Global Reaction Rates

As with the other surface reactions discussed above, the steps m a catalytic reaction (neglecting diffiision) are as follows the adsorption of reactant molecules or atoms to fomi bound surface species, the reaction of these surface species with gas phase species or other surface species and subsequent product desorption. The global reaction rate is governed by the slowest of these elementary steps, called the rate-detemiming or rate-limiting step. In many cases, it has been found that either the adsorption or desorption steps are rate detemiining. It is not surprising, then, that the surface stmcture of the catalyst, which is a variable that can influence adsorption and desorption rates, can sometimes affect the overall conversion and selectivity. 

The key-step is the NO decomposition (Eqn. 23) the global reaction rate depends for a great part of the rate on this step. 

The rates at which chemical transformations take place are in some circumstances strongly influenced by mass and heat transfer processes (see Sections 12.3 to 12.5). In the design of heterogeneous catalytic reactors, it is essential to utilize a rate expression that takes into account the influence of physical transport processes on the rate at which reactants are converted to products. Smith (93) has popularized the use of the term global reaction rate to characterize the overall rate of transformation of reactants to... 

At steady state, the rates of each of the individual steps will be the same, and this equality is used to develop an expression for the global reaction rate in terms of bulk-fluid properties. Actually, we have already employed a relation of this sort in the development of equation 12.4.28 where we examined the influence of external mass transfer limitations on observed reaction rates. Generally, we must worry not only about concentration differences between the bulk fluid and the external surface of the catalyst, but also about temperature differences between these points and intraparticle gradients in temperature and composition. 

Let us now turn our attention to the problem of determining the global reaction rate at some arbitrary point in a heterogeneous catalytic reactor from a knowledge of the following parameters. 

Values of all of these parameters must be available or estimated if we are to determine the global reaction rate. Some of these quantities can be evaluated from standard handbooks of physical property data, or generalized correlations such as those compiled by Reid and Sherwood (87). Others can be determined only by experimental measurements on the specific reactant/catalyst system under consideration. 

Determination of the global reaction rate that applies to a given segment of reactor volume involves the use of equations developed earlier. 

The time-to-rimaway can be calculated using dT/dt and Tmax values. This calculated time is a measure of the possible global reaction rate. ARC experimental results may also be used to develop required mathematical models for process design. 

Apparent activation energy in this book, the constant Ea that defines the effect of temperature on the global reaction rate. 

It is possible to combine the resistances of internal and external mass transfer through an overall effectiveness factor, for isothermal particles and first-order reaction. Two approaches can be applied. The general idea is that the catalyst can be divided into two parts its exterior surface and its interior surface. Therefore, the global reaction rates used here are per unit surface area of catalyst. 

Such global reaction expressions can be found for oxidation of a range of hydrocarbon fuels [107], They may be useful for engineering considerations but should be used very cautiously. Global reaction rates are only valid in a narrow range of conditions and cannot be extrapolated with any confidence. 

Table 10.7 illustrates the results of Gloyna and Li (1993) for treatment of hazardous wastes by SCWO. Pressure is given in psi, where 1 bar = 14.50 psi. The following equations describe global reaction rates for the SCWO of six different substituted phenols. The rates of phenolic compound expressions were obtained at 460°C and 250 atm with [organic] = 100 pmol/L and [02] = 7 mmol/L. This rate was calculated as pseudo first order for SCWO of each phenolic compound. 

In order to calculate the theoretically predicted dependence of the global reaction rate on potential, the value of the symmetry factor p is missing. In many one-electron transfer reactions, p approximates a value of 0.5. A reminder should be given here that the intention is to find out whether a postulated reaction mechanism is possible or should be rejected. In this perspective, it is not necessary to have an exact value for p, and it is not indefensible to presuppose that p = 0.5. 

In order to determine the relative importance of mass-transport processes in gas-liquid-solid-reactions, it is recommended to measure the global reaction rate as function of catalyst concentration w (keeping all other operating variables constant). With the assumption of spherical catalyst particles, the specific surface of the catalyst can be calculated as... 

In the case of a simple first-order reaction with respect to the gaseous reactant (assuming that the liquid reactant is not limiting), the effective global reaction rate can be formulated as... 

The question remains as to when the various diffusion effects really influence the conversion rate in fluid-solid reactions. Many criteria have been developed in the past for the determination of the absence of diffusion resistance. In using the many criteria no more information is required than the diffusion coefficient DA for fluid phase diffusion and for internal diffusion in a porous pellet, the heat of reaction and the physical properties of the gas and the solid or catalyst, together with an experimental value of the observed global reaction rate (R ) per unit volume or weight of solid or catalyst. For the time being the following criteria are recommended. Note that intraparticle criteria are discussed in much greater detail in Chapter 6. 

In some cases, evaluating a global reaction rate based on the total radiation absorbed by the reactor is not equivalent to evaluate rates based on the radiation absorbed locally, especially when mass transfer limitations occur. Thus, appropriate analysis of radiative transfer in reactors can be a valuable tool in making design decisions. 

The film theory was originally proposed by Whitman,195 who obtained his idea from the Nernst117 concept of the diffusion layer. It was first applied to the analysis of gas absorption accompanied by a chemical reaction by Hatta.85,86 It is a steady-state theory and assumes that mass-transfer resistances across the interface are restricted to thin films in each phase near the interface. If more than one species is involved in a multiphase reaction process, this theory assumes that the thickness of the film near any interface (gas-liquid or liquid-solid) is the same for all reactants and products. Although the theory gives a rather simplified description of the multiphase reaction process, it gives a good answer for the global reaction rates, in many instances, particularly when the diffusivities of all reactants and products are identical. It is simple to use, particularly when the... 

Thus, the overall (global) reaction rate is dependent upon four mass-transfer1 resistances plus a kinetic resistance. 

Once again, if A C, = HAiL, and if the global reaction rate R is expressed as... 

This reaction was studied [10-13] in a heated furnace (both horizontal and vertical) and a magnetically rotated dc plasma reactor. In the magnetically rotated dc plasma reactor Mahawili and Weinberg [10] found the reassociation of Cl radicals affects the global reaction rate at low oxygen concentration. Under these conditions, the reaction was zero order with respect to TiCl4 and oxygen... 

The pseudo-homogeneous assumption means that both the solid and fluid phases are are considered a single phase. Therefore, we avoid considering mass and heat transfer from and to the catalytic pellets. This model assumes that the conqionent concentrations and the temperature in the pellets are the same as those in the fluid phase. This assumption is approximated when the catalyst pellet is small and mass and heat transfer between the pellets and the fluid phase are rapid. The reaction rate for this model, called the global reaction rate, includes heat and mass transfer. If heat and mass transfer are made insignificant, then the reaction rate is called the intrinsic reaction rate. 

Rate-determining step(s) i.e., the global reaction rate is determined by the rate(s) or the slowest stepfs) in the reaction network composing the overall or global reaction... 

This model is applicable to the reactions of nonporous pellets and to porous pellets when the global rate is controlled by pore diffusion. Reaction is limited to a surface separating the solid reactant at the core of the pellet surrounded by a porous layer of solid product. It occurs initially on the external surface of the pellet, and the thickness of the product layer increases as the reaction proceeds, as illustrated in Fig. 1. The global reaction rate is determined by three resistances— mass transfer from bulk gas to particle surface, diffusion... 

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