Thermal reaction number

This group of characteristic numbers is supplemented by the so-called thermal reaction number... 

It provides a direct measure of the hazard potential related to the process. It combines thermodynamics and reaction kinetics by being directly proportional to the temperature dependence of the reaction rate represented by the activation temperature E/R and the adiabatic temperature increase. Reactions with a small to moderate hazard potential are characterized by thermal reaction number values around 2, and processes with an extremely high potential have values up to 50 and more. To illustrate the meaning especially of this number, which, if applied correctly, has a similar significance to the adiabatic temperature increase for chemical hazard assessment, the relationship between activation temperature, adiabatic temperature increase and the thermal reaction number B is presented in Fig. 4-4. As a typical process temperature 25°C is assumed. 

This value is compared with the thermal reaction number of the process to be assessed ... 

This demonstrates the advantage of the graphical over the pure calculation method, which compares the values of two thermal reaction number values only. If the graphical presentation shows no operating point in the relevant range to be enveloped by the limiting curve of dynamic instability, it may also be concluded that all these points are statically stable. 

However, Figure 4-39 shows that this correction may be neglected if the degree of overheating is small, i.e. f < 0.4, and if the value for the thermal reaction number is moderate, i.e. B < 5. 

Two facts can easily be recognized. The sensitivity of a process with known thermal reaction number depends on the degree of overheating. Furthermore, there are batch processes with a sensitivity formally approaching infinity. In other words, the BR ignites. This is shown graphically in Figures 4-41 and 4-42 for clarification. 

Fig. 4-42. s in dependence on overheating for small thermal reaction numbers... 

Safety technically, an ignited state of operation must be avoided for cooled BRs at all events. In consequence the observed singularity must be investigated closer. For this purpose an examination of processes with a small thermal reaction number is helpfiil. Due to the mathematical character of Equ.(4-159) and (4-160), respectively, the point of maximmn sensitivity always occurs for the same degree of overheating. 

With the help of Equ.(4-160) and (4-162), a limit value diagram can now be developed which allows the determination of the maximum sensitivity in its dependence on the thermal reaction number at the point. This is shown in Fig. 4-43. All operating conditions with B values which form an intersection with a desired sensitivity below or right of the limit curve can only be conducted safely if the overheating is limited to less than 4/9 of the adiabatic temperature increase. By inserting the value for Smt into the condition for an ignition... 

Processes with thermal reaction numbers higher than the ignition point value must not be performed in cooled batch reactors unless extreme precautions have been undertaken [49],... 

Batch processes which are to be performed in isoperibolic mode, and which have a value for the thermal reaction number greater than 6 may only be performed if a cooling capacity is available which ensures a significantly lower degree of overheating than 40% of the adiabatic temperature increase. 

In daily practice, a frequently asked question looks for the tolerable value of the thermal reaction number if the maximum sensitivity value is fixed. The background to this situation usually is a given plant with a certain instrumentation and a known variability for the coolant temperature under normal operating conditions. Usually more than 5 K variability in the maximum reaction temperature cannot be tolerated in the production of specialties such as those manufactured in the fine chemicals and pharmaceutical industry. This information fixes the value for the maximum sensitivity. 

With the help of Equ.(4-159), a limit value diagram can be calculated which provides information on the maximum tolerable thermal reaction number in its dependence on the degree of overheating. The maximum sensitivity is a parameter in this case. An example is given in Figure 4-45. The operating point in question can be marked and safety technically assessed as being critical or imcritical. 

To compare isothermal and isoperibolic operation the limit curve for S = 2 under isoperibolic conditions has been assumed. It becomes obvious that isothermal processes can only be performed safely and uncritically if the thermal reaction number has a very small value, or, in other words, if the reaction proceeds at low rates and only with moderate exothermicity. If reaction rate and thermal reaction number have higher... 

When the thermal reaction number was introduced, it was shown that B takes on values greater than 1 (c.f. Figure 4-4 in Section 4.1.4). In conclusion it becomes obvious that isothermal batch processes are safety technically tolerable only if the ratio of Damkoehler to Stanton number is less than 1. In the case of the sample process investigated this is not the case. In concrete terms the value for Da/St should be less than... 

An alternative would be the modification of the isothermal to an isoperibolic process with the side condition that the internal reaction temperature mtist not exceed a value of 383 K. The data given can be used to determine the initial temperature with the help of Equ.(4-157). The initial temperature is identical with the coolant temperature if this is kept constant during the process. As the thermal reaction number amounts to the relatively low value of 1.82, the correction fimction may be set to 1. 

If this equation is substituted into the one describing the minimum condition, the following requirement with respect to the thermal reaction number is obtained. This must be fiilfilled in order to have an optimization possibility regarding the lowest MTSR available. 

As a special solution to Equ.(4-238), the following requirement regarding the thermal reaction number is obtained, which must be fulfilled to have an optimization potential available in respect to the MTSR ... 

The logical conclusion is that batch processes should be performed at low temperatures and low concentrations (that is, low reaction rates). Under these conditions (Da/St < 0.1) dilution is equivalent to a reduction in the adiabatic temperature rise and leads to a lower value of the thermal reaction number B. 

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