Porous catalyst, chemical reaction isothermal

Petersen EE. Non-isothermal chemical reaction in porous catalysts. Chemical Engineering Science 1962 17 987-995. 

The general theoretical approach is to develop the mathematical equations for simultaneous mass transfer and chemical reaction, as the reactants and products difHise into and out of the porous catalyst. When reaction occurs simultaneously with mass transfer within a porous structure, a concentration gradient is established. Since interior surfaces are thus exposed to lower reactant concentrations than surfaces near the exterior, the overall reaction rate throughout the catalyst particle under isothermal conditions is less than it would be if there were no mass transfer limitations. As will be shown, the apparent activation energy, the catalyst selectivity, and other important observed characteristics of a reaction are also dependent upon the structure of the catalyst and the effective diffusivity of reactants and products (Charles and Thomas, 1963). 

The analysis of simultaneous diffusion and chemical reaction in porous catalysts in terms of effective diffusivities is readily extended to geometries other than a sphere. Consider a flat plate of porous catalyst in contact with a reactant on one side, but sealed with an impermeable material along the edges and on the side opposite the reactant. If we assume simple power law kinetics, a reaction in which there is no change in the number of moles on reaction, and an isothermal flat plate, a simple material balance on a differential thickness of the plate leads to the following differential equation... 

In practice, of course, it is rare that the catalytic reactor employed for a particular process operates isothermally. More often than not, heat is generated by exothermic reactions (or absorbed by endothermic reactions) within the reactor. Consequently, it is necessary to consider what effect non-isothermal conditions have on catalytic selectivity. The influence which the simultaneous transfer of heat and mass has on the selectivity of catalytic reactions can be assessed from a mathematical model in which diffusion and chemical reactions of each component within the porous catalyst are represented by differential equations and in which heat released or absorbed by reaction is described by a heat balance equation. The boundary conditions ascribed to the problem depend on whether interparticle heat and mass transfer are considered important. To illustrate how the model is constructed, the case of two concurrent first-order reactions is considered. As pointed out in the last section, if conditions were isothermal, selectivity would not be affected by any change in diffusivity within the catalyst pellet. However, non-isothermal conditions do affect selectivity even when both competing reactions are of the same kinetic order. The conservation equations for each component are described by... 

A fraction ( of the active surface of some porous slab-shaped catalyst pellets becomes poisoned. The pellets are used to catalyse a first-order isothermal chemical reaction. Find an expression for the ratio of the activity of the poisoned catalyst to the original activity of the unpoisoned catalyst when (a) homogeneous poisoning occurs, (b) selective poisoning occurs. 

The analysis is concerned with a one-dimensional model of electrodes in which reaction rates are distributed unevenly due to diffusion as well as a variation in electrode potential.4,5 The treatment of the problem of a simultaneous variation in electrolyte concentration and potential distribution in the electrode is treated in an analogous manner to that of non-isothermal chemical reactions in porous catalysts.16 The results show that several dimensionless groups or numbers control the electrode behavior. Figure 8 shows a back fed porous anode used in the model. 

The whole of the internal surface area of a porous catalyst will be available for the catalytic reaction if the rates of diffusion of reactant into the pores, and of product out of them, are fast compared with the rate of the surface reaction. In contrast, if the reactant diffuses slowly but reacts rapidly, conversion to product will occur near the pore entrances and the interior of the pores will play no role in the catalysis. Ion exchange resins are typical examples of catalysts for which such considerations are important (cf. Sect. 2.3). The detailed mathematics of this problem have been treated in several texts [49-51] and we shall now quote some of the main theoretical results derived for isothermal conditions. The parameters involved tend to be those employed by chemical engineers and differ somewhat from those used elsewhere in this chapter. In particular, the catalyst material (active + support) is present in the form of pellets of volume Vp and the catalytic rates vv are given per unit volume of pellet (mols m 3). The decrease in vv brought about by pore diffusion is then expressed by an effectiveness factor, rj, defined by... 

Consider one-dimensional diffusion and zeroth-order chemical reaction in a flat-slab porous wafer-type catalyst. The conditions are approximately isothermal and the inirapellet Damkohler number of reactant A is Aa. intrapellet = VS. The mass transfer equation is solved numerically, not analytically. 

Burghardt and Aerts [12] proposed a method for evaluation of the pressure change in an isothermal porous pellet within which a single chemical reaction takes place, accompanied by mass transfer by Knudsen diffusion, bulk diffusion and viscous convective flow of the reacting mixture. The pressure change did also depend on the reaction and on the mixture composition on the pellet surface. It was concluded that the pressure changes in a catalyst pellet under conditions normally encountered in industry are most likely so small that they can be neglected in process simulations. 

Elnashaie and Abashar [34] developed a mathematical model to investigate the phenomena of diffusion and chemical reactions in porous catalyst pellets for steam reforming. The rigorous dusty gas model was compared to the simpler Wilke-Bosanquet model under the assumptions of steady-state, negligible viscous flow and isothermal conditions. It was found that at low steam to methane ratios the simplified diffusion model is adequate for simulating the reforming process, while at high steam to methane ratios the implementation of the dusty gas model is essential for accurate prediction of the behavior for this gas-solid system. 

The oxidation of propylene oxide on porous polycrystalline Ag films supported on stabilized zirconia was studied in a CSTR at temperatures between 240 and 400°C and atmospheric total pressure. The technique of solid electrolyte potentiometry (SEP) was used to monitor the chemical potential of oxygen adsorbed on the catalyst surface. The steady state kinetic and potentiometric results are consistent with a Langmuir-Hinshelwood mechanism. However over a wide range of temperature and gaseous composition both the reaction rate and the surface oxygen activity were found to exhibit self-sustained isothermal oscillations. The limit cycles can be understood assuming that adsorbed propylene oxide undergoes both oxidation to CO2 and H2O as well as conversion to an adsorbed polymeric residue. A dynamic model based on the above assumption explains qualitatively the experimental observations. 

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