Shape of the catalyst

A weU-known feature of olefin polymerisation with Ziegler-Natta catalysts is the repHcation phenomenon ia which the growing polymer particle mimics the shape of the catalyst (101). This phenomenon allows morphological control of the polymer particle, particularly sise, shape, sise distribution, and compactness, which greatiy influences the polymerisation processes (102). In one example, the polymer particle has the same spherical shape as the catalyst particle, but with a diameter approximately 40 times larger (96). 

A catalyst manufactured using a shaped support assumes the same general size and shape of the support, and this is an important consideration in the process design, since these properties determine packing density and the pressure drop across the reactor. Depending on the nature of the main reaction and any side reactions, the contact time of the reactants and products with the catalyst must be optimized for maximum overall efficiency. Since this is frequendy accompHshed by altering dow rates, described in terms of space velocity, the size and shape of the catalyst must be selected carehiUy to allow operation within the capabiUties of the hardware. 

The effectiveness factor depends, not only on the reaction rate constant and the effective diffusivity, but also on the size and shape of the catalyst pellets. In the following analysis detailed consideration is given to particles of two regular shapes ... 

The shape of the catalyst body influences the mass transport characteristics as well as the pressure drop in a catalyst bed, as the following example shows. If one... 

Solid catalysts can be subdivided further according to the reactor chosen. Dependent on the type of reactor the optimal dimensions and shapes of the catalyst particles differ. Catalysts applied in fixed beds are relatively large particles (typically several mm in diameter) in order to avoid excessive pressure drops. Extrudates, tablets, and rings are the common shapes. Figure 3.9 shows some commonly encountered particle shapes. 

The effectiveness factor depends on the size and shape of the catalyst pellet and the distribution of active material within the pellet. 

Internal diffusion ofreactants. This step depends on the porosity of the catalyst and the size and shape of the catalyst particles, and occurs together with the surface reaction. The active catalyst component is usually highly dispersed within the three-dimensional porous support. The reactant molecules have to diffuse through the network of pores toward the active sites. The activation energy for pore diffusion li2 may represent a substantial share of the activation energy of the chemical reaction itself. 

The catalyst activity depends not only on the chemical composition but also on the diffusion properties of the catalyst material and on the size and shape of the catalyst pellets because transport limitations through the gas boundary layer around the pellets and through the porous material reduce the overall reaction rate. The influence of gas film restrictions, which depends on the pellet size and gas velocity, is usually low in sulphuric acid converters. The effective diffusivity in the catalyst depends on the porosity, the pore size distribution, and the tortuosity of the pore system. It may be improved in the design of the carrier by e.g. increasing the porosity or the pore size, but usually such improvements will also lead to a reduction of mechanical strength. The effect of transport restrictions is normally expressed as an effectiveness factor q defined as the ratio between observed reaction rate for a catalyst pellet and the intrinsic reaction rate, i.e. the hypothetical reaction rate if bulk or surface conditions (temperature, pressure, concentrations) prevailed throughout the pellet [11], For particles with the same intrinsic reaction rate and the same pore system, the surface effectiveness factor only depends on an equivalent particle diameter given by... 

In order to optimize the size and shape of the catalyst particle, activities for pellets produced from the same material were measured for different sizes and shapes. Some of the results are reported in Table 2. The measured ki values show that 9-mm particles are 35% more active than 12-mm particles and that the activity of a 9-mm VK69 is 2.3 times better than a conventional VK38 in the form of a 12-mm Daisy. 

CuO nanostructures of variable shapes CuO nanospheres (5-10 run), CuO nanorods (WXL = 24-27 nmxl24-140 run) and CuO nanowires (WXL= 8-10 nmx230-270 nm) have been synthesised to study the effect of shape of the catalyst on the Cu(I)-catalyzed click azide-alkyne cycloaddition. Cu(I) species were generated in situ by the reduction of CuO nanostructures in the presence of sodium... 

The shape of the catalyst pellets. The shape (cylinders, rings, spheres, monoliths) influence the void fraction, the flow and diffusion phenomena and the mechanical strength. 

The flow phenomena in TBR are not easy to predict, because of the large number of variables such a bed porosity, size and shape of the catalyst, viscosity, density, interfacial tension, flowrates, and reactor dimensions. 

The shape of the catalysts does not appreciably affect the effectiveness factor. Emig and Holfman (5) have shown that the greatest difference between the effectiveness factors of such diverse shapes as sphere and infinite plate remain within 10%. Therefore, if effectiveness factor is known for one catalyst shape, it can be used for other forms with slight error. 

The region over which this balance is invoked is the heterogeneous porous catalyst pellet which, for the sake of simplicity, is described as a pscudohomoge-ncous substitute system with regular pore structure. This virtual replacement of the heterogeneous catalyst pellet by a fictitious continuous phase allows a convenient representation of the mass and enthalpy conservation laws in the form of differential equations. Moreover, the three-dimensional shape of the catalyst pellet is replaced by assuming a one-dimensional model... 

Obviously the effectiveness factor, r, depends upon the effective diffusion coefficient, DeA, and kinetic parameters such as a first-order rate coefficient, kVipi as well as on the shape of the catalyst pellet. 

The final size and shape of the catalyst particles are determined in the shape formation process, which may also affect the pore size and pore size distribution. Larger pores can be introduced into a catalyst by incorporating in the mixture 5 to 15 % wood, flour, cellulose, starch, or other materials that can subsequently be burned out. As a result, bidisperse catalyst particles are obtained. 

Here, T is the geometry factor (described in Chapter 6), which depends only on the shape of the catalyst pellet, and 0 is the Thiele modulus defined by... 

In the extrinsic reaction rate, mass transfer plays a dominant role. The combined effect of the molecular diflusion of the reactants from the bulk gas through the gas film around a catalyst particle to the geometrical surface of the particle, and to some extent the Knudsen diflusion within the catalyst pores, are the limiting factors. As the intrinsic reaction is fast, the reactants will have reacted before they travel down the lenght of the pore. The effectivity of a steam reforming catalyst, that is, how much of the catalyst particle is utilized, varies with the reaction conditions and is only about 1 % at the exit. Because of this, the apparent activity increases with decreasing particle size, and the geometrical shape of the catalyst particle also has a distinct influence (Section 4.1.1.3). 

Also important is the effect of the size and shape of the catalysts [428] on heat transfer and consequently performance. Unlike the most processes carried out under substantially adiabatic conditions, the endothermic steam reforming reaction in the tubes of the primary reformer has to be supplied continuously with heat as the gas passes through the catalyst. The strong dependency of the reaction rate on the surface temperature of the catalyst clearly underlines the need for efficient heat transfer over the whole length and crosssection of the catalyst. However, the catalyst material itself is a very poor conductor and does not transfer heat to any significant extent. Therefore, the main mechanism of heat transfer from the inner tube wall to the gas is convection, and its efficiency will depend on how well the gas flow is distributed in the catalyst bed. It is thus evident that the geometry of the catalyst particles is important. 

In many processes of interest to the hydrocarbon processing industry the size and shape of the catalyst has been chosen as a compromise between catalyst effectiveness and pressure drop. Hence, with effectiveness factors for the main reaction somewhat below 1, intraparticle pore diffusion is generally a factor to be reckoned with. Its effect is not easily quantified since the processing of a practical feedstock involves the conversion of a large variety of molecules with widely different reaction rates and therefore the translation of catalyst performance data obtained with crushed particles to that of the actual catalyst may be difficult and of questionable validity. 

It is found by HRTEM analysis that (002) graphite planes are parallel to (111) planes of fee lattiees for most eatalyst partieles and fillings. Sometimes fee partieles were found oriented inside a nanotube in aecordanee with the following relationship (002)graphite II (002)n, ai- A Ni eatalyst partiele of octahedron shape, located inside carbon nanofiber is shown in Fig. 1. The [100] direction of the particle coincides with the longitudinal nanofiber axis. Faceted shape of the catalyst indicates that diffusion of carbon atoms (bulk and surface) takes place, because otherwise catalyst particles of spherical shape are usually supposed. Authors of [1,2] found other orientations of Ni particles inside carbon nanofibers in addition to the above mentioned [110] and [111]. 

The extent of mass transport control in the reaction is a function of the gas pressure and flow rate as well as the quantity and shape of the catalyst. As described for the two phase liquid flow reactions, the possibility of mass transport limitation can be determined by examining the change in product formation for a given flow rate produced by varying the substratexatalyst contact time or the catalyst substrate ratio. 

Obviously, the internal effectiveness factor, qi, depends on the effective diffusivity, Dg, and kinetic parameters such as the rate coefficient, fcy,p/ but also on the shape of the catalyst particle. 

Figure 3. Appearance of a carton filament generated from the interaction of Cu-Fc (2 8) with a CO/Hi (4 1) mixture at tOO C, Note the geometric shape of the catalyst particle.

As expected, the behavior of Catalyst System-C was similar to that of Catalyst System-B in view of similar HDM catalyst guard at the front end. However, the reactors pressure drop was much higher from the SOR itself, enforcing a lower Gas/Oil ratio that resulted in enhanced catalyst fouling and deactivation. The higher pressure drop was related to the characteristics (i.e. size and shape) of the catalyst. The products yield was, as expected, similar to that of Catalyst System-B. 

The polymer flake size and shape is an enlarged copy in size and shape of the catalyst particle. The average diameter of the polymer particles depends on the average diameter of the catalyst and on the extent of polymerization. 

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