Tubular reactor adiabatic case

In lUusIration 10.2 we saw that when one nses a battery of stirred tanks for carrying out an exothermic reaction under isothermal conditions, there may be occasions when the heat requirements for the various tanks may be of opposite sign. Some tanks will require a net input of theamal energy, while others will need to be cooled. It is often useful in such situations to consider the possibility of adiabatic operation of one or more of the tanks in series, remembering the constraints that one desires to place on the temperatures of the process streams. Another means of achieving autothermal operation is to use a network consisting of a stirred-tank reactor followed by a tubular reactor. This case is considered in Illustration 10.6. 

The summation involves the effluent molal flow rates. This equation and equation 10.4.2 must be solved simultaneously in order to determine the tubular reactor size and to determine the manner in which the heat transfer requirements are to be met. For either isothermal or adiabatic operation one of the three terms in equation 10.4.7 will drop out, and the analysis will be much simpler than in the general case. In the illustrations which follow two examples are treated in detail to indicate the types of situations that one may encounter in practice and to indicate in more detail the nature of the design calculations. 

A tubular reactor is to be designed in such a way that it can be stopped safely. The reaction mass is thermally instable and a decomposition reaction with a high energetic potential may be triggered if heat accumulation conditions occur. The time to maximum rate under adiabatic conditions of the decomposition is 24 hours at 200 °C. The activation energy of the decomposition is 100 kj mol-1. The operating temperature of the reactor is 120 °C. Determine the maximum diameter of the reactor tubes, resulting in a stable temperature profile, in case the reactor is suddenly stopped at 120 °C. 

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 multi-mode model for a tubular reactor, even in its simplest form (steady state, Pet 1), is an index-infinity differential algebraic system. The local equation of the multi-mode model, which captures the reaction-diffusion phenomena at the local scale, is algebraic in nature, and produces multiple solutions in the presence of autocatalysis, which, in turn, generates multiplicity in the solution of the global evolution equation. We illustrate this feature of the multi-mode models by considering the example of an adiabatic (a = 0) tubular reactor under steady-state operation. We consider the simple case of a non-isothermal first order reaction... 

It is the purpose of this chapter to discuss presently known methods for predicting the performance of nonisothermal continuous catalytic reactors, and to point out some of the problems that remain to be solved before a complete description of such reactors can be worked out. Most attention will be given to packed catalytic reactors of the heat-exchanger type, in which a major requirement is that enough heat be transferred to control the temperature within permissible limits. This choice is justified by the observation that adiabatic catalytic reactors can be treated almost as special cases of packed tubular reactors. There will be no discussion of reactors in which velocities are high enough to make kinetic energy important, or in which the flow pattern is determined critically by acceleration effects. 

In the case of refinery cuts from FCC units, having a relatively low isobutene concentration (Table 11.2), the plant layout is less sophisticated because it is sufficient to achieve 90-95% of isobutene conversion in this case the plant configuration is based on a single reaction stage with tubular and adiabatic reactors in series with intermediate cooling. 

Development of a comprehensive model for a real tubular reactor is a significant undertaking. Refer to the advice on debugging in Section 5.2.1. Begin with simple cases such as isothermal and adiabatic PFRs. Add and test complications one at a time. Verify continuously. Examples of reasonably comprehensive models are discussed in Chapter 13 in the industrially relevant context of polymer reaction engineering. 

There are a variety of limiting forms of equation (8.0.3) that are appropriate for use with different types of reactors and different modes of operation. For stirred tanks the reactor contents are uniform in temperature and composition throughout, and it is possible to write the energy balance over the entire reactor. In the case of a batch reactor, only the first two terms need be retained. For continuous flow systems operating at steady state, the accumulation term disappears. For adiabatic operation in the absence of shaft work effects the energy transfer term is omitted. For the case of semibatch operation it may be necessary to retain all four terms. For tubular reactors neither the composition nor the temperature need be independent of position, and the energy balance must be written on a differential element of reactor volume. The resulting differential equation... 

Figure 3.5 Temperature in the reaction zone as a fnnction of the length of tubular reactor in the case of piperylene oligomerisation imder adiabatic conditions (1-5) and with external heat removal (6-10). Catalysts TiCl4 (1, 10), TiCl4-Al(/-C4H9)3 (2, 9), AlC2H5Cl2-0(CgH5)2 (3, 8), AlC2HgCl2 (4, 7), and AlCl3-0(CgH5)2 (5, 6).

Thus, even in an adiabatic mode of tubular turbulent chlorination reactor operation (without heat removal), the temperature growth in the reaction zone in the case of BR chlorination (12-15% solution) with molecular chlorine in a tubular reactor, operating in the optimum plug-flow mode in turbulent flows, does not exceed 2 1 °C. The process can be thought to proceed under quasi-isothermal conditions and does not require external or internal heat removal, or special stirring devices for heat and mass exchange intensification. 

The material and energy balances provide the basis for steady-state operability analysis [19,24]. For a simple isomerization reaction, the production rate in terms of recycle ratio and subsequently control structure can be devised. Similar approach is taken for the case of adiabatic tubular reactor. 

However, in many cases the system variables depend on the location and coordinates for example, in the radial direction in a spherical particle, in the axial direction in an adiabatic tubular reactor, or in both the radial and axial direction in a cooled or heated tubular reactor. Then infinitesimal balances are needed and a control space must be selected that is so small that the variables involved are constant or linear variables with regard to the coordinates. Mathematically speaking, we have to solve the differential equations to obtain integral data such as the effective mean concentration in a particle or the conversion in a tubular reactor. 

For strong exothermic or endothermic reactions with an adiabatic temperature rise of several hundred degrees, the rack type reactor is not sufficient. Then, a multi-tubular reactor is used, where the catalyst is located in up to 30 000 individual tubes, the outside of which is exposed to the flow of a heat transfer medium. In many cases, cooling is provided by boiling water, and the cooling temperature can easily be controlled by the pressure. For elevated temperatures molten salts can be employed as cooling or heating medium. 

If we use Eq. (4.10.71), we have to keep in mind that pronounced radial temperature gradients may be present in cooled tubular reactors, even if the gradient is small or confined to a small region near the wall. Thus, Eq. (4.10.71) is strictly speaking only valid for an ideal PER with a uniform radial temperature, but for the subsequent examination of the basic principles of the behavior of non-isothermal tubular reactors we neglect this aspect and use an overall heat transfer coefficient Uh. The more complicated radial heat transfer in the case of pronounced radial temperature gradients in tubular reactors such as packed bed reactors will be treated in Section 4.10.7.3. Subsequently, we inspect the adiabatic operation of a tubular reactor first. Thereafter, we take a closer look at a wall[Pg.329]

Reactors most commonly used in the process consist of cylindrical vessels containing the catalyst in an adiabatic fixed bed with a maximum depth of about 10 ft. The bed depth-to-diameter ratio is normally less than 1 1. In cases where the concentration of acetylene in the feed gas is sufficiently high to cause an excessive temperature increase during the conversion operation, isothermal tubular reactors are used, with the catalyst inside the tube and a coolant on the outside. 

---