Catalysts, general cylindrical

Figure 43 Schematic of an electrochemically promoted metal catalyst film supported on an 0 conductor (top) and schematic of cylindrical or, more generally, fixed cross-section nanoparticles deposited on an 0 conducting support (bottom). (From Ref. 138.)...

The typical radial flow fixed bed reactor configuration shown in Fig. 13.1b is considered here. The reactor configuration is axis symmetric. Details of reactor construction are shown in Fig. 13.2 (only half of the reactor is shown since it is symmetric). The annular catalyst bed is supported by permeable cylindrical screens (inner and outer) and impermeable top and bottom cover plates. The top cover plate also comprises of a shroud as shown in Fig. 13.2. Such a shroud is generally provided to compensate for possible shrinkage in catalyst bed height with time. Reactants are fed to the reactor from the top end. The flow changes direction after hitting the cover plate. The feed enters the catalyst bed from the annular space between the catalyst bed and the... 

The reactor system and general experimental procedures were similar to those described by Zmcevic et al. [11] and are discussed in detail in our former paper [12]. Deactivation measurements were carried out in an isothermal fixed-bed reactor with a hydrogen partial pressure of 99.82 kPa, benzene partial pressure of 7.55 kPa, thiophene partial pressure of 0.032 kPa and reaction temperatures fi om 403 to 473 K. The size of commercial cylindrical catalyst pellets suppli by BASF was 5x5 mm (21% Ni on alumina). The catalyst was activated by reduction with hydrogen at 743 K for 10 h. 

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 ... 

The following discussion represents a detailed description of the mass balance for any species in a reactive mixture. In general, there are four mass transfer rate processes that must be considered accumulation, convection, diffusion, and sources or sinks due to chemical reactions. The units of each term in the integral form of the mass transfer equation are moles of component i per time. In differential form, the units of each term are moles of component i per volnme per time. This is achieved when the mass balance is divided by the finite control volume, which shrinks to a point within the region of interest in the limit when aU dimensions of the control volume become infinitesimally small. In this development, the size of the control volume V (t) is time dependent because, at each point on the surface of this volume element, the control volnme moves with velocity surface, which could be different from the local fluid velocity of component i, V,. Since there are several choices for this control volume within the region of interest, it is appropriate to consider an arbitrary volume element with the characteristics described above. For specific problems, it is advantageous to use a control volume that matches the symmetry of the macroscopic boundaries. This is illustrated in subsequent chapters for catalysts with rectangular, cylindrical, and spherical symmetry. 

The first boundary condition is equivalent to a finite value of I a at the symmetry point in spherical coordinates. This condition was invoked in Section 17.2 along the symmetry axis of long cylindrical catalysts to eliminate the modified zeroth-order Bessel function of the second kind, = 0), from the general solution given by equation (17-22). When the symmetry condition at the center of a spherical pellet is used to evaluate the integration constants, one finds that B = 0 in equation (17-28) because ... 

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. 

The use of cylindrical internal reflectance cells for HP-IR was pioneered by Moser and further modified by others.This method involves the use of an optically transparent internal reflectance crystal (typically ZnS, ZnSe, sapphire). Due to the inherently short path length, the method is not as sensitive as transmission-based IR, and a Fourier transform infrared (FTIR) spectrometer is therefore generally required. In addition, the type of crystal may need to be changed depending on the reaction of interest, as the optics may be corroded by some reagents or catalysts. However, as the path length is fixed regardless of conditions, it is much easier to quantify catalyst species, and unlike transmission systems the cells can also be used for the study of liquid-solid and gas-liquid-solid mixtures. ... 

A single cylindrical pore of length L and radius of r (=d) located in a microscopic section of the catalyst particle is generally used for modeling the diffusion-reaction process (Figure 2.3). The steady-state component mass balance for a control volume extending over the cross section of the pore includes diffusion of reactant into and out of the control volume as well as reaction on the inner wall surface. The simple case taken as an example is that of an isothermal, irreversihle first-order reaction ... 

The single pore model is equivalent to the model for a slab-like particle. In fact, the conservation equation for the liquid phase (Eq. 1.5) can be written in a general form applicable to slab-like, cylindrical, and spherical particles (Lee 1984). The catalyst distribution at the end of the pore-filling period (Z), which is the approximate distribution that results after fast drying, is given by ... 

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