Fixed adiabatically operated

Consider a two-stage fixed-bed catalytic reactor (FBCR), with axial flow, for the dehydrogenation of ethylbenzene (A) to styrene (S) (monomer). From the data given below, for adiabatic operation, calculate the amount of catalyst required in the first stage, W /kg. 

The last term on the left-hand side of eq. (3.301) corresponds to the heat transfer to the external fixed-bed wall. The overall heat transfer resistance is the sum of the internal, external, and wall resistances. In an adiabatic operation, the overall heat transfer coefficient is zero so the corresponding term in the energy balance expression drops out, while in an isothermal operation this coefficient is infinite, so that 7 f 7 s 7W. 

In general, large industrial fixed beds operate under near-adiabatic conditions, whereas small laboratory-scale fixed beds may approach isothermal operation (Ruthven, 1984). Especially, for most environmental applications, for catalytic, adsorption, and ion-exchange operations, the species to be removed are in such low concentrations that the operarion is nearly isothermal. Thus, the heat transfer to the external fixed-bed wall is often of minimal importance. 

The basic equations that describe fixed-bed reactors have been presented in Section 3.6.2. In the present Section Isothermal, Adiabatic and Non-isobaric fixed bed operations as well as the case of Monolithic catalysts are presented. 

As we see, for a specific reaction, the higher the inlet concentration, the higher the conversion and the exit temperature. This is a result of the positive effect of the temperature rise, due to the exothermic nature of the reaction, on the rate coefficient and thus on the reaction rate and conversion. Note that for higher inlet CO concentration, the conversion for the isothermal operation is the same, while for the adiabatic operation the conversion is higher for higher inlet concentrations. Furthermore, the conversion in the adiabatic fixed bed is always higher in comparison to the isothermal fixed bed. Of course, these results are such because the reaction is of first order in respect to CO. 

Some of the possibilities are illustrated in Figures 17.13 and 17.18. Variations from a single large bed are primarily because of a need for control of temperature by appropriate heat transfer, but also for redistribution of the flow or for control of pressure drop. There are few fixed bed units that do not have some provision for heat transfer. Only when the heat of reaction is small is it possible to regulate the inlet temperature so as to make adiabatic operation feasible butane dehydrogenation, for example, is done this way. 

A theoretical and experimental study of multiplicity and transient axial profiles in adiabatic and non-adiabatic fixed bed tubular reactors has been performed. A classification of possible adiabatic operation is presented and is extended to the nonadiabatic case. The catalytic oxidation of CO occurring on a Pt/alumina catalyst has been used as a model reaction. Unlike the adiabatic operation the speed of the propagating temperature wave in a nonadiabatic bed depends on its axial position. For certain inlet CO concentration multiplicity of temperature fronts have been observed. For a downstream moving wave large fluctuation of the wave velocity, hot spot temperature and exit conversion have been measured. For certain operating conditions erratic behavior of temperature profiles in the reactor has been observed. 

The phenomenon of multiplicity and propagating fronts in adiabatic fixed bed reactors has received much attention in the literature and is the subject of a rather exhaustive treatment [1-6]. Unlike the adiabatic operation, the nonadiabatic case enjoyed far less attention and many questions are still to be answered. Hence, the principal interest in this work was to investigate experimentally the theoretically the characteristic features of multiplicity and propagating fronts created under different conditions in a nonadiabatically operated packed bed reactors and to make a comparison with the adiabatic operation. 

With regard to application and construction, it is convenient to differentiate between fixed-bed reactors for adiabatic operation and those for nonadiabatic operation. Since temperature control is one of the most important methods to influence a chemical reaction, adiabatic reactors are used only where the heat of reaction is small, or where there is only one major reaction pathway in these cases no adverse effects on selectivity or yield due to the adiabatic temperature development are expected. The characteristic feature of an adiabatic reactor is that the catalyst is present in the form of a uniform fixed bed that is surrounded by an outer insulating jacket (Fig. 1A). Adiabatic reactor designs are discussed in Section 10.1.3.1. 

Unit operation (b) in Table 6.2 is to be heated by injecting live steam directly into the bottom plate of the column instead of by using a reboiler, for a separation involving ethanol and water. Assuming a fixed feed, an adiabatic operation, atmospheric pressure throughout, and a top alcohol concentration specification ... 

In discussing the preliminary design of fixed bed reactors in Sec. 11.3 we mentioned that adiabatic operation is frequently considered in industrial operation because of the simplicity of construction of the reactor. It was also mentioned why straight adiabatic operation may not always be feasible and examples of multibed adiabatic reactors were given. With such reactors the question is how the beds should be sized. Should they be designed to have equal ATs or is there some optimum in the AT s, therefore in the number of beds and catalyst distribution In Section 11.3. this problem was already discussed in a qualitative way. It is taken up in detail on the basis of an example drawn from SOj oxidation, an exothermic reversible reaction. To simplify somewhat it will be assumed, however, that no internal gradients occur inside the catalyst so that the effectiveness factor is one. 

Dehydrogenation of ethylbenzene to styrene is normally accomplished in a fixed-bed reactor. A catalyst is packed in tubes to form the fixed bed. Steam is often fed with the styrene to moderate the temperature excursions that are characteristic of adiabatic operation. The steam also serves to prolong the life of the catalyst. Consider the situation in which we model the behavior of this reactor as an isothermal plug flow reactor in which the dehydrogenation reaction occurs homogeneously across each cross section of the reactor. The stoichiometry of the primary reaction is... 

Consider a simple mixer for extraction. In minimal entropy production, size V, time t, and duty J are specified and the average driving force is also fixed. We can also define the flow rate Q and the input concentration of the solute, and at steady state, output concentration is determined. The only unknown variables are the solvent flow rate and composition, and one of them is a decision variable specifying the flow rate will determine the solvent composition. Cocurrent and countercurrent flow configurations of the extractor can now be compared with the same initial specifications (y, t, J, Q, c). Cocurrent operation will yield a larger entropy production P2 than the countercurrent operation, whose yield is expressed as Pi, and investigating the implications of this on the decision variable is important. For a steady-state and adiabatic operation, for processes 1 and 2 with the solvent flow rates of Qi and Q2, we have (Tondeur, 1990)... 

If the reactor were a single adiabatically operated fixed bed, the heat release would raise the temperature to 600 °C, which corresponds to an equilibrium conversion of SO2 of only 70% (Figure 6.3.4), but even this far from sufficient conversion would only be reached for an infinite residence time and reactor length. For isothermal operation, a conversion of about 98% would be possible, but this would require an expensive reactor (e.g., a multi-tubular reactor intensively cooled by a molten salt. Figure 4.10.7). 

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