Time to maximum rate

T = bulk heat-up rate driven by an external heat source, °C/sec TIME-TO-MAXIMUM RATE... 

An onset temperature can be selected based on an arbitrary time-to-maximum-rate from the relation... 

Equation 12-5 gives an onset temperature that eorresponds to a time-to-maximum rate t. (min) using a sueeessive substitution solution proeedure. An initial guess of T = 350 K for the right side of Equation 12-5 will give a solution value of on the left side of Equation 12-5 within 1% or on an absolute basis 3°C. Con-vergenee is reaehed within several sueeessive substitution iterations. 

T = bulk heat-up rate due to external heating alone, °C/min tj j. = time-to-maximum rate as determined by Equation 12-5 with tempertaure T set equal to min... 

The temperature eorresponding to the equipment timeline on the time to maximum rate (TMR) plot is the temperature of no return. Above the temperature of no return, the rate of heat generation from... 

Time to maximum rate (TMR) The time taken for a material to selfheat to tlie maximum rate of decomposition from a specific temperamre. 

Therefore, consideration of this mass in heat-transfer phenomenon leads to a significant temperature decrease reached after deviation and increases the time to maximum rate. This reveals an intrinsically safer behavior of this apparatus compared to that of batch reactors. 

When prepared by thermal dehydration of 4-hydroxybenzenesulfonic acid, the reaction mixture begins to decompose exothermally around 240° C. Decomposition is delayed but still occurs at lower temperatures (160°C), and the presence of iron reduces the time to maximum rate of decomposition. Above 800 ppm of iron, the time to maximum rate is less than the dehydration reaction time, leading to severe control problems. Improved processing conditions were developed. 

Explanation of Principal Application Codes 1 = screening 6 = reaction due to oxidation 2 = thermal stability 7 = runaway behavior (initial phase) 3 = sensitive thermal stability 8 = complete runaway behavior and 4 = very sensitive thermal stability simultaneous pressure measurements 5 = study autocatalysis, contaminations, 9 = time to maximum rate of reaction inhibitor depletion ... 

Further, the time to maximum rate (TMR) is measured in the ARC, which can indicate the time available for taking defensive or mitigation measures in process upset situations. 

Equations for determining the time-to-maximum rate (TMR) and the adiabatic zero-order time to maximum rate at temperature Tnr are given in [123]. 

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. 

A thermal scan showed that the exotherm of the principal reaction can be significant if the system is neither controlled nor vented. From isothermal studies (i.e., experiments at constant temperature), time-to-maximum rate was determined which was comparable to that obtained from the DCS data. The larger scale data showed, not surprisingly, more rapid reactions at elevated temperatures. Thus, it was decided to use the DSC data at lower temperatures, and the larger scale test data at higher temperatures for hazard evaluation. 

A thermal stability study was first carried out to determine the following information (1) the solidification temperature as a function of the concentration of the sulfonate (2) the enthalpy of decomposition by DTA (3) the autocatalytic nature of the decomposition by Dewar flask (4) kinetic data for decomposition by Dewar flask (5) the time to maximum rate by ARC, and (6) the heat generation as a function of temperature, also by ARC. In addition, the enthalpy of dilution was determined for various potential water leak rates. These data were useful in defining emergency response times. 

Keller, A., Stark, D., Fierz, H., Heinzle, E. and Hungerbiihler, K. (1997) Estimation of the Time to Maximum Rate Using Dynamic DSC Experiments. J. Loss Prev. Process Ind. 10, 31-41. 

In this case history, the control of the TMRaa (adiabatic Time-to-Maximum-Rate) is to be achieved in a semi-continuous reactor process by the dynamic optimization of the feed rate. Here it is desired to have the highest possible space-time-yield STY and it is necessary to achieve a thermally safe process (Keller, 1998). The reaction involves the addition of a sulfur trioxide on a nitro-aromatic compound... 

If DSC data have been obtained for a pure material or a reaction mixture, several thermal stability indicators (ASTM E 1231-96) may be estimated from the data. These are adiabatic temperature rise, explosion potential, instantaneous power density, time to maximum rate, and NFPA instability index (Leggett 2002). 

The Accelerating Rate Calorimeter (ARC ) is another adiabatic test instrument that can be used to test small samples. The ARC with the clamshell containment design can handle explosive compounds. It is a sensitive instrument that can indicate the onset of exothermicity where the reaction mixture can be accurately simulated (HSE 2000). ARC testing results can be used in determining a time to maximum rate of decomposition, as well as in calculating a temperature of no return for a container or vessel with specific heat removal characteristics. Further information and references related to the ARC are given in CCPS (1995a) and Urben (1999). 

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) ... 

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). 

This time factor must be estimated for the effective design of safety measures and compared with the Time to Maximum Rate (TMRld), giving the upper limit of the time frame. In fact, by applying Van t Hoff rule, the reaction rate doubles for a temperature increase of 10 K. If a temperature alarm is typically set at 10 K... 

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... 

C with an instrument having a detection limit of 1 Wkg-1, and at 109°C with an instrument having a detection limit of 0.1 Wkg-1. Thus, it becomes obvious that the distance rule must be replaced by a more scientifically sound concept, as with the time to maximum rate based on reaction kinetics. 

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... 

The heat release rate qm can, in turn, be used to calculate the time to maximum rate (TMRld) at the temperature T ... 

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... 

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. 

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. 

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