Global and intrinsic rates

As intrinsic rate equations cannot yet be predicted, they must be evaluated from laboratory data. Such data are measurements of the global rate of reaction. The first part of the problem is to extract the equation for the intrinsic rate from the global rate data. Since laboratory reactors are small and relatively low in cost, there is great flexibility in designing them. In particular, construction and operating conditions can be chosen to reduce or eliminate the differences between the global and intrinsic rates, so that more accurate equations for the intrinsic rate can be extracted from the... 

When comparisons between global and intrinsic rates are made, it is understood that the comparison is for the same temperature and concentration. Note that in a reactor operating at steady state the two rates are always the same, but the temperature and composition in the bulk fluid (i.e., the global conditions) are different from those at a site within the catalyst pellet. -For porous pellets with uniform distribution of catalytic material. If the catalyst is deposited only on the outer layer of the pellet, this is not true. 

The book has been written from the viewpoint that the design of a chemical reactor requires, first, a laboratory study to establish the intrinsic rate of reaction, and subsequently a combination of the rate expression with a model of the commercial-scale reactor to predict performance. In Chap. 12 types of laboratory reactors are analyzed, with special attention given to how data can be reduced so as to obtain global and intrinsic rate equations. Then the modeling problem is examined. Here it is assumed that a global rate equation is available, and the objective is to use it, and a model, to predict the performance of a large-scale unit. Several reactors are considered, but major attention is devoted to the fixed-bed type. Finally, in the... 

This procedure obviously requires machine computation capability if it is to employed in reactor design calculations. Fortunately, there are many reactions for which the global rate reduces to the intrinsic rate, which avoids the necessity for calculations of this type. On the other hand, several high tonnage processes (e.g., S02 oxidation) are influenced by heat and mass transfer effects and one must be fully cognizant of their implications for design purposes. 

Global compartmental analysis can be used to recover association and dissociation rate constants in some specific cases when the lifetimes are much shorter than the lifetimes for the association and dissociation processes. An example is the study for the binding dynamics of 2-naphthol (34, Scheme 14) with / -CD.207 Such an analysis is possible only if the observed lifetimes change with CD concentration and at least one of the decay parameters is known independently, in this case the lifetime of the singlet excited state of 33 (5.3 ns). From the analysis the association and dissociation rate constants, as well as intrinsic decay rate constants and iodide quenching rate constants, were recovered. The association and dissociation rate constants were found to be 2.5 x 109M-1 s 1 and 520 s 1, respectively.207... 

In heterogeneous reactions, phase boundaries exist between phases and transport processes the intrinsic rate of reaction should be taken into account simultaneously in reactor design. The combination of mass transfer rates and reaction rates leads to the so-called overall rate. The goal is to express the global rate in terms of the bulk properties of the phases, eliminating the interphase properties. 

It is obvious that the calculation of the reaction rate is very easy in this reactor. Now, let us sketch the reaction rate versus the rotation speed using the data obtained at 203C. As shown in Figure 5.9, the reaction rate is stabilized at rotation speeds above 400-450 rpm. This means that the external mass transfer does not affect the global rate, and thus values of the intrinsic rate can be safely considered to be obtained at those rotation speeds. 

In order to develop a suitable kinetic model of the full NH3-N0-N02/02 SCR reacting system, first the active reactions depending on N0/N02 feed ratio and temperature were identified then a dedicated study was performed aimed at clarifying the catalytic mechanism of the fast SCR reaction on the basis of such a reaction chemistry a detailed kinetic model was eventually derived, whose intrinsic rate parameters were estimated from global non-linear regression of a large set of experimental transient runs. 

At low catalyst loadings, (1 to 2 %) the solid liquid interface area will be small, and so it becomes limiting, hence k0 depends only on kc and on the intrinsic rate, k tj. Then the global rate is proportional to the catalyst loading, m, as can be seen from Eqn. 5.3-5... 

Catalyst poisoning is one of the most severe problems associated with the commercial application of catalysts. It is a phenomenon whose global behavior is studied extensively in industrial laboratories to allow adequate prediction of commercial catalyst life and commercial behavior. Yet, a quantitative understanding of the intrinsic rates and mechanisms of catalyst poisoning is generally lacking, partly because of the complexity of poisoning processes and partly because of the lack of sufficiently careful studies of these processes. 

No matter how active a catalyst particle is, it can be effective only if the reactants can reach the catalytic surface. The transfer of reactant from the bulk fluid to the outer surface of the catalyst particle requires a driving force, the concentration difference. Whether this difference in concentration between bulk fluid and particle surface is significant or negligible depends on the velocity pattern in the fluid near the surface, on the physical properties of the fluid, and on the intrinsic rate of the chemical reaction at the catalyst that is, it depends on the mass-transfer coefficient between fluid and surface and the rate constant for the catalytic reaction In every case the concentration of reactant is less at the surface than in the bulk fluid. Hence the observed rate, the global rate, is less than that corresponding to the concentration of reactants in the bulk fluid. 

The resultant values of A and E and the nature of/(C) establish the desired equation for the intrinsic rate. However, for step 3 we must know or estimate the effective diffusivity. Alternately, the global rate may be measured for small catalyst particles for which -> 1.0. Now internal (and usually external) transport resistances are negligible the bulk temperature and concentrations may be taken as equal to those at a catalyst site, and the observed rate and bulk temperature and concentration data can thus be used directly to obtain /(Q and A and E. 

For use in reactor design the global rate should be calculable at all locations in the reactor. We suppose that the intrinsic rate equation is available. The problem is to evaluate the global rate corresponding to possible bulk concentrations Q, bulk temperatures 7, and flow conditions. If external and internal temperature differences can be neglected, the problem is straightforward and is essentially the reverse of the stepwise solution outlined in Sec. 12-1. The double-trial procedure is not necessary, because /(C) is known. The effective diffusivity of the catalyst pellet is required. The equations we need are Eq. (10-1) for external diffusion,... 

Example 12-2 Using the intrinsic rate equation obtained in Example 12-1, calculate the global rate of the reaction o-Hj p- % at 400 psig and — 196°C, at a location where the mole fraction of ortho hydrogen in the bulk-gas stream is 0.65. The reactor is the same as described in Example 12-1 that is, it is a fixed-bed type with tube of 0.50 in. ID and with x -in. cylindrical catalyst pellets of Ni on AljOj. The superficial mass velocity of gas in the reactor is 15 lb/(hr)(ft ). The effective diffusivity can be estimated from the random-pore model if we assume that diffusion is predominately in the macropores where Knudsen diffusion is insignificant. The macroporosity of the pellets is 0.36. Other properties and conditions are those given in Example 12-1. 

When external and internal temperature differences are also significant, trial solution is required to evaluate the global rate for a given Q and 7, regardless of the order of the intrinsic-rate equation. The effective thermal conductivity is needed, as well as D. Equation (10-1) is applicable, and it is necessary to relate Tf, and 7] by Eq. (10-13), written as... 

After the intrinsic rate equation has been established, it is used to develop a mathematical model of the large-scale reactor. The first step is to obtain the global rate at any point in the reactor, as illustrated in Example 12-2. To complete the model, equations are derived to give the conversion and selectivities in the product stream in terms of the proposed operating conditions. These equations and their solution are the subject of Chapter 13. 

The objective of Chaps. 10 and 11 is to combine intrinsic rate equations with intrapellet and fluid-to-pellet transport rates in order to obtain global rate equations useful for design. It is at this point that models of porous catalyst pellets and effectiveness factors are introduced. Slurry reactors offer an excellent example of the interrelation between chemical and physical processes, and such systems are used to illustrate the formulation of global rates of reaction. 

The rate expressions obtained by chemical kinetics describe file dependency of the reaction rate on kinetic parameters related to the chemical reactions. These rate expressions are commonly referred to as the intrinsic rate expressions of the chemical reactions (or intrinsic kinetics). However, in many instances, file local species concentrations depend also on the rate that the species are transported in the reacting medium. Consequently, the actual reaction rate (also referred to as the global reaction rate) is affected by the transport rates of the reactants and products. 

All these factors are functions of the concentration of the chemical species, temperature and pressure of the system. At constant diffu-sionai resistance, the increase in the rate of chemical reaction decreases the effectiveness factor while al a constant intrinsic rate of reaction, the increase of the diffusional resistances decreases the effectiveness factor. Elnashaie et al. (1989a) showed that the effect of the diffusional resistances and the intrinsic rate of reactions are not sufficient to explain the behaviour of the effectiveness factor for reversible reactions and that the effect of the equilibrium constant should be introduced. They found that the effectiveness factor increases with the increase of the equilibrium constants and hence the behaviour of the effectiveness factor should be explained by the interaction of the effective diffusivities, intrinsic rates of reaction as well as the equilibrium constants. The equations of the dusty gas model for the steam reforming of methane in the porous catalyst pellet, are solved accurately using the global orthogonal collocation technique given in Appendix B. Kinetics and other physico-chemical parameters for the steam reforming case are summarized in Appendix A. 

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. 

In previous sections, we have considered some physical phenomena, which can complicate the processes occurring in a catalyst particle and influence the global (observable) reaction rate or effectiveness factor. Meanwhile, the presence of liquid condensate in some pores can also affect the intrinsic kinetics of the reaction due to the features discussed in Section II. 

This chapter deals with the microkinetics of gas-solid catalytic reaction systems. An applied approach is adopted in the discussion, which starts with the formulation of intrinsic rate equations that account for chemical processes of adsorption and surfece reaction on solid catalysts and then proceeds with the construction of global rate expressions that include the individual and simultaneous effects of physical external and internal mass and heat transport phenomena occurring at the particle scale. 

Figure 2.3 Reactant concentration profiles in different global rate regimes I, external mass transfer limitation II, pore diffusion limitation III, both external and internal mass transfer limitations IV, no mass transfer limitations on the intrinsic rate.

The most significant result of these studies is the internal effectiveness factor which links the intrinsic rate to the actually measured global rate and is also a measure of the efficacy with which the available surface area of the catalyst is utilized. The internal effectiveness factor is defined as... 

The concept of effectiveness developed separately for external or internal transport resistances can be extended to an overall effectiveness factor for treating the general diffusion-reaction problem where both external and internal concentration and temperature gradients exist The overall effectiveness factor, D, is defined for relating the actual global rate to the intrinsic rate, that is, -Ra)p to (-Ra)6- To stun up the definitions for y, 7], and D,... 

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