Reaction Rate under Adiabatic Conditions

Running an exothermal reaction under adiabatic conditions leads to a temperature increase, and therefore to acceleration of the reaction, but at the same time, the reactant depletion leads to a decreasing reaction rate. Hence, these two effects act in an opposite way the temperature increase leads to an exponential increase of the rate constant and therefore of the reaction rate. The reactant depletion slows 

For a first-order reaction performed under adiabatic conditions, the rate varies with temperature as 

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Table 2.8 Reaction rate under adiabatic conditions with different reaction enthalpies, corresponding to an adiabatic temperature increase of 20 and 200 K.

A correct assessment of the situation would have predicted the explosion. The main error was considering the storage isothermal. In fact, such large vessels, when they are not agitated, behave quasi adiabatically. The correct estimation of the initial heat release rate allows calculation of the temperature increase rate under adiabatic conditions. By taking into account the acceleration of the reaction with increasing temperature, the approximate time of the explosion would have been predictable. This is left as an exercise for the reader (see Worked Example 2.1). 

Another important characteristic of a runaway reaction is the time a thermal explosion takes to develop under adiabatic conditions, or Time to Maximum Rate under adiabatic conditions (TMRai). To calculate this time, we consider the heat balance under adiabatic conditions for a zero-order reaction ... 

Since the temperature of the MTSR is higher than the intended process temperature, secondary reactions may be triggered. This will lead to further mnaway due to the uncontrolled secondary reaction, which may be through decomposition. The dynamics of the secondary reaction plays an important role in the determination of the probability of an incident. The concept of Time to Maximum Rate under adiabatic conditions (TMRld) [3] was used for that purpose (see Section 2.5.5) ... 

Then we consider a reaction presenting a given accumulation corresponding to a known adiabatic temperature rise. In the case of cooling failure, the reaction proceeds under adiabatic conditions it is accelerated by the temperature increase, but at the same time, the reactant depletion decreases the reaction rate. Thus, the reaction rate passes a maximum, as described in Figure 10.7 (see also section 10.6.2.1). For the design of the relief system, the maximum heat release rate at... 

For cases where the secondary reaction plays a role (class 5), or if the gas release rate must be checked (classes 2 or 4), the heat release rate can be calculated from the thermal stability tests (DSC or Calvet calorimeter). Secondary reactions are often characterized using the concept of Time to Maximum Rate under adiabatic conditions (TMRad). A long time to maximum rate means that the time available to take risk-reducing measures is sufficient. However, a short time means that the... 

The induction time is the time involved between the instant where the sample reaches its initial temperature and the instant where the reaction rate reaches its maximum. In practice, two types of induction times must be considered the isothermal and the adiabatic. The isothermal induction time is the time a reaction takes to reach its maximum rate under isothermal conditions. It can typically be measured by DSC or DTA. This assumes that the heat release rate can be removed by an appropriate heat exchange system. Since the induction time is the result of a reaction producing the catalyst, the isothermal induction time is an exponential function of temperature. Thus, a plot of its natural logarithm, as a function of the inverse absolute temperature, delivers a straight line. The adiabatic induction time corresponds to the time to maximum rate under adiabatic conditions (TMRJ). It can be measured by adiabatic calorimetry or calculated from kinetic data. This time is valid if the temperature is left increasing at the instantaneous heat release rate. In general, adiabatic induction time is shorter than isothermal induction time. 

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. 

For a zero order reaction proceeding under adiabatic conditions the rate of reaction can be related to the adiabatic self-heat rate by ... 

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. 

The concept of time to maximum rate under adiabatic conditions, or TMRad, of a decomposition reaction is often used to give an indication of the time available, at different temperatures, to take corrective action in the event of a failure. The TMRad can be calculated using the following formula ... 

Time to maximum rate under adiabatic condition for zero order reaction... 

How fast is the runaway of the deshed reaction Generally, industrial reactors are operated at temperatures where the deshed reaction is fast. Hence, a temperature increase above the normal process temperature will cause a significant acceleration of the reaction therefore, in most cases, this period of time is short. For polymerization reactions, where decomposition of the reaction mass is not critical, this time will determine the choice of technical risk reduction measures. The concept of time to maximum rate under adiabatic conditions (TMRad) as used for decomposition reactions can be applied to the polymerization itself, starting from the process temperature. It allows estimation of the probability of entering a runaway situation, as explained below for decomposition reactions. 

For experiments conducted at slower heating rates under adiabatic conditions, the accelerating-rate calorimeter (ARC) is the instrument of choice [13]. The ARC allows precise control of temperature and exposes the cell to more uniform conditions over longer periods. A typical experiment requires a few days rather than a few hours, as in the case of the heating block. Because of the adiabatic environment, the onset of self-heating due to chemical reactions in the interior of the cell can be detected with greater sensitivity. 

Liquid ethylene oxide under adiabatic conditions requires about 200°C before a self-heating rate of 0.02°C/min is observed (190,191). However, in the presence of contaminants such as acids and bases, or reactants possessing a labile hydrogen atom, the self-heating temperature can be much lower (190). In large containers, mnaway reaction can occur from ambient temperature, and destmctive explosions may occur (268,269). 

In the ARC (Figure 12-9), the sample of approximately 5 g or 4 ml is placed in a one-inch diameter metal sphere (bomb) and situated in a heated oven under adiabatic conditions. Tliese conditions are achieved by heating the chamber surrounding the bomb to the same temperature as the bomb. The thermocouple attached to the sample bomb is used to measure the sample temperature. A heat-wait-search mode of operation is used to detect an exotherm. If the temperature of the bomb increases due to an exotherm, the temperature of the surrounding chamber increases accordingly. The rate of temperature increase (selfheat rate) and bomb pressure are also tracked. Adiabatic conditions of the sample and the bomb are both maintained for self-heat rates up to 10°C/min. If the self-heat rate exceeds a predetermined value ( 0.02°C/min), an exotherm is registered. Figure 12-10 shows the temperature versus time curve of a reaction sample in the ARC test. 

We now consider operation of the batch reactor under adiabatic conditions. We will assume that we need not worry about reaching the boiling point of the liquid and that the rate of energy release by reaction does not become sufficiently great that an explosion ensues. 

A tubular flow reactor is used for the gas phase reaction, A => 2B, under adiabatic conditions with a constant pressure of 2 atm. Pure A is charged at 600 R. The heat of reaction is AHr = -2000 Btu/lbmol of A. Heat capacities are 20 and 15 Btu/(Ibmol)(R) for A and B and the specific rate is... 

Under adiabatic conditions with external diffusion, temperature and concentration differences will develop between the bulk of the fluid and the surface of the catalyst. The rate of reaction is the rate of diffusion, r = kga(Cg-Cs) and the heat balance is... 

The reactor is run initially as a batch reactor (F = 0) under adiabatic conditions (Fco = 0) to obtain a high initial rates of reaction. At time TIMEON the cooling flow rate is set to FCON and the reaction temperature reduced to obtain favourable equilibrium conditions. 

If a polymerisation is too fast for the reaction mixture to be kept isothermal, then the rate of temperature rise under adiabatic conditions can be used with advantage as a measure of the rate of the reaction. By means of a conventional electrical calibration and the experimentally established relation between Am and AT, the rate of temperature change, dT/dt, is converted to -dm/dt, and the enthalpy of the polymerisation, AHp, can be found as well. A version of the technique suitable for cationic polymerisations was developed by Biddulph and Plesch (1959) and subsequently used by many workers substantial improvements were made by Sigwalt s group (Cheradame etal, 1968 Favier etal., 1974) and by Pask and Plesch (1989). The method is most useful for reactions which have half-lives in the range of 5 to 300 s, and... 

Therefore the sensitivity usually ranges between 2 and 20Wkg 1. This heat release rate corresponds to a temperature increase rate of about 4 to 40 °C hour-1 under adiabatic conditions. This also means that an exothermal reaction is detected at a temperature where the time to explosion (TMRJ) is in the order of magnitude of one hour only. 

This system is the most complex, but also the most versatile. In fact, with this type of system, all the previous modes are accessible without further modification. The temperature set point corresponds to a predefined function of time (Figure 9.12). Polytrophic conditions can be achieved (see Section 6.6). The reactor is heated up at a temperature lower than that of the reaction and is then run under adiabatic conditions, Finally, cooling is started to stabilize the temperature at the desired level. By doing so, energy is saved because it is the heat of reaction that attains the process temperature. Moreover, for batch reactions, the cooling capacity is not oversized, since the low temperature at the beginning of the reaction diminishes the heat production rate. Other control strategies are possible, such as the ramped reactor, where the temperature varies with time (see Section 7.7). 

Thus, the main contribution is by the synthesis reaction, but the heat release rate of the decomposition will be used to calculate the gas release rate. The heat release rate of 64Wkg 1 would lead to a fast temperature increase under adiabatic conditions (TMR < 1 hour). The question is as to whether or not the reaction may be controlled at the boiling point. 

The probability of triggering a secondary decomposition reaction may be assessed using the time-scale as defined in Section 3.3.3. The principle is that the longer the time available for taking protective measures, the lower the probability of triggering a runaway reaction. The concept of Time to Maximum Rate (TMRld) was developed for this purpose and is presented in Section 2.5.5. The TMRld under adiabatic conditions is given by... 

With the approach using isothermal thermograms, the different thermograms must be checked for consistency. In certain cases when the peaks are well separated, as for consecutive reactions, they may be treated individually and the heat release rates can be extrapolated separately, and used for the TMRai calculation. The reaction that is active at lower temperature will raise the temperature to a certain level where the second becomes active, and so on. So under adiabatic conditions, one reaction triggers the next as in a chain reaction. In certain cases, in particular for the assessment of stability at storage, it is recommended to use a more sensitive calorimetric method as, for example, Calvet calorimetry or the Thermal Activity Monitor (see Section 4.3), to determine heat release rates at lower temperatures and thus to allow a reliable extrapolation over a large temperature range. Complex reactions can also easily be handled with the iso-conversional method, as mentioned below. 

This model gives a symmetrical peak with its maximum at half conversion. Hence the model is unable to describe non-symmetrical peaks as they are often observed in practice. Moreover, in order to obtain a reaction rate other than zero, some product B must be present in the reaction mass. Therefore, the initial concentration of B (CBo) or the initial conversion (X0) is a required parameter for describing the behavior of the reaction mass. This also means that the behavior of the reacting system depends on its thermal history, that is, on the time of exposure to a given temperature. This simple model requires three parameters the frequency factor, the activation energy, and the initial conversion that must be fitted to the measurement in order to predict the behavior of such a reaction under adiabatic conditions. 

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