Time to maximum rate under adiabatic conditions

Worst-case analysis based on the DSC data, namely, the test with the lowest onset temperature, resulted in a graph showing the relationship between initial temperature and time-to-maximum rate under adiabatic conditions. For an initial temperature of 170°C, it would take 2 hours to reach the maximum rate. Venting simulation tests were undertaken on a larger scale to detect safe venting requirements for the separator and for the MNB hold tank. Several vent sizes were tested. It was found that a 10-cm rupture disc with a burst pressure 1 bar above the operating pressure was adequate. 

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 ... 

T0 q0E q0E The time to maximum rate under adiabatic conditions is... 

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) ... 

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. 

This type of experiment can be repeated at other temperatures, determining the activation energy and the estimation of time to explosion. The concept of time to explosion or TMRad (Time to Maximum Rate under Adiabatic conditions) is extremely useful for that purpose [18]. This TMRad can be estimated by... 

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. 

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. 

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. 

Alternatively to the 100 K rule, the safety assessment of a process can be based on the time to maximum rate under adiabatic conditions calculated from the results of isothermal DTA / DSC measurements. It has to be emphasized that the time to maxi-... 

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. 

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... 

Since autocatalytic reactions often show only a low initial heat release rate, the temperature rise under adiabatic condition will be difficult to detect. Therefore, the sensitivity of the adiabatic calorimeter must be carefully adjusted. A small deviation in temperature control may lead to large differences in the measured time to maximum rate. This method should only be applied by specialists and is often used to confirm results obtained by other methods. 

The adiabatic time to maximum rate, TMR, gives a measure of the time required to reach, from a given temperature, the maximum selfheating rate for a system under conditions of no heat transfer. A plot of TMR vs. temperature is shown in Figure 1 for the decomposition of di-tert-butyl peroxide. The time to maximum rate is best measured directly rather than calculated because of the very large errors associated with the exponential term involved in the calculations. (2) TMR can be measured directly using an adiabatic calorimeter such as the Accelerating Rate Calorimeter. 

Investigations performed for reactions following a formal kinetic rate law of the second-order have shown that in the case of the SBR the acciunulation reaches its maximum, independent of isothermal or isoperibolic mode of operation, at that point in the feed time, at which a stoichiometric amount has been added [47]. The maximum temperature to be reached under adiabatic conditions with this maximum accumulation can be precalculated with the help of the following relationships. 

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... 

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. 

The TMR is the time taken for the reaction system to reach its maximum self-heating rate under completely adiabatic conditions. Because it assumes that no heat is lost from the reactor to the surroundings it represents the worst possible case. The TMR is based on an integrated form of the equation... 

The hydration reactions are exothermic, i. e., heat is evolved. The heat evolution of cement hardening under adiabatic test conditions attains a maximum after 1 to 3 days and then proceeds at a diminishing rate. The heat given off, in terms of quantity and in relation to time, depends on the type of cement (more particularly its constituent phases), its fineness and the presence of additives, if any (blastfurnace slag, pozzolana). 

To + q°Ypo/Cp is the adiabatic flame temperature, R° is the universal gas constant, and E represents the overall activation energy. The limit p -> ao is considered with times a suitable power of p held fixed [see, for example, the expression above equation (5-75)]. As exemplified by equation (5-66), the function co z) depends exponentially on p, and for large P we expect that there will be a narrow reaction zone centered about the position of maximum t. Outside this reaction zone, the reaction-rate term in equation (10) will be exponentially small. Under the assumption that all the fuel is consumed in the reaction zone, we may readily derive the expression rnYpo = w dx from the fuel-conservation equation, where / identifies conditions just downstream from the reaction zone. Use of equations (10) and (11) in this expression gives... 

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