Global Rates of Reaction

Investigation of the global rates of reaction can be carried out in instrumented bench-scale equipment, such as the RC1 (Mettler-Toledo) plus on-line chemical analysis. Commercially available equipment allows well-controlled process conditions, and can be used in a variety of modes (e.g., isothermal, adiabatic, temperature programmed). The test volumes, which may be up to 2 liters depending on the energy involved, enable reasonable simulation of process conditions, and are more representative than very small samples, particularly for mixed phase systems. The scale of such equipment permits the collection of accurate data. 

Alternative expressions for the global rates of Reactions 14 and 16 were tried while developing the model. For the CO + CO2 conversion (Reaction 16) the overall correlation derived by Howard et al. (2) was initially used, but with this the calculated values of SL were considerably lower than the measured ones. For the methane disappearance rate (Reaction 14) the correlations proposed by Westbrook and Dryer (7) were tried, and these gave results negligibly different from those obtained by Equation 18. 

High liquid holdup may cause the liquid-phase diffusional resistance to the gaseous reactant to be an important factor affecting the global rate of reaction. 

This is the expression for the global rate in terms of the bulk-reactant concentration. The concentration profile in this case is shown by the solid line in Fig. 7-1. It is a very restricted illustration of a global rate, since heat-transfer resistances were not considered (constant temperature was assumed) and only external mass transfer is involved (the catalyst particle is non-porous). These restrictions are removed in the detailed treatment in Chaps. 10 and 11, but this simple example illustrates the meaning of global rates of reaction for heterogeneous systems. 

When the major catalytic surface is in the interior of a solid particle, the resistance to transport of mass and energy from the external surface to the interior can have a significant effect on the global rate of reaction. Quantitative treatment of this problem is the objective in Chap. 11. It is sufficient here to note that this treatment rests on a geometric model for the extent and distribution of void spaces within the complex porous structure of the particle. It would be best to know the size and shape of each void space in the particle. In the absence of this information the parameters in the model should be evaluated from reliable and readily obtainable geometric properties. In addition to the surface area, three other properties fall into this classification void volume, the density of the solid material in the particle, and the distribution of void volume according to void size (pore-volume distribution). The methods of measurement of these four properties are considered in Secs. 8-5 to 8-7. 

The design of slurry reactors is, as usual for heterogeneous reactions, a two-step process formulation of the global rate of reaction, followed by design of an integral reactor by the procedures presented for homo-... 

Predict the global rate of reaction for the oxidation of SO2 at bulk-gas conditions of 20% conversion at 480°C. Other conditions are as given in Prob. 10-2. The rate at the catalyst surface is to be calculated from Eq. (G) of Example 9-2. Assume isothermal conditions. The constants in this equation at 480°C are... 

The extent to which surface transport affects global rates of reaction has not been established. For it to be important, adsorption must occur, but this is also a requirement for catalytic activity. Indirect evidence suggests that in some cases the effect is considerable. For example. Miller and Kirk found higher rates of dehydration of alcohols on silica-alumina than could be explained with only pore-volume diffusion to account for intraparticle resistances. They attributed the discrepancy to surface diffusion. Masamune and Smith found that surface transport of ethanol on silica gel at temperatures as high as 175°C predominated over gas-phase diffusion in the pore. In view of the data available, it seems wise at least to consider the possibility of surface migration in any evaluation of intraparticle effects. This can be done by adding a surface-diffusion contribution to the effective diffusivity considered in the previous section. The method of doing this is presented below, but its usefulness is still limited because of inadequate experimental and theoretical aspects of surface transport. 

From the assumptions and approximations presented, it is clear that, surface diffusion js Jiot jvell junderstoad. lt is. hope.d that impro.V d -interpretations of surface migration will permit a more accurate assessment of its effect on global rates of reaction. When we consider the effect of intraparticle resistances in Secs. 11-6 to 11-11 we shall suppose that the used is the most appropriate value and includes, if necessary, a surface contribution. 

Example 11-7 illustrates one of the problems in scale-up of catalytic reactors. The results showed that for all but -in. pellets intrapellet diffusion significantly reduced the global rate of reaction. If this reduction were not considered, erroneous design could result. For example, suppose the laboratory kinetic studies to determine a rate equation were made with f-in. pellets. Then suppose it was decide tojise f-ih. pellets in the commercial reactor to reduce the pressure drop through the bed. If the rate equation were used for the -in. pellets without modification, the rate would be erroneously high. At the conditions of part b) of Example 11-7 the correct would be only 0.68/0.93, or 73% of the rate measured with -in. pellets. 

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... 

The entering concentration of nitrobenzene was 5.0 x 10 g mole/cm. The global rate of reaction was represented by the expression... 

A reaction 2A - B is being studied in a fluidized-bed reactor at atmospheric pressure and 200°F. It appears that the global rate of reaction may be approximated by a second-order irreversible equation... 

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. 

This gives, for the global rate of reaction in equation (7-50)... 

The development of the correlation is based on the global rates of reaction, i.e. considering the entire available volume for the reaction in the equipment, whereas Naidu et al. (1994) placed the test tube containing the reacting medium at a particular location where there was a maximum intensity of cavitation as detected by the hydrophones. The intensities of cavitation are different at different points in the ultrasonic reactor, which will result into different rates of reaction. The mapping studies... 

A relationship may easily be derived between intraparticle temperature and concentration differences (AT and AQ) just by considering a boundary surface enclosing some section or all of an arbitrary porous structure as the starting point. Under steady-state conditions, the diffusion of reactants across this boundary surface is equal to the global rate of reaction within the boundary surface. Then, the heat released by reaction within the surface can be expressed in terms of the diffusion rate across the boundary ... 

Two-phase flow in three-phase fixed-bed reactors makes the reactor design problem complex [12], Interphase mass transfer can be important between gas and liquid as also between liquid and catalyst particle. Also, in the case of trickle-bed reactors, the rivulet-type flow of the liquid falling through the fixed bed may result (particularly at low liquid flow rates) in only part of the catalyst particle surface being covered with the liquid phase. This introduces a third mass transfer process from gas to the so-called gas-covered surface. Also, the reaction rates in three-phase fixed-bed catalytic reactors are highly affected by the heat transfer resistances resistance to radial heat transfer and resistance to fluid-to-particle heat transfer. As a result of these and other factors, predicting the local (global) rate of reaction for a catalyst particle in three-phase fixed-bed reactors requires not only... 

Herskowitz, M., and S. P. Mosseri. Global Rates of Reaction in Trickle-Bed Reactors Effects of Gas and Liquid Flow Rates. Ind. Eng. Chem. Fundam. 22 (1983) 4-6. 

Tsukamoto, T., S. Morita and J. Okada. Oxidation of Glucose on Immobilized Glucose Oxidase in a Trickle-Bed Reactor Effect of Liquid-Solid Contacting Efficiency on the Global Rate of Reaction. Ken. Eng. Farm. Bull. 30 (1982) (5) 1539-... 

These relationships state that the mass and energy transferred across the interface are equal to the fluxes at the pellet surface, which in turn are respectively equal to the global rate of reaction per unit area and the rate at which the heat is generated by the reaction. These relationships can be used if desired, to eliminate... 

Therefore, the global rate of reaction as affected by diffusion and pore-mouth deactivation is described by Eqs. 5.55, 5.64, and 5.68. These results are also summarized in Table 5.3. When the Thiele modulus for the deactivation reaction ([Pg.95]

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