Pellet size reaction rate, effect

The effectiveness of a given size of pellet can be found experimentally by running tests of reaction conversion with a series of diminishing sizes of pellets until a hmiting rate is found. Then T will be the ratio of the rate with the pellet size in question to the limiting value. 

The effectiveness factor depends, not only on the reaction rate constant and the effective diffusivity, but also on the size and shape of the catalyst pellets. In the following analysis detailed consideration is given to particles of two regular shapes ... 

The catalyst activity depends not only on the chemical composition but also on the diffusion properties of the catalyst material and on the size and shape of the catalyst pellets because transport limitations through the gas boundary layer around the pellets and through the porous material reduce the overall reaction rate. The influence of gas film restrictions, which depends on the pellet size and gas velocity, is usually low in sulphuric acid converters. The effective diffusivity in the catalyst depends on the porosity, the pore size distribution, and the tortuosity of the pore system. It may be improved in the design of the carrier by e.g. increasing the porosity or the pore size, but usually such improvements will also lead to a reduction of mechanical strength. The effect of transport restrictions is normally expressed as an effectiveness factor q defined as the ratio between observed reaction rate for a catalyst pellet and the intrinsic reaction rate, i.e. the hypothetical reaction rate if bulk or surface conditions (temperature, pressure, concentrations) prevailed throughout the pellet [11], For particles with the same intrinsic reaction rate and the same pore system, the surface effectiveness factor only depends on an equivalent particle diameter given by... 

The influence of pellet size has been generally used to identify the rate controlling mechanism of the overall reaction rate. If the rate controlling mechanism is chemical-reaction limited then the pellet size will have no effect on the reaction rate. If the diffusion of by-products to the pellet surface is the rate controlling mechanism, then the reaction rate will decrease as the pellet size increases, due to the increase in the length of the diffusion path. 

At 250 °C, the reaction rate was shown to be affected by pellet sizes as small as 0.2mm [31]. At 210 °C, the reaction rate was found to be by-product diffusion limited at a particle size >16-18mesh (ca. 1.3mm) [27], while at 160°C no effect of pellet size was seen for particle sizes <2.1 mm [29], Therefore, it can be seen that the influence of the pellet size on reaction rate becomes more pronounced as the temperature increases. Under normal industrial SSP conditions, where the pellet size is between 2 and 3 mm and temperatures are >200 °C, decreasing the pellet size will lead to an increasing of the reaction rate. 

The effective diffusivity Dn decreases rapidly as carbon number increases. The readsorption rate constant kr n depends on the intrinsic chemistry of the catalytic site and on experimental conditions but not on chain size. The rest of the equation contains only structural catalyst properties pellet size (L), porosity (e), active site density (0), and pore radius (Rp). High values of the Damkohler number lead to transport-enhanced a-olefin readsorption and chain initiation. The structural parameters in the Damkohler number account for two phenomena that control the extent of an intrapellet secondary reaction the intrapellet residence time of a-olefins and the number of readsorption sites (0) that they encounter as they diffuse through a catalyst particle. For example, high site densities can compensate for low catalyst surface areas, small pellets, and large pores by increasing the probability of readsorption even at short residence times. This is the case, for example, for unsupported Ru, Co, and Fe powders. 

The support has an internal pore structure (i.e., pore volume and pore size distribution) that facilitates transport of reactants (products) into (out of) the particle. Low pore volume and small pores limit the accessibility of the internal surface because of increased diffusion resistance. Diffusion of products outward also is decreased, and this may cause product degradation or catalyst fouling within the catalyst particle. As discussed in Sec. 7, the effectiveness factor Tj is the ratio of the actual reaction rate to the rate in the absence of any diffusion limitations. When the rate of reaction greatly exceeds the rate of diffusion, the effectiveness factor is low and the internal volume of the catalyst pellet is not utilized for catalysis. In such cases, expensive catalytic metals are best placed as a shell around the pellet. The rate of diffusion may be increased by optimizing the pore structure to provide larger pores (or macropores) that transport the reactants (products) into (out of) the pellet and smaller pores (micropores) that provide the internal surface area needed for effective catalyst dispersion. Micropores typically have volume-averaged diameters of 50 to... 

An experimental test to verify the absence of significant concentration gradients inside the catalyst pellet is based on the inverse proportional relation between the effectiveness factor and the pellet diameter for strong internal diffusion limitations. Hence, a measured rate which is independent of the pellet size indicates that internal diffusion limitations can be neglected. Care should be taken to avoid artifacts. External heat transfer effects also depend on pellet size and for exothermic reactions might compensate the internal diffusion limitations. If the catalyst pellet consists of a support with an non-uniformly distributed active phase, crushing and sieving to obtain smaller pellets is hazardous. 

The nature and arrangement of the pores determine transport within the interior porous structure of the catalyst pellet. To evaluate pore size and pore size distributions providing the maximum activity per unit volume, simple reactions are considered for which the concept of the effectiveness factor is applicable. This means that reaction rates can be presented as a function of the key component. A only, hence RA(CA). Various systems belonging to this category have been discussed in Chapters 6 and 7. The focus is on gaseous systems, assuming the resistance for mass transfer from fluid to outer catalyst surface can be neglected and the effectiveness factor does not exceed unity. The mean reaction rate per unit particle volume can be rewritten as... 

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. 

The importance of diffusion in catalyst pellets can often be determined by measuring the effect of pellet size on the observed reaction rate. In this exercise, consider an irreversible first-order reaction occurring in catalyst pellets where the surface concentration of reactant A is C s = 0.15 M. 

In many industrial reactions, the overall rate of reaction is limited by the rate of mass transfer of reactants and products between the bulk fluid and the catalytic surface. In the rate laws and cztalytic reaction steps (i.e., dilfusion, adsorption, surface reaction, desorption, and diffusion) presented in Chapter 10, we neglected the effects of mass transfer on the overall rate of reaction. In this chapter and the next we discuss the effects of diffusion (mass transfer) resistance on the overall reaction rate in processes that include both chemical reaction and mass transfer. The two types of diffusion resistance on which we focus attention are (1) external resistance diffusion of the reactants or products between the bulk fluid and the external smface of the catalyst, and (2) internal resistance diffusion of the reactants or products from the external pellet sm-face (pore mouth) to the interior of the pellet. In this chapter we focus on external resistance and in Chapter 12 we describe models for internal diffusional resistance with chemical reaction. After a brief presentation of the fundamentals of diffusion, including Pick s first law, we discuss representative correlations of mass transfer rates in terms of mass transfer coefficients for catalyst beds in which the external resistance is limiting. Qualitative observations will bd made about the effects of fluid flow rate, pellet size, and pressure drop on reactor performance. 

After drying and reduction, the Pd-Ag/C catalysts are composed of bimetallic Eilloy nanoparticles ( 3 nm). CO chemisorption coupled to TEM and XRD analysis showed that that, for catalysts 1.5% wt. in each metal, the bulk composition of the alloy is close to 50% in each metal, whereas the surface is 90% in Ag and 10% in Pd [9]. Mass transfer limitations can be detected by testing the same catalyst with various pellet sizes [18]. Indeed, if the reactants diffusion is slow due to small pore sizes, the longer the distance between the pellet surface and the metal particle, the larger the influence of the difiusion rate on the apparent reaction rate. Pd-Ag catalysts with various pellet sizes were thus tested in hydrodechlorination of 1,2-dichloroethane. Results were compared to those obtained with a Pd-Ag/activated charcoal catalyst. Fig. 4 shows the evolution of the effectiveness factor of the catalysts, i.e. the ratio between the apparent reaction rate and the intrinsic reaction rate, as a function of the pellet size. The intrinsic reaction rate was considered equal to the reaction rate obtained with the smallest pellet size. When rf = 1, no diffusional limitations occur, and the catalyst works in chemical regime. When j < 1, the observed reaction rate is lower than the intrinsic reaction rate due to a slow diffusion of the reactants and products and the catalyst works in diffusional regime [18]. 

A support with small mesopores ( 10 nm) leads to diffusional limitations, whatever the temperature chosen, as soon as the pellet size is larger than 250 pm. Indeed, 1,2-dichloroethane conversion, ethylene selectivity and reaction rate were found to decrease when the pellet size increases. Fig. 3 shows that the effectiveness factor decreases when the pellet size increases. The conversion and reaction rate are lower when the pellet size is larger due to diffusional limitations in the pore texture of the support. The selectivity decrease can be explained by the fact that the hydrodechlorination of 1,2-dichloroethane into ethylene may be followed by hydrogenation of ethylene into ethane [13]. This last reaction is favoured when diffusional limitations prevent ethylene from... 

The current catalyst has reached the end of its useful lifetime and needs to be replaced. Your project is to make a design change with the new catalyst to improve the reactor efficiency. In particular you are considering changing the catalyst size. The catalyst vendor has told you that they easily can make spherical pellets with diameters of 0-075 cm, 0.15 cm, and 0.30 cm. You also have been assured that the effective diffusivity, bed density, and reaction rate constant do not vary among the catalysts in this size range. One of your team members wants to use the smallest diameter catalyst to minimize the total mass of catalyst required. Another team member wants to use the largest diameter catalyst to miminize the pressure drop. 

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