Nonadiabatic reactors

Develop the model equations, simplify them as done in this section, and repeat problem I for a nonadiabatic reactor with a cocurrent cooling jacket. 

The third difference is the issue of heat transfer in nonadiabatic reactors. Ideally we would like to be able to control the temperature at each axial position down the reactor. However, it is mechanically very difficult to achieve independent heat transfer at various axial positions. About all that can be done is to have the cooling/heating medium flow either cocurrent or countercurrent to the direction of the process flow. The only two variables that can be manipulated are the flowrate of the medium and its inlet temperature. The former is the normal manipulated variable. The result is that only a single temperature can be controlled, which can be the peak temperature or the exit temperature. However, because of the significant dynamics of the tubular reactor, the control of these temperatures is sometimes quite difficult and tight control cannot be achieved in the face of load disturbances. 

The flow patterns, composition profiles, and temperature profiles in a real tubular reactor can often be quite complex. Temperature and composition gradients can exist in both the axial and radial dimensions. Flow can be laminar or turbulent. Axial diffusion and conduction can occur. All of these potential complexities are eliminated when the plug flow assumption is made. A plug flow tubular reactor (PFR) assumes that the process fluid moves with a uniform velocity profile over the entire cross-sectional area of the reactor and no radial gradients exist. This assumption is fairly reasonable for adiabatic reactors. But for nonadiabatic reactors, radial temperature gradients are inherent features. If tube diameters are kept small, the plug flow assumption in more correct. Nevertheless the PFR can be used for many systems, and this idealized tubular reactor will be assumed in the examples considered in this book. We also assume that there is no axial conduction or diffusion. 

These results indicate that a process change would probably be required to handle the dynamic problems. There are several alternatives. A cooled nonadiabatic reactor should reduce the sensitivity since more heat will be removed as temperatures increase. Probably a more practical solution would be to design for a lower concentration of one of the reactants. This mode of operation would prevent reaction runaways because the reaction rate would drop olf quickly as the concentration of the limiting reactant declined. The economic penalties would include requiring a larger reactor and more recycle than in the equimolar pure reactant feed mode of operation. Alternatively, the concentrations of both reactants could be reduced by recycling an inert substance (probably product C). This would also increase reactor size and recycle flowrate. 

The reaction front was ignited at the reactor outlet and moved upstream. The hot spot temperature increased toward the reactor inlet. Decreasing the inlet temperature the reaction front moves downstream and disappears in the middle part of the reactor. Experiments and numerical simulation indicated that in long nonadiabatic reactor the ignition process does not start at the reactor outlet but inside the bed [21]. 

For the same type of catalyst we have observed in a recirculation laboratory reactor multiplicity, periodic and chaotic behavior. Unfortunately, so far we are not able to suggest such a reaction rate expression which would be capable of predicting all three regimes [8]. However, there is a number of complex kinetic expressions which can describe periodic activity. One can expect that such kinetic expressions combined with heat and mass balances of a tubular nonadiabatic reactor may give rise to oscillatory behavior. Detailed calculations of oscillatory behavior of singularly perturbed parabolic systems describing heat and mass transfer and exothermic reaction are apparently beyond, the capability of both standard current computers and mathematical software. 

At present there is no systematic work on simulation and design of packed bed nonadiabatic reactors of industrial size where a deactivation process occurs. The purpose of this work is to analyze the operation of a nonadiabatic deactivating catalyst bed and to develop simple techniques for simulation. Based on hydrogenation of benzene,full-scale reactor behavior is calcu lated for a number of different operational conditions. Radial transport processes are incorporated in the model, and it is shown that the two-dimensional model is necessary in some cases. 

The deactivation process in a tubular nonisothermal nonadiabatic reactor depends on a number of kinetic and operational parameters. There are two major questions which we would like to answer (a) can we use the one-dimensional model for simulation... 

Effect of Operational Variables. There are three important operational variables which can affect the operation of a deactivating nonadiabatic reactor (1) inlet temperature (2) inlet poison concentration and (3) tube diameter. 

For a reactor operating with constant output, the criterion for optimal performance is for the cooling medium to have the highest possible temperature in the heat removal system. For a working example of the nonadiabatic reactor, there are 4631 cylindrical tubes with inner diameters of 7 mm packed with a catalyst and surrounded by a constantly boiling liquid at 703 K. Sulfur dioxide and air are fed into the reactor at a total pressure PT, in volume fractions of > s,, 2 =0.11 and >v,2 =0.10. The empirical expression oftakes into account diffusion and reaction kinetics, and we have... 

Nonadiabatic Reactor Operation Oxidation of Sulfur Dioxide Example... 

The form of the radial temperature profile in a nonadiabatic fixed-bed reactor has been observed experimentally to have a parabolic shape. Data for the oxidation of sulfur dioxide with a platinum catalyst on x -in. cylindrical pellets in a 2-in.-ID reactor are illustrated in Fig. 13-9. Results are shown for several catalyst-bed depths. The reactor wall was maintained at 197°C by a jacket of boiling glycol. This is an extreme case. The low wall temperature resulted in severe radial temperature gradients, more so than would exist in a commercial reactor, where the wall temperature would be higher. The longitudinal profiles are shown in Fig. 13-10 for the same experiment. These curves show the typical hot spots, or maxima, characteristic of exothermic reactions in a nonadiabatic reactor. The greatest increase above the reactants temperature entering the bed is at the center,... 

A completely satisfactory design method for nonadiabatic reactors entails ljredictinr-the f5dial and lon fudmal yariations in temperature, such as fho in Figs. 13-9 and analogous concentration... 

Table 13-2 Data for conversion of ethyl benzene to styrene in a nonadiabatic reactor...

The simplified approach to the design of nonadiabatic reactors led to good results in Example 13-4 partly, at least, because radial temperature variations were not large. This is because the wall temperature was the same as the temperature of the entering reactants. Thus radial variations in temperature at the entrance to the reactor were zero. At the hot spot the maximum temperature difference between the center and the wall was about 100°C. In Example 13-5 much larger radial temperature gradients exist, and the simplified method is not so suitable. 

We can use Equation (8-28) to relate temperature and conversion and then proceed to evaluate the algorithm described in Example 8-1. However, unless the reaction is carried out adiabatically. Equation (8-28) is still difficult to evaluate because in nonadiabatic reactors, the heat added to or removed from the system varies along the length of the reactor. This problem does not occur in adiabatic reactors, which are frequently found in industry. Therefore, the adiabatic tubular reactor will be analyzed first. 

Use of Rate Equations in Reactor Design. The method of using the rate equations for catalytic reactions to calculate the reactor size and amount of catalyst needed for a specified conversion and feed rate is very similar to the method used for noncatalytic reactions. The calculations may be divided into three types, namely, those for isothermal reactors, adiabatic reactors, and nonisothermal nonadiabatic reactors. In all three cases where the feed rate F and the desired conversion x are specified, the weight of catalyst needed can be calculated from the expression... 

In the isothermal case, just enough heat is added or removed to keep the temperature constant throughout. In the adiabatic reactor, no heat is added or, removed during the course of the reaction. In the noniaothemud nonadiabatic reactor, some heat is either added or removed during the reaction but the temperature does not remain constant. Almost all commercial reactors are operated as nonisothermal nonadiabatic reactions. 

Table 12.1 Classification of models for nonisothermal nonadiabatic reactors... 

Figure 12.2 Axial conversion and temperature profiles for aniline production in a non-isothermal nonadiabatic reactor (model A2-a).

In this Section we shall tentatively apply the results of the previous study to investigate the feasibility of a nonadiabatic reactor loaded with ceramic monolith catalysts for the reaction of ethylene oxychlorination to DCE. Such a reaction is the heart of modern balanced processes for the production of monomer vynil chloride (Naworski Velez, 1983). The reaction... 

A Closed System does not exchange matter with the surroundings but exchanges energy. Thermodynamically it tends to the state of thermodynamic equilibrium (maximum entropy). An example is a batch nonadiabatic reactor. 

The heat balance for a nonadiabatic reactor is given in Figure 2.26. i represents the numbering of all components involved in the reaction (reactants and products). If any product does not exist in the feed, then we put its Hif = 0 if any reactant does not exist in the output, then we put its , = 0. Enthalpy balance is... 

Nonadiabatic reactors in which heat exchange occurs with the environment are not considered here, since then radial dispersion would dominate over axial dispersion. For an isothermal reactor for which tRq is a function only of concentration. 

For a nonadiabatic reactor, consider the analysis by Carbeny and White (1969) for the oxidation of naphthalene over V2O5. For the simplified network of first-order reactions ... 

---