Runaway region

Runaway criteria developed for plug-flow tubular reactors, which are mathematically isomorphic with batch reactors with a constant coolant temperature, are also included in the tables. They can be considered conservative criteria for batch reactors, which can be operated safer due to manipulation of the coolant temperature. Balakotaiah et al. (1995) showed that in practice safe and runaway regions overlap for the three types of reactors for homogeneous reactions (1) batch reactor (BR), and, equivalently, plug-flow reactor (PFR), (2) CSTR, and (3) continuously operated bubble column reactor (BCR). 

Balakotaiah, Kodra, and Nguyen also studied the CSTR. They found that the boundary between the insensitive and runaway region is where there are two limit points (a point of infinite slope - there are two such limit points in Fig. 2) in the reaction path connecting the initial and final states. They foimd identical criteria to the batch reactor in the special limit of 7 —> oo and Og = 0. That is, the safe criteria under adiabatic conditions (a = 0) is given... 

Monolithic diesel particulate filters (DPF) are widely used in diesel particulate emission control. They consist of many parallel channels which are alternately plugged at either end in order to force the exhaust gases through the porous ceramic walls. The particulates are deposited on the inside wall of the inlet channel to form a thin, porous soot bed. Once a sufficient mass of particulates is collected, it is burned off to regenerate the filter. Thus, in order to achieve a successful regeneration, the DPF should operate in the thermal runaway region. 

The runaway limits determined by Morbidelli and Varma [1982] are based on the occurrence of an inflection point in the temperature profile before the hot spot. They used the method of isoclines, which requires the numerical integration of a differential equation. The method is also applicable to reaction orders different from 1, as shown in Fig. 11.5.3-1. The runaway region becomes more important as the order decreases. Tjahjadi et al. [1987] developed a new approach, applicable to more complex reactions, for example, the radical polymerization of ethylene in a tubular reactor. Hosten and Froment [1986]... 

From the analysis of reactor operation (influence of feed temperature,wall temperature,inlet o-xylene partial pressure) a runaway diagram can be presented showing the safe region of operation as well as the runaway region. 

Finally, also for this kind of reactor model, it can be shown that once the region of parametric sensitivity is avoided, steady - state multiplicity is also automatically avoided. This conclusion is illustrated in Figure 10, where it is seen that the multiplicity region is entirely contained in the runaway region. 

The variations were mainly due to operating conditions very close to the parametrically sensitive region, i.e., to the incipient temperature runaway. Small errors in the estimation of temperature effects caused runaways and, consequently, large differences. 

Several other changes that are supposed to slow down the reaction can cause runaway. In the case of ethylene oxidation, chlorinated hydrocarbons are used as inhibitors. These slow down both the total and the epoxidation, although the latter somewhat less. When the reaction is running too high and the inhibitor feed is suddenly increased in an attempt to control it, a runaway may occur. The reason is similar to that for the feed temperature cut situation. Here the inhibitor that is in the ppm region reacts with the front of the catalytic bed and slowly moves down stream. The unconverted reactants reach the hotter zone before the increased inhibitor concentration does. 

Equation (8.29) provides no guarantee of stability. It is a necessary condition for stability that is imposed by the discretization scheme. Practical experience indicates that it is usually a sufficient condition as well, but exceptions exist when reaction rates (or heat-generation rates) become very high, as in regions near thermal runaway. There is a second, physical stability criterion that prevents excessively large changes in concentration or temperature. For example. An, the calculated change in the concentration of a component that is consumed by the reaction, must be smaller than a itself Thus, there are two stability conditions imposed on Az numerical stability and physical stability. Violations of either stability criterion are usually easy to detect. The calculation blows up. Example 8.8 shows what happens when the numerical stability limit is violated. 

Example 9.6 Compare the nonisothermal axial dispersion model with piston flow for a first-order reaction in turbulent pipeline flow with Re= 10,000. Pick the reaction parameters so that the reactor is at or near a region of thermal runaway. 

In these equations, e represents the relative volume increase due to the feed and Rh the ratio of the heat capacities of both liquid phases. By representing the reactivity number as a function of the exothermicity number (Figure 5.3), different regions are obtained. The region where runaway occurs is clearly delimited by a boundary line. Above this region, for a high reactivity, the reaction is operated in the QFS conditions (Quick onset, Fair conversion and Smooth temperature profile) and leads to a fast reaction with low accumulation and easy temperature control (see Section 7.6). 

Figure 4 Regions of the density vs. temperature plane in which the various hydrogen-burning processes are dominant [MAT84c]. The normal CNO cycle occurs in stars slightly larger than the sun. The hot (beta-limited) CNO cycle is particularly important in supermassive stars. The rp-process is important during the thermonuclear runaways on accreting neutron stars which may be the source of X-ray bursts.

However, several exothermic reactions are characterized by moderate or low values of the B number here, the transition stages from safe to runaway conditions may cover a quite wide range of the parameter values, and the choice of the boundaries for the safe region is very discretional. Hence, not surprisingly, the main discrepancies among the different criteria are found at low B numbers [14, 15]. Moreover, in this case, runaway is a less dramatic phenomenon posing the problem to decide whether a bland explosion still represents a safety issue. In this case, an effective runaway criterion should be more properly determined on the basis of the actual ability of the system to comply with certain levels of temperature and pressure. 

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