Effectiveness factor determination

ILLUSTRATION 12.4 EFFECTIVENESS FACTOR DETERMINATION FOR A NONISOTHERMAL CATALYST PELLET-EXOTHERMIC REACTION... 

The catalyst effectiveness factor, determined by experiment, was defined as the ratio of catalyst activity of specified pellet size to that of well-crushed catalyst (pellet radius 0.1 mm) [20]. 

Substrate (and product) profiles are obtained from the numerical resolution of the above differential equations (system of differential equations in the case of product inhibition). The corresponding local effectiveness factors (ratio of effective and intrinsic reaction rates) are then calculated and the global effectiveness factor determined from their profiles, as in the case of simple Michaels-Menten kinetics. Results are represented in three-dimensional plots in Figs. 4.15 to 4.18 respectively. 

ILLUSTRATION 12.4 Effectiveness Factor Determination for a Nonisothermal Catalyst Pellet Employed to Effect an Exothermic Reaction... 

Having thus seen that enviromental factors determine viscosity largely by their effect on free volume let us now consider the influence of molecular factors which affect viscosity largely by entanglement effects. 

Chapter 2 discussed the possible influence of atmospheric dispersion on vapor cloud explosion or flash fire effects. Factors such as flammable cloud size, homogeneity, and location are largely determined by the manner of flammable material released and turbulent dispersion into the atmosphere following release. Several models for calculating release and dispersion effects have been developed. Hanna and Drivas (1987) provide clear guidance on model selection for various accident scenarios. 

The preceding section described the state of transition expected in a deflagration process when the mixture in front of the flame is sufficiently preconditioned by a combination of compression effects and local quenching by turbulent mixing. However, additional factors determine whether the onset of detonation can actually occur and whether the onset of detonation will be followed by a self-sustaining detonation wave. 

All of these factors determine the stress experienced by the workers and the extent to which operational errors will be recovered before disastrous consequences have ensued. In this context, hazard identification techniques, such as hazard and operability studies (HAZOP), failure modes and effects and criticality analysis (FMECA), fault trees, and others are useful in making the process environment more forgiving. 

Equilibrium (continued) calculations, 192 constant, 151, table, 154 crystallization and, 144 dynamic nature of, 144, 165 effect of catalyst, 148 effect of concentration, 148 of energy, 167 of randomness, 166 of temperature, 67. 148, 167 factors determining, 155, 158 law of chemical, 152, 173 liquid-gas, 66 qualitative aspects of, 142 quantitative aspects of, 151 recognizing, 143 slate of, 142, 147 sugars, 425 thermal, 56... 

It should be noted that hydrolysis of the PAAm chains in hydrogels can also occur in aqueous medium at the application conditions, i.e. in the soil. This should obviously cause an increase in swelling but at the same time it makes the risk of irreversible ionic collapse more real. This tendency is irresistible and can serve as one of the factors determining the lifetime of SAH in soil. Abrupt disappearance of the SAH effects were observed in some of our long-term experiments. 

Factors determining the efficiency of conjugation, and the effect of these factors on the properties of PCSs. 

A clear demonstration of the relative importance of steric and resonance factors in radical additions to carbon-carbon double bonds can be found by considering the effect of (non-polar) substituents on the rate of attack of (nonpolar) radicals. Substituents on the double bond strongly retard addition at the substituted carbon while leaving the rate of addition to the other end essentially unaffected (for example, Table 1.3). This is in keeping with expectation if steric factors determine the regiospeeificity of addition, but contrary to expectation if resonance factors are dominant. 

Example 10.6 A commercial process for the dehydrogenation of ethylbenzene uses 3-mm spherical catalyst particles. The rate constant is 15s , and the diffusivity of ethylbenzene in steam is 4x 10 m /s under reaction conditions. Assume that the pore diameter is large enough that this bulk diffusivity applies. Determine a likely lower bound for the isothermal effectiveness factor. 

The concentration of gas over the active catalyst surface at location / in a pore is ai [). The pore diffusion model of Section 10.4.1 linked concentrations within the pore to the concentration at the pore mouth, a. The film resistance between the external surface of the catalyst (i.e., at the mouths of the pore) and the concentration in the bulk gas phase is frequently small. Thus, a, and the effectiveness factor depends only on diffusion within the particle. However, situations exist where the film resistance also makes a contribution to rj so that Steps 2 and 8 must be considered. This contribution can be determined using the principle of equal rates i.e., the overall reaction rate equals the rate of mass transfer across the stagnant film at the external surface of the particle. Assume A is consumed by a first-order reaction. The results of the previous section give the overall reaction rate as a function of the concentration at the external surface, a. ... 

Reactions other than hrst order can be treated numerically, but a priori predictions of effectiveness factors are rarely possible, even for the simple cases considered here. The approach of Examples 10.6 through 10.8 can sometimes be used to estimate whether mass transfer resistances are important. When mass transfer is important, effectiveness factors are determined experimentally. 

Consider a nonporous catalyst particle where the active surface is all external. There is obviously no pore resistance, but a film resistance to mass transfer can still exist. Determine the isothermal effectiveness factor for first-order kinetics. 

Suppose that catalyst pellets in the shape of right-circular cylinders have a measured effectiveness factor of r] when used in a packed-bed reactor for a first-order reaction. In an effort to increase catalyst activity, it is proposed to use a pellet with a central hole of radius i /, < Rp. Determine the best value for RhjRp based on an effective diffusivity model similar to Equation (10.33). Assume isothermal operation ignore any diffusion limitations in the central hole, and assume that the ends of the cylinder are sealed to diffusion. You may assume that k, Rp, and eff are known. 

The effects of dispersion of the electrocatalyst and of particle size on the kinetics of electrooxidation of methanol have been the subject of numerous studies because of the utilization of carbon support in DMFC anodes. The main objective is to determine the optimum size of the platinum anode particles in order to increase the effectiveness factor of platinum. Such a size effect, which is widely recognized in the case of the reduction of oxygen, is still a subject of discussion for the oxidation of methanol. According to some investigators, an optimum of 2 nm for the platinum particle size exists, but studying particle sizes up to 1.4 nm, other authors observed no size effect. According to a recent study, the rate of oxidation of methanol remains constant for particles greater than 4.5 nm, but decreases with size for smaller particles (up to 2.2 nm). 

Microlevel. The starting point in multiphase reactor selection is the determination of the best particle size (catalyst particles, bubbles, and droplets). The size of catalyst particles should be such that utilization of the catalyst is as high as possible. A measure of catalyst utilization is the effectiveness factor q (see Sections 3.4.1 and 5.4.3) that is inversely related to the Thiele modulus (Eqn. 5.4-78). Generally, the effectiveness factor for Thiele moduli less than 0.5 are sufficiently high, exceeding 0.9. For the reaction under consideration, the particles size should be so small that these limits are met. 

Based on the available atomic-level information and other relevant literature data, factors determining the effect of anion adsorption on the ORR include the following ... 

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