Nonadiabatic operator

In the formulation of the boundary conditions, it is presumed that there is no dispersion in the feed line and that the entering fluid is uniform in temperature and composition. In addition to the above boundary conditions, it is also necessary to formulate appropriate equations to express the energy transfer constraints imposed on the system (e.g., adiabatic, isothermal, or nonisothermal-nonadiabatic operation). For the one-dimensional models, boundary conditions 12.7.34 and 12.7.35 hold for all R, and not just at R = 0. 

For nonadiabatic operation and an exothermic reaction, the overall situation is similar, but is complicated by the inclusion of the heat transfer term for Q in the energy balance in equation 14.3-10. 

In Figure 21.1, for axial flow of fluid, the main division for thermal considerations is between adiabatic and nonadiabatic operation. 

In nonadiabatic operation, heat transfer for control of T is accomplished within the bed itself. This means that the reactor is essentially a shell-and-tube exchanger, with catalyst particles either inside or outside the tubes, and with a heating or cooling fluid flowing in the shell or in the tubes accordingly. 

Operating at the middle unstable steady state requires using some means of control for the plant, such as a stabilizing controller or nonadiabatic operation with carefully chosen parameters to stabilize the saddle-point type of the unstable steady state. 

For many such systems the maximum yield of the desired product corresponds to a middle steady state that may be unstable as shown earlier. For such systems, an efficient adiabatic operation is not possible and nonadiabatic operation is mandatory. Flowever, the choice of the heat-transfer coefficient U, the area of heat transfer Ah and the cooling jacket temperature are critical for the stable operation of the system. The value of the dimensionless heat-transfer coefficient Kc should exceed a critical value KCtCrit in order to stabilize an unstable middle steady state. The value of iFc,crit corresponds to the line... 

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. 

Example 13-3 Under actual conditions the reactor described in Example 13-1 would not be truly adiabatic. Suppose that with reasonable insulation the heat loss U would correspond to a heat-transfer coefficient of 1.6 Btu/(hr)(ft inside tube area) (°F). This value of U is based on the difference in temperature between the reaction mixture and the surroundings at 70°F. Determine revised curves of temperature and conversion vs catalyst-bed depth for this nonadiabatic operation. 

Proceeding further with the calculations leads to the results shown in Table 13-2. The results are also plotted in Fig. 13-6 (labeled nonadiabatic operation). The bed depth for a given conversion is greater than for the adiabatic case, because the temperature is less. For example, for a conversion of 50%, 5.8 ft of catalyst is required, in comparison with 4.8 ft in Example 13-1. 

Evaporative cooling—when drying a solid with free or bound moisture, the effect of a phase change from the liquid state to the vapor state removes energy from the liquid-solid mass. This results in a reduction of temperature in a nonadiabatic operation, whereas in an... 

In addition energy can be supplied by the circulation device and, for nonadiabatic operation, heat can be exchanged with the environment. If the crystallizer is operated at steady-state conditions, the following energy balance for the crystallizer is obtained ... 

The case when an inequality opposite to (44) holds but the inequality (45) is still valid corresponds to a partly adiabatic reaction. This means that the nonadiabaticity operator for the adiabatic electron terms is small and, in the course of the transition, the system remains on the lower adiabatic potential energy surface for all the heavy particles including the proton. However, the probability of transition to the final state is still small owing to the small value of the probability of the proton sub-barrier transition. 

Note that no such relationship exists for nonadiabatic operation. 

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