Heat production rate

The reaction rate and therefore the heat production rate can be tempered by diluting the S03 concentration (or partial pressure) in the gas phase and their reducing the S03 flow (kmol/m2,s) to the gas-liquid interface. In other words, the rate of reaction will be controlled by the transport of S03 through the gasphase. Volumetric (or molar) levels of between 2.5% S03 and 7% will be applied in practice 2.5% for delicate alcohol ethoxylate sulfation and 7% for... 

Essential modelling for scale-up relates to heat production (ref.4), and the universally applied calculation relates to the disaster calculation where the runaway instant temperature rise is always calculated for any one-shot exothermic reaction. In addition, the normal heat production rate is calculated to determine optimum feed rates, safety margins on cooling coil and condensers, etc. Increasingly, kinetic models are used as these become available. 

The micro reactor can be operated at temperatures up to 480 °C [44]. Platelet exchange can be performed in a short time, needing only 15-30 min of cooling from operational to ambient temperature. Heat production rates of about 30 W can be achieved without the need for external cooling [43]. 

Runaway reactions can be triggered by a number of causes, but, in most cases., their resultant features after initiation are similar [31]. Whenever the heat production rate exceeds the heat removal rate in a reaction system, the temperature begins to rise and can get out of control. The runaway starts slowly but the rate of reaction accelerates, and the rate of heat release is very high at the end. Most runaways occur because of self-heating with the reaction rate (and reaction heat output) increasing exponentially with temperature, while the heat dissipation is increasing only as a linear function of the temperature. 

Critical heat production rates (i.e., heat production rates that still do not lead to a runaway), are often determined by small scale experiments. However, the effect of scale-up on these rates, as discussed in [161], must be taken into account. An indication of the effect of scaling in an unstirred system is shown in Figure 3.2. In this figure, the heat production rate (logarithmic scale) is shown as a function of the reciprocal temperature. Point A in the figure represents critical conditions (equivalent heat generation and heat removal) obtained in a 200 cm3 Dewar vessel set-up. It can be calculated from the Frank-Kamenetskii theory on heat accumulation [157, 162] that the critical conditions are lowered by a factor of about 12 for a 200 liter insulated drum. These conditions are represented by... 

FIGURE 3.2. Relation between Critical Heat Production Rates of Small Scale and of Plant Scale (small scale = 200 cm3 Dewar vessel, point A) (large scale = 200 liter drum, line B)... 

It should be noted that there are cases in which some selectivity will be lost in choosing a semi-batch mode over a simple batch reactor. If the desired product decomposes by a consecutive reaction, the yield will be higher in the batch reactor [177]. If, on the other hand, the reactants are producing by-products by a parallel reaction, the semi-batch process will give the higher yield. In any case, if the heat production rate per unit mass is very high, the reaction can then be run safely under control only in a semi-batch reactor. 

The state of mixing generally controls tire mass transfer. In a liquid-liquid system, for example, the reaction rate is based on the mass transfer which depends on the interface area of the two liquid layers. This area is dramatically changed by a change in the mixing rate. If, for example, the agitator is started late, the increase in mass transfer area will lead to a rapid increase in the conversion rate and hence in the heat production rate. 

The Frank-Kamenetskii model, which applies to solids and unstirred liquids, is represented by Equation (3-29) below. The heat production rate is in the numerator and the heat removal rate is in the denominator. 

FIGURE 3.2. Relation between Critical Heat Production Rates... 

In differential scanning calorimetry, the selected chemical reaction is carried out in a cmcible and the temperature difference AT compared to that of an empty crucible is measured. The temperature is increased by heating and from the measured AT the heat production rate, q, can be calculated (Fig. 3.19). Integration of the value of q with respect to time yields measures of the total heats... 

The point where the heat production rate reaches its maximum value is of critical importance for a chemical process. This maximum value needs to be compared with the total given maximum heat removal capacity. A reaction going to completion can be considered safe, for normal operation, if the maximum heat removal capacity is greater than the maximum heat production rate. For more precise analysis see the literature 19, 10, 11/. 

During the increase of the heat production rate, the succession of populations was very rapid, the strains isolated at different incubation times never clustered at a similarly high level. The values of index of utilization of small molecules (amino acids, carbohydrates, alcohols) showed a net tendency to decrease and reach a minimum indicating physiological specialization, paralleled by the maximum value of the specific heat dissipation rate q. ... 

Since heat accumulation is the consequence of the difference between heat production rate and cooling rate, it results in a variation of the temperature of the reactor contents. Hence, if the heat exchange does not compensate exactly the heat release rate of the reaction, the temperature will vary as... 

If the power of the cooling system is lower than the heat production rate of a reaction, the temperature increases. The higher temperature results in a higher reaction rate, which in turn causes a further increase in heat production rate. Because the heat production of the reaction can increase exponentially, while the cooling capacity of the reactor increases only linearly with the temperature, the cooling capacity becomes insufficient and the temperature increases. A mnaway reaction or thermal explosion develops. 

Whereas the cooling capacity depends linearly on temperature, the heat production rate depends exponentially following the Arrhenius law. This may result in extremely high temperature maxima, if the control is not appropriate. Thus, it is important to characterize the effect of temperature on the heat balance. 

For exothermal reactions, the addition controls the heat production rate and therefore adjusts the reaction rate to the cooling capacity of the reactor. 

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). 

The thermal characteristics of a reaction, including its heat production rate, the necessary cooling power, and the reactant accumulation, are fundamental for safe reactor operation and process design. A successful scale-up is achieved, only when the different characteristic time constants of the process, such as reaction kinetics, thermal dynamics of the reactor, and its mixing characteristics are in good agreement [9]. If we focus on the reaction kinetics and thermal dynamics, that is, we consider that the reaction rate is slow compared to the mixing rate, in principle, there are two ways to predict the behavior of the industrial reactors ... 

Calorimeters are instruments used for the direct measurement of heat quantities including heat production rates and heat capacities. Different measurement principles are employed and a very large number of calorimetric designs have been described since the first calorimetric experiments were reported more than 200 years ago. The amount of heat evolved in a chemical reaction is proportional to the amount of material taking part in the reaction and the heat production rate the thermal power, is proportional to the rate of the reaction. Calorimeters can therefore be employed as quantitative analytical instruments and in kinetic investigations, in addition to their use as thermodynamic instruments. Important uses of calorimeters in the medical field are at present in research on the biochemical level and in studies of living cellular systems. Such investigations are often linked to clinical applications but, so far, calorimetric techniques have hardly reached a state where one may call them clinical (analytical) instruments. ... 

The heat production rate or the thermal power, P, is thus... 

For the ideal case where no significant thermal gradients exist in the vessel, the heat production rate will be related to the heat flow through the thermopile, dQ/dt, and to the change of the vessel temperature, dT/dt ... 

Equation (17) is usually called the Tian equation. In cases where significant temperature gradients are present within the reaction vessel, two or more time constants must be used. When the change in rate of a process is small, the value for X(dU/dt) will often be insignificant compared to the value for U (equation (17)). With heat conduction calorimeters used in work on cellular systems, this is typically the case and the heat production rate is then, with a good approximation, given by the simple expression... 

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