Energy balance porous catalyst

The rate-based models usually use the two-film theory and comprise the material and energy balances of a differential element of the two-phase volume in the packing (148). The classical two-film model shown in Figure 13 is extended here to consider the catalyst phase (Figure 33). A pseudo-homogeneous approach is chosen for the catalyzed reaction (see also Section 2.1), and the corresponding overall reaction kinetics is determined by fixed-bed experiments (34). This macroscopic kinetics includes the influence of the liquid distribution and mass transfer resistances at the liquid-solid interface as well as dififusional transport phenomena inside the porous catalyst. 

In any catalytic system not only chemical reactions per se but mass and heat transfer effects should be considered. For example, mass and heat transfer effects are present inside the porous catalyst particles as well as at the surrounding fluid films. In addition, heat transfer from and to the catalytic reactor gives an essential contribution to the energy balance. The core of modelling a two-phase catalytic reactor is 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. 

THERMAL ENERGY BALANCE IN MULTICOMPONENT MIXTURES AND NONISOTHERMAL EFFECTIVENESS FACTORS VIA COUPLED HEAT AND MASS TRANSFER IN POROUS CATALYSTS... 

Consider the nonisothermal porous spherical catalyst particle of radius R in which a single, irreversible, first-order reaction takes place at steady state (Figure 2.11). Taking the same spherical shell of thickness Ar at a radius r from the center, the steady-state energy balance over a differential shell of volume 4nt Ar includes conduction into and out of the control volume in the radial direction as well as heat release by reaction within the control volume ... 

The term r ej is called the effectiveness factor. Expression 5.14 should be inserted into the balance equations instead of R. If diffusion does not affect the reaction rates, all effectiveness factors, riej, become equal to unity (=1). In the following, the logical and theoretical appearance of the effectiveness factor is discussed by studying the (molar) mass and energy balances of porous catalyst particles in detail. 

Considering the properties of materials and biosystems thus involves (a) thinking in terms of colloids, interfaces, and space disttlbution, (b) keeping in mind that interfaces are zones where interaction forces are not balanced, which is responsible for an excess free energy. Porous and dispersed solids (adsorbents, catalysts) represent a case in which different levels of characterization are clear-cut ... 

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