External mass transfer effective rate

To illustrate the masking effects that arise from intraparticle and external mass transfer effects, consider a surface reaction whose intrinsic kinetics are second-order in species A. For this rate expression, equation 12.4.20 can be written as... 

Schematic representation of reactant concentration profiles in various global rate regimes. I External mass transfer limits rate. II Pore diffusion limits rate. Ill Both mass transfer effects are present. IV Mass transfer has no influence on rate.

To study the kinetics of immobilized enzymes a recirculation reactor may be used. This reactor allows one to perform kinetic measurements with defined external mass transfer effects, reached by establishing a high flow rate near the catalyst, minimizing mass transfer resistance. The reactor behaves as a differential gradientless reactor allowing initial-rate kinetic measurements to be made. 

When the reaction rates in the monolith channels are sufficiently high, a significant gradient will develop between the concentration at the channel center and that at the catalyst surfaces. This external mass transfer effect must be considered in addition to internal diffusion effects. The rate of external mass transfer at a given value of z is equal to the reaction rate inside the catalyst at steady state ... 

Notice that O2 is in excess and both CO and C3H6 reach very low values within the pellet. The log scale in Figure 7.23 shows that the concentrations of these reactants change by seven orders of magnitude. Obviously the consumption rate is large compared to the diffusion rate for these species. The external mass-transfer effect is noticeable, but not dramatic. 

Although the external mass transfer controlled polymer dissolution approach [51] may be intuitive, experiments have indicated that external mass transfer effects are insignificant. Papanu et al. [40] showed that for dissolution of PMMA in MIBK, vigorous agitation of the solvent increased the dissolution rate by only 15% relative to that for a stagnant solvent. Also, since the chain disentanglement mechanism was not considered, these models fail to explain the swelling time needed before dissolution. 

The Weisz-Prater criterion makes use of observable quantities like -Ra)p, the measured global rate (kmol/kg-s) dp, the particle diameter (m) pp, the particle density (kg/m ) Dg, the effective mass diffusivity (m /s) and the surface concentration of reactant (kmol/m ). The intrinsic reaction rate constant ky need not be known in order to use the Weisz-Prater criterion. If external mass transfer effects are eliminated, CAb can be used, and the effective diffusivity can be estimated using catalyst and fluid physical properties. The criterion can be extended to other reaction orders and multiple reactions by using the generalized Thiele modulus, and various functional forms are quoted in the literature [17, 26, 28]. 

Note that fem,e F or rra,eS re the effective (measured) values of the rate constant and rate, respectively, which includes all internal and external mass transfer effects. 

In a fixed-bed PFR, the flow rate is varied at constant space time and if the rate remains constant, external mass transfer effects are assumed to be unimportant however, this test can become insensitive at low Reynolds number [61]. 

To illustrate the influence of the various parameters investigated, Rj. was defined as the "kinetic" conversion rate Rk calculated at the average concentration in the bed, neglecting external mass transfer effects and assuming total catalyst utilization ... 

A simple system is shown in Figure 5.10a to depict heterogeneous polymerization. A gaseous monomer is continuously fed into a glass vessel. The vessel (serving as a reactor) has a suitable solvent (usually hexane for propylene) in which the catalyst-cocatalyst system is xmiformly dispersed. In Figure 5.10b, the effect of stirring speed on the rate of propylene polymerization is shown schematically. These results clearly demonstrate the external mass transfer effect. 

If the surface reaction is the rate-controlling step, any effects of external mass transfer and pore-diffusion are negligible in comparison. The interpretation of this, in terms of the various parameters, is that Ag kA, cAs - cAg, and T) and 17 both approach the value of 1. Thus, the rate law, from equation 8.5-50, is just that for a homogeneous gas-phase... 

There are a number of examples of tube waU reactors, the most important being the automotive catalytic converter (ACC), which was described in the previous section. These reactors are made by coating an extruded ceramic monolith with noble metals supported on a thin wash coat of y-alumina. This reactor is used to oxidize hydrocarbons and CO to CO2 and H2O and also reduce NO to N2. The rates of these reactions are very fast after warmup, and the effectiveness factor within the porous wash coat is therefore very smaU. The reactions are also eternal mass transfer limited within the monohth after warmup. We wUl consider three limiting cases of this reactor, surface reaction limiting, external mass transfer limiting, and wash coat diffusion limiting. In each case we wiU assume a first-order irreversible reaction. 

In order to solve the mathematical model for the emulsion hquid membrane, the model parameters, i. e., external mass transfer coefficient (Km), effective diffu-sivity (D ff), and rate constant of the forward reaction (kj) can be estimated by well known procedures reported in the Hterature [72 - 74]. The external phase mass transfer coefficient can be calculated by the correlation of Calderback and Moo-Young [72] with reasonable accuracy. The value of the solute diffusivity (Da) required in the correlation can be calculated by the well-known Wilke-Chang correlation [73]. The value of the diffusivity of the complex involved in the procedure can also be estimated by Wilke-Chang correlation [73] and the internal phase mass transfer co-efficient (surfactant resistance) by the method developed by Gu et al. [75]. 

A high Damkohler number means that the global rate is controlled by mass transfer phenomena. So, the process rate can be rewritten in terms of the Damkohler number and the external effectiveness factor for each reaction order can be deduced, as shown in Table 5.5. In Figure 5.3, the external effectiveness factor versus the Damkohler number is depicted for various reaction orders. It is clear that the higher the reaction order, the more obvious the external mass transfer limitation. For Damkohler numbers higher than 0.10, external mass transfer phenomena control the global rate. In the case of n = 1, the external effec-... 

It is possible to combine the resistances of internal and external mass transfer through an overall effectiveness factor, for isothermal particles and first-order reaction. Two approaches can be applied. The general idea is that the catalyst can be divided into two parts its exterior surface and its interior surface. Therefore, the global reaction rates used here are per unit surface area of catalyst. 

In the cases above, a two-parameter model well represents the data. A model with more parameters would be more flexible, but by using a partition constant, K, or a desorption rate constant ka and k, , for the mass-transfer coefficients, the data are well described (see Figs. 3.4-15 and 3.4-13). While K would be a value experimentally determined, kp can be estimated from eqn. (3.4-97) with the external mass-transfer coefficient, km, estimated from the correlation of Stiiber et al. [25] or from that of Tan et al. [27], and the effective diffusivity from the Wakao Smith model [36], Typical values of kp obtained by fitting the data of Tan and Liou are shown in Fig. 3.4-16. As expected, they are below the usual mass-transfer correlations, because internal resistance diminishes the global mass transfer coefficient. These data correspond to the regeneration of spent activated carbon loaded with ethyl acetate, using high-pressure carbon dioxide, published by Tan and Liou [45]. 

We see that, in principle, the overall reaction rate can be expressed in terms of coefficients such as the reaction rate constant and the mass transfer coefficient. To be of any use for design purposes, however, we must have knowledge of these parameters. By measuring the kinetic constant in the absence of mass transfer effects and using correlations to estimate the mass transfer coefficient we are really implying that these estimated parameters are independent of one another. This would only be true if each element of external surface behaved kinetically as all other surface elements. Such conditions are only fulfilled if the surface is uniformly accessible. It is fortuitous, however, that predictions of overall rates based on such assumptions are often within the accuracy of the kinetic information, and for this reason values of k and hD obtained independently are frequently employed for substitution into overall rate expressions. 

A controls the overall rate of conversion, equation 3.81 could be used directly as the rate equation for design purposes. If, however, external mass transfer were important the partial pressures in equation 3.81 would be values at the interface and an equation (such as equation 3.66) for each component would be required to express interfacial partial pressures in terms of bulk partial pressures. If internal diffusion were also important, the overall rate equation would be multiplied by an effectiveness factor either estimated experimentally, or alternatively obtained by theoretical considerations similar to those discussed earlier. 

The actual reaction rate, according to the external mass-transfer limitation model, is as given in Eq. (3.2). The rate that would be obtained with no mass-transfer resistance at the interface is the same as Eq. (3.5) except that Cs is replaced by Csb. Therefore, the effectiveness factor is... 

Calculate the isothermal effectiveness factor rj for the porous catalyst pellet in problem 1 as a function of the Thiele modulus d> for the first reaction A —> B utilizing the fact that the rate constant of the second reaction B —> C is half the rate constant of A —> B, the pellet is isothermal, and the external mass transfer resistance is negligible. 

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... 

Table 6.8 presents the details of calculations for spherical particles with an equivalent diameter of 2.4mm. It may be observed that the pore diffusion considerably affects the process rate, particularly at higher temperatures. The external mass transfer plays a minor role. Their combination leads to a global effectiveness that drops from 75% to 35% when the temperature varies from 160 to 220°C. Based on the above elements the apparent reaction constant may be expressed by the following Arrhenius law ... 

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. 

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