Catalytic mass transfer coefficient

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... 

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). 

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. 

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... 

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. 

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. 

Bubble columns are convenient for catalytic slurry reactions also (67). It is therefore important to know how the hydrodynamic properties of the gas-in-liquid dispersion is influenced by the presence of suspended solid particles. In the slurry reactor absorption enhancement due to chemical reaction cannot be expected. However, if particle sizes are very small, say less than 5 yum, and if, in addition, the catalytic reaction rate is high a small absorption enhancement can occur ( 8). Usually the reaction is in the slow reaction regime of mass transfer theory. Hence, it is sufficient to know the volumetric mass transfer coefficient, kj a, and there is no need to separate k a into the individual values. 

In catalytic slurry reactors the locale of the reaction is the catalyst surface. Hence, in addition to the mass transfer resistance at the gas-liquid interface a further transport resistance may occur at the boundary layer around the catalyst particle. This is characterized by the solid-liquid mass transfer coefficient, kg, which has been the subject of many theoretical and experimental studies. Brief reviews are given by Shah (82). In general, the liquid-solid mass transfer coefficient is correlated by expressions like... 

While the above criteria are useful for diagnosing the effects of transport limitations on reaction rates of heterogeneous catalytic reactions, they require knowledge of many physical characteristics of the reacting system. Experimental properties like effective diffusivity in catalyst pores, heat and mass transfer coefficients at the fluid-particle interface, and the thermal conductivity of the catalyst are needed to utilize Equations (6.5.1) through (6.5.5). However, it is difficult to obtain accurate values of those critical parameters. For example, the diffusional characteristics of a catalyst may vary throughout a pellet because of the compression procedures used to form the final catalyst pellets. The accuracy of the heat transfer coefficient obtained from known correlations is also questionable because of the low flow rates and small particle sizes typically used in laboratory packed bed reactors. 

Cybulski and Moulijn [27] proposed an experimental method for simultaneous determination of kinetic parameters and mass transfer coefficients in washcoated square channels. The model parameters are estimated by nonlinear regression, where the objective function is calculated by numerical solution of balance equations. However, the method is applicable only if the structure of the mathematical model has been identified (e.g., based on literature data) and the model parameters to be estimated are not too numerous. Otherwise the estimates might have a limited physical meaning. The method was tested for the catalytic oxidation of CO. The estimate of effective diffusivity falls into the range that is typical for the washcoat material (y-alumina) and reacting species. The Sherwood number estimated was in between those theoretically predicted for square and circular ducts, and this clearly indicates the influence of rounding the comers on the external mass transfer. 

In many industrial reactions, the overall rate of reaction is limited by the rate of mass transfer of reactants and products between the bulk fluid and the catalytic surface. In the rate laws and cztalytic reaction steps (i.e., dilfusion, adsorption, surface reaction, desorption, and diffusion) presented in Chapter 10, we neglected the effects of mass transfer on the overall rate of reaction. In this chapter and the next we discuss the effects of diffusion (mass transfer) resistance on the overall reaction rate in processes that include both chemical reaction and mass transfer. The two types of diffusion resistance on which we focus attention are (1) external resistance diffusion of the reactants or products between the bulk fluid and the external smface of the catalyst, and (2) internal resistance diffusion of the reactants or products from the external pellet sm-face (pore mouth) to the interior of the pellet. In this chapter we focus on external resistance and in Chapter 12 we describe models for internal diffusional resistance with chemical reaction. After a brief presentation of the fundamentals of diffusion, including Pick s first law, we discuss representative correlations of mass transfer rates in terms of mass transfer coefficients for catalyst beds in which the external resistance is limiting. Qualitative observations will bd made about the effects of fluid flow rate, pellet size, and pressure drop on reactor performance. 

The reason that kbOt, is higher than calculated from Eq. (6-12) may be explained qualitatively by three effects (1) splitting, coalescence, and rupture of bubbles (T18, T20) (2) direct contact of gas and particles in the transition zone from dense phase to dilute phase (F18) (3) the influence of the particle capacitance effect (M21, M22) as a result of a small steady interchange of particles between the bubble void and the emulsion. An example of this is the case where particles are raining through the bubble (D18, R8, Wl) and (4) asphericity of the bubbles (D18). If the particle capacitance effect (discussed in the next section) is responsible for high experimental values for kb b. such values should not be applied to the usual catalytic reactions, where m is on the order of unity and particle capacitance has little effect on kbOt,. For design purposes it is normally better to use experimental mass-transfer coefficients obtained by a properly sized fluid bed for the reaction system of interest. 

There are a few drawbacks associated with catalytic combustion. First, as noted by Pfefferle, the power density is low. The volumetric heat release rates of catalytic combustors (without a homogenous flame downstream) are much lower than those found in conventional flame combustors because catalytic combustors are mass transfer limited, and mass transfer coefficients are relatively low. 

Much effort has been made to study this light-off behavior of catalytic monolith. Oh and Cavendish studied the response of the monolith to a step increase in the feed stream temperature by using a onedimensional two-phase (gas and solid) model. They tracked the cross-sectional average temperature and concentration in each phase and used heat and mass transfer coefficients to describe interphase transport. The results indicated that the light-off occurs at the monolith entrance for a sufficiently high inlet exhaust temperature. For a lower inlet exhaust temperature, the light-off occurs in the downstream section, and the... 

No matter how active a catalyst particle is, it can be effective only if the reactants can reach the catalytic surface. The transfer of reactant from the bulk fluid to the outer surface of the catalyst particle requires a driving force, the concentration difference. Whether this difference in concentration between bulk fluid and particle surface is significant or negligible depends on the velocity pattern in the fluid near the surface, on the physical properties of the fluid, and on the intrinsic rate of the chemical reaction at the catalyst that is, it depends on the mass-transfer coefficient between fluid and surface and the rate constant for the catalytic reaction In every case the concentration of reactant is less at the surface than in the bulk fluid. Hence the observed rate, the global rate, is less than that corresponding to the concentration of reactants in the bulk fluid. 

This case study is concerned with a three-phase gas-liquid-solid (catalytic) reaction. A systematic stepwise procedure has been described for determining the rate-controlling step, which depends on the catalyst type, particle size, operating pressure and temperature, mass transfer coefficient, and concentrations of reactants and products. As indicated, the rate-controlling step may change with location in a continuous reactor and with time in a batch reactor. 

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