and heat transfer effects. For example, mass and heat transfer effects are present inside the ...... fusion, is calculated as L ¼Vp/Ap. ...... naphthalene. 298. 0.061.
CHAPTER 10
Mass Transfer and Catalytic Reactions 10.1. CATALYTIC MULTI-PHASE SYSTEMS In any catalytic system, not only should chemical reactions be considered, but also mass and heat transfer effects. For example, mass and heat transfer effects are present inside the porous catalyst particles, as well as in the surrounding fluid films. In addition, heat transfer to and from the catalytic reactor gives an essential contribution to the energy balance. The core of modeling for a two-phase catalytic reactor is related to processes in the catalyst particle; namely, simultaneous reaction and diffusion in the pores of the particle should be accounted for. These effects are completely analogous to reaction-diffusion effects in liquid films appearing in gas-liquid systems. Thus, the formulae presented in the next section are valid for both catalytic reactions and gas-liquid processes. Gas-liquid diffusion can be essential in homogeneous and enzymatic reactions, if the catalyst is dissolved in the fluid phase and one of the reactants has to be first dissolved. As an example, we can refer to alkylation of aromatic compounds by olefins in the presence of AlCl3, where diffusion in the fluid film is of importance. Mass transfer in gas-liquid nocatalytic reactions will not be considered in this book, as that is a subject described in general chemical engineering textbooks. Such a type of diffusion is also present in heterogeneous catalysis for three-phase systems (three-phase catalytic hydrogenations or oxidations), as illustrated in Fig. 10.1. Physical transport processes can play an especially important role in heterogeneous catalysis. Besides film diffusion on the gas/liquid boundary, there can also be diffusion of the reactants (products) through a boundary layer to (from) the external surface of the solid material, as well as through the porous interior to (for reactants) or from (for products ) the active catalyst sites. Heat and mass transfer processes influence the observed catalytic rates. For instance, as discussed previously, the intrinsic rates of catalytic processes follow the Arrhenius law, while mass transfer hinders such pronounced dependence, decreasing the apparent activation energy. The intraparticle and interphase mass transfer coefficients display a lower temperature dependence as visualized in Fig. 10.2 and discussed later. Moreover, the mechanism for the transport of mass and heat is different from the one for chemical reaction; therefore, a different dependence on concentration can also be expected.
Catalytic Kinetics http://dx.doi.org/10.1016/B978-0-444-63753-6.00010-5
© 2016 Elsevier B.V. All rights reserved.
589
590
Catalytic Kinetics
ca
Gas
Gas-liquid diffusion
pA
Liquid Catalyst
Absorption equilibrium
cA
Fig. 10.1 Mass transfer processes in three-phase systems.
ln ka
Film diffusion
Pore diffusion
Slope = 0
Slope =
Kinetic region
– EA 2R
Slope = Transition region
Transition region
– EA R
1/T
Fig. 10.2 Temperature dependence of catalytic reactions.
10.2. SIMULTANEOUS REACTION AND DIFFUSION IN FLUID FILMS AND IN POROUS MATERIALS The mathematical description of the influence of mass transfer will be based on the general conservation laws. Balancing the amount of mass for a given volume element we have: IN + GENERATION ¼ OUT + ACCUMULATION A general continuity equation (mass balance) for a component in a layer, where diffusion and chemical reactions take place simultaneously, is written for an infinitesimal volume element: ðNi AÞin + ri αΔV ¼ ðNi AÞout +
dni dt
(10.1)
Mass Transfer and Catalytic Reactions
where Ni and ri denote the flux and the generation rate; respectively, A is the crosssection area of the flux, ΔV is the element volume and n is the amount of substance in the volume element. The factor α equals 1 for homogeneous kinetics and the catalyst density (α ¼ ρp) for catalytic systems. The amount of substance in the volume element, ni, is expressed by the concentration (ci) and the volume of fluid phase in the volume element (εΔV). The factor (ε) is 1 for homogeneous systems being
