Heat Accumulation Situations

In the chapters devoted to reactors, it was considered that a situation is thermally stable due to the relatively high heat removal capacity of reactors compensating for the high heat release rate of the reaction. We considered that in the case of a cooling failure, adiabatic conditions were a good approximation for the prediction of the temperature course of a reacting mass. This is true, in the sense that it represents the worst case scenario. Between these two extremes, the actively cooled reactor and adiabatic conditions, there are situations where a small heat removal rate may control the situation, when a slow reaction produces a small heat release rate. These situations with reduced heat removal, compared to active cooling, are called heat accumulation conditions or thermal confinement. 

Thermal confinement situations are encountered as nominal conditions in storage and transport of reactive material. The may also happen in failure of production equipment, such as loss of agitation, pump failure, and so on. 

In practice, truly adiabatic conditions are difficult to realize (see also Chapter 4), being seldom encountered and then only for short time periods. Therefore, considering a situation to be adiabatic may lead to a pointlessly severe assessment that may lead to abandoning a process, which in fact would have been possible to carry through safely, if a more realistic judgement had been made. 

As an introduction, it is worth qualitatively analysing some common industrial situations. In an analogy to the two film theory (Section 9.3.1), we consider three contributions to the resistance against heat transport [1]  

Agitated jacketed vessel the main resistance to heat transfer is located at the wall, where there is practically no resistance to heat transfer inside the reaction mass. Due to agitation, there is no temperature gradient in the reactor contents. Only the film near the wall presents a resistance. The same happens outside the reactor in its jacket, where the external film presents a resistance. The wall itself also presents a resistance. In summary, the resistance against heat transfer is located at the wall. 

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In this section, different typical heat accumulation situations encountered in the process industry are reviewed and analysed. The next section introduces different types of heat balance used in assessment of heat confinement situations. 

A practical approach of heat balance, often used in assessment of heat accumulation situations, is the time-scale approach. The principle is as in any race the fastest wins the race. For heat production, the time frame is obviously given by the time to maximum rate under adiabatic conditions. Then the removal is also characterized by a time that is dependent of the situation and this is defined in the next sections. If the TMRld is longer than the cooling time, the situation is stable, that is, the heat removal is faster. At the opposite, when the TMRld is shorter than the characteristic cooling time, the heat release rate is stronger than cooling and so runaway results. 

The situation is similar to class 1, except that the MTT is above Tm4. This means that under heat accumulation conditions, the activity of secondary reactions cannot be neglected, leading to a slow but significant pressure increase, or gas or vapor release. Nevertheless, the situation may become critical only if the reaction mass is left for a longer time at the level MTT. The assessment can be made using the same procedure as for criticality class 1, represented in Figure 10.8. The gas or vapor flow rate is an important parameter for the design of the required protection measures such as condenser, scrubber, or other treatment units. 

It can be observed, in one line, that under severe heat accumulation conditions, there is no difference in the time-scale that corresponds to the time to maximum rate under adiabatic conditions (TMRld). Thus, severe heat accumulation conditions are close to adiabatic conditions. At the highest temperature, even the small container experienced a runaway situation. Even at this scale, only a small fraction of the heat release rate could be dissipated across the solid the final temperature was only 191 °C instead of 200 °C. For small masses, the heat released is only partly dissipated to the surroundings, which leads to a stable temperature profile with time. Finally, it must be noted that for large volumes, the time-scale on which the heat balance must be considered is also large. This is especially critical during storage and transport. 

Generally, in classical reaction calorimetry only the liquid phase is taken into account in the heat balance. This means that the gas phase in equihbrium with it is neglected because of its small contribution in terms of heat transfer and heat capacity. The situation with supercritical fluids becomes complicated as soon as they occupy all the available volume. This implies that the whole inner reactor surface has to be thermally perfectly controlled when working with supercritical fluids. In this case, the cover and the flange temperature are adjusted on-line to the reaction temperature in order to neglect the heat accumulation term. 

Class 2 After loss of control of the synthesis reaction, the MTT cannot be reached and the decomposition reaction cannot be triggered. The situation is very similar to Class 1, but if the reaction mass is maintained for a longer time under heat accumulation conditions, the decomposition reaction could be triggered and reach the MTT. In this case, reaching this temperature could be a hazard if the heat release rate at the MTT is too high with respect to vaporization or pressure rise. If the reaction mass is not kept for a longer time under heat accumulation conditions, the process is thermally safe. 

Control of a deflagration after initiation by a source such as a hot spot, a flame, or a spark, depends on the rate of deflagration, the confinement, and the accumulation of heat from the evolved energy. Very slow deflagrations can sometimes be controlled under nonconfined situations. Under confined conditions, pressure builds up with simultaneous energy accumulation, which increases the deflagration velocity, most likely to an unacceptable level in processing. 

In this situation, the reaction cannot immediately be stopped by shutting the feed and further, the feed cannot be used to directly control the heat release rate or the gas release rate of a reaction. If, after a deviation from the design conditions, one decides to shut down the feed, the amount of accumulated B will react away despite the feed being stopped. If the reaction is accompanied by a gas release, gas production will continue and if the reaction is exothermal, heat will be released even after the interruption of the feed. 

An immense number of analytical solutions for conduction heat-transfer problems have been accumulated in the literature over the past 100 years. Even so, in many practical situations the geometry or boundary conditions are such that an analytical solution has not been obtained at all, or if the solution has been developed, it involves such a complex series solution that numerical evaluation becomes exceedingly difficult. For such situations the most fruitful approach to the problem is one based on finite-difference techniques, the basic principles of which we shall outline in this section. 

One or both blocks are equipped with holes to which tubes are soldered for the solvent inlet, including sample injection and eluate outlet. Figure 17 illustrates the case in which inlet and outlet capillaries are placed in the upper heated block. It is, however, more advantageous to situate these capillaries in the lower cooled block for the reason that the lower wall is the accumulation wall of the channel so that the sample, after being injected, is transferred to the vicinity of this wall. In this way equilibration at the head of the channel is facilitated and the time required for primary relaxation is reduced. At the channel end, the solute is concentrated at the accumulation wall, and its exit is easier if the capillary is situated in this block so that the sample does not have to overcome the field strength. 

If the system had been chosen to be everything but the steam chest and lines, we would have a situation as shown in Fig. E4.24b. Under these circumstances heat would be transferred from the steam chest. From a balance on the steam chest (no accumulation),... 

Recent studies have made it easier to design reactors with vertical tubular inserts. This arises from the observation (Gunn and Hilal, 1994, 1996, 1997) that the heat transfer coefficients for these systems are almost equal to those for the corresponding open fluidized beds of the same diameter operating with the same particles. Hence, correlations for the latter (which are readily available) can be used for vertical inserts without significant loss of accuracy. Vertical inserts have an additional advantage over horizontal inserts. In horizontal inserts there is accumulation of particles on top of the tubes and depletion of particles at the bottom, a situation that does not exist in the vertical orientation. 

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