Catalysts parallel-pore model

Q. To proceed further at this point one has to specify a pore model for the catalyst, and a model for the active site distribution. Froment and co-workers have examined a variety of cases such as single pore models (single-ended pores and pores open on both sides) with both deterministic and stochastic active site distributions, the bundle of parallel pores model and various tree-like models of the porous structure, which were earlier used by Pismen (40) to describe transport and reaction in porous systems. Such treelike models contain interconnected pores but lack any closed loops and are usually called Bethe networks or lattices. They are completely characterized by their coordination number Z, which is the number of pores connected to the same site of the network. 

Fresh Zeolite. The diffusivities within usual porous catalyst (pore radius a few nm) can be estimated by the parallel pore model (18) or the random pore model (19). However, configurational diffusion occurs within the pores of zeolites (pore diameter < 1 nm) and there are only a few reports on the measurement or estimation methods of the diffusivities of zeolites, especially at higher temperature range (20,21). Here we will review the results of ZSM-5, which first explains the diffusivity of fresh ZSM-5, then the results of coke loaded ZSM-5. 

A single pore is evidently an oversimplified model of a catalyst particle A relatively stralghtforvard extension, accounting up to a certain extent for the pore size distribution, is the parallel pore model. This is still unsatisfactory with complex, multilayered catalysts and/or when blockage by metal or coke deposition occurs For such cases the location of the blockage matters and pore branching and types of interconnection between pores become of importance. 

The Parallel-pore Model Wheeler proposed a model, based on the first three of these properties, to represent the monodisperse pore-size distribution in a catalyst pellet. From p and Vg the porosity e is obtained from Eq. (8-16). Then a mean pore radius d is evaluated by writing equations for the total pore volume and total pore surface in a pellet. The result, developed as Eq. (8-26), is... 

Blue et al. have studied the dehydrogenation of butane at atmospheric pressure, using a chromia-alumina catalyst at 530°C. For a spherical catalyst size of dp = 0.32 cm the experimental data suggest a first-order rate constant of about 0.94 cm /(sec)(g catalyst). The pore radius is given as 110 A. Assuming Knudsen diffusivity at this low pressure and estimating the pore volume as 0.35 cm /g, predict an effectiveness factor for the catalyst. Use the parallel-pore model with a tortuosity factor of 2.0. 

The parallel-pore model provides an in-depth description of the void volume fraction and tortuosity factor Tor based on averages over the distribution in size and orientation, respectively, of catalytic pores that are modeled as straight cylinders. These catalyst-dependent strncture factors provide the final tools that are required to calculate the effective intrapellet diffusion coefficients for reactants and prodncts, as well as intrapellet Damkohler numbers. The following conditions are invoked ... 

The only other variable required for predicting D is the length of the diffusion path, which is the thickness of the particle multiplied also by the adjustable tortuosity factor, S, that accounts for distorted diffusion pathways and also for varying pore cross sections in interconnections and constrictions the value of 5 varies between V2 and 10 but is typically 3 or 4 in most industrial catalysts. The simplest geometric model which is still commonly used in practical applications for estimating is the parallel-pore model ... 

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 ... 

Broad Pore-Size Distribution Several models have been developed to estimate the effective diffusivity in catalysts with broad pore-size distributions." One of the simplest is the parallel pore model of Johnson and Stewart. In their approach, the value ofDp ir) is calculated by averaging over the whole range of pore sizes ... 

Satterfield and Cadle [38] determined the tortuosity factors for 17 commercially manufactured, pelleted catalysts and catalyst supports using the parallel-pore model. Except for two materials that had been calcined at very high temperatures, all tortuosity factors fell between 3 and 7. For about half the catalysts, the tortuosity factor was about 4, regardless of macroporosity or composition. 

A trickle-bed reactor was used to study catalyst deactivation during hydrotreatment of a mixture of 30 wt% SRC and process solvent. The catalyst was Shell 324, NiMo/Al having monodispersed, medium pore diameters. The catalyst zones of the reactors were separated into five sections, and analyzed for pore sizes and coke content. A parallel fouling model is developed to represent the experimental observations. Both model predictions and experimental results consistently show that 1) the coking reactions are parallel to the main reactions, 2) hydrogenation and hydrodenitrogenation activities can be related to catalyst coke content with both time and space, and 3) the coke severely reduces the pore size and restricts the catalyst efficiency. The model is significant because it incorporates a variable diffusi-vity as a function of coke deposition, both time and space profiles for coke are predicted within pellet and reactor, activity is related to coke content, and the model is supported by experimental data. 

Early efforts to model catalyst deactivation either utilized simplified models of the catalyst s porous structure, such as a bundle of nonintersecting parallel pores, or pseudo-homogeneous descriptions in terms of effective diffusivities and tortuosity... 

One of the simplest ways of extending this single-pore model is to assume that variations in the size of pore spaces can be represented by a variable-diameter assembly of such pores, referred to as a parallel bundle of pores. An example is shown in Fig. 3, for a variation of the model applied to a supported zeolite cracking catalyst. In this example [10] the zeolite pores are simply configured along the pore walls, so that the parallel bundle represents the Si/Alumina-support pore spaces. 

Several authors have investigated the differences in deactivation for small or for large pores within the catalysts. In general, the researchers have employed mercury porosimetry for the characterization of the actual catalysts and they have employed mostly models of parallel pores of differing dimensions (as contrasted with an interconnected network) in their simulations. 

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... 

To elucidate methanol crossover at the DMFC cathode, the active electrode surface of the cathode was divided into two separate parts one for oxygen reduction and the other for oxidation of crossover methanol. In this model, the methanol oxidation and oxygen reduction occur in parallel at different sites or pores because of the porous structure of the catalyst layer. The equivalent circuit for this model is presented in Figure 6.69. 

In the present study, our interest is focused on a membrane reactor in which the membrane can be employed as a large pore catalyst for the convection flow of reactants. Propylene epoxidation to produce propylene oxide (PO) is taken as a model reaction of parallel-consecutive reactions by using a Re-Ag immobilized in the pores of a micro-porous-glass membrane (MPG). The objectives of this paper are to clarify (1) the reaction kinetics in partial and total oxidation differing from the packed bed reactors,... 

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