Adiabatic reactor multiplicities

Root and Schmitz ( ), and Votruba et al. ( ) for adiabatic reactor systems. Adiabatic reactor multiplicities were also investigated by Aris and Schruben ( ), who computed the ultimate conversions achieved from various initial conditions. 

Fig. 3. Multiple fixed-bed configurations (a) adiabatic fixed-bed reactor, (b) tubular fixed beds, (c) staged adiabatic reactor witb interbed beating (cooling),...

The need to keep a concave temperature profile for a tubular reactor can be derived from the former multi-stage adiabatic reactor example. For this, the total catalyst volume is divided into more and more stages, keeping the flow cross-section and mass flow rate unchanged. It is not too difficult to realize that at multiple small stages and with similar small intercoolers this should become something like a cooled tubular reactor. Mathematically the requirement for a multi-stage reactor can be manipulated to a different form ... 

Note several features of these solutions. First the C (t) and T(t) solutions have identical shapes (but T increases as Ca decreases for the exothermic reaction) for the adiabatic reaction in these reactors or in any adiabatic reactor. If we plot Cao Ca versus T from these solutions we obtain Figure 5-8, because, by the previous arguments, this must be a straight line for any single reaction in any reactor as long as parameters do not depend on temperature or composition. Second, note that the CSTR in this example requires a shorter residence time for a given conversion than a PFTR. Third, note that the CSTR exhibits multiple values of Ca and T for a range of x. This situation is physically real and will be the subject of the next chapter. 

Figure 5-10 Residence times in a PFTR md CSTR for adiabatic reactors. The CSTR cm reqmre a much smdler i T than the PFTR and can exhibit multiple steady states for some T (arrows). 

It cuts. the axis at 0ad = 4 as 1/tn tends to zero (adiabatic limit). We have already seen that this is the condition for transition from multiple stationary states (hysteresis loop) to unique solutions for adiabatic reactors, so the line is the continuation of this condition to non-adiabatic systems. Above this line the stationary-state locus has a hysteresis loop this loop opens out as the line is crossed and does not exist below it. Thus, as heat loss becomes more significant (l/iN increases), the requirement on the exothermicity of the reaction for the hysteresis loop to exist increases. 

Experimental Observations of Multiple Steady States in Tubular Catalytic Adiabatic Reactors... 

Adiabatic with Intermediate Heat Transfer. Many tubular reactor systems use a series of adiabatic reactors with heating or cooling between the reactor vessels. For example, naphtha reforming has endothermic reactions of removing hydrogen from saturated cyclical naphthene hydrocarbons to form aromatics. The process has multiple adiabatic reactors with fired furnaces between the reactors to heat the material back up to the required reactor inlet temperature. 

Results for Multiple Adiabatic Reactors with Interstage Cooling... 

It might be wise to point out that there can be other problems with a cooled reactor that will influence the selection of reactor type. An adiabatic reactor with a bed of catalyst is certainly mechanically straightforward to construct and maintain. Catalyst is easily loaded or discharged. A cooled reactor with multiple parallel tubes is mechanically more complex. Loading and emptying the tubes of catalyst can be difficult. 

We noted earlier in this chapter that many reactions in the chemical industries are exothermic and require heat removal. A simple way of meeting this objective is to design an adiabatic reactor. The reaction heat is then automatically exported with the hot exit stream. No control system is required, making this a preferred way of designing the process. However, adiabatic operation may not always be feasible. In plug-flow systems the exit temperature may be too hot due to a minimum inlet temperature and the adiabatic temperature rise. Systems with baekmixing suffer from other problems in that they face the awkward possibilities of multiplicity and open-loop instability. The net result is that we need external cooling on many industrial reactors. This also carries with it a control system to ensure that the correct amount of heat is removed at all times. 

There are two classes of reaction systems for which the single-stage adiabatic reactor is incapable of satisfying the demands that can be placed upon reactant conversion and selectivity. The first class is reversible exothermic reactions. Multiple stages with interstage cooling are required for these reactions to achieve an acceptable conversion level with a reasonable reactor volume. 

This figure clearly illustrates that the range within which multiple steady states can occur is very narrow. It is true that, as Hlavacek and Hofmann calculated, the adiabatic temperature rise is sufficiently high in ammonia, methanol and oxo-synthesis and in ethylene, naphthalene, and o-xylene oxidation. None of the reactions are carried out in adiabatic reactors, however, although multibed adiabatic reactors are sometimes used. According to Beskov (mentioned in Hlavacek and Hofmann) in methanol synthesis the effect of axial mixing would have to be taken into account when Pe < 30. In industrial methanol synthesis reactors Pe is of the order of 600 and more. In ethylene oxidation Pe would have to be smaller than 200 for axial effective transport to be of some importance, but in industrial practice Pe exceeds 2500. Baddour et al. in their simulation of the TVA ammonia synthesis converter found that the axial diffusion of heat altered the steady-state temperature profile by less than 0.6°C. Therefore, the length of... 

Steam reforming HEX-reactor (multiple adiabatic bedPCR)... 

We shall first consider a straightforward single bed for the entire reaction with no heating or cooling and then explain both the methods mentioned above for multiple-bed reactors. Since the basis for aU these methods is the unique conversion-temperature relationship that exists for the adiabatic reactor, we begin by a consideration of this plot. 

Figure 10.27 Design and analysis procedures for multiple reactions in an adiabatic reactor. 

Consider multiple reactions taking place in an adiabatic reactor. If Aq is designated as the nriain reactant from which all key species At (i = 1,2,. . . , JV) at each node shown in Figure 10.26 originate, the reactor conservation equations are ... 

CSTRs and combinations of an adiabatic reactor and a feed/ product heat exchanger can exhibit multiple steady states and associated phenomena, such as feed-temperature hysteresis and blowout ... 

In the DTP process, the DME/methanol mixture is thought to react in the presence of steam on an alkaline earth metal-containing zeolite catalyst from the ZSM-5 type. The preferable alkaline earth metal is said to be calcium [53]. The reaction proceeds at a temperature in the 500°C range under near atmospheric pressure through multiple fixed-bed adiabatic reactors connected in series. 

FIG. 23-17 Multiple steady states of CSTRs, stable and unstable, adiabatic except the last item, (a) First-order reaction, A and C stable, B unstable, A is no good for a reactor, the dashed line is of a reversible reaction, (h) One, two, or three steady states depending on the combination Cj, Ty). (c) The reactions A B C, with five steady states, points 1, 3, and 5 stable, (d) Isothermal operation with the rate equation = 0 /(1 -I- C y = (C o Cy/t. 

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