Porous Catalyst Pellets

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... 

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. 

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. 

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]. 

Galerldn Finite Element Method In the finite element method, the domain is divided into elements and an expansion is made for the solution on each finite element. In the Galerldn finite element method an additional idea is introduced the Galerldn method is used to solve the equation. The Galerldn method is explained before the finite element basis set is introduced, using the equations for reaction and diffusion in a porous catalyst pellet. 

S. Stapf, X. Ren, E. Talnishnikh, B. Bliimich 2005, (Spatial distribution of coke residues in porous catalyst pellets analyzed by field-cycling relaxometry and parameter imaging), Magn. Reson. Imag. 23, 383. 

The success of periodic flow interruption is due to the liquid static holdup within the porous catalyst pellets and the interstices of the catalyst bed. 

The Effectiveness Factor Analysis in Terms of Effective Diffusivities First-Order Reactions on Spherical Pellets. Useful expressions for catalyst effectiveness factors may also be developed in terms of the concept of effective diffusivities. This approach permits one to write an expression for the mass transfer within the pellet in terms of a form of Fick s first law based on the superficial cross-sectional area of a porous medium. We thereby circumvent the necessity of developing a detailed mathematical model of the pore geometry and size distribution. This subsection is devoted to an analysis of simultaneous mass transfer and chemical reaction in porous catalyst pellets in terms of the effective diffusivity. In order to use the analysis with confidence, the effective diffusivity should be determined experimentally, since it is difficult to obtain accurate estimates of this parameter on an a priori basis. 

Thus a zero-order reaction appears to be 1/2 order and a second-order reaction appears to be 3/2 order when dealing with a fast reaction taking place in porous catalyst pellets. First-order reactions do not appear to undergo a shift in reaction order in going from high to low effectiveness factors. These statements presume that the combined diffusivity lies in the Knudsen range, so that this parameter is pressure independent. 

For porous catalyst pellets with practical loadings, this quantity is typically much larger than the pellet void fraction e, indicating that the dynamic behavior of supported catalysts il dominated by the relaxation of surface phenomena (e.g., 35, 36). This implies that a quasi-static approximation for Equation (1) (i.e., e = 0) can often be safely invoked in the transient modeling of porous catalyst pellets. The calculations showed that the quasi-static approximation is indeed valid in our case the model predicted virtually the same step responses, even when the value of tp was reduced by a factor of 10. 

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. 

A reaction A R is to take place on a porous catalyst pellet (dp = 6 mm, = 10" m /m cat s). How much is the rate slowed by pore diffu-sional resistance if the concentration of reactant bathing the particle is 100 mol/m and the diffusion-free kinetics are given by... 

The observed deactivation of a porous catalyst pellet depends on a number of factors the actual decay reactions, the presence or absence of pore diffusion slowdown, the way poisons act on the surface, etc. We consider these in turn. 

Figure 7-5 Porous catalyst pellets consisting of spheres or grains pressed together into spheres or cylinders. Reactants must diffuse into the pellet in the space between spheres or grains and products must diffuse out of the pellet for reaction to occur. At the right is shown a monolith catalyst in which a ceramic is coated with a wash coat (gray) of porous catalyst.

Thus most catalysts consist of porous catalyst pellets that may be spherical, cylindrical, or planar and have a characteristic size chosen for desired reactor properties, as we will consider later in this chapter. In most situations reaction occurs throughout the porous peUet, not just on its external surface. 

We are also concerned with gradients in composition throughout the reactor. We have thus far been concerned only with the very small gradient dCj/dz down the reactor from inlet to exit, which we encounter in the species mass balance, which we must ultimately solve. Then there is the gradient in Cj around the catalyst pellet Finally, there is the gradient within the porous catalyst pellet and around the catalytic reaction site within the pellet As we consider... 

Figure 7-7 Reactant concentration profiles in directionx, which is perpendicular to the flow direction z expected for flow over porous catalyst pellets in a packed bed or sluny reactor. External mass transfer and pore diffusion produce the reactant concentration profiles shown.

Figure 7-9 Reactant concentration profiles around and within a porous catalyst pellet for the cases of reaction control, external mass transfer control, and pore difliision control. Each of these situations leads to different reaclion rate expressions.

Figure 7-11 Reactant concentration profiles within a porous catalyst pellet for situations where surface reaction controls aid vdiere pore difiusion controls the reactions.

Figure 7-13 Plots of effectiveness factor 17 versus Thiele modulus

Thus we can in general write for the pseudohomogeneous rate of a catalytic reaction in a reactor with porous catalyst pellets... 

As with the falling film reactor, the rate of mass transfer to the catalyst goes as R, while the size of the reactor goes as R, so this reactor becomes very inefficient except for very small-diameter tubes. However, we can overcome this problem, not by using many small tubes in parallel, but by allowing the gas and liquid to flow (trickle) over porous catalyst pellets in a trickle bed reactor rather than down a vertical wall, as in the catalytic wall reactor. 

All types of catalytic reactors with the catalyst in a fixed bed have some common drawbacks, which are characteristic of stationary beds (Mukhlyonov et al., 1979). First, only comparatively large-grain catalysts, not less that 4 mm in diameter, can be used in a filtering bed, since smaller particles cause increased pressure drop. Second, the area of the inner surface of large particles is utilized poorly and this results in a decrease in the utilization (capacity) of the catalyst. Moreover, the particles of a stationary bed tend to sinter and cake, which results in an increased pressure drop, uneven distribution of the gas, and lower catalyst activity. Finally, porous catalyst pellets exhibit low heat conductivity and as a result the rate of heat transfer from the bed to the heat exchanger surface is very low. Intensive heat removal and a uniform temperature distribution over the cross-section of a stationary bed cannot, therefore, be achieved. The poor conditions of heat transfer within... 

The problem is also more complex when heterogeneous catalysed reactions are considered. With porous catalyst pellets, reaction occurs at gas- or liquid-solid interfaces at the outer or inner sphere. When the reactants diffuse only slowly from the bulk phase to the exterior surface of the catalyst, gas or liquid film resistance must be taken into account. Pore diffusion resistance may be involved when the reactants move through the pores into the pellet. 

Temperature gradients in porous catalyst pellets. Ind. Eng. Chem. Fund. 17,309-313 (1978). 

Show that the selectivity of two concurrent first-order reactions occurring in flat-shaped porous catalyst pellets is independent of the effect of either heat or mass transfer if the activation energies of both reactions are equal. 

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