Single adiabatic temperature rise

Fig. 21. Single absorption equilibrium-stage diagram where the equiUbrium curve is for 8% SO2, 12.9% the diagonal lines represent the adiabatic temperature rise of the process gas within each converter pass the horizontal lines represent gas cooling between passes, where no appreciable conversion...

The curve in Figure 21 represents SO2 equiUbrium conversions vs temperature for the initial SO2 and O2 gas concentrations. Each initial SO2 gas concentration has its own characteristic equiUbrium curve. For a given gas composition, the adiabatic temperature rise lines can approach the equiUbrium curve but never cross it. The equiUbrium curve limits conversion in a single absorption plant to slightly over 98% using a conventional catalyst. The double absorption process removes this limitation by removing the SO from the gas stream, thereby altering the equiUbrium curve. 

In the analysis, I have taken the rate of this equivalent reaction as being proportional to the product of a function of a single composition variable, which I call "conversion," and normal Arrhenius function of temperature. In particular, there is a specific rate constant, a reaction order, an activation energy, and an adiabatic temperature rise. These four parameters are presumed to be sufficient to describe the reaction well enough to determine its stability characteristics. Finding appropriate values for them may be a bit complicated in some cases, but it can always be done, and in what follows I assume that it has been done. 

We shall develop next a single-channel model that captures the key features of a catalytic combustor. The catalytic materials are deposited on the walls of a monolithic structure comprising a bundle of identical parallel tubes. The combustor includes a fuel distributor providing a uniform fuel/air composition and temperature over the cross section of the combustor. Natural gas, typically >98% methane, is the fuel of choice for gas turbines. Therefore, we will neglect reactions of minor components and treat the system as a methane combustion reactor. The fuel/air mixture is lean, typically 1/25 molar, which corresponds to an adiabatic temperature rise of about 950°C and to a maximum outlet temperature of 1300°C for typical compressor discharge temperatures ( 350°C). Oxygen is present in large stoichiometric excess and thus only methane mass balances are needed to solve this problem. 

For systems where the adiabatic temperature rise is low (as is the case considered here) the thermal spikes introduced by the flow reversals do not dramatically affect the reactor performance. However, the concentration of feed streams to such treatment reactors can fluctuate to a high level which can result in a high temperature thermal spike developing within the reactor. Pinjala, Chen, and Luss characterized this dynamic response and showed that reactor runaway could occur within the single-pass reactor. Their work is directly applicable to the RFR as the forced oscillations in the gas flow direction can result in a thermal spike formation at the beginning of each half cycle. Thus, there is a need to understand thermal stability within these systems. Further complicating the matter is the fact that the temperature spikes are very narrow and are thus difficult to detect using thermocouples or other sensors imbedded within the reactor. 

The adiabatic temperature rise for a single-injection reactor is defined as... 

The adiabatic temperature rise for a single-injection reactor (AT j) is calculated with Equation 5.65. Thus, the temperature rise at each injection point referred to the adiabatic temperature rise obtained in reactors with only one inlet N = 1) is expressed in Equation 5.72... 

When the plant is operating normally, the synthesis gas contains around 0.3-0.7% oxides of carbon, which need to be removed during the methanation stage. A simple, single-bed reactor can be used at an inlet temperature in the range 250°-320°C depending on the catalyst activity and the concentration of the oxides of caibon (Figure 9.8). There is an adiabatic temperature rise of about 7.4°C for every 0.1% carbon monoxide and 6°C for every 0.1% caibon dioxide con-... 

This is the temperature rise which would occur if the reactor were designed and operated as a single adiabatic stage. 

Further insight can be gained from the idealized T - S diagram for the cycle. Figure 9-14. The compression of the air and fuel streams is represented here as a single adiabatic reversible (constant S) process in which the temperature of the gases rises above ambient. The heating of... 

It is often necessary to employ more than one adiabatic reactor to achieve a desired conversion. In the first place chemical equilibrium may have been established in the first reactor and it is then 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 single reactor. It is necessary, however, to consider carefully how many reactors in series it is economic to operate. 

The commercial trickle-bed reactors, such as hydrodesulfurization and hydrocracking reactors, are often operated adiabatically. The temperature rise in such reactors is often controlled by the additions of a quench fluid (normally hydrogen) at one or more positions along the length of the reactor. A schematic of an adiabatic trickle-bed HDS reactor with a single quench is shown in Fig. 4-7. 

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