Reaction rate apparent

Reaction and Transport Interactions. The importance of the various design and operating variables largely depends on relative rates of reaction and transport of reactants to the reaction sites. If transport rates to and from reaction sites are substantially greater than the specific reaction rate at meso-scale reactant concentrations, the overall reaction rate is uncoupled from the transport rates and increasing reactor size has no effect on the apparent reaction rate, the macro-scale reaction rate. When these rates are comparable, they are coupled, that is they affect each other. In these situations, increasing reactor size alters mass- and heat-transport rates and changes the apparent reaction rate. Conversions are underestimated in small reactors and selectivity is affected. Selectivity does not exhibit such consistent impacts and any effects of size on selectivity must be deterrnined experimentally. 

Table 5.1 presents the intrinsic kinetic parameters (Km and Vln lx) for the free lipase system and apparent kinetic parameters (K and V ) for the immobilised lipase in the EMR using fixed 2g-l 1 lipase concentration. The immobilised lipase showed higher maximum apparent reaction rate and greater enzyme-substrate (ES) affinity compared with free lipase. 

The apparent reaction rate constant for the first order reaction, k, was calculated from the conversion of CO2. Since the gas-volume reduction rate increased with k, a poor fluidization was induced by high reaction rate. We investigated the effect of the rate of the gas-volume change on the fluidization quality. The rate of the gas-volume change can be defined as rc=EA(dxA/dt), where Sa is the increase in the number of moles when the reactants completely react per the initial number of moles. This parameter is given by 7-1. When the parameter, Ea, is negative, the gas volume decreases as the reaction proceeds. 

It should be emphasized that, in all the topochemical photoreactions without exception, an apparent reaction rate at the initial stage increases with increase in the irradiation temperature, as long as the temperature is sufficiently low to maintain the molecular orientation in the crystal. 

Figure 8. Apparent reaction rate constant kapp, equation 27, in cm3/molecule s, vs.

Changes in the potentiometer reading may be assumed to be proportional to the temperature change of the reaction mixture. Determine the order of the reaction with respect to pinacolin and the apparent reaction rate constant. 

Figure 1. Apparent reaction-rate constant vs. reactor diameter and bed height. (From Frye etal., 1958.)...

The transesterification and glycolysis reactions proceed via the Aac2 mechanism described above in Section 2.1. The reactions are acid catalyzed as demonstrated by Chegolya el al. [27], who added TPA to the polycondensation of PET and observed a significant increase of the apparent reaction rate. The industrial polycondensation process is accelerated by the use of metal catalysts, with these being mainly antimony compounds. 

Calculated reaction rates can be in the spatially ID model corrected using the generalized effectiveness factor (rf) approach for non-linear rate laws. The effect of internal diffusion limitations on the apparent reaction rate Reff is then lumped into the parameter evaluated in dependence on Dc>r, 8 and Rj (cf. Aris, 1975 Froment and Bischoff, 1979, 1990 Leclerc and Schweich, 1993). 

Effects of Mass Transfer Around and within Catalyst or Enzymatic Particles on the Apparent Reaction Rates... 

For liquid-phase catalytic or enzymatic reactions, catalysts or enzymes are used as homogeneous solutes in the hquid, or as sohd particles suspended in the hquid phase. In the latter case, (i) the particles per se may be catalysts (ii) the catalysts or enzymes are uniformly distributed within inert particles or (hi) the catalysts or enzymes exist at the surface of pores, inside the particles. In such heterogeneous catalytic or enzymatic systems, a variety of factors that include the mass transfer of reactants and products, heat effects accompanying the reactions, and/or some surface phenomena, may affect the apparent reaction rates. For example, in situation (iii) above, the reactants must move to the catalytic reaction sites within catalyst particles by various mechanisms of diffusion through the pores. In general, the apparent rates of reactions with catalyst or enzymatic particles are lower than the intrinsic reaction rates this is due to the various mass transfer resistances, as is discussed below. 

The apparent reaction rate depends on the magnitude of Damkohler number (Da) as defined by Equation 7.14 - that is, the ratio of the maximum reaction rate to the maximum mass transfer rate. 

In the case where mass transfer of the reactants through the liquid film on the surface of the catalyst or enzyme particles is much slower than the reaction itself (Da 1), the apparent reaction rate becomes almost equal to the rate of mass transfer. This is analogous to the case of two electrical resistances of different magnitudes in series, where the overall resistance is almost equal to the higher resistance. In such a case, the apparent reaction rate is given by... 

The resistance to mass transfer of reactants within catalyst particles results in lower apparent reaction rates, due to a slower supply of reactants to the catalytic reaction sites. Ihe long diffusional paths inside large catalyst particles, often through tortuous pores, result in a high resistance to mass transfer of the reactants and products. The overall effects of these factors involving mass transfer and reaction rates are expressed by the so-called (internal) effectiveness factor f, which is defined by the following equation, excluding the mass transfer resistance of the liquid film on the particle surface [1, 2] ... 

Under steady state conditions the rate of reactant transfer to the outside surface of the catalyst particles should correspond to the apparent reaction rate within catalyst particles. Thus, the effectiveness factor Ef is given by the following equation ... 

In Figure 7.4 the effectiveness factor is plotted against the Thiele modulus for spherical catalyst particles. For low values of 0, Ef is almost equal to unity, with reactant transfer within the catalyst particles having little effect on the apparent reaction rate. On the other hand, Ef decreases in inverse proportion to 0 for higher values of 0, with reactant diffusion rates limiting the apparent reaction rate. Thus, decreases with increasing reaction rates and the radius of catalyst spheres, and with decreasing effective diffusion coefficients of reactants within the catalyst spheres. 

Apparent reaction rates with immobilized enzyme particles also decrease due to the mass transfer resistance of reactants (substrates). The Thiele modulus of spherical particles of radius R for the Michaelis-Menten type reactions is given as... 

Effect of surfactants on stability. Many organic reactions have been found to be accelerated or inhibited in the presence of micellar media. The apparent reaction rates are altered in micellar solutions because of the distribution of substrate between the micellar and aqueous bulk phases in which different reaction rates occur (Fendler and Fendler, 1975). 

Considering the dissociation of phosphate in the pH range investigated (pk - 2.15, pk2 - 7.21, pk3 - 12.67) it becomes clear, that the concentrations of the phosphate, and the monohydrogen phosphate ions are too low to give a substantial contribution to the apparent reaction rate as shown in the formula. The formula may therefore be simplified to ... 

In the first one,the apparent reaction rate is empirically related to the operating conditions on the basis of experimental observations. The models suggested by Henry et al. (3) and by Mears (4) belong to this category. The apparent reaction rate is assumed to be proportional to the liquid holdup in the first model and to the catalyst irrigation rate in the second one. These hydrodynamic quantities are estimated using empirical correlations based on experiments. 

Actually, both models lead to the following relation between the apparent reaction rate and the liquid superficial velocity . 

The following developments will be restricted to laminar liquid flow with weak gas-liquid interactions. However, this is not a limitation of the proposed methodology which could be easily applied to any other flow regime. Applications will be presented for the modelling of the irrigation rate, the dynamic liquid holdup and the apparent reaction rate in the absence of external mass transfer limitations and in the case of non volatile liquid reactants (i.e. approximatively the operating conditions of petroleum hydrotreatment). 

The apparent reaction rate ra at the level of one pore results from the exchange of mass between the liquid flow and the porous structure of the catalyst particle as depicted in the close-up of Figure 3. In the absence of external mass transfer limitations, ra equals the product of the intrinsic reaction rate r0 and the particle effectiveness factor rip, the variables being expressed... 

The averaged value of apparent reaction rate is obtained readily using the same procedure as for the irrigation rate. 

Figure 6. Apparent reaction rate against the liquid superficial velocity. Key , Ref. 22 ------------------------, Ref. 23 and-------, Equation 18.

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