Diffusion in catalyst particles

Thus, considering diffusion in pores leads to very similar results to those we obtained when describing diffusion in catalyst particles. 

Information about transport diffusion in catalyst particles can also be deduced during the initial, unsteady state period of a permeation experiment. In this stage, the number of molecules passing the plug of catalyst per unit time will increase from zero until the rate of permeation characterizing the steady state behavior is attained. In the limit t - oo, the total amount of molecules which have permeated in the time interval 0... t is given by the relation [1,2, 12]... 

A series of CoMo/Alumina-Aluminum Phosphate catalysts with various pore diameters was prepared. These catalysts have a narrow pore size distribution and, therefore, are suitable for studying the effect of pore structure on the deactivation of reaction. Hydrodesulfurization of res id oils over these catalysts was carried out in a trickle bed reactor- The results show that the deactivation of reaction can be masked by pore diffusion in catalyst particle leading to erro neous measurements of deactivation rate constants from experimental data. A theoretical model is developed to calculate the intrinsic rate constant of major reaction. A method developed by Nojcik (1986) was then used to determine the intrinsic deactivation rate constant and deactivation effectiveness factor- The results indicate that the deactivation effectiveness factor is decreased with decreasing pore diameter of the catalyst, indicating that the pore diffusion plays a dominant role in deactivation of catalyst. 

Table 8.2 Computations Using Orthogonal Collocation Diffusion in Catalyst Particle...

Taking into account this estimation, Ostrovskii and Bukhavtsova [8] have considered the simplified model of reaction/diffusion in catalyst particle under capillary condensation. According to Equation (23.7), we can suppose that diffusion limitation inside the globule (Figure 23.1) is negligible, even in the case where it is filled with liquid. Then the diffusion/reaction equation has the form... 

The presence (or absence) of pore-diffusion resistance in catalyst particles can be readily determined by evaluation of the Thiele modulus and subsequently the effectiveness factor, if the intrinsic kinetics of the surface reaction are known. When the intrinsic rate law is not known completely, so that the Thiele modulus cannot be calculated, there are two methods available. One method is based upon measurement of the rate for differing particle sizes and does not require any knowledge of the kinetics. The other method requires only a single measurement of rate for a particle size of interest, but requires knowledge of the order of reaction. We describe these in turn. 

A reactant in liquid will be converted to a product by an irreversible first-order reaction using spherical catalyst particles that are 0.4cm in diameter. The first-order reaction rate constant and the effective diffusion coefficient of the reactant in catalyst particles are 0.001 s and 1.2 X 10 ( ii s , respectively. The liquid film mass transfer resistance of the particles can be neglected. 

Although equation 3.41 is only applicable to competing first-order reactions in catalyst particles, at large values of where diffusion is rate controlling the equation is equivalent at the asymptotes to equations obtained for reaction orders other than one. 

Where intraparticle diffusion appreciably affects the rate of the reaction, reduction in catalyst particle size would be necessary to increase the effectiveness factor and hence conversion. But this may not be possible due to the pressure drop limitations in conventional packed beds. In such situations, the use of Monoliths would provide the advantage of higher effectiveness factor. 

Characterization of Nonisobaric Diffusion Due to Nonequimolar Fluxes in Catalyst Particles... 

The coupling of kinetics with intra- and extraparticle transport has been the traditional focus of chemical reaction engineering major accomplishments have been admirably summarized by Aris [10]. The effectiveness factor and Thiele parameter of diffusion-influenced catalyst particles represent a balance between their reactive and diffusive properties. In this section, we shall concentrate on the latter. 

The influence of mass-transport resistance in the particles can only be excluded if the critical reaction rate is substantially lower than the mass transfer velocity. This leads to the need for good external mass transfer (i.e. to a sufficiently rapid flow rate in the packed bed), as well as to short diffusion paths in catalyst particles. 

While the above criteria are useful for diagnosing the effects of transport limitations on reaction rates of heterogeneous catalytic reactions, they require knowledge of many physical characteristics of the reacting system. Experimental properties like effective diffusivity in catalyst pores, heat and mass transfer coefficients at the fluid-particle interface, and the thermal conductivity of the catalyst are needed to utilize Equations (6.5.1) through (6.5.5). However, it is difficult to obtain accurate values of those critical parameters. For example, the diffusional characteristics of a catalyst may vary throughout a pellet because of the compression procedures used to form the final catalyst pellets. The accuracy of the heat transfer coefficient obtained from known correlations is also questionable because of the low flow rates and small particle sizes typically used in laboratory packed bed reactors. 

An interesting technique for the measurement of intraparticle diffusivity as well as longitudinal diffusion in the particle bed has been described by Deisler and Wilhelm (21). It deviates from all other techniques mentioned in that it is based on a dynamic flow study, analyzing the effect of the particles on the propagation of a sinusoidal variation of composition of a binary gas mixture passed through the catalyst bed. The authors have demonstrated the versatility of their general technique for determination of diffusion properties, as well as adsorption equilibria between the solids and the gas composition employed. If this general technique were modified to measure specifically the particle diffusivity, a very convenient and accurate method may result. 

Vanadium molecular size distributions in residual oils are measured by size exclusion chromatography with an inductively coupled plasma detector (SEC-ICP). These distributions are then used as input for a reactor model which incorporates reaction and diffusion in cylindrical particles to calculate catalyst activity, product vanadium size distributions, and catalyst deactivation. Both catalytic and non-catalytic reactions are needed to explain the product size distribution of the vanadium-containing molecules. Metal distribution parameters calculated from the model compare well with experimental values determined by electron microprobe analysis, Modelling with feed molecular size distributions instead of an average molecular size results in predictions of shorter catalyst life at high conversion and longer catalyst life at low conversions. 

Kinetics of HCR can be affected by adsorption of reactants on the support followed by diffusion to catalyst particles, and vice versa (spillover). In the case of CO oxidation, for example, the first experimental reports indicating that the CO supply via the support may be important for model nm catalysts, obtained by evaporating Pd onto mica, AI2O3, Si02, and MgO(lOO), were published in the 1980s (see the reviews [14,32]). On the noble metals, this reaction runs via the standard Langmuir-... 

Wheeler has summarized the work on internal diffusion for catalytic cracking of gas-oil. At 500°C the rate data for fixed-bed operation, with relatively large ( -in.) catalyst particles and that for fluidized-bed reactors (very small particle size) are about the same. This suggests that the effectiveness factor for the large particles is high. Confirm this by estimating rj for the -in. catalyst if the... 

A effective diffusion coefficient of species i in catalyst particle l2t ... 

The mechanism of nanotube formation in chemical vapor deposition features characteristics rather distinct from those found for the synthesis by arc discharge or laser ablation. Contrary to the latter, a solution of small carbon clusters in and subsequent diffusion through catalyst particles play a minor role in the deposition from the gas phase. The employed hydrocarbons decompose directly on the surface of the catalytic particle. The carbon, therefore, becomes immediately available for nanotube growth. 

Reaction rates can be controlled by the rate of conversion of the reactants or by nonchemical rate processes such as the rate of diflusion of reactants or the rate of heat transfer. In the study of chemical kinetics we will be interested in the rates of chemical change governed by the speed of chemical processes. Any investigation of reaction rates meant for mechanistic studies must first establish that this is what we are measuring. Fortunately, it is relatively easy to check for extraneous effects before the kinetic investigation is undertaken. The effects that are most likely to cause problems involve diffusion of mass and heat in catalyst particles and mixing in the reactor. 

Pore network models are an example of a discrete model. The earlier pore network models consisted of parallel pores [18] and randomly oriented cross-linked pores [19]. Bethe lattice [20], and regular networks [21] have also been used to represent catalyst structures. Pore network models have been used to analyze the complicated interactions between diffusion and reaction that may occur in catalyst particles, for example Sharatt and Mann [21] used their cubic network... 

The combined diffusivity, Dcomb> calculated for a single cylindrical pore is based on the cross-sectional area of the pore perpendicular to the direction of diffusion. A catalyst particle consists of an assembly of single pores. Therefore, the ultimate aim is to find the effective diffusivity of the porous catalyst particle, Dg, based on the total area exposed by the cross sections of all the pores in the particle, which constitutes the total mass transfer area normal to the direction of diffusion. 

In may be noted that a level [I] reactor selection can be done even with the effective reaction rate expressions (Equations 6.3 and 6.4). For instance, one should always attempt to select a reactor that helps to quicken the otherwise slowest step in the effective rate. For instance, if internal diffusion within catalyst particles is the limiting step, then one has to use fine particles in a slurry bubble column. If liquid-solid mass transfer is... 

Effective diffusion coefficients in catalyst particles are calculated as functions of bulk gas diffusion coefficients, pore volume distribution specified as particle porosity, 8p, as a function of pore radius and the so-called tortuosity factor, x, which describes the actual road a molecule must travel. The use of different effective diffusion models is discussed in the literature [199] [436] and performance of measurements in [221], Below is shown the basic parallel pore model, where the effective diffusion coefficient, De is calculated from the particle porosity, the tortuosity factor, and the diffusion coefficient in the bulk and the Knudsen diffusion coefficient, Dbuik and Dk [199] [389] [440] as ... 

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