Pellet catalyst

In the example discussed above, both the boundary conditions are of the Neumann type. However, many problems involve derivative boundary conditions. These problems can be handled by using the three point forward and backward differences at x = 0 and x = 1, respectively. This is illustrated by solving the cylindrical pellet problem solved in example 3.6 with a different boundary condition at the surface (x = 1)  

The Maple program developed for the previous example can be modified to handle the derivative boundary conditions  

The three point forward and backward difference expressions for the derivative are  

Now the result obtained is plotted for different values of the Thiele modulus O  

Now the result obtained is plotted for different values of Thiele modulus O. The results obtained for N = 10 interior node points are given below. 

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However, before extrapolating the arguments from the gross patterns through the reactor for homogeneous reactions to solid-catalyzed reactions, it must be recognized that in catalytic reactions the fluid in the interior of catalyst pellets may diSer from the main body of fluid. The local inhomogeneities caused by lowered reactant concentration within the catalyst pellets result in a product distribution different from that which would otherwise be observed. 

The final chapters, 11 and 12, are concerned with the particular application of transport theory to which this monograph is principally directed, namely the modeling of porous catalyst pellets. The behavior of a porous catalyst is described by differencial equations obtained from material and... 

In principle, Chen, given the flux relations there is no difficulty in constructing differencial equations to describe the behavior of a catalyst pellet in steady or unsteady states. In practice, however, this simple procedure is obstructed by the implicit nature of the flux relations, since an explicit solution of usefully compact form is obtainable only for binary mixtures- In steady states this impasse is avoided by using certain, relations between Che flux vectors which are associated with the stoichiometry of Che chemical reaction or reactions taking place in the pellet, and the major part of Chapter 11 is concerned with the derivation, application and limitations of these stoichiometric relations. Fortunately they permit practicable solution procedures to be constructed regardless of the number of substances in the reaction mixture, provided there are only one or two stoichiomeCrically independent chemical reactions. 

There is a further simplification which is often justifiable, but not by consideration of the flux equations above. The nature of many problems is such that, when the permeability becomes large, pressure gradients become very small ialuci uidiii iiux.es oecoming very large. in catalyst pellets, tor example, reaction rates limit Che attainable values of the fluxes, and it then follows from equation (5,19) that grad p - 0 as . But then the... 

This simplification must be used with caution, of course, making sure that the specification of the problem does not determine the magnitude of the pressure gradient, but it is very useful in the important case of a coarsely porous catalyst pellet. 

When a model is based on a picture of an interconnected network of pores of finite size, the question arises whether it may be assumed that the composition of the gas in the pores can be represented adequately by a smooth function of position in the medium. This is always true in the dusty gas model, where the solid material is regarded as dispersed on a molecular scale in the gas, but Is by no means necessarily so when the pores are pictured more realistically, and may be long compared with gaseous mean free paths. To see this, consider a reactive catalyst pellet with Long non-branching pores. The composition at a point within a given pore is... 

To be specific let us have in mind a picture of a porous catalyst pellet as an assembly of powder particles compacted into a rigid structure which is seamed by a system of pores, comprising the spaces between adjacent particles. Such a pore network would be expected to be thoroughly cross-linked on the scale of the powder particles. It is useful to have some quantitative idea of the sizes of various features of the catalyst structur< so let us take the powder particles to be of the order of 50p, in diameter. Then it is unlikely that the macropore effective diameters are much less than 10,000 X, while the mean free path at atmospheric pressure and ambient temperature, even for small molecules such as nitrogen, does not exceed... 

Chapter 11. STEADY STATE MATERIAL AND ENTHALPY BALANCES IN POROUS catalyst PELLETS... 

Having discussed at some length the formulation and testing of flux models for porous media, we will now review v at Is, perhaps, their most Important application - the formulation of material balances In porous catalyst pellets. 

We see, then, that pressure gradients must necessarily exist in catalyst pellets to free the fluxes from the constraints Imposed by Graham s relation (11,42), or Its generalization = 0 in multicomponent systems. Without this freedom the fluxes are unable to adjust to the demands... 

Now consider a catalyst pellet of arbitrary shape occupying a region V... 

A proper resolution of Che status of Che stoichiometric relations in the theory of steady states of catalyst pellets would be very desirable. Stewart s argument and the other fragmentary results presently available suggest they may always be satisfied for a single reaction when the boundary conditions correspond Co a uniform environment with no mass transfer resistance at the surface, regardless of the number of substances in Che mixture, the shape of the pellet, or the particular flux model used. However, this is no more than informed and perhaps wishful speculation. 

Reactions in porous catalyst pellets are Invariably accompanied by thermal effects associated with the heat of reaction. Particularly In the case of exothermic reactions these may have a marked influence on the solutions, and hence on the effectiveness factor, leading to effectiveness factors greater than unity and, In certain circumstances, multiple steady state solutions with given boundary conditions [78]. These phenomena have attracted a great deal of interest and attention in recent years, and an excellent account of our present state of knowledge has been given by Arls [45]. 

Despite the very restricted circumstances In which these equations properly describe the dynamical behavior, they are the starting point for almost all the extensive literature on the stability of steady states in catalyst pellets. It is therefore Interesting to examine the case of a binary mixture at the opposite limit, where bulk diffusion controls, to see what form the dynamical equations should take in a coarsely porous pellet. 

Apart from this simple result, comparison of stability predictions for the two limiting situations can be made only by direct numerical computation, and for this purpose a specific algebraic form must be assumed for the reaction rate function, and a specific shape for che catalyst pellet. In particular, Lee and Luss considered a spherical pellet and a first order... 

Navler-Stokes equation, 26 Non-isothermal catalyst pellet, 156-... 

Maintenance of isothermal conditions requires special care. Temperature differences should be minimised and heat-transfer coefficients and surface areas maximized. Electric heaters, steam jackets, or molten salt baths are often used for such purposes. Separate heating or cooling circuits and controls are used with inlet and oudet lines to minimize end effects. Pressure or thermal transients can result in longer Hved transients in the individual catalyst pellets, because concentration and temperature gradients within catalyst pores adjust slowly. 

Incieased catalyst-bed piessuie diop caused by dust fouling reduces production of acid and significantly increases energy consumption by the plant s blower. To avoid these problems, first converter-pass catalyst pellets are screened at every significant turnaround, typically every 12—24 months. 

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