EQUILIBRIUM REACTOR ADIABATIC TEMPERATURE CHANGE

Sometimes, especially when referring to commercial process simulators, the term equilibrium reactor is used. A chemical system can be approximated with a so-called equilibrium reactor, in which the reaction rates are so high that one can assume that the chemical reaction resides at the equilibrium at the given temperature. The extreme performance limits of a chemical reactor can be mapped with the aid of the equilibrium approximation, which does not, however, help in the design of a real reactor. 

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Figure 6.4a shows the behavior of an endothermic reaction as a plot of equilibrium conversion against temperature. The plot can be obtained from values of AG° over a range of temperatures and the equilibrium conversion calculated as illustrated in Examples 6.1 and 6.2. If it is assumed that the reactor is operated adiabatically, a heat balance can be carried out to show the change in temperature with reaction conversion. If the mean molar heat capacity of the reactants and products are assumed constant, then for a given starting temperature for the reaction Ttn, the temperature of the reaction mixture will be proportional to the reactor conversion X for adiabatic operation, Figure 6.4a. As the conversion increases, the temperature decreases because of the reaction endotherm. If the reaction could proceed as far as equilibrium, then it would reach the equilibrium temperature TE. Figure 6.4b shows how equilibrium conversion can be increased by dividing the reaction into stages and reheating the reactants...

The single bed reactor is simply a vessel of relatively large diameter, as sketched in Fig. 11.1. This simple reactor design is best suited for adiabatic processes and not applicable for very exothermic or endothermic processes. If the reaction is very endothermic, the temperature change may be such as to extinguish the reaction before the desired conversion is attained. Strongly exothermic reactions, on the other hand, can lead to a temperature rise that is prohibitive due to its unfavorable influence on the equilibrium conversion, the product selectivity, the catalyst stability, and in extreme cases unsafe operation. 

CHjOH). This means that a comparison of the catalysts in a fixed-bed reactor at different conversion levels or at different methanol flow rates and equal conversion may potentially mean different temperatures and is relatively tricky. That is a reason why most of the publications use a highly diluted methanol feed [29,92,93]. The dilution media acts as a heat vector in this case to smooth over the adiabatic temperature increase. However, the presence of dilution media greatly decreases methanol partial pressure. The latter masks mechanistic details and may change reaction pathways. Some important studies also highlight the role of diffusion, adsorption equilibrium, role of water, and the role of surface species, which could hardly be seen with diluted feed [24,28,60,119]. 

When we can predict the response of the reacting system to changes in operating conditions (how rates and equilibrium conversion change with temperature and pressure), when we are able to compare yields for alternative designs (adiabatic versus isothermal operations, single versus multiple reactor units, flow versus batch system), and when we can estimate the economics of these various alternatives, then and only then will we feel sure that we can arrive at the design well fitted for the purpose at hand. Unfortunately, real situations are rarely simple. 

Most reactors used in industrial operations run isother-mally. For adiabatic operation, principles of thermodynamics are combined with reactor design equations to predict conversion with changing temperature. Rates of reaction normally increase with temperature, but chemical equilibrium must be checked to determine ultimate levels of conversion. The search for an optimum isothermal temperature is common for series or parallel reactions, since the rate constants change differently for each reaction. Special operating conditions must be considered for any highly endothermic or exothermic reaction. 

Analysis In this example we applied the CRE algorithm to a reversible-first-order reaction carried out adiabatically in a PFR and in a CSTR. We note that at the CSTR volume necessary to achieve 40% conversion is smaller than that to achieve the same conversion in a PFR. In Figure El 1-3.1(c) we also see that at a PFR volume of three m , equilibrium is essentially reached about half way through the reactor, and no further changes in temperature, reaction rate, equilibrium conversion, or conversion take place further down the reactor. 

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