Mass and Heat Transfer Limitations

1 Mass and Heat Transfer Limitations - The methane oxidation reaction is very exothermic and relatively fast. Therefore, it presents the possibility of heat and mass transfer limitations during the measurement of reaction rates. One of the methods that can be used to check for heat and mass transfer limitations is the Koros-Nowak test. Ribeiro et al. have employed this test to demonstrate that their data were not affected by heat or mass transfer limitations. In the Koros-Nowak test, rate measurements are conducted on catalysts with similar dispersions but different metal loadings. The comparison should be done at the same conversion, since, as mentioned above, the combustion products inhibit the reaction. If the observed TOFs are the same, it can be concluded that, under the tested conditions, those samples are not subject to heat or mass transfer limitations. This has been the case for the samples tested by Ribeiro et al. As shown in Table 2, the same TOF was obtained on two samples with the same Pd dispersions, but with loadings varying by an order of magnitude. 

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The following are some of the reasons that microreactors can be be used (i) reduced mass and heat transfer limitations, (ii) high area to volume ratio, (iii) safer operation, and (iv) ease of seating up by numbering out. The advantages of scaling down zeolite membranes are that it could be easier to create defect-free membranes and... 

The catalytic experiments were performed at the stationnary state and at atmospheric pressure, in a gas flow microreactor. The gas composition (NO, CO, O2, C3H, CO2 and H2O diluted with He) is representative of the composition of exhaust gases. The analysis, performed by gas chromatography (TCD detector for CO2, N2O, O2, N2, CO and flame ionisation detector for C3H6) and by on line IR spectrometry (NO and NO2) has been previously described (1). A small amount of the sample (10 mg diluted with 40 mg of inactive a AI2O3 ) was used in order to prevent mass and heat transfer limitations, at least at low conversion. The hourly space velocity varied between 120 000 and 220 000 h T The reaction was studied at increasing and decreasing temperatures (2 K/min) between 423 and 773 K. The redox character of the feedstream is defined by the number "s" equal to 2[02]+[N0] / [C0]+9[C3H6]. ... 

At this point it is instructive to consider the possible presence of intraparticle and external mass and heat transfer limitations using the methods developed in Chapter 12. In order to evaluate the catalyst effectiveness factor we first need to know the combined diffusivity for use... 

All reactor-cells used had a volume of 30 ml and have been shown to be well mixed over the range of flowrates employed in the present study (22). Both external and internal mass and heat transfer limitations have been shown to be negligible (12,22). Reactants were certified standards of ethylene diluted in N2 and Matheson zero grade air. They could be further diluted in N2. Reactants and products were analyzed by one line Gas Chromatography. The carbon dioxide concentration in the product stream was also continuously monitored using a non-dispersive IR CO2 Analyzer (Beckman 864). 

This physical limitation is the result of mass and heat transfer limitations, which are stoichiometrically related to product formation. The vertieal dotted line in Figure 11.1 symbolizes the limitation which is a conseqnence of the faet that the eoneentration of the biocatalyst is bound to certain defined limits, for instanee solnbihty in case of isolated enzymes and space in case of suspended eells. Fignre 11.1 also shows that the biocatalyst should have a minimum speeifie aetivity to be able to operate the bioreactor close to its physical ceiling. 

The first role of agitation is to keep the catalyst particles uniformly suspended in the reaction medium. When gas and liquid reactants are simultaneously used, agitation plays an essential role in facilitating the gas to liquid mass transfer.1201 Moreover, an efficient stirring is needed to avoid external (i.e. from the organic phase to the external surface of the catalyst particles) mass and heat transfer limitations.1113-151... 

In the evaluation of industrial catalysts the total conversion rate per unit reactor volume is of importance. Without mass and heat transfer limitations this rate is proportional to the active surface area exposed to the fluid per unit volume or weight of the catalyst. A high surface area is achieved with small particles or even powders. However, there are practical limitations to the size of particles that can be used, such as ... 

The advantages of the ring-shaped particles are also found for other type of reactions. To demonstrate this, consider an adiabatic plug flow reactor assuming that the external mass and heat transfer limitations are negligible. Equations for fluid-phase concentration and temperature (which are equal to the concentration and temperature at the surface of the pellet) are... 

The TEOM is a promising tool for investigation of the influence of coke on adsorption and diffusion in catalysts. As a consequence of high flow rates of the carrier gas through the sample bed, the technique minimizes the external mass and heat transfer limitations in transient experiments without affecting the accuracy of the measurements. The data are not influenced by buoyancy and flow patterns, which are significant when conventional methods are used. 

The discussion in the previous sections has evidenced that the use of biphasic systems has solved, at least in various cases, the problem of homogeneous catalyst recovery and recycle, but there still exists the problem of the cost of recycle and especially of reaction rate per volume of reactor, which derives in large part from mass- and heat-transfer limitations, but also from the low amount of catalytic centers per volume of reactor necessary to avoid side reactions and maintain a high selectivity, and/or limit catalyst deactivation or loss. These aspects often emerge only during the scaling-up and industrialization of the reaction and this is one of the reasons why many interesting reactions at the laboratory scale fail in commercialization. 

The reaction was studied at increasing temperatures ( 2 K/mn) between 423 and 773-873 K. The catalyst (10 mg) was diluted with 40 mg of inactive a-Al203 in order to prevent both mass and heat transfer limitations, at least at low conversion. The hourly space velocity, 120000- 130000 h is in the margin of the values found for the exhaust gas of the gasoline motors. The redox character of the feedstream is defined by the number ... 

Consequently, in a recycle loop reactor, the leading part of the LO cu e plotted versus the outlet temperatme gives a meaningiur apparent activation energy. Mass and heat transfer limitations do not induce bias. 

Figure 6 Comparison between the light-(0curves assuming either a zero-order or the Langmuir-Hinshelwood kinetic expression. Adiabatic case, no mass and heat transfer limitation. Left plug flow. Right complete mixing.

The experimental procedure was as follows a small amount of the catalyst (10 mg diluted with 40 mg of inactive a AI2O3) was used in order to prevent the mass and heat transfer limitations, at least for the low conversions. After heating in a flow of N2 up to 423 K the catalyst was contacted with the reactant gases (between 12 and 22 Ih l, hourly space velocity between 120 000 and 220 000). The analysis was performed at increasing and decreasing temperatures between 423 and 773 K with programmed rates of 2 K/mn. The stoichiometry of the feedstream was defined by the "s ratio" = 2(62) + (NO)/(CO) + (2x + y/2)(CxHy). 

Currently, it is accepted that the main reason behind broad MWDs is the presence of more than one type of active site in these catalysts, with mass and heat transfer limitations being a secondary broadening effect of varying importance depending on catalyst type and polymerization conditions. 

Use the thermogravimetric data that follow to determine if this reaction obeys first-order kinetics and the value of the rate constant at 673 K. Very small particles were employed to eliminate potential mass and heat transfer limitations on the reaction rate. The zero of time is taken as the start of the constant-temperature period, but some reaction has taken place during heating from room temperature to 673 K. Hence, the amount of kerogen present at time zero is not known. Employ a variation of the Guggenheim approach to solve this problem. 

In the previous section a one-dimensional model was developed and used to demonstrate the possible benefits of packed-bed membrane reactors as compared to the established fixed-bed reactors. Basic phenomena can be described with sufficient accuracy even with this simple model. However, when the goal is to predict reactor behavior in more detail the one-dimensional model may reach its limits due to radial mass- and heat-transfer limitations. Additionally, flow-maldistribution effects can also not be captured. Taking advantage of improvements in computation speed, it is nowadays possible to predict the influence of these phenomena with two- or even three-dimensional models and use this knowledge to optimize reactor performance. However, detailed modeling of membrane reactors is not as straightforward as in the case of fixed-bed reactors. There are still a couple of open questions e.g. whether semiempirical correlations obtained under nonreactive conditions in fixed beds are applicable also to membrane reactors or not. Until these questions have been completely clarified one has to rely on the available database and correlations as the best possible estimate. 

The thermal effects are very important for the reactor behaviour and the product distribution. Comparing predictions of ID and 2D models, it was found that the simple model overestimates the reactor performance. Radial mass and heat transfer limitations can not be neglected if more precise predictions are required. 

The particle size is sufficiently small so that both intra-particle mass and heat transfer limitations and external mass and heat transfer limitations from the gas bulk to the catalyst surface can be neglected. 

The extent of mass and heat transfer limitations in packed bed membrane reactors have forced researchers to investigate other solutions to circumvent those limitations. In this respect, membrane assisted fluidized bed reactors have... 

Negligible pressure drop no internal mass and heat transfer limitations because of the small particle sizes that can be employed... 

Besides the flow, one shonld consider the mass and heat transfer limitations. In reactors without bed, one may calculate the heat and mass exchange and determine the conditions for an adiabatic or isothermal operation, since the temperatnre profile in the reactor is known. For uniform velocities, the heat transfer depends on the heat capacities if they are constant, the temperature profile is uniform. Otherwise, there are considerable deviations and consequently large temperatnre variations. In catalytic reactors, there is also the influence of conductive heat of the particles. The temperature affects substantially the rate constant and conseqnently the reaction rate. At the same time, mass transfer limitation may be present dne to convection and diffnsion inside the pores of the particles, which depend on the flnid flow and the diffnsive properties of molecules. Mass transfer limitation affects significantly the rate constant and consequently the reaction rate causing different residence times of the molecnles. 

The intrinsic rate is defined by the kinetics on the pore surface or at the surface sites under the reaction conditions and r] is called the effectiveness factor. For now, let us not consider external mass and heat transfer limitations. 

The modehng problem becomes more intricate when a heterogeneous catalyst, such as PhiUips, Ziegler-Natta and supported metallocenes, is used for polymerization. In this case, temperature and reactant concentrations may vary as a function of radial position in the particle due to mass and heat transfer limitations. The models developed thus far are still valid, but only locally for the conditions existing at each radial position in the catalyst/polymer particle. 

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