Catalytic kinetics porous particle

For a more detailed analysis of measured transport restrictions and reaction kinetics, a more complex reactor simulation tool developed at Haldor Topsoe was used. The model used for sulphuric acid catalyst assumes plug flow and integrates differential mass and heat balances through the reactor length [16], The bulk effectiveness factor for the catalyst pellets is determined by solution of differential equations for catalytic reaction coupled with mass and heat transport through the porous catalyst pellet and with a film model for external transport restrictions. The model was used both for optimization of particle size and development of intrinsic rate expressions. Even more complex models including radial profiles or dynamic terms may also be used when appropriate. 

Multiphase reactors include, for instance, gas-liquid-solid and gas-liq-uid-liquid reactions. In many important cases, reactions between gases and liquids occur in the presence of a porous solid catalyst. The reaction typically occurs at a catalytic site on the solid surface. The kinetics and transport steps include dissolution of gas into the liquid, transport of dissolved gas to the catalyst particle surface, and diffusion and reaction in the catalyst particle. Say the concentration of dissolved gas A in equilibrium with the gas-phase concentration of A is CaLt. Neglecting the gas-phase resistance, the series of rates involved are from the liquid side of the gas-liquid interface to the bulk liquid where the concentration is CaL, and from the bulk liquid to the surface of catalyst where the concentration is C0 and where the reaction rate is r wkC",. At steady state,... 

In heterogeneous catalysis reactants have to be transported to the catalyst and (if the catalyst is a porous, solid particle) also through the pores of the particle to the active material. In this case all kinds of transport resistance s may play a role, which prevent the catalyst from being fully effective in its industrial application. Furthermore, because appreciable heat effects accompany most reactions, heat has to be removed from the particle or supplied to it in order to keep it in the appropriate temperature range (where the catalyst is really fully effective). Furthermore, heterogeneous catalysis is one of the most complex branches of chemical kinetics. Rarely do we know the compositions, properties or concentrations of the reaction intermediates that exist on the surfaces covered with the catalytically effective material. TTie chemical factors that govern reaction rates under these conditions are less well known than in homogeneous catalysis. Yet solid catalysts display specificities for particular reactions, and selectivity s for desired products, that in most practical cases cannot be equaled in other ways. Thus use of solid catalysts and the proper (mathematical) tools to describe their performance are essential. 

It is, of course, fully realized that the activity of the porous catalyst will not be in all instances directly proportional to the total surface area of the solid as measured by the gas-adsorption technique. Actually, a thorough analysis of the kinetics of reaction in small pores has been shown by Wheeler (33, 34) to lead to the conclusion that under some conditions one would expect the reaction rate to be independent of the total surface area of a porous solid and proportional only to the outer or geometric area of the catalyst particle. Under still other conditions, the rate might be expected to depend on the square root of the surface area. In some instances, on the other hand, one might reasonably expect and indeed workers have already observed (35) a linear proportionality between the total surface area of a porous solid and its catalytic activity. 

The principles of homogeneous reaction kinetics and the equations derived there remain valid for the kinetics of heterogeneous catalytic reactions, provided that the concentrations and temperatures substituted in the equations are really those prevailing at the point of reaction. The formation of a surface complex is an essential feature of reactions catalyzed by solids and the kinetic equation must account for this. In addition, transport processes may influence the overall rate heat and mass transfer between the fluid and the solid or inside the porous solid, > that the conditions over the local reation site do not correspond to those in the bulk fluid around the catalyst particle. Figure 2.1-1 shows the seven steps involved when a molecule moves into the catalyst, reacts, and the product moves back to the bulk fluid stream. To simplify the notation the index s, referring to concentrations inside the solid, will be dropped in this chapter. 

Kinetics models of gas-solid non-catalytic reaction include uniform conversion model (UCN), multiple fine particle model (GPM), crack core model (CCM), phase-change model (PCM), change void model (CVM), thermal decomposition model (TDM), shrinking core model with multi-step reactions, and multi-step reaction model of formation porous structure in reaction etc. Among these models, the shrinking core model (SCM) is the most important and most widely used. For conversion of solid it is also the most simple and practical model. Commonly it is suitable for experimental data. However, it can only be used in some reactions of many solid reactions. A more complex model must be used in other cases. 

In addition to these kinetic steps, there are also physical processes of heat and mass transfer to be considered. The external transport problem is one of heat and species exchange through the boundary layer between the surrounding bulk fluid and the catalyst surface (Figure 5). Concentration and temperature gradients are necessarily present in this case and would have to be accounted for in the modeling equations. Also, there is often an internal transport problem of heat conduction through the catalytic material -- and in the case of porous catalyst particles, an internal diffusion problem as well. Internal transport problems are beyond the scope of this paper. It must be noted, however, that any model intended to describe real-life systems will have to account for these effects. 

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