Heat Balance Using Time Scale

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. 

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A special section then deals with the use of time-scales for the heat balance, which provides a simple to use assessment technique. The third section is devoted to the heat balance with purely conductive heat removal. The chapter closes on practical aspects for the assessment of industrial heat confinement situations. 

It is sometimes possible to estimate those properties of a polymerization reactor which are not measurable. The most common application of these techniques is the use of a heat balance to estimate the rate of reaction. If the coolant duty necessary to remove the heat of polymerization is carefully monitored, the rate of polymerization can be calculated if the heat of reaction (propagation) is known. Unlike most situations where scale-up is detrimental, this is one case where the use of a large reactor is beneficial. A large reactor has a low surface-to-volume ratio, and therefore heat losses tend to be smaller (relatively) and more constant (and hence, characterizable) than in a smaller kettle. If the rate of polymerization is known as a function of time, monomer conversion can be calculated by integrating the rate of polymerization over time. This technique is inexpensive to implement and is applied in many latex reactors with surprisingly good results. Heat balance estimates of conversion can be combined with other, less frequent conversion measurements within the framework of a state estimator. 

The second type of the blow-off mechanism occurs when the heated reaction products mix with the unbumed stream so fast that there is no time for ignition before the temperature and the radical concentrations drop lower than some critical value. This blow-off mechanism was proposed in [16]. The balance between the chemical time scale determined by the laminar flame velocity and the physical time scale determined by the isothermal characteristics of the flow was used for the correlation equations in [16]. 

The time-averaged velocities and gas holdups in the compartments, as well as the fluid interactions between the zones, are first calculated by computational fluid dynamics (CFD). Then, balance equations for heat and mass transfer and for chemical reactions are evaluated and solved using appropriate software. First results from a simulation of a cumene oxidation reactor on an industrial scale were impressive, as they matched real temperature and concentration fields. 

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