Intraparticle transport resistance

For subsequent tests of intraparticle transport resistance, the catalyst was dry sieved into seven fractions. The mean particle size of these seven fractions were 18, 29, 35,44, 57, 81, and 93 pm. The particle size distributions of these seven fractions are shown in Figure 1, the platinum loading and dispersion are depicted in Figure 2. It is clear from Figure 2 that the platinum loading is a strong function of the catalyst particle size i.e. 5.42% for the 18 pm fraction and 3.25% for... 

For simultaneous treatment of interphase and intraparticle transport resistances, the boundary conditions at the external pellet surface are now given by eqs 15 and 16, whereas eqs 11 and 12 still hold for the case of negligible interphase transport resistance. The bound-... 

In a study of intrinsic kinetics, if data are taken in a laboratory PER where intraparticle transport resistances are appreciable, and if this circmnstance is arbitrarily neglected, experimental results will lead to falsified reaction kinetics ... 

The significance or even presence of intraparticle transport resistances must be demonstrated either by conducting diagnostic experiments or by utilizing well-established criteria. 

The influence of inter and intraparticle transport resistances on the region of generalized parametric sensitivity is shown in Figure 4. For sufficiently large values of and the reactor becomes transport - limited, and runaway does not occur. On the other hand, in the region of small Ag values, as Ag increases (with Le fixed), transport limitations increase, so that it becomes more and more difficult to remove heat from the particle. This leads sooner to runaway, i.e. for lower values of the heat of reaction parameter a. 

Diffusion and transport of the molecules through the porous structure of the adsorbent particle lead to the intraparticle transport resistance. 

The external fluid film resistance (the corresponding mass-transfer coefficient ki from equations (3.4.32a,b)) is in series with the intraparticle transport resistance. The flux of a species through a porous/mesoporous/microporous adsorbent particle consists, in general, of simultaneous contributions from the four transport mechanisms described earlier for gas transport in Section 3.1.3.2 (for molecular diffusion, where (Dak/T>ab) 2> 1) ... 

Intraparticle mass transport resistance can lead to disguises in selectivity. If a series reaction A — B — C takes place in a porous catalyst particle with a small effectiveness factor, the observed conversion to the intermediate B is less than what would be observed in the absence of a significant mass transport influence. This happens because as the resistance to transport of B in the pores increases, B is more likely to be converted to C rather than to be transported from the catalyst interior to the external surface. This result has important consequences in processes such as selective oxidations, in which the desired product is an intermediate and not the total oxidation product CO2. 

Based on the studies on the KD306-type sulfur-resisting methanation catalyst, the non-isothermal one-dimensional and two-dimensional reaction-diffusion models for the key-components have been established, which were solved using an orthogonal collocation method. The simulation values of the effectiveness factors for the methanation reaction ch4 and the shift reaction fco2are in fair agreement with the experimental values, which indicates that both models are able to predict intraparticle transport and reaction processes within catalyst pellets. 

The Biot number Bim for mass transport. This can be interpreted as the ratio of internal to external transport resistance (intraparticle diffusion versus interphase diffusion) ... 

For negligible intraparticle mass transport resistance, the criterion is... 

The intraparticle transport effects, both isothermal and nonisothermal, have been analyzed for a multitude of kinetic rate equations and particle geometries. It has been shown that the concentration gradients within the porous particle are usually much more serious than the temperature gradients. Hudgins [17] points out that intraparticle heat effects may not always be negligible in hydrogen-rich reaction systems. The classical experimental test to check for internal resistances in a porous particle is to measure the dependence of the reaction rate on the particle size. Intraparticle effects are absent if no dependence exists. In most cases a porous particle can be considered isothermal, but the absence of internal concentration gradients has to be proven experimentally or by calculation (Chapter 6). 

To eliminate intraparticle transport limitations, the particle size and average pore size must be carefully controlled during manufacture. Other physical properties that become important in industry have to do with the physical integrity of the catalyst particles. These properties include bulk density, crush strength, resistance to abrasion, and attrition. These properties are very important when working with reactors that contain a large amount of a particular catalyst. Fig. 2 lists a number of chemical and physical properties that affect catalyst performance. 

Under these circumstances, the interparticle transport resistances can be neglected. What are left are the intraparticle resistances, i.e. the heat and mass transfer effects inside the catalyst particles. Since the current case reflects the situation that few reactant and product molecules exist in an environment of solvent molecules, the simplest Fick s law approach with effective diffusion coefficients can be considered as sufficient for the description of molecular diffusion. 

Table 4.3 lists some typical gas-liquid hydrogenation reactions investigated in order to explore the features of three-phase catalytic membrane reactors. An example of the application of three-phase catalytic membrane reactors to the hydrogenation of sunflower seed oil can be found in Veldsmk (2001), where it was shown that for this hydrogenation running under kinet-ically controlled conditions the interfacial transport resistances and intraparticle diffusion limitations did not have any effect. Unfortunately the catalyst underwent a serious deactivation process. 

As pointed out earlier, the major external resistance is that of mass transfer, and therefore, the effect of external heat transfer can be neglected. Furthermore, internal (intraparticle) transport effects can be neglected in slurry reactors except under some unusual reaction conditions since the size of the catalyst particles is of the order of 100 microns. In trickle-beds, however, both the internal heat and mass transport effects can be important. 

We consider each of the possible resistances to rapid adsorption which are listed above and examine their significance and magnitude. Interparticle (external to particles) transport resistance occurs in series with the intraparticle (within particles) transport resistances, enumerated 2,3 and 4, which, if each were present, would be in parallel. 

The ratio of the observed reaction rate to the rate in the absence of intraparticle mass and heat transfer resistance is defined as the elFectiveness factor. When the effectiveness factor is ignored, simulation results for catalytic reactors can be inaccurate. Since it is used extensively for simulation of large reaction systems, its fast computation is required to accelerate the simulation time and enhance the simulation accuracy. This problem is to solve the dimensionless equation describing the mass transport of the key component in a porous catalyst[l,2]... 

In this study the ratio of the particle sizes was set to two based on the average value for the two samples. As a result, if the diffusion is entirely controlled by secondary pore structure (interparticle diffusion) the ratio of the effective diffusion time constants (Defl/R2) will be four. In contrast, if the mass transport process is entirely controlled by intraparticle (platelet) diffusion, the ratio will become equal to unity (diffusion independent of the composite particle size). For transient situations (in which both resistances are important) the values of the ratio will be in the one to four range. Diffusional time constants for different sorbates in the Si-MCM-41 sample were obtained from experimental ZLC response curves according to the analysis discussed in the experimental section. Experiments using different purge flow rates, as well as different purge gases... 

Even better yields of C result if components X and Y are incorporated in the same catalyst particle, rather than if they exist as separate particles. In effect, the intermediate product B no longer has to be desorbed from particles of the X type catalyst, transported through the gas phase and thence readsorbed on Y type particles prior to reaction. Resistance to intraparticle mass transfer is therefore reduced or eliminated by bringing X type catalyst sites into close proximity to Y type catalyst sites. Curve 4 in Fig. 3.10 illustrates this point and shows that for such a composite catalyst, containing both X and Y in the same particle, the yield of C for reaction 3 is higher than it would have been had discrete particles of X and Y been used (curve 3). 

During transport, both external and intraparticle mass transfer resistances play a role to a varying degree. A first step in adsorber design is to predict or... 

In general, as an adsorbate is transported in the internal matrix of adsorbent, there is tendency of adsorbate-adsorbate interaction in the pores and hopping, from site to site, of adsorbed species along the wall of the adsorbent. These phenomena give rise to pore and surface diffusion resistances to intraparticle... 

The Biot number Bib for heat transport. Analogous to Bim, this is defined as the ration of the internal to external heat transfer resistance (intraparticle heat conduction versus interphase heat transfer). 

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