Cylindrical catalyst pellet

Ross (R2) measured liquid-phase holdup and residence-time distribution by a tracer-pulse technique. Experiments were carried out for cocurrent flow in model columns of 2- and 4-in. diameter with air and water as fluid media, as well as in pilot-scale and industrial-scale reactors of 2-in. and 6.5-ft diameters used for the catalytic hydrogenation of petroleum fractions. The columns were packed with commercial cylindrical catalyst pellets of -in. diameter and length. The liquid holdup was from 40 to 50% of total bed volume for nominal liquid velocities from 8 to 200 ft/hr in the model reactors, from 26 to 32% of volume for nominal liquid velocities from 6 to 10.5 ft/hr in the pilot unit, and from 20 to 27 % for nominal liquid velocities from 27.9 to 68.6 ft/hr in the industrial unit. In that work, a few sets of results of residence-time distribution experiments are reported in graphical form, as tracer-response curves. 

Our very first experiments with the reactor depicted in Figure 5.4.1 were carried out with a 15% Pt-Y-Al203 single cylindrical catalyst pellet [10-12], The acquisition time of 2D images of an axial slice at that time was about 260 s. Despite this, the first direct MRI visualization of the operation of a model gas-liquid-solid reactor has revealed the existence of large gradients of the liquid phase content within the catalyst pellet upon imbibition of liquid a-methylstyrene (AMS) under conditions... 

No practical catalyst pellet can be described by the geometry of the wafer, yet it will be shown that eqn. (6), albeit with a slightly different interpretation of the Thiele modulus, 0, is of practical value. For a cylindrical catalyst pellet (a shape often used in practice) of radius r and sealed at its flat ends... 

Hollow cylindrical catalyst pellets are sometimes employed in commercial chemical reactors in order to avoid excessive pressure drops across a packed bed of catalyst. A more complex expression for the effectiveness factor is obtained for such geometry. This case was first discussed by Gunn [4]. Figure 2 illustrates the effectiveness factor curves obtained for the slab, sphere and cylinder. 

Derive an expression for the effectiveness factor of a cylindrical catalyst pellet, scaled at both ends, in which a first-order chemical reaction occurs. 

The kinetic experiments, activity tests, and poisoning experiments were carried out in a gas-flow isothermal fixed bed reactor [6) at the benzene partial pressure of 7.55 kPa hydro gen partial pressure 99.82 kPa thiophene partial pressure 0.032 kPa and the reaction temperatures 403, 427 and 448 K. The size of the commercial cylindrical catalyst pellet was 5x5mm (21% Ni on alumina, supplied by BASF). The nickel oxide containing precursor was activated by reduction with hydrogen at 743 K for 10 hr. 

Without any prove it is stated here that the geometry factor T falls between the two extremes of 2/3 for the infinitely long slab and of 6/s for the sphere for almost all practical cases. Thus T is almost always close to unity. This holds for any catalyst geometry, hence also for catalyst geometry s commonly found in industry, for example ring-shaped or cylindrical catalyst pellets. For this type of pellet it can be shown (Appendix C) that the geometry factor T equals ... 

Thus for < = 0 the ring-shaped catalyst pellet becomes a cylindrical catalyst pellet. Equation 6.41 is illustrated in Figure 6.10. In this diagram 1 is plotted versus A lines with a constant geometry factor T are drawn. The four comers of the diagram represent... 

Cylindrical catalyst pellets, whether hollow or not, are often given shape by extrusion of a paste of wet catalyst (Chapter 3). During this process the diameter of pores in the radial direction will become smaller, whereas for pores in the longitudinal direction the length will decrease. This can result in a radial effective diffusivity being smaller than the longitudinal one. Thus cylindrical catalyst pellets can be anistropic. 

The following reaction is carried out in a cylindrical catalyst pellet A + 2B- P... 

Ross 3 Model Cylindrical catalyst pellets, 0.48 cm diameter and length 5.1 cm 192.6 cm... 

This corresponds to the usual arrangement for testing cylindrical catalyst pellets. If the pore system is isotropic (randomly oriented) then B. k, and are also isotropic, with magnitudes B, k, and Vg. 

Next, the classical problem of diffusion with reaction in a cylindrical catalyst pellet is considered [8] [4]... 

Consider diffusion with a second-order reaction in a cylindrical catalyst pellet (exercise problem 2 chapter 3). Solve this problem using recursion technique described in section 10.1.2. 

Example 12-2 Using the intrinsic rate equation obtained in Example 12-1, calculate the global rate of the reaction o-Hj p- % at 400 psig and — 196°C, at a location where the mole fraction of ortho hydrogen in the bulk-gas stream is 0.65. The reactor is the same as described in Example 12-1 that is, it is a fixed-bed type with tube of 0.50 in. ID and with x -in. cylindrical catalyst pellets of Ni on AljOj. The superficial mass velocity of gas in the reactor is 15 lb/(hr)(ft ). The effective diffusivity can be estimated from the random-pore model if we assume that diffusion is predominately in the macropores where Knudsen diffusion is insignificant. The macroporosity of the pellets is 0.36. Other properties and conditions are those given in Example 12-1. 

Let us consider the potential and concentration distribution across a cylindrical catalyst pellet. The geometry is set up as shown in Figure 18.6. The electrolyte flows along the axial direction and the charge-transfer reaction takes place on the surface of the catalyst pellet. 

FIGURE 18.6 Concentration and potential distribution within the electrolyte undergoing an electrochemical reaction on a cylindrical catalyst pellet the definition of the geometric coordinates. 

FIGURE 18.7 Potential and concentration distribution in the vicinity of a cylindrical catalyst pellet Y— 1.0 corresponds to the surface of the pellet and Y — 0.0 corresponds to the bulk electrolyte. X = 0 is the initial point of contact of the incoming stream to the catalyst and X — 1 is the point of exit. 

Thermal effects constitute a significant portion of the study devoted to catalysis. This is true of electrochemical reactions as well. In general the reaction rate constants, diffusion coefficients, and conductivities all exhibit Arrhenius-type dependence on temperature, and as a rule of the thumb, for every 10°C rise in temperature, most reaction rates are doubled. Hence, temperature effects must be incorporated into the parameter values. Fourier s law governs the distribution of temperature. For the example with the cylindrical catalyst pellet described in the previous section, the equation corresponding to the energy balance can be written in the dimensionless form as follows ... 

A partial oxidation is carried out by passing air with 1.2 mole percent hydrocarbon through 40-rnm tubes packed with 2 m of 3-by-3-mm cylindrical catalyst pellets. The air enters at 350 C and 2.0 atm with a superficial velocity of 1 m/s. What is the pressure drop through the packed tubes How much would the pressure drop be reduced by using 4-mm pellets Assume = 0.40. 

Cylindrical catalyst pellets can be prepared by extrusion or by pelletization. For short, stubby cylinders L/dp = 1), the effectiveness factor equation for a sphere is generally used with R equal to the cylinder radius. (The surface-to-volume ratio for the cylinder is i /3, the same as for the sphere, though the cylinder has 30% more surface area than a sphere of the same volume.) For long cylinders, the effectiveness factor is less than for a sphere of the same radius, since the surface-to-volume ratio is lower. Numerical solutions are available for different L/dp ratios, but the solution for spheres can be used for approximate values of if i in the modulus is replaced with. 2R for L/d = 2, 1.33 R for L/d = 4, and 1.5i for a very long cylinder. 

We were unable to complete the solution to Example 3.3 in order to find the effectiveness factor for cylindrical catalyst pellets. Thus, we found the expression for composition profile to be... 

In place of the earlier cylindrical catalyst pellets, spherical pellets with smooth or porous surfaces made from porcelain, magnesium silicate, quartz and silicon carbide are used to obtain higher space velocities. A very thin layer of V205/T102 is applied to the carrier to manufacture the catalyst a ratio of Ti02 to V2O5 with 2 to 15% V2O5 in the active mass has been found to be very efficient. Contact time is between 0.15 to 0.6 sec. Current service life of the catalyst is of the order of 2 to 4 years. 

Figure 6.17.11 shows experimental results of the epimerization at three different temperatures for a small particle size (0.5-1 mm), which represent the intrinsic kinetics, and for the original 6 x 6 mm cylindrical catalyst pellets, where pore diffusion limitations lead to a decrease of the effective reaction rate. The experiments were conducted in the well-mixed batch reactor. As expected, the influence of mass transfer increases with increasing temperature and becomes strong at 200°C. Note that for clarity Figure 6.17.11 only shows the change of menthol concentration and not of the other two stereoisomers (as in Figure 6.17.5). In addition, note that the initial menthol concentration is not zero as an industrially relevant feed was used. The dashed and solid lines in Figure 6.17.11 represent the results of the calculation by the method described before, showing a good agreement with the experimental data.

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