Reaction rate mass transport effect

The result is shown in Figure 10, which is a plot of the dimensionless effectiveness factor as a function of the dimensionless Thiele modulus ( ), which is R.(k/Dwhere R is the radius of the catalyst particle and k is the reaction rate constant. The effectiveness factor is defined as the ratio of the rate of the reaction divided by the rate that would be observed in the absence of a mass transport influence. The effectiveness factor would be unity if the catalyst were nonporous. Therefore, the reaction rate is... 

For a triphasic reaction to work, reactants from a solid phase and two immiscible liquid phases must come together. The rates of reactions conducted under triphasic conditions are therefore very sensitive to mass transport effects. Fast mixing reduces the thickness of the thin, slow moving liquid layer at the surface of the solid (known as the quiet film or Nemst layer), so there is little difference in the concentration between the bulk liquid and the catalyst surface. When the intrinsic reaction rate is so high (or diffusion so slow) that the reaction is mass transport limited, the reaction will occur only at the catalyst surface, and the rate of diffusion into the polymeric matrix becomes irrelevant. Figure 5.17 shows schematic representations of the effect of mixing on the substrate concentration. 

Because rates of reduction by Fe° vary considerably over the range of treatable contaminants, it is possible that there is a continuum of kinetic regimes from purely reaction controlled, to intermediate, to purely mass transport controlled. Fig. 9 illustrates the overlap of estimated mass transport coefficients (kmt) and measured rate coefficients (kSA). The values of kSA are, in most cases, similar to or slower than the kmi values estimated for batch and column reactors. The slower kSA values suggest that krxu < kml, and therefore removal of most contaminants by Fe° should be reaction limited or only slightly influenced by mass transport effects (i.e., an intermediate kinetic regime). 

The second necessary condition is isothermal operation. This is apparent from the results of Sections 6.2.3.3 and 6.2.3.4 where it has been shown that heat and mass transport may drive the effective reaction rate in opposite directions. Normally, mass transfer control of a reaction means a drop of the effective reaction rate (for positive reaction order), whereas a limited heat transfer in the case of an exothermal reaction will cause the temperature inside the catalyst pellet to rise, and will thus increase the effective reaction rate. When both effects occur simultaneously, an increase as well as a decrease of the effective rate may be observed, indicating either a lower or a higher apparent activation... 

The mass transfer effects cause, in general, a decrease of the measured reaction rate. The heat transfer effects may lead in the case of endothermic reactions also to a decrease of the equilibrium value and the resulting negative effect may be more pronounced. With exothermic reactions, an insufficient heat removal causes an increase of the reaction rate. In such a case, if both the heat and mass transfer effects are operating, they can either compensate each other or one of them prevails. In the case of internal transfer, mass transport effects are usually more important than heat transport, but in the case of external transfer the opposite prevails. Heat transport effects frequently play a more important role, especially in catalytic reactions of gases. The influence of heat and mass transfer effects should be evaluated before the determination of kinetics. These effects should preferably be completely eliminated. 

The effect of altering the rate of mass transport to the electrode surface was also studied (see Fig. 2.20). At low rotation rates, the reaction is mass transport-controlled but as the rotation speed is increased, the current tends to a rotation speed-independent value indicating that the current becomes limited by some other process. 

A detailed examination of the mass transport effects of the HMRDE has been made. At low rotation speeds and for small amplitude modulations (as defined in Section 10.3.6.2) the response of the current is found to agree exactly with that predicted by the steady-state Levich theory (equations (10.15)-(10.17)) [27, 36, 37]. Theoretical and experimental application of the HMRDE, under these conditions, to cases where the electrode reaction rate constant was comparable to the mass-transfer coefficient has also been made [36]. At higher rotation speeds and/or larger amplitude modulations, the observed current response deviated from the expected Levich behaviour. 

As described in Section 4.1.1.2, in most catalytic reactions, the reactant molecules diffuse through a boundary layer and through the pores to the active center, react, and diffuse back. If the velocity of any of these two diffusion processes is smaller than the conversion of the reactants at the active center, the overall reaction rate for the whole process is limited by the mass transport and not by the chemical reaction. If the reaction is influenced by mass transport effects, a comparison of the catalytic activity of different catalysts is impossible ... 

When <5A is large, L>cat - PAcA/dA and the reaction is predominantly diffusion-controlled while, at small values of SA, i cal -> kcA and the catalytic rate is controlled by the surface reaction. Thus sufficiently rapid stirring can often purge the system of mass transport effects and permit the kinetics at the surface to be studied. The situation has been graphically illustrated in Fig. 4. 

The evaluation of catalyst effectiveness requires a knowledge of the intrinsic chemical reaction rates at various reaction conditions and compositions. These data have to be used for catalyst improvement and for the design and operation of many reactors. The determination of the real reaction rates presents many problems because of the speed, complexity and high exo- or endothermicity of the reactions involved. The measured conversion rate may not represent the true reaction kinetics due to interface and intraparticle heat and mass transfer resistances and nonuniformities in the temperature and concentration profiles in the fluid and catalyst phases in the experimental reactor. Therefore, for the interpretation of experimental data the experiments should preferably be done under reaction conditions, where transport effects can be either eliminated or easily taken into account. In particular, the concentration and temperature distributions in the experimental reactor should preferably be described by plug flow or ideal mixing models. 

There is a variety of fundamental physical and chemical principles lhat can control the deposition rate and quality of a film resulting from a CVD process. We briefly introduce them here, but refer the reader to Chapter 2 and other books on CVD for more detailed discussions. The basic processes underlying CVD can be subdivided into mass transport effects and chemical effects, each of which can occur in both the gas and solid phases. Chemical effects can be further subdivided into thermodynamic effects and kinetic effects. In some cases, a particular effect can be separated out as rate limiting, and a CVD process can be said to be mass-transport controlled or surface-kinetics controlled. In reality, transport and chemical reactions are closely coupled, with their relative importance varying with the details of the operating conditions. 

Fig. 5.6 shows a plot of Eqn 5.5 which represents a reaction run with varying quantities of catalyst at a fixed pressure, temperature and agitation rate. When mass transport is an insignificant factor in the reaction, km approaches zero and the rate, r, equals kfX, which is the asymptote of the curve at low catalyst quantities. With larger amounts of catalyst, the curve approaches the second asymptote, r = km, for a reaction controlled by mass transport effects. There is... 

To illustrate the combined effects of chemical reaction and mass transport, a simple lake model treated as a continuous stirred tank reactor (CSTR) will now he examined. The inflow and outflow rates are constant and equal to one another ... 

The catalytic behavior of enzymes in immobilized form may dramatically differ from that of soluble homogeneous enzymes. In particular, mass transport effects (the transport of a substrate to the catalyst and diffusion of reaction products away from the catalyst matrix) may result in the reduction of the overall activity. Mass transport effects are usually divided into two categories - external and internal. External effects stem from the fact that substrates must be transported from the bulk solution to the surface of an immobilized enzyme. Internal diffusional limitations occur when a substrate penetrates inside the immobilized enzyme particle, such as porous carriers, polymeric microspheres, membranes, etc. The classical treatment of mass transfer in heterogeneous catalysis has been successfully applied to immobilized enzymes I27l There are several simple experimental criteria or tests that allow one to determine whether a reaction is limited by external diffusion. For example, if a reaction is completely limited by external diffusion, the rate of the process should not depend on pH or enzyme concentration. At the same time the rate of reaction will depend on the stirring in the batch reactor or on the flow rate of a substrate in the column reactor. 

For small Damkohler numbers (Da <3C 1) the mass transport is much faster than the surface reaction itself and therefore the mass transport effect may be ignored. On the other hand, if the Damkohler munber is high (Da 1) the sensorgram profile is completely controlled by the diffusion mass transfer and is it not possible to determine rate constants of the surface reaction. 

The reactants for aqueous-phase atmospheric reactions are transferred to the interior of cloud droplets from the gas phase by a series of mass transport processes. We would like to compare the rates of mass transport in the gas phase, at the gas-water interface, and in the aqueous phase in an effort to quantify the mass transport effects on the rates of aqueous-phase reactions. If there are no mass transport limitations, the gas and aqueous phases will remain at Henry s law equilibrium at all times. Our objective will be to identify cases where mass transport limits the aqueous-phase reaction rates and then to develop approaches to quantify these effects. 

The reactions of linear or branched alkenes containing more than four carbon atoms reveal no types of reaction not already met, but their lower volatility permits their study as liquids or in solution as well as in the vapour phase. Thus for example the relative isomerisation rate r,7r/, of liquid 1-pentene over Pd/C at 290 K was independent of the conditions of agitation, showing there were no mass-transport effects attributable to the hydrocarbons. The presence of solvents was also without effect. ... 

We mentioned that MTBE synthesis has a special kinetic behavior. Depending on the concentration of methanol in the feed, the reaction rate can be very fast at low methanol concentrations or rather fast at high methanol concentrations (a range from about 2 to 160 mol/m s is covered). The reasons for this are mass-transport effects in the pores of the catalyst. To avoid this, the pores in the new catalyst should be large larger than in commercial macroporous resins. 

The analogy in the mass transport effects in electrode reaction and homogeneous second-order fast reactions in solution becomes clear. In electrode kinetics, however, the charge-transfer rate coefficient can be externally varied over many orders of magnitude through the electrode potential and kd can be controlled by means of hydrodynamic electrodes. For instance the mass transport rate coefficient, kd, for a rotating disc electrode at the maximum practical rotation speed of 10 000 per min is approximately 2 x 10... 

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