Equilibrium conversions exothermic reactions

For exothermic reactions, equilibrium conversion decreases with increasing temperature... 

The local reactor temperature affects the rates of reaction, equilibrium conversion, and catalyst deactivation. As such, the local temperature has to be controlled to maximize reaction rate and to minimize deactivation. In the case of an exothermic (endothermic) reaction, higher (lower) local temperatures can cause suboptimal local concentrations. Heat will have to be removed (added) to maintain more uniform temperature conditions. The mode of heat removal (addition) will depend on the application and on the required heat-transfer rate. 

Exothermic Reactions. The conversion-temperaiure plot for this scheme is shown in Figure 11-6. We see that with three interstage coolers, 88% conversion can be achieved, compared to an equilibrium conversion of 35% for no interstage cooling. 

We can see from Table 9.2 that the equilibrium constant depends on the temperature. For an exothermic reaction, the formation of products is found experimentally to be favored by lowering the temperature. Conversely, for an endothermic reaction, the products are favored by an increase in temperature. 

As the temperature increases, the equilibrium conversion increases for endothermic reactions and decreases for exothermic reactions. 

Table VIII demonstrates the inverse relationship of conversion to S02 concentration in the feed that is a consequence of applying flow reversal to S02 oxidation using a single reactor. As the S02 concentration in the table moves from 0.8 to over 8 vol%, the conversion drops from 96-97% down to 85%. At the same time, the maximum bed temperature changes from 450 to 610°C. For an equilibrium-limited, exothermic reaction, this behavior is explained by variation of the equilibrium conversion with temperature.

Figure 6.3b shows a plot of equilibrium conversion versus temperature. It can be seen that as the temperature increases, the equilibrium conversion decreases (for this reaction). This is consistent with the fact that this is an exothermic reaction. 

Example 6.2 shows that for an exothermic reaction, the equilibrium conversion decreases with increasing temperature. This is consistent with Le Chatelier s Principle. If the temperature of an exothermic reaction is decreased, the equilibrium will be displaced in a direction to oppose the effect of the change, that is, increase the conversion. 

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. 

This behavior can be shown graphically by constructing the rD-7 -/A relation from equation 5.3-16, in which kp kr, and Keq depend on T. This is a surface in three-dimensional space, but Figure 5.2 shows the relation in two-dimensional contour form, both for an exothermic reaction and an endothermic reaction, with /A as a function of T and ( rA) (as a parameter). The full line in each case represents equilibrium conversion. Two constant-rate ( -rA) contours are shown in each case (note the direction of increase in (- rA) in each case). As expected, each rate contour exhibits a maximum for the exothermic case, but not for the endothermic case. 

With an irreversible reaction, virtually complete conversion can be achieved in principle, although a very long time may be required if the reaction is slow. With a reversible reaction, it is never possible to exceed the conversion corresponding to thermodynamic equilibrium under the prevailing conditions. Equilibrium calculations have been reviewed briefly in Chap. 1 and it will be recalled that, with an exothermic reversible reaction, the conversion falls as the temperature is raised. The reaction rate increases with temperature for any fixed value of VjF and there is therefore an optimum temperature for isothermal operation of the reactor. At this temperature, the rate of reaction is great enough for the equilibrium state to be approached reasonably closely and the conversion achieved in the reactor is greater than at any other temperature. 

With an exothermic reaction, on the other hand, it may be necessary to remove heat to control the reaction and, if the reaction is reversible, to ensure a reasonable equilibrium conversion. The possibility of thermal runaway is always present with an exothermic process and this, with its implications for safety, must always be examined in any full reactor design. 

It is often necessary to employ more than one adiabatic reactor to achieve a desired conversion. The catalytic oxidation of SOj to SO3 is a case in point. In the first place, chemical equilibrium may have been established in the first reactor and it would be necessary to cool and/or remove the product before entering the second reactor. This, of course, is one good reason for choosing a catalyst which will function at the lowest possible temperature. Secondly, for an exothermic reaction, the temperature may rise to a point at which it is deleterious to the catalyst activity. At this point, the products from the first reactor are cooled prior to entering a second adiabatic reactor. To design such a system, it is only necessary to superimpose on the rate contours the adiabatic temperature paths for each of the reactors. The volume requirements for each reactor can then be computed from the rate contours in the same way as for a... 

For an increase in temperature, equilibrium conversion rises for endothermic reactions and drops for exothermic reactions. 

Figure 5-11 Equilibrium conversion versus T for an exothermic reversible reaction in preceding example.

Another way of visualizing the optimal trajectory for the exothermic reversible reaction is to consider isothermal reaction rates at increasing temperatures. At T the equilibrium conversion is high but the rate is low, at T2 the rate is higher but the equihbrium conversion is lower, at the rate has increased further and the equihbrium conversion is even lower, and at a high temperature T4 the initial rate is very high but the equihbririm conversion is very low. 

Figure 5-18 Illustration of isothermal trajectories for an exothermic reversible reaction. At the lowest temperature the rate is low but the eqmlibiium conversion is high, while at the highest temperature the initial rate is high but the equilibrium conversion is low. From the 1/r versus X plot at these temperatures, it is evident that T should decrease as X increases to require a minimum residence time,...

The shapes of these curves is plotted in Figure 6-13 for endothermic and exothermic reactions. If AH > 0, then the shape of the X(T) curve is nearly unchanged because the equilibrium conversion is lower at low temperatures, but if AH < 0, then X(T) increases with T initially but then decreases at high T as the reversibihty of the reaction causes X to decrease. However, the multiplicity behavior is essentially unchanged with reversible reactions. 

This mode is used industrially for exothermic reactions such as NH3 oxidation and in CH3OH synthesis, where exothermic and reversible reactions need to operate at temperatures where the rate is high but not so high that the equilibrium conversion is low. Interstage cooling is frequently accomplished along with separation of reactants from products in units such as water quenchers or distillation columns, where the cooled reactant can be recycled back into the reactor. In these operations the heat of water vaporization and the heat removed from the top of the distillation column provides the energy to cool the reactant back to the proper feed temperature. 

Stripping of chlorine from hydroxides such as Cl2Sn(OH)2 could eventually lead to gas-phase SnO or Sn02. However, at the relatively low temperatures typical of tin oxide CVD ( 873-973 K), we do not expect these oxides to form, based on the equilibrium calculations described above. Thus, the formation of tin hydroxides is not only thermodynamically favored (i.e., based on minimization of the Gibbs free energy), but there are also exothermic reaction pathways that we expect to be kinetically favorable. The primary tin carrier in the CVD process could therefore be a tin hydroxide. Complete conversion to Sn02 would most likely occur via reactions on the surface. 

Originally, the hydration of olefins to alcohols was carried out with dilute aqueous sulphuric acid as the catalyst. Recently, the direct vapour phase hydration of olefins with solid catalysts has become the predominant method of operation. From the thermodynamic point of view, the formation of alcohols by the exothermic reaction (A) is favoured by low temperatures though even at room temperature the equilibrium is still in favour of dehydration. To induce a rapid reaction, the solid catalysts require an elevated temperatue, which shifts the equilibrium so far in favour of the olefin that the maximum attainable conversion may be very low. High pressures are therefore necessary to bring the conversion to an economic level (Fig. 11). To select an optimum combination of reaction conditions with respect to both rate limitation and equilibrium limitation,... 

The chemical equilibrium assumption often results in modeling predictions similar to those obtained assuming infinitely fast reaction, at least for overall aspects of practical systems such as combustion. However, the increased computational complexity of the chemical equilibrium approach is often justified, since the restrictions that the equilibrium constraint places on the reaction system are accounted for. The fractional conversion of reactants to products at chemical equilibrium typically depends strongly on temperature. For an exothermic reaction system, complete conversion to products is favored thermodynamically at low temperatures, while at high temperatures the equilibrium may shift toward reactants. The restrictions that equilibrium place on the reaction system are obviously not accounted for by the fast chemistry approximation. 

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