External mass transfer limitations

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... 

Most of the actual reactions involve a three-phase process gas, liquid, and solid catalysts are present. Internal and external mass transfer limitations in porous catalyst layers play a central role in three-phase processes. The governing phenomena are well known since the days of Thiele [43] and Frank-Kamenetskii [44], but transport phenomena coupled to chemical reactions are not frequently used for complex organic systems, but simple - often too simple - tests based on the use of first-order Thiele modulus and Biot number are used. Instead, complete numerical simulations are preferable to reveal the role of mass and heat transfer at the phase boundaries and inside the porous catalyst particles. 

Prior to conducting the DOE (design of experiments) described in Table 3, it was established that no reaction took place in the absence of a catalyst and that the reactions were conducted in the region where chemical kinetics controlled the reaction rate. The results indicated that operating the reactor at 1000 rpm was sufficient to minimize the external mass-transfer limitations. Pore diffusion limitations were expected to be minimal as the median catalyst particle size is <25 pm. Further, experiments conducted under identical conditions to ensure repeatability and reproducibility in the two reactors yielded results that were within 5%. 

Tests for external mass transfer limitations on conversion rates, (a) External mass transfer probably does not limit conversion rate. (b) Mass transfer limitations are present, (c) External mass transfer probably does not limit conversion rate, (id) Mass transfer limitations are present at low velocities. Adapted from Chemical Engineers Handbook, Fourth Edition, edited by R. H. Perry, C. H. Chilton, and S. D. Kirkpatrick. Copyright (c) 1969. Used with permission of McGraw-Hill Book Company.)... 

In the presence of intraparticle mass transfer limitations, the rate per particle is expressed in terms of the species concentrations prevailing at the exterior of the catalyst. However, when external mass transfer limitations are also present, these concentrations will differ from those prevailing in the bulk. Since bulk concentrations are what one measures in the laboratory, exterior surface concentrations must be eliminated to express the observed conversion rate in terms of measurable concentrations. In the paragraphs that follow, the manner in which one eliminates surface concentrations is indicated in some detail for a specific case. 

Equations 12.4.22 and 12.4.24 indicate that the observed reaction order will differ from the intrinsic reaction order in the presence of intraparticle and/or external mass transfer limitations. To avoid drawing erroneous conclusions about intrinsic reaction kinetics, we must be careful to either eliminate these limitations by proper choice of experimental conditions or to properly take them into account in our data analysis. 

The difference in mole fractions is most significant in the case of S02 where this difference is 15% of the bulk phase level. This result indicates that external mass transfer limitations are indeed significant, and that this difference should be taken into account in the analysis of kinetic data from this system. Note that there is a difference in nitrogen concentration between the bulk fluid and the external surface because there is a change in the number of moles on reaction, and there is a net molar flux toward... 

Before terminating the discussion of external mass transfer limitations on catalytic reaction rates, we should note that in the regime where external mass transfer processes limit the reaction rate, the apparent activation energy of the reaction will be quite different from the intrinsic activation energy of the catalytic reaction. In the limit of complete external mass transfer control, the apparent activation energy of the reaction becomes equal to that of the mass transfer coefficient, typically a kilocalorie or so per gram mole. This decrease in activation energy is obviously... 

At steady state, the rates of each of the individual steps will be the same, and this equality is used to develop an expression for the global reaction rate in terms of bulk-fluid properties. Actually, we have already employed a relation of this sort in the development of equation 12.4.28 where we examined the influence of external mass transfer limitations on observed reaction rates. Generally, we must worry not only about concentration differences between the bulk fluid and the external surface of the catalyst, but also about temperature differences between these points and intraparticle gradients in temperature and composition. 

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.

If external mass-transfer limitations can be neglected, then the surface concentration in eq 58 (via eq 13) can be set equal to the bulk concentration, which is assumed uniform throughout the catalyst layer in the simple agglomerate models. Otherwise, the surface concentration is unknown and must be... 

This equation is the governing equation for the agglomerate models for the cathode, and without external mass-transfer limitations, it results in eq 58. For the anode, a similar analysis can be done. 

The results confirm that the adsorption of ammonia is very fast and that ammonia is strongly adsorbed on the catalyst surface. The data were analyzed by a dynamic isothermal plug flow reactor model and estimates of the relevant kinetic parameters were obtained by global nonlinear regression over the entire set of runs. The influences of both intra-particle and external mass transfer limitations were estimated to be negligible, on the basis of theoretical diagnostic criteria. 

Figure 7-15 Plots of r versus T and log i versus 1/r. We expect the rate to exhibit breaks on the 1/r plot as the reaction process goes from reaction limited at low temperature, pore diffusion limited at intermediate temperature, and external mass transfer limited at high temperature.

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. 

For these biocatalysts, no profound influence of stirrer rate could be detected. Apparently no external mass transfer limitations are present in the system. 

Internal and external mass transfer limitations in porous catalyst layers play a central role in three-phase processes. The governing phenomena are well-known since the days of Thiele (1) and Frank-Kamenetskii (2). Transport phenomena coupled to chemical reactions is not frequently used for complex organic systems. A systematic approach to the problem is presented. 

We have presented a general reaction-diffusion model for porous catalyst particles in stirred semibatch reactors applied to three-phase processes. The model was solved numerically for small and large catalyst particles to elucidate the role of internal and external mass transfer limitations. The case studies (citral and sugar hydrogenation) revealed that both internal and external resistances can considerably affect the rate and selectivity of the process. In order to obtain the best possible performance of industrial reactors, it is necessary to use this kind of simulation approach, which helps to optimize the process parameters, such as temperature, hydrogen pressure, catalyst particle size and the stirring conditions. 

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-... 

External mass transfer-limited reactions In the expression (5.191), km has to be known, but it is not necessaiy if the external mass transfer phenomena are very intense. Actually, if strong mass resistance exists, the knowledge of the rate law is not essential, because the rate can be written as... 

For SK-500 the rate at 573°K and 400 sec after the initiation of reactant flow is independent of reactant mole ratio for Ce C2 = 0.7 to 10. Under these conditions the 400-sec point is just beyond the maximum in the rate curve. Similar behavior was observed at one other condition. Initial rate of reaction estimated by extrapolating the decay portion of the rate curves for this data to zero time (see below) indicates a maximum in the rate at C6 C2 == 3.5 (Figure 2). Error bars represent estimated 95% confidence limits. The observed activity for HY is about twice that of SK-500, that for LaY is about two-thirds that of SK-500 (Figure 2). This is consistent with the trend expected (7) since all catalysts were activated to the same temperature. The temperature dependence of the observed rate is large for all systems studied indicating the absence of external mass transfer limitations. 

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... 

No external mass transfer limitation No activity loss upon immobilization Easy addition of fresh enzyme Constant space—time-yield possible Immobilized enzymes often more stable Bigger effort for enzyme preparation Soluble substrates and products only... 

At catalytically active centers in the center of carrier particles, external mass transfer (film diffusion) and/or internal mass transfer (pore diffusion) can alter or even dominate the observed reaction rate. External mass transfer limitations occur if the rate of diffusive transport of relevant solutes through the stagnating layer at a macroscopic surface becomes rate-limiting. Internal mass transfer limitations in porous carriers indicate that transport of solutes from the surface of the particle towards the active site in the interior is the slowest step. 

Mass transfer can alter the observed kinetic parameter of enzyme reactions. Hints of this are provided by non-linear Lineweaver-Burk plots (or other linearization methods), non-linear Arrhenius plots, or differing Ku values for native and immobilized enzymes. Different expressions have been developed for the description of apparent Michaelis constants under the influence of external mass transfer limitations by Homby (1968) [Eq. (5.69)], Kobayashi (1971), [Eq. (5.70)], and Schuler (1972) [Eq. (5.71)]. 

To obtain a simple kinetic model for this heterogeneous reaction, it has to be assumed that the concentration of hydrogen as a reactant, in terms of partial pressure, is constant, and that the hydrogen is thoroughly mixed with the reaction mass to avoid external mass-transfer limitations. Consequently, experiments were carried out in which the speed of the stirrer was varied from 600 to 1800 rpm. For stirrer speeds up to 1200 rpm, a strong dependence of the rate of reaction on the stirrer speed was found. For stirrer speeds above 1200 rpm, no significant increase in the reaction rate was found therefore, a speed of 1200 rpm was... 

Figure 11.3 Partial fluxes of isoamyl alcohol, ethyl acetate, isoamyl acetate and ethyl hexanoate as a function of their feed crossflow velocity (bottom axis) and Reynolds number (top axis) in a singlechannel module, using a POMS-PEI composite membrane. Notice that external mass-transfer limitations are not fully overcome when soluteswith a high affinity towardsthe membrane are processed (Adapted from Ref. 32.)...

A simple experimental method can be used to specify the minimum stirring rate to be chosen in order to avoid external mass transfer limitation (provided, however, there is no large temperature gradient between the bulk and surface of the catalyst). Indeed the reaction rate first increases with the stirring rate, then becomes constant, indicating that the rate is then limited by chemical steps. This type of experiment... 

External mass transfer limitations, which cause a decrease in both the reaction rate and selectivity, have to be avoided. As in the batch reactor, there is a simple experimental test in order to verify the absence of these transport limitations in isothermal operations. The mass transfer coefficient increases with the fluid velocity in the catalyst bed. Therefore, when the flow rate and amount of catalyst are simultaneously changed while keeping their ratio constant (which is proportional to the contact time), identical conversion values should be found for flow rate high enough to avoid external mass transfer limitations.[15]... 

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... 

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