Global Rate Equation

Rate equations have been derived for catalyst pellets of different shapes (slab, sphere) by combining the equation for the rate of internal pore diffusion and rate of reaction (Sections 4.2.1.1 and 4.2.1.2). This rate equation (or flux equation), which is a function of concentration of A, Qs on the external surface of the catalyst pellet, is written as 

Substituting Equation 4.219 for Cp,s into Equation 4.216, we get the global rate equation (or flux equation) 

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A possible explanation for the pseudo-limiting-current formation is as follows considering the global rate equations of stages 3 and 4 of mechanism 1 (without restrictions, only anodic terms) ... 

Assuming pseudo-steady state for the concentrations of the free radicals H and Br , the global rate equation becomes... 

This rate can be added to the global rate equation. Here, a is the porosity and the superficial velocity. 

At steady state the rates of the individual steps will be identical. This equality can be used to develop a global rate equation in terms of the concentrations and temperatures of the bulk fluid. The derivation of such equations will be considered in detail in Chaps. 10 to 12, but a very simple treatment is given next to illustrate the nature of the problem. 

In the next section various reaction models are considered. Then global rate equations are developed in Sec. 14-3 for one model (shrinking core). In Sec. 14-4 integrated conversion-vs-time relationships (for single particles) are presented. Such relationships are suitable for use in design of reactors in which the fluid phase is completely mixed. In Secs. 14-5 and 14-6 all these results will be applied to reactor design. 

Global Rate Equations (Shrinking-core Mode ... 

SECTION 14-3 GLOBAL. RATE EQUATIONS (SHRINKING-CORE MODEL)... 

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 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... 

In the following sections, we derive global rate equations (or flux equations) for the three cases listed above. 

By equating rate expressions ry r2 and r, the internal concentration terms Aa and Qs are eliminated from the rate equation and the global rate equation for is derived as a function of bulk gas concentration The global rate expression takes into account the transfer of A across three resistances connected in series ... 

As a first step towards obtaining the global rate equation r, a rate equation is derived by taking into account the rate of diffusion through the internal pores of the catalyst and the rate of reaction at the active sites (r2 and r,). The derivation of this rate equation for a slabshaped catalyst pellet and a spherical catalyst pellet is presented in the following sections. 

Combining all the rate Equations 4.237,4.239,4.240 and 4.241 and eliminating the intermediate concentration terms from the rate expressions, we obtain the global rate equation as a function of CAg, which is the bulk concentration of A in the gas phase. The final equation for the global rate rA is... 

Introduces global rate equations and explicit design equations for a variety of non-catalytic reactors... 

For elementary-step reactions, is equal to stoichiometric coefficient of species i (t ), whereas for global rate equations, the order of the reaction may vary. For the forward reaction rate, the rate coefficient k can be expressed by the Arrhenius model ... 

Examples of application of rate determining steps will be encountered in Section 1.5 and in the formulation of the kinetics of catalytic processes in Chapter 2. In Section 2.3.1 a single reaction A R, consisting of 3 steps chemisorption of A, chemical reaction and desorption of R, proceeding sequentially, is dealt with. The introduction of a rate determining step reduces a complicated global rate equation to a much more tractable form. Of course, the three possible rate determining steps have to be considered and this leads to three... 

For example, finite stirring will lead to a shift in the mean concentration of the jth qhemical species away from the steady state, Xgj, of the global rate equation (5)... 

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