Catalytic transfer coefficient

Product Quality Considerations of product quahty may require low holdup time and low-temperature operation to avoid thermal degradation. The low holdup time eliminates some types of evaporators, and some types are also eliminated because of poor heat-transfer charac teristics at low temperature. Product quality may also dic tate special materials of construction to avoid met hc contamination or a catalytic effect on decomposition of the product. Corrosion may also influence evaporator selection, since the advantages of evaporators having high heat-transfer coefficients are more apparent when expensive materials of construction are indicated. Corrosion and erosion are frequently more severe in evaporators than in other types of equipment because of the high hquid and vapor velocities used, the frequent presence of sohds in suspension, and the necessary concentration differences. 

The half-wave potentials of (FTF4)Co2-mediated O2 reduction at pH 0-3 shifts by — 60 mV/pH [Durand et ah, 1983], which indicates that the turnover-determining part of the catalytic cycle contains a reversible electron transfer (ET) and a protonation, or two reversible ETs and two protonation steps. In contrast, if an irreversible ET step were present, the pH gradient would be 60/( + a) mV/pH, where n is the number of electrons transferred in redox equilibria prior to the irreversible ET and a is the transfer coefficient of the irreversible ET. The —60 mV/pH slope is identical to that manifested by simple Ee porphyrins (see Section 18.4.1). The turnover rate of ORR catalysis by (ETE4)Co2 was reported to be proportional to the bulk O2 concentration [Collman et ah, 1994], suggesting that the catalyst is not saturated with O2. 

Steps 1 and 7 are highly dependent on the fluid flow characteristics of the system. The mass velocity of the fluid stream, the particle size, and the diffusional characteristics of the various molecular species are the pertinent parameters on which the rates of these steps depend. These steps limit the observed rate only when the catalytic reaction is very rapid and the mass transfer is slow. Anything that tends to increase mass transfer coefficients will enhance the rates of these processes. Since the rates of these steps are only slightly influenced by temperature, the influence of these processes... 

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... 

The One-Dimensional Pseudo Homogeneous Model of Fixed Bed Reactors. The design of tubular fixed bed catalytic reactors has generally been based on a one-dimensional model that assumes that species concentrations and fluid temperature vary only in the axial direction. Heat transfer between the reacting fluid and the reactor walls is considered by presuming that all of the resistance is contained within a very thin boundary layer next to the wall and by using a heat transfer coefficient based on the temperature difference between the fluid and the wall. Per unit area of the tube... 

The rate constant of electron transfer (ks) and anodic and cathodic electron transfer coefficients (aa and ac) of the SODs at various pH values were estimated with Laviron s equation and summarized in Table 6.5. Interestingly, the fastest electron transfer of the SODs was essentially achieved in a neutral solution, probably in agreement with the biological conditions for the inherent catalytic mechanisms of the SODs for 02" dismutation, although the electrode processes of the SODs follow a different mechanism. 

This simplified description of molecular transfer of hydrogen from the gas phase into the bulk of the liquid phase will be used extensively to describe the coupling of mass transfer with the catalytic reaction. Beside the Henry coefficient (which will be described in Section 45.2.2.2 and is a thermodynamic constant independent of the reactor used), the key parameters governing the mass transfer process are the mass transfer coefficient kL and the specific contact area a. Correlations used for the estimation of these parameters or their product (i.e., the volumetric mass transfer coefficient kLo) will be presented in Section 45.3 on industrial reactors and scale-up issues. Note that the reciprocal of the latter coefficient has a dimension of time and is the characteristic time for the diffusion mass transfer process tdifl-GL=l/kLa (s). 

In this section, the analysis of the data reconciliation problem is restricted to quasi-steady-state process operations. That is, those processes where the dominant time constant of the dynamic response of the system is much smaller than the period with which disturbances enter the system. Under this assumption the system displays quasi-steady-state behavior. The disturbances that cause the change in the operating conditions may be due to a slow variation in the heat transfer coefficients, catalytic... 

When heat is transferred between a fluid and a packed bed of particles, e.g. in a fixed bed catalytic reactor, the heat transfer coefficient depends on the flow conditions. A simple correlation due to Chilton and Colburn [37]... 

The equations are also coupled by the mass transfer coefficient This is the standard mass transfer problem we encountered with catalytic reactions. As with catalytic reactors, processes are very often limited by mass transfer so that the kinetics become unimportant in predicting performance. 

Modeling of the packed bed catalytic reactor under adiabatic operation simply involves a slight modification of the boundary conditions for the catalyst and gas energy balances. A zero flux condition is needed at the outer reactor wall and can be obtained by setting the outer wall heat transfer coefficients /iws and /iwg (or corresponding Biot numbers) equal to zero. Simulations under adiabatic operation do not significantly alter any of the conclusions presented throughout this work and are often used for verification... 

In the case of two fluids, two films are developed, one for each fluid, and the corresponding mass-transfer coefficients are determined (Figure 3.2). In a fluid-solid system, there is only one film whereas the resistance within the solid phase is expressed by the solid-phase diffusion coefficient, however, in many cases an effective mass-transfer coefficient is used in the case of solids as well. Consider the irreversible catalytic reaction of the form... 

The mass and heat transfer coefficients depend on the fluid and catalytic particle properties, flow conditions, and the reactor type. Analytical equations for estimating these coefficients according to the reactor type have been presented previously in Chapter 3. 

Q = rate of heat transfer per unit mass of catalyst hf = heat transfer coefficient per unit of external surface area Tb = temperature at the bulk of the fluid Ts = temperature at catalytic surface. 

The following, well-acceptable assumptions are applied in the presented models of automobile exhaust gas converters Ideal gas behavior and constant pressure are considered (system open to ambient atmosphere, very low pressure drop). Relatively low concentration of key reactants enables to approximate diffusion processes by the Fick s law and to assume negligible change in the number of moles caused by the reactions. Axial dispersion and heat conduction effects in the flowing gas can be neglected due to short residence times ( 0.1 s). The description of heat and mass transfer between bulk of flowing gas and catalytic washcoat is approximated by distributed transfer coefficients, calculated from suitable correlations (cf. Section III.C). All physical properties of gas (cp, p, p, X, Z>k) and solid phase heat capacity are evaluated in dependence on temperature. Effective heat conductivity, density and heat capacity are used for the entire solid phase, which consists of catalytic washcoat layer and monolith substrate (wall). 

Transfer coefficients in catalytic monolith for automotive applications typically exhibit a maximum at the channel inlet and then decrease relatively fast (within the length of several millimeters) to the limit values for fully developed concentration and temperature profiles in laminar flow. Proper heat and mass transfer coefficients are important for correct prediction of cold-start behavior and catalyst light-off. The basic issue is to obtain accurate asymptotic Nu and Sh numbers for particular shape of the channel and washcoat layer (Hayes et al., 2004 Ramanathan et al., 2003). Even if different correlations provide different kc and profiles at the inlet region of the monolith, these differences usually have minor influence on the computed outlet values of concentrations and temperature under typical operating conditions. 

In some cases, however, anomalous Tafel slopes have been observed for strongly catalytic processes [40—42] if the transfer coefficient is temperature-dependent an extra term, d a/d(l/T), must be considered in eqn. (101). 

Liquid-solid mass transfer has also been studied, on a limited basis. Application to systems with catalytic surfaces or electrodes would benefit from such studies. The theoretical equations have been proposed based on film-flow theory (32) and surface-renewal theory (39). Using an electrochemical cell with rotating screen disks, liquid-solid mass transfer was shown to increase with rotor speed and increased spacing between disks but to decrease with the addition of more disks (39). Water flow over naphthalene pellets provided 4-6 times higher volumetric mass transfer coefficients compared to gravity flow and similar superficial liquid velocities (17). 

Cyclohexene hydrogenation is a well-studied process that serves as model reaction to evaluate performance of gas-liquid reactors because it is a fast process causing mass transfer limitations for many reactors [277,278]. Processing at room temperature and atmospheric pressure reduces the technical expenditure for experiments so that the cyclohexene hydrogenation is accepted as a simple and general method for mass transfer evaluation. Flow-pattern maps and kinetics were determined for conventional fixed-bed reactors as well as overall mass transfer coefficients and energy dissipation. In this way, mass transfer can be analyzed quantitatively for new reactor concepts and processing conditions. Besides mass transfer, heat transfer is an issue, as the reaction is exothermic. Hot spot formation should be suppressed as these would decrease selectivity and catalytic activity [277]. 

The various volumetric mass-transfer coefficients are defined in a manner similar to that discussed for gas-liquid and fluid-solid mass transfer in previous sections. There are a large number of correlations obtained from different gas-liquid-solid systems. For more details see Shah (Gas-Liquid-Solid Reactor Design, McGraw-Hill, 1979), Ramachandran and Chaudhari (Three-Phase Catalytic Reactors, Gordon and Breach, 1983), and Shah and Sharma [Gas-Liquid-Solid Reactors in Carberry and Varma (eds.), Chemical Reaction and Reactor Engineering, Marcel Dekker, 1987],... 

For homogeneous catalytic reactions the last two factors may be ignored. The rate of gas transfer into a liquid medium is given by Q = k,a(C f - C,), where ki is the mass transfer coefficient, a, the interfacial area between the gas and liquid, Cf and C are equilibrium concentrations of the gas in the liquid phase and the concentration of gas in the liquid, respectively. 

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