Reaction parameters pore diffusion

The coking and regeneration of a reforming catalyst was studied by physical characterization methods (pore volume, tortuosity, porosity, carbon distribution) as well as by kinetic investigations on the reaction rate of coke bum-off. For temperatures of industrial relevance for the Pt/Re-A Os catalyst, i.e. below 550°C (deactivation), the bum-off rate is determined by the interplay of chemical reaction and pore diffusion limitation by external mass transfer can be excluded. Based on the kinetic parameters, the process of the regeneration of a technical reactor is discussed. 

Figure 8.10(b) shows a plot of if/ = cAlcAs as a function of z, the fractional distance into the particle, with the Thiele modulus cj) as parameter. For = 0, characteristic of a very porous particle, the concentration of A remains the same throughout the particle. For (f> = 0.5, characteristic of a relatively porous particle with almost negligible pore-diffusion resistance, cA decreases slightly as z —> 1. At the other extreme, for = 10, characteristic of relatively strong pore-diffusion resistance, cA drops rapidly as z increases, indicating that reaction takes place mostly in the outer part (on the side of the permeable face) of the particle, and the inner part is relatively ineffective. 

If the surface reaction is the rate-controlling step, any effects of external mass transfer and pore-diffusion are negligible in comparison. The interpretation of this, in terms of the various parameters, is that Ag kA, cAs - cAg, and T) and 17 both approach the value of 1. Thus, the rate law, from equation 8.5-50, is just that for a homogeneous gas-phase... 

Zeolite crystal size can be a critical performance parameter in case of reactions with intracrystalline diffusion limitations. Minimizing diffusion limitations is possible through use of nano-zeolites. However, it should be noted that, due to the high ratio of external to internal surface area nano-zeolites may enhance reactions that are catalyzed in the pore mouths relative to reactions for which the transition states are within the zeolite channels. A 1.0 (xm spherical zeolite crystal has an external surface area of approximately 3 m /g, no more than about 1% of the BET surface area typically measured for zeolites. However, if the crystal diameter were to be reduced to 0.1 (xm, then the external surface area becomes closer to about 10% of the BET surface area [41]. For example, the increased 1,2-DMCP 1,3-DMCP ratio observed with decreased crystallite size over bifunctional SAPO-11 catalyst during methylcyclohexane ring contraction was attributed to the increased role of the external surface in promoting non-shape selective reactions [65]. 

The porous structure of either a catalyst or a solid reactant may have a considerable influence on the measured reaction rate, especially if a large proportion of the available surface area is only accessible through narrow pores. The problem of chemical reaction within porous solids was first considered quantitatively by Thiele [1] who developed mathematical models describing chemical reaction and intraparticle diffusion. Wheeler [2] later extended Thiele s work and identified model parameters which could be measured experimentally and used to predict reaction rates in... 

The above discussion shows that the progress of deactivation may occur in different ways depending on the type of decay reaction occurring and on the value of the pore diffusion factor. For parallel and series poisoning, the Thiele modulus for the main reaction is the pertinent pore diffusion parameter. For side-by-side reactions, the Thiele modulus for the deactivation is the prime parameter. 

Kodama et al. (1980) developed a detailed HDS and HDM model for deactivation of pellets and reactor beds. The model included reversible kinetics for coke formation, which contributed to loss of porosity. Second-order kinetics were used to describe both HDM and HDS reaction rates, and diffusivities were adjusted on the basis of contaminant volume in the pores. The model accurately traced the history of a reactor undergoing deactivation. This model, however, contains many parameters and is thus more correlative than theoretical or discriminating. 

The whole of the internal surface area of a porous catalyst will be available for the catalytic reaction if the rates of diffusion of reactant into the pores, and of product out of them, are fast compared with the rate of the surface reaction. In contrast, if the reactant diffuses slowly but reacts rapidly, conversion to product will occur near the pore entrances and the interior of the pores will play no role in the catalysis. Ion exchange resins are typical examples of catalysts for which such considerations are important (cf. Sect. 2.3). The detailed mathematics of this problem have been treated in several texts [49-51] and we shall now quote some of the main theoretical results derived for isothermal conditions. The parameters involved tend to be those employed by chemical engineers and differ somewhat from those used elsewhere in this chapter. In particular, the catalyst material (active + support) is present in the form of pellets of volume Vp and the catalytic rates vv are given per unit volume of pellet (mols m 3). The decrease in vv brought about by pore diffusion is then expressed by an effectiveness factor, rj, defined by... 

At present two models are available for description of pore-transport of multicomponent gas mixtures the Mean Transport-Pore Model (MTPM)[4,5] and the Dusty Gas Model (DGM)[6,7]. Both models permit combination of multicomponent transport steps with other rate processes, which proceed simultaneously (catalytic reaction, gas-solid reaction, adsorption, etc). These models are based on the modified Maxwell-Stefan constitutive equation for multicomponent diffusion in pores. One of the experimentally performed transport processes, which can be used for evaluation of transport parameters, is diffusion of simple gases through porous particles packed in a chromatographic column. 

Other models directly couple chemical reaction with mass transport and fluid flow. The UNSATCHEM model (Suarez and Simunek, 1996) describes the chemical evolution of solutes in soils and includes kinetic expressions for a limited number of silicate phases. The model mathematically combines one- and two-dimensional chemical transport with saturated and unsaturated pore-water flow based on optimization of water retention, pressure head, and saturated conductivity. Heat transport is also considered in the model. The IDREAT and GIMRT codes (Steefel and Lasaga, 1994) and Geochemist s Workbench (Bethke, 2001) also contain coupled chemical reaction and fluid transport with input parameters including diffusion, advection, and dispersivity. These models also consider the coupled effects of chemical reaction and changes in porosity and permeability due to mass transport. 

In our discussion of surface reactions in Chapter 11 we assumed that each point in the interior of the entire catalyst surface was accessible to the same reactant concentration. However, where the reactants diffuse into the pores within the catalyst pellet, the concentration at the pore mouth will be higher than that inside the pore, and we see that the entire catalytic surface is not accessible to the same concentration. To account for variations in concentration throughout the pellet, we introduce a parameter known as the effectiveness factor. In this chapter we will develop models for diffusion and reaction in two-phase systems, which include catalyst pellets and CVD reactors. The types of reactors discussed in this chapter will include packed beds, bubbling fluidized beds, slurry reactors, and trickle beds. After studying this chapter you will be able to describe diffusion and reaction in two- and three-phase systems, determine when internal pore diffusion limits the overall rate of reaction, describe how to go about eliminating this limitation, and develop models for systems in which both diffusion and reaction play a role (e.g., CVD). 

The ways in which reaction parameters affect a two phase batch reaction are similar to those considered above for the three phase systems. Since there is no gas phase, agitation only serves to keep the catalyst suspended making it more accessible to the dissolved reactants so it only has a secondary effect on mass transfer processes. Substrate concentration and catalyst quantity are the two most important reaction variables in such reactions since both have an influence on the rate of migration of the reactants through the liquid/solid interface. Also of significant importance are the factors involved in minimizing pore diffusion factors the size of the catalyst particles and their pore structure. 

A measure of the absence of internal (pore diffusion) mass transfer limitations is provided by the internal effectiveness factor, t, which is defined as the ratio of the actual overall rate of reaction to the rate that would be observed if the entire interior surface were exposed to the reactant concentration and temperature existing at the exterior of the catalyst pellet. A value of 1 for rj implies that all of the sites are being utilized to their potential, while a value below, say, 0.5, signals that mass transfer is limiting performance. The value of rj can be related to that of the Thiele modulus, 4>, which is an important dimensionless parameter that roughly expresses a ratio of surface reaction rate to diffusion rate. For the specific case of an nth order irreversible reaction occurring in a porous sphere,... 

The rate expressions derived above describe the dependence of die reaction rate expressions on kinetic parameters related to the chemical reactions. These rate expressions are commonly called the intrinsic rate expressions of the chemical reactions. However, as discussed in Chapter 1, in many instances, the local species concentrations depend also on the rate that the species are transported in the reaction medium. Hence, the actual reaction rates are affected by the transport rates of reactants and products. This is manifested in two general cases (i) gas-solid heterogeneous reactions, where species diffusion through the pore plays an important role, and (ii) gas-hquid reactions, where interfacial species mass-transfer rate as wen as solubility and diffusion play an important role. Considering the effect of transport phenomena on the global rates of the chemical reactions represents a very difficult task in the design of many chemical reactors. These topics are beyond the scope of this text, but the reader should remember to take them into consideration. 

Equation 21.7 includes the mass transfer, pore diffusion, and chemical reaction. Figure 21.3 allows observing the effect of each step, represented by Equation 21.7. As measure parameters, one has the inverse of the mass on the abscissa and the inverse of the global rate on the ordinate. 

In both runs, a variation of temperature and partial pressures was performed to determine the effective kinetic parameters, which is summarized in Table 16.5. The rather low activation energies might indicate a possible influence of mass transfer due to pore diffusion. Interestingly, the boehmite-supported catalyst showed almost no dependence on the CO partial pressure, whereas the y-alumina-supported system showed a partial reaction order of 0.17. Water partial reaction order was found to be almost of first order in both cases (Figure 16.9). 

In an effective properties model, the porous microstructures of the SOFC electrodes are treated as continua and microstructural properties such as porosity, tortuosity, grain size, and composition are used to calculate the effective transport and reaction parameters for the model. The microstmctural properties are determined by a number of methods, including fabrication data such as composition and mass fractions of the solid species, characteristic features extracted from micrographs such as particle sizes, pore size, and porosity, experimental measurements, and smaller meso- and nanoscale modeling. Effective transport and reaction parameters are calculated from the measured properties of the porous electrodes and used in the governing equations of the ceU-level model. For example, the effective diffusion coefficients of the porous electrodes are typically calculated from the diffusion coefficient of Eq. (26.4), and the porosity ( gas) and tortuosity I of the electrode ... 

We may now calculate the situation in an industrial fixed bed reactor (trickle bed) based on the parameters for the chemical reaction, liquid-solid mass transfer, and pore diffusion, thereby assuming ideal plug flow behavior. In practice, the reaction rate in a trickle bed reactor will be lower because of imperfect wetting of the catalyst. As an example, a pressure of 10 bar, pure octene at the inlet of the reactor, and a constant temperature of 100 °C were assumed, although the latter assumption is unrealistic for a simple fixed bed reactor, as the reaction is highly exothermic. For simplification, the gas-liquid mass transfer is neglected (CH2,iiq CH2,sat)> and for the liquid-solid mass transfer we take a value of 3.8 for Sh, which is the minimal value for spheres in a fixed bed. 

The common and classical approach to considering pore diffusion limitations is the utilization of an effectiveness factor as a single parameter, which was developed by Damkoehler, Thiele and Zddovkh in the 1930s (Damkoehler, 1936,1937a, 1937b, 1939 Thiele, 1939 Zeldowitsch, 1939). However, an exact calculation of the effectiveness factor is only possible for simple power law kinetics, isothermal particles, or simple reaction networks, for example, for two parallel or serial reactions, as described in many textbooks (e.g., Froment and Bischoff, 1990 or Levenspiel, 1996,... 

Another approach to evaluate the influence of pore diffusion on a catalytic reaction is that taken by Weisz [20,21]. It is particularly useful because it provides a dimensionless number containing only observable parameters that can be readily measured or calculated. Let us again choose a spherical catalyst particle as our model, with volume V, surface area A, and radius Rp, as indicated in Figure 4.9. This figure also has axes to represent the decrease... 

These models are also grouped from a different point of view as grain models, pore models, volume reaction models and deactivation models. In number of these models, changes in pore structure during the reaction and variations in diffusion and reaction parameters are considered. 

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