Pellet model

For this reason we have undertaken the study of the deactivation of a Y zeolite in the form of a model pellet, firstly by the NMR of adsorbed Xe and then by H NMR imaging. 

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... 

When a model is based on a picture of an interconnected network of pores of finite size, the question arises whether it may be assumed that the composition of the gas in the pores can be represented adequately by a smooth function of position in the medium. This is always true in the dusty gas model, where the solid material is regarded as dispersed on a molecular scale in the gas, but Is by no means necessarily so when the pores are pictured more realistically, and may be long compared with gaseous mean free paths. To see this, consider a reactive catalyst pellet with Long non-branching pores. The composition at a point within a given pore is... 

The simplest way of introducing Che pore size distribution into the model is to permit just two possible sizes--Tnlcropores and macropotes--and this simple pore size distribution is not wholly unrealistic, since pelleted materials are prepared by compressing powder particles which are themselves porous on a much smaller scale. The small pores within the powder grains are then the micropores, while the interstices between adjacent grains form the macropores. An early and well known model due to Wakao and Smith [32] represents such a material by the Idealized structure shown in Figure 8,2,... 

They then compared measured and predicted fluxes for diffusion experiments in the mixture He-N. The tests covered a range of pressures and a variety of compositions at the pellet faces but, like the model itself, they were confined to binary mixtures and isobaric conditions. Feng and Stewart [49] compared their models with isobaric flux measurements in binary mixtures and with some non-isobaric measurements in mixtures of helium and nitrogen, using data from a variety of sources. Unfortunately the information on experimental conditions provided in their paper is very sparse, so it is difficult to assess how broadly based are the conclusions they reached about the relative merits oi their different models. 

The bimodal pore distribution model used by Gibilaro et aL may also be used to analyze the results of this type of experiment. If it is assumed that all extraneous effects due to mixing in the interstices between the pellets have been eliminated by means of a control experiment, the results corresponding to equations (10.39) and (10.40) are now... 

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. 

At the opposite limit of bulk diffusion control and high permeability, all flux models are required to he consistent with the Stefan-Maxwell relations (8.3). Since only (n-1) of these are independent, they are insufficient to determine all the flux vectors, and they permit the problem to be formulated in closed form only when they can be supplemented by the stoichiometric relations (11.3). At this limit, therefore, attention must be restricted from the beginning to those simple pellet shapes for ich equations (11.3) have been justified. Furthermore, since the permeability tends to infininty, pressure gradients within the pellet tend to zero and... 

Let us compare computations of the effectiveness factor, using each of the three approximations we have described, with exact values from the complete dusty gas model. The calculations are performed for a first order reaction of the form A lOB in a spherical pellet. The stoichiometric coefficient 10 for the product is unrealistically large, but is chosen to emphasize any differences between the different approaches. 

The nearest thing to a complete justification of equations (11.3)i for pellets of arbitrary shape, is an argument given by W. E. Stewart [74], which does not depend on any particular choice of flux relations. In Chapter 10 it was pointed out that all isothermal flux models must have the general form... 

A proper resolution of Che status of Che stoichiometric relations in the theory of steady states of catalyst pellets would be very desirable. Stewart s argument and the other fragmentary results presently available suggest they may always be satisfied for a single reaction when the boundary conditions correspond Co a uniform environment with no mass transfer resistance at the surface, regardless of the number of substances in Che mixture, the shape of the pellet, or the particular flux model used. However, this is no more than informed and perhaps wishful speculation. 

This model is supported by an experiment described by Wei where a pellet bed at 80°F is swept suddenly by air at 800°F (127). The temperature rise in the bed is illustrated by considering the bed to be a series of cells. Each cell consists of 3 to 4 rows of catalysts, as shown in Fig. 24. 

Many elements of a mathematical model of the catalytic converter are available in the classical chemical reactor engineering literature. There are also many novel features in the automotive catalytic converter that need further analysis or even new formulations the transient analysis of catalytic beds, the shallow pellet bed, the monolith and the stacked and rolled screens, the negative order kinetics of CO oxidation over platinum,... 

Steady state models of the automobile catalytic converter have been reported in the literature 138), but only a dynamic model can do justice to the demands of an urban car. The central importance of the transient thermal behavior of the reactor was pointed out by Vardi and Biller, who made a model of the pellet bed without chemical reactions as a onedimensional continuum 139). The gas and the solid are assumed to have different temperatures, with heat transfer between the phases. The equations of heat balance are ... 

A comprehensive mathematical model of the pellet bed was developed in the IIEC program, and described by Wei 127) and by Kuo ei al. 21, H0). This model seeks to replace the catalytic bed by a series of cells with uniform temperatures and concentrations. The heat balance of the solid in cell i is given by... 

A Del Electronics, Model ESP-100A, electrostatic precipitator was used for sample collection. Cigarette smoke particles were found to give approx the same particle distribution pattern on the collection filter paper as the gunshot residue, and since the smoke stains the paper, this provided a v rapid technique for optimizing operation conditions. With a flow rate of 15cfm and a corona current of 125 uA, the residue collects primarily on a narrow band across the sample paper. Samples were collected on Whatman No 1541 filter paper which lined the inside of the sample collection tube. The presence of this paper allowed air to flow only thru the center of the tube, so particle collection was made upon the filter paper exclusively. The filter paper samples were pelletized prior to neutron activation analysis... 

K. Niu, Analytical Model for Super-Compression of Multi-Structured Pellet , Rept No IPPJ-230, Nagoya Univ (Jap) (1975)... 

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. 

Measurements. Infra-red spectra for the region 600-4000 cm-1 were measured with a Perkin-Elmer Model 710B spectrometer on samples pressed in KBr pellets. Magnetic susceptibilities were measured with a vibrating sample magnetometer (Princeton Applied Physics) as previously described.(4)... 

Suppose that catalyst pellets in the shape of right-circular cylinders have a measured effectiveness factor of r] when used in a packed-bed reactor for a first-order reaction. In an effort to increase catalyst activity, it is proposed to use a pellet with a central hole of radius i /, < Rp. Determine the best value for RhjRp based on an effective diffusivity model similar to Equation (10.33). Assume isothermal operation ignore any diffusion limitations in the central hole, and assume that the ends of the cylinder are sealed to diffusion. You may assume that k, Rp, and eff are known. 

Charge the reactor with the optimized pellets from Problem 10.14 or 10.15. What does it do to the value for r] 0)pcac[ i A]hetewgeneous = r] ff) totai [ A]homogeneous sed to model the reactor If you have not worked Problem 10.14 or 10.15, assume the new pellet increases the reaction rate per pellet by a factor of 1.5 when R/,jRp = 0.5. 

Modeling the Effect of Polymer Rheology on the Performance of Underwater Pelletizers... 

One of the common problems associated with underwater pelletizers is the tendency of the die holes to freeze off. This results in nonuniform polymer melt flow, increased pressure drop, and irregular extrudate shape. A detailed engineering analysis of pelletizers is performed which accounts for the complex interaction between the fluid mechanics and heat transfer processes in a single die hole. The pelletizer model is solved numerically to obtain velocity, temperature, and pressure profiles. Effect of operating conditions, and polymer rheology on die performance is evaluated and discussed. 

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