Reversible exothermic

Adesina [14] considered the four main types of reactions for variable density conditions. It was shown that if the sums of the orders of the reactants and products are the same, then the OTP path is independent of the density parameter, implying that the ideal reactor size would be the same as no change in density. The optimal rate behavior with respect to T and the optimal temperature progression (T p ) have important roles in the design and operation of reactors performing reversible, exothermic reactions. Examples include the oxidation of SO2 to SO3 and the synthesis of NH3 and methanol CH3OH. 

MINIMUM REACTOR VOLUME AT THE OTP OF A SINGLE CFSTR WITH A REVERSIBLE EXOTHERMIC REACTION ... 

For reversible exothermic reactions, the situation is more complex. Figure 6.5a shows the behavior of an exothermic reaction as a plot of equilibrium conversion against temperature. Again, the plot can be obtained from values of AG° over a range of temperatures and the equilibrium conversion calculated as discussed previously. If it is assumed that the reactor is operated adiabatically, and the mean molar heat capacity of the reactants and products is constant, then for a given starting temperature for the reaction Tin, the temperature of the reaction mixture will be proportional to the reactor conversion X for adiabatic operation, Figure 6.5a. 

Thus, if an exothermic reaction is reversible, then Le Chatelier s principle dictates that operation at a low temperature increases maximum conversion. However, operation at a low temperature decreases the rate of reaction, thereby increasing the reactor volume. Then ideally, when far from equilibrium, it is advantageous to use a high temperature to increase the rate of reaction. As equilibrium is approached, the temperature should be lowered to increase the maximum conversion. For reversible exothermic reactions, the ideal temperature is continuously decreasing as conversion increases. 

Other reactions will have somewhat different forms for the curve of Qq versus T. For example, in the case of a reversible exothermic reaction, the equilibrium yield decreases with increasing temperature. Since one cannot expect to exceed the equilibrium yield within a reactor, the fraction conversion obtained at high temperatures may be less than a subequilibrium value obtained at lower temperatures. Since the rate of energy release by reaction depends only on the fraction conversion attained and not on the position of equilibrium, the value of Qg will thus be lower at the higher temperature than it was at a lower temperature. Figure 10.2 indicates the general shape of a Qg versus T plot for a reversible exothermic reaction. For other reaction networks, different shaped plots of Qg versus T will exist. 

Rate of energy release by reaction versus temperature for a reversible exothermic reaction. 

These stability considerations are not limited to first-order irreversible reactions. Figure 10.4 depicts the Qg and Qr curves for a reversible exothermic reaction. The intersections of the Qg curve and lines 3 and 4 represent stable... 

Energy release and energy loss curves for reversible exothermic reaction in a CSTR. 

ILLUSTRATION 10.8 DETERMINATION OF OPTIMUM TEMPERATURE FOR OPERATION OF A SINGLE CSTR IN WHICH A REVERSIBLE EXOTHERMIC REACTION IS BEING CARRIEb OUT... 

One of the most important industrial chemical processes is the manufacture of sulfuric acid. A major step in this process is the oxidation of SO, with air or oxygen-enriched air in the reversible, exothermic reaction corresponding to equation (A) in Example 1-2 ... 

The answers to these questions are contained in part in the reversible, exothermic nature of the reaction, in the adiabatic mode of operation, and in the characteristics of the catalyst. We explore these issues further in Chapters 5 and 21. 

The optimal rate behavior with respect to T has important consequences for the design and operation of reactors for carrying out reversible, exothermic reactions. Examples are the oxidation of SO, to SO, and the synthesis of NH,. 

This is a reversible, exothermic reaction carried out adiabatically in a multistage, fixed-bed reactor with axial flow of fluid and interstage heat transfer for temperature adjustment see Figure 1.4. The catalyst is promoted V205. 

This is also a reversible, exothermic reaction carried out in various types of fixed-bed reactors, involving different arrangements for flow (axial or radial), and temperature adjustment see Figure 11.5. The traditional catalyst is promoted Fe, but more active Ru-based catalysts are finding use, despite the added... 

This is also a reversible, exothermic reaction. Some reactors used for this reaction are similar to those used for ammonia synthesis see Figure 11.6. The standard catalyst is Cu/Zn0/Al203. 

Sulphur is combusted with dry air at about 1100°C to a gas with typically 10-12% SO2 and 9-11% 02. The gas is cooled in a steam boiler to 380-440°C and passed to the converter, where S02 is oxidised to SO3 according to the reversible exothermic reaction... 

Truly isothermal operation of a tubular reactor may not be feasible in practice because of large enthalpies of reaction or poor heat transfer characteristics. Nor is it always desirable, as, for example, in the case of a reversible exothermic reaction (see Sect. 3.2.4). In an exothermic catalytic reaction, it may be necessary to provide adequate means for heat transfer to prevent the development of local hot-spots on which coking may occur and reduce the catalyst activity. An excessive temperature rise may also cause the catalyst particles to sinter, thereby reducing their surface area and causing an irreversible decrease in catalytic activity. 

Figure 10 shows a curve of conversion x plotted against temperature T, for a particular reaction with fixed values of V and F . The maximum is characteristic of all reversible exothermic reactions and the greatest conversion is achieved when the reactor is operated at Top. ... 

The arguments advanced in Sect. 3.2.3 apply equally well to a continuous stirred tank reactor. With a reversible exothermic reaction and a fixed mean residence time, t, there is an optimum temperature for operation of a continuous stirred tank reactor. Since the conditions in an ideal stirred tank are, by definition, uniform, there is no opportunity to employ a temperature gradient, as with the plug-flow reactor, to achieve an even better performance. 

Fig. 24. Heat generation and heat loss lines for a reversible exothermic reaction in a continuous stirred tank reactor.

Inspection of Fig. 24, which represents the behaviour of a reversible exothermic reaction with various cooling rates, shows that autothermal operation is possible (point A), but that a somewhat reduced cooling rate results in a greater Qq, and hence conversion (point B) excessive cooling will, of course, quench the reaction (point C). 

For exothermic reversible reactions the situation is different, for here two opposing factors are at work when the temperature is raised—the rate of forward reaction speeds up but the maximum attainable conversion decreases. Thus, in general, a reversible exothermic reaction starts at a high temperature which decreases as conversion rises. Figure 9.5 shows this progression, and its precise values are found by connecting the maxima of the different rate curves. We call this line the locus of maximum rates. 

For reversible exothermic reactions the same three cases occur, as shown in Fig. 9.15. However, it can be seen that here there is an optimum operating temperature for the given r value where conversion is maximized. Above or below this temperature the conversion drops thus, proper control of heat removal is essential. 

Figure 9.15 Solution of energy and material balances for reversible exothermic reaction.

D. C. Dyson, F. J. M. Horn, R. Jackson, and C. B. Schlesinger. Reactor optimization problems for reversible exothermic reactions. Canadian J. ofChem. Eng., 45 310,1967. 

The chemical equilibrium constant of a reversible exothermic reaction decreases as temperature increases. 

TABLE 2.3 Reversible Exothermic Reaction Kinetic Parameters... 

Multiple CSTRs with Reversible Exothermic Reactions... 

W. L. Luyben, Design and control of gas-phase reactor /recycle processes with reversible exothermic reactions, Ind. Eng. Chem. Research 39, 1529 (2000). 

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