic Heterogeneous Solid-Fluid Reaction Models, Ind. Eng. Chem. 60(9) 34-54 (1968), Fig. 11.]... 

The overall effectiveness factor of a catalyst pellet can be characterized by the ratio of the observed reaction rate to the rate in the absence of poisoning or external mass transfer resistance. It is expressed in the form of a power-law kinetic model for benzene hydrogenation as... 

For the n-butane-5A system both sorption and ZLC results are in substantial agreement with NMR PFG self diffusivity data. However, for all NaX systems studied the NMR self diffusivities are approximately two orders of magnitude larger than the ZLC values. This discrepancy is difficult to understand. Most of the more obvious explanations can be ruled out on the basis of the experimental evidence. For example, the possible intrusion of extraneous heat and/or mass transfer resistances is excluded by the agreement between the sorption, exchange and ZLC results. For NaX crystals both NMR and ZLC results show that differences in the origin of the sample and the initial dehydration procedure have only a relatively small effect on the diffusivity. (27) The absence of significant surface barriers (for aromatics-NaX) is... 

Effect of Agitation Speed A few experiments were carried out at 333 K at various agitation speeds and the results are shown in Figure 3. For agitation speeds > 700 rpm, the initial rates were found to be unaffected by agitation indicating the absence of external mass transfer resistance at 333 K. 

Prior to the systematic kinetic e q)eriments a screening of the mass transfer effect was carried out. A conparison of erqjeriments performed widi a catalyst particle mean diameter of 760-960 pm and of 250-500 pm showed quite similar results which indicate the absence of internal mass transfer resistances. Moreover, ejq)eriments performed with different agitation velocities (800 and 200 rpm) gave similar results, suggesting the absence of macro-mixing effects and external mass transfer resistances around the catalyst particles. 

Reactors.- Stirred-type reactors are not common in experiments correlating selectivity to deactivation high flow rates are used to ensure the absence of external mass transfer resistance. Of the bed-type reactors, a number of flow patterns are used. 

For the separation of a binary mixture of species A and B, in the absence of external film mass-transfer resistances, the transport fluxes are given by equation (9-9) as... 

Figure 3 shows that beyond 750 rev/min for the hydrolysis (curve A) and beyond S(X)rev/min for oxidation the speed (curve B) had no effect on conversion and hence on the rates of reaction, thereby indicating absence of liquid-to-membrane surface mass transfer resistance both inside and outside the capsules. The reaction could be taken as kinetically controlled and governed by eq.(5) beyond the said speeds in each case. This was further confirmed by studying the effect of temperature and the values of activation energies, which will be discussed later. Since the capsules were well dispersed in the agitated outer phase the bulk concentration of benzyl chloride within a capsule would be uniform. Further experiments were conducted beyond these speeds which were safe to maintain the fidelity of the capsules. 

Equation 21.25 is an important general equation for current density that accounts for both mass and charge transfer resistances. In the absence of mass transfer resistance, it reduces to the Tafel equation (Equation 21.15a). 

This strong influence of the IL layer on selectivity cannot be explained by the influence of the IL on the effective concentrations of COD and COE compared to the uncoated catalyst For two first-order reactions occurring in series in a porous catalyst (here hydrogenation of COD to COE and to COA), the maximum yield of the intermediate COE in the absence of any mass transfer resistances (//po e = V... 

In general, the influence of external mass transfer leads to a lower yield and selectivity of the intermediate for a series reaction. This is shown in Figure 4.5.29 by comparison of the yield and the integral selectivity of the intermediate for the absence of an external mass transfer resistance (case 1) with the case of a strong influence of mass transfer (case 2). 

Figure 4.5.32 shows that with increasing influence of pore diffusion (increasing 4>i), selectivity to the intermediate decreases to a minimum value for a strong influence of pore diffusion. For example, for km,2/km,i = 0-1 nd 1, YB.max is 45% and 18%, respectively. The corresponding values in the absence of a mass transfer resistance are 77% and 37%. 

At a sufficiently high temperature, the evaporation rate from a wetted surface into its pure superheated vapor is higher than into perfectly dry air. The temperature at which this transition rate occurs is called the inversion value. Experimental values for this temperature range between 160 [103] and 230°C [104] in comparing steam with air. The inversion occurs because of the difference in properties between steam and air (which have different temperature coefficients) and the absence of a gas side mass transfer resistance when... 

In the absence of mass transfer resistances, the mass balance of A is written as... 

A good experimental approach to check the presence/absence of internal mass transfer resistance is to carry out experiments with various particle sizes. By gradually minimizing the particle size, the conversions, yields, and selectivities should approach a limiting value corresponding to the intrinsic kinetics. Sometimes this approach can, however, lead to a cul-de-saq the pressure drop increases, as the particle size is diminished and the kinetic conditions are not attained. Another type of test reactor should then be considered, for instance, a fluidized bed (for gas-phase reactions) or a slurry reactor (for liquid-phase reactions). 

---