Reversible Exothermic Reaction

This is not a reversible reaction in the strict sense and does not spontaneously seek equilibrium between products and reactants. The exothermic reverse reaction, respiration, occurs in a different part of phytoplankton cells or is mediated by heterotrophic organisms. 

Optimal Cooling for a Reactor with an Exothermic Reversible Reaction... 

An important characteristic of an exothermic reversible reaction is that the rate has an optimal value (a maximum) with respect to Tat a given composition (e.g., as measured by /A). This can be shown from equation 5.3-14 (with n = 1 and Keq = Kceq). Since gf and gr are independent of T, and r = rD/vD (in equation 5.3-1),... 

For an exothermic reversible reaction, since AH is negative, (drDldT)jA is positive or negative depending on the relative magnitudes of the two terms on the right in equation 5.3-22. This suggests the possibility of a maximum in rD, and, to explore this further, it is convenient to return to equation 5.3-3. That is, for a maximum in rD,... 

For exothermic, reversible reactions, the existence of a locus of maximum rates, as shown in Section 5.3.4, and illustrated in Figures 5.2(a) and 18.3, introduces the opportunity to optimize (minimize) the reactor volume or mean residence time for a specified throughput and fractional conversion of reactant. This is done by choice of an appropriate T (for a CSTR) or T profile (for a PFR) so that the rate is a maximum at each point. The mode of operation (e.g., adiabatic operation for a PFR) may not allow a faithful interpretation of this requirement. For illustration, we consider the optimization of both a CSTR and a PFR for the model reaction... 

In Section 5.3 for reversible reactions, it is shown that the rate of an exothermic, reversible reaction goes through a maximum with respect to T at constant fractional conversion /, but decreases with respect to increasing / at constant T. (These canchisians apply whether the reaction is catalytic or noncatalytic.) Both features are illustrated graphically in Figure 21.4 for the oxidation of SO, based on the rate law of Eklund (1956) ... 

From equation 21.5-4, the amount of catalyst is a minimum, Wmin, if (-rA) is the maximum rate at /A. For an exothermic, reversible reaction, this means operating... 

Figure 21.8 Operating lines (AB and CD) from energy equation 21.58 for two-stage (adiabatic) FBCR (a) exothermic reversible reaction (b) endothermic reversible reaction...

Figure 21.12 Conversion-temperature diagram showing operating lines for cold-shot cooling operation of FBCR for exothermic, reversible reaction...

Figure 21.13 Interpretation of AT in equation 21.5-23 for exothermic, reversible reaction with cold-shot cooling, ith stage...

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. 

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. 

Thus in this example, the prod t indicated is fed into the next stage, where it is reacted with other species (H2O, N2, O2, toluene). Different temperatures and pressures are usually used in each stage to attain optimum performance of that reactor. For example, NH3 synthesis requires very high pressure (200 atm) and low temperature (250°C) because it is an exothermic reversible reaction, while NH3 oxidation operates at lower pressurse (-10 atm) and the reaction spontaneously heats the reactor to -800°C because it is strongly exothermic but irreversible. Formation of hquid HNO3 requires a temperature and pressure where liquid is stable. 

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

Figure 5-12 Plots of lines of constant rate in the X — T plane for an exothermic reversible reaction.

Figure 5-13 Possible region of trajectories for exothermic reversible reactions, starting at feed temperature To with cooling...

In designing a wall-cooled tubular reactor, we want to operate such that the trajectory stays near the maximum rate for all temperatures. Thus for an exothermic reversible reaction the temperature should increase initially while the conversion is low and decrease as the conversion increases to stay away from the equilibrium constraint. One can easily program a computer to compute conversion and T versus t to attain a desired conversion for rninimum T in a PFTR. These curves are shown in Figure 5-17 for the three situations. 

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. 

It is interesting to note that the exothermic reversible reaction A B is identical to the same endothermic reversible reaction B A. This can be seen by plotting X versus T and noting that the r = 0 equihbrium hue separates these two reactions. In the reaction A B the rate in the upper portion where r < 0 is exactly the reaction B A. We defined all rates as positive quantities, but if we write the reaction as its reverse, both r and AZ/y reverse signs. This is plotted in Figure 5-19. 

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,...

Figure 5-19 Plot of X versus 7" for an exothermic reversible reaction A B. The upper portion of this curve where r <0 can be regarded as the endothermic reversible reactions tfi A if the sign of r is reversed or if X is replaced by 1 - X...

D. C. Dyson and F. J. M. Horn. Optimum distributed feed reactors for exothermic reversible reactions. J. Optim. Theory and Appl., 1 40, 1967. 

Glasser B, Hildebrandt D, Glasser D. Optimal mixing for exothermic reversible reactions. Ind Eng Chem Res 1992 31 1541. 

From the previous discussion about the temperature sensitivity of reaction rate as a function of activation energy, we can understand why the chemical equilibrium constant of an exothermic reversible reaction decreases with increasing temperature. An exothermic reaction has a negative heat of reaction, since the activation energy of the reverse reaction exceeds that of the forward reaction. As temperature increases, the reverse reaction increases relatively more rapidly than the forward reaction, which means that at chemical equilibrium we have relatively more reactants than products and a lower equilibrium constant. 

The next type of reaction considered is an exothermic reversible reaction with two reactants and two products ... 

Example The following questions refer to a slightly exothermic reversible reaction where NO2 is a brown gas and N2O4 is colorless. Select the correct response. 

B Young, D Hildebrandt, D Glaser, Analysis of an Exothermic Reversible Reaction in a Catalytic Reactor with Periodic Flow Reversal , Chem Eng Set 1992, 47, 1825-1837... 

An important feature of a reactor operating with reversing flows is a gradual decrease of temperature of the packed bed outlet that allows for higher conversion in an adiabatic catalyst bed than for steady-state performance of an exothermic reversible reaction such as SO2 oxidation or ammonia synthesis. Conventional operation can provide only the temperature rise along the adiabatic catalyst bed. 

Figure 8. Temperature (curves 1-5) and conversion (curves 1 -5 ) profiles in the reactor with periodic flow reversal. Example of exothermic reversible reaction.

Interstage cooling used for exothermic reversible reactions... 

P8-15 Exothermic reversible reaction with a variable coolant temperature. The elementary reaction... 

Glasser, B., Hildebrandt, D., and Glasser, D. Optimal Mixing for Exothermic Reversible Reactions, Paper 70g, Annual AIChE Meeting, Chicago (1990). 

---