Models which include external mass-transfer effects

4-5 MODELS WHICH INCLUDE EXTERNAL MASS-TRANSFER EFFECTS 

Sylvester and Pitayagulsarn53,54 considered combined effects of axial dispersion, external diffusion (gas-liquid, liquid-solid), intraparticle diffusion, and the intrinsic kinetics (surface reaction) on the conversion for a first-order irreversible reaction in an isothermal, trickle-bed reactor. They used the procedure developed by Suzuki and Smith,51,52 where the zero, first, and second moments of the reactant concentration in the effluent from a reactor, in response to a pulse introduced, are taken. The equation for the zero moment can be related to the conversion X, in the form 

the parameter F = Uo]dJ2De( — t) considers the effect of intraparticle diffusion, Pe = V dJlEzi. takes into account the effect of axial dispersion, S = 3(1 — e)Kt/U0L considers the effect of total external mass-transfer resistance, and A0 = /j (l — )k dp/2UoL considers the effect of surface reaction on the conversion. In these reactions L/0l, s the superficial liquid velocity, dp is the particle 

We now look at the mathematical equations for a general isothermal steady-state model for the trickle-bed reactor, which takes into account external mass-transfer resistances, i.e., gas-liquid and liquid-solid, axial dispersion, and the intraparticle mass-transfer resistances, along with the intrinsic kinetics occurring at the catalyst surface. Since many practical reactions can be characterized as 

In general, the above equations are best solved in a computer. Goto et al.9 obtained a solution to the case where species C is in excess so that the reaction is pseudo-first-order. They used the solution to analyze the efficiency of reaction systems such as oxidation of ethanol, hydrogenation of a-methyl styrene, and hydrogenation of aniline. They defined 

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Since in the macroscale model, the reaction rate and diffusion coefficient are effective ones that are obtained on an ensemble-averaged basis, the internal diffusion will not appear in the controlling equations explicitly. The effective reaction rate already includes the influence of internal diffusion inside catalyst pellets. The external mass transfer term, which mainly accounts for the species transport outside catalyst pellets, is used in the controlling equations in macroscale models. So, the diffusion mentioned in macroscale model normally represents species diffusion outside catalyst pellets. In fluidized bed, species diffusion is closely related to the flow regime in the reactor (Abba et al., 2003). Abba et al. (2003) summarized the formulae for calculating diffusion coefficients in different flow regimes in fluidized bed. 

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 degree of effective wetting, important in trickle operation, which also depends on fluiddynamics, is included correctly in the reaction rate term of the respective balance equations either by apparent rate constant or an effective pore diffusivity respectively or, more useful in reactor modeling, as a contribution to an overall efficiency T, which includes also the external and intraparticle mass transfer limitations [51]. 

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