Concentration profile catalyst pore

GL 18] [R 6a] [P 17] CFD calculations were performed to give the Pd concentration profile in a nanopore of the oxide catalyst carrier layer [17]. For wet-chemical deposition most of the catalyst was deposited in the pore mouth, in the first 4 pm of the pore. Hence most of the hydrogenation reaction is expected to occur in this location. For electrochemical deposition, large fractions of the catalyst are located in both the pore mouth and base. Since the pore base is not expected to contribute to large extent to hydrogenation, a worse performance was predicted for this case. 

Ordinary or bulk diffusion is primarily responsible for molecular transport when the mean free path of a molecule is small compared with the diameter of the pore. At 1 atm the mean free path of typical gaseous species is of the order of 10 5 cm or 103 A. In pores larger than 1CT4 cm the mean free path is much smaller than the pore dimension, and collisions with other gas phase molecules will occur much more often than collisions with the pore walls. Under these circumstances the effective diffusivity will be independent of the pore diameter and, within a given catalyst pore, ordinary bulk diffusion coefficients may be used in Fick s first law to evaluate the rate of mass transfer and the concentration profile in the pore. In industrial practice there are three general classes of reaction conditions for which the bulk value of the diffusion coefficient is appropriate. For all catalysts these include liquid phase reactions... 

Assuming that there are only axial and no radial concentration gradients in the pore due to the negligible size of the pore diameter, the modeled concentration profiles of CO, H2, and H20 in a wax-filled cylindrical pore are given in Figure 12.2 (left, Presto Kinetics). For verification reasons of the underlying model and to obtain a better visual impression of the respective processes in the catalyst pore,... 

A kinetics or reaction model must take into account the various individual processes involved in the overall process. We picture the reaction itself taking place on solid B surface somewhere within the particle, but to arrive at the surface, reactant A must make its way from the bulk-gas phase to the interior of the particle. This suggests the possibility of gas-phase resistances similar to those in a catalyst particle (Figure 8.9) external mass-transfer resistance in the vicinity of the exterior surface of the particle, and interior diffusion resistance through pores of both product formed and unreacted reactant. The situation is illustrated in Figure 9.1 for an isothermal spherical particle of radius A at a particular instant of time, in terms of the general case and two extreme cases. These extreme cases form the bases for relatively simple models, with corresponding concentration profiles for A and B. 

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 7-12 Reactant concentration profiles down a single catalyst pore of length and diameter dp with a catalytic reaction occurring on the walls of the pore. The concentration is Cm t the pore mouth, x = (, and the gradient is zero at the end of the pore because the end is assumed to be unreactive and there is therefore no flux of reactant through the end.

Figure 7-20 Sketch of tube wall reactor with a porous catalyst film of thickness t on walls. Expected reactant concentration profiles with reaction-limited, mass-transfer-limited, and pore-diffusion-limited reaction.

An effect of pore diffusion in residuum demetallation is illustrated in Figure 9, which shows nickel and vanadium concentration profiles measured through a catalyst pill after residuum desulfurizing service. The catalyst originally contained neither of these metals. These profiles confirm that the rate of reaction of the metal-containing molecules in the feed (particularly the vanadium compounds) is high compared with their rate of diffusion. 

In addition to catalyst pore structure, catalytic metals content can also influence the distribution of deposited metals. Vanadium radial profile comparisons of aged catalysts demonstrated that a high concentration of Co + Mo increases the reaction rate relative to diffusion, lowering the effectiveness factor and the distribution parameter (Pazos et al., 1983). While minimizing the content of Co and Mo on the catalyst is effective for increasing the effectiveness factor for HDM, it may also reduce the reaction rate for the HDS reactions. Lower space velocity or larger reactors would then be needed to attain the same desulfurization severity. 

Figure 5 shows the dependence of the effectiveness factor on the Thiele modulus for the different pellet shapes. At small values of 4> the effectiveness factor approaches unity in all cases. Here, the chemical reaction constitutes the rate determining step—the corresponding concentration profiles over the pellet cross-section arc flat (sec Fig. 4). This situation may occur at low catalyst activity (k is small), large pore size and high porosity (Dc is large), and/or small catalyst pellets (R is small, i.c. in fluidized bed reactors R is typically around 50 /im).

The conditions are substantially more favorable for the microporous catalytic membrane reactor concept. In this case the membrane wall consists of catalyti-cally active, microporous material. If a simple reaction A -> B takes place and no permeate is withdrawn, the concentration profiles are identical to those in a catalyst slab (Fig. 29a). By purging the permeate side with an inert gas or by applying a small total pressure difference, a permeate with a composition similar to that in the center of the catalyst pellet can be obtained (Fig. 29b). In this case almost 100% conversion over a reaction length of only a few millimeters is possible. The advantages are even more pronounced, if a selectivity-limited reaction is considered. This is shown with the simple consecutive reaction A- B- C where B is the desired product. Pore diffusion reduces the yield of B since in a catalyst slab B has to diffuse backwards from the place where it was formed, thereby being partly converted to C (Fig. 29c). This is the reason why in practice rapid consecutive reactions like partial oxidations are often run in pellets composed of a thin shell of active catalyst on an inert support [30],... 

The work of Rostrup-Nielsen is very informative, but it also raises a number of important questions. How can more realistic temperature and concentration profiles through the reactor be incorporated into a reactor deactivation model Could experimental measurements be performed to determine how sulfur is actually distributed in the catalyst pellets and in the bed and how this distribution changes as a function of time at various H2S concentrations Would it be worthwhile to consider a modification of the model by Wise and co-workers (195,233) for steam reforming in which pore... 

Because of the large pores of the catalysts and the dilution with steam in a wa-ter butene ratio of 12, constant molecular diffusion coefficients of 9.69 xlO 5 mV1 (butene/water) and 9.95 xlO"5 m2 s1 (butadiene/water) at a temperature of 933 K can be assumed The porous structure of the catalyst is represented by a sjyp value of 0.1. The concentration profiles are given by Equations 8.22 and 8.23 for plate geometry. The results for R = 10 mm and R = 2 mm are shown in Figure 8.11 with = 0. 

Eifect of Thiele modulus on the normalized concentration profiles in a catalyst pore with first-order surface reaction. 

The modeling of mass transfer and reaction in catalytic filters can be compared, in a first approximation, with the twin problem concerning honeycomb catalysts. The pores of the filters will have as counterparts the channels of the monolith, whereas the catalyst layer deposited on the pore walls of the filter will be related to the wall separating the honeycomb channels, which in general are made exclusively of catalytic material. Considering, for example, the DeNOx reaction. Fig. 9 shows schematically the NO concentration profiles within the channels/pores and the catalyst wall/layer of the two reactor configurations. 

Deactivation of large-pore slab catalysts where intraparticle convection, diffusion and first order reaction are competing mechanisms was analyzed by uniform and shelLprogressive models. For each situation, analytical solutions for concentration profiles, effectiveness factor and enhancement factor due to convection were developed thus providing a sound basis for steady-state reactor design. 

Figure 10 Schematic of catalyst particle showing concentration profiles inside a pore and two reactor configurations for large-scale conversion.

In the general case where the active material is dispersed through the pellet and the catalyst is porous, internal diffusion of the species within the pores of the pellet must be included. In fact, for many cases diffusion through catalyst pores represents the main resistance to mass transfer. Therefore, the concentration and temperature profiles inside the catalyst particles are usually not flat and the reaction rates in the solid phase are not constant. As there is a continuous variation in concentration and temperature inside the pellet, differential conservation equations are required to describe the concentration and temperature profiles. These profiles are used with intrinsic rate equations to integrate through the pellet and to obtain the overall rate of reaction for the pellet. The differential equations for the catalyst pellet are two point boundary value differential equations and besides the intrinsic kinetics they require the effective diffusivity and thermal conductivity of the porous pellet. 

BET surface areas of the porous films were measured by nitrogen adsorption at -196 °C after the BET method by using a Fisons Sorptomatic 1900. The surface of the catalysts and the pore structure were examined by scanning electron microscopy (SEM) in a Hitachi S-570 scanning electron microscope. The concentration profile of the chemical elements along the oxide film was determined by energy-dispersive X-ray spectroscopy (EDX). 

Diffusion of reactants to the external surface is the first step in a solid-catalyzed reaction, and this is followed by simultaneous diffusion and reaction in the pores, as discussed in Chapter 4. In developing the solutions for pore diffusion plus reaction, the surface concentrations of reactants and products are assumed to be known, and in many cases these concentrations are essentially the same as in the bulk fluid. However, for fast reactions, the concentration driving force for external mass transfer may become an appreciable fraction of the bulk concentration, and both external and internal diffusion must be allowed for. There may also be temperature differences to consider these will be discussed later. Typical concentration profiles near and in a catalyst particle are depicted in Figure 5.6. As a simplification, a linear concentration gradient is shown in the boundary layer, though the actual concentration profile is generally curved. 

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