Mass-Transfer Limitations

Reaction rates typically are strongly affected by temperature (76,77), usually according to the Arrhenius exponential relationship. However, side reactions, catalytic or equiHbrium effects, mass-transfer limitations in heterogeneous (multiphase) reactions, and formation of intermediates may produce unusual behavior (76,77). Proposed or existing reactions should be examined carefully for possible intermediate or side reactions, and the kinetics of these side reactions also should be observed and understood. 

In principle, the catalytic converter is a fixed-bed reactor operating at 500—620°C to which is fed 200—3500 Hters per minute of auto engine exhaust containing relatively low concentrations of hydrocarbons, carbon monoxide, and nitrogen oxides that must be reduced significantly. Because the auto emission catalyst must operate in an environment with profound diffusion or mass-transfer limitations (51), it is apparent that only a small fraction of the catalyst s surface area can be used and that a system with the highest possible surface area is required. 

M. Luoma, P. Lappi, and R. Lylykangas, Evaluation of High Cell Density E-Flow Catalyst, SAE 930940, Society of Automotive Engineers, Warrendale, Pa., 1993. Good reference for mass-transfer limited model reactions. 

In the mass-transfer limited region, conversion is most commonly increased by using more catalyst volume or by increasing cell density, which increases the catalytic wall area per volume of catalyst. When the temperature reaches a point where thermal oxidation begins to play a role, catalyst deactivation may become a concern. 

It should be noted that the highest possible absorption rates will occur under conditions in which the hquid-phase resistance is negligible and the equilibrium back pressure of the gas over the solvent is zero. Such situations would exist, for instance, for NH3 absorption into an acid solution, for SO9 absorption into an alkali solution, for vaporization of water into air, and for H9S absorption from a dilute-gas stream into a strong alkali solution, provided there is a large excess of reagent in solution to consume all the dissolved gas. This is known as the gas-phase mass-transfer limited condition, wrien both the hquid-phase resistance and the back pressure of the gas equal zero. Even when the reaction is sufficiently reversible to allow a small back pres-... 

If the liqmd-phase reaction is extremely fast and irreversible, the rate of absorption may in some cases be completely governed by the gas-phase resistance. For practical design purposes one may assume (for example) that this gas-phase mass-transfer limited condition will exist when the ratio yj/y is less than 0.05 everywhere in the apparatus. 

Figure 14-10 illustrates the gas-film and liquid-film concentration profiles one might find in an extremely fast (gas-phase mass-transfer limited) second-order irreversible reaction system. The solid curve for reagent B represents the case in which there is a large excess of bulk-liquid reagent B. The dashed curve in Fig. 14-10 represents the case in which the bulk concentration B is not sufficiently large to prevent the depletion of B near the liquid interface and for which the equation ( ) = I -t- B /vCj is applicable. 

Table 14-3 presents a typical range of values for chemically reacting systems. The first two entries in the table represent systems that can be designed by the use of purely physical design methods, for they are completely gas-phase mass-transfer limited. To ensure a negligible liquid-phase resistance in these two tests, the HCl was absorbed into a solution maintained at less than 8 percent weight HCl and the NH3 was absorbed into a water solution maintained below pH 7 by the addition of acid. The last two entries in Table 14-3 represent liquid-phase mass-transfer hmited systems. 

This is the gas-phase mass-transfer limited condition, which can be substituted into Eq. (14-71) to obtain the following equation for calculating the height of packing for a dilute system ... 

This is known as the liquid-phase mass-transfer limited condition, as illustrated in Fig. 14-13. 

Inspection of Eqs. (14-71) and (14-78) reveals that for fast chemical reactions which are liquid-phase mass-transfer limited the only unknown quantity is the mass-transfer coefficient /cl. The problem of rigorous absorber design therefore is reduced to one of defining the influence of chemical reactions upon k. Since the physical mass-transfer coefficient /c is already known for many tower packings, it... 

FIG. 14-13 Gas-phase and liquid-phase solute-concentration profiles for a liquid-phase mass-transfer limited reaction system in which is larger than 3. 

For an isothermal absorber involving a dilute system in which a liquid-phase mass-transfer limited first-order irreversible chemic reaction is occurring, the packed-tower design equation is derived as... 

For a dilute system in which the liquid-phase mass-transfer limited condition is valid, in which a veiy fast second-order reaction is involved, and for which Nna E veiy large, the equation... 

Carbon dioxide gas diluted with nitrogen is passed continuously across the surface of an agitated aqueous lime solution. Clouds of crystals first appear just beneath the gas-liquid interface, although soon disperse into the bulk liquid phase. This indicates that crystallization occurs predominantly at the gas-liquid interface due to the localized high supersaturation produced by the mass transfer limited chemical reaction. The transient mean size of crystals obtained as a function of agitation rate is shown in Figure 8.16. 

Possible applications of MIP membranes are in the field of sensor systems and separation technology. With respect to MIP membrane-based sensors, selective ligand binding to the membrane or selective permeation through the membrane can be used for the generation of a specific signal. Practical chiral separation by MIP membranes still faces reproducibility problems in the preparation methods, as well as mass transfer limitations inside the membrane. To overcome mass transfer limitations, MIP nanoparticles embedded in liquid membranes could be an alternative approach to develop chiral membrane separation by molecular imprinting [44]. 

In the elucidation of retention mechanisms, an advantage of using enantiomers as templates is that nonspecific binding, which affects both enantiomers equally, cancels out. Therefore the separation factor (a) uniquely reflects the contribution to binding from the enantioselectively imprinted sites. As an additional comparison the retention on the imprinted phase is compared with the retention on a nonimprinted reference phase. The efficiency of the separations is routinely characterized by estimating a number of theoretical plates (N), a resolution factor (R ) and a peak asymmetry factor (A ) [19]. These quantities are affected by the quality of the packing and mass transfer limitations, as well as of the amount and distribution of the binding sites. 

Mass transfer limits rate of reaction Treatment of spent water... 

A rapidly decreasing efficiency with a relatively slight increase in gas rate (mass-transfer limitation) develops. 

The minimum oxygen utihsation rate is xjjbnvJY0l. If the system is mass-transfer limited, C, approaches zero. Then the amount of oxygen absorbed is exactly equal to the amount of oxygen consumed. Equation (3.11.8) leads to the following ... 

The following equation has been derived for testing mass transfer limitation to the gross catalyst particle (19). 

Provided that the catalyst is active enough, there will be sufficient conversion of the pollutant gases through the pellet bed and the screen bed. The Sherwood number of CO is almost equal to the Nusselt number, and 2.6% of the inlet CO will not be converted in the monolith. The diffusion coefficient of benzene is somewhat smaller, and 10% of the inlet benzene is not converted in the monolith, no matter how active is the catalyst. This mass transfer limitation can be easily avoided by forcing the streams to change flow direction at the cost of some increased pressure drop. These calculations are comparable with the data in Fig. 22, taken from Carlson 112). 

This objection is supported by recent results of Moffat ef al. (109, 110), who observed severe interphase mass transfer limitations for the same system, in spite of calculations which predicted the mass transfer rate to be several orders of magnitude greater than the observed rate. As... 

Pathway temperatures must be strictly controlled (especially in single-phase systems) to create a balance between low-temperature oxide dissolution and high-temperature mass transfer limitations. 

A final, obvious but important, caution about catalyst film preparation Its thickness and surface area Ac must be low enough, so that the catalytic reaction under study is not subject to external or internal mass transfer limitations within the desired operating temperature range. Direct impingement of the reactant stream on the catalyst surface1,19 is advisable in order to diminish the external mass transfer resistance. 

A lot of work is currently carried out to extend this idea to fully dispersed two-dimensional (on a YSZ surface) or three-dimensional (in a porous YSZ structure) metal catalysts. The main problems to be overcome is current bypass and internal mass transfer limitations due to the high catalytic activity of such fully dispersed Pt/YSZ catalyst systems. 

IV. External mass transfer limitations. Symptoms Rate insensitivity to temperature, rate variation with flowrate. Remedy Decrease operating temperature, force reactants to directly impinge on the catalyst surface. 

Checking the absence of external mass transfer limitations is a rather easy procedure. One has simply to vary the total volumetric flowrate while keeping constant the partial pressures of the reactants. In the absence of external mass transfer limitations the rate of consumption of reactants does not change with varying flowrate. As kinetic rate constants increase exponentially with increasing temperature while the dependence of mass transfer coefficient on temperature is weak ( T in the worst case), absence... 

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