Induction time adiabatic

Adiabatic induction time Induction period or time to an event (spontaneous ignition, explosion, etc.) under adiabatic conditions, starting at operating conditions. 

Adiabatic calorimetry. Dewar tests are carried out at atmospheric and elevated pressure. Sealed ampoules, Dewars with mixing, isothermal calorimeters, etc. can be used. Temperature and pressure are measured as a function of time. From these data rates of temperature and pressure rises as well as the adiabatic temperature ri.se may be determined. If the log p versus UT graph is a straight line, this is likely to be the vapour pressure. If the graph is curved, decomposition reactions should be considered. Typical temperature-time curves obtained from Dewar flask experiments are shown in Fig. 5.4-60. The adiabatic induction time can be evaluated as a function of the initial temperature and as a function of the temperature at which the induction time, tmi, exceeds a specified value. 

Adiabatic induction times are always shorter than induction times from isothermal experiments,. see Fig. 5.4-61 (Grewer ef a/., 1989). 

The safety engineering data can also be determined from the adiabatic induction times tad (or TMRad) for various initial temperatures at adiabatic conditions (U = 0). The following analytical solution of Eqn. (5.4-209) for 6 = I, i e. for unlimited supply of reactants, then is... 

The adiabatic induction time can be approximately evaluated from graphs in Fig. 5.4-68. They are plotted for the condition qR qp, which is nearly equivalent to adiabatic operation if the initial temperature is greater than Tr.i- Eqn. (5.4-214) is the basis of the graph in Fig. 5.4-68. From both graphs in Fig. 5.4-68 the apparent activation energies (E/Rf.) for pseudo-zero order reactions can be determined. 

An important feature of the adiabatic measuring technique is the determination of the adiabatic induction time, Ti. The influence of the temperature on the adiabatic induction time is illustrated in Figure 2.23. 

Temperature CC) [Scale 1/T (K)l FIGURE 2.23. Adiabatic Induction Time. 

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. 

Figure 12.2 Comparison of an autocatalytic (solid line) and an nth-order reaction (dashed line) under adiabatic conditions starting from 150°C. Both reactions have the same adiabatic induction time orTMRad of 10 hours. If an alarm level is set at 160°C,...

Under these conditions, the time within which a given value of 9 is attained is proportional tothe magnitude x. Consequently, the induction period in the instance of adiabatic explosion is proportional to ri. The proportionality constant has been shown to be unity. Conceptually, this induction period can be related to the time period for the ignition of droplets for different air (or ambient) temperatures. Thus r can be the adiabatic induction time and is simply... 

To derive the mathematical equation for the adiabatic induction time the imsteady adiabatic heat balance of the BR is required. If the thermal inertia of the system is neglected, the balance may be obtained fi om Equ. (4-56), formally setting the heat exchange term equal to zero. 

Under adiabatic conditions X = d is valid. Substituting the conversion X in the heat balance with the help of Equ. (4-82) results in a formulation, in which the temperature remains the only variable. Integration of this adiabatic heat balance provides the general equation for the determination of the adiabatic induction time ... 

Additionally, the upper integration limit is also known, as the temperature increases in a steady and monotone way in this special case. On the other hand, the dimensionless temperature increase d may not become greater than 1 by definition. This way, for the special case of a zero order reaction, the equation for the adiabatic induction time is reduced to ... 

For this pmpose the adiabatic induction time, which has been deduced in Section... 

With respect to the adiabatic temperature increase observed, it has to be checked whether the final temperature truly is a consequence of the complete consumption of all educts, or whether it is an artificial final value because evaporation has prevented the temperature to rise any further. If all runs are started from different initial temperature levels, which is recommendable anyhow, then the dependency of the adiabatic induction time on temperature can directly be seen. For this purpose the measured temperature curve are differentiated once with respect to time and the resulting gradient profile is evaluated. For the above example this is shown in Figure 4-92. 

If the adiabatic induction time thus determined is plotted in semilogarithmic scale over the reciprocal value of the initial temperatures in degrees Kelvin, then the ADT24 or any other induction time corresponding to a temperature of interest can be determined graphically. This is shown in Figine 4-93 for clarification purposes. 

However, if the thermokinetic evaluation procedure is applied, which was explained in Section 4.3.3.3, very reliable kinetic models can be obtained from adiabatic measurements. The parameters thus determined can reliably be used for the prediction of the reactor behaviour in other maloperation scenarios. In a first approximation, other adiabatic induction times may be estimated with the help of the following equation... 

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