Catalyst efficiency factor

Practically, mathematical models are based on the conservation laws of mass, energy and momentum, which lead to mass, energy and momentum balances. The balances, together with transport and kinetics equations, form a set of equations (ODE or PDE) whose solution gives the component concentrations, temperature and pressure profiles inside the reactor. Mass and heat transport coefficients, reactants and products physical properties, catalyst efficiency factor and all parameters appearing in model equations have to be expressed. 

This ratio is called the catalyst efficiency factor. The rate is therefore ... 

When a solid acts as a catalyst for a reaction, reactant molecules are converted into product molecules at the fluid-solid interface. To use the catalyst efficiently, we must ensure that fresh reactant molecules are supplied and product molecules removed continuously. Otherwise, chemical equilibrium would be established in the fluid adjacent to the surface, and the desired reaction would proceed no further. Ordinarily, supply and removal of the species in question depend on two physical rate processes in series. These processes involve mass transfer between the bulk fluid and the external surface of the catalyst and transport from the external surface to the internal surfaces of the solid. The concept of effectiveness factors developed in Section 12.3 permits one to average the reaction rate over the pore structure to obtain an expression for the rate in terms of the reactant concentrations and temperatures prevailing at the exterior surface of the catalyst. In some instances, the external surface concentrations do not differ appreciably from those prevailing in the bulk fluid. In other cases, a significant concentration difference arises as a consequence of physical limitations on the rate at which reactant molecules can be transported from the bulk fluid to the exterior surface of the catalyst particle. Here, we discuss... 

Figure 11.14b illustrates the dependence of the Thiele modulus q> on the efficiency factor //. Two characteristic regimes can be seen for small values of the Thiele modulus, q> < 0.18, the efficiency factor will be close to 1, i] I for values of the Thiele modulus larger than 3,

3, the efficiency factor will be antiproportional to the Thiele modulus, r 1/ cp. Practically this means that from a value of the efficiency factor of 3 onwards no educt reaches the interior of the catalyst particle (which in our case is approximated as a plate). 

Baylis-Hillman reactions, the protonated amine was the governing factor in determining catalyst efficiency, thus making quinuclidine itself a better catalyst than 3-heteroatom substituted analogs, which are of reduced basicity/nucleophilic-ity and consequently give lower reaction rates. 

The importance of the wetting efficiency results mainly from the fact that it is closely related to the reaction yield, and more specifically to the catalyst effectiveness factor (Burghardt et al., 1995). The reaction rate over incompletely covered catalytic particles can be smaller or greater than the rate observed on completely wetted packing, depending on whether the limiting reactant is present only in the liquid-phase or in both gas and liquid-phases. 

Adlington and Thompson (28) have pointed out that the advantages of a fluidized system are not likely to be associated with any marked improvement in catalyst efficiency. Other factors, like freedom from pressure drop increases when processing feeds which contain particulate... 

The effect of diffusion on the rate of a heterogeneous catalytic reaction is characterized by the efficiency factor of a catalyst, tj, defined as the ratio of the actual reaction rate to the rate that would be in the kinetic region under the same conditions. 

In industry large pellets of a catalyst were employed (e.g., 6-8 mm in size), and the rate of the process was essentially affected by the slowness of the diffusion of ammonia in the pores of the catalyst the efficiency factor at this size of pellets is about 0.5. The effect of diffusion retardation of the ammonia synthesis was studied both at high pressures (99), when the free path of molecules is much smaller than the radius of catalyst pores so that the bulk diffusion is operative, and at pressures near to 1 atm (116), where there is a transition from the bulk to the Knudsen diffusion. 

Recently the industry turned to smaller catalyst pellets or to pellets containing, along with narrow pores determining the surface area of the catalyst, wide transport pores in this way the efficiency factor approaches unity. 

The experiments were done at 70, 100, and 130°C and at pressures somewhat lower than atmospheric. Under these conditions reaction (368) is practically irreversible. Activated charcoal of the trademark Bayer AKT-4 ground to grain size 0.25-0.5 mm served as a catalyst. Estimation of the efficiency factor on the basis of the determination of the effective difusion coefficient of hydrogen in nitrogen or helium has shown that for this grain size the results of reaction rate measurements refer to the kinetic region. Estimation of relaxation time of the reaction rate from (67) showed the reaction to be quasi-steady at the condition of our experiments in the closed system. 

Whenever the kinetics of a chemical transformation can be represented by a single reaction, it is sufficient to consider the conversion of just a single reactant. The concentration change of the remaining reactants and products is then related to the conversion of the selected key species by stoichiometry, and the rates of production or consumption of the various species differ only by their stoichiometric coefficients. In this special case, the combined influence of heat and mass transfer on the effective reaction rate can be reduced to a single number, termed the catalyst efficiency or effectiveness factor rj. From the pioneering work of Thiele [98] on this subject, the expressions pore-efficiency concept and Thiele concept have been coined. 

For practical purposes however, eq 60 again suffers from the disadvantage that the Thiele modulus must be specified in order to calculate the catalyst efficiency. Thus, the intrinsic rate constant must be known. In this situation, instead of directly plotting eq 60, it is more convenient to relate the effectiveness factor to the Weisz modulus, calculated from eq 58. For selected values of the Biot number Bim, such a diagram is given in Fig. 9. 

From this figure, it can be concluded that the reduction of the effectiveness factor at large values of becomes more pronounced as the Biot number is decreased. This arises from the fact that the reactant concentration at the external pellet surface drops significantly at low Biot numbers. However, a clear effect of interphase diffusion is seen only at Biot numbers below 100. In practice, Bim typically ranges from 100 to 200. Hence, the difference between the overall and pore effectiveness factor is usually small. In other words, the influence of intraparticle diffusion is normally by far more crucial than the influence of interphase diffusion. Thus, in many practical situations the overall catalyst efficiency may be replaced by the pore efficiency, as a good approximation. 

For very small catalyst partides, this equation must itsdf be corrected by an efficiency factor to account for diffusion in industrial catalyst systems, in which the particle diameter reaches 6 to 12 mm. 

Owing to the comparatively small size of the pores (up to 100 p.m, compared to a pitch of a few millimeters for the honeycomb channels) and the small thickness of the catalyst layer (a few microns, compared to some tenths of a millimeter for the catalytic wall of the honeycomb channels), both internal and external mass transfer limitations to NO conversion in catalytic filters can easily be neglected. An efficiency factor equal to unity can thus be assumed with confidence for NO reduction, contrary to honeycomb catalysts, for which this parameter is hardly higher than 0.05% at the conventional operating temperatures (320-380 C). 

A second advantage of catalytic fillers over honeycomb converters for the DeNOx reaction lies in the comparatively small degree of SO2 oxidation they should allow. This last reaction has to be kept to a minimum, since the formed SO3 would react with the ammonia slip to form ammonium sulphate deposits in the pipeline and apparatuses downstream of the NO converter, causing their obstruction in a relatively short time. Oxidation of SO2 on V-Ti catalysts is a rather slow reaction compared with NO reduction, so the efficiency factor of honeycomb catalysts for this reaction is practically 1, despite the relatively thick catalyst walls. Figure 10 shows, for kinetics and operating parameters given in Ref. 38, the conversion attained for the NO reduction and the SO2 reaction as a function of the wall s thickness of a typical DeNOx honeycomb catalyst. As expected,... 

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