Constant Cooling Medium Temperature

If we assume an average jacket temperature of 15 °C, with cold water as a coolant (brine is also an option), and with the given heat transfer coefficient of 200 Wm 2 K the cooling capacity is 

Additionally we could also account for the convective cooling due to the cold feed  

the temperature can be controlled using cold water as a coolant, but the reaction requires practically the full available cooling capacity of the reactor (Question 1 in the cooling failure scenario Section 3.3.1). 

At 127 °C, the decomposition reaction is critical, that is, the time to maximum rate (Question 6 in the cooling failure scenario) is shorter than 8 hours (see Table 5.4). 

Hence the intended process belongs to the criticality class 5  

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Additionally the semi-batch reactor with constant cooling medium temperature, also in cases where a stationary temperature can be achieved, shows a high sensitivity to its control parameters, that is, initial temperature and coolant temperature. This means that even for small changes in these temperatures, the behavior of the reactor may suddenly change from a stable situation into a runaway course. 

Figu re 7.9 Semi-batch reactor with the example slow reaction and constant cooling medium temperature at 50, 70, 90, 103, and 104°C. The feed time is 6 hours initial and cooling medium temperatures are equal. 

The polytropic mode this is a combination of different types of control. As an example, the polytropic mode can be used to reduce the initial heat release rate by starting the feed and the reaction, at a lower temperature. The heat of reaction can then be used to heat up the reactor to the desired temperature. During the heating period, different strategies of temperature control can be applied adiabatic heating until a certain temperature level is reached, constant cooling medium temperature (isoperibolic control), or ramped to the desired reaction temperature in the reactor temperature controlled mode. Almost after the... 

A reliable control of the reaction course can be obtained by isothermal operation. Nevertheless, to maintain a constant reaction medium temperature, the heat exchange system must be able to remove even the maximum heat release rate of the reaction. Strictly isothermal behavior is difficult to achieve due to the thermal inertia of the reactor. However, in actual practice, the reaction temperature (Tr) can be controlled within 2°C, by using a cascade temperature controller (see Section 9.2.3). Isothermal conditions may also be achieved by using reflux cooling (see Section 9.2.3.3), provided the boiling point of the reaction mass does not change with composition. 

If there is no possibility to maintain a constant temperature by manipulating the temperature of the cooling medium the reaction can be slowed down by diluting the reaction mixture and/or the catalyst. After some components of the reaction mixture have been consumed to a sufficient extent and the reaction becomes too slow, more catalyst or reactants can be added to complete the reaction with the rate of heat generation not yet exceeding that of heat removal. This is the normally used semibatch operation. 

Reactor temperature will normally be controlled by regulating the flow of the heating or cooling medium. Pressure is usually held constant. Material balance control will be necessary to maintain the correct flow of reactants to the reactor and the flow of products and unreacted materials from the reactor. A typical reactor control scheme is shown in Figure 5.23 (see p. 235). 

This takes place in a jacketed tubular reactor. Pure acetone enters the reactor at a temperature of To = 1030 K and a pressure of P0 = 160 kPa. The temperature of the external cooling medium in the heat exchanger is constant at Tj = 1200 K. The other... 

The isoperibolic mode the temperature of the cooling medium is maintained constant. This type of temperature control was described in (Section 7.6). 

The condition for the practical implementation of such a feed control is the availability of a computer controlled feed system and of an on-line measurement of the accumulation. The later condition can be achieved either by an on-line measurement of the reactant concentration, using analytical methods or indirectly, by using a heat balance of the reactor. The amount of reactant fed to the reactor corresponds to a certain energy of reaction and can be compared to the heat removed from the reaction mass by the heat exchange system. For such a measurement, the required data are the mass flow rate of the cooling medium, its inlet temperature, and its outlet temperature. The feed profile can also be simplified into three constant feed rates, which approximate the ideal profile. This kind of semi-batch process shortens the time-cycle of the process and maintains safe conditions during the whole process time. This procedure was shown to work with different reaction schemes [16, 19, 20], as long as the fed compound B does not enter parallel reactions. 

Isoperibolic the system exchanges heat with a cooling medium kept at constant temperature. 

The consumption of the cooling medium is calculated from an energy balance around the perfectly mixed jacket at temperature T,. Constant physical properties of the cooling medium are assumed... 

The heating or cooling medium has a constant inlet temperature. 

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... 

For a correct perception of relation (3.128), we must notice that this is a heat sink that keeps its constant temperature due to a rapid heat exchange between the surface with a cooling medium maintained at constant (t j,) temperature. The assembly of relations (3.124)-(3.126) represents in fact an abstract mathematical model for the above described heating case because the numerical value is given neither for the system geometry nor for the material properties. Apart from the temperature, all the other variables of the model can be transformed into a dimensionless form introducing the following dimensionless coordinates ... 

In the case of a very large overall heat transfer coefficient k — oo the wall temperature is constant and equal to the temperature 0C of the cooling medium. The heat flux transferred from the vapour to the condensate surface is... 

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